LMFDB - Embedded newform 547.2.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.73479 q^{2} +0.987380 q^{3} +1.00948 q^{4} +2.62354 q^{5} +1.71289 q^{6} -1.48197 q^{7} -1.71833 q^{8} -2.02508 q^{9} +O(q^{10})$	\(q+1.73479 q^{2} +0.987380 q^{3} +1.00948 q^{4} +2.62354 q^{5} +1.71289 q^{6} -1.48197 q^{7} -1.71833 q^{8} -2.02508 q^{9} +4.55128 q^{10} +4.92574 q^{11} +0.996745 q^{12} +4.98211 q^{13} -2.57090 q^{14} +2.59043 q^{15} -4.99991 q^{16} +0.723571 q^{17} -3.51308 q^{18} +2.66542 q^{19} +2.64842 q^{20} -1.46327 q^{21} +8.54511 q^{22} -6.02478 q^{23} -1.69665 q^{24} +1.88297 q^{25} +8.64290 q^{26} -4.96166 q^{27} -1.49602 q^{28} +6.48373 q^{29} +4.49385 q^{30} -9.70750 q^{31} -5.23711 q^{32} +4.86358 q^{33} +1.25524 q^{34} -3.88801 q^{35} -2.04429 q^{36} -5.26162 q^{37} +4.62394 q^{38} +4.91924 q^{39} -4.50812 q^{40} -7.85163 q^{41} -2.53846 q^{42} +3.94563 q^{43} +4.97246 q^{44} -5.31288 q^{45} -10.4517 q^{46} -1.56571 q^{47} -4.93681 q^{48} -4.80377 q^{49} +3.26655 q^{50} +0.714440 q^{51} +5.02936 q^{52} -3.81676 q^{53} -8.60743 q^{54} +12.9229 q^{55} +2.54652 q^{56} +2.63178 q^{57} +11.2479 q^{58} -14.1861 q^{59} +2.61500 q^{60} +4.29610 q^{61} -16.8404 q^{62} +3.00111 q^{63} +0.914550 q^{64} +13.0708 q^{65} +8.43727 q^{66} +0.167962 q^{67} +0.730434 q^{68} -5.94875 q^{69} -6.74486 q^{70} +15.5235 q^{71} +3.47976 q^{72} +16.6105 q^{73} -9.12780 q^{74} +1.85921 q^{75} +2.69070 q^{76} -7.29979 q^{77} +8.53382 q^{78} +5.42363 q^{79} -13.1175 q^{80} +1.17619 q^{81} -13.6209 q^{82} -2.15006 q^{83} -1.47715 q^{84} +1.89832 q^{85} +6.84482 q^{86} +6.40191 q^{87} -8.46406 q^{88} -9.27607 q^{89} -9.21672 q^{90} -7.38333 q^{91} -6.08193 q^{92} -9.58500 q^{93} -2.71617 q^{94} +6.99285 q^{95} -5.17102 q^{96} +2.94098 q^{97} -8.33351 q^{98} -9.97502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.73479	1.22668	0.613340	−	0.789819i	$-0.289826\pi$
$2$	1.73479	1.22668	0.613340	+	0.789819i	$0.289826\pi$
$3$	0.987380	0.570064	0.285032	−	0.958518i	$-0.407996\pi$
$3$	0.987380	0.570064	0.285032	+	0.958518i	$0.407996\pi$
$4$	1.00948	0.504742
$5$	2.62354	1.17328	0.586642	−	0.809847i	$-0.300450\pi$
$5$	2.62354	1.17328	0.586642	+	0.809847i	$0.300450\pi$
$6$	1.71289	0.699286
$7$	−1.48197	−0.560132	−0.280066	−	0.959981i	$-0.590356\pi$
$7$	−1.48197	−0.560132	−0.280066	+	0.959981i	$0.590356\pi$
$8$	−1.71833	−0.607522
$9$	−2.02508	−0.675027
$10$	4.55128	1.43924
$11$	4.92574	1.48517	0.742583	−	0.669754i	$-0.233600\pi$
$11$	4.92574	1.48517	0.742583	+	0.669754i	$0.233600\pi$
$12$	0.996745	0.287735
$13$	4.98211	1.38179	0.690894	−	0.722956i	$-0.257217\pi$
$13$	4.98211	1.38179	0.690894	+	0.722956i	$0.257217\pi$
$14$	−2.57090	−0.687102
$15$	2.59043	0.668847
$16$	−4.99991	−1.24998
$17$	0.723571	0.175492	0.0877459	−	0.996143i	$-0.472034\pi$
$17$	0.723571	0.175492	0.0877459	+	0.996143i	$0.472034\pi$
$18$	−3.51308	−0.828042
$19$	2.66542	0.611490	0.305745	−	0.952113i	$-0.401095\pi$
$19$	2.66542	0.611490	0.305745	+	0.952113i	$0.401095\pi$
$20$	2.64842	0.592206
$21$	−1.46327	−0.319311
$22$	8.54511	1.82182
$23$	−6.02478	−1.25625	−0.628127	−	0.778111i	$-0.716178\pi$
$23$	−6.02478	−1.25625	−0.628127	+	0.778111i	$0.716178\pi$
$24$	−1.69665	−0.346327
$25$	1.88297	0.376594
$26$	8.64290	1.69501
$27$	−4.96166	−0.954873
$28$	−1.49602	−0.282722
$29$	6.48373	1.20400	0.601999	−	0.798497i	$-0.294371\pi$
$29$	6.48373	1.20400	0.601999	+	0.798497i	$0.294371\pi$
$30$	4.49385	0.820461
$31$	−9.70750	−1.74352	−0.871760	−	0.489934i	$-0.837021\pi$
$31$	−9.70750	−1.74352	−0.871760	+	0.489934i	$0.837021\pi$
$32$	−5.23711	−0.925799
$33$	4.86358	0.846640
$34$	1.25524	0.215272
$35$	−3.88801	−0.657193
$36$	−2.04429	−0.340715
$37$	−5.26162	−0.865006	−0.432503	−	0.901633i	$-0.642369\pi$
$37$	−5.26162	−0.865006	−0.432503	+	0.901633i	$0.642369\pi$
$38$	4.62394	0.750102
$39$	4.91924	0.787708
$40$	−4.50812	−0.712796
$41$	−7.85163	−1.22622	−0.613109	−	0.789998i	$-0.710081\pi$
$41$	−7.85163	−1.22622	−0.613109	+	0.789998i	$0.710081\pi$
$42$	−2.53846	−0.391692
$43$	3.94563	0.601703	0.300851	−	0.953671i	$-0.402729\pi$
$43$	3.94563	0.601703	0.300851	+	0.953671i	$0.402729\pi$
$44$	4.97246	0.749626
$45$	−5.31288	−0.791998
$46$	−10.4517	−1.54102
$47$	−1.56571	−0.228382	−0.114191	−	0.993459i	$-0.536428\pi$
$47$	−1.56571	−0.228382	−0.114191	+	0.993459i	$0.536428\pi$
$48$	−4.93681	−0.712567
$49$	−4.80377	−0.686253
$50$	3.26655	0.461960
$51$	0.714440	0.100042
$52$	5.02936	0.697447
$53$	−3.81676	−0.524272	−0.262136	−	0.965031i	$-0.584427\pi$
$53$	−3.81676	−0.524272	−0.262136	+	0.965031i	$0.584427\pi$
$54$	−8.60743	−1.17132
$55$	12.9229	1.74252
$56$	2.54652	0.340293
$57$	2.63178	0.348588
$58$	11.2479	1.47692
$59$	−14.1861	−1.84687	−0.923434	−	0.383758i	$-0.874630\pi$
$59$	−14.1861	−1.84687	−0.923434	+	0.383758i	$0.874630\pi$
$60$	2.61500	0.337595
$61$	4.29610	0.550059	0.275029	−	0.961436i	$-0.411312\pi$
$61$	4.29610	0.550059	0.275029	+	0.961436i	$0.411312\pi$
$62$	−16.8404	−2.13874
$63$	3.00111	0.378104
$64$	0.914550	0.114319
$65$	13.0708	1.62123
$66$	8.43727	1.03856
$67$	0.167962	0.0205198	0.0102599	−	0.999947i	$-0.496734\pi$
$67$	0.167962	0.0205198	0.0102599	+	0.999947i	$0.496734\pi$
$68$	0.730434	0.0885781
$69$	−5.94875	−0.716146
$70$	−6.74486	−0.806165
$71$	15.5235	1.84229	0.921147	−	0.389214i	$-0.127253\pi$
$71$	15.5235	1.84229	0.921147	+	0.389214i	$0.127253\pi$
$72$	3.47976	0.410094
$73$	16.6105	1.94411	0.972054	−	0.234759i	$-0.0754300\pi$
$73$	16.6105	1.94411	0.972054	+	0.234759i	$0.0754300\pi$
$74$	−9.12780	−1.06108
