LMFDB - Embedded newform 4010.2.a.n.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.44141 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.44141 q^{6} -0.373089 q^{7} +1.00000 q^{8} +2.96048 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.44141 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.44141 q^{6} -0.373089 q^{7} +1.00000 q^{8} +2.96048 q^{9} +1.00000 q^{10} -0.329378 q^{11} +2.44141 q^{12} -2.31450 q^{13} -0.373089 q^{14} +2.44141 q^{15} +1.00000 q^{16} +5.06085 q^{17} +2.96048 q^{18} +2.50946 q^{19} +1.00000 q^{20} -0.910862 q^{21} -0.329378 q^{22} -0.918663 q^{23} +2.44141 q^{24} +1.00000 q^{25} -2.31450 q^{26} -0.0964843 q^{27} -0.373089 q^{28} +9.10084 q^{29} +2.44141 q^{30} +6.14402 q^{31} +1.00000 q^{32} -0.804147 q^{33} +5.06085 q^{34} -0.373089 q^{35} +2.96048 q^{36} -6.62998 q^{37} +2.50946 q^{38} -5.65064 q^{39} +1.00000 q^{40} +0.669461 q^{41} -0.910862 q^{42} +5.35467 q^{43} -0.329378 q^{44} +2.96048 q^{45} -0.918663 q^{46} -2.60630 q^{47} +2.44141 q^{48} -6.86080 q^{49} +1.00000 q^{50} +12.3556 q^{51} -2.31450 q^{52} -6.08460 q^{53} -0.0964843 q^{54} -0.329378 q^{55} -0.373089 q^{56} +6.12663 q^{57} +9.10084 q^{58} +1.49105 q^{59} +2.44141 q^{60} +8.48665 q^{61} +6.14402 q^{62} -1.10452 q^{63} +1.00000 q^{64} -2.31450 q^{65} -0.804147 q^{66} -8.86294 q^{67} +5.06085 q^{68} -2.24283 q^{69} -0.373089 q^{70} +6.00063 q^{71} +2.96048 q^{72} +11.0226 q^{73} -6.62998 q^{74} +2.44141 q^{75} +2.50946 q^{76} +0.122887 q^{77} -5.65064 q^{78} +3.23847 q^{79} +1.00000 q^{80} -9.11700 q^{81} +0.669461 q^{82} -14.7915 q^{83} -0.910862 q^{84} +5.06085 q^{85} +5.35467 q^{86} +22.2189 q^{87} -0.329378 q^{88} +0.593446 q^{89} +2.96048 q^{90} +0.863513 q^{91} -0.918663 q^{92} +15.0001 q^{93} -2.60630 q^{94} +2.50946 q^{95} +2.44141 q^{96} -10.5813 q^{97} -6.86080 q^{98} -0.975117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.44141	1.40955	0.704774	−	0.709432i	$-0.251048\pi$
$3$	2.44141	1.40955	0.704774	+	0.709432i	$0.251048\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.44141	0.996701
$7$	−0.373089	−0.141014	−0.0705071	−	0.997511i	$-0.522462\pi$
$7$	−0.373089	−0.141014	−0.0705071	+	0.997511i	$0.522462\pi$
$8$	1.00000	0.353553
$9$	2.96048	0.986827
$10$	1.00000	0.316228
$11$	−0.329378	−0.0993112	−0.0496556	−	0.998766i	$-0.515812\pi$
$11$	−0.329378	−0.0993112	−0.0496556	+	0.998766i	$0.515812\pi$
$12$	2.44141	0.704774
$13$	−2.31450	−0.641927	−0.320963	−	0.947092i	$-0.604007\pi$
$13$	−2.31450	−0.641927	−0.320963	+	0.947092i	$0.604007\pi$
$14$	−0.373089	−0.0997122
$15$	2.44141	0.630369
$16$	1.00000	0.250000
$17$	5.06085	1.22744	0.613718	−	0.789525i	$-0.289673\pi$
$17$	5.06085	1.22744	0.613718	+	0.789525i	$0.289673\pi$
$18$	2.96048	0.697792
$19$	2.50946	0.575710	0.287855	−	0.957674i	$-0.407058\pi$
$19$	2.50946	0.575710	0.287855	+	0.957674i	$0.407058\pi$
$20$	1.00000	0.223607
$21$	−0.910862	−0.198766
$22$	−0.329378	−0.0702236
$23$	−0.918663	−0.191555	−0.0957773	−	0.995403i	$-0.530534\pi$
$23$	−0.918663	−0.191555	−0.0957773	+	0.995403i	$0.530534\pi$
$24$	2.44141	0.498351
$25$	1.00000	0.200000
$26$	−2.31450	−0.453911
$27$	−0.0964843	−0.0185684
$28$	−0.373089	−0.0705071
$29$	9.10084	1.68998	0.844992	−	0.534779i	$-0.179605\pi$
$29$	9.10084	1.68998	0.844992	+	0.534779i	$0.179605\pi$
$30$	2.44141	0.445738
$31$	6.14402	1.10350	0.551750	−	0.834010i	$-0.313960\pi$
$31$	6.14402	1.10350	0.551750	+	0.834010i	$0.313960\pi$
$32$	1.00000	0.176777
$33$	−0.804147	−0.139984
$34$	5.06085	0.867928
$35$	−0.373089	−0.0630635
$36$	2.96048	0.493413
$37$	−6.62998	−1.08996	−0.544981	−	0.838448i	$-0.683463\pi$
$37$	−6.62998	−1.08996	−0.544981	+	0.838448i	$0.683463\pi$
$38$	2.50946	0.407089
$39$	−5.65064	−0.904827
$40$	1.00000	0.158114
$41$	0.669461	0.104552	0.0522762	−	0.998633i	$-0.483352\pi$
$41$	0.669461	0.104552	0.0522762	+	0.998633i	$0.483352\pi$
$42$	−0.910862	−0.140549
$43$	5.35467	0.816579	0.408290	−	0.912852i	$-0.366125\pi$
$43$	5.35467	0.816579	0.408290	+	0.912852i	$0.366125\pi$
$44$	−0.329378	−0.0496556
$45$	2.96048	0.441322
$46$	−0.918663	−0.135450
$47$	−2.60630	−0.380169	−0.190084	−	0.981768i	$-0.560876\pi$
$47$	−2.60630	−0.380169	−0.190084	+	0.981768i	$0.560876\pi$
$48$	2.44141	0.352387
$49$	−6.86080	−0.980115
$50$	1.00000	0.141421
$51$	12.3556	1.73013
$52$	−2.31450	−0.320963
$53$	−6.08460	−0.835784	−0.417892	−	0.908497i	$-0.637231\pi$
$53$	−6.08460	−0.835784	−0.417892	+	0.908497i	$0.637231\pi$
$54$	−0.0964843	−0.0131299
$55$	−0.329378	−0.0444133
$56$	−0.373089	−0.0498561
$57$	6.12663	0.811491
$58$	9.10084	1.19500
$59$	1.49105	0.194119	0.0970594	−	0.995279i	$-0.469056\pi$
$59$	1.49105	0.194119	0.0970594	+	0.995279i	$0.469056\pi$
$60$	2.44141	0.315185
$61$	8.48665	1.08660	0.543302	−	0.839537i	$-0.317174\pi$
$61$	8.48665	1.08660	0.543302	+	0.839537i	$0.317174\pi$
$62$	6.14402	0.780292
$63$	−1.10452	−0.139157
$64$	1.00000	0.125000
$65$	−2.31450	−0.287078
$66$	−0.804147	−0.0989836
$67$	−8.86294	−1.08278	−0.541390	−	0.840772i	$-0.682102\pi$
$67$	−8.86294	−1.08278	−0.541390	+	0.840772i	$0.682102\pi$
$68$	5.06085	0.613718
$69$	−2.24283	−0.270005
$70$	−0.373089	−0.0445926
$71$	6.00063	0.712144	0.356072	−	0.934459i	$-0.384116\pi$
$71$	6.00063	0.712144	0.356072	+	0.934459i	$0.384116\pi$
$72$	2.96048	0.348896
$73$	11.0226	1.29010	0.645048	−	0.764142i	$-0.276837\pi$
$73$	11.0226	1.29010	0.645048	+	0.764142i	$0.276837\pi$
$74$	−6.62998	−0.770720
$75$	2.44141	0.281910
$76$	2.50946	0.287855
$77$	0.122887	0.0140043
$78$	−5.65064	−0.639809
$79$	3.23847	0.364356	0.182178	−	0.983266i	$-0.441685\pi$
