LMFDB - Embedded newform 547.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71387 q^{2} -2.58580 q^{3} +0.937360 q^{4} +0.849164 q^{5} +4.43173 q^{6} -2.18891 q^{7} +1.82123 q^{8} +3.68636 q^{9} +O(q^{10})$	\(q-1.71387 q^{2} -2.58580 q^{3} +0.937360 q^{4} +0.849164 q^{5} +4.43173 q^{6} -2.18891 q^{7} +1.82123 q^{8} +3.68636 q^{9} -1.45536 q^{10} -6.43154 q^{11} -2.42383 q^{12} -0.0958018 q^{13} +3.75151 q^{14} -2.19577 q^{15} -4.99608 q^{16} +1.27125 q^{17} -6.31796 q^{18} -2.66271 q^{19} +0.795972 q^{20} +5.66007 q^{21} +11.0228 q^{22} -3.64481 q^{23} -4.70934 q^{24} -4.27892 q^{25} +0.164192 q^{26} -1.77480 q^{27} -2.05179 q^{28} +0.787930 q^{29} +3.76327 q^{30} -1.39752 q^{31} +4.92018 q^{32} +16.6307 q^{33} -2.17876 q^{34} -1.85874 q^{35} +3.45545 q^{36} +8.37352 q^{37} +4.56355 q^{38} +0.247724 q^{39} +1.54652 q^{40} +5.17283 q^{41} -9.70065 q^{42} +9.89571 q^{43} -6.02866 q^{44} +3.13033 q^{45} +6.24674 q^{46} +4.41120 q^{47} +12.9189 q^{48} -2.20869 q^{49} +7.33353 q^{50} -3.28720 q^{51} -0.0898008 q^{52} +10.2981 q^{53} +3.04178 q^{54} -5.46143 q^{55} -3.98650 q^{56} +6.88523 q^{57} -1.35041 q^{58} +6.44026 q^{59} -2.05823 q^{60} -13.4689 q^{61} +2.39517 q^{62} -8.06910 q^{63} +1.55959 q^{64} -0.0813514 q^{65} -28.5029 q^{66} -5.75369 q^{67} +1.19162 q^{68} +9.42475 q^{69} +3.18564 q^{70} +12.9909 q^{71} +6.71371 q^{72} -2.65079 q^{73} -14.3511 q^{74} +11.0644 q^{75} -2.49592 q^{76} +14.0780 q^{77} -0.424568 q^{78} -2.33430 q^{79} -4.24249 q^{80} -6.46982 q^{81} -8.86558 q^{82} +11.8585 q^{83} +5.30553 q^{84} +1.07950 q^{85} -16.9600 q^{86} -2.03743 q^{87} -11.7133 q^{88} -5.04096 q^{89} -5.36498 q^{90} +0.209701 q^{91} -3.41650 q^{92} +3.61370 q^{93} -7.56024 q^{94} -2.26108 q^{95} -12.7226 q^{96} -1.62265 q^{97} +3.78541 q^{98} -23.7090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) $ 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9 - q^10 + 10 * q^11 + 14 * q^12 + 19 * q^13 + 9 * q^14 + 5 * q^15 + 16 * q^16 + 40 * q^17 - 8 * q^18 + 33 * q^20 - 8 * q^21 - 10 * q^22 + 26 * q^23 - 16 * q^24 + 36 * q^25 - 8 * q^26 + 11 * q^27 - 8 * q^28 + 30 * q^29 - 20 * q^30 - 5 * q^31 + 6 * q^32 + 10 * q^33 - 7 * q^34 + 11 * q^35 + 13 * q^36 + 26 * q^37 + 25 * q^38 - 17 * q^39 - 25 * q^40 + 9 * q^41 - 16 * q^42 - 10 * q^43 + 64 * q^45 - 34 * q^46 + 28 * q^47 + 23 * q^48 + 20 * q^49 - 9 * q^50 - 9 * q^51 - 2 * q^52 + 80 * q^53 - 13 * q^54 - q^55 + 7 * q^56 - 8 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 22 * q^61 + 36 * q^62 - 9 * q^63 - 28 * q^64 + 30 * q^65 - 42 * q^66 - 16 * q^67 + 59 * q^68 + 22 * q^69 - 61 * q^70 - q^71 - 44 * q^72 + 2 * q^73 - 8 * q^74 - 31 * q^75 - 46 * q^76 + 67 * q^77 - q^78 - 34 * q^79 + 30 * q^80 - 11 * q^81 - 4 * q^82 + 15 * q^83 - 87 * q^84 + 15 * q^85 - 44 * q^86 - 29 * q^87 - 55 * q^88 + 38 * q^89 - 90 * q^90 - 41 * q^91 + 40 * q^92 - 4 * q^93 - 46 * q^94 - 46 * q^95 - 87 * q^96 - 2 * q^97 - 14 * 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 $

$2$	−1.71387	−1.21189	−0.605946	−	0.795506i	$-0.707205\pi$
$2$	−1.71387	−1.21189	−0.605946	+	0.795506i	$0.707205\pi$
$3$	−2.58580	−1.49291	−0.746456	−	0.665434i	$-0.768246\pi$
$3$	−2.58580	−1.49291	−0.746456	+	0.665434i	$0.768246\pi$
$4$	0.937360	0.468680
$5$	0.849164	0.379758	0.189879	−	0.981808i	$-0.439190\pi$
$5$	0.849164	0.379758	0.189879	+	0.981808i	$0.439190\pi$
$6$	4.43173	1.80925
$7$	−2.18891	−0.827329	−0.413664	−	0.910429i	$-0.635751\pi$
$7$	−2.18891	−0.827329	−0.413664	+	0.910429i	$0.635751\pi$
$8$	1.82123	0.643902
$9$	3.68636	1.22879
$10$	−1.45536	−0.460225
$11$	−6.43154	−1.93918	−0.969591	−	0.244733i	$-0.921300\pi$
$11$	−6.43154	−1.93918	−0.969591	+	0.244733i	$0.921300\pi$
$12$	−2.42383	−0.699698
$13$	−0.0958018	−0.0265706	−0.0132853	−	0.999912i	$-0.504229\pi$
$13$	−0.0958018	−0.0265706	−0.0132853	+	0.999912i	$0.504229\pi$
$14$	3.75151	1.00263
$15$	−2.19577	−0.566945
$16$	−4.99608	−1.24902
$17$	1.27125	0.308323	0.154162	−	0.988046i	$-0.450732\pi$
$17$	1.27125	0.308323	0.154162	+	0.988046i	$0.450732\pi$
$18$	−6.31796	−1.48916
$19$	−2.66271	−0.610867	−0.305434	−	0.952213i	$-0.598801\pi$
$19$	−2.66271	−0.610867	−0.305434	+	0.952213i	$0.598801\pi$
$20$	0.795972	0.177985
$21$	5.66007	1.23513
$22$	11.0228	2.35008
$23$	−3.64481	−0.759995	−0.379998	−	0.924987i	$-0.624075\pi$
$23$	−3.64481	−0.759995	−0.379998	+	0.924987i	$0.624075\pi$
$24$	−4.70934	−0.961289
$25$	−4.27892	−0.855784
$26$	0.164192	0.0322007
$27$	−1.77480	−0.341560
$28$	−2.05179	−0.387752
$29$	0.787930	0.146315	0.0731575	−	0.997320i	$-0.476692\pi$
$29$	0.787930	0.146315	0.0731575	+	0.997320i	$0.476692\pi$
$30$	3.76327	0.687075
$31$	−1.39752	−0.251002	−0.125501	−	0.992094i	$-0.540054\pi$
$31$	−1.39752	−0.251002	−0.125501	+	0.992094i	$0.540054\pi$
$32$	4.92018	0.869773
$33$	16.6307	2.89503
$34$	−2.17876	−0.373654
$35$	−1.85874	−0.314184
$36$	3.45545	0.575908
$37$	8.37352	1.37660	0.688299	−	0.725427i	$-0.258358\pi$
$37$	8.37352	1.37660	0.688299	+	0.725427i	$0.258358\pi$
$38$	4.56355	0.740305
$39$	0.247724	0.0396676
$40$	1.54652	0.244527
$41$	5.17283	0.807861	0.403930	−	0.914790i	$-0.367644\pi$
$41$	5.17283	0.807861	0.403930	+	0.914790i	$0.367644\pi$
$42$	−9.70065	−1.49684
$43$	9.89571	1.50908	0.754541	−	0.656253i	$-0.227860\pi$
$43$	9.89571	1.50908	0.754541	+	0.656253i	$0.227860\pi$
$44$	−6.02866	−0.908855
$45$	3.13033	0.466642
$46$	6.24674	0.921032
$47$	4.41120	0.643440	0.321720	−	0.946835i	$-0.395739\pi$
$47$	4.41120	0.643440	0.321720	+	0.946835i	$0.395739\pi$
$48$	12.9189	1.86468
$49$	−2.20869	−0.315527
$50$	7.33353	1.03712
$51$	−3.28720	−0.460299
$52$	−0.0898008	−0.0124531
$53$	10.2981	1.41456	0.707279	−	0.706934i	$-0.249922\pi$
$53$	10.2981	1.41456	0.707279	+	0.706934i	$0.249922\pi$
$54$	3.04178	0.413934
$55$	−5.46143	−0.736419
$56$	−3.98650	−0.532719