$75$	1.85921	0.214683
$76$	2.69070	0.308645
$77$	−7.29979	−0.831889
$78$	8.53382	0.966265
$79$	5.42363	0.610206	0.305103	−	0.952319i	$-0.401309\pi$
$79$	5.42363	0.610206	0.305103	+	0.952319i	$0.401309\pi$
$80$	−13.1175	−1.46658
$81$	1.17619	0.130688
$82$	−13.6209	−1.50418
$83$	−2.15006	−0.235999	−0.118000	−	0.993014i	$-0.537648\pi$
$83$	−2.15006	−0.235999	−0.118000	+	0.993014i	$0.537648\pi$
$84$	−1.47715	−0.161170
$85$	1.89832	0.205902
$86$	6.84482	0.738096
$87$	6.40191	0.686356
$88$	−8.46406	−0.902272
$89$	−9.27607	−0.983262	−0.491631	−	0.870804i	$-0.663599\pi$
$89$	−9.27607	−0.983262	−0.491631	+	0.870804i	$0.663599\pi$
$90$	−9.21672	−0.971527
$91$	−7.38333	−0.773983
$92$	−6.08193	−0.634085
$93$	−9.58500	−0.993918
$94$	−2.71617	−0.280152
$95$	6.99285	0.717451
$96$	−5.17102	−0.527765
$97$	2.94098	0.298611	0.149306	−	0.988791i	$-0.452296\pi$
$97$	2.94098	0.298611	0.149306	+	0.988791i	$0.452296\pi$
$98$	−8.33351	−0.841812
$99$	−9.97502	−1.00253
$100$	1.90083	0.190083
$101$	7.04074	0.700580	0.350290	−	0.936641i	$-0.386083\pi$
$101$	7.04074	0.700580	0.350290	+	0.936641i	$0.386083\pi$
$102$	1.23940	0.122719
$103$	5.81410	0.572880	0.286440	−	0.958098i	$-0.407528\pi$
$103$	5.81410	0.572880	0.286440	+	0.958098i	$0.407528\pi$
$104$	−8.56092	−0.839467
$105$	−3.83894	−0.374642
$106$	−6.62126	−0.643114
$107$	−18.0514	−1.74509	−0.872547	−	0.488530i	$-0.837533\pi$
$107$	−18.0514	−1.74509	−0.872547	+	0.488530i	$0.837533\pi$
$108$	−5.00872	−0.481965
$109$	−5.36834	−0.514194	−0.257097	−	0.966386i	$-0.582766\pi$
$109$	−5.36834	−0.514194	−0.257097	+	0.966386i	$0.582766\pi$
$110$	22.4184	2.13751
$111$	−5.19522	−0.493109
$112$	7.40971	0.700152
$113$	4.16702	0.392000	0.196000	−	0.980604i	$-0.437205\pi$
$113$	4.16702	0.392000	0.196000	+	0.980604i	$0.437205\pi$
$114$	4.56558	0.427606
$115$	−15.8063	−1.47394
$116$	6.54523	0.607709
$117$	−10.0892	−0.932744
$118$	−24.6098	−2.26551
$119$	−1.07231	−0.0982985
$120$	−4.45123	−0.406339
$121$	13.2629	1.20572
$122$	7.45281	0.674746
$123$	−7.75254	−0.699023
$124$	−9.79958	−0.880028
$125$	−8.17766	−0.731432
$126$	5.20628	0.463812
$127$	8.91093	0.790717	0.395358	−	0.918527i	$-0.370620\pi$
$127$	8.91093	0.790717	0.395358	+	0.918527i	$0.370620\pi$
$128$	12.0608	1.06603
$129$	3.89583	0.343009
$130$	22.6750	1.98873
$131$	9.38482	0.819955	0.409978	−	0.912096i	$-0.365537\pi$
$131$	9.38482	0.819955	0.409978	+	0.912096i	$0.365537\pi$
$132$	4.90971	0.427335
$133$	−3.95007	−0.342515
$134$	0.291378	0.0251712
$135$	−13.0171	−1.12034
$136$	−1.24334	−0.106615
$137$	2.84375	0.242958	0.121479	−	0.992594i	$-0.461236\pi$
$137$	2.84375	0.242958	0.121479	+	0.992594i	$0.461236\pi$
$138$	−10.3198	−0.878481
$139$	−1.26523	−0.107315	−0.0536576	−	0.998559i	$-0.517088\pi$
$139$	−1.26523	−0.107315	−0.0536576	+	0.998559i	$0.517088\pi$
$140$	−3.92488	−0.331713
$141$	−1.54595	−0.130193
$142$	26.9299	2.25990
$143$	24.5406	2.05219
$144$	10.1252	0.843768
$145$	17.0103	1.41263
$146$	28.8156	2.38480
$147$	−4.74314	−0.391208
$148$	−5.31153	−0.436605
$149$	13.2753	1.08756	0.543778	−	0.839229i	$-0.316994\pi$
$149$	13.2753	1.08756	0.543778	+	0.839229i	$0.316994\pi$
$150$	3.22533	0.263347
$151$	−21.9719	−1.78805	−0.894024	−	0.448019i	$-0.852130\pi$
$151$	−21.9719	−1.78805	−0.894024	+	0.448019i	$0.852130\pi$
$152$	−4.58008	−0.371494
$153$	−1.46529	−0.118462
$154$	−12.6636	−1.02046
$155$	−25.4680	−2.04564
$156$	4.96589	0.397590
$157$	−0.146026	−0.0116541	−0.00582705	−	0.999983i	$-0.501855\pi$
$157$	−0.146026	−0.0116541	−0.00582705	+	0.999983i	$0.501855\pi$
$158$	9.40884	0.748527
$159$	−3.76859	−0.298869
$160$	−13.7398	−1.08622
$161$	8.92854	0.703668
$162$	2.04044	0.160312
$163$	13.1954	1.03354	0.516770	−	0.856124i	$-0.327134\pi$
$163$	13.1954	1.03354	0.516770	+	0.856124i	$0.327134\pi$
$164$	−7.92610	−0.618924
$165$	12.7598	0.993349
$166$	−3.72989	−0.289496
$167$	−16.4383	−1.27203	−0.636015	−	0.771677i	$-0.719418\pi$
$167$	−16.4383	−1.27203	−0.636015	+	0.771677i	$0.719418\pi$
$168$	2.51438	0.193989
$169$	11.8214	0.909339
$170$	3.29318	0.252575
$171$	−5.39769	−0.412772
$172$	3.98305	0.303705
$173$	13.0894	0.995167	0.497584	−	0.867416i	$-0.334221\pi$
$173$	13.0894	0.995167	0.497584	+	0.867416i	$0.334221\pi$
$174$	11.1059	0.841939
$175$	−2.79050	−0.210942
$176$	−24.6283	−1.85642
$177$	−14.0070	−1.05283
$178$	−16.0920	−1.20615
$179$	21.7674	1.62697	0.813487	−	0.581583i	$-0.197566\pi$
$179$	21.7674	1.62697	0.813487	+	0.581583i	$0.197566\pi$
$180$	−5.36327	−0.399755
$181$	4.15089	0.308533	0.154266	−	0.988029i	$-0.450699\pi$
$181$	4.15089	0.308533	0.154266	+	0.988029i	$0.450699\pi$
$182$	−12.8085	−0.949430
$183$	4.24188	0.313569
$184$	10.3526	0.763203
$185$	−13.8041	−1.01490
$186$	−16.6279	−1.21922
$187$	3.56412	0.260634
$188$	−1.58056	−0.115274
$189$	7.35303	0.534854
$190$	12.1311	0.880082
$191$	−20.0736	−1.45248	−0.726238	−	0.687444i	$-0.758733\pi$
$191$	−20.0736	−1.45248	−0.726238	+	0.687444i	$0.758733\pi$
$192$	0.903008	0.0651690
$193$	10.5832	0.761795	0.380897	−	0.924617i	$-0.375615\pi$
$193$	10.5832	0.761795	0.380897	+	0.924617i	$0.375615\pi$
$194$	5.10197	0.366300
$195$	12.9058	0.924205
$196$	−4.84933	−0.346381
$197$	21.2887	1.51676	0.758379	−	0.651814i	$-0.225992\pi$
$197$	21.2887	1.51676	0.758379	+	0.651814i	$0.225992\pi$
$198$	−17.3045	−1.22978
$199$	−19.6882	−1.39566	−0.697828	−	0.716265i	$-0.745850\pi$
$199$	−19.6882	−1.39566	−0.697828	+	0.716265i	$0.745850\pi$
$200$	−3.23557	−0.228789
$201$	0.165842	0.0116976
$202$	12.2142	0.859387
$203$	−9.60869	−0.674398
$204$	0.721216	0.0504952
