LMFDB - Embedded newform 1573.2.a.s.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,2,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1573.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:	$12.5604682379$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 19 x^{11} + 169 x^{10} - 136 x^{9} - 649 x^{8} + 455 x^{7} + 1207 x^{6} + \cdots - 29 $ x^14 - x^13 - 21x^12 + 19x^11 + 169x^10 - 136x^9 - 649x^8 + 455x^7 + 1207x^6 - 708x^5 - 1001x^4 + 414x^3 + 343x^2 - 67x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.52999$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52999 q^{2} +0.0803684 q^{3} +4.40087 q^{4} -1.24791 q^{5} +0.203332 q^{6} +3.27614 q^{7} +6.07419 q^{8} -2.99354 q^{9} +O(q^{10})$	\(q+2.52999 q^{2} +0.0803684 q^{3} +4.40087 q^{4} -1.24791 q^{5} +0.203332 q^{6} +3.27614 q^{7} +6.07419 q^{8} -2.99354 q^{9} -3.15719 q^{10} +0.353691 q^{12} +1.00000 q^{13} +8.28863 q^{14} -0.100292 q^{15} +6.56592 q^{16} +3.04287 q^{17} -7.57364 q^{18} +7.55280 q^{19} -5.49187 q^{20} +0.263299 q^{21} +4.15102 q^{23} +0.488173 q^{24} -3.44273 q^{25} +2.52999 q^{26} -0.481692 q^{27} +14.4179 q^{28} +2.43823 q^{29} -0.253739 q^{30} -4.50315 q^{31} +4.46336 q^{32} +7.69846 q^{34} -4.08832 q^{35} -13.1742 q^{36} +2.25832 q^{37} +19.1086 q^{38} +0.0803684 q^{39} -7.58001 q^{40} -3.09222 q^{41} +0.666144 q^{42} -6.90049 q^{43} +3.73566 q^{45} +10.5020 q^{46} +3.65635 q^{47} +0.527693 q^{48} +3.73312 q^{49} -8.71009 q^{50} +0.244551 q^{51} +4.40087 q^{52} +7.93413 q^{53} -1.21868 q^{54} +19.8999 q^{56} +0.607007 q^{57} +6.16870 q^{58} -14.5148 q^{59} -0.441373 q^{60} -2.62830 q^{61} -11.3929 q^{62} -9.80727 q^{63} -1.83956 q^{64} -1.24791 q^{65} -10.2252 q^{67} +13.3913 q^{68} +0.333611 q^{69} -10.3434 q^{70} +13.3254 q^{71} -18.1833 q^{72} +5.38084 q^{73} +5.71354 q^{74} -0.276687 q^{75} +33.2389 q^{76} +0.203332 q^{78} -5.56800 q^{79} -8.19365 q^{80} +8.94191 q^{81} -7.82329 q^{82} -3.04699 q^{83} +1.15874 q^{84} -3.79722 q^{85} -17.4582 q^{86} +0.195957 q^{87} -17.2560 q^{89} +9.45119 q^{90} +3.27614 q^{91} +18.2681 q^{92} -0.361911 q^{93} +9.25055 q^{94} -9.42518 q^{95} +0.358714 q^{96} -7.54136 q^{97} +9.44478 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

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 $

$2$	2.52999	1.78898	0.894488	−	0.447092i	$-0.147540\pi$
$2$	2.52999	1.78898	0.894488	+	0.447092i	$0.147540\pi$
$3$	0.0803684	0.0464007	0.0232004	−	0.999731i	$-0.492614\pi$
$3$	0.0803684	0.0464007	0.0232004	+	0.999731i	$0.492614\pi$
$4$	4.40087	2.20044
$5$	−1.24791	−0.558080	−0.279040	−	0.960279i	$-0.590016\pi$
$5$	−1.24791	−0.558080	−0.279040	+	0.960279i	$0.590016\pi$
$6$	0.203332	0.0830098
$7$	3.27614	1.23827	0.619133	−	0.785286i	$-0.287484\pi$
$7$	3.27614	1.23827	0.619133	+	0.785286i	$0.287484\pi$
$8$	6.07419	2.14755
$9$	−2.99354	−0.997847
$10$	−3.15719	−0.998392
$11$	0	0
$11$	0	0
$12$	0.353691	0.102102