$79$	3.23847	0.364356	0.182178	+	0.983266i	$0.441685\pi$
$80$	1.00000	0.111803
$81$	−9.11700	−1.01300
$82$	0.669461	0.0739297
$83$	−14.7915	−1.62358	−0.811791	−	0.583948i	$-0.801507\pi$
$83$	−14.7915	−1.62358	−0.811791	+	0.583948i	$0.801507\pi$
$84$	−0.910862	−0.0993832
$85$	5.06085	0.548926
$86$	5.35467	0.577409
$87$	22.2189	2.38211
$88$	−0.329378	−0.0351118
$89$	0.593446	0.0629052	0.0314526	−	0.999505i	$-0.489987\pi$
$89$	0.593446	0.0629052	0.0314526	+	0.999505i	$0.489987\pi$
$90$	2.96048	0.312062
$91$	0.863513	0.0905208
$92$	−0.918663	−0.0957773
$93$	15.0001	1.55544
$94$	−2.60630	−0.268820
$95$	2.50946	0.257465
$96$	2.44141	0.249175
$97$	−10.5813	−1.07437	−0.537184	−	0.843465i	$-0.680512\pi$
$97$	−10.5813	−1.07437	−0.537184	+	0.843465i	$0.680512\pi$
$98$	−6.86080	−0.693046
$99$	−0.975117	−0.0980030
$100$	1.00000	0.100000
$101$	14.4968	1.44248	0.721242	−	0.692684i	$-0.243572\pi$
$101$	14.4968	1.44248	0.721242	+	0.692684i	$0.243572\pi$
$102$	12.3556	1.22339
$103$	−1.80201	−0.177558	−0.0887788	−	0.996051i	$-0.528296\pi$
$103$	−1.80201	−0.177558	−0.0887788	+	0.996051i	$0.528296\pi$
$104$	−2.31450	−0.226955
$105$	−0.910862	−0.0888911
$106$	−6.08460	−0.590988
$107$	10.1996	0.986030	0.493015	−	0.870021i	$-0.335895\pi$
$107$	10.1996	0.986030	0.493015	+	0.870021i	$0.335895\pi$
$108$	−0.0964843	−0.00928421
$109$	1.27166	0.121803	0.0609016	−	0.998144i	$-0.480602\pi$
$109$	1.27166	0.121803	0.0609016	+	0.998144i	$0.480602\pi$
$110$	−0.329378	−0.0314050
$111$	−16.1865	−1.53635
$112$	−0.373089	−0.0352536
$113$	−3.87906	−0.364911	−0.182456	−	0.983214i	$-0.558405\pi$
$113$	−3.87906	−0.364911	−0.182456	+	0.983214i	$0.558405\pi$
$114$	6.12663	0.573811
$115$	−0.918663	−0.0856658
$116$	9.10084	0.844992
$117$	−6.85203	−0.633470
$118$	1.49105	0.137263
$119$	−1.88815	−0.173086
$120$	2.44141	0.222869
$121$	−10.8915	−0.990137
$122$	8.48665	0.768345
$123$	1.63443	0.147372
$124$	6.14402	0.551750
$125$	1.00000	0.0894427
$126$	−1.10452	−0.0983986
$127$	−4.11897	−0.365500	−0.182750	−	0.983159i	$-0.558500\pi$
$127$	−4.11897	−0.365500	−0.182750	+	0.983159i	$0.558500\pi$
$128$	1.00000	0.0883883
$129$	13.0729	1.15101
$130$	−2.31450	−0.202995
$131$	−4.87060	−0.425546	−0.212773	−	0.977102i	$-0.568250\pi$
$131$	−4.87060	−0.425546	−0.212773	+	0.977102i	$0.568250\pi$
$132$	−0.804147	−0.0699920
$133$	−0.936252	−0.0811834
$134$	−8.86294	−0.765641
$135$	−0.0964843	−0.00830405
$136$	5.06085	0.433964
$137$	−0.747792	−0.0638882	−0.0319441	−	0.999490i	$-0.510170\pi$
$137$	−0.747792	−0.0638882	−0.0319441	+	0.999490i	$0.510170\pi$
$138$	−2.24283	−0.190923
$139$	−4.34484	−0.368525	−0.184262	−	0.982877i	$-0.558990\pi$
$139$	−4.34484	−0.368525	−0.184262	+	0.982877i	$0.558990\pi$
$140$	−0.373089	−0.0315318
$141$	−6.36306	−0.535866
$142$	6.00063	0.503562
$143$	0.762345	0.0637505
$144$	2.96048	0.246707
$145$	9.10084	0.755784
$146$	11.0226	0.912235
$147$	−16.7500	−1.38152
$148$	−6.62998	−0.544981
$149$	9.92853	0.813377	0.406688	−	0.913567i	$-0.366683\pi$
$149$	9.92853	0.813377	0.406688	+	0.913567i	$0.366683\pi$
$150$	2.44141	0.199340
$151$	−23.6113	−1.92146	−0.960730	−	0.277483i	$-0.910500\pi$
$151$	−23.6113	−1.92146	−0.960730	+	0.277483i	$0.910500\pi$
$152$	2.50946	0.203544
$153$	14.9825	1.21127
$154$	0.122887	0.00990254
$155$	6.14402	0.493500
$156$	−5.65064	−0.452413
$157$	2.43505	0.194338	0.0971690	−	0.995268i	$-0.469021\pi$
$157$	2.43505	0.194338	0.0971690	+	0.995268i	$0.469021\pi$
$158$	3.23847	0.257639
$159$	−14.8550	−1.17808
$160$	1.00000	0.0790569
$161$	0.342743	0.0270119
$162$	−9.11700	−0.716299
$163$	−14.8129	−1.16023	−0.580117	−	0.814533i	$-0.696993\pi$
$163$	−14.8129	−1.16023	−0.580117	+	0.814533i	$0.696993\pi$
$164$	0.669461	0.0522762
$165$	−0.804147	−0.0626027
$166$	−14.7915	−1.14805
$167$	9.41654	0.728674	0.364337	−	0.931267i	$-0.381296\pi$
$167$	9.41654	0.728674	0.364337	+	0.931267i	$0.381296\pi$
$168$	−0.910862	−0.0702746
$169$	−7.64309	−0.587930
$170$	5.06085	0.388149
$171$	7.42921	0.568126
$172$	5.35467	0.408290
$173$	−12.4501	−0.946561	−0.473280	−	0.880912i	$-0.656930\pi$
$173$	−12.4501	−0.946561	−0.473280	+	0.880912i	$0.656930\pi$
$174$	22.2189	1.68441
$175$	−0.373089	−0.0282029
$176$	−0.329378	−0.0248278
$177$	3.64027	0.273620
$178$	0.593446	0.0444807
$179$	10.4748	0.782923	0.391461	−	0.920195i	$-0.371970\pi$
$179$	10.4748	0.782923	0.391461	+	0.920195i	$0.371970\pi$
$180$	2.96048	0.220661
$181$	−15.5172	−1.15339	−0.576694	−	0.816960i	$-0.695657\pi$
$181$	−15.5172	−1.15339	−0.576694	+	0.816960i	$0.695657\pi$
$182$	0.863513	0.0640079
$183$	20.7194	1.53162
$184$	−0.918663	−0.0677248
$185$	−6.62998	−0.487446
$186$	15.0001	1.09986
$187$	−1.66693	−0.121898
$188$	−2.60630	−0.190084
$189$	0.0359972	0.00261841
$190$	2.50946	0.182056
$191$	−0.482573	−0.0349178	−0.0174589	−	0.999848i	$-0.505558\pi$
$191$	−0.482573	−0.0349178	−0.0174589	+	0.999848i	$0.505558\pi$
$192$	2.44141	0.176194
$193$	23.3432	1.68028	0.840141	−	0.542368i	$-0.182472\pi$
$193$	23.3432	1.68028	0.840141	+	0.542368i	$0.182472\pi$
$194$	−10.5813	−0.759693
$195$	−5.65064	−0.404651
$196$	−6.86080	−0.490057
$197$	−19.6898	−1.40284	−0.701420	−	0.712748i	$-0.747450\pi$
$197$	−19.6898	−1.40284	−0.701420	+	0.712748i	$0.747450\pi$
$198$	−0.975117	−0.0692986
$199$	6.17255	0.437561	0.218780	−	0.975774i	$-0.429792\pi$
$199$	6.17255	0.437561	0.218780	+	0.975774i	$0.429792\pi$
$200$	1.00000	0.0707107
$201$	−21.6381	−1.52623
$202$	14.4968	1.01999
$203$	−3.39542	−0.238312
$204$	12.3556	0.865065
$205$	0.669461	0.0467572
$206$	−1.80201	−0.125552