$205$	−20.5991	−1.43870
$206$	10.0862	0.702740
$207$	12.2007	0.848005
$208$	−24.9101	−1.72720
$209$	13.1292	0.908164
$210$	−6.65974	−0.459566
$211$	−18.6724	−1.28546	−0.642731	−	0.766092i	$-0.722199\pi$
$211$	−18.6724	−1.28546	−0.642731	+	0.766092i	$0.722199\pi$
$212$	−3.85296	−0.264622
$213$	15.3275	1.05023
$214$	−31.3153	−2.14067
$215$	10.3515	0.705968
$216$	8.52579	0.580107
$217$	14.3862	0.976600
$218$	−9.31292	−0.630751
$219$	16.4008	1.10827
$220$	13.0454	0.879524
$221$	3.60491	0.242492
$222$	−9.01260	−0.604886
$223$	15.4470	1.03441	0.517204	−	0.855862i	$-0.326973\pi$
$223$	15.4470	1.03441	0.517204	+	0.855862i	$0.326973\pi$
$224$	7.76124	0.518569
$225$	−3.81317	−0.254211
$226$	7.22888	0.480858
$227$	−6.07365	−0.403122	−0.201561	−	0.979476i	$-0.564601\pi$
$227$	−6.07365	−0.403122	−0.201561	+	0.979476i	$0.564601\pi$
$228$	2.65675	0.175947
$229$	16.4341	1.08600	0.542999	−	0.839733i	$-0.317289\pi$
$229$	16.4341	1.08600	0.542999	+	0.839733i	$0.317289\pi$
$230$	−27.4205	−1.80805
$231$	−7.20767	−0.474230
$232$	−11.1412	−0.731456
$233$	8.15562	0.534292	0.267146	−	0.963656i	$-0.413919\pi$
$233$	8.15562	0.534292	0.267146	+	0.963656i	$0.413919\pi$
$234$	−17.5026	−1.14418
$235$	−4.10771	−0.267957
$236$	−14.3206	−0.932192
$237$	5.35518	0.347857
$238$	−1.86023	−0.120581
$239$	−14.3485	−0.928125	−0.464063	−	0.885802i	$-0.653609\pi$
$239$	−14.3485	−0.928125	−0.464063	+	0.885802i	$0.653609\pi$
$240$	−12.9519	−0.836044
$241$	−7.31372	−0.471118	−0.235559	−	0.971860i	$-0.575692\pi$
$241$	−7.31372	−0.471118	−0.235559	+	0.971860i	$0.575692\pi$
$242$	23.0083	1.47903
$243$	16.0463	1.02937
$244$	4.33684	0.277638
$245$	−12.6029	−0.805169
$246$	−13.4490	−0.857477
$247$	13.2794	0.844949
$248$	16.6807	1.05923
$249$	−2.12292	−0.134535
$250$	−14.1865	−0.897232
$251$	11.8369	0.747136	0.373568	−	0.927603i	$-0.378134\pi$
$251$	11.8369	0.747136	0.373568	+	0.927603i	$0.378134\pi$
$252$	3.02957	0.190845
$253$	−29.6765	−1.86575
$254$	15.4586	0.969956
$255$	1.87436	0.117377
$256$	19.0938	1.19336
$257$	17.0978	1.06653	0.533265	−	0.845948i	$-0.320965\pi$
$257$	17.0978	1.06653	0.533265	+	0.845948i	$0.320965\pi$
$258$	6.75844	0.420762
$259$	7.79757	0.484517
$260$	13.1947	0.818303
$261$	−13.1301	−0.812731
$262$	16.2807	1.00582
$263$	20.6871	1.27562	0.637811	−	0.770193i	$-0.279840\pi$
$263$	20.6871	1.27562	0.637811	+	0.770193i	$0.279840\pi$
$264$	−8.35724	−0.514353
$265$	−10.0134	−0.615120
$266$	−6.85253	−0.420156
$267$	−9.15901	−0.560522
$268$	0.169555	0.0103572
$269$	3.69659	0.225385	0.112692	−	0.993630i	$-0.464053\pi$
$269$	3.69659	0.225385	0.112692	+	0.993630i	$0.464053\pi$
$270$	−22.5819	−1.37429
$271$	−3.59931	−0.218643	−0.109321	−	0.994006i	$-0.534868\pi$
$271$	−3.59931	−0.218643	−0.109321	+	0.994006i	$0.534868\pi$
$272$	−3.61779	−0.219361
$273$	−7.29015	−0.441220
$274$	4.93330	0.298032
$275$	9.27502	0.559305
$276$	−6.00517	−0.361469
$277$	−19.4665	−1.16963	−0.584813	−	0.811168i	$-0.698832\pi$
$277$	−19.4665	−1.16963	−0.584813	+	0.811168i	$0.698832\pi$
$278$	−2.19490	−0.131641
$279$	19.6585	1.17692
$280$	6.68089	0.399260
$281$	25.6332	1.52915	0.764574	−	0.644536i	$-0.222949\pi$
$281$	25.6332	1.52915	0.764574	+	0.644536i	$0.222949\pi$
$282$	−2.68190	−0.159705
$283$	14.8883	0.885018	0.442509	−	0.896764i	$-0.354088\pi$
$283$	14.8883	0.885018	0.442509	+	0.896764i	$0.354088\pi$
$284$	15.6707	0.929884
$285$	6.90460	0.408993
$286$	42.5726	2.51737
$287$	11.6359	0.686844
$288$	10.6056	0.624939
$289$	−16.4764	−0.969203
$290$	29.5093	1.73285
$291$	2.90386	0.170228
$292$	16.7680	0.981273
$293$	−0.478187	−0.0279360	−0.0139680	−	0.999902i	$-0.504446\pi$
$293$	−0.478187	−0.0279360	−0.0139680	+	0.999902i	$0.504446\pi$
$294$	−8.22834	−0.479887
$295$	−37.2177	−2.16690
$296$	9.04122	0.525510
$297$	−24.4399	−1.41814
$298$	23.0298	1.33408
$299$	−30.0161	−1.73588
$300$	1.87684	0.108359
$301$	−5.84730	−0.337033
$302$	−38.1166	−2.19336
$303$	6.95189	0.399376
$304$	−13.3269	−0.764348
$305$	11.2710	0.645375
$306$	−2.54196	−0.145314
$307$	−5.20605	−0.297125	−0.148563	−	0.988903i	$-0.547465\pi$
$307$	−5.20605	−0.297125	−0.148563	+	0.988903i	$0.547465\pi$
$308$	−7.36903	−0.419889
$309$	5.74072	0.326578
$310$	−44.1816	−2.50935
$311$	33.2705	1.88660	0.943300	−	0.331942i	$-0.107704\pi$
$311$	33.2705	1.88660	0.943300	+	0.331942i	$0.107704\pi$
$312$	−8.45288	−0.478550
$313$	6.24706	0.353105	0.176552	−	0.984291i	$-0.443505\pi$
$313$	6.24706	0.353105	0.176552	+	0.984291i	$0.443505\pi$
$314$	−0.253323	−0.0142959
$315$	7.87353	0.443623
$316$	5.47507	0.307997
$317$	−23.5190	−1.32096	−0.660478	−	0.750845i	$-0.729647\pi$
$317$	−23.5190	−1.32096	−0.660478	+	0.750845i	$0.729647\pi$
$318$	−6.53770	−0.366616
$319$	31.9372	1.78814
$320$	2.39936	0.134128
$321$	−17.8236	−0.994816
$322$	15.4891	0.863175
$323$	1.92862	0.107311
$324$	1.18735	0.0659638
$325$	9.38116	0.520373
$326$	22.8911	1.26782
$327$	−5.30059	−0.293123
$328$	13.4917	0.744955
$329$	2.32034	0.127924
$330$	22.1355	1.21852
$331$	−13.4670	−0.740213	−0.370106	−	0.928989i	$-0.620679\pi$
$331$	−13.4670	−0.740213	−0.370106	+	0.928989i	$0.620679\pi$
$332$	−2.17045	−0.119119
$333$	10.6552	0.583902
$334$	−28.5169	−1.56037
$335$	0.440655	0.0240756
$336$	7.31620	0.399132
$337$	−10.8679	−0.592011	−0.296005	−	0.955186i	$-0.595655\pi$
$337$	−10.8679	−0.592011	−0.296005	+	0.955186i	$0.595655\pi$
$338$	20.5076	1.11547
$339$	4.11443	0.223465
$340$	1.91632	0.103927
$341$	−47.8166	−2.58942
$342$	−9.36385	−0.506339
$343$	17.4928	0.944523
$344$	−6.77990	−0.365548
$345$	−15.6068	−0.840242