$57$	6.88523	0.911972
$58$	−1.35041	−0.177318
$59$	6.44026	0.838450	0.419225	−	0.907882i	$-0.362302\pi$
$59$	6.44026	0.838450	0.419225	+	0.907882i	$0.362302\pi$
$60$	−2.05823	−0.265716
$61$	−13.4689	−1.72451	−0.862256	−	0.506473i	$-0.830949\pi$
$61$	−13.4689	−1.72451	−0.862256	+	0.506473i	$0.830949\pi$
$62$	2.39517	0.304187
$63$	−8.06910	−1.01661
$64$	1.55959	0.194949
$65$	−0.0813514	−0.0100904
$66$	−28.5029	−3.50846
$67$	−5.75369	−0.702925	−0.351462	−	0.936202i	$-0.614315\pi$
$67$	−5.75369	−0.702925	−0.351462	+	0.936202i	$0.614315\pi$
$68$	1.19162	0.144505
$69$	9.42475	1.13461
$70$	3.18564	0.380757
$71$	12.9909	1.54173	0.770865	−	0.636998i	$-0.219824\pi$
$71$	12.9909	1.54173	0.770865	+	0.636998i	$0.219824\pi$
$72$	6.71371	0.791219
$73$	−2.65079	−0.310251	−0.155126	−	0.987895i	$-0.549578\pi$
$73$	−2.65079	−0.310251	−0.155126	+	0.987895i	$0.549578\pi$
$74$	−14.3511	−1.66829
$75$	11.0644	1.27761
$76$	−2.49592	−0.286301
$77$	14.0780	1.60434
$78$	−0.424568	−0.0480728
$79$	−2.33430	−0.262629	−0.131315	−	0.991341i	$-0.541920\pi$
$79$	−2.33430	−0.262629	−0.131315	+	0.991341i	$0.541920\pi$
$80$	−4.24249	−0.474324
$81$	−6.46982	−0.718868
$82$	−8.86558	−0.979040
$83$	11.8585	1.30164	0.650818	−	0.759234i	$-0.274426\pi$
$83$	11.8585	1.30164	0.650818	+	0.759234i	$0.274426\pi$
$84$	5.30553	0.578881
$85$	1.07950	0.117088
$86$	−16.9600	−1.82884
$87$	−2.03743	−0.218435
$88$	−11.7133	−1.24864
$89$	−5.04096	−0.534340	−0.267170	−	0.963649i	$-0.586089\pi$
$89$	−5.04096	−0.534340	−0.267170	+	0.963649i	$0.586089\pi$
$90$	−5.36498	−0.565519
$91$	0.209701	0.0219826
$92$	−3.41650	−0.356195
$93$	3.61370	0.374724
$94$	−7.56024	−0.779779
$95$	−2.26108	−0.231982
$96$	−12.7226	−1.29850
$97$	−1.62265	−0.164755	−0.0823777	−	0.996601i	$-0.526251\pi$
$97$	−1.62265	−0.164755	−0.0823777	+	0.996601i	$0.526251\pi$
$98$	3.78541	0.382384
$99$	−23.7090	−2.38284
$100$	−4.01089	−0.401089
$101$	−4.00631	−0.398643	−0.199321	−	0.979934i	$-0.563874\pi$
$101$	−4.00631	−0.398643	−0.199321	+	0.979934i	$0.563874\pi$
$102$	5.63383	0.557833
$103$	−11.5656	−1.13959	−0.569796	−	0.821786i	$-0.692978\pi$
$103$	−11.5656	−1.13959	−0.569796	+	0.821786i	$0.692978\pi$
$104$	−0.174477	−0.0171089
$105$	4.80633	0.469050
$106$	−17.6497	−1.71429
$107$	14.7792	1.42876	0.714381	−	0.699757i	$-0.246709\pi$
$107$	14.7792	1.42876	0.714381	+	0.699757i	$0.246709\pi$
$108$	−1.66363	−0.160082
$109$	16.2858	1.55989	0.779946	−	0.625847i	$-0.215246\pi$
$109$	16.2858	1.55989	0.779946	+	0.625847i	$0.215246\pi$
$110$	9.36019	0.892459
$111$	−21.6522	−2.05514
$112$	10.9359	1.03335
$113$	−2.95809	−0.278274	−0.139137	−	0.990273i	$-0.544433\pi$
$113$	−2.95809	−0.278274	−0.139137	+	0.990273i	$0.544433\pi$
$114$	−11.8004	−1.10521
$115$	−3.09504	−0.288614
$116$	0.738574	0.0685749
$117$	−0.353160	−0.0326497
$118$	−11.0378	−1.01611
$119$	−2.78264	−0.255085
$120$	−3.99900	−0.365057
$121$	30.3647	2.76042
$122$	23.0839	2.08992
$123$	−13.3759	−1.20607
$124$	−1.30998	−0.117639
$125$	−7.87932	−0.704748
$126$	13.8294	1.23202
$127$	−7.38545	−0.655353	−0.327676	−	0.944790i	$-0.606266\pi$
$127$	−7.38545	−0.655353	−0.327676	+	0.944790i	$0.606266\pi$
$128$	−12.5133	−1.10603
$129$	−25.5883	−2.25293
$130$	0.139426	0.0122285
$131$	13.4415	1.17439	0.587193	−	0.809447i	$-0.300233\pi$
$131$	13.4415	1.17439	0.587193	+	0.809447i	$0.300233\pi$
$132$	15.5889	1.35684
$133$	5.82842	0.505388
$134$	9.86109	0.851868
$135$	−1.50709	−0.129710
$136$	2.31524	0.198530
$137$	0.0768732	0.00656772	0.00328386	−	0.999995i	$-0.498955\pi$
$137$	0.0768732	0.00656772	0.00328386	+	0.999995i	$0.498955\pi$
$138$	−16.1528	−1.37502
$139$	1.57398	0.133503	0.0667515	−	0.997770i	$-0.478737\pi$
$139$	1.57398	0.133503	0.0667515	+	0.997770i	$0.478737\pi$
$140$	−1.74231	−0.147252
$141$	−11.4065	−0.960600
$142$	−22.2647	−1.86841
$143$	0.616153	0.0515253
$144$	−18.4174	−1.53478
$145$	0.669082	0.0555642
$146$	4.54312	0.375991
$147$	5.71123	0.471054
$148$	7.84900	0.645184
$149$	−5.39646	−0.442095	−0.221047	−	0.975263i	$-0.570948\pi$
$149$	−5.39646	−0.442095	−0.221047	+	0.975263i	$0.570948\pi$
$150$	−18.9630	−1.54833
$151$	−9.08756	−0.739535	−0.369768	−	0.929124i	$-0.620563\pi$
$151$	−9.08756	−0.739535	−0.369768	+	0.929124i	$0.620563\pi$
$152$	−4.84941	−0.393339
$153$	4.68628	0.378864
$154$	−24.1280	−1.94429
$155$	−1.18672	−0.0953198
$156$	0.232207	0.0185914
$157$	0.189205	0.0151002	0.00755011	−	0.999971i	$-0.497597\pi$
$157$	0.189205	0.0151002	0.00755011	+	0.999971i	$0.497597\pi$
$158$	4.00070	0.318278
$159$	−26.6289	−2.11181
$160$	4.17804	0.330303
$161$	7.97815	0.628766
$162$	11.0884	0.871190
$163$	18.1881	1.42460	0.712302	−	0.701873i	$-0.247653\pi$
$163$	18.1881	1.42460	0.712302	+	0.701873i	$0.247653\pi$
$164$	4.84881	0.378628
$165$	14.1222	1.09941
$166$	−20.3239	−1.57744
$167$	21.9307	1.69705	0.848524	−	0.529156i	$-0.177492\pi$
$167$	21.9307	1.69705	0.848524	+	0.529156i	$0.177492\pi$
$168$	10.3083	0.795302
$169$	−12.9908	−0.999294
$170$	−1.85012	−0.141898
$171$	−9.81571	−0.750626
$172$	9.27584	0.707276
$173$	−2.36289	−0.179647	−0.0898234	−	0.995958i	$-0.528630\pi$
$173$	−2.36289	−0.179647	−0.0898234	+	0.995958i	$0.528630\pi$
$174$	3.49190	0.264720
$175$	9.36616	0.708015
$176$	32.1324	2.42207
$177$	−16.6532	−1.25173
$178$	8.63956	0.647562
$179$	−11.4130	−0.853047	−0.426523	−	0.904477i	$-0.640262\pi$
$179$	−11.4130	−0.853047	−0.426523	+	0.904477i	$0.640262\pi$
$180$	2.93424	0.218706
$181$	18.4440	1.37094	0.685468	−	0.728103i	$-0.259598\pi$
$181$	18.4440	1.37094	0.685468	+	0.728103i	$0.259598\pi$
$182$	−0.359401	−0.0266406
$183$	34.8278	2.57455
$184$	−6.63804	−0.489363
$185$	7.11049	0.522773
$186$	−6.19343	−0.454124
$187$	−8.17608	−0.597894
$188$	4.13489	0.301568
$189$	3.88487	0.282583
$190$	3.87520	0.281136
$191$	13.4802	0.975391	0.487696	−	0.873014i	$-0.337838\pi$