$207$	−2.71968	−0.189031
$208$	−2.31450	−0.160482
$209$	−0.826562	−0.0571745
$210$	−0.910862	−0.0628555
$211$	−9.43859	−0.649780	−0.324890	−	0.945752i	$-0.605327\pi$
$211$	−9.43859	−0.649780	−0.324890	+	0.945752i	$0.605327\pi$
$212$	−6.08460	−0.417892
$213$	14.6500	1.00380
$214$	10.1996	0.697228
$215$	5.35467	0.365185
$216$	−0.0964843	−0.00656493
$217$	−2.29227	−0.155609
$218$	1.27166	0.0861279
$219$	26.9106	1.81845
$220$	−0.329378	−0.0222067
$221$	−11.7133	−0.787924
$222$	−16.1865	−1.08637
$223$	2.57857	0.172674	0.0863371	−	0.996266i	$-0.472484\pi$
$223$	2.57857	0.172674	0.0863371	+	0.996266i	$0.472484\pi$
$224$	−0.373089	−0.0249280
$225$	2.96048	0.197365
$226$	−3.87906	−0.258031
$227$	−9.14901	−0.607241	−0.303621	−	0.952793i	$-0.598196\pi$
$227$	−9.14901	−0.607241	−0.303621	+	0.952793i	$0.598196\pi$
$228$	6.12663	0.405746
$229$	23.5226	1.55442	0.777208	−	0.629244i	$-0.216636\pi$
$229$	23.5226	1.55442	0.777208	+	0.629244i	$0.216636\pi$
$230$	−0.918663	−0.0605749
$231$	0.300018	0.0197397
$232$	9.10084	0.597500
$233$	−19.1283	−1.25313	−0.626567	−	0.779367i	$-0.715541\pi$
$233$	−19.1283	−1.25313	−0.626567	+	0.779367i	$0.715541\pi$
$234$	−6.85203	−0.447931
$235$	−2.60630	−0.170017
$236$	1.49105	0.0970594
$237$	7.90643	0.513578
$238$	−1.88815	−0.122390
$239$	15.0493	0.973459	0.486730	−	0.873553i	$-0.338190\pi$
$239$	15.0493	0.973459	0.486730	+	0.873553i	$0.338190\pi$
$240$	2.44141	0.157592
$241$	4.24007	0.273127	0.136564	−	0.990631i	$-0.456394\pi$
$241$	4.24007	0.273127	0.136564	+	0.990631i	$0.456394\pi$
$242$	−10.8915	−0.700133
$243$	−21.9689	−1.40930
$244$	8.48665	0.543302
$245$	−6.86080	−0.438321
$246$	1.63443	0.104207
$247$	−5.80815	−0.369564
$248$	6.14402	0.390146
$249$	−36.1122	−2.28852
$250$	1.00000	0.0632456
$251$	−4.37658	−0.276247	−0.138124	−	0.990415i	$-0.544107\pi$
$251$	−4.37658	−0.276247	−0.138124	+	0.990415i	$0.544107\pi$
$252$	−1.10452	−0.0695783
$253$	0.302588	0.0190235
$254$	−4.11897	−0.258447
$255$	12.3556	0.773738
$256$	1.00000	0.0625000
$257$	−16.3121	−1.01752	−0.508761	−	0.860908i	$-0.669896\pi$
$257$	−16.3121	−1.01752	−0.508761	+	0.860908i	$0.669896\pi$
$258$	13.0729	0.813885
$259$	2.47357	0.153700
$260$	−2.31450	−0.143539
$261$	26.9429	1.66772
$262$	−4.87060	−0.300907
$263$	−25.9320	−1.59904	−0.799518	−	0.600641i	$-0.794912\pi$
$263$	−25.9320	−1.59904	−0.799518	+	0.600641i	$0.794912\pi$
$264$	−0.804147	−0.0494918
$265$	−6.08460	−0.373774
$266$	−0.936252	−0.0574053
$267$	1.44885	0.0886679
$268$	−8.86294	−0.541390
$269$	−26.1006	−1.59138	−0.795691	−	0.605702i	$-0.792892\pi$
$269$	−26.1006	−1.59138	−0.795691	+	0.605702i	$0.792892\pi$
$270$	−0.0964843	−0.00587185
$271$	−23.0904	−1.40264	−0.701320	−	0.712846i	$-0.747406\pi$
$271$	−23.0904	−1.40264	−0.701320	+	0.712846i	$0.747406\pi$
$272$	5.06085	0.306859
$273$	2.10819	0.127593
$274$	−0.747792	−0.0451758
$275$	−0.329378	−0.0198622
$276$	−2.24283	−0.135003
$277$	−26.3917	−1.58572	−0.792862	−	0.609401i	$-0.791410\pi$
$277$	−26.3917	−1.58572	−0.792862	+	0.609401i	$0.791410\pi$
$278$	−4.34484	−0.260586
$279$	18.1893	1.08896
$280$	−0.373089	−0.0222963
$281$	2.14553	0.127992	0.0639958	−	0.997950i	$-0.479616\pi$
$281$	2.14553	0.127992	0.0639958	+	0.997950i	$0.479616\pi$
$282$	−6.36306	−0.378914
$283$	−19.6412	−1.16755	−0.583774	−	0.811916i	$-0.698425\pi$
$283$	−19.6412	−1.16755	−0.583774	+	0.811916i	$0.698425\pi$
$284$	6.00063	0.356072
$285$	6.12663	0.362910
$286$	0.762345	0.0450784
$287$	−0.249769	−0.0147434
$288$	2.96048	0.174448
$289$	8.61219	0.506599
$290$	9.10084	0.534420
$291$	−25.8333	−1.51437
$292$	11.0226	0.645048
$293$	22.8310	1.33380	0.666900	−	0.745147i	$-0.267621\pi$
$293$	22.8310	1.33380	0.666900	+	0.745147i	$0.267621\pi$
$294$	−16.7500	−0.976882
$295$	1.49105	0.0868125
$296$	−6.62998	−0.385360
$297$	0.0317798	0.00184405
$298$	9.92853	0.575144
$299$	2.12625	0.122964
$300$	2.44141	0.140955
$301$	−1.99777	−0.115149
$302$	−23.6113	−1.35868
$303$	35.3926	2.03325
$304$	2.50946	0.143928
$305$	8.48665	0.485944
$306$	14.9825	0.856495
$307$	4.56829	0.260726	0.130363	−	0.991466i	$-0.458386\pi$
$307$	4.56829	0.260726	0.130363	+	0.991466i	$0.458386\pi$
$308$	0.122887	0.00700215
$309$	−4.39945	−0.250276
$310$	6.14402	0.348957
$311$	17.3122	0.981687	0.490843	−	0.871248i	$-0.336689\pi$
$311$	17.3122	0.981687	0.490843	+	0.871248i	$0.336689\pi$
$312$	−5.65064	−0.319904
$313$	3.96876	0.224328	0.112164	−	0.993690i	$-0.464222\pi$
$313$	3.96876	0.224328	0.112164	+	0.993690i	$0.464222\pi$
$314$	2.43505	0.137418
$315$	−1.10452	−0.0622327
$316$	3.23847	0.182178
$317$	22.0156	1.23652	0.618260	−	0.785974i	$-0.287838\pi$
$317$	22.0156	1.23652	0.618260	+	0.785974i	$0.287838\pi$
$318$	−14.8550	−0.833027
$319$	−2.99762	−0.167834
$320$	1.00000	0.0559017
$321$	24.9013	1.38986
$322$	0.342743	0.0191003
$323$	12.7000	0.706648
$324$	−9.11700	−0.506500
$325$	−2.31450	−0.128385
$326$	−14.8129	−0.820409
$327$	3.10465	0.171688
$328$	0.669461	0.0369648
$329$	0.972383	0.0536092
$330$	−0.804147	−0.0442668
$331$	−21.6379	−1.18933	−0.594664	−	0.803975i	$-0.702715\pi$
$331$	−21.6379	−1.18933	−0.594664	+	0.803975i	$0.702715\pi$
$332$	−14.7915	−0.811791
$333$	−19.6279	−1.07560
$334$	9.41654	0.515250
$335$	−8.86294	−0.484234
$336$	−0.910862	−0.0496916
$337$	8.79200	0.478931	0.239465	−	0.970905i	$-0.423028\pi$
$337$	8.79200	0.478931	0.239465	+	0.970905i	$0.423028\pi$
$338$	−7.64309	−0.415730
$339$	−9.47038	−0.514360
$340$	5.06085	0.274463
$341$	−2.02371	−0.109590
$342$	7.42921	0.401726
$343$	5.17131	0.279224
$344$	5.35467	0.288704
$345$	−2.24283	−0.120750
