LMFDB - Embedded newform 547.2.a.c.1.11

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			1.11
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)

$f(q)$	$=$	$q-0.106981 q^{2} +0.649055 q^{3} -1.98856 q^{4} -2.10046 q^{5} -0.0694367 q^{6} +0.493203 q^{7} +0.426701 q^{8} -2.57873 q^{9} +O(q^{10})$	\(q-0.106981 q^{2} +0.649055 q^{3} -1.98856 q^{4} -2.10046 q^{5} -0.0694367 q^{6} +0.493203 q^{7} +0.426701 q^{8} -2.57873 q^{9} +0.224710 q^{10} +5.42323 q^{11} -1.29068 q^{12} +1.33548 q^{13} -0.0527635 q^{14} -1.36332 q^{15} +3.93146 q^{16} +3.05264 q^{17} +0.275876 q^{18} +5.61982 q^{19} +4.17689 q^{20} +0.320116 q^{21} -0.580184 q^{22} +3.92639 q^{23} +0.276952 q^{24} -0.588056 q^{25} -0.142872 q^{26} -3.62090 q^{27} -0.980762 q^{28} -2.34163 q^{29} +0.145849 q^{30} +5.46702 q^{31} -1.27399 q^{32} +3.51997 q^{33} -0.326575 q^{34} -1.03596 q^{35} +5.12794 q^{36} +2.01724 q^{37} -0.601216 q^{38} +0.866801 q^{39} -0.896269 q^{40} -1.47915 q^{41} -0.0342464 q^{42} +1.71874 q^{43} -10.7844 q^{44} +5.41652 q^{45} -0.420050 q^{46} +10.7954 q^{47} +2.55173 q^{48} -6.75675 q^{49} +0.0629110 q^{50} +1.98133 q^{51} -2.65568 q^{52} -0.235550 q^{53} +0.387369 q^{54} -11.3913 q^{55} +0.210450 q^{56} +3.64757 q^{57} +0.250511 q^{58} -10.5854 q^{59} +2.71103 q^{60} -6.86905 q^{61} -0.584869 q^{62} -1.27184 q^{63} -7.72663 q^{64} -2.80513 q^{65} -0.376571 q^{66} +5.66862 q^{67} -6.07034 q^{68} +2.54844 q^{69} +0.110828 q^{70} +13.6646 q^{71} -1.10035 q^{72} -11.5461 q^{73} -0.215807 q^{74} -0.381681 q^{75} -11.1753 q^{76} +2.67475 q^{77} -0.0927315 q^{78} +13.3971 q^{79} -8.25789 q^{80} +5.38602 q^{81} +0.158242 q^{82} +15.9517 q^{83} -0.636568 q^{84} -6.41195 q^{85} -0.183873 q^{86} -1.51985 q^{87} +2.31410 q^{88} +10.7028 q^{89} -0.579466 q^{90} +0.658664 q^{91} -7.80784 q^{92} +3.54840 q^{93} -1.15490 q^{94} -11.8042 q^{95} -0.826892 q^{96} -8.23233 q^{97} +0.722846 q^{98} -13.9850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.106981	−0.0756472	−0.0378236	−	0.999284i	$-0.512042\pi$
$2$	−0.106981	−0.0756472	−0.0378236	+	0.999284i	$0.512042\pi$
$3$	0.649055	0.374732	0.187366	−	0.982290i	$-0.440005\pi$
$3$	0.649055	0.374732	0.187366	+	0.982290i	$0.440005\pi$
$4$	−1.98856	−0.994278
$5$	−2.10046	−0.939356	−0.469678	−	0.882838i	$-0.655630\pi$
$5$	−2.10046	−0.939356	−0.469678	+	0.882838i	$0.655630\pi$
$6$	−0.0694367	−0.0283474
$7$	0.493203	0.186413	0.0932067	−	0.995647i	$-0.470288\pi$
$7$	0.493203	0.186413	0.0932067	+	0.995647i	$0.470288\pi$
$8$	0.426701	0.150862
$9$	−2.57873	−0.859576
$10$	0.224710	0.0710596
$11$	5.42323	1.63517	0.817583	−	0.575811i	$-0.195314\pi$
$11$	5.42323	1.63517	0.817583	+	0.575811i	$0.195314\pi$
$12$	−1.29068	−0.372588
$13$	1.33548	0.370396	0.185198	−	0.982701i	$-0.440707\pi$
$13$	1.33548	0.370396	0.185198	+	0.982701i	$0.440707\pi$
$14$	−0.0527635	−0.0141016
$15$	−1.36332	−0.352007
$16$	3.93146	0.982865
$17$	3.05264	0.740373	0.370187	−	0.928957i	$-0.379294\pi$
$17$	3.05264	0.740373	0.370187	+	0.928957i	$0.379294\pi$
$18$	0.275876	0.0650245
$19$	5.61982	1.28928	0.644638	−	0.764488i	$-0.277008\pi$
$19$	5.61982	1.28928	0.644638	+	0.764488i	$0.277008\pi$
$20$	4.17689	0.933980
$21$	0.320116	0.0698551
$22$	−0.580184	−0.123696
$23$	3.92639	0.818709	0.409354	−	0.912375i	$-0.365754\pi$
$23$	3.92639	0.818709	0.409354	+	0.912375i	$0.365754\pi$
$24$	0.276952	0.0565326
$25$	−0.588056	−0.117611
$26$	−0.142872	−0.0280194
$27$	−3.62090	−0.696843
$28$	−0.980762	−0.185347
$29$	−2.34163	−0.434830	−0.217415	−	0.976079i	$-0.569763\pi$
$29$	−2.34163	−0.434830	−0.217415	+	0.976079i	$0.569763\pi$
$30$	0.145849	0.0266283
$31$	5.46702	0.981907	0.490953	−	0.871186i	$-0.336649\pi$
$31$	5.46702	0.981907	0.490953	+	0.871186i	$0.336649\pi$
$32$	−1.27399	−0.225213
$33$	3.51997	0.612749
$34$	−0.326575	−0.0560072
$35$	−1.03596	−0.175108
$36$	5.12794	0.854657
$37$	2.01724	0.331632	0.165816	−	0.986157i	$-0.446974\pi$
$37$	2.01724	0.331632	0.165816	+	0.986157i	$0.446974\pi$
$38$	−0.601216	−0.0975300
$39$	0.866801	0.138799
$40$	−0.896269	−0.141713
$41$	−1.47915	−0.231005	−0.115502	−	0.993307i	$-0.536848\pi$
$41$	−1.47915	−0.231005	−0.115502	+	0.993307i	$0.536848\pi$
$42$	−0.0342464	−0.00528434
$43$	1.71874	0.262106	0.131053	−	0.991375i	$-0.458164\pi$
$43$	1.71874	0.262106	0.131053	+	0.991375i	$0.458164\pi$
$44$	−10.7844	−1.62581
$45$	5.41652	0.807447
$46$	−0.420050	−0.0619330
$47$	10.7954	1.57467	0.787334	−	0.616526i	$-0.211461\pi$
$47$	10.7954	1.57467	0.787334	+	0.616526i	$0.211461\pi$
$48$	2.55173	0.368311
$49$	−6.75675	−0.965250
$50$	0.0629110	0.00889696
$51$	1.98133	0.277442
$52$	−2.65568	−0.368276
$53$	−0.235550	−0.0323552	−0.0161776	−	0.999869i	$-0.505150\pi$
$53$	−0.235550	−0.0323552	−0.0161776	+	0.999869i	$0.505150\pi$
$54$	0.387369	0.0527142
$55$	−11.3913	−1.53600
$56$	0.210450	0.0281226
$57$	3.64757	0.483133
$58$	0.250511	0.0328937
$59$	−10.5854	−1.37810	−0.689052	−	0.724712i	$-0.741973\pi$
$59$	−10.5854	−1.37810	−0.689052	+	0.724712i	$0.741973\pi$
$60$	2.71103	0.349992
$61$	−6.86905	−0.879491	−0.439746	−	0.898122i	$-0.644931\pi$
$61$	−6.86905	−0.879491	−0.439746	+	0.898122i	$0.644931\pi$
$62$	−0.584869	−0.0742785
$63$	−1.27184	−0.160236
$64$	−7.72663	−0.965829
$65$	−2.80513	−0.347933
$66$	−0.376571	−0.0463527
$67$	5.66862	0.692532	0.346266	−	0.938136i	$-0.387450\pi$
$67$	5.66862	0.692532	0.346266	+	0.938136i	$0.387450\pi$
$68$	−6.07034	−0.736137
$69$	2.54844	0.306797
$70$	0.110828	0.0132465
$71$	13.6646	1.62169	0.810843	−	0.585264i	$-0.199009\pi$
$71$	13.6646	1.62169	0.810843	+	0.585264i	$0.199009\pi$
$72$	−1.10035	−0.129677
$73$	−11.5461	−1.35137	−0.675685	−	0.737191i	$-0.736152\pi$