$191$	13.4802	0.975391	0.487696	+	0.873014i	$0.337838\pi$
$192$	−4.03279	−0.291041
$193$	−4.25828	−0.306518	−0.153259	−	0.988186i	$-0.548977\pi$
$193$	−4.25828	−0.306518	−0.153259	+	0.988186i	$0.548977\pi$
$194$	2.78102	0.199666
$195$	0.210358	0.0150641
$196$	−2.07034	−0.147881
$197$	5.81284	0.414148	0.207074	−	0.978325i	$-0.433606\pi$
$197$	5.81284	0.414148	0.207074	+	0.978325i	$0.433606\pi$
$198$	40.6342	2.88775
$199$	7.09998	0.503304	0.251652	−	0.967818i	$-0.419026\pi$
$199$	7.09998	0.503304	0.251652	+	0.967818i	$0.419026\pi$
$200$	−7.79290	−0.551041
$201$	14.8779	1.04940
$202$	6.86631	0.483112
$203$	−1.72471	−0.121051
$204$	−3.08129	−0.215733
$205$	4.39258	0.306791
$206$	19.8220	1.38106
$207$	−13.4361	−0.933873
$208$	0.478633	0.0331872
$209$	17.1253	1.18458
$210$	−8.23744	−0.568437
$211$	5.45186	0.375322	0.187661	−	0.982234i	$-0.439909\pi$
$211$	5.45186	0.375322	0.187661	+	0.982234i	$0.439909\pi$
$212$	9.65307	0.662975
$213$	−33.5918	−2.30167
$214$	−25.3297	−1.73150
$215$	8.40308	0.573085
$216$	−3.23232	−0.219931
$217$	3.05904	0.207661
$218$	−27.9117	−1.89042
$219$	6.85441	0.463178
$220$	−5.11932	−0.345145
$221$	−0.121788	−0.00819234
$222$	37.1092	2.49061
$223$	−20.8596	−1.39687	−0.698433	−	0.715676i	$-0.746119\pi$
$223$	−20.8596	−1.39687	−0.698433	+	0.715676i	$0.746119\pi$
$224$	−10.7698	−0.719588
$225$	−15.7737	−1.05158
$226$	5.06979	0.337238
$227$	−14.7960	−0.982047	−0.491024	−	0.871146i	$-0.663377\pi$
$227$	−14.7960	−0.982047	−0.491024	+	0.871146i	$0.663377\pi$
$228$	6.45394	0.427423
$229$	−20.6611	−1.36532	−0.682662	−	0.730735i	$-0.739178\pi$
$229$	−20.6611	−1.36532	−0.682662	+	0.730735i	$0.739178\pi$
$230$	5.30451	0.349769
$231$	−36.4030	−2.39514
$232$	1.43500	0.0942125
$233$	−10.6706	−0.699054	−0.349527	−	0.936926i	$-0.613658\pi$
$233$	−10.6706	−0.699054	−0.349527	+	0.936926i	$0.613658\pi$
$234$	0.605272	0.0395678
$235$	3.74583	0.244351
$236$	6.03684	0.392965
$237$	6.03604	0.392083
$238$	4.76910	0.309135
$239$	−16.5572	−1.07099	−0.535497	−	0.844537i	$-0.679876\pi$
$239$	−16.5572	−1.07099	−0.535497	+	0.844537i	$0.679876\pi$
$240$	10.9702	0.708125
$241$	21.0814	1.35797	0.678987	−	0.734150i	$-0.262419\pi$
$241$	21.0814	1.35797	0.678987	+	0.734150i	$0.262419\pi$
$242$	−52.0412	−3.34533
$243$	22.0540	1.41477
$244$	−12.6252	−0.808244
$245$	−1.87554	−0.119824
$246$	22.9246	1.46162
$247$	0.255092	0.0162311
$248$	−2.54520	−0.161620
$249$	−30.6636	−1.94323
$250$	13.5042	0.854078
$251$	−5.63111	−0.355432	−0.177716	−	0.984082i	$-0.556871\pi$
$251$	−5.63111	−0.355432	−0.177716	+	0.984082i	$0.556871\pi$
$252$	−7.56366	−0.476465
$253$	23.4417	1.47377
$254$	12.6577	0.794216
$255$	−2.79137	−0.174802
$256$	18.3270	1.14544
$257$	16.6259	1.03710	0.518548	−	0.855049i	$-0.326473\pi$
$257$	16.6259	1.03710	0.518548	+	0.855049i	$0.326473\pi$
$258$	43.8551	2.73030
$259$	−18.3288	−1.13890
$260$	−0.0762556	−0.00472917
$261$	2.90460	0.179790
$262$	−23.0370	−1.42323
$263$	7.35165	0.453322	0.226661	−	0.973974i	$-0.427219\pi$
$263$	7.35165	0.453322	0.226661	+	0.973974i	$0.427219\pi$
$264$	30.2883	1.86411
$265$	8.74481	0.537189
$266$	−9.98917	−0.612475
$267$	13.0349	0.797723
$268$	−5.39327	−0.329447
$269$	20.8191	1.26936	0.634681	−	0.772774i	$-0.281132\pi$
$269$	20.8191	1.26936	0.634681	+	0.772774i	$0.281132\pi$
$270$	2.58297	0.157194
$271$	−21.6334	−1.31414	−0.657068	−	0.753831i	$-0.728204\pi$
$271$	−21.6334	−1.31414	−0.657068	+	0.753831i	$0.728204\pi$
$272$	−6.35125	−0.385101
$273$	−0.542245	−0.0328182
$274$	−0.131751	−0.00795936
$275$	27.5200	1.65952
$276$	8.83439	0.531768
$277$	−18.6754	−1.12210	−0.561049	−	0.827783i	$-0.689602\pi$
$277$	−18.6754	−1.12210	−0.561049	+	0.827783i	$0.689602\pi$
$278$	−2.69760	−0.161791
$279$	−5.15176	−0.308428
$280$	−3.38519	−0.202304
$281$	−6.47633	−0.386345	−0.193173	−	0.981165i	$-0.561878\pi$
$281$	−6.47633	−0.386345	−0.193173	+	0.981165i	$0.561878\pi$
$282$	19.5493	1.16414
$283$	18.6292	1.10739	0.553697	−	0.832718i	$-0.313217\pi$
$283$	18.6292	1.10739	0.553697	+	0.832718i	$0.313217\pi$
$284$	12.1771	0.722578
$285$	5.84669	0.346328
$286$	−1.05601	−0.0624430
$287$	−11.3228	−0.668367
$288$	18.1376	1.06877
$289$	−15.3839	−0.904937
$290$	−1.14672	−0.0673378
$291$	4.19586	0.245965
$292$	−2.48474	−0.145409
$293$	−0.753240	−0.0440048	−0.0220024	−	0.999758i	$-0.507004\pi$
$293$	−0.753240	−0.0440048	−0.0220024	+	0.999758i	$0.507004\pi$
$294$	−9.78832	−0.570867
$295$	5.46883	0.318408
$296$	15.2501	0.886394
$297$	11.4147	0.662347
$298$	9.24884	0.535771
$299$	0.349179	0.0201936
$300$	10.3714	0.598791
$301$	−21.6608	−1.24851
$302$	15.5749	0.896236
$303$	10.3595	0.595139
$304$	13.3031	0.762985
$305$	−11.4373	−0.654896
$306$	−8.03170	−0.459141
$307$	−2.55511	−0.145828	−0.0729139	−	0.997338i	$-0.523230\pi$
$307$	−2.55511	−0.145828	−0.0729139	+	0.997338i	$0.523230\pi$
$308$	13.1962	0.751922
$309$	29.9063	1.70131
$310$	2.03389	0.115517
$311$	22.2862	1.26373	0.631867	−	0.775077i	$-0.282289\pi$
$311$	22.2862	1.26373	0.631867	+	0.775077i	$0.282289\pi$
$312$	0.451163	0.0255421
$313$	22.5717	1.27583	0.637914	−	0.770107i	$-0.279797\pi$
$313$	22.5717	1.27583	0.637914	+	0.770107i	$0.279797\pi$
$314$	−0.324274	−0.0182998
$315$	−6.85199	−0.386066
$316$	−2.18808	−0.123089
$317$	−13.9454	−0.783250	−0.391625	−	0.920125i	$-0.628087\pi$
$317$	−13.9454	−0.783250	−0.391625	+	0.920125i	$0.628087\pi$
$318$	45.6386	2.55929
$319$	−5.06760	−0.283731
$320$	1.32435	0.0740333
$321$	−38.2161	−2.13302
$322$	−13.6735	−0.761996
$323$	−3.38497	−0.188345
$324$	−6.06455	−0.336919
$325$	0.409928	0.0227387
$326$	−31.1721	−1.72646
$327$	−42.1117	−2.32878
$328$	9.42092	0.520183
$329$	−9.65571	−0.532337
$330$	−24.2036	−1.33236
$331$	24.5755	1.35079	0.675395	−	0.737456i	$-0.263973\pi$
$331$	24.5755	1.35079	0.675395	+	0.737456i	$0.263973\pi$
$332$	11.1157	0.610051
$333$	30.8678	1.69155