$346$	22.7073	1.22075
$347$	−1.32433	−0.0710935	−0.0355467	−	0.999368i	$-0.511317\pi$
$347$	−1.32433	−0.0710935	−0.0355467	+	0.999368i	$0.511317\pi$
$348$	6.46262	0.346433
$349$	18.8883	1.01107	0.505534	−	0.862807i	$-0.331296\pi$
$349$	18.8883	1.01107	0.505534	+	0.862807i	$0.331296\pi$
$350$	−4.84093	−0.258759
$351$	−24.7196	−1.31943
$352$	−25.7966	−1.37497
$353$	−20.1409	−1.07199	−0.535995	−	0.844221i	$-0.680063\pi$
$353$	−20.1409	−1.07199	−0.535995	+	0.844221i	$0.680063\pi$
$354$	−24.2992	−1.29149
$355$	40.7264	2.16153
$356$	−9.36405	−0.496294
$357$	−1.05878	−0.0560364
$358$	37.7619	1.99578
$359$	5.33558	0.281601	0.140800	−	0.990038i	$-0.455032\pi$
$359$	5.33558	0.281601	0.140800	+	0.990038i	$0.455032\pi$
$360$	9.12930	0.481156
$361$	−11.8955	−0.626080
$362$	7.20090	0.378471
$363$	13.0955	0.687337
$364$	−7.45336	−0.390662
$365$	43.5782	2.28099
$366$	7.35876	0.384648
$367$	−10.7210	−0.559633	−0.279817	−	0.960053i	$-0.590274\pi$
$367$	−10.7210	−0.559633	−0.279817	+	0.960053i	$0.590274\pi$
$368$	30.1234	1.57029
$369$	15.9002	0.827730
$370$	−23.9472	−1.24495
$371$	5.65632	0.293661
$372$	−9.67591	−0.501672
$373$	−30.0707	−1.55700	−0.778502	−	0.627643i	$-0.784020\pi$
$373$	−30.0707	−1.55700	−0.778502	+	0.627643i	$0.784020\pi$
$374$	6.18299	0.319715
$375$	−8.07446	−0.416963
$376$	2.69041	0.138747
$377$	32.3026	1.66367
$378$	12.7559	0.656095
$379$	−12.4630	−0.640183	−0.320091	−	0.947387i	$-0.603714\pi$
$379$	−12.4630	−0.640183	−0.320091	+	0.947387i	$0.603714\pi$
$380$	7.05917	0.362128
$381$	8.79847	0.450759
$382$	−34.8234	−1.78172
$383$	−34.5273	−1.76426	−0.882132	−	0.471001i	$-0.843893\pi$
$383$	−34.5273	−1.76426	−0.882132	+	0.471001i	$0.843893\pi$
$384$	11.9086	0.607706
$385$	−19.1513	−0.976041
$386$	18.3596	0.934478
$387$	−7.99021	−0.406165
$388$	2.96887	0.150722
$389$	33.2184	1.68424	0.842121	−	0.539289i	$-0.181307\pi$
$389$	33.2184	1.68424	0.842121	+	0.539289i	$0.181307\pi$
$390$	22.3888	1.13370
$391$	−4.35936	−0.220462
$392$	8.25447	0.416914
$393$	9.26638	0.467427
$394$	36.9314	1.86058
$395$	14.2291	0.715945
$396$	−10.0696	−0.506018
$397$	−5.13635	−0.257786	−0.128893	−	0.991658i	$-0.541142\pi$
$397$	−5.13635	−0.257786	−0.128893	+	0.991658i	$0.541142\pi$
$398$	−34.1547	−1.71202
$399$	−3.90022	−0.195255
$400$	−9.41468	−0.470734
$401$	31.5314	1.57460	0.787302	−	0.616568i	$-0.211477\pi$
$401$	31.5314	1.57460	0.787302	+	0.616568i	$0.211477\pi$
$402$	0.287701	0.0143492
$403$	−48.3638	−2.40917
$404$	7.10752	0.353612
$405$	3.08579	0.153334
$406$	−16.6690	−0.827270
$407$	−25.9174	−1.28468
$408$	−1.22764	−0.0607775
$409$	19.2636	0.952526	0.476263	−	0.879303i	$-0.341991\pi$
$409$	19.2636	0.952526	0.476263	+	0.879303i	$0.341991\pi$
$410$	−35.7350	−1.76483
$411$	2.80787	0.138502
$412$	5.86924	0.289157
$413$	21.0233	1.03449
$414$	21.1656	1.04023
$415$	−5.64076	−0.276894
$416$	−26.0919	−1.27926
$417$	−1.24926	−0.0611765
$418$	22.7763	1.11403
$419$	−25.8404	−1.26239	−0.631193	−	0.775626i	$-0.717435\pi$
$419$	−25.8404	−1.26239	−0.631193	+	0.775626i	$0.717435\pi$
$420$	−3.87535	−0.189098
$421$	23.1071	1.12617	0.563085	−	0.826399i	$-0.309614\pi$
$421$	23.1071	1.12617	0.563085	+	0.826399i	$0.309614\pi$
$422$	−32.3926	−1.57685
$423$	3.17069	0.154164
$424$	6.55846	0.318507
$425$	1.36246	0.0660891
$426$	26.5900	1.28829
$427$	−6.36668	−0.308105
$428$	−18.2226	−0.880823
$429$	24.2309	1.16988
$430$	17.9577	0.865996
$431$	−25.8861	−1.24689	−0.623445	−	0.781867i	$-0.714267\pi$
$431$	−25.8861	−1.24689	−0.623445	+	0.781867i	$0.714267\pi$
$432$	24.8079	1.19357
$433$	−21.4450	−1.03058	−0.515290	−	0.857016i	$-0.672316\pi$
$433$	−21.4450	−1.03058	−0.515290	+	0.857016i	$0.672316\pi$
$434$	24.9570	1.19798
$435$	16.7957	0.805291
$436$	−5.41926	−0.259535
$437$	−16.0586	−0.768187
$438$	28.4520	1.35949
$439$	7.64238	0.364751	0.182375	−	0.983229i	$-0.441621\pi$
$439$	7.64238	0.364751	0.182375	+	0.983229i	$0.441621\pi$
$440$	−22.2058	−1.05862
$441$	9.72802	0.463239
$442$	6.25375	0.297460
$443$	−18.1709	−0.863328	−0.431664	−	0.902035i	$-0.642073\pi$
$443$	−18.1709	−0.863328	−0.431664	+	0.902035i	$0.642073\pi$
$444$	−5.24450	−0.248893
$445$	−24.3362	−1.15364
$446$	26.7973	1.26889
$447$	13.1078	0.619976
$448$	−1.35533	−0.0640336
$449$	−9.91048	−0.467705	−0.233852	−	0.972272i	$-0.575133\pi$
$449$	−9.91048	−0.467705	−0.233852	+	0.972272i	$0.575133\pi$
$450$	−6.61503	−0.311836
$451$	−38.6751	−1.82114
$452$	4.20654	0.197859
$453$	−21.6946	−1.01930
$454$	−10.5365	−0.494502
$455$	−19.3705	−0.908102
$456$	−4.52228	−0.211775
$457$	−18.0877	−0.846107	−0.423053	−	0.906105i	$-0.639042\pi$
$457$	−18.0877	−0.846107	−0.423053	+	0.906105i	$0.639042\pi$
$458$	28.5097	1.33217
$459$	−3.59012	−0.167572
$460$	−15.9562	−0.743961
$461$	35.7098	1.66317	0.831586	−	0.555395i	$-0.187433\pi$
$461$	35.7098	1.66317	0.831586	+	0.555395i	$0.187433\pi$
$462$	−12.5038	−0.581728
$463$	20.0478	0.931699	0.465849	−	0.884864i	$-0.345749\pi$
$463$	20.0478	0.931699	0.465849	+	0.884864i	$0.345749\pi$
$464$	−32.4181	−1.50497
$465$	−25.1466	−1.16615
$466$	14.1483	0.655405
$467$	−8.35057	−0.386418	−0.193209	−	0.981158i	$-0.561890\pi$
$467$	−8.35057	−0.386418	−0.193209	+	0.981158i	$0.561890\pi$
$468$	−10.1849	−0.470795
$469$	−0.248914	−0.0114938
$470$	−7.12600	−0.328698
$471$	−0.144183	−0.00664359
$472$	24.3764	1.12201
$473$	19.4351	0.893628
$474$	9.29010	0.426708
$475$	5.01891	0.230283
$476$	−1.08248	−0.0496154
$477$	7.72924	0.353898
$478$	−24.8915	−1.13851
$479$	6.86722	0.313771	0.156886	−	0.987617i	$-0.449855\pi$