$73$	−11.5461	−1.35137	−0.675685	+	0.737191i	$0.736152\pi$
$74$	−0.215807	−0.0250870
$75$	−0.381681	−0.0440727
$76$	−11.1753	−1.28190
$77$	2.67475	0.304817
$78$	−0.0927315	−0.0104998
$79$	13.3971	1.50730	0.753648	−	0.657279i	$-0.228292\pi$
$79$	13.3971	1.50730	0.753648	+	0.657279i	$0.228292\pi$
$80$	−8.25789	−0.923260
$81$	5.38602	0.598446
$82$	0.158242	0.0174749
$83$	15.9517	1.75092	0.875462	−	0.483288i	$-0.160558\pi$
$83$	15.9517	1.75092	0.875462	+	0.483288i	$0.160558\pi$
$84$	−0.636568	−0.0694553
$85$	−6.41195	−0.695474
$86$	−0.183873	−0.0198276
$87$	−1.51985	−0.162945
$88$	2.31410	0.246683
$89$	10.7028	1.13449	0.567246	−	0.823549i	$-0.308009\pi$
$89$	10.7028	1.13449	0.567246	+	0.823549i	$0.308009\pi$
$90$	−0.579466	−0.0610811
$91$	0.658664	0.0690467
$92$	−7.80784	−0.814024
$93$	3.54840	0.367952
$94$	−1.15490	−0.119119
$95$	−11.8042	−1.21109
$96$	−0.826892	−0.0843944
$97$	−8.23233	−0.835867	−0.417933	−	0.908478i	$-0.637245\pi$
$97$	−8.23233	−0.835867	−0.417933	+	0.908478i	$0.637245\pi$
$98$	0.722846	0.0730185
$99$	−13.9850	−1.40555
$100$	1.16938	0.116938
$101$	2.05291	0.204272	0.102136	−	0.994770i	$-0.467432\pi$
$101$	2.05291	0.204272	0.102136	+	0.994770i	$0.467432\pi$
$102$	−0.211965	−0.0209877
$103$	−6.59981	−0.650298	−0.325149	−	0.945663i	$-0.605415\pi$
$103$	−6.59981	−0.650298	−0.325149	+	0.945663i	$0.605415\pi$
$104$	0.569851	0.0558785
$105$	−0.672392	−0.0656187
$106$	0.0251994	0.00244758
$107$	−7.71776	−0.746104	−0.373052	−	0.927811i	$-0.621689\pi$
$107$	−7.71776	−0.746104	−0.373052	+	0.927811i	$0.621689\pi$
$108$	7.20036	0.692855
$109$	8.85070	0.847744	0.423872	−	0.905722i	$-0.360671\pi$
$109$	8.85070	0.847744	0.423872	+	0.905722i	$0.360671\pi$
$110$	1.21866	0.116194
$111$	1.30930	0.124273
$112$	1.93901	0.183219
$113$	−1.61098	−0.151548	−0.0757742	−	0.997125i	$-0.524143\pi$
$113$	−1.61098	−0.151548	−0.0757742	+	0.997125i	$0.524143\pi$
$114$	−0.390222	−0.0365476
$115$	−8.24724	−0.769059
$116$	4.65646	0.432342
$117$	−3.44384	−0.318383
$118$	1.13244	0.104250
$119$	1.50557	0.138015
$120$	−0.581728	−0.0531043
$121$	18.4114	1.67377
$122$	0.734859	0.0665310
$123$	−0.960051	−0.0865649
$124$	−10.8715	−0.976288
$125$	11.7375	1.04983
$126$	0.136063	0.0121214
$127$	−18.4435	−1.63659	−0.818297	−	0.574795i	$-0.805082\pi$
$127$	−18.4435	−1.63659	−0.818297	+	0.574795i	$0.805082\pi$
$128$	3.37459	0.298275
$129$	1.11556	0.0982195
$130$	0.300096	0.0263202
$131$	0.0700687	0.00612193	0.00306097	−	0.999995i	$-0.499026\pi$
$131$	0.0700687	0.00612193	0.00306097	+	0.999995i	$0.499026\pi$
$132$	−6.99966	−0.609242
$133$	2.77171	0.240338
$134$	−0.606436	−0.0523881
$135$	7.60557	0.654583
$136$	1.30256	0.111694
$137$	−16.1390	−1.37885	−0.689425	−	0.724357i	$-0.742137\pi$
$137$	−16.1390	−1.37885	−0.689425	+	0.724357i	$0.742137\pi$
$138$	−0.272636	−0.0232083
$139$	8.39117	0.711729	0.355865	−	0.934537i	$-0.384186\pi$
$139$	8.39117	0.711729	0.355865	+	0.934537i	$0.384186\pi$
$140$	2.06005	0.174106
$141$	7.00680	0.590079
$142$	−1.46185	−0.122676
$143$	7.24262	0.605658
$144$	−10.1382	−0.844847
$145$	4.91851	0.408460
$146$	1.23522	0.102227
$147$	−4.38550	−0.361710
$148$	−4.01139	−0.329734
$149$	−5.26038	−0.430947	−0.215474	−	0.976510i	$-0.569130\pi$
$149$	−5.26038	−0.430947	−0.215474	+	0.976510i	$0.569130\pi$
$150$	0.0408327	0.00333398
$151$	17.1490	1.39556	0.697782	−	0.716310i	$-0.254170\pi$
$151$	17.1490	1.39556	0.697782	+	0.716310i	$0.254170\pi$
$152$	2.39798	0.194502
$153$	−7.87192	−0.636407
$154$	−0.286149	−0.0230585
$155$	−11.4833	−0.922359
$156$	−1.72368	−0.138005
$157$	−7.75151	−0.618638	−0.309319	−	0.950958i	$-0.600101\pi$
$157$	−7.75151	−0.618638	−0.309319	+	0.950958i	$0.600101\pi$
$158$	−1.43324	−0.114023
$159$	−0.152885	−0.0121245
$160$	2.67598	0.211555
$161$	1.93651	0.152618
$162$	−0.576203	−0.0452708
$163$	−15.3781	−1.20450	−0.602252	−	0.798306i	$-0.705730\pi$
$163$	−15.3781	−1.20450	−0.602252	+	0.798306i	$0.705730\pi$
$164$	2.94138	0.229683
$165$	−7.39358	−0.575589
$166$	−1.70653	−0.132452
$167$	20.8947	1.61688	0.808439	−	0.588580i	$-0.200313\pi$
$167$	20.8947	1.61688	0.808439	+	0.588580i	$0.200313\pi$
$168$	0.136594	0.0105384
$169$	−11.2165	−0.862807
$170$	0.685959	0.0526106
$171$	−14.4920	−1.10823
$172$	−3.41782	−0.260606
$173$	13.1899	1.00281	0.501403	−	0.865214i	$-0.332817\pi$
$173$	13.1899	1.00281	0.501403	+	0.865214i	$0.332817\pi$
$174$	0.162595	0.0123263
$175$	−0.290031	−0.0219243
$176$	21.3212	1.60715
$177$	−6.87052	−0.516420
$178$	−1.14500	−0.0858211
$179$	−22.3612	−1.67136	−0.835678	−	0.549220i	$-0.814925\pi$
$179$	−22.3612	−1.67136	−0.835678	+	0.549220i	$0.814925\pi$
$180$	−10.7711	−0.802827
$181$	−14.6153	−1.08635	−0.543174	−	0.839620i	$-0.682778\pi$
$181$	−14.6153	−1.08635	−0.543174	+	0.839620i	$0.682778\pi$
$182$	−0.0704647	−0.00522319
$183$	−4.45839	−0.329574
$184$	1.67539	0.123512
$185$	−4.23713	−0.311520
$186$	−0.379612	−0.0278345
$187$	16.5552	1.21063
$188$	−21.4672	−1.56566
$189$	−1.78584	−0.129901
$190$	1.26283	0.0916154
$191$	−0.977419	−0.0707236	−0.0353618	−	0.999375i	$-0.511258\pi$
$191$	−0.977419	−0.0707236	−0.0353618	+	0.999375i	$0.511258\pi$
$192$	−5.01501	−0.361927
$193$	−13.1179	−0.944251	−0.472125	−	0.881531i	$-0.656513\pi$
$193$	−13.1179	−0.944251	−0.472125	+	0.881531i	$0.656513\pi$
$194$	0.880706	0.0632310
$195$	−1.82068	−0.130382
$196$	13.4362	0.959726
$197$	7.34184	0.523084	0.261542	−	0.965192i	$-0.415769\pi$
$197$	7.34184	0.523084	0.261542	+	0.965192i	$0.415769\pi$
$198$	1.49614	0.106326
$199$	−20.4950	−1.45285	−0.726427	−	0.687244i	$-0.758820\pi$
$199$	−20.4950	−1.45285	−0.726427	+	0.687244i	$0.758820\pi$