$346$	−12.4501	−0.669320
$347$	12.2151	0.655743	0.327871	−	0.944722i	$-0.393669\pi$
$347$	12.2151	0.655743	0.327871	+	0.944722i	$0.393669\pi$
$348$	22.2189	1.19106
$349$	12.9658	0.694041	0.347021	−	0.937858i	$-0.387193\pi$
$349$	12.9658	0.694041	0.347021	+	0.937858i	$0.387193\pi$
$350$	−0.373089	−0.0199424
$351$	0.223313	0.0119196
$352$	−0.329378	−0.0175559
$353$	−4.52035	−0.240594	−0.120297	−	0.992738i	$-0.538385\pi$
$353$	−4.52035	−0.240594	−0.120297	+	0.992738i	$0.538385\pi$
$354$	3.64027	0.193478
$355$	6.00063	0.318480
$356$	0.593446	0.0314526
$357$	−4.60974	−0.243973
$358$	10.4748	0.553610
$359$	22.3853	1.18145	0.590727	−	0.806872i	$-0.298841\pi$
$359$	22.3853	1.18145	0.590727	+	0.806872i	$0.298841\pi$
$360$	2.96048	0.156031
$361$	−12.7026	−0.668558
$362$	−15.5172	−0.815568
$363$	−26.5906	−1.39565
$364$	0.863513	0.0452604
$365$	11.0226	0.576948
$366$	20.7194	1.08302
$367$	10.5525	0.550834	0.275417	−	0.961325i	$-0.411184\pi$
$367$	10.5525	0.550834	0.275417	+	0.961325i	$0.411184\pi$
$368$	−0.918663	−0.0478886
$369$	1.98193	0.103175
$370$	−6.62998	−0.344676
$371$	2.27009	0.117857
$372$	15.0001	0.777718
$373$	−5.02649	−0.260262	−0.130131	−	0.991497i	$-0.541540\pi$
$373$	−5.02649	−0.260262	−0.130131	+	0.991497i	$0.541540\pi$
$374$	−1.66693	−0.0861950
$375$	2.44141	0.126074
$376$	−2.60630	−0.134410
$377$	−21.0639	−1.08485
$378$	0.0359972	0.00185150
$379$	−13.7494	−0.706261	−0.353131	−	0.935574i	$-0.614883\pi$
$379$	−13.7494	−0.706261	−0.353131	+	0.935574i	$0.614883\pi$
$380$	2.50946	0.128733
$381$	−10.0561	−0.515190
$382$	−0.482573	−0.0246906
$383$	−4.79139	−0.244829	−0.122414	−	0.992479i	$-0.539064\pi$
$383$	−4.79139	−0.244829	−0.122414	+	0.992479i	$0.539064\pi$
$384$	2.44141	0.124588
$385$	0.122887	0.00626291
$386$	23.3432	1.18814
$387$	15.8524	0.805822
$388$	−10.5813	−0.537184
$389$	15.8124	0.801720	0.400860	−	0.916139i	$-0.368711\pi$
$389$	15.8124	0.801720	0.400860	+	0.916139i	$0.368711\pi$
$390$	−5.65064	−0.286131
$391$	−4.64922	−0.235121
$392$	−6.86080	−0.346523
$393$	−11.8911	−0.599828
$394$	−19.6898	−0.991958
$395$	3.23847	0.162945
$396$	−0.975117	−0.0490015
$397$	38.6391	1.93924	0.969621	−	0.244612i	$-0.0786605\pi$
$397$	38.6391	1.93924	0.969621	+	0.244612i	$0.0786605\pi$
$398$	6.17255	0.309402
$399$	−2.28577	−0.114432
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−21.6381	−1.07921
$403$	−14.2203	−0.708366
$404$	14.4968	0.721242
$405$	−9.11700	−0.453027
$406$	−3.39542	−0.168512
$407$	2.18377	0.108245
$408$	12.3556	0.611694
$409$	−12.7224	−0.629081	−0.314541	−	0.949244i	$-0.601850\pi$
$409$	−12.7224	−0.629081	−0.314541	+	0.949244i	$0.601850\pi$
$410$	0.669461	0.0330623
$411$	−1.82567	−0.0900535
$412$	−1.80201	−0.0887788
$413$	−0.556296	−0.0273735
$414$	−2.71968	−0.133665
$415$	−14.7915	−0.726088
$416$	−2.31450	−0.113478
$417$	−10.6075	−0.519453
$418$	−0.826562	−0.0404285
$419$	−0.488748	−0.0238769	−0.0119384	−	0.999929i	$-0.503800\pi$
$419$	−0.488748	−0.0238769	−0.0119384	+	0.999929i	$0.503800\pi$
$420$	−0.910862	−0.0444455
$421$	27.5288	1.34167	0.670837	−	0.741605i	$-0.265935\pi$
$421$	27.5288	1.34167	0.670837	+	0.741605i	$0.265935\pi$
$422$	−9.43859	−0.459464
$423$	−7.71591	−0.375160
$424$	−6.08460	−0.295494
$425$	5.06085	0.245487
$426$	14.6500	0.709795
$427$	−3.16627	−0.153227
$428$	10.1996	0.493015
$429$	1.86120	0.0898594
$430$	5.35467	0.258225
$431$	−0.292051	−0.0140676	−0.00703380	−	0.999975i	$-0.502239\pi$
$431$	−0.292051	−0.0140676	−0.00703380	+	0.999975i	$0.502239\pi$
$432$	−0.0964843	−0.00464210
$433$	17.1752	0.825388	0.412694	−	0.910870i	$-0.364588\pi$
$433$	17.1752	0.825388	0.412694	+	0.910870i	$0.364588\pi$
$434$	−2.29227	−0.110032
$435$	22.2189	1.06531
$436$	1.27166	0.0609016
$437$	−2.30535	−0.110280
$438$	26.9106	1.28584
$439$	−4.02672	−0.192185	−0.0960923	−	0.995372i	$-0.530634\pi$
$439$	−4.02672	−0.192185	−0.0960923	+	0.995372i	$0.530634\pi$
$440$	−0.329378	−0.0157025
$441$	−20.3113	−0.967204
$442$	−11.7133	−0.557146
$443$	−21.2818	−1.01113	−0.505566	−	0.862788i	$-0.668716\pi$
$443$	−21.2818	−1.01113	−0.505566	+	0.862788i	$0.668716\pi$
$444$	−16.1865	−0.768177
$445$	0.593446	0.0281321
$446$	2.57857	0.122099
$447$	24.2396	1.14649
$448$	−0.373089	−0.0176268
$449$	−24.6679	−1.16415	−0.582075	−	0.813135i	$-0.697759\pi$
$449$	−24.6679	−1.16415	−0.582075	+	0.813135i	$0.697759\pi$
$450$	2.96048	0.139558
$451$	−0.220506	−0.0103832
$452$	−3.87906	−0.182456
$453$	−57.6449	−2.70839
$454$	−9.14901	−0.429384
$455$	0.863513	0.0404821
$456$	6.12663	0.286906
$457$	−18.4650	−0.863757	−0.431878	−	0.901932i	$-0.642149\pi$
$457$	−18.4650	−0.863757	−0.431878	+	0.901932i	$0.642149\pi$
$458$	23.5226	1.09914
$459$	−0.488293	−0.0227915
$460$	−0.918663	−0.0428329
$461$	−39.4509	−1.83741	−0.918705	−	0.394945i	$-0.870764\pi$
$461$	−39.4509	−1.83741	−0.918705	+	0.394945i	$0.870764\pi$
$462$	0.300018	0.0139581
$463$	15.4407	0.717591	0.358796	−	0.933416i	$-0.383188\pi$
$463$	15.4407	0.717591	0.358796	+	0.933416i	$0.383188\pi$
$464$	9.10084	0.422496
$465$	15.0001	0.695612
$466$	−19.1283	−0.886100
$467$	−27.5946	−1.27693	−0.638463	−	0.769652i	$-0.720430\pi$
$467$	−27.5946	−1.27693	−0.638463	+	0.769652i	$0.720430\pi$
$468$	−6.85203	−0.316735
$469$	3.30666	0.152687
$470$	−2.60630	−0.120220
$471$	5.94495	0.273929
$472$	1.49105	0.0686313
$473$	−1.76371	−0.0810955
$474$	7.90643	0.363154
$475$	2.50946	0.115142
$476$	−1.88815	−0.0865430
$477$	−18.0133	−0.824774
$478$	15.0493	0.688340
$479$	30.4586	1.39169	0.695845	−	0.718192i	$-0.255030\pi$
$479$	30.4586	1.39169	0.695845	+	0.718192i	$0.255030\pi$