$479$	6.86722	0.313771	0.156886	+	0.987617i	$0.449855\pi$
$480$	−13.5664	−0.619218
$481$	−26.2140	−1.19526
$482$	−12.6877	−0.577911
$483$	8.81587	0.401136
$484$	13.3887	0.608577
$485$	7.71578	0.350356
$486$	27.8370	1.26271
$487$	7.81254	0.354020	0.177010	−	0.984209i	$-0.443358\pi$
$487$	7.81254	0.354020	0.177010	+	0.984209i	$0.443358\pi$
$488$	−7.38212	−0.334173
$489$	13.0288	0.589184
$490$	−21.8633	−0.987684
$491$	−11.3257	−0.511121	−0.255560	−	0.966793i	$-0.582260\pi$
$491$	−11.3257	−0.511121	−0.255560	+	0.966793i	$0.582260\pi$
$492$	−7.82607	−0.352826
$493$	4.69144	0.211292
$494$	23.0370	1.03648
$495$	−26.1699	−1.17625
$496$	48.5366	2.17936
$497$	−23.0053	−1.03193
$498$	−3.68282	−0.165031
$499$	−14.4076	−0.644972	−0.322486	−	0.946574i	$-0.604518\pi$
$499$	−14.4076	−0.644972	−0.322486	+	0.946574i	$0.604518\pi$
$500$	−8.25522	−0.369185
$501$	−16.2308	−0.725139
$502$	20.5344	0.916496
$503$	18.6710	0.832498	0.416249	−	0.909251i	$-0.363345\pi$
$503$	18.6710	0.832498	0.416249	+	0.909251i	$0.363345\pi$
$504$	−5.15690	−0.229707
$505$	18.4717	0.821979
$506$	−51.4824	−2.28867
$507$	11.6722	0.518382
$508$	8.99544	0.399108
$509$	−25.3440	−1.12335	−0.561677	−	0.827356i	$-0.689844\pi$
$509$	−25.3440	−1.12335	−0.561677	+	0.827356i	$0.689844\pi$
$510$	3.25162	0.143984
$511$	−24.6162	−1.08896
$512$	9.00206	0.397839
$513$	−13.2249	−0.583895
$514$	29.6610	1.30829
$515$	15.2535	0.672151
$516$	3.93278	0.173131
$517$	−7.71228	−0.339186
$518$	13.5271	0.594347
$519$	12.9242	0.567309
$520$	−22.4599	−0.984933
$521$	−7.76779	−0.340313	−0.170156	−	0.985417i	$-0.554427\pi$
$521$	−7.76779	−0.340313	−0.170156	+	0.985417i	$0.554427\pi$
$522$	−22.7779	−0.996961
$523$	−12.5160	−0.547285	−0.273642	−	0.961832i	$-0.588228\pi$
$523$	−12.5160	−0.547285	−0.273642	+	0.961832i	$0.588228\pi$
$524$	9.47383	0.413866
$525$	−2.75529	−0.120251
$526$	35.8877	1.56478
$527$	−7.02407	−0.305973
$528$	−24.3174	−1.05828
$529$	13.2980	0.578175
$530$	−17.3712	−0.754555
$531$	28.7279	1.24668
$532$	−3.98754	−0.172882
$533$	−39.1177	−1.69437
$534$	−15.8889	−0.687581
$535$	−47.3586	−2.04749
$536$	−0.288615	−0.0124663
$537$	21.4927	0.927480
$538$	6.41279	0.276475
$539$	−23.6621	−1.01920
$540$	−13.1406	−0.565481
$541$	3.11976	0.134129	0.0670644	−	0.997749i	$-0.478637\pi$
$541$	3.11976	0.134129	0.0670644	+	0.997749i	$0.478637\pi$
$542$	−6.24404	−0.268204
$543$	4.09850	0.175884
$544$	−3.78942	−0.162470
$545$	−14.0841	−0.603295
$546$	−12.6469	−0.541236
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	2.87072	0.122631
$549$	−8.69994	−0.371304
$550$	16.0902	0.686088
$551$	17.2819	0.736233
$552$	10.2219	0.435075
$553$	−8.03765	−0.341796
$554$	−33.7701	−1.43476
$555$	−13.6299	−0.578556
$556$	−1.27723	−0.0541665
$557$	10.0197	0.424547	0.212273	−	0.977210i	$-0.431913\pi$
$557$	10.0197	0.424547	0.212273	+	0.977210i	$0.431913\pi$
$558$	34.1033	1.44371
$559$	19.6575	0.831426
$560$	19.4397	0.821477
$561$	3.51914	0.148578
$562$	44.4681	1.87578
$563$	−7.47153	−0.314887	−0.157444	−	0.987528i	$-0.550325\pi$
$563$	−7.47153	−0.314887	−0.157444	+	0.987528i	$0.550325\pi$
$564$	−1.56061	−0.0657137
$565$	10.9323	0.459927
$566$	25.8280	1.08563
$567$	−1.74308	−0.0732026
$568$	−26.6745	−1.11924
$569$	16.8267	0.705412	0.352706	−	0.935734i	$-0.385262\pi$
$569$	16.8267	0.705412	0.352706	+	0.935734i	$0.385262\pi$
$570$	11.9780	0.501703
$571$	−26.9825	−1.12918	−0.564590	−	0.825371i	$-0.690966\pi$
$571$	−26.9825	−1.12918	−0.564590	+	0.825371i	$0.690966\pi$
$572$	24.7733	1.03582
$573$	−19.8203	−0.828004
$574$	20.1857	0.842537
$575$	−11.3445	−0.473098
$576$	−1.85204	−0.0771682
$577$	3.32529	0.138434	0.0692169	−	0.997602i	$-0.477950\pi$
$577$	3.32529	0.138434	0.0692169	+	0.997602i	$0.477950\pi$
$578$	−28.5831	−1.18890
$579$	10.4496	0.434272
$580$	17.1717	0.713015
$581$	3.18632	0.132191
$582$	5.03758	0.208815
$583$	−18.8004	−0.778631
$584$	−28.5423	−1.18109
$585$	−26.4694	−1.09437
$586$	−0.829552	−0.0342685
$587$	15.6039	0.644044	0.322022	−	0.946732i	$-0.395638\pi$
$587$	15.6039	0.644044	0.322022	+	0.946732i	$0.395638\pi$
$588$	−4.78813	−0.197459
$589$	−25.8746	−1.06614
$590$	−64.5648	−2.65809
$591$	21.0200	0.864649
$592$	26.3077	1.08124
$593$	38.5438	1.58280	0.791402	−	0.611296i	$-0.209352\pi$
$593$	38.5438	1.58280	0.791402	+	0.611296i	$0.209352\pi$
$594$	−42.3979	−1.73961
$595$	−2.81325	−0.115332
$596$	13.4012	0.548935
$597$	−19.4397	−0.795614
$598$	−52.0716	−2.12937
$599$	26.0546	1.06456	0.532281	−	0.846568i	$-0.321335\pi$
$599$	26.0546	1.06456	0.532281	+	0.846568i	$0.321335\pi$
$600$	−3.19474	−0.130425
$601$	−9.12783	−0.372332	−0.186166	−	0.982518i	$-0.559606\pi$
$601$	−9.12783	−0.372332	−0.186166	+	0.982518i	$0.559606\pi$
$602$	−10.1438	−0.413431
$603$	−0.340137	−0.0138514
$604$	−22.1803	−0.902504
$605$	34.7958	1.41465
$606$	12.0600	0.489906
$607$	−36.1288	−1.46642	−0.733212	−	0.680001i	$-0.761979\pi$
$607$	−36.1288	−1.46642	−0.733212	+	0.680001i	$0.761979\pi$
$608$	−13.9591	−0.566117
$609$	−9.48743	−0.384450
$610$	19.5528	0.791668
$611$	−7.80054	−0.315576
$612$	−1.47919	−0.0597926
$613$	−20.5652	−0.830623	−0.415311	−	0.909679i	$-0.636327\pi$
$613$	−20.5652	−0.830623	−0.415311	+	0.909679i	$0.636327\pi$
$614$	−9.03139	−0.364477
$615$	−20.3391	−0.820152
$616$	12.5435	0.505391
$617$	42.1065	1.69514	0.847572	−	0.530681i	$-0.178064\pi$
$617$	42.1065	1.69514	0.847572	+	0.530681i	$0.178064\pi$
$618$	9.95893	0.400607
$619$	−36.9578	−1.48546	−0.742729	−	0.669592i	$-0.766469\pi$
$619$	−36.9578	−1.48546	−0.742729	+	0.669592i	$0.766469\pi$
$620$	−25.7096	−1.03252