$334$	−37.5864	−2.05664
$335$	−4.88582	−0.266941
$336$	−28.2782	−1.54270
$337$	−11.2851	−0.614739	−0.307370	−	0.951590i	$-0.599449\pi$
$337$	−11.2851	−0.614739	−0.307370	+	0.951590i	$0.599449\pi$
$338$	22.2646	1.21104
$339$	7.64903	0.415439
$340$	1.01188	0.0548768
$341$	8.98819	0.486738
$342$	16.8229	0.909677
$343$	20.1570	1.08837
$344$	18.0224	0.971701
$345$	8.00316	0.430876
$346$	4.04969	0.217712
$347$	3.75547	0.201604	0.100802	−	0.994906i	$-0.467859\pi$
$347$	3.75547	0.201604	0.100802	+	0.994906i	$0.467859\pi$
$348$	−1.90981	−0.102376
$349$	−16.2620	−0.870487	−0.435244	−	0.900313i	$-0.643338\pi$
$349$	−16.2620	−0.870487	−0.435244	+	0.900313i	$0.643338\pi$
$350$	−16.0524	−0.858037
$351$	0.170029	0.00907547
$352$	−31.6443	−1.68665
$353$	22.0221	1.17212	0.586060	−	0.810267i	$-0.300678\pi$
$353$	22.0221	1.17212	0.586060	+	0.810267i	$0.300678\pi$
$354$	28.5415	1.51696
$355$	11.0314	0.585484
$356$	−4.72519	−0.250435
$357$	7.19536	0.380819
$358$	19.5604	1.03380
$359$	−15.9008	−0.839210	−0.419605	−	0.907707i	$-0.637831\pi$
$359$	−15.9008	−0.839210	−0.419605	+	0.907707i	$0.637831\pi$
$360$	5.70104	0.300471
$361$	−11.9100	−0.626841
$362$	−31.6107	−1.66142
$363$	−78.5169	−4.12107
$364$	0.196565	0.0103028
$365$	−2.25095	−0.117820
$366$	−59.6904	−3.12007
$367$	30.4701	1.59053	0.795263	−	0.606265i	$-0.207333\pi$
$367$	30.4701	1.59053	0.795263	+	0.606265i	$0.207333\pi$
$368$	18.2097	0.949249
$369$	19.0689	0.992690
$370$	−12.1865	−0.633545
$371$	−22.5417	−1.17031
$372$	3.38734	0.175625
$373$	−12.9695	−0.671533	−0.335766	−	0.941945i	$-0.608995\pi$
$373$	−12.9695	−0.671533	−0.335766	+	0.941945i	$0.608995\pi$
$374$	14.0128	0.724583
$375$	20.3744	1.05213
$376$	8.03382	0.414312
$377$	−0.0754851	−0.00388768
$378$	−6.65817	−0.342459
$379$	−28.5460	−1.46631	−0.733154	−	0.680063i	$-0.761952\pi$
$379$	−28.5460	−1.46631	−0.733154	+	0.680063i	$0.761952\pi$
$380$	−2.11944	−0.108725
$381$	19.0973	0.978385
$382$	−23.1033	−1.18207
$383$	−19.1823	−0.980168	−0.490084	−	0.871675i	$-0.663034\pi$
$383$	−19.1823	−0.980168	−0.490084	+	0.871675i	$0.663034\pi$
$384$	32.3569	1.65121
$385$	11.9546	0.609260
$386$	7.29815	0.371466
$387$	36.4792	1.85434
$388$	−1.52101	−0.0772176
$389$	−5.55998	−0.281902	−0.140951	−	0.990017i	$-0.545016\pi$
$389$	−5.55998	−0.281902	−0.140951	+	0.990017i	$0.545016\pi$
$390$	−0.360528	−0.0182560
$391$	−4.63346	−0.234324
$392$	−4.02253	−0.203169
$393$	−34.7570	−1.75326
$394$	−9.96247	−0.501902
$395$	−1.98220	−0.0997355
$396$	−22.2238	−1.11679
$397$	31.9785	1.60495	0.802477	−	0.596683i	$-0.203515\pi$
$397$	31.9785	1.60495	0.802477	+	0.596683i	$0.203515\pi$
$398$	−12.1685	−0.609950
$399$	−15.0711	−0.754500
$400$	21.3778	1.06889
$401$	29.2966	1.46300	0.731502	−	0.681839i	$-0.238820\pi$
$401$	29.2966	1.46300	0.731502	+	0.681839i	$0.238820\pi$
$402$	−25.4988	−1.27176
$403$	0.133885	0.00666927
$404$	−3.75536	−0.186836
$405$	−5.49393	−0.272996
$406$	2.95593	0.146700
$407$	−53.8546	−2.66947
$408$	−5.98674	−0.296388
$409$	7.90809	0.391030	0.195515	−	0.980701i	$-0.437362\pi$
$409$	7.90809	0.391030	0.195515	+	0.980701i	$0.437362\pi$
$410$	−7.52833	−0.371798
$411$	−0.198779	−0.00980503
$412$	−10.8411	−0.534104
$413$	−14.0971	−0.693674
$414$	23.0278	1.13175
$415$	10.0698	0.494306
$416$	−0.471362	−0.0231104
$417$	−4.06999	−0.199308
$418$	−29.3506	−1.43559
$419$	−37.8794	−1.85053	−0.925266	−	0.379319i	$-0.876158\pi$
$419$	−37.8794	−1.85053	−0.925266	+	0.379319i	$0.876158\pi$
$420$	4.50526	0.219834
$421$	28.7797	1.40264	0.701320	−	0.712847i	$-0.252595\pi$
$421$	28.7797	1.40264	0.701320	+	0.712847i	$0.252595\pi$
$422$	−9.34380	−0.454849
$423$	16.2613	0.790651
$424$	18.7553	0.910837
$425$	−5.43957	−0.263858
$426$	57.5720	2.78937
$427$	29.4821	1.42674
$428$	13.8534	0.669632
$429$	−1.59325	−0.0769227
$430$	−14.4018	−0.694517
$431$	−16.9029	−0.814186	−0.407093	−	0.913387i	$-0.633458\pi$
$431$	−16.9029	−0.814186	−0.407093	+	0.913387i	$0.633458\pi$
$432$	8.86703	0.426615
$433$	10.5869	0.508775	0.254388	−	0.967102i	$-0.418126\pi$
$433$	10.5869	0.508775	0.254388	+	0.967102i	$0.418126\pi$
$434$	−5.24280	−0.251662
$435$	−1.73011	−0.0829525
$436$	15.2656	0.731090
$437$	9.70507	0.464256
$438$	−11.7476	−0.561322
$439$	25.0433	1.19525	0.597625	−	0.801776i	$-0.296111\pi$
$439$	25.0433	1.19525	0.597625	+	0.801776i	$0.296111\pi$
$440$	−9.94651	−0.474181
$441$	−8.14203	−0.387716
$442$	0.208729	0.00992822
$443$	−22.4341	−1.06588	−0.532938	−	0.846154i	$-0.678912\pi$
$443$	−22.4341	−1.06588	−0.532938	+	0.846154i	$0.678912\pi$
$444$	−20.2959	−0.963203
$445$	−4.28060	−0.202920
$446$	35.7508	1.69285
$447$	13.9542	0.660009
$448$	−3.41380	−0.161287
$449$	−28.3647	−1.33862	−0.669308	−	0.742985i	$-0.733409\pi$
$449$	−28.3647	−1.33862	−0.669308	+	0.742985i	$0.733409\pi$
$450$	27.0340	1.27440
$451$	−33.2693	−1.56659
$452$	−2.77280	−0.130421
$453$	23.4986	1.10406
$454$	25.3585	1.19013
$455$	0.178071	0.00834808
$456$	12.5396	0.587220
$457$	−19.2691	−0.901369	−0.450685	−	0.892683i	$-0.648820\pi$
$457$	−19.2691	−0.901369	−0.450685	+	0.892683i	$0.648820\pi$
$458$	35.4105	1.65462
$459$	−2.25621	−0.105311
$460$	−2.90117	−0.135268
$461$	22.0030	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$461$	22.0030	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$462$	62.3901	2.90265
$463$	1.99925	0.0929131	0.0464566	−	0.998920i	$-0.485207\pi$
$463$	1.99925	0.0929131	0.0464566	+	0.998920i	$0.485207\pi$
$464$	−3.93656	−0.182750
$465$	3.06863	0.142304
$466$	18.2880	0.847177
$467$	11.4294	0.528888	0.264444	−	0.964401i	$-0.414812\pi$
$467$	11.4294	0.528888	0.264444	+	0.964401i	$0.414812\pi$
$468$	−0.331038	−0.0153022
$469$	12.5943	0.581550
$470$	−6.41988	−0.296127
$471$	−0.489247	−0.0225433
$472$	11.7292	0.539880
$473$	−63.6446	−2.92638
$474$	−10.3450	−0.475162
$475$	11.3935	0.522771
$476$	−2.60834	−0.119553