$480$	2.44141	0.111435
$481$	15.3451	0.699676
$482$	4.24007	0.193130
$483$	0.836776	0.0380746
$484$	−10.8915	−0.495069
$485$	−10.5813	−0.480472
$486$	−21.9689	−0.996528
$487$	6.83833	0.309874	0.154937	−	0.987924i	$-0.450483\pi$
$487$	6.83833	0.309874	0.154937	+	0.987924i	$0.450483\pi$
$488$	8.48665	0.384173
$489$	−36.1643	−1.63541
$490$	−6.86080	−0.309940
$491$	−26.4274	−1.19265	−0.596325	−	0.802743i	$-0.703373\pi$
$491$	−26.4274	−1.19265	−0.596325	+	0.802743i	$0.703373\pi$
$492$	1.63443	0.0736858
$493$	46.0580	2.07435
$494$	−5.80815	−0.261321
$495$	−0.975117	−0.0438283
$496$	6.14402	0.275875
$497$	−2.23877	−0.100422
$498$	−36.1122	−1.61823
$499$	29.4513	1.31842	0.659211	−	0.751958i	$-0.270890\pi$
$499$	29.4513	1.31842	0.659211	+	0.751958i	$0.270890\pi$
$500$	1.00000	0.0447214
$501$	22.9896	1.02710
$502$	−4.37658	−0.195336
$503$	10.6448	0.474628	0.237314	−	0.971433i	$-0.423733\pi$
$503$	10.6448	0.474628	0.237314	+	0.971433i	$0.423733\pi$
$504$	−1.10452	−0.0491993
$505$	14.4968	0.645098
$506$	0.302588	0.0134517
$507$	−18.6599	−0.828716
$508$	−4.11897	−0.182750
$509$	−8.39472	−0.372089	−0.186045	−	0.982541i	$-0.559567\pi$
$509$	−8.39472	−0.372089	−0.186045	+	0.982541i	$0.559567\pi$
$510$	12.3556	0.547115
$511$	−4.11240	−0.181922
$512$	1.00000	0.0441942
$513$	−0.242124	−0.0106900
$514$	−16.3121	−0.719497
$515$	−1.80201	−0.0794061
$516$	13.0729	0.575504
$517$	0.858459	0.0377550
$518$	2.47357	0.108682
$519$	−30.3957	−1.33422
$520$	−2.31450	−0.101497
$521$	−33.5850	−1.47139	−0.735693	−	0.677315i	$-0.763144\pi$
$521$	−33.5850	−1.47139	−0.735693	+	0.677315i	$0.763144\pi$
$522$	26.9429	1.17926
$523$	−23.0380	−1.00738	−0.503690	−	0.863884i	$-0.668025\pi$
$523$	−23.0380	−1.00738	−0.503690	+	0.863884i	$0.668025\pi$
$524$	−4.87060	−0.212773
$525$	−0.910862	−0.0397533
$526$	−25.9320	−1.13069
$527$	31.0940	1.35448
$528$	−0.804147	−0.0349960
$529$	−22.1561	−0.963307
$530$	−6.08460	−0.264298
$531$	4.41424	0.191562
$532$	−0.936252	−0.0405917
$533$	−1.54947	−0.0671149
$534$	1.44885	0.0626977
$535$	10.1996	0.440966
$536$	−8.86294	−0.382821
$537$	25.5733	1.10357
$538$	−26.1006	−1.12528
$539$	2.25980	0.0973364
$540$	−0.0964843	−0.00415202
$541$	−42.9144	−1.84503	−0.922517	−	0.385956i	$-0.873872\pi$
$541$	−42.9144	−1.84503	−0.922517	+	0.385956i	$0.873872\pi$
$542$	−23.0904	−0.991817
$543$	−37.8840	−1.62576
$544$	5.06085	0.216982
$545$	1.27166	0.0544720
$546$	2.10819	0.0902222
$547$	28.9892	1.23949	0.619743	−	0.784804i	$-0.287237\pi$
$547$	28.9892	1.23949	0.619743	+	0.784804i	$0.287237\pi$
$548$	−0.747792	−0.0319441
$549$	25.1246	1.07229
$550$	−0.329378	−0.0140447
$551$	22.8382	0.972941
$552$	−2.24283	−0.0954613
$553$	−1.20824	−0.0513795
$554$	−26.3917	−1.12128
$555$	−16.1865	−0.687079
$556$	−4.34484	−0.184262
$557$	1.66714	0.0706391	0.0353195	−	0.999376i	$-0.488755\pi$
$557$	1.66714	0.0706391	0.0353195	+	0.999376i	$0.488755\pi$
$558$	18.1893	0.770013
$559$	−12.3934	−0.524184
$560$	−0.373089	−0.0157659
$561$	−4.06966	−0.171821
$562$	2.14553	0.0905037
$563$	−36.2108	−1.52610	−0.763051	−	0.646338i	$-0.776299\pi$
$563$	−36.2108	−1.52610	−0.763051	+	0.646338i	$0.776299\pi$
$564$	−6.36306	−0.267933
$565$	−3.87906	−0.163193
$566$	−19.6412	−0.825581
$567$	3.40145	0.142847
$568$	6.00063	0.251781
$569$	11.2923	0.473398	0.236699	−	0.971583i	$-0.423934\pi$
$569$	11.2923	0.473398	0.236699	+	0.971583i	$0.423934\pi$
$570$	6.12663	0.256616
$571$	−16.0249	−0.670622	−0.335311	−	0.942108i	$-0.608841\pi$
$571$	−16.0249	−0.670622	−0.335311	+	0.942108i	$0.608841\pi$
$572$	0.762345	0.0318753
$573$	−1.17816	−0.0492183
$574$	−0.249769	−0.0104251
$575$	−0.918663	−0.0383109
$576$	2.96048	0.123353
$577$	26.2916	1.09453	0.547266	−	0.836959i	$-0.315669\pi$
$577$	26.2916	1.09453	0.547266	+	0.836959i	$0.315669\pi$
$578$	8.61219	0.358220
$579$	56.9904	2.36844
$580$	9.10084	0.377892
$581$	5.51856	0.228948
$582$	−25.8333	−1.07082
$583$	2.00413	0.0830027
$584$	11.0226	0.456118
$585$	−6.85203	−0.283296
$586$	22.8310	0.943139
$587$	10.5706	0.436297	0.218149	−	0.975916i	$-0.429998\pi$
$587$	10.5706	0.436297	0.218149	+	0.975916i	$0.429998\pi$
$588$	−16.7500	−0.690760
$589$	15.4182	0.635296
$590$	1.49105	0.0613857
$591$	−48.0709	−1.97737
$592$	−6.62998	−0.272491
$593$	43.7043	1.79472	0.897361	−	0.441297i	$-0.145482\pi$
$593$	43.7043	1.79472	0.897361	+	0.441297i	$0.145482\pi$
$594$	0.0317798	0.00130394
$595$	−1.88815	−0.0774064
$596$	9.92853	0.406688
$597$	15.0697	0.616763
$598$	2.12625	0.0869486
$599$	−6.24019	−0.254967	−0.127484	−	0.991841i	$-0.540690\pi$
$599$	−6.24019	−0.254967	−0.127484	+	0.991841i	$0.540690\pi$
$600$	2.44141	0.0996701
$601$	11.8232	0.482280	0.241140	−	0.970490i	$-0.422479\pi$
$601$	11.8232	0.482280	0.241140	+	0.970490i	$0.422479\pi$
$602$	−1.99777	−0.0814229
$603$	−26.2385	−1.06852
$604$	−23.6113	−0.960730
$605$	−10.8915	−0.442803
$606$	35.3926	1.43772
$607$	30.0093	1.21804	0.609020	−	0.793155i	$-0.291563\pi$
$607$	30.0093	1.21804	0.609020	+	0.793155i	$0.291563\pi$
$608$	2.50946	0.101772
$609$	−8.28962	−0.335912
$610$	8.48665	0.343614
$611$	6.03229	0.244040
$612$	14.9825	0.605633
$613$	22.8945	0.924702	0.462351	−	0.886697i	$-0.347006\pi$
$613$	22.8945	0.924702	0.462351	+	0.886697i	$0.347006\pi$
$614$	4.56829	0.184361
$615$	1.63443	0.0659066
$616$	0.122887	0.00495127
$617$	23.5691	0.948857	0.474429	−	0.880294i	$-0.342655\pi$
$617$	23.5691	0.948857	0.474429	+	0.880294i	$0.342655\pi$
$618$	−4.39945	−0.176972
$619$	20.6036	0.828128	0.414064	−	0.910248i	$-0.364109\pi$
$619$	20.6036	0.828128	0.414064	+	0.910248i	$0.364109\pi$