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	8.28863	2.21523
$15$	−0.100292	−0.0258953
$16$	6.56592	1.64148
$17$	3.04287	0.738006	0.369003	−	0.929428i	$-0.379699\pi$
$17$	3.04287	0.738006	0.369003	+	0.929428i	$0.379699\pi$
$18$	−7.57364	−1.78512
$19$	7.55280	1.73273	0.866366	−	0.499409i	$-0.166450\pi$
$19$	7.55280	1.73273	0.866366	+	0.499409i	$0.166450\pi$
$20$	−5.49187	−1.22802
$21$	0.263299	0.0574565
$22$	0	0
$23$	4.15102	0.865547	0.432773	−	0.901503i	$-0.357535\pi$
$23$	4.15102	0.865547	0.432773	+	0.901503i	$0.357535\pi$
$24$	0.488173	0.0996479
$25$	−3.44273	−0.688547
$26$	2.52999	0.496173
$27$	−0.481692	−0.0927016
$28$	14.4179	2.72472
$29$	2.43823	0.452768	0.226384	−	0.974038i	$-0.427310\pi$
$29$	2.43823	0.452768	0.226384	+	0.974038i	$0.427310\pi$
$30$	−0.253739	−0.0463261
$31$	−4.50315	−0.808790	−0.404395	−	0.914584i	$-0.632518\pi$
$31$	−4.50315	−0.808790	−0.404395	+	0.914584i	$0.632518\pi$
$32$	4.46336	0.789019
$33$	0	0
$34$	7.69846	1.32027
$35$	−4.08832	−0.691052
$36$	−13.1742	−2.19570
$37$	2.25832	0.371266	0.185633	−	0.982619i	$-0.440566\pi$
$37$	2.25832	0.371266	0.185633	+	0.982619i	$0.440566\pi$
$38$	19.1086	3.09982
$39$	0.0803684	0.0128692
$40$	−7.58001	−1.19851
$41$	−3.09222	−0.482923	−0.241462	−	0.970410i	$-0.577627\pi$
$41$	−3.09222	−0.482923	−0.241462	+	0.970410i	$0.577627\pi$
$42$	0.666144	0.102788
$43$	−6.90049	−1.05232	−0.526158	−	0.850387i	$-0.676368\pi$
$43$	−6.90049	−1.05232	−0.526158	+	0.850387i	$0.676368\pi$
$44$	0	0
$45$	3.73566	0.556879
$46$	10.5020	1.54844
$47$	3.65635	0.533334	0.266667	−	0.963789i	$-0.414078\pi$
$47$	3.65635	0.533334	0.266667	+	0.963789i	$0.414078\pi$
$48$	0.527693	0.0761659
$49$	3.73312	0.533303
$50$	−8.71009	−1.23179
$51$	0.244551	0.0342440
$52$	4.40087	0.610291
$53$	7.93413	1.08984	0.544918	−	0.838489i	$-0.316561\pi$
$53$	7.93413	1.08984	0.544918	+	0.838489i	$0.316561\pi$
$54$	−1.21868	−0.165841
$55$	0	0
$56$	19.8999	2.65924
$57$	0.607007	0.0804001
$58$	6.16870	0.809990
$59$	−14.5148	−1.88967	−0.944835	−	0.327546i	$-0.893778\pi$
$59$	−14.5148	−1.88967	−0.944835	+	0.327546i	$0.893778\pi$
$60$	−0.441373	−0.0569810
$61$	−2.62830	−0.336519	−0.168260	−	0.985743i	$-0.553815\pi$
$61$	−2.62830	−0.336519	−0.168260	+	0.985743i	$0.553815\pi$
$62$	−11.3929	−1.44691
$63$	−9.80727	−1.23560
$64$	−1.83956	−0.229945
$65$	−1.24791	−0.154784
$66$	0	0
$67$	−10.2252	−1.24920	−0.624601	−	0.780944i	$-0.714738\pi$
$67$	−10.2252	−1.24920	−0.624601	+	0.780944i	$0.714738\pi$
$68$	13.3913	1.62393
$69$	0.333611	0.0401620
$70$	−10.3434	−1.23628
$71$	13.3254	1.58144	0.790720	−	0.612178i	$-0.209707\pi$
$71$	13.3254	1.58144	0.790720	+	0.612178i	$0.209707\pi$
$72$	−18.1833	−2.14293
$73$	5.38084	0.629780	0.314890	−	0.949128i	$-0.398032\pi$
$73$	5.38084	0.629780	0.314890	+	0.949128i	$0.398032\pi$
$74$	5.71354	0.664186
$75$	−0.276687	−0.0319491
$76$	33.2389	3.81277
$77$	0	0
$78$	0.203332	0.0230228
$79$	−5.56800	−0.626449	−0.313225	−	0.949679i	$-0.601409\pi$