$477$	37.9627	1.73819
$478$	28.3769	1.29793
$479$	−8.56470	−0.391331	−0.195666	−	0.980671i	$-0.562687\pi$
$479$	−8.56470	−0.391331	−0.195666	+	0.980671i	$0.562687\pi$
$480$	−10.8036	−0.493113
$481$	−0.802198	−0.0365771
$482$	−36.1309	−1.64572
$483$	−20.6299	−0.938693
$484$	28.4626	1.29376
$485$	−1.37790	−0.0625671
$486$	−37.7978	−1.71454
$487$	−31.1719	−1.41253	−0.706266	−	0.707946i	$-0.749622\pi$
$487$	−31.1719	−1.41253	−0.706266	+	0.707946i	$0.749622\pi$
$488$	−24.5299	−1.11042
$489$	−47.0308	−2.12681
$490$	3.21444	0.145213
$491$	−16.2882	−0.735075	−0.367537	−	0.930009i	$-0.619799\pi$
$491$	−16.2882	−0.735075	−0.367537	+	0.930009i	$0.619799\pi$
$492$	−12.5380	−0.565259
$493$	1.00166	0.0451123
$494$	−0.437196	−0.0196704
$495$	−20.1328	−0.904902
$496$	6.98211	0.313506
$497$	−28.4358	−1.27552
$498$	52.5536	2.35498
$499$	−14.3102	−0.640611	−0.320306	−	0.947314i	$-0.603786\pi$
$499$	−14.3102	−0.640611	−0.320306	+	0.947314i	$0.603786\pi$
$500$	−7.38576	−0.330301
$501$	−56.7084	−2.53355
$502$	9.65100	0.430745
$503$	−13.9904	−0.623800	−0.311900	−	0.950115i	$-0.600965\pi$
$503$	−13.9904	−0.623800	−0.311900	+	0.950115i	$0.600965\pi$
$504$	−14.6957	−0.654598
$505$	−3.40201	−0.151388
$506$	−40.1761	−1.78605
$507$	33.5917	1.49186
$508$	−6.92283	−0.307151
$509$	−21.6399	−0.959171	−0.479585	−	0.877495i	$-0.659213\pi$
$509$	−21.6399	−0.959171	−0.479585	+	0.877495i	$0.659213\pi$
$510$	4.78405	0.211841
$511$	5.80233	0.256680
$512$	−6.38359	−0.282117
$513$	4.72577	0.208648
$514$	−28.4947	−1.25685
$515$	−9.82108	−0.432769
$516$	−23.9855	−1.05590
$517$	−28.3708	−1.24775
$518$	31.4133	1.38022
$519$	6.10995	0.268197
$520$	−0.148160	−0.00649723
$521$	32.4140	1.42008	0.710042	−	0.704159i	$-0.248676\pi$
$521$	32.4140	1.42008	0.710042	+	0.704159i	$0.248676\pi$
$522$	−4.97811	−0.217886
$523$	23.5184	1.02839	0.514193	−	0.857674i	$-0.328091\pi$
$523$	23.5184	1.02839	0.514193	+	0.857674i	$0.328091\pi$
$524$	12.5995	0.550412
$525$	−24.2190	−1.05700
$526$	−12.5998	−0.549377
$527$	−1.77659	−0.0773896
$528$	−83.0881	−3.61594
$529$	−9.71536	−0.422407
$530$	−14.9875	−0.651015
$531$	23.7411	1.03028
$532$	5.46333	0.236865
$533$	−0.495567	−0.0214654
$534$	−22.3402	−0.966754
$535$	12.5500	0.542583
$536$	−10.4788	−0.452614
$537$	29.5117	1.27352
$538$	−35.6813	−1.53833
$539$	14.2053	0.611864
$540$	−1.41269	−0.0607925
$541$	36.5602	1.57185	0.785923	−	0.618325i	$-0.212188\pi$
$541$	36.5602	1.57185	0.785923	+	0.618325i	$0.212188\pi$
$542$	37.0769	1.59259
$543$	−47.6926	−2.04669
$544$	6.25477	0.268171
$545$	13.8293	0.592381
$546$	0.929339	0.0397721
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	0.0720578	0.00307816
$549$	−49.6511	−2.11906
$550$	−47.1658	−2.01116
$551$	−2.09803	−0.0893790
$552$	17.1646	0.730576
$553$	5.10957	0.217281
$554$	32.0073	1.35986
$555$	−18.3863	−0.780455
$556$	1.47538	0.0625702
$557$	20.9887	0.889318	0.444659	−	0.895700i	$-0.353325\pi$
$557$	20.9887	0.889318	0.444659	+	0.895700i	$0.353325\pi$
$558$	8.82946	0.373781
$559$	−0.948027	−0.0400973
$560$	9.28641	0.392422
$561$	21.1417	0.892604
$562$	11.0996	0.468208
$563$	8.09790	0.341286	0.170643	−	0.985333i	$-0.445416\pi$
$563$	8.09790	0.341286	0.170643	+	0.985333i	$0.445416\pi$
$564$	−10.6920	−0.450214
$565$	−2.51190	−0.105677
$566$	−31.9282	−1.34204
$567$	14.1618	0.594740
$568$	23.6593	0.992723
$569$	3.16559	0.132709	0.0663543	−	0.997796i	$-0.478863\pi$
$569$	3.16559	0.132709	0.0663543	+	0.997796i	$0.478863\pi$
$570$	−10.0205	−0.419712
$571$	33.7766	1.41351	0.706753	−	0.707460i	$-0.250159\pi$
$571$	33.7766	1.41351	0.706753	+	0.707460i	$0.250159\pi$
$572$	0.577557	0.0241489
$573$	−34.8570	−1.45617
$574$	19.4059	0.809988
$575$	15.5959	0.650392
$576$	5.74922	0.239551
$577$	−22.0064	−0.916139	−0.458070	−	0.888916i	$-0.651459\pi$
$577$	−22.0064	−0.916139	−0.458070	+	0.888916i	$0.651459\pi$
$578$	26.3661	1.09668
$579$	11.0111	0.457604
$580$	0.627170	0.0260418
$581$	−25.9571	−1.07688
$582$	−7.19116	−0.298083
$583$	−66.2329	−2.74309
$584$	−4.82770	−0.199772
$585$	−0.299891	−0.0123990
$586$	1.29096	0.0533290
$587$	28.6795	1.18373	0.591866	−	0.806037i	$-0.298392\pi$
$587$	28.6795	1.18373	0.591866	+	0.806037i	$0.298392\pi$
$588$	5.35348	0.220774
$589$	3.72118	0.153329
$590$	−9.37289	−0.385876
$591$	−15.0308	−0.618286
$592$	−41.8347	−1.71940
$593$	15.4150	0.633019	0.316509	−	0.948589i	$-0.397489\pi$
$593$	15.4150	0.633019	0.316509	+	0.948589i	$0.397489\pi$
$594$	−19.5633	−0.802692
$595$	−2.36292	−0.0968703
$596$	−5.05842	−0.207201
$597$	−18.3591	−0.751389
$598$	−0.598449	−0.0244724
$599$	43.6710	1.78435	0.892174	−	0.451691i	$-0.149179\pi$
$599$	43.6710	1.78435	0.892174	+	0.451691i	$0.149179\pi$
$600$	20.1509	0.822656
$601$	43.7280	1.78370	0.891851	−	0.452329i	$-0.149407\pi$
$601$	43.7280	1.78370	0.891851	+	0.452329i	$0.149407\pi$
$602$	37.1238	1.51305
$603$	−21.2102	−0.863745
$604$	−8.51832	−0.346605
$605$	25.7846	1.04829
$606$	−17.7549	−0.721244
$607$	−25.1769	−1.02190	−0.510949	−	0.859611i	$-0.670706\pi$
$607$	−25.1769	−1.02190	−0.510949	+	0.859611i	$0.670706\pi$
$608$	−13.1010	−0.531316
$609$	4.45974	0.180718
$610$	19.6020	0.793663
$611$	−0.422601	−0.0170966
$612$	4.39274	0.177566
$613$	9.09386	0.367298	0.183649	−	0.982992i	$-0.441209\pi$
$613$	9.09386	0.367298	0.183649	+	0.982992i	$0.441209\pi$
$614$	4.37913	0.176727
$615$	−11.3583	−0.458013
$616$	25.6393	1.03304
$617$	29.2054	1.17576	0.587882	−	0.808947i	$-0.299962\pi$
$617$	29.2054	1.17576	0.587882	+	0.808947i	$0.299962\pi$
$618$	−51.2556	−2.06180
$619$	38.5936	1.55121	0.775605	−	0.631219i	$-0.217445\pi$
$619$	38.5936	1.55121	0.775605	+	0.631219i	$0.217445\pi$
$620$	−1.11239	−0.0446745
$621$	6.46880	0.259584
$622$	−38.1957	−1.53151
$623$	11.0342	0.442075
$624$	−1.23765	−0.0495456
$625$	14.7038	0.588151
$626$	−38.6850	−1.54617
$627$	−44.2826	−1.76848