$200$	−0.250924	−0.0177430
$201$	3.67924	0.259514
$202$	−0.219622	−0.0154526
$203$	−1.15490	−0.0810581
$204$	−3.93998	−0.275854
$205$	3.10690	0.216996
$206$	0.706056	0.0491932
$207$	−10.1251	−0.703742
$208$	5.25039	0.364049
$209$	30.4776	2.10818
$210$	0.0719334	0.00496387
$211$	−4.00330	−0.275599	−0.137799	−	0.990460i	$-0.544003\pi$
$211$	−4.00330	−0.275599	−0.137799	+	0.990460i	$0.544003\pi$
$212$	0.468404	0.0321701
$213$	8.86906	0.607698
$214$	0.825655	0.0564406
$215$	−3.61016	−0.246211
$216$	−1.54504	−0.105127
$217$	2.69635	0.183040
$218$	−0.946860	−0.0641294
$219$	−7.49406	−0.506402
$220$	22.6522	1.52721
$221$	4.07674	0.274231
$222$	−0.140070	−0.00940091
$223$	5.31598	0.355984	0.177992	−	0.984032i	$-0.443040\pi$
$223$	5.31598	0.355984	0.177992	+	0.984032i	$0.443040\pi$
$224$	−0.628338	−0.0419826
$225$	1.51644	0.101096
$226$	0.172345	0.0114642
$227$	10.4150	0.691268	0.345634	−	0.938369i	$-0.387664\pi$
$227$	10.4150	0.691268	0.345634	+	0.938369i	$0.387664\pi$
$228$	−7.25340	−0.480368
$229$	10.8225	0.715172	0.357586	−	0.933880i	$-0.383600\pi$
$229$	10.8225	0.715172	0.357586	+	0.933880i	$0.383600\pi$
$230$	0.882300	0.0581771
$231$	1.73606	0.114225
$232$	−0.999176	−0.0655991
$233$	14.4689	0.947891	0.473946	−	0.880554i	$-0.342829\pi$
$233$	14.4689	0.947891	0.473946	+	0.880554i	$0.342829\pi$
$234$	0.368427	0.0240848
$235$	−22.6753	−1.47917
$236$	21.0497	1.37022
$237$	8.69548	0.564832
$238$	−0.161068	−0.0104405
$239$	14.6986	0.950776	0.475388	−	0.879776i	$-0.342308\pi$
$239$	14.6986	0.950776	0.475388	+	0.879776i	$0.342308\pi$
$240$	−5.35982	−0.345975
$241$	−11.8481	−0.763204	−0.381602	−	0.924327i	$-0.624627\pi$
$241$	−11.8481	−0.763204	−0.381602	+	0.924327i	$0.624627\pi$
$242$	−1.96968	−0.126616
$243$	14.3585	0.921100
$244$	13.6595	0.874458
$245$	14.1923	0.906713
$246$	0.102708	0.00654839
$247$	7.50516	0.477542
$248$	2.33278	0.148132
$249$	10.3535	0.656127
$250$	−1.25569	−0.0794170
$251$	−29.7811	−1.87976	−0.939882	−	0.341500i	$-0.889065\pi$
$251$	−29.7811	−1.87976	−0.939882	+	0.341500i	$0.889065\pi$
$252$	2.52912	0.159319
$253$	21.2937	1.33872
$254$	1.97311	0.123804
$255$	−4.16171	−0.260616
$256$	15.0922	0.943265
$257$	17.8819	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$257$	17.8819	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$258$	−0.119344	−0.00743003
$259$	0.994908	0.0618206
$260$	5.57815	0.345942
$261$	6.03843	0.373770
$262$	−0.00749604	−0.000463107 0
$263$	12.4323	0.766610	0.383305	−	0.923622i	$-0.374786\pi$
$263$	12.4323	0.766610	0.383305	+	0.923622i	$0.374786\pi$
$264$	1.50198	0.0924402
$265$	0.494763	0.0303931
$266$	−0.296522	−0.0181809
$267$	6.94669	0.425130
$268$	−11.2724	−0.688569
$269$	4.42443	0.269762	0.134881	−	0.990862i	$-0.456935\pi$
$269$	4.42443	0.269762	0.134881	+	0.990862i	$0.456935\pi$
$270$	−0.813654	−0.0495174
$271$	1.86417	0.113240	0.0566201	−	0.998396i	$-0.481968\pi$
$271$	1.86417	0.113240	0.0566201	+	0.998396i	$0.481968\pi$
$272$	12.0013	0.727687
$273$	0.427509	0.0258740
$274$	1.72657	0.104306
$275$	−3.18916	−0.192314
$276$	−5.06772	−0.305041
$277$	13.6838	0.822181	0.411091	−	0.911594i	$-0.365148\pi$
$277$	13.6838	0.822181	0.411091	+	0.911594i	$0.365148\pi$
$278$	−0.897698	−0.0538403
$279$	−14.0980	−0.844023
$280$	−0.442043	−0.0264171
$281$	3.51406	0.209631	0.104815	−	0.994492i	$-0.466575\pi$
$281$	3.51406	0.209631	0.104815	+	0.994492i	$0.466575\pi$
$282$	−0.749596	−0.0446378
$283$	−19.3392	−1.14959	−0.574797	−	0.818296i	$-0.694919\pi$
$283$	−19.3392	−1.14959	−0.574797	+	0.818296i	$0.694919\pi$
$284$	−27.1727	−1.61241
$285$	−7.66159	−0.453833
$286$	−0.774825	−0.0458164
$287$	−0.729523	−0.0430624
$288$	3.28528	0.193587
$289$	−7.68140	−0.451847
$290$	−0.526189	−0.0308989
$291$	−5.34324	−0.313226
$292$	22.9601	1.34364
$293$	−15.6698	−0.915439	−0.457719	−	0.889097i	$-0.651334\pi$
$293$	−15.6698	−0.915439	−0.457719	+	0.889097i	$0.651334\pi$
$294$	0.469167	0.0273624
$295$	22.2343	1.29453
$296$	0.860757	0.0500305
$297$	−19.6370	−1.13945
$298$	0.562763	0.0326000
$299$	5.24362	0.303246
$300$	0.758993	0.0438205
$301$	0.847690	0.0488600
$302$	−1.83462	−0.105571
$303$	1.33245	0.0765472
$304$	22.0941	1.26718
$305$	14.4282	0.826155
$306$	0.842148	0.0481424
$307$	27.8779	1.59107	0.795536	−	0.605906i	$-0.207189\pi$
$307$	27.8779	1.59107	0.795536	+	0.605906i	$0.207189\pi$
$308$	−5.31890	−0.303072
$309$	−4.28364	−0.243688
$310$	1.22850	0.0697739
$311$	−18.7487	−1.06314	−0.531570	−	0.847014i	$-0.678398\pi$
$311$	−18.7487	−1.06314	−0.531570	+	0.847014i	$0.678398\pi$
$312$	0.369865	0.0209395
$313$	20.5219	1.15997	0.579984	−	0.814628i	$-0.303059\pi$
$313$	20.5219	1.15997	0.579984	+	0.814628i	$0.303059\pi$
$314$	0.829267	0.0467982
$315$	2.67145	0.150519
$316$	−26.6409	−1.49867
$317$	8.81980	0.495369	0.247685	−	0.968841i	$-0.420330\pi$
$317$	8.81980	0.495369	0.247685	+	0.968841i	$0.420330\pi$
$318$	0.0163558	0.000917188 0
$319$	−12.6992	−0.711019
$320$	16.2295	0.907256
$321$	−5.00925	−0.279589
$322$	−0.207170	−0.0115451
$323$	17.1553	0.954545
$324$	−10.7104	−0.595022
$325$	−0.785338	−0.0435627
$326$	1.64517	0.0911173
$327$	5.74459	0.317677
$328$	−0.631155	−0.0348497
$329$	5.32432	0.293539
$330$	0.790974	0.0435417
$331$	7.96208	0.437636	0.218818	−	0.975766i	$-0.429780\pi$
$331$	7.96208	0.437636	0.218818	+	0.975766i	$0.429780\pi$
$332$	−31.7208	−1.74090
$333$	−5.20191	−0.285063
$334$	−2.23534	−0.122312
$335$	−11.9067	−0.650533
$336$	1.25852	0.0686581
$337$	−23.1994	−1.26375	−0.631876	−	0.775070i	$-0.717715\pi$
$337$	−23.1994	−1.26375	−0.631876	+	0.775070i	$0.717715\pi$
$338$	1.19995	0.0652689
$339$	−1.04562	−0.0567901
$340$	12.7505	0.691494