$620$	6.14402	0.246750
$621$	0.0886366	0.00355686
$622$	17.3122	0.694157
$623$	−0.221408	−0.00887053
$624$	−5.65064	−0.226207
$625$	1.00000	0.0400000
$626$	3.96876	0.158624
$627$	−2.01798	−0.0805902
$628$	2.43505	0.0971690
$629$	−33.5533	−1.33786
$630$	−1.10452	−0.0440052
$631$	−33.5274	−1.33470	−0.667352	−	0.744743i	$-0.732572\pi$
$631$	−33.5274	−1.33470	−0.667352	+	0.744743i	$0.732572\pi$
$632$	3.23847	0.128819
$633$	−23.0435	−0.915896
$634$	22.0156	0.874352
$635$	−4.11897	−0.163456
$636$	−14.8550	−0.589039
$637$	15.8793	0.629162
$638$	−2.99762	−0.118677
$639$	17.7647	0.702763
$640$	1.00000	0.0395285
$641$	23.2794	0.919481	0.459740	−	0.888053i	$-0.347942\pi$
$641$	23.2794	0.919481	0.459740	+	0.888053i	$0.347942\pi$
$642$	24.9013	0.982777
$643$	−23.5187	−0.927489	−0.463744	−	0.885969i	$-0.653494\pi$
$643$	−23.5187	−0.927489	−0.463744	+	0.885969i	$0.653494\pi$
$644$	0.342743	0.0135060
$645$	13.0729	0.514746
$646$	12.7000	0.499675
$647$	−2.17998	−0.0857038	−0.0428519	−	0.999081i	$-0.513644\pi$
$647$	−2.17998	−0.0857038	−0.0428519	+	0.999081i	$0.513644\pi$
$648$	−9.11700	−0.358150
$649$	−0.491121	−0.0192782
$650$	−2.31450	−0.0907821
$651$	−5.59636	−0.219339
$652$	−14.8129	−0.580117
$653$	24.7273	0.967653	0.483826	−	0.875164i	$-0.339247\pi$
$653$	24.7273	0.967653	0.483826	+	0.875164i	$0.339247\pi$
$654$	3.10465	0.121401
$655$	−4.87060	−0.190310
$656$	0.669461	0.0261381
$657$	32.6321	1.27310
$658$	0.972383	0.0379074
$659$	22.3816	0.871864	0.435932	−	0.899980i	$-0.356419\pi$
$659$	22.3816	0.871864	0.435932	+	0.899980i	$0.356419\pi$
$660$	−0.804147	−0.0313014
$661$	−24.1344	−0.938719	−0.469359	−	0.883007i	$-0.655515\pi$
$661$	−24.1344	−0.938719	−0.469359	+	0.883007i	$0.655515\pi$
$662$	−21.6379	−0.840981
$663$	−28.5970	−1.11062
$664$	−14.7915	−0.574023
$665$	−0.936252	−0.0363063
$666$	−19.6279	−0.760567
$667$	−8.36061	−0.323724
$668$	9.41654	0.364337
$669$	6.29536	0.243393
$670$	−8.86294	−0.342405
$671$	−2.79532	−0.107912
$672$	−0.910862	−0.0351373
$673$	12.5108	0.482254	0.241127	−	0.970494i	$-0.422483\pi$
$673$	12.5108	0.482254	0.241127	+	0.970494i	$0.422483\pi$
$674$	8.79200	0.338655
$675$	−0.0964843	−0.00371368
$676$	−7.64309	−0.293965
$677$	21.8829	0.841027	0.420514	−	0.907286i	$-0.361850\pi$
$677$	21.8829	0.841027	0.420514	+	0.907286i	$0.361850\pi$
$678$	−9.47038	−0.363708
$679$	3.94776	0.151501
$680$	5.06085	0.194075
$681$	−22.3365	−0.855936
$682$	−2.02371	−0.0774917
$683$	38.6607	1.47931	0.739656	−	0.672985i	$-0.234988\pi$
$683$	38.6607	1.47931	0.739656	+	0.672985i	$0.234988\pi$
$684$	7.42921	0.284063
$685$	−0.747792	−0.0285717
$686$	5.17131	0.197442
$687$	57.4282	2.19102
$688$	5.35467	0.204145
$689$	14.0828	0.536512
$690$	−2.24283	−0.0853832
$691$	38.6534	1.47044	0.735222	−	0.677826i	$-0.237078\pi$
$691$	38.6534	1.47044	0.735222	+	0.677826i	$0.237078\pi$
$692$	−12.4501	−0.473280
$693$	0.363805	0.0138198
$694$	12.2151	0.463680
$695$	−4.34484	−0.164809
$696$	22.2189	0.842205
$697$	3.38804	0.128331
$698$	12.9658	0.490761
$699$	−46.6999	−1.76635
$700$	−0.373089	−0.0141014
$701$	−35.9566	−1.35806	−0.679031	−	0.734110i	$-0.737600\pi$
$701$	−35.9566	−1.35806	−0.679031	+	0.734110i	$0.737600\pi$
$702$	0.223313	0.00842840
$703$	−16.6377	−0.627502
$704$	−0.329378	−0.0124139
$705$	−6.36306	−0.239647
$706$	−4.52035	−0.170126
$707$	−5.40858	−0.203411
$708$	3.64027	0.136810
$709$	32.8029	1.23194	0.615970	−	0.787770i	$-0.288764\pi$
$709$	32.8029	1.23194	0.615970	+	0.787770i	$0.288764\pi$
$710$	6.00063	0.225200
$711$	9.58743	0.359557
$712$	0.593446	0.0222403
$713$	−5.64429	−0.211380
$714$	−4.60974	−0.172515
$715$	0.762345	0.0285101
$716$	10.4748	0.391461
$717$	36.7415	1.37214
$718$	22.3853	0.835414
$719$	9.62321	0.358885	0.179443	−	0.983768i	$-0.442571\pi$
$719$	9.62321	0.358885	0.179443	+	0.983768i	$0.442571\pi$
$720$	2.96048	0.110331
$721$	0.672310	0.0250381
$722$	−12.7026	−0.472742
$723$	10.3518	0.384986
$724$	−15.5172	−0.576694
$725$	9.10084	0.337997
$726$	−26.5906	−0.986871
$727$	−35.0595	−1.30028	−0.650142	−	0.759812i	$-0.725291\pi$
$727$	−35.0595	−1.30028	−0.650142	+	0.759812i	$0.725291\pi$
$728$	0.863513	0.0320039
$729$	−26.2840	−0.973482
$730$	11.0226	0.407964
$731$	27.0992	1.00230
$732$	20.7194	0.765811
$733$	24.4384	0.902652	0.451326	−	0.892359i	$-0.350951\pi$
$733$	24.4384	0.902652	0.451326	+	0.892359i	$0.350951\pi$
$734$	10.5525	0.389499
$735$	−16.7500	−0.617834
$736$	−0.918663	−0.0338624
$737$	2.91926	0.107532
$738$	1.98193	0.0729558
$739$	16.8309	0.619135	0.309567	−	0.950878i	$-0.399816\pi$
$739$	16.8309	0.619135	0.309567	+	0.950878i	$0.399816\pi$
$740$	−6.62998	−0.243723
$741$	−14.1801	−0.520918
$742$	2.27009	0.0833378
$743$	−9.59126	−0.351869	−0.175935	−	0.984402i	$-0.556295\pi$
$743$	−9.59126	−0.351869	−0.175935	+	0.984402i	$0.556295\pi$
$744$	15.0001	0.549930
$745$	9.92853	0.363753
$746$	−5.02649	−0.184033
$747$	−43.7901	−1.60219
$748$	−1.66693	−0.0609491
$749$	−3.80534	−0.139044
$750$	2.44141	0.0891477
$751$	47.6517	1.73884	0.869418	−	0.494077i	$-0.164494\pi$
$751$	47.6517	1.73884	0.869418	+	0.494077i	$0.164494\pi$
$752$	−2.60630	−0.0950421
$753$	−10.6850	−0.389384
$754$	−21.0639	−0.767102
$755$	−23.6113	−0.859303
$756$	0.0359972	0.00130921
$757$	−11.8957	−0.432358	−0.216179	−	0.976354i	$-0.569359\pi$
$757$	−11.8957	−0.432358	−0.216179	+	0.976354i	$0.569359\pi$
$758$	−13.7494	−0.499402
$759$	0.738740	0.0268146
$760$	2.50946	0.0910278
$761$	−0.193866	−0.00702765	−0.00351383	−	0.999994i	$-0.501118\pi$
$761$	−0.193866	−0.00702765	−0.00351383	+	0.999994i	$0.501118\pi$