$628$	0.177353	0.00707717
$629$	10.6448	0.424437
$630$	11.7434	0.467870
$631$	−15.2890	−0.608646	−0.304323	−	0.952569i	$-0.598430\pi$
$631$	−15.2890	−0.608646	−0.304323	+	0.952569i	$0.598430\pi$
$632$	−4.25130	−0.169108
$633$	−14.0974	−0.560323
$634$	23.9006	0.949213
$635$	−6.27146	−0.248875
$636$	−24.9609	−0.989764
$637$	0.211596	0.00838376
$638$	8.68522	0.343851
$639$	47.8890	1.89446
$640$	−10.6258	−0.420023
$641$	−19.4443	−0.768004	−0.384002	−	0.923332i	$-0.625454\pi$
$641$	−19.4443	−0.768004	−0.384002	+	0.923332i	$0.625454\pi$
$642$	65.4976	2.58498
$643$	−10.4510	−0.412147	−0.206073	−	0.978537i	$-0.566069\pi$
$643$	−10.4510	−0.412147	−0.206073	+	0.978537i	$0.566069\pi$
$644$	7.47840	0.294690
$645$	−21.7287	−0.855566
$646$	5.80140	0.228253
$647$	12.6436	0.497071	0.248535	−	0.968623i	$-0.420051\pi$
$647$	12.6436	0.497071	0.248535	+	0.968623i	$0.420051\pi$
$648$	−11.7830	−0.462881
$649$	−41.4208	−1.62591
$650$	−0.702565	−0.0275569
$651$	−7.91006	−0.310020
$652$	17.0488	0.667683
$653$	−0.596253	−0.0233332	−0.0116666	−	0.999932i	$-0.503714\pi$
$653$	−0.596253	−0.0233332	−0.0116666	+	0.999932i	$0.503714\pi$
$654$	72.1741	2.82223
$655$	11.4140	0.445982
$656$	−25.8439	−1.00903
$657$	−9.77177	−0.381233
$658$	16.5487	0.645134
$659$	48.8102	1.90138	0.950688	−	0.310149i	$-0.100379\pi$
$659$	48.8102	1.90138	0.950688	+	0.310149i	$0.100379\pi$
$660$	13.2375	0.515271
$661$	12.4393	0.483833	0.241917	−	0.970297i	$-0.422224\pi$
$661$	12.4393	0.483833	0.241917	+	0.970297i	$0.422224\pi$
$662$	−42.1193	−1.63701
$663$	0.314919	0.0122304
$664$	21.5970	0.838126
$665$	4.94928	0.191925
$666$	−52.9035	−2.04997
$667$	−2.87186	−0.111199
$668$	20.5570	0.795373
$669$	53.9389	2.08540
$670$	8.37368	0.323503
$671$	86.6255	3.34414
$672$	27.8486	1.07428
$673$	25.9944	1.00201	0.501006	−	0.865444i	$-0.332964\pi$
$673$	25.9944	1.00201	0.501006	+	0.865444i	$0.332964\pi$
$674$	19.3412	0.744997
$675$	7.59422	0.292302
$676$	−12.1771	−0.468349
$677$	37.6269	1.44612	0.723059	−	0.690786i	$-0.242736\pi$
$677$	37.6269	1.44612	0.723059	+	0.690786i	$0.242736\pi$
$678$	−13.1095	−0.503466
$679$	3.55183	0.136307
$680$	1.96601	0.0753932
$681$	38.2596	1.46611
$682$	−15.4046	−0.589873
$683$	−5.33897	−0.204290	−0.102145	−	0.994770i	$-0.532571\pi$
$683$	−5.33897	−0.204290	−0.102145	+	0.994770i	$0.532571\pi$
$684$	−9.20086	−0.351804
$685$	0.0652779	0.00249414
$686$	−34.5465	−1.31899
$687$	53.4255	2.03831
$688$	−49.4397	−1.88487
$689$	−0.986580	−0.0375857
$690$	−13.7164	−0.522174
$691$	49.6289	1.88797	0.943987	−	0.329984i	$-0.107043\pi$
$691$	49.6289	1.88797	0.943987	+	0.329984i	$0.107043\pi$
$692$	−2.21487	−0.0841969
$693$	51.8967	1.97139
$694$	−6.43640	−0.244322
$695$	1.33656	0.0506988
$696$	−3.71063	−0.140651
$697$	6.57596	0.249082
$698$	27.8711	1.05494
$699$	27.5920	1.04363
$700$	8.77946	0.331832
$701$	−33.7924	−1.27632	−0.638161	−	0.769903i	$-0.720305\pi$
$701$	−33.7924	−1.27632	−0.638161	+	0.769903i	$0.720305\pi$
$702$	−0.291408	−0.0109985
$703$	−22.2962	−0.840919
$704$	−10.0306	−0.378041
$705$	−9.68598	−0.364795
$706$	−37.7432	−1.42048
$707$	8.76944	0.329809
$708$	−15.6101	−0.586662
$709$	−1.74532	−0.0655467	−0.0327734	−	0.999463i	$-0.510434\pi$
$709$	−1.74532	−0.0655467	−0.0327734	+	0.999463i	$0.510434\pi$
$710$	−18.9064	−0.709543
$711$	−8.60508	−0.322716
$712$	−9.18074	−0.344063
$713$	5.09369	0.190760
$714$	−12.3319	−0.461511
$715$	0.523215	0.0195671
$716$	−10.6981	−0.399806
$717$	42.8135	1.59890
$718$	27.2519	1.01703
$719$	33.5912	1.25274	0.626371	−	0.779525i	$-0.284540\pi$
$719$	33.5912	1.25274	0.626371	+	0.779525i	$0.284540\pi$
$720$	−15.6393	−0.582844
$721$	25.3160	0.942817
$722$	20.4122	0.759663
$723$	−54.5123	−2.02734
$724$	17.2887	0.642530
$725$	−3.37149	−0.125214
$726$	134.568	4.99429
$727$	−6.64670	−0.246513	−0.123256	−	0.992375i	$-0.539334\pi$
$727$	−6.64670	−0.246513	−0.123256	+	0.992375i	$0.539334\pi$
$728$	0.381914	0.0141547
$729$	−37.6179	−1.39326
$730$	3.85785	0.142785
$731$	12.5799	0.465285
$732$	32.6462	1.20664
$733$	−27.4747	−1.01480	−0.507401	−	0.861710i	$-0.669394\pi$
$733$	−27.4747	−1.01480	−0.507401	+	0.861710i	$0.669394\pi$
$734$	−52.2219	−1.92754
$735$	4.84977	0.178886
$736$	−17.9331	−0.661024
$737$	37.0050	1.36310
$738$	−32.6817	−1.20303
$739$	−5.28363	−0.194362	−0.0971808	−	0.995267i	$-0.530983\pi$
$739$	−5.28363	−0.194362	−0.0971808	+	0.995267i	$0.530983\pi$
$740$	6.66509	0.245013
$741$	−0.659618	−0.0242317
$742$	38.6336	1.41828
$743$	−39.0181	−1.43144	−0.715718	−	0.698389i	$-0.753900\pi$
$743$	−39.0181	−1.43144	−0.715718	+	0.698389i	$0.753900\pi$
$744$	6.58138	0.241285
$745$	−4.58248	−0.167889
$746$	22.2280	0.813825
$747$	43.7146	1.59944
$748$	−7.66393	−0.280221
$749$	−32.3503	−1.18206
$750$	−34.9191	−1.27506
$751$	12.3552	0.450846	0.225423	−	0.974261i	$-0.427624\pi$
$751$	12.3552	0.450846	0.225423	+	0.974261i	$0.427624\pi$
$752$	−22.0387	−0.803669
$753$	14.5609	0.530629
$754$	0.129372	0.00471145
$755$	−7.71683	−0.280844
$756$	3.64152	0.132441
$757$	29.4588	1.07070	0.535350	−	0.844630i	$-0.320180\pi$
$757$	29.4588	1.07070	0.535350	+	0.844630i	$0.320180\pi$
$758$	48.9241	1.77701
$759$	−60.6156	−2.20021
$760$	−4.11794	−0.149373
$761$	53.9988	1.95745	0.978727	−	0.205167i	$-0.0657737\pi$
$761$	53.9988	1.95745	0.978727	+	0.205167i	$0.0657737\pi$
$762$	−32.7304	−1.18570
$763$	−35.6480	−1.29054
$764$	12.6358	0.457146
$765$	3.97942	0.143876
$766$	32.8760	1.18786
$767$	−0.616988	−0.0222782
$768$	−47.3900	−1.71004
$769$	−16.8676	−0.608263	−0.304131	−	0.952630i	$-0.598366\pi$
$769$	−16.8676	−0.608263	−0.304131	+	0.952630i	$0.598366\pi$
$770$	−20.4886	−0.738357
$771$	−42.9913	−1.54829
$772$	−3.99154	−0.143659
$773$	−12.3953	−0.445827	−0.222914	−	0.974838i	$-0.571557\pi$
$773$	−12.3953	−0.445827	−0.222914	+	0.974838i	$0.571557\pi$
$774$	−62.5207	−2.24726
$775$	5.97987	0.214803