$341$	29.6489	1.60558
$342$	1.55037	0.0838345
$343$	−6.78488	−0.366349
$344$	0.733389	0.0395417
$345$	−5.35291	−0.288191
$346$	−1.41107	−0.0758595
$347$	13.3799	0.718271	0.359135	−	0.933285i	$-0.383072\pi$
$347$	13.3799	0.718271	0.359135	+	0.933285i	$0.383072\pi$
$348$	3.02230	0.162012
$349$	−4.33553	−0.232076	−0.116038	−	0.993245i	$-0.537019\pi$
$349$	−4.33553	−0.232076	−0.116038	+	0.993245i	$0.537019\pi$
$350$	0.0310279	0.00165851
$351$	−4.83565	−0.258108
$352$	−6.90916	−0.368260
$353$	16.8608	0.897411	0.448705	−	0.893680i	$-0.351885\pi$
$353$	16.8608	0.897411	0.448705	+	0.893680i	$0.351885\pi$
$354$	0.735017	0.0390657
$355$	−28.7019	−1.52334
$356$	−21.2831	−1.12800
$357$	0.977198	0.0517188
$358$	2.39223	0.126433
$359$	10.5231	0.555387	0.277694	−	0.960670i	$-0.410430\pi$
$359$	10.5231	0.555387	0.277694	+	0.960670i	$0.410430\pi$
$360$	2.31123	0.121813
$361$	12.5824	0.662230
$362$	1.56357	0.0821792
$363$	11.9500	0.627214
$364$	−1.30979	−0.0686516
$365$	24.2522	1.26942
$366$	0.476964	0.0249313
$367$	−22.6463	−1.18213	−0.591065	−	0.806624i	$-0.701292\pi$
$367$	−22.6463	−1.18213	−0.591065	+	0.806624i	$0.701292\pi$
$368$	15.4365	0.804681
$369$	3.81433	0.198566
$370$	0.453294	0.0235656
$371$	−0.116174	−0.00603145
$372$	−7.05619	−0.365846
$373$	−24.6880	−1.27830	−0.639148	−	0.769084i	$-0.720713\pi$
$373$	−24.6880	−1.27830	−0.639148	+	0.769084i	$0.720713\pi$
$374$	−1.77109	−0.0915810
$375$	7.61829	0.393407
$376$	4.60640	0.237557
$377$	−3.12721	−0.161059
$378$	0.191052	0.00982663
$379$	−7.56088	−0.388376	−0.194188	−	0.980964i	$-0.562207\pi$
$379$	−7.56088	−0.388376	−0.194188	+	0.980964i	$0.562207\pi$
$380$	23.4733	1.20416
$381$	−11.9708	−0.613285
$382$	0.104566	0.00535004
$383$	−12.9946	−0.663992	−0.331996	−	0.943281i	$-0.607722\pi$
$383$	−12.9946	−0.663992	−0.331996	+	0.943281i	$0.607722\pi$
$384$	2.19030	0.111773
$385$	−5.61822	−0.286331
$386$	1.40338	0.0714299
$387$	−4.43217	−0.225300
$388$	16.3705	0.831084
$389$	7.49062	0.379789	0.189895	−	0.981804i	$-0.439185\pi$
$389$	7.49062	0.379789	0.189895	+	0.981804i	$0.439185\pi$
$390$	0.194779	0.00986302
$391$	11.9858	0.606150
$392$	−2.88311	−0.145619
$393$	0.0454785	0.00229409
$394$	−0.785439	−0.0395699
$395$	−28.1402	−1.41589
$396$	27.8100	1.39751
$397$	−4.41646	−0.221656	−0.110828	−	0.993840i	$-0.535350\pi$
$397$	−4.41646	−0.221656	−0.110828	+	0.993840i	$0.535350\pi$
$398$	2.19258	0.109904
$399$	1.79899	0.0900624
$400$	−2.31192	−0.115596
$401$	−1.63103	−0.0814499	−0.0407250	−	0.999170i	$-0.512967\pi$
$401$	−1.63103	−0.0814499	−0.0407250	+	0.999170i	$0.512967\pi$
$402$	−0.393610	−0.0196315
$403$	7.30111	0.363694
$404$	−4.08232	−0.203103
$405$	−11.3131	−0.562154
$406$	0.123553	0.00613182
$407$	10.9399	0.542273
$408$	0.845435	0.0418553
$409$	−17.1384	−0.847438	−0.423719	−	0.905794i	$-0.639276\pi$
$409$	−17.1384	−0.847438	−0.423719	+	0.905794i	$0.639276\pi$
$410$	−0.332381	−0.0164151
$411$	−10.4751	−0.516699
$412$	13.1241	0.646577
$413$	−5.22076	−0.256897
$414$	1.08320	0.0532361
$415$	−33.5059	−1.64474
$416$	−1.70140	−0.0834178
$417$	5.44633	0.266708
$418$	−3.26053	−0.159478
$419$	12.0759	0.589944	0.294972	−	0.955506i	$-0.404690\pi$
$419$	12.0759	0.589944	0.294972	+	0.955506i	$0.404690\pi$
$420$	1.33709	0.0652432
$421$	15.8866	0.774265	0.387132	−	0.922024i	$-0.373466\pi$
$421$	15.8866	0.774265	0.387132	+	0.922024i	$0.373466\pi$
$422$	0.428279	0.0208483
$423$	−27.8384	−1.35355
$424$	−0.100509	−0.00488116
$425$	−1.79512	−0.0870762
$426$	−0.948823	−0.0459706
$427$	−3.38784	−0.163949
$428$	15.3472	0.741834
$429$	4.70086	0.226960
$430$	0.386219	0.0186251
$431$	−40.0820	−1.93068	−0.965341	−	0.260993i	$-0.915950\pi$
$431$	−40.0820	−1.93068	−0.965341	+	0.260993i	$0.915950\pi$
$432$	−14.2354	−0.684903
$433$	−27.3917	−1.31636	−0.658181	−	0.752860i	$-0.728674\pi$
$433$	−27.3917	−1.31636	−0.658181	+	0.752860i	$0.728674\pi$
$434$	−0.288460	−0.0138465
$435$	3.19238	0.153063
$436$	−17.6001	−0.842892
$437$	22.0656	1.05554
$438$	0.801724	0.0383079
$439$	−22.9705	−1.09632	−0.548162	−	0.836372i	$-0.684672\pi$
$439$	−22.9705	−1.09632	−0.548162	+	0.836372i	$0.684672\pi$
$440$	−4.86067	−0.231723
$441$	17.4238	0.829706
$442$	−0.436135	−0.0207448
$443$	−29.4665	−1.39999	−0.699997	−	0.714145i	$-0.746816\pi$
$443$	−29.4665	−1.39999	−0.699997	+	0.714145i	$0.746816\pi$
$444$	−2.60361	−0.123562
$445$	−22.4808	−1.06569
$446$	−0.568710	−0.0269292
$447$	−3.41428	−0.161490
$448$	−3.81080	−0.180043
$449$	11.7695	0.555438	0.277719	−	0.960662i	$-0.410422\pi$
$449$	11.7695	0.555438	0.277719	+	0.960662i	$0.410422\pi$
$450$	−0.162230	−0.00764761
$451$	−8.02178	−0.377731
$452$	3.20353	0.150681
$453$	11.1306	0.522963
$454$	−1.11421	−0.0522925
$455$	−1.38350	−0.0648594
$456$	1.55642	0.0728861
$457$	−19.3291	−0.904178	−0.452089	−	0.891973i	$-0.649321\pi$
$457$	−19.3291	−0.904178	−0.452089	+	0.891973i	$0.649321\pi$
$458$	−1.15781	−0.0541008
$459$	−11.0533	−0.515924
$460$	16.4001	0.764658
$461$	−13.0842	−0.609394	−0.304697	−	0.952449i	$-0.598555\pi$
$461$	−13.0842	−0.609394	−0.304697	+	0.952449i	$0.598555\pi$
$462$	−0.185726	−0.00864077
$463$	31.8576	1.48055	0.740275	−	0.672304i	$-0.234695\pi$
$463$	31.8576	1.48055	0.740275	+	0.672304i	$0.234695\pi$
$464$	−9.20604	−0.427379
$465$	−7.45328	−0.345638
$466$	−1.54791	−0.0717053
$467$	27.4348	1.26953	0.634766	−	0.772704i	$-0.281096\pi$
$467$	27.4348	1.26953	0.634766	+	0.772704i	$0.281096\pi$
$468$	6.84827	0.316561
$469$	2.79578	0.129097
$470$	2.42583	0.111895
$471$	−5.03116	−0.231824
$472$	−4.51680	−0.207903
$473$	9.32114	0.428586
$474$	−0.930253	−0.0427280
$475$	−3.30477	−0.151633
$476$	−2.99391	−0.137226