$762$	−10.0561	−0.364294
$763$	−0.474443	−0.0171760
$764$	−0.482573	−0.0174589
$765$	14.9825	0.541695
$766$	−4.79139	−0.173120
$767$	−3.45104	−0.124610
$768$	2.44141	0.0880968
$769$	22.1098	0.797301	0.398650	−	0.917103i	$-0.369479\pi$
$769$	22.1098	0.797301	0.398650	+	0.917103i	$0.369479\pi$
$770$	0.122887	0.00442855
$771$	−39.8246	−1.43425
$772$	23.3432	0.840141
$773$	−21.6037	−0.777029	−0.388515	−	0.921443i	$-0.627012\pi$
$773$	−21.6037	−0.777029	−0.388515	+	0.921443i	$0.627012\pi$
$774$	15.8524	0.569802
$775$	6.14402	0.220700
$776$	−10.5813	−0.379846
$777$	6.03900	0.216648
$778$	15.8124	0.566902
$779$	1.67999	0.0601918
$780$	−5.65064	−0.202325
$781$	−1.97648	−0.0707239
$782$	−4.64922	−0.166256
$783$	−0.878089	−0.0313803
$784$	−6.86080	−0.245029
$785$	2.43505	0.0869106
$786$	−11.8911	−0.424143
$787$	32.4983	1.15844	0.579219	−	0.815172i	$-0.303358\pi$
$787$	32.4983	1.15844	0.579219	+	0.815172i	$0.303358\pi$
$788$	−19.6898	−0.701420
$789$	−63.3107	−2.25392
$790$	3.23847	0.115220
$791$	1.44723	0.0514577
$792$	−0.975117	−0.0346493
$793$	−19.6423	−0.697520
$794$	38.6391	1.37125
$795$	−14.8550	−0.526852
$796$	6.17255	0.218780
$797$	2.53436	0.0897718	0.0448859	−	0.998992i	$-0.485708\pi$
$797$	2.53436	0.0897718	0.0448859	+	0.998992i	$0.485708\pi$
$798$	−2.28577	−0.0809156
$799$	−13.1901	−0.466633
$800$	1.00000	0.0353553
$801$	1.75689	0.0620765
$802$	1.00000	0.0353112
$803$	−3.63060	−0.128121
$804$	−21.6381	−0.763115
$805$	0.342743	0.0120801
$806$	−14.2203	−0.500890
$807$	−63.7223	−2.24313
$808$	14.4968	0.509995
$809$	40.0524	1.40817	0.704084	−	0.710117i	$-0.251358\pi$
$809$	40.0524	1.40817	0.704084	+	0.710117i	$0.251358\pi$
$810$	−9.11700	−0.320339
$811$	9.86749	0.346494	0.173247	−	0.984878i	$-0.444574\pi$
$811$	9.86749	0.346494	0.173247	+	0.984878i	$0.444574\pi$
$812$	−3.39542	−0.119156
$813$	−56.3731	−1.97709
$814$	2.18377	0.0765411
$815$	−14.8129	−0.518872
$816$	12.3556	0.432533
$817$	13.4373	0.470113
$818$	−12.7224	−0.444828
$819$	2.55641	0.0893284
$820$	0.669461	0.0233786
$821$	−35.8720	−1.25194	−0.625971	−	0.779846i	$-0.715297\pi$
$821$	−35.8720	−1.25194	−0.625971	+	0.779846i	$0.715297\pi$
$822$	−1.82567	−0.0636775
$823$	37.6397	1.31204	0.656019	−	0.754744i	$-0.272239\pi$
$823$	37.6397	1.31204	0.656019	+	0.754744i	$0.272239\pi$
$824$	−1.80201	−0.0627761
$825$	−0.804147	−0.0279968
$826$	−0.556296	−0.0193560
$827$	−19.9933	−0.695236	−0.347618	−	0.937636i	$-0.613009\pi$
$827$	−19.9933	−0.695236	−0.347618	+	0.937636i	$0.613009\pi$
$828$	−2.71968	−0.0945156
$829$	−20.2454	−0.703152	−0.351576	−	0.936159i	$-0.614354\pi$
$829$	−20.2454	−0.703152	−0.351576	+	0.936159i	$0.614354\pi$
$830$	−14.7915	−0.513422
$831$	−64.4330	−2.23515
$832$	−2.31450	−0.0802408
$833$	−34.7215	−1.20303
$834$	−10.6075	−0.367309
$835$	9.41654	0.325873
$836$	−0.826562	−0.0285872
$837$	−0.592802	−0.0204902
$838$	−0.488748	−0.0168835
$839$	4.56061	0.157450	0.0787249	−	0.996896i	$-0.474915\pi$
$839$	4.56061	0.157450	0.0787249	+	0.996896i	$0.474915\pi$
$840$	−0.910862	−0.0314277
$841$	53.8254	1.85605
$842$	27.5288	0.948706
$843$	5.23812	0.180410
$844$	−9.43859	−0.324890
$845$	−7.64309	−0.262930
$846$	−7.71591	−0.265279
$847$	4.06350	0.139624
$848$	−6.08460	−0.208946
$849$	−47.9522	−1.64572
$850$	5.06085	0.173586
$851$	6.09072	0.208787
$852$	14.6500	0.501901
$853$	−35.0254	−1.19925	−0.599624	−	0.800282i	$-0.704683\pi$
$853$	−35.0254	−1.19925	−0.599624	+	0.800282i	$0.704683\pi$
$854$	−3.16627	−0.108348
$855$	7.42921	0.254074
$856$	10.1996	0.348614
$857$	−5.96109	−0.203627	−0.101813	−	0.994804i	$-0.532464\pi$
$857$	−5.96109	−0.203627	−0.101813	+	0.994804i	$0.532464\pi$
$858$	1.86120	0.0635402
$859$	−11.8254	−0.403479	−0.201739	−	0.979439i	$-0.564659\pi$
$859$	−11.8254	−0.403479	−0.201739	+	0.979439i	$0.564659\pi$
$860$	5.35467	0.182593
$861$	−0.609787	−0.0207815
$862$	−0.292051	−0.00994730
$863$	−24.3616	−0.829280	−0.414640	−	0.909986i	$-0.636092\pi$
$863$	−24.3616	−0.829280	−0.414640	+	0.909986i	$0.636092\pi$
$864$	−0.0964843	−0.00328246
$865$	−12.4501	−0.423315
$866$	17.1752	0.583637
$867$	21.0259	0.714077
$868$	−2.29227	−0.0778046
$869$	−1.06668	−0.0361847
$870$	22.2189	0.753291
$871$	20.5133	0.695065
$872$	1.27166	0.0430639
$873$	−31.3257	−1.06021
$874$	−2.30535	−0.0779797
$875$	−0.373089	−0.0126127
$876$	26.9106	0.909226
$877$	3.73262	0.126042	0.0630208	−	0.998012i	$-0.479927\pi$
$877$	3.73262	0.126042	0.0630208	+	0.998012i	$0.479927\pi$
$878$	−4.02672	−0.135895
$879$	55.7398	1.88006
$880$	−0.329378	−0.0111033
$881$	−9.18536	−0.309463	−0.154731	−	0.987957i	$-0.549451\pi$
$881$	−9.18536	−0.309463	−0.154731	+	0.987957i	$0.549451\pi$
$882$	−20.3113	−0.683916
$883$	6.77764	0.228086	0.114043	−	0.993476i	$-0.463620\pi$
$883$	6.77764	0.228086	0.114043	+	0.993476i	$0.463620\pi$
$884$	−11.7133	−0.393962
$885$	3.64027	0.122366
$886$	−21.2818	−0.714978
$887$	−13.7686	−0.462306	−0.231153	−	0.972917i	$-0.574250\pi$
$887$	−13.7686	−0.462306	−0.231153	+	0.972917i	$0.574250\pi$
$888$	−16.1865	−0.543183
$889$	1.53674	0.0515407
$890$	0.593446	0.0198924
$891$	3.00294	0.100602
$892$	2.57857	0.0863371
$893$	−6.54042	−0.218867
$894$	24.2396	0.810694
$895$	10.4748	0.350134
$896$	−0.373089	−0.0124640
$897$	5.19104	0.173324
$898$	−24.6679	−0.823179
$899$	55.9158	1.86490
$900$	2.96048	0.0986827
$901$	−30.7932	−1.02587
$902$	−0.220506	−0.00734204
$903$	−4.87736	−0.162309
$904$	−3.87906	−0.129016
$905$	−15.5172	−0.515811
$906$	−57.6449	−1.91512
$907$	−25.5539	−0.848502	−0.424251	−	0.905545i	$-0.639463\pi$