$776$	−2.95522	−0.106086
$777$	47.3947	1.70028
$778$	9.52910	0.341635
$779$	−13.7738	−0.493496
$780$	0.197182	0.00706024
$781$	−83.5511	−2.98969
$782$	7.94116	0.283975
$783$	−1.39842	−0.0499754
$784$	11.0348	0.394099
$785$	0.160666	0.00573442
$786$	59.5690	2.12476
$787$	35.5818	1.26835	0.634176	−	0.773189i	$-0.281339\pi$
$787$	35.5818	1.26835	0.634176	+	0.773189i	$0.281339\pi$
$788$	5.44873	0.194103
$789$	−19.0099	−0.676770
$790$	3.39725	0.120869
$791$	6.47499	0.230224
$792$	−43.1795	−1.53432
$793$	1.29034	0.0458214
$794$	−54.8071	−1.94503
$795$	−22.6123	−0.801977
$796$	6.65524	0.235889
$797$	−7.11049	−0.251867	−0.125933	−	0.992039i	$-0.540193\pi$
$797$	−7.11049	−0.251867	−0.125933	+	0.992039i	$0.540193\pi$
$798$	25.8300	0.914372
$799$	5.60774	0.198387
$800$	−21.0531	−0.744338
$801$	−18.5828	−0.656591
$802$	−50.2107	−1.77300
$803$	17.0486	0.601634
$804$	13.9459	0.491835
$805$	6.77475	0.238779
$806$	−0.229461	−0.00808243
$807$	−53.8340	−1.89505
$808$	−7.29641	−0.256687
$809$	−15.0555	−0.529323	−0.264661	−	0.964341i	$-0.585260\pi$
$809$	−15.0555	−0.529323	−0.264661	+	0.964341i	$0.585260\pi$
$810$	9.41590	0.330841
$811$	−39.9775	−1.40380	−0.701900	−	0.712276i	$-0.747665\pi$
$811$	−39.9775	−1.40380	−0.701900	+	0.712276i	$0.747665\pi$
$812$	−1.61667	−0.0567340
$813$	55.9397	1.96189
$814$	92.2999	3.23511
$815$	15.4447	0.541004
$816$	16.4231	0.574923
$817$	−26.3494	−0.921849
$818$	−13.5535	−0.473886
$819$	0.773035	0.0270120
$820$	4.11743	0.143787
$821$	46.0570	1.60740	0.803700	−	0.595035i	$-0.202862\pi$
$821$	46.0570	1.60740	0.803700	+	0.595035i	$0.202862\pi$
$822$	0.340681	0.0118826
$823$	42.5003	1.48147	0.740734	−	0.671799i	$-0.234478\pi$
$823$	42.5003	1.48147	0.740734	+	0.671799i	$0.234478\pi$
$824$	−21.0636	−0.733785
$825$	−71.1613	−2.47752
$826$	24.1607	0.840657
$827$	−37.7368	−1.31224	−0.656118	−	0.754659i	$-0.727803\pi$
$827$	−37.7368	−1.31224	−0.656118	+	0.754659i	$0.727803\pi$
$828$	−12.5945	−0.437688
$829$	−6.85008	−0.237913	−0.118957	−	0.992899i	$-0.537955\pi$
$829$	−6.85008	−0.237913	−0.118957	+	0.992899i	$0.537955\pi$
$830$	−17.2583	−0.599045
$831$	48.2909	1.67519
$832$	−0.149412	−0.00517991
$833$	−2.80779	−0.0972843
$834$	6.97545	0.241540
$835$	18.6228	0.644467
$836$	16.0526	0.555190
$837$	2.48031	0.0857322
$838$	64.9206	2.24264
$839$	−29.6919	−1.02508	−0.512538	−	0.858664i	$-0.671295\pi$
$839$	−29.6919	−1.02508	−0.512538	+	0.858664i	$0.671295\pi$
$840$	8.75343	0.302022
$841$	−28.3792	−0.978592
$842$	−49.3248	−1.69985
$843$	16.7465	0.576780
$844$	5.11036	0.175906
$845$	−11.0313	−0.379489
$846$	−27.8698	−0.958183
$847$	−66.4654	−2.28378
$848$	−51.4503	−1.76681
$849$	−48.1715	−1.65324
$850$	9.32273	0.319767
$851$	−30.5199	−1.04621
$852$	−31.4876	−1.07875
$853$	38.0909	1.30421	0.652104	−	0.758129i	$-0.273886\pi$
$853$	38.0909	1.30421	0.652104	+	0.758129i	$0.273886\pi$
$854$	−50.5285	−1.72905
$855$	−8.33515	−0.285056
$856$	26.9164	0.919982
$857$	10.1650	0.347229	0.173615	−	0.984814i	$-0.444455\pi$
$857$	10.1650	0.347229	0.173615	+	0.984814i	$0.444455\pi$
$858$	2.73062	0.0932220
$859$	−3.34587	−0.114160	−0.0570798	−	0.998370i	$-0.518179\pi$
$859$	−3.34587	−0.114160	−0.0570798	+	0.998370i	$0.518179\pi$
$860$	7.87671	0.268594
$861$	29.2786	0.997813
$862$	28.9695	0.986705
$863$	51.5663	1.75534	0.877669	−	0.479266i	$-0.159097\pi$
$863$	51.5663	1.75534	0.877669	+	0.479266i	$0.159097\pi$
$864$	−8.73233	−0.297080
$865$	−2.00648	−0.0682223
$866$	−18.1446	−0.616580
$867$	39.7798	1.35099
$868$	2.86742	0.0973265
$869$	15.0131	0.509286
$870$	2.96519	0.100529
$871$	0.551213	0.0186772
$872$	29.6601	1.00442
$873$	−5.98169	−0.202449
$874$	−16.6333	−0.562628
$875$	17.2471	0.583058
$876$	6.42505	0.217082
$877$	−26.1243	−0.882155	−0.441078	−	0.897469i	$-0.645404\pi$
$877$	−26.1243	−0.882155	−0.441078	+	0.897469i	$0.645404\pi$
$878$	−42.9210	−1.44851
$879$	1.94773	0.0656952
$880$	27.2857	0.919801
$881$	−9.32247	−0.314082	−0.157041	−	0.987592i	$-0.550195\pi$
$881$	−9.32247	−0.314082	−0.157041	+	0.987592i	$0.550195\pi$
$882$	13.9544	0.469869
$883$	51.6265	1.73737	0.868684	−	0.495366i	$-0.164966\pi$
$883$	51.6265	1.73737	0.868684	+	0.495366i	$0.164966\pi$
$884$	−0.114159	−0.00383959
$885$	−14.1413	−0.475355
$886$	38.4492	1.29173
$887$	−10.1947	−0.342303	−0.171152	−	0.985245i	$-0.554749\pi$
$887$	−10.1947	−0.342303	−0.171152	+	0.985245i	$0.554749\pi$
$888$	−39.4337	−1.32331
$889$	16.1661	0.542192
$890$	7.33640	0.245917
$891$	41.6108	1.39402
$892$	−19.5530	−0.654683
$893$	−11.7458	−0.393057
$894$	−23.9157	−0.799859
$895$	−9.69150	−0.323951
$896$	27.3904	0.915050
$897$	−0.902908	−0.0301472
$898$	48.6136	1.62226
$899$	−1.10115	−0.0367253
$900$	−14.7856	−0.492853
$901$	13.0915	0.436141
$902$	57.0193	1.89853
$903$	56.0105	1.86391
$904$	−5.38736	−0.179181
$905$	15.6620	0.520623
$906$	−40.2737	−1.33800
$907$	20.3481	0.675648	0.337824	−	0.941209i	$-0.390309\pi$
$907$	20.3481	0.675648	0.337824	+	0.941209i	$0.390309\pi$
$908$	−13.8692	−0.460266
$909$	−14.7687	−0.489847
$910$	−0.305190	−0.0101170
$911$	−14.1498	−0.468803	−0.234402	−	0.972140i	$-0.575313\pi$
$911$	−14.1498	−0.468803	−0.234402	+	0.972140i	$0.575313\pi$
$912$	−34.3992	−1.13907
$913$	−76.2682	−2.52411
$914$	33.0247	1.09236
$915$	29.5745	0.977703
$916$	−19.3669	−0.639900
$917$	−29.4221	−0.971604
$918$	3.86686	0.127625
$919$	47.5657	1.56905	0.784524	−	0.620098i	$-0.212907\pi$
$919$	47.5657	1.56905	0.784524	+	0.620098i	$0.212907\pi$
$920$	−5.63678	−0.185839
$921$	6.60701	0.217708
$922$	−37.7103	−1.24192
$923$	−1.24455	−0.0409648
$924$	−34.1227	−1.12255
$925$	−35.8296	−1.17807
$926$	−3.42646	−0.112601
$927$	−42.6350	−1.40032
$928$	3.87676	0.127261
$929$	24.3575	0.799143	0.399572	−	0.916702i	$-0.369159\pi$
$929$	24.3575	0.799143	0.399572	+	0.916702i	$0.369159\pi$
$930$	−5.25923	−0.172457