$477$	0.607419	0.0278118
$478$	−1.57248	−0.0719235
$479$	0.530850	0.0242552	0.0121276	−	0.999926i	$-0.496140\pi$
$479$	0.530850	0.0242552	0.0121276	+	0.999926i	$0.496140\pi$
$480$	1.73686	0.0792763
$481$	2.69398	0.122835
$482$	1.26753	0.0577342
$483$	1.25690	0.0571910
$484$	−36.6121	−1.66419
$485$	17.2917	0.785176
$486$	−1.53609	−0.0696786
$487$	−29.1736	−1.32198	−0.660990	−	0.750395i	$-0.729863\pi$
$487$	−29.1736	−1.32198	−0.660990	+	0.750395i	$0.729863\pi$
$488$	−2.93103	−0.132681
$489$	−9.98121	−0.451366
$490$	−1.51831	−0.0685903
$491$	−1.33706	−0.0603408	−0.0301704	−	0.999545i	$-0.509605\pi$
$491$	−1.33706	−0.0603408	−0.0301704	+	0.999545i	$0.509605\pi$
$492$	1.90911	0.0860695
$493$	−7.14815	−0.321937
$494$	−0.802912	−0.0361247
$495$	29.3750	1.32031
$496$	21.4934	0.965082
$497$	6.73941	0.302304
$498$	−1.10763	−0.0496342
$499$	−10.4066	−0.465864	−0.232932	−	0.972493i	$-0.574832\pi$
$499$	−10.4066	−0.465864	−0.232932	+	0.972493i	$0.574832\pi$
$500$	−23.3407	−1.04383
$501$	13.5618	0.605896
$502$	3.18602	0.142199
$503$	9.76116	0.435229	0.217614	−	0.976035i	$-0.430173\pi$
$503$	9.76116	0.435229	0.217614	+	0.976035i	$0.430173\pi$
$504$	−0.542694	−0.0241735
$505$	−4.31205	−0.191884
$506$	−2.27803	−0.101271
$507$	−7.28012	−0.323321
$508$	36.6759	1.62723
$509$	−26.9932	−1.19645	−0.598227	−	0.801327i	$-0.704128\pi$
$509$	−26.9932	−1.19645	−0.598227	+	0.801327i	$0.704128\pi$
$510$	0.445225	0.0197149
$511$	−5.69458	−0.251913
$512$	−8.36377	−0.369630
$513$	−20.3488	−0.898422
$514$	−1.91303	−0.0843803
$515$	13.8626	0.610861
$516$	−2.21835	−0.0976574
$517$	58.5459	2.57484
$518$	−0.106437	−0.00467655
$519$	8.56094	0.375784
$520$	−1.19695	−0.0524898
$521$	−12.5942	−0.551764	−0.275882	−	0.961192i	$-0.588970\pi$
$521$	−12.5942	−0.551764	−0.275882	+	0.961192i	$0.588970\pi$
$522$	−0.645999	−0.0282746
$523$	17.5745	0.768481	0.384240	−	0.923233i	$-0.374463\pi$
$523$	17.5745	0.768481	0.384240	+	0.923233i	$0.374463\pi$
$524$	−0.139336	−0.00608690
$525$	−0.188246	−0.00821574
$526$	−1.33003	−0.0579919
$527$	16.6888	0.726977
$528$	13.8386	0.602250
$529$	−7.58346	−0.329716
$530$	−0.0529304	−0.00229915
$531$	27.2969	1.18458
$532$	−5.51171	−0.238963
$533$	−1.97538	−0.0855632
$534$	−0.743166	−0.0321599
$535$	16.2109	0.700857
$536$	2.41880	0.104476
$537$	−14.5137	−0.626311
$538$	−0.473332	−0.0204068
$539$	−36.6434	−1.57834
$540$	−15.1241	−0.650837
$541$	−36.0347	−1.54925	−0.774625	−	0.632420i	$-0.782062\pi$
$541$	−36.0347	−1.54925	−0.774625	+	0.632420i	$0.782062\pi$
$542$	−0.199431	−0.00856630
$543$	−9.48615	−0.407090
$544$	−3.88904	−0.166741
$545$	−18.5906	−0.796333
$546$	−0.0457355	−0.00195730
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	32.0933	1.37096
$549$	17.7134	0.755989
$550$	0.341181	0.0145480
$551$	−13.1596	−0.560616
$552$	1.08742	0.0462838
$553$	6.60751	0.280980
$554$	−1.46391	−0.0621957
$555$	−2.75013	−0.116737
$556$	−16.6863	−0.707656
$557$	−9.76135	−0.413602	−0.206801	−	0.978383i	$-0.566305\pi$
$557$	−9.76135	−0.413602	−0.206801	+	0.978383i	$0.566305\pi$
$558$	1.50822	0.0638480
$559$	2.29535	0.0970830
$560$	−4.07282	−0.172108
$561$	10.7452	0.453663
$562$	−0.375938	−0.0158580
$563$	23.6853	0.998218	0.499109	−	0.866539i	$-0.333661\pi$
$563$	23.6853	0.998218	0.499109	+	0.866539i	$0.333661\pi$
$564$	−13.9334	−0.586702
$565$	3.38381	0.142358
$566$	2.06893	0.0869636
$567$	2.65640	0.111558
$568$	5.83068	0.244650
$569$	−8.39071	−0.351757	−0.175878	−	0.984412i	$-0.556277\pi$
$569$	−8.39071	−0.351757	−0.175878	+	0.984412i	$0.556277\pi$
$570$	0.819647	0.0343312
$571$	−14.7123	−0.615690	−0.307845	−	0.951437i	$-0.599608\pi$
$571$	−14.7123	−0.615690	−0.307845	+	0.951437i	$0.599608\pi$
$572$	−14.4024	−0.602193
$573$	−0.634399	−0.0265024
$574$	0.0780453	0.00325755
$575$	−2.30894	−0.0962893
$576$	19.9249	0.830203
$577$	−20.6874	−0.861229	−0.430615	−	0.902536i	$-0.641703\pi$
$577$	−20.6874	−0.861229	−0.430615	+	0.902536i	$0.641703\pi$
$578$	0.821767	0.0341810
$579$	−8.51427	−0.353841
$580$	−9.78073	−0.406123
$581$	7.86742	0.326395
$582$	0.571627	0.0236947
$583$	−1.27744	−0.0529062
$584$	−4.92673	−0.203870
$585$	7.23366	0.299075
$586$	1.67637	0.0692504
$587$	18.3978	0.759360	0.379680	−	0.925118i	$-0.376034\pi$
$587$	18.3978	0.759360	0.379680	+	0.925118i	$0.376034\pi$
$588$	8.72081	0.359640
$589$	30.7237	1.26595
$590$	−2.37865	−0.0979275
$591$	4.76526	0.196016
$592$	7.93069	0.325949
$593$	−4.27476	−0.175543	−0.0877716	−	0.996141i	$-0.527975\pi$
$593$	−4.27476	−0.175543	−0.0877716	+	0.996141i	$0.527975\pi$
$594$	2.10079	0.0861964
$595$	−3.16240	−0.129646
$596$	10.4606	0.428481
$597$	−13.3024	−0.544431
$598$	−0.560969	−0.0229397
$599$	−23.3231	−0.952957	−0.476478	−	0.879186i	$-0.658087\pi$
$599$	−23.3231	−0.952957	−0.476478	+	0.879186i	$0.658087\pi$
$600$	−0.162863	−0.00664887
$601$	−1.86001	−0.0758716	−0.0379358	−	0.999280i	$-0.512078\pi$
$601$	−1.86001	−0.0758716	−0.0379358	+	0.999280i	$0.512078\pi$
$602$	−0.0906870	−0.00369613
$603$	−14.6178	−0.595283
$604$	−34.1017	−1.38758
$605$	−38.6725	−1.57226
$606$	−0.142547	−0.00579058
$607$	2.00439	0.0813557	0.0406778	−	0.999172i	$-0.487048\pi$
$607$	2.00439	0.0813557	0.0406778	+	0.999172i	$0.487048\pi$
$608$	−7.15962	−0.290361
$609$	−0.749594	−0.0303751
$610$	−1.54354	−0.0624963
$611$	14.4170	0.583251
$612$	15.6537	0.632765
$613$	37.7597	1.52510	0.762549	−	0.646930i	$-0.223948\pi$
$613$	37.7597	1.52510	0.762549	+	0.646930i	$0.223948\pi$
$614$	−2.98241	−0.120360
$615$	2.01655	0.0813152
$616$	1.14132	0.0459851
$617$	−45.6774	−1.83890	−0.919451	−	0.393205i	$-0.871366\pi$
$617$	−45.6774	−1.83890	−0.919451	+	0.393205i	$0.871366\pi$
$618$	0.458269	0.0184343