$907$	−25.5539	−0.848502	−0.424251	+	0.905545i	$0.639463\pi$
$908$	−9.14901	−0.303621
$909$	42.9174	1.42348
$910$	0.863513	0.0286252
$911$	−18.0121	−0.596767	−0.298384	−	0.954446i	$-0.596447\pi$
$911$	−18.0121	−0.596767	−0.298384	+	0.954446i	$0.596447\pi$
$912$	6.12663	0.202873
$913$	4.87201	0.161240
$914$	−18.4650	−0.610768
$915$	20.7194	0.684962
$916$	23.5226	0.777208
$917$	1.81717	0.0600081
$918$	−0.488293	−0.0161161
$919$	−43.6598	−1.44020	−0.720102	−	0.693869i	$-0.755905\pi$
$919$	−43.6598	−1.44020	−0.720102	+	0.693869i	$0.755905\pi$
$920$	−0.918663	−0.0302874
$921$	11.1531	0.367506
$922$	−39.4509	−1.29925
$923$	−13.8885	−0.457144
$924$	0.300018	0.00986987
$925$	−6.62998	−0.217992
$926$	15.4407	0.507414
$927$	−5.33482	−0.175218
$928$	9.10084	0.298750
$929$	−4.31201	−0.141473	−0.0707363	−	0.997495i	$-0.522535\pi$
$929$	−4.31201	−0.141473	−0.0707363	+	0.997495i	$0.522535\pi$
$930$	15.0001	0.491872
$931$	−17.2169	−0.564262
$932$	−19.1283	−0.626567
$933$	42.2663	1.38374
$934$	−27.5946	−0.902924
$935$	−1.66693	−0.0545145
$936$	−6.85203	−0.223966
$937$	7.10374	0.232069	0.116034	−	0.993245i	$-0.462982\pi$
$937$	7.10374	0.232069	0.116034	+	0.993245i	$0.462982\pi$
$938$	3.30666	0.107966
$939$	9.68937	0.316201
$940$	−2.60630	−0.0850083
$941$	26.1020	0.850901	0.425451	−	0.904982i	$-0.360116\pi$
$941$	26.1020	0.850901	0.425451	+	0.904982i	$0.360116\pi$
$942$	5.94495	0.193697
$943$	−0.615010	−0.0200275
$944$	1.49105	0.0485297
$945$	0.0359972	0.00117099
$946$	−1.76371	−0.0573432
$947$	−29.2062	−0.949073	−0.474537	−	0.880236i	$-0.657384\pi$
$947$	−29.2062	−0.949073	−0.474537	+	0.880236i	$0.657384\pi$
$948$	7.90643	0.256789
$949$	−25.5118	−0.828147
$950$	2.50946	0.0814177
$951$	53.7491	1.74293
$952$	−1.88815	−0.0611952
$953$	−49.2810	−1.59637	−0.798184	−	0.602414i	$-0.794206\pi$
$953$	−49.2810	−1.59637	−0.798184	+	0.602414i	$0.794206\pi$
$954$	−18.0133	−0.583203
$955$	−0.482573	−0.0156157
$956$	15.0493	0.486730
$957$	−7.31841	−0.236571
$958$	30.4586	0.984073
$959$	0.278993	0.00900915
$960$	2.44141	0.0787962
$961$	6.74904	0.217711
$962$	15.3451	0.494745
$963$	30.1956	0.973040
$964$	4.24007	0.136564
$965$	23.3432	0.751445
$966$	0.836776	0.0269228
$967$	7.42804	0.238870	0.119435	−	0.992842i	$-0.461892\pi$
$967$	7.42804	0.238870	0.119435	+	0.992842i	$0.461892\pi$
$968$	−10.8915	−0.350066
$969$	31.0059	0.996054
$970$	−10.5813	−0.339745
$971$	37.6160	1.20715	0.603577	−	0.797305i	$-0.293742\pi$
$971$	37.6160	1.20715	0.603577	+	0.797305i	$0.293742\pi$
$972$	−21.9689	−0.704652
$973$	1.62101	0.0519672
$974$	6.83833	0.219114
$975$	−5.65064	−0.180965
$976$	8.48665	0.271651
$977$	11.7060	0.374507	0.187253	−	0.982312i	$-0.440041\pi$
$977$	11.7060	0.374507	0.187253	+	0.982312i	$0.440041\pi$
$978$	−36.1643	−1.15641
$979$	−0.195468	−0.00624719
$980$	−6.86080	−0.219160
$981$	3.76473	0.120199
$982$	−26.4274	−0.843332
$983$	38.9551	1.24247	0.621237	−	0.783622i	$-0.286630\pi$
$983$	38.9551	1.24247	0.621237	+	0.783622i	$0.286630\pi$
$984$	1.63443	0.0521037
$985$	−19.6898	−0.627369
$986$	46.0580	1.46679
$987$	2.37398	0.0755648
$988$	−5.80815	−0.184782
$989$	−4.91914	−0.156419
$990$	−0.975117	−0.0309913
$991$	12.9708	0.412031	0.206016	−	0.978549i	$-0.433950\pi$
$991$	12.9708	0.412031	0.206016	+	0.978549i	$0.433950\pi$
$992$	6.14402	0.195073
$993$	−52.8270	−1.67641
$994$	−2.23877	−0.0710094
$995$	6.17255	0.195683
$996$	−36.1122	−1.14426
$997$	17.6177	0.557960	0.278980	−	0.960297i	$-0.410004\pi$
$997$	17.6177	0.557960	0.278980	+	0.960297i	$0.410004\pi$
$998$	29.4513	0.932265
$999$	0.639689	0.0202389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.44141 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.44141 q^{6} -0.373089 q^{7} +1.00000 q^{8} +2.96048 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.44141 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.44141 q^{6} -0.373089 q^{7} +1.00000 q^{8} +2.96048 q^{9} +1.00000 q^{10} -0.329378 q^{11} +2.44141 q^{12} -2.31450 q^{13} -0.373089 q^{14} +2.44141 q^{15} +1.00000 q^{16} +5.06085 q^{17} +2.96048 q^{18} +2.50946 q^{19} +1.00000 q^{20} -0.910862 q^{21} -0.329378 q^{22} -0.918663 q^{23} +2.44141 q^{24} +1.00000 q^{25} -2.31450 q^{26} -0.0964843 q^{27} -0.373089 q^{28} +9.10084 q^{29} +2.44141 q^{30} +6.14402 q^{31} +1.00000 q^{32} -0.804147 q^{33} +5.06085 q^{34} -0.373089 q^{35} +2.96048 q^{36} -6.62998 q^{37} +2.50946 q^{38} -5.65064 q^{39} +1.00000 q^{40} +0.669461 q^{41} -0.910862 q^{42} +5.35467 q^{43} -0.329378 q^{44} +2.96048 q^{45} -0.918663 q^{46} -2.60630 q^{47} +2.44141 q^{48} -6.86080 q^{49} +1.00000 q^{50} +12.3556 q^{51} -2.31450 q^{52} -6.08460 q^{53} -0.0964843 q^{54} -0.329378 q^{55} -0.373089 q^{56} +6.12663 q^{57} +9.10084 q^{58} +1.49105 q^{59} +2.44141 q^{60} +8.48665 q^{61} +6.14402 q^{62} -1.10452 q^{63} +1.00000 q^{64} -2.31450 q^{65} -0.804147 q^{66} -8.86294 q^{67} +5.06085 q^{68} -2.24283 q^{69} -0.373089 q^{70} +6.00063 q^{71} +2.96048 q^{72} +11.0226 q^{73} -6.62998 q^{74} +2.44141 q^{75} +2.50946 q^{76} +0.122887 q^{77} -5.65064 q^{78} +3.23847 q^{79} +1.00000 q^{80} -9.11700 q^{81} +0.669461 q^{82} -14.7915 q^{83} -0.910862 q^{84} +5.06085 q^{85} +5.35467 q^{86} +22.2189 q^{87} -0.329378 q^{88} +0.593446 q^{89} +2.96048 q^{90} +0.863513 q^{91} -0.918663 q^{92} +15.0001 q^{93} -2.60630 q^{94} +2.50946 q^{95} +2.44141 q^{96} -10.5813 q^{97} -6.86080 q^{98} -0.975117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 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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