$621$	29.8930	1.19956
$622$	57.7173	2.31425
$623$	13.7469	0.550756
$624$	−24.5957	−0.984617
$625$	−30.8693	−1.23477
$626$	10.8373	0.433146
$627$	12.9635	0.517712
$628$	−0.147411	−0.00588232
$629$	−3.80716	−0.151801
$630$	13.6589	0.544183
$631$	−17.7647	−0.707200	−0.353600	−	0.935397i	$-0.615043\pi$
$631$	−17.7647	−0.707200	−0.353600	+	0.935397i	$0.615043\pi$
$632$	−9.31960	−0.370714
$633$	−18.4368	−0.732795
$634$	−40.8004	−1.62039
$635$	23.3782	0.927735
$636$	−3.80433	−0.150852
$637$	−23.9329	−0.948256
$638$	55.4042	2.19347
$639$	−31.4362	−1.24360
$640$	31.6419	1.25076
$641$	−34.4686	−1.36143	−0.680713	−	0.732550i	$-0.738330\pi$
$641$	−34.4686	−1.36143	−0.680713	+	0.732550i	$0.738330\pi$
$642$	−30.9201	−1.22032
$643$	−21.5734	−0.850771	−0.425385	−	0.905012i	$-0.639861\pi$
$643$	−21.5734	−0.850771	−0.425385	+	0.905012i	$0.639861\pi$
$644$	9.01323	0.355171
$645$	10.2209	0.402447
$646$	3.34575	0.131637
$647$	38.9572	1.53157	0.765783	−	0.643100i	$-0.222352\pi$
$647$	38.9572	1.53157	0.765783	+	0.643100i	$0.222352\pi$
$648$	−2.02109	−0.0793960
$649$	−69.8768	−2.74290
$650$	16.2743	0.638331
$651$	14.2047	0.556725
$652$	13.3205	0.521671
$653$	37.2643	1.45826	0.729132	−	0.684373i	$-0.239924\pi$
$653$	37.2643	1.45826	0.729132	+	0.684373i	$0.239924\pi$
$654$	−9.19540	−0.359568
$655$	24.6215	0.962040
$656$	39.2574	1.53275
$657$	−33.6375	−1.31232
$658$	4.02529	0.156922
$659$	−14.8021	−0.576606	−0.288303	−	0.957539i	$-0.593091\pi$
$659$	−14.8021	−0.576606	−0.288303	+	0.957539i	$0.593091\pi$
$660$	12.8808	0.501385
$661$	25.3441	0.985772	0.492886	−	0.870094i	$-0.335942\pi$
$661$	25.3441	0.985772	0.492886	+	0.870094i	$0.335942\pi$
$662$	−23.3624	−0.908004
$663$	3.55942	0.138236
$664$	3.69451	0.143375
$665$	−10.3632	−0.401867
$666$	18.4845	0.716261
$667$	−39.0631	−1.51253
$668$	−16.5942	−0.642047
$669$	15.2521	0.589679
$670$	0.764443	0.0295330
$671$	21.1614	0.816929
$672$	7.66329	0.295618
$673$	−5.08052	−0.195840	−0.0979198	−	0.995194i	$-0.531219\pi$
$673$	−5.08052	−0.195840	−0.0979198	+	0.995194i	$0.531219\pi$
$674$	−18.8534	−0.726207
$675$	−9.34267	−0.359599
$676$	11.9335	0.458982
$677$	24.2884	0.933479	0.466739	−	0.884395i	$-0.345429\pi$
$677$	24.2884	0.933479	0.466739	+	0.884395i	$0.345429\pi$
$678$	7.13766	0.274120
$679$	−4.35844	−0.167262
$680$	−3.26194	−0.125090
$681$	−5.99700	−0.229805
$682$	−82.9517	−3.17638
$683$	−20.7481	−0.793905	−0.396952	−	0.917839i	$-0.629932\pi$
$683$	−20.7481	−0.793905	−0.396952	+	0.917839i	$0.629932\pi$
$684$	−5.44889	−0.208343
$685$	7.46070	0.285059
$686$	30.3463	1.15863
$687$	16.2267	0.619089
$688$	−19.7278	−0.752115
$689$	−19.0155	−0.724433
$690$	−27.0745	−1.03071
$691$	−5.87547	−0.223514	−0.111757	−	0.993736i	$-0.535648\pi$
$691$	−5.87547	−0.223514	−0.111757	+	0.993736i	$0.535648\pi$
$692$	13.2135	0.502303
$693$	14.7827	0.561547
$694$	−2.29742	−0.0872089
$695$	−3.31938	−0.125911
$696$	−11.0006	−0.416977
$697$	−5.68121	−0.215191
$698$	32.7672	1.24026
$699$	8.05269	0.304581
$700$	−2.81697	−0.106471
$701$	2.73505	0.103301	0.0516506	−	0.998665i	$-0.483552\pi$
$701$	2.73505	0.103301	0.0516506	+	0.998665i	$0.483552\pi$
$702$	−42.8831	−1.61852
$703$	−14.0245	−0.528942
$704$	4.50483	0.169782
$705$	−4.05587	−0.152753
$706$	−34.9401	−1.31499
$707$	−10.4342	−0.392417
$708$	−14.1399	−0.531409
$709$	3.26226	0.122517	0.0612583	−	0.998122i	$-0.480489\pi$
$709$	3.26226	0.122517	0.0612583	+	0.998122i	$0.480489\pi$
$710$	70.6516	2.65151
$711$	−10.9833	−0.411905
$712$	15.9394	0.597353
$713$	58.4856	2.19030
$714$	−1.83675	−0.0687387
$715$	64.3832	2.40780
$716$	21.9739	0.821203
$717$	−14.1674	−0.529091
$718$	9.25609	0.345434
$719$	−11.9207	−0.444569	−0.222284	−	0.974982i	$-0.571351\pi$
$719$	−11.9207	−0.444569	−0.222284	+	0.974982i	$0.571351\pi$
$720$	26.5639	0.989980
$721$	−8.61631	−0.320888
$722$	−20.6362	−0.768000
$723$	−7.22142	−0.268568
$724$	4.19026	0.155730
$725$	12.2087	0.453419
$726$	22.7179	0.843142
$727$	46.8278	1.73675	0.868373	−	0.495912i	$-0.165166\pi$
$727$	46.8278	1.73675	0.868373	+	0.495912i	$0.165166\pi$
$728$	12.6870	0.470212
$729$	12.3153	0.456121
$730$	75.5989	2.79804
$731$	2.85494	0.105594
$732$	4.28211	0.158271
$733$	39.7221	1.46717	0.733584	−	0.679599i	$-0.237846\pi$
$733$	39.7221	1.46717	0.733584	+	0.679599i	$0.237846\pi$
$734$	−18.5987	−0.686490
$735$	−12.4438	−0.458998
$736$	31.5525	1.16304
$737$	0.827337	0.0304753
$738$	27.5834	1.01536
$739$	15.3943	0.566287	0.283144	−	0.959077i	$-0.408623\pi$
$739$	15.3943	0.566287	0.283144	+	0.959077i	$0.408623\pi$
$740$	−13.9350	−0.512261
$741$	13.1118	0.481675
$742$	9.81250	0.360228
$743$	43.6355	1.60083	0.800416	−	0.599445i	$-0.204612\pi$
$743$	43.6355	1.60083	0.800416	+	0.599445i	$0.204612\pi$
$744$	16.4702	0.603827
$745$	34.8283	1.27601
$746$	−52.1663	−1.90994
$747$	4.35404	0.159306
$748$	3.59793	0.131553
$749$	26.7516	0.977483
$750$	−14.0075	−0.511480
$751$	−9.24304	−0.337283	−0.168642	−	0.985677i	$-0.553938\pi$
$751$	−9.24304	−0.337283	−0.168642	+	0.985677i	$0.553938\pi$
$752$	7.82842	0.285473
$753$	11.6875	0.425915
$754$	56.0382	2.04079
$755$	−57.6442	−2.09789
$756$	7.42277	0.269964
$757$	−50.4645	−1.83416	−0.917082	−	0.398699i	$-0.869462\pi$
$757$	−50.4645	−1.83416	−0.917082	+	0.398699i	$0.869462\pi$
$758$	−21.6207	−0.785299
$759$	−29.3020	−1.06360
$760$	−12.0160	−0.435867
$761$	−48.5994	−1.76173	−0.880863	−	0.473372i	$-0.843037\pi$
$761$	−48.5994	−1.76173	−0.880863	+	0.473372i	$0.843037\pi$
$762$	15.2635	0.552937
$763$	7.95571	0.288016
$764$	−20.2640	−0.733126
$765$	−3.84425	−0.138989