$79$	−5.56800	−0.626449	−0.313225	+	0.949679i	$0.601409\pi$
$80$	−8.19365	−0.916078
$81$	8.94191	0.993546
$82$	−7.82329	−0.863938
$83$	−3.04699	−0.334451	−0.167225	−	0.985919i	$-0.553481\pi$
$83$	−3.04699	−0.334451	−0.167225	+	0.985919i	$0.553481\pi$
$84$	1.15874	0.126429
$85$	−3.79722	−0.411866
$86$	−17.4582	−1.88257
$87$	0.195957	0.0210088
$88$	0	0
$89$	−17.2560	−1.82913	−0.914565	−	0.404438i	$-0.867467\pi$
$89$	−17.2560	−1.82913	−0.914565	+	0.404438i	$0.867467\pi$
$90$	9.45119	0.996243
$91$	3.27614	0.343433
$92$	18.2681	1.90458
$93$	−0.361911	−0.0375284
$94$	9.25055	0.954122
$95$	−9.42518	−0.967004
$96$	0.358714	0.0366111
$97$	−7.54136	−0.765709	−0.382855	−	0.923809i	$-0.625059\pi$
$97$	−7.54136	−0.765709	−0.382855	+	0.923809i	$0.625059\pi$
$98$	9.44478	0.954067
$99$	0	0
$100$	−15.1510	−1.51510
$101$	1.08351	0.107814	0.0539069	−	0.998546i	$-0.482833\pi$
$101$	1.08351	0.107814	0.0539069	+	0.998546i	$0.482833\pi$
$102$	0.618713	0.0612617
$103$	−19.5742	−1.92870	−0.964352	−	0.264624i	$-0.914752\pi$
$103$	−19.5742	−1.92870	−0.964352	+	0.264624i	$0.914752\pi$
$104$	6.07419	0.595623
$105$	−0.328572	−0.0320653
$106$	20.0733	1.94969
$107$	−13.3694	−1.29247	−0.646233	−	0.763140i	$-0.723656\pi$
$107$	−13.3694	−1.29247	−0.646233	+	0.763140i	$0.723656\pi$
$108$	−2.11986	−0.203984
$109$	−9.28926	−0.889749	−0.444875	−	0.895593i	$-0.646752\pi$
$109$	−9.28926	−0.889749	−0.444875	+	0.895593i	$0.646752\pi$
$110$	0	0
$111$	0.181498	0.0172270
$112$	21.5109	2.03259
$113$	10.8948	1.02489	0.512446	−	0.858719i	$-0.328739\pi$
$113$	10.8948	1.02489	0.512446	+	0.858719i	$0.328739\pi$
$114$	1.53572	0.143834
$115$	−5.18007	−0.483044
$116$	10.7303	0.996286
$117$	−2.99354	−0.276753
$118$	−36.7225	−3.38058
$119$	9.96890	0.913847
$120$	−0.609194	−0.0556115
$121$	0	0
$122$	−6.64958	−0.602025
$123$	−0.248517	−0.0224080
$124$	−19.8178	−1.77969
$125$	10.5357	0.942344
$126$	−24.8123	−2.21046
$127$	−11.0188	−0.977764	−0.488882	−	0.872350i	$-0.662595\pi$
$127$	−11.0188	−0.977764	−0.488882	+	0.872350i	$0.662595\pi$
$128$	−13.5808	−1.20038
$129$	−0.554582	−0.0488282
$130$	−3.15719	−0.276904
$131$	−1.73858	−0.151900	−0.0759500	−	0.997112i	$-0.524199\pi$
$131$	−1.73858	−0.151900	−0.0759500	+	0.997112i	$0.524199\pi$
$132$	0	0
$133$	24.7441	2.14558
$134$	−25.8696	−2.23479
$135$	0.601105	0.0517349
$136$	18.4830	1.58490
$137$	6.60107	0.563968	0.281984	−	0.959419i	$-0.409008\pi$
$137$	6.60107	0.563968	0.281984	+	0.959419i	$0.409008\pi$
$138$	0.844033	0.0718489
$139$	13.9786	1.18565	0.592824	−	0.805332i	$-0.298013\pi$
$139$	13.9786	1.18565	0.592824	+	0.805332i	$0.298013\pi$
$140$	−17.9922	−1.52061
$141$	0.293855	0.0247471
$142$	33.7133	2.82916
$143$	0	0
$144$	−19.6554	−1.63795
$145$	−3.04268	−0.252681
$146$	13.6135	1.12666
$147$	0.300025	0.0247457
$148$	9.93858	0.816947
$149$	11.5393	0.945333	0.472666	−	0.881241i	$-0.343292\pi$
$149$	11.5393	0.945333	0.472666	+	0.881241i	$0.343292\pi$