$619$	12.7954	0.514292	0.257146	−	0.966373i	$-0.417218\pi$
$619$	12.7954	0.514292	0.257146	+	0.966373i	$0.417218\pi$
$620$	22.8351	0.917081
$621$	−14.2171	−0.570511
$622$	2.00576	0.0804236
$623$	5.27864	0.211484
$624$	3.40779	0.136421
$625$	−21.7139	−0.868556
$626$	−2.19546	−0.0877484
$627$	19.7816	0.790002
$628$	15.4143	0.615098
$629$	6.15789	0.245531
$630$	−0.285795	−0.0113863
$631$	−26.6777	−1.06202	−0.531011	−	0.847365i	$-0.678188\pi$
$631$	−26.6777	−1.06202	−0.531011	+	0.847365i	$0.678188\pi$
$632$	5.71657	0.227393
$633$	−2.59836	−0.103276
$634$	−0.943554	−0.0374733
$635$	38.7399	1.53734
$636$	0.304020	0.0120552
$637$	−9.02351	−0.357525
$638$	1.35858	0.0537866
$639$	−35.2372	−1.39396
$640$	−7.08821	−0.280186
$641$	−5.40348	−0.213425	−0.106712	−	0.994290i	$-0.534032\pi$
$641$	−5.40348	−0.213425	−0.106712	+	0.994290i	$0.534032\pi$
$642$	0.535896	0.0211501
$643$	45.8847	1.80952	0.904758	−	0.425926i	$-0.140052\pi$
$643$	45.8847	1.80952	0.904758	+	0.425926i	$0.140052\pi$
$644$	−3.85085	−0.151745
$645$	−2.34319	−0.0922630
$646$	−1.83529	−0.0722086
$647$	−39.9658	−1.57122	−0.785608	−	0.618724i	$-0.787650\pi$
$647$	−39.9658	−1.57122	−0.785608	+	0.618724i	$0.787650\pi$
$648$	2.29822	0.0902825
$649$	−57.4071	−2.25343
$650$	0.0840165	0.00329540
$651$	1.75008	0.0685911
$652$	30.5801	1.19761
$653$	−19.0410	−0.745134	−0.372567	−	0.928005i	$-0.621522\pi$
$653$	−19.0410	−0.745134	−0.372567	+	0.928005i	$0.621522\pi$
$654$	−0.614564	−0.0240314
$655$	−0.147177	−0.00575067
$656$	−5.81523	−0.227047
$657$	29.7743	1.16160
$658$	−0.569603	−0.0222054
$659$	−45.0530	−1.75502	−0.877509	−	0.479561i	$-0.840796\pi$
$659$	−45.0530	−1.75502	−0.877509	+	0.479561i	$0.840796\pi$
$660$	14.7025	0.572295
$661$	25.6704	0.998464	0.499232	−	0.866468i	$-0.333616\pi$
$661$	25.6704	0.998464	0.499232	+	0.866468i	$0.333616\pi$
$662$	−0.851794	−0.0331059
$663$	2.64603	0.102763
$664$	6.80659	0.264147
$665$	−5.82188	−0.225763
$666$	0.556507	0.0215642
$667$	−9.19416	−0.355999
$668$	−41.5502	−1.60762
$669$	3.45036	0.133399
$670$	1.27380	0.0492110
$671$	−37.2524	−1.43811
$672$	−0.407826	−0.0157322
$673$	44.8000	1.72691	0.863456	−	0.504425i	$-0.168295\pi$
$673$	44.8000	1.72691	0.863456	+	0.504425i	$0.168295\pi$
$674$	2.48190	0.0955993
$675$	2.12929	0.0819565
$676$	22.3046	0.857869
$677$	16.9021	0.649601	0.324801	−	0.945783i	$-0.394703\pi$
$677$	16.9021	0.649601	0.324801	+	0.945783i	$0.394703\pi$
$678$	0.111861	0.00429601
$679$	−4.06021	−0.155817
$680$	−2.73598	−0.104920
$681$	6.75991	0.259040
$682$	−3.17188	−0.121458
$683$	−25.8450	−0.988933	−0.494467	−	0.869197i	$-0.664637\pi$
$683$	−25.8450	−0.988933	−0.494467	+	0.869197i	$0.664637\pi$
$684$	28.8181	1.10189
$685$	33.8994	1.29523
$686$	0.725855	0.0277133
$687$	7.02441	0.267998
$688$	6.75717	0.257615
$689$	−0.314572	−0.0119842
$690$	0.572661	0.0218008
$691$	46.1110	1.75415	0.877073	−	0.480356i	$-0.159493\pi$
$691$	46.1110	1.75415	0.877073	+	0.480356i	$0.159493\pi$
$692$	−26.2288	−0.997068
$693$	−6.89746	−0.262013
$694$	−1.43140	−0.0543352
$695$	−17.6253	−0.668567
$696$	−0.648520	−0.0245821
$697$	−4.51531	−0.171030
$698$	0.463820	0.0175559
$699$	9.39114	0.355205
$700$	0.576743	0.0217988
$701$	33.3947	1.26130	0.630649	−	0.776068i	$-0.282789\pi$
$701$	33.3947	1.26130	0.630649	+	0.776068i	$0.282789\pi$
$702$	0.517324	0.0195251
$703$	11.3365	0.427565
$704$	−41.9033	−1.57929
$705$	−14.7175	−0.554294
$706$	−1.80379	−0.0678866
$707$	1.01250	0.0380790
$708$	13.6624	0.513464
$709$	−12.1775	−0.457336	−0.228668	−	0.973504i	$-0.573437\pi$
$709$	−12.1775	−0.457336	−0.228668	+	0.973504i	$0.573437\pi$
$710$	3.07057	0.115236
$711$	−34.5476	−1.29563
$712$	4.56688	0.171151
$713$	21.4657	0.803896
$714$	−0.104542	−0.00391238
$715$	−15.2129	−0.568929
$716$	44.4665	1.66179
$717$	9.54023	0.356286
$718$	−1.12577	−0.0420135
$719$	−31.0757	−1.15893	−0.579463	−	0.814998i	$-0.696738\pi$
$719$	−31.0757	−1.15893	−0.579463	+	0.814998i	$0.696738\pi$
$720$	21.2948	0.793612
$721$	−3.25505	−0.121224
$722$	−1.34608	−0.0500959
$723$	−7.69007	−0.285997
$724$	29.0634	1.08013
$725$	1.37701	0.0511409
$726$	−1.27843	−0.0474469
$727$	29.0355	1.07687	0.538433	−	0.842668i	$-0.319016\pi$
$727$	29.0355	1.07687	0.538433	+	0.842668i	$0.319016\pi$
$728$	0.281052	0.0104165
$729$	−6.83858	−0.253281
$730$	−2.59453	−0.0960278
$731$	5.24670	0.194056
$732$	8.86575	0.327688
$733$	18.9678	0.700590	0.350295	−	0.936639i	$-0.386081\pi$
$733$	18.9678	0.700590	0.350295	+	0.936639i	$0.386081\pi$
$734$	2.42274	0.0894248
$735$	9.21159	0.339774
$736$	−5.00220	−0.184384
$737$	30.7422	1.13240
$738$	−0.408062	−0.0150210
$739$	23.4947	0.864266	0.432133	−	0.901810i	$-0.357761\pi$
$739$	23.4947	0.864266	0.432133	+	0.901810i	$0.357761\pi$
$740$	8.42577	0.309737
$741$	4.87126	0.178950
$742$	0.0124284	0.000456262 0
$743$	−11.2292	−0.411961	−0.205980	−	0.978556i	$-0.566038\pi$
$743$	−11.2292	−0.411961	−0.205980	+	0.978556i	$0.566038\pi$
$744$	1.51410	0.0555098
$745$	11.0492	0.404813
$746$	2.64115	0.0966995
$747$	−41.1350	−1.50505
$748$	−32.9208	−1.20370
$749$	−3.80642	−0.139084
$750$	−0.815014	−0.0297601
$751$	−47.5855	−1.73642	−0.868210	−	0.496197i	$-0.834730\pi$
$751$	−47.5855	−1.73642	−0.868210	+	0.496197i	$0.834730\pi$
$752$	42.4416	1.54769
$753$	−19.3295	−0.704408
$754$	0.334553	0.0121837
$755$	−36.0208	−1.31093
$756$	3.55124	0.129157
$757$	19.4143	0.705626	0.352813	−	0.935694i	$-0.385225\pi$
$757$	19.4143	0.705626	0.352813	+	0.935694i	$0.385225\pi$
$758$	0.808872	0.0293796
$759$	13.8208	0.501663
$760$	−5.03687	−0.182707
$761$	25.9744	0.941571	0.470785	−	0.882248i	$-0.343971\pi$
$761$	25.9744	0.941571	0.470785	+	0.882248i	$0.343971\pi$