$766$	−59.8976	−2.16419
$767$	−70.6765	−2.55198
$768$	18.8528	0.680292
$769$	−13.0936	−0.472169	−0.236084	−	0.971733i	$-0.575864\pi$
$769$	−13.0936	−0.472169	−0.236084	+	0.971733i	$0.575864\pi$
$770$	−33.2234	−1.19729
$771$	16.8820	0.607990
$772$	10.6836	0.384510
$773$	23.5321	0.846392	0.423196	−	0.906038i	$-0.360908\pi$
$773$	23.5321	0.846392	0.423196	+	0.906038i	$0.360908\pi$
$774$	−13.8613	−0.498235
$775$	−18.2789	−0.656599
$776$	−5.05358	−0.181413
$777$	7.69916	0.276206
$778$	57.6269	2.06602
$779$	−20.9279	−0.749820
$780$	13.0282	0.466485
$781$	76.4645	2.73611
$782$	−7.56256	−0.270436
$783$	−32.1701	−1.14967
$784$	24.0184	0.857800
$785$	−0.383104	−0.0136736
$786$	16.0752	0.573383
$787$	−14.8143	−0.528072	−0.264036	−	0.964513i	$-0.585054\pi$
$787$	−14.8143	−0.528072	−0.264036	+	0.964513i	$0.585054\pi$
$788$	21.4906	0.765572
$789$	20.4260	0.727186
$790$	24.6845	0.878235
$791$	−6.17539	−0.219572
$792$	17.1404	0.609058
$793$	21.4036	0.760065
$794$	−8.91048	−0.316221
$795$	−9.88705	−0.350658
$796$	−19.8749	−0.704447
$797$	8.02895	0.284400	0.142200	−	0.989838i	$-0.454582\pi$
$797$	8.02895	0.284400	0.142200	+	0.989838i	$0.454582\pi$
$798$	−6.76606	−0.239516
$799$	−1.13290	−0.0400792
$800$	−9.86133	−0.348651
$801$	18.7848	0.663728
$802$	54.7003	1.93153
$803$	81.8188	2.88732
$804$	0.167415	0.00590428
$805$	23.4244	0.825602
$806$	−83.9009	−2.95528
$807$	3.64994	0.128484
$808$	−12.0983	−0.425618
$809$	−46.4788	−1.63411	−0.817054	−	0.576561i	$-0.804394\pi$
$809$	−46.4788	−1.63411	−0.817054	+	0.576561i	$0.804394\pi$
$810$	5.35319	0.188092
$811$	10.5853	0.371701	0.185850	−	0.982578i	$-0.440496\pi$
$811$	10.5853	0.371701	0.185850	+	0.982578i	$0.440496\pi$
$812$	−9.69982	−0.340397
$813$	−3.55389	−0.124640
$814$	−44.9611	−1.57589
$815$	34.6186	1.21264
$816$	−3.57213	−0.125050
$817$	10.5168	0.367935
$818$	33.4183	1.16844
$819$	14.9518	0.522460
$820$	−20.7944	−0.726173
$821$	56.9970	1.98921	0.994605	−	0.103738i	$-0.0330804\pi$
$821$	56.9970	1.98921	0.994605	+	0.103738i	$0.0330804\pi$
$822$	4.87105	0.169897
$823$	−17.2178	−0.600175	−0.300087	−	0.953912i	$-0.597016\pi$
$823$	−17.2178	−0.600175	−0.300087	+	0.953912i	$0.597016\pi$
$824$	−9.99055	−0.348037
$825$	9.15797	0.318840
$826$	36.4709	1.26899
$827$	−7.24892	−0.252070	−0.126035	−	0.992026i	$-0.540225\pi$
$827$	−7.24892	−0.252070	−0.126035	+	0.992026i	$0.540225\pi$
$828$	12.3164	0.428024
$829$	−27.9776	−0.971704	−0.485852	−	0.874041i	$-0.661491\pi$
$829$	−27.9776	−0.971704	−0.485852	+	0.874041i	$0.661491\pi$
$830$	−9.78552	−0.339660
$831$	−19.2208	−0.666762
$832$	4.55639	0.157964
$833$	−3.47587	−0.120432
$834$	−2.16720	−0.0750440
$835$	−43.1264	−1.49245
$836$	13.2537	0.458389
$837$	48.1654	1.66484
$838$	−44.8276	−1.54854
$839$	21.1525	0.730267	0.365134	−	0.930955i	$-0.381023\pi$
$839$	21.1525	0.730267	0.365134	+	0.930955i	$0.381023\pi$
$840$	6.59658	0.227604
$841$	13.0388	0.449612
$842$	40.0859	1.38145
$843$	25.3097	0.871713
$844$	−18.8495	−0.648827
$845$	31.0140	1.06691
$846$	5.50047	0.189110
$847$	−19.6552	−0.675361
$848$	19.0834	0.655328
$849$	14.7004	0.504517
$850$	2.36358	0.0810702
$851$	31.7002	1.08667
$852$	15.4729	0.530094
$853$	45.5957	1.56117	0.780583	−	0.625052i	$-0.214922\pi$
$853$	45.5957	1.56117	0.780583	+	0.625052i	$0.214922\pi$
$854$	−11.0448	−0.377946
$855$	−14.1611	−0.484299
$856$	31.0183	1.06018
$857$	−21.6076	−0.738103	−0.369051	−	0.929409i	$-0.620317\pi$
$857$	−21.6076	−0.738103	−0.369051	+	0.929409i	$0.620317\pi$
$858$	42.0354	1.43506
$859$	1.15504	0.0394094	0.0197047	−	0.999806i	$-0.493727\pi$
$859$	1.15504	0.0394094	0.0197047	+	0.999806i	$0.493727\pi$
$860$	10.4497	0.356332
$861$	11.4890	0.391545
$862$	−44.9068	−1.52953
$863$	−26.3243	−0.896089	−0.448044	−	0.894011i	$-0.647879\pi$
$863$	−26.3243	−0.896089	−0.448044	+	0.894011i	$0.647879\pi$
$864$	25.9848	0.884020
$865$	34.3405	1.16761
$866$	−37.2025	−1.26419
$867$	−16.2685	−0.552508
$868$	14.5227	0.492931
$869$	26.7154	0.906257
$870$	29.1369	0.987833
$871$	0.836805	0.0283540
$872$	9.22459	0.312384
$873$	−5.95572	−0.201571
$874$	−27.8582	−0.942319
$875$	12.1190	0.409698
$876$	16.5564	0.559389
$877$	22.7315	0.767587	0.383794	−	0.923419i	$-0.374617\pi$
$877$	22.7315	0.767587	0.383794	+	0.923419i	$0.374617\pi$
$878$	13.2579	0.447432
$879$	−0.472152	−0.0159253
$880$	−64.6132	−2.17811
$881$	−28.9219	−0.974403	−0.487202	−	0.873290i	$-0.661982\pi$
$881$	−28.9219	−0.974403	−0.487202	+	0.873290i	$0.661982\pi$
$882$	16.8760	0.568246
$883$	9.84749	0.331395	0.165697	−	0.986177i	$-0.447013\pi$
$883$	9.84749	0.331395	0.165697	+	0.986177i	$0.447013\pi$
$884$	3.63910	0.122396
$885$	−36.7480	−1.23527
$886$	−31.5227	−1.05903
$887$	16.5706	0.556388	0.278194	−	0.960525i	$-0.410264\pi$
$887$	16.5706	0.556388	0.278194	+	0.960525i	$0.410264\pi$
$888$	8.92712	0.299575
$889$	−13.2057	−0.442906
$890$	−42.2180	−1.41515
$891$	5.79362	0.194094
$892$	15.5935	0.522110
$893$	−4.17328	−0.139654
$894$	22.7392	0.760512
$895$	57.1078	1.90890
$896$	−17.8737	−0.597118
$897$	−29.6373	−0.989562
$898$	−17.1926	−0.573724
$899$	−62.9408	−2.09919
$900$	−3.84933	−0.128311
$901$	−2.76170	−0.0920054
$902$	−67.0930	−2.23395
$903$	−5.77351	−0.192130
$904$	−7.16032	−0.238149
$905$	10.8900	0.361997
$906$	−37.6355	−1.25036
$907$	27.9878	0.929319	0.464660	−	0.885489i	$-0.346177\pi$
$907$	27.9878	0.929319	0.464660	+	0.885489i	$0.346177\pi$
$908$	−6.13125	−0.203473
$909$	−14.2581	−0.472910
$910$	−33.6036	−1.11395
$911$	−50.1247	−1.66071	−0.830353	−	0.557238i	$-0.811861\pi$