$931$	5.88110	0.192745
$932$	−10.0022	−0.327633
$933$	−57.6277	−1.88665
$934$	−19.5885	−0.640955
$935$	−6.94283	−0.227055
$936$	−0.643186	−0.0210232
$937$	47.5365	1.55295	0.776476	−	0.630147i	$-0.217006\pi$
$937$	47.5365	1.55295	0.776476	+	0.630147i	$0.217006\pi$
$938$	−21.5850	−0.704775
$939$	−58.3659	−1.90470
$940$	3.51120	0.114523
$941$	−8.76389	−0.285695	−0.142847	−	0.989745i	$-0.545626\pi$
$941$	−8.76389	−0.285695	−0.142847	+	0.989745i	$0.545626\pi$
$942$	0.838507	0.0273200
$943$	−18.8540	−0.613971
$944$	−32.1760	−1.04724
$945$	3.29889	0.107313
$946$	109.079	3.54646
$947$	−30.5075	−0.991362	−0.495681	−	0.868505i	$-0.665081\pi$
$947$	−30.5075	−0.991362	−0.495681	+	0.868505i	$0.665081\pi$
$948$	5.65794	0.183761
$949$	0.253950	0.00824358
$950$	−19.5270	−0.633541
$951$	36.0599	1.16932
$952$	−5.06783	−0.164249
$953$	11.2847	0.365547	0.182774	−	0.983155i	$-0.441492\pi$
$953$	11.2847	0.365547	0.182774	+	0.983155i	$0.441492\pi$
$954$	−65.0632	−2.10650
$955$	11.4469	0.370412
$956$	−15.5200	−0.501953
$957$	13.1038	0.423586
$958$	14.6788	0.474251
$959$	−0.168268	−0.00543366
$960$	−3.42450	−0.110525
$961$	−29.0469	−0.936998
$962$	1.37487	0.0443274
$963$	54.4816	1.75564
$964$	19.7609	0.636455
$965$	−3.61598	−0.116402
$966$	35.3570	1.13759
$967$	−25.9538	−0.834618	−0.417309	−	0.908765i	$-0.637027\pi$
$967$	−25.9538	−0.834618	−0.417309	+	0.908765i	$0.637027\pi$
$968$	55.3010	1.77744
$969$	8.75284	0.281182
$970$	2.36154	0.0758245
$971$	−36.1106	−1.15885	−0.579423	−	0.815027i	$-0.696722\pi$
$971$	−36.1106	−1.15885	−0.579423	+	0.815027i	$0.696722\pi$
$972$	20.6726	0.663073
$973$	−3.44529	−0.110451
$974$	53.4246	1.71184
$975$	−1.05999	−0.0339469
$976$	67.2915	2.15395
$977$	39.9196	1.27714	0.638571	−	0.769563i	$-0.279526\pi$
$977$	39.9196	1.27714	0.638571	+	0.769563i	$0.279526\pi$
$978$	80.6049	2.57746
$979$	32.4211	1.03618
$980$	−1.75806	−0.0561590
$981$	60.0352	1.91678
$982$	27.9158	0.890830
$983$	−19.3318	−0.616588	−0.308294	−	0.951291i	$-0.599758\pi$
$983$	−19.3318	−0.616588	−0.308294	+	0.951291i	$0.599758\pi$
$984$	−24.3606	−0.776588
$985$	4.93605	0.157276
$986$	−1.71671	−0.0546712
$987$	24.9677	0.794732
$988$	0.239113	0.00760721
$989$	−36.0680	−1.14690
$990$	34.5051	1.09664
$991$	−30.3867	−0.965264	−0.482632	−	0.875823i	$-0.660319\pi$
$991$	−30.3867	−0.965264	−0.482632	+	0.875823i	$0.660319\pi$
$992$	−6.87604	−0.218314
$993$	−63.5473	−2.01661
$994$	48.7353	1.54579
$995$	6.02905	0.191134
$996$	−28.7429	−0.910753
$997$	−45.5381	−1.44220	−0.721102	−	0.692829i	$-0.756364\pi$
$997$	−45.5381	−1.44220	−0.721102	+	0.692829i	$0.756364\pi$
$998$	24.5258	0.776351
$999$	−14.8613	−0.470191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.6	✓	25
3.2	odd	2		4923.2.a.n.1.20		25
4.3	odd	2		8752.2.a.v.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.6	✓	25	1.1	even	1	trivial
4923.2.a.n.1.20		25	3.2	odd	2
8752.2.a.v.1.23		25	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71387 q^{2} -2.58580 q^{3} +0.937360 q^{4} +0.849164 q^{5} +4.43173 q^{6} -2.18891 q^{7} +1.82123 q^{8} +3.68636 q^{9} +O(q^{10})\)	\(q-1.71387 q^{2} -2.58580 q^{3} +0.937360 q^{4} +0.849164 q^{5} +4.43173 q^{6} -2.18891 q^{7} +1.82123 q^{8} +3.68636 q^{9} -1.45536 q^{10} -6.43154 q^{11} -2.42383 q^{12} -0.0958018 q^{13} +3.75151 q^{14} -2.19577 q^{15} -4.99608 q^{16} +1.27125 q^{17} -6.31796 q^{18} -2.66271 q^{19} +0.795972 q^{20} +5.66007 q^{21} +11.0228 q^{22} -3.64481 q^{23} -4.70934 q^{24} -4.27892 q^{25} +0.164192 q^{26} -1.77480 q^{27} -2.05179 q^{28} +0.787930 q^{29} +3.76327 q^{30} -1.39752 q^{31} +4.92018 q^{32} +16.6307 q^{33} -2.17876 q^{34} -1.85874 q^{35} +3.45545 q^{36} +8.37352 q^{37} +4.56355 q^{38} +0.247724 q^{39} +1.54652 q^{40} +5.17283 q^{41} -9.70065 q^{42} +9.89571 q^{43} -6.02866 q^{44} +3.13033 q^{45} +6.24674 q^{46} +4.41120 q^{47} +12.9189 q^{48} -2.20869 q^{49} +7.33353 q^{50} -3.28720 q^{51} -0.0898008 q^{52} +10.2981 q^{53} +3.04178 q^{54} -5.46143 q^{55} -3.98650 q^{56} +6.88523 q^{57} -1.35041 q^{58} +6.44026 q^{59} -2.05823 q^{60} -13.4689 q^{61} +2.39517 q^{62} -8.06910 q^{63} +1.55959 q^{64} -0.0813514 q^{65} -28.5029 q^{66} -5.75369 q^{67} +1.19162 q^{68} +9.42475 q^{69} +3.18564 q^{70} +12.9909 q^{71} +6.71371 q^{72} -2.65079 q^{73} -14.3511 q^{74} +11.0644 q^{75} -2.49592 q^{76} +14.0780 q^{77} -0.424568 q^{78} -2.33430 q^{79} -4.24249 q^{80} -6.46982 q^{81} -8.86558 q^{82} +11.8585 q^{83} +5.30553 q^{84} +1.07950 q^{85} -16.9600 q^{86} -2.03743 q^{87} -11.7133 q^{88} -5.04096 q^{89} -5.36498 q^{90} +0.209701 q^{91} -3.41650 q^{92} +3.61370 q^{93} -7.56024 q^{94} -2.26108 q^{95} -12.7226 q^{96} -1.62265 q^{97} +3.78541 q^{98} -23.7090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9 - q^10 + 10 * q^11 + 14 * q^12 + 19 * q^13 + 9 * q^14 + 5 * q^15 + 16 * q^16 + 40 * q^17 - 8 * q^18 + 33 * q^20 - 8 * q^21 - 10 * q^22 + 26 * q^23 - 16 * q^24 + 36 * q^25 - 8 * q^26 + 11 * q^27 - 8 * q^28 + 30 * q^29 - 20 * q^30 - 5 * q^31 + 6 * q^32 + 10 * q^33 - 7 * q^34 + 11 * q^35 + 13 * q^36 + 26 * q^37 + 25 * q^38 - 17 * q^39 - 25 * q^40 + 9 * q^41 - 16 * q^42 - 10 * q^43 + 64 * q^45 - 34 * q^46 + 28 * q^47 + 23 * q^48 + 20 * q^49 - 9 * q^50 - 9 * q^51 - 2 * q^52 + 80 * q^53 - 13 * q^54 - q^55 + 7 * q^56 - 8 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 22 * q^61 + 36 * q^62 - 9 * q^63 - 28 * q^64 + 30 * q^65 - 42 * q^66 - 16 * q^67 + 59 * q^68 + 22 * q^69 - 61 * q^70 - q^71 - 44 * q^72 + 2 * q^73 - 8 * q^74 - 31 * q^75 - 46 * q^76 + 67 * q^77 - q^78 - 34 * q^79 + 30 * q^80 - 11 * q^81 - 4 * q^82 + 15 * q^83 - 87 * q^84 + 15 * q^85 - 44 * q^86 - 29 * q^87 - 55 * q^88 + 38 * q^89 - 90 * q^90 - 41 * q^91 + 40 * q^92 - 4 * q^93 - 46 * q^94 - 46 * q^95 - 87 * q^96 - 2 * q^97 - 14 * q^98 - 41 * q^99

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