$762$	1.28066	0.0463933
$763$	4.36520	0.158031
$764$	1.94365	0.0703189
$765$	16.5347	0.597812
$766$	1.39018	0.0502291
$767$	−14.1366	−0.510444
$768$	9.79569	0.353472
$769$	−36.9822	−1.33361	−0.666806	−	0.745231i	$-0.732339\pi$
$769$	−36.9822	−1.33361	−0.666806	+	0.745231i	$0.732339\pi$
$770$	0.601045	0.0216601
$771$	11.6064	0.417993
$772$	26.0858	0.938847
$773$	15.4954	0.557331	0.278666	−	0.960388i	$-0.410108\pi$
$773$	15.4954	0.557331	0.278666	+	0.960388i	$0.410108\pi$
$774$	0.474159	0.0170433
$775$	−3.21492	−0.115483
$776$	−3.51274	−0.126100
$777$	0.645750	0.0231662
$778$	−0.801356	−0.0287300
$779$	−8.31257	−0.297829
$780$	3.62053	0.129636
$781$	74.1061	2.65172
$782$	−1.28226	−0.0458536
$783$	8.47882	0.303008
$784$	−26.5639	−0.948711
$785$	16.2818	0.581121
$786$	−0.00486535	−0.000173541 0
$787$	22.1934	0.791110	0.395555	−	0.918442i	$-0.370552\pi$
$787$	22.1934	0.791110	0.395555	+	0.918442i	$0.370552\pi$
$788$	−14.5996	−0.520091
$789$	8.06927	0.287274
$790$	3.01047	0.107108
$791$	−0.794542	−0.0282507
$792$	−5.96742	−0.212043
$793$	−9.17348	−0.325760
$794$	0.472479	0.0167677
$795$	0.321129	0.0113893
$796$	40.7555	1.44454
$797$	−33.1295	−1.17351	−0.586754	−	0.809765i	$-0.699595\pi$
$797$	−33.1295	−1.17351	−0.586754	+	0.809765i	$0.699595\pi$
$798$	−0.192459	−0.00681297
$799$	32.9544	1.16584
$800$	0.749180	0.0264875
$801$	−27.5995	−0.975182
$802$	0.174490	0.00616146
$803$	−62.6172	−2.20971
$804$	−7.31638	−0.258029
$805$	−4.06756	−0.143363
$806$	−0.781082	−0.0275124
$807$	2.87170	0.101089
$808$	0.875976	0.0308167
$809$	36.4939	1.28306	0.641528	−	0.767100i	$-0.278301\pi$
$809$	36.4939	1.28306	0.641528	+	0.767100i	$0.278301\pi$
$810$	1.21029	0.0425254
$811$	−27.2943	−0.958433	−0.479216	−	0.877697i	$-0.659079\pi$
$811$	−27.2943	−0.958433	−0.479216	+	0.877697i	$0.659079\pi$
$812$	2.29658	0.0805943
$813$	1.20995	0.0424347
$814$	−1.17037	−0.0410214
$815$	32.3011	1.13146
$816$	7.78952	0.272688
$817$	9.65903	0.337927
$818$	1.83349	0.0641063
$819$	−1.69851	−0.0593509
$820$	−6.17825	−0.215754
$821$	−32.5051	−1.13444	−0.567218	−	0.823568i	$-0.691980\pi$
$821$	−32.5051	−1.13444	−0.567218	+	0.823568i	$0.691980\pi$
$822$	1.12064	0.0390868
$823$	8.50744	0.296551	0.148275	−	0.988946i	$-0.452628\pi$
$823$	8.50744	0.296551	0.148275	+	0.988946i	$0.452628\pi$
$824$	−2.81614	−0.0981050
$825$	−2.06994	−0.0720661
$826$	0.558524	0.0194335
$827$	31.7519	1.10412	0.552061	−	0.833804i	$-0.313841\pi$
$827$	31.7519	1.10412	0.552061	+	0.833804i	$0.313841\pi$
$828$	20.1343	0.699715
$829$	−21.1405	−0.734239	−0.367120	−	0.930174i	$-0.619656\pi$
$829$	−21.1405	−0.734239	−0.367120	+	0.930174i	$0.619656\pi$
$830$	3.58450	0.124420
$831$	8.88156	0.308098
$832$	−10.3188	−0.357739
$833$	−20.6259	−0.714645
$834$	−0.582655	−0.0201757
$835$	−43.8885	−1.51882
$836$	−60.6063	−2.09611
$837$	−19.7956	−0.684235
$838$	−1.29189	−0.0446276
$839$	36.9463	1.27553	0.637764	−	0.770232i	$-0.279860\pi$
$839$	36.9463	1.27553	0.637764	+	0.770232i	$0.279860\pi$
$840$	−0.286910	−0.00989934
$841$	−23.5168	−0.810923
$842$	−1.69957	−0.0585710
$843$	2.28082	0.0785555
$844$	7.96079	0.274022
$845$	23.5598	0.810482
$846$	2.97818	0.102392
$847$	9.08057	0.312012
$848$	−0.926055	−0.0318008
$849$	−12.5522	−0.430790
$850$	0.192044	0.00658707
$851$	7.92046	0.271510
$852$	−17.6366	−0.604220
$853$	−32.2923	−1.10567	−0.552834	−	0.833291i	$-0.686454\pi$
$853$	−32.2923	−1.10567	−0.552834	+	0.833291i	$0.686454\pi$
$854$	0.362435	0.0124023
$855$	30.4399	1.04102
$856$	−3.29317	−0.112558
$857$	−50.1115	−1.71178	−0.855889	−	0.517160i	$-0.826989\pi$
$857$	−50.1115	−1.71178	−0.855889	+	0.517160i	$0.826989\pi$
$858$	−0.502904	−0.0171689
$859$	−2.56245	−0.0874298	−0.0437149	−	0.999044i	$-0.513919\pi$
$859$	−2.56245	−0.0874298	−0.0437149	+	0.999044i	$0.513919\pi$
$860$	7.17900	0.244802
$861$	−0.473500	−0.0161369
$862$	4.28802	0.146051
$863$	34.5586	1.17639	0.588194	−	0.808720i	$-0.299839\pi$
$863$	34.5586	1.17639	0.588194	+	0.808720i	$0.299839\pi$
$864$	4.61301	0.156938
$865$	−27.7048	−0.941991
$866$	2.93040	0.0995791
$867$	−4.98565	−0.169322
$868$	−5.36185	−0.181993
$869$	72.6557	2.46468
$870$	−0.341525	−0.0115788
$871$	7.57033	0.256511
$872$	3.77660	0.127892
$873$	21.2289	0.718491
$874$	−2.36061	−0.0798487
$875$	5.78898	0.195703
$876$	14.9023	0.503504
$877$	42.8424	1.44669	0.723343	−	0.690489i	$-0.242604\pi$
$877$	42.8424	1.44669	0.723343	+	0.690489i	$0.242604\pi$
$878$	2.45742	0.0829338
$879$	−10.1706	−0.343044
$880$	−44.7844	−1.50968
$881$	19.9855	0.673330	0.336665	−	0.941625i	$-0.390701\pi$
$881$	19.9855	0.673330	0.336665	+	0.941625i	$0.390701\pi$
$882$	−1.86402	−0.0627649
$883$	49.7566	1.67444	0.837221	−	0.546865i	$-0.184179\pi$
$883$	49.7566	1.67444	0.837221	+	0.546865i	$0.184179\pi$
$884$	−8.10682	−0.272662
$885$	14.4313	0.485102
$886$	3.15236	0.105906
$887$	−5.04201	−0.169294	−0.0846470	−	0.996411i	$-0.526976\pi$
$887$	−5.04201	−0.169294	−0.0846470	+	0.996411i	$0.526976\pi$
$888$	0.558679	0.0187480
$889$	−9.09639	−0.305083
$890$	2.40502	0.0806165
$891$	29.2096	0.978559
$892$	−10.5711	−0.353947
$893$	60.6681	2.03018
$894$	0.365264	0.0122163
$895$	46.9689	1.57000
$896$	1.66436	0.0556024
$897$	3.40340	0.113636
$898$	−1.25912	−0.0420174
$899$	−12.8018	−0.426963
$900$	−3.01552	−0.100517
$901$	−0.719048	−0.0239550
$902$	0.858180	0.0285743
$903$	0.550197	0.0183094
$904$	−0.687407	−0.0228628
$905$	30.6989	1.02047
$906$	−1.19077	−0.0395607
$907$	24.4048	0.810347	0.405174	−	0.914240i	$-0.367211\pi$
$907$	24.4048	0.810347	0.405174	+	0.914240i	$0.367211\pi$
$908$	−20.7108	−0.687312
$909$	−5.29388	−0.175587
$910$	0.148009	0.00490643