$911$	−50.1247	−1.66071	−0.830353	+	0.557238i	$0.811861\pi$
$912$	−13.1587	−0.435728
$913$	−10.5906	−0.350498
$914$	−31.3783	−1.03790
$915$	11.1287	0.367905
$916$	16.5900	0.548149
$917$	−13.9080	−0.459283
$918$	−6.22809	−0.205557
$919$	15.3693	0.506987	0.253493	−	0.967337i	$-0.418420\pi$
$919$	15.3693	0.506987	0.253493	+	0.967337i	$0.418420\pi$
$920$	27.1604	0.895453
$921$	−5.14035	−0.169380
$922$	61.9489	2.04018
$923$	77.3395	2.54566
$924$	−7.27603	−0.239364
$925$	−9.90748	−0.325756
$926$	34.7786	1.14290
$927$	−11.7740	−0.386709
$928$	−33.9560	−1.11466
$929$	−5.50243	−0.180529	−0.0902645	−	0.995918i	$-0.528771\pi$
$929$	−5.50243	−0.180529	−0.0902645	+	0.995918i	$0.528771\pi$
$930$	−43.6240	−1.43049
$931$	−12.8041	−0.419636
$932$	8.23297	0.269680
$933$	32.8507	1.07548
$934$	−14.4865	−0.474011
$935$	9.35062	0.305798
$936$	17.3366	0.566663
$937$	33.3298	1.08884	0.544419	−	0.838814i	$-0.316750\pi$
$937$	33.3298	1.08884	0.544419	+	0.838814i	$0.316750\pi$
$938$	−0.431813	−0.0140992
$939$	6.16823	0.201292
$940$	−4.14667	−0.135249
$941$	−42.8619	−1.39726	−0.698630	−	0.715483i	$-0.746207\pi$
$941$	−42.8619	−1.39726	−0.698630	+	0.715483i	$0.746207\pi$
$942$	−0.250126	−0.00814955
$943$	47.3044	1.54044
$944$	70.9290	2.30854
$945$	19.2910	0.627536
$946$	33.7158	1.09620
$947$	5.45022	0.177108	0.0885542	−	0.996071i	$-0.471775\pi$
$947$	5.45022	0.177108	0.0885542	+	0.996071i	$0.471775\pi$
$948$	5.40598	0.175578
$949$	82.7551	2.68635
$950$	8.70674	0.282484
$951$	−23.2222	−0.753030
$952$	1.84259	0.0597185
$953$	31.6295	1.02458	0.512291	−	0.858812i	$-0.328797\pi$
$953$	31.6295	1.02458	0.512291	+	0.858812i	$0.328797\pi$
$954$	13.4086	0.434119
$955$	−52.6640	−1.70417
$956$	−14.4846	−0.468464
$957$	31.5341	1.01935
$958$	11.9132	0.384897
$959$	−4.21435	−0.136089
$960$	2.36908	0.0764617
$961$	63.2356	2.03986
$962$	−45.4757	−1.46619
$963$	36.5555	1.17799
$964$	−7.38309	−0.237793
$965$	27.7654	0.893801
$966$	15.2936	0.492065
$967$	−16.7423	−0.538396	−0.269198	−	0.963085i	$-0.586759\pi$
$967$	−16.7423	−0.538396	−0.269198	+	0.963085i	$0.586759\pi$
$968$	−22.7901	−0.732501
$969$	1.90428	0.0611744
$970$	13.3852	0.429774
$971$	−1.27275	−0.0408445	−0.0204222	−	0.999791i	$-0.506501\pi$
$971$	−1.27275	−0.0408445	−0.0204222	+	0.999791i	$0.506501\pi$
$972$	16.1985	0.519568
$973$	1.87503	0.0601106
$974$	13.5531	0.434269
$975$	9.26277	0.296646
$976$	−21.4801	−0.687561
$977$	−8.03932	−0.257201	−0.128600	−	0.991697i	$-0.541048\pi$
$977$	−8.03932	−0.257201	−0.128600	+	0.991697i	$0.541048\pi$
$978$	22.6022	0.722740
$979$	−45.6915	−1.46031
$980$	−12.7224	−0.406403
$981$	10.8713	0.347095
$982$	−19.6476	−0.626981
$983$	34.9948	1.11616	0.558081	−	0.829786i	$-0.311538\pi$
$983$	34.9948	1.11616	0.558081	+	0.829786i	$0.311538\pi$
$984$	13.3214	0.424672
$985$	55.8518	1.77959
$986$	8.13864	0.259187
$987$	2.29105	0.0729250
$988$	13.4054	0.426482
$989$	−23.7716	−0.755891
$990$	−45.3991	−1.44288
$991$	30.9377	0.982767	0.491383	−	0.870943i	$-0.336491\pi$
$991$	30.9377	0.982767	0.491383	+	0.870943i	$0.336491\pi$
$992$	50.8393	1.61415
$993$	−13.2970	−0.421969
$994$	−39.9092	−1.26584
$995$	−51.6527	−1.63750
$996$	−2.14306	−0.0679054
$997$	−37.0442	−1.17320	−0.586601	−	0.809876i	$-0.699534\pi$
$997$	−37.0442	−1.17320	−0.586601	+	0.809876i	$0.699534\pi$
$998$	−24.9941	−0.791173
$999$	26.1064	0.825970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.18	✓	25
3.2	odd	2		4923.2.a.n.1.8		25
4.3	odd	2		8752.2.a.v.1.11		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.18	✓	25	1.1	even	1	trivial
4923.2.a.n.1.8		25	3.2	odd	2
8752.2.a.v.1.11		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)

\(f(q)\)	\(=\)	\(q+1.73479 q^{2} +0.987380 q^{3} +1.00948 q^{4} +2.62354 q^{5} +1.71289 q^{6} -1.48197 q^{7} -1.71833 q^{8} -2.02508 q^{9} +O(q^{10})\)	\(q+1.73479 q^{2} +0.987380 q^{3} +1.00948 q^{4} +2.62354 q^{5} +1.71289 q^{6} -1.48197 q^{7} -1.71833 q^{8} -2.02508 q^{9} +4.55128 q^{10} +4.92574 q^{11} +0.996745 q^{12} +4.98211 q^{13} -2.57090 q^{14} +2.59043 q^{15} -4.99991 q^{16} +0.723571 q^{17} -3.51308 q^{18} +2.66542 q^{19} +2.64842 q^{20} -1.46327 q^{21} +8.54511 q^{22} -6.02478 q^{23} -1.69665 q^{24} +1.88297 q^{25} +8.64290 q^{26} -4.96166 q^{27} -1.49602 q^{28} +6.48373 q^{29} +4.49385 q^{30} -9.70750 q^{31} -5.23711 q^{32} +4.86358 q^{33} +1.25524 q^{34} -3.88801 q^{35} -2.04429 q^{36} -5.26162 q^{37} +4.62394 q^{38} +4.91924 q^{39} -4.50812 q^{40} -7.85163 q^{41} -2.53846 q^{42} +3.94563 q^{43} +4.97246 q^{44} -5.31288 q^{45} -10.4517 q^{46} -1.56571 q^{47} -4.93681 q^{48} -4.80377 q^{49} +3.26655 q^{50} +0.714440 q^{51} +5.02936 q^{52} -3.81676 q^{53} -8.60743 q^{54} +12.9229 q^{55} +2.54652 q^{56} +2.63178 q^{57} +11.2479 q^{58} -14.1861 q^{59} +2.61500 q^{60} +4.29610 q^{61} -16.8404 q^{62} +3.00111 q^{63} +0.914550 q^{64} +13.0708 q^{65} +8.43727 q^{66} +0.167962 q^{67} +0.730434 q^{68} -5.94875 q^{69} -6.74486 q^{70} +15.5235 q^{71} +3.47976 q^{72} +16.6105 q^{73} -9.12780 q^{74} +1.85921 q^{75} +2.69070 q^{76} -7.29979 q^{77} +8.53382 q^{78} +5.42363 q^{79} -13.1175 q^{80} +1.17619 q^{81} -13.6209 q^{82} -2.15006 q^{83} -1.47715 q^{84} +1.89832 q^{85} +6.84482 q^{86} +6.40191 q^{87} -8.46406 q^{88} -9.27607 q^{89} -9.21672 q^{90} -7.38333 q^{91} -6.08193 q^{92} -9.58500 q^{93} -2.71617 q^{94} +6.99285 q^{95} -5.17102 q^{96} +2.94098 q^{97} -8.33351 q^{98} -9.97502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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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