$911$	−10.2748	−0.340419	−0.170209	−	0.985408i	$-0.554444\pi$
$911$	−10.2748	−0.340419	−0.170209	+	0.985408i	$0.554444\pi$
$912$	14.3403	0.474854
$913$	86.5096	2.86305
$914$	2.06785	0.0683985
$915$	9.36468	0.309587
$916$	−21.5212	−0.711080
$917$	0.0345581	0.00114121
$918$	1.18250	0.0390282
$919$	39.7302	1.31058	0.655289	−	0.755378i	$-0.272547\pi$
$919$	39.7302	1.31058	0.655289	+	0.755378i	$0.272547\pi$
$920$	−3.51910	−0.116021
$921$	18.0943	0.596226
$922$	1.39977	0.0460989
$923$	18.2488	0.600666
$924$	−3.45226	−0.113571
$925$	−1.18625	−0.0390036
$926$	−3.40817	−0.111999
$927$	17.0191	0.558981
$928$	2.98323	0.0979292
$929$	28.4071	0.932007	0.466003	−	0.884783i	$-0.345693\pi$
$929$	28.4071	0.932007	0.466003	+	0.884783i	$0.345693\pi$
$930$	0.797362	0.0261465
$931$	−37.9717	−1.24447
$932$	−28.7723	−0.942467
$933$	−12.1689	−0.398393
$934$	−2.93501	−0.0960366
$935$	−34.7735	−1.13721
$936$	−1.46949	−0.0480318
$937$	−11.2515	−0.367572	−0.183786	−	0.982966i	$-0.558835\pi$
$937$	−11.2515	−0.367572	−0.183786	+	0.982966i	$0.558835\pi$
$938$	−0.299096	−0.00976584
$939$	13.3199	0.434678
$940$	45.0911	1.47071
$941$	39.5265	1.28853	0.644264	−	0.764803i	$-0.277164\pi$
$941$	39.5265	1.28853	0.644264	+	0.764803i	$0.277164\pi$
$942$	0.538240	0.0175368
$943$	−5.80773	−0.189126
$944$	−41.6161	−1.35449
$945$	3.75109	0.122023
$946$	−0.997188	−0.0324214
$947$	−22.4627	−0.729938	−0.364969	−	0.931020i	$-0.618920\pi$
$947$	−22.4627	−0.729938	−0.364969	+	0.931020i	$0.618920\pi$
$948$	−17.2914	−0.561600
$949$	−15.4196	−0.500542
$950$	0.353548	0.0114706
$951$	5.72454	0.185631
$952$	0.642428	0.0208212
$953$	−55.0446	−1.78307	−0.891534	−	0.452953i	$-0.850370\pi$
$953$	−55.0446	−1.78307	−0.891534	+	0.452953i	$0.850370\pi$
$954$	−0.0649824	−0.00210388
$955$	2.05303	0.0664346
$956$	−29.2291	−0.945335
$957$	−8.24248	−0.266442
$958$	−0.0567911	−0.00183484
$959$	−7.95982	−0.257036
$960$	10.5338	0.339978
$961$	−1.11164	−0.0358594
$962$	−0.288206	−0.00929213
$963$	19.9020	0.641333
$964$	23.5606	0.758836
$965$	27.5538	0.886987
$966$	−0.134465	−0.00432634
$967$	28.6510	0.921354	0.460677	−	0.887568i	$-0.347607\pi$
$967$	28.6510	0.921354	0.460677	+	0.887568i	$0.347607\pi$
$968$	7.85617	0.252507
$969$	11.1347	0.357699
$970$	−1.84989	−0.0593964
$971$	−14.0405	−0.450583	−0.225291	−	0.974291i	$-0.572333\pi$
$971$	−14.0405	−0.450583	−0.225291	+	0.974291i	$0.572333\pi$
$972$	−28.5527	−0.915829
$973$	4.13855	0.132676
$974$	3.12102	0.100004
$975$	−0.509727	−0.0163243
$976$	−27.0054	−0.864421
$977$	−7.80427	−0.249681	−0.124840	−	0.992177i	$-0.539842\pi$
$977$	−7.80427	−0.249681	−0.124840	+	0.992177i	$0.539842\pi$
$978$	1.06780	0.0341446
$979$	58.0436	1.85508
$980$	−28.2222	−0.901524
$981$	−22.8236	−0.728700
$982$	0.143041	0.00456461
$983$	−43.0140	−1.37193	−0.685967	−	0.727633i	$-0.740621\pi$
$983$	−43.0140	−1.37193	−0.685967	+	0.727633i	$0.740621\pi$
$984$	−0.409655	−0.0130593
$985$	−15.4213	−0.491362
$986$	0.764719	0.0243536
$987$	3.45578	0.109999
$988$	−14.9244	−0.474809
$989$	6.74846	0.214588
$990$	−3.14258	−0.0998777
$991$	−15.8637	−0.503926	−0.251963	−	0.967737i	$-0.581076\pi$
$991$	−15.8637	−0.503926	−0.251963	+	0.967737i	$0.581076\pi$
$992$	−6.96496	−0.221138
$993$	5.16783	0.163996
$994$	−0.720991	−0.0228684
$995$	43.0490	1.36475
$996$	−20.5885	−0.652372
$997$	−23.2483	−0.736280	−0.368140	−	0.929770i	$-0.620005\pi$
$997$	−23.2483	−0.736280	−0.368140	+	0.929770i	$0.620005\pi$
$998$	1.11331	0.0352413
$999$	−7.30422	−0.231095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.11	✓	25
3.2	odd	2		4923.2.a.n.1.15		25
4.3	odd	2		8752.2.a.v.1.14		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.11	✓	25	1.1	even	1	trivial
4923.2.a.n.1.15		25	3.2	odd	2
8752.2.a.v.1.14		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)

\(f(q)\)	\(=\)	\(q-0.106981 q^{2} +0.649055 q^{3} -1.98856 q^{4} -2.10046 q^{5} -0.0694367 q^{6} +0.493203 q^{7} +0.426701 q^{8} -2.57873 q^{9} +O(q^{10})\)	\(q-0.106981 q^{2} +0.649055 q^{3} -1.98856 q^{4} -2.10046 q^{5} -0.0694367 q^{6} +0.493203 q^{7} +0.426701 q^{8} -2.57873 q^{9} +0.224710 q^{10} +5.42323 q^{11} -1.29068 q^{12} +1.33548 q^{13} -0.0527635 q^{14} -1.36332 q^{15} +3.93146 q^{16} +3.05264 q^{17} +0.275876 q^{18} +5.61982 q^{19} +4.17689 q^{20} +0.320116 q^{21} -0.580184 q^{22} +3.92639 q^{23} +0.276952 q^{24} -0.588056 q^{25} -0.142872 q^{26} -3.62090 q^{27} -0.980762 q^{28} -2.34163 q^{29} +0.145849 q^{30} +5.46702 q^{31} -1.27399 q^{32} +3.51997 q^{33} -0.326575 q^{34} -1.03596 q^{35} +5.12794 q^{36} +2.01724 q^{37} -0.601216 q^{38} +0.866801 q^{39} -0.896269 q^{40} -1.47915 q^{41} -0.0342464 q^{42} +1.71874 q^{43} -10.7844 q^{44} +5.41652 q^{45} -0.420050 q^{46} +10.7954 q^{47} +2.55173 q^{48} -6.75675 q^{49} +0.0629110 q^{50} +1.98133 q^{51} -2.65568 q^{52} -0.235550 q^{53} +0.387369 q^{54} -11.3913 q^{55} +0.210450 q^{56} +3.64757 q^{57} +0.250511 q^{58} -10.5854 q^{59} +2.71103 q^{60} -6.86905 q^{61} -0.584869 q^{62} -1.27184 q^{63} -7.72663 q^{64} -2.80513 q^{65} -0.376571 q^{66} +5.66862 q^{67} -6.07034 q^{68} +2.54844 q^{69} +0.110828 q^{70} +13.6646 q^{71} -1.10035 q^{72} -11.5461 q^{73} -0.215807 q^{74} -0.381681 q^{75} -11.1753 q^{76} +2.67475 q^{77} -0.0927315 q^{78} +13.3971 q^{79} -8.25789 q^{80} +5.38602 q^{81} +0.158242 q^{82} +15.9517 q^{83} -0.636568 q^{84} -6.41195 q^{85} -0.183873 q^{86} -1.51985 q^{87} +2.31410 q^{88} +10.7028 q^{89} -0.579466 q^{90} +0.658664 q^{91} -7.80784 q^{92} +3.54840 q^{93} -1.15490 q^{94} -11.8042 q^{95} -0.826892 q^{96} -8.23233 q^{97} +0.722846 q^{98} -13.9850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more