$150$	−0.700017	−0.0571561
$151$	17.4396	1.41921	0.709607	−	0.704598i	$-0.248873\pi$
$151$	17.4396	1.41921	0.709607	+	0.704598i	$0.248873\pi$
$152$	45.8772	3.72113
$153$	−9.10897	−0.736417
$154$	0	0
$155$	5.61951	0.451370
$156$	0.353691	0.0283180
$157$	1.27279	0.101580	0.0507899	−	0.998709i	$-0.483826\pi$
$157$	1.27279	0.101580	0.0507899	+	0.998709i	$0.483826\pi$
$158$	−14.0870	−1.12070
$159$	0.637654	0.0505692
$160$	−5.56985	−0.440336
$161$	13.5993	1.07178
$162$	22.6230	1.77743
$163$	17.7144	1.38750	0.693749	−	0.720217i	$-0.255958\pi$
$163$	17.7144	1.38750	0.693749	+	0.720217i	$0.255958\pi$
$164$	−13.6085	−1.06264
$165$	0	0
$166$	−7.70887	−0.598324
$167$	−13.9398	−1.07869	−0.539347	−	0.842084i	$-0.681329\pi$
$167$	−13.9398	−1.07869	−0.539347	+	0.842084i	$0.681329\pi$
$168$	1.59933	0.123391
$169$	1.00000	0.0769231
$170$	−9.60694	−0.736819
$171$	−22.6096	−1.72900
$172$	−30.3682	−2.31555
$173$	6.94106	0.527719	0.263860	−	0.964561i	$-0.415004\pi$
$173$	6.94106	0.527719	0.263860	+	0.964561i	$0.415004\pi$
$174$	0.495769	0.0375842
$175$	−11.2789	−0.852604
$176$	0	0
$177$	−1.16653	−0.0876821
$178$	−43.6575	−3.27227
$179$	9.12972	0.682388	0.341194	−	0.939993i	$-0.389169\pi$
$179$	9.12972	0.682388	0.341194	+	0.939993i	$0.389169\pi$
$180$	16.4401	1.22538
$181$	4.97968	0.370137	0.185068	−	0.982726i	$-0.440749\pi$
$181$	4.97968	0.370137	0.185068	+	0.982726i	$0.440749\pi$
$182$	8.28863	0.614394
$183$	−0.211232	−0.0156147
$184$	25.2141	1.85880
$185$	−2.81817	−0.207196
$186$	−0.915633	−0.0671375
$187$	0	0
$188$	16.0911	1.17357
$189$	−1.57809	−0.114789
$190$	−23.8457	−1.72995
$191$	9.52589	0.689269	0.344634	−	0.938737i	$-0.388003\pi$
$191$	9.52589	0.689269	0.344634	+	0.938737i	$0.388003\pi$
$192$	−0.147842	−0.0106696
$193$	−20.1699	−1.45186	−0.725929	−	0.687770i	$-0.758590\pi$
$193$	−20.1699	−1.45186	−0.725929	+	0.687770i	$0.758590\pi$
$194$	−19.0796	−1.36984
$195$	−0.100292	−0.00718207
$196$	16.4290	1.17350
$197$	−15.1633	−1.08034	−0.540170	−	0.841556i	$-0.681640\pi$
$197$	−15.1633	−1.08034	−0.540170	+	0.841556i	$0.681640\pi$
$198$	0	0
$199$	−0.389071	−0.0275805	−0.0137903	−	0.999905i	$-0.504390\pi$
$199$	−0.389071	−0.0275805	−0.0137903	+	0.999905i	$0.504390\pi$
$200$	−20.9118	−1.47869
$201$	−0.821780	−0.0579639
$202$	2.74128	0.192876
$203$	7.98799	0.560647
$204$	1.07624	0.0753517
$205$	3.85880	0.269510
$206$	−49.5226	−3.45040
$207$	−12.4262	−0.863683
$208$	6.56592	0.455265
$209$	0	0
$210$	−0.831285	−0.0573641
$211$	−14.2095	−0.978224	−0.489112	−	0.872221i	$-0.662679\pi$
$211$	−14.2095	−0.978224	−0.489112	+	0.872221i	$0.662679\pi$
$212$	34.9171	2.39812
$213$	1.07095	0.0733800
$214$	−33.8244	−2.31219
$215$	8.61116	0.587276
$216$	−2.92589	−0.199081
$217$	−14.7530	−1.00150
$218$	−23.5018	−1.59174
$219$	0.432450	0.0292222
$220$	0	0
$221$	3.04287	0.204686
$222$	0.459188	0.0308187
$223$	3.03991	0.203567	0.101784	−	0.994807i	$-0.467545\pi$
$223$	3.03991	0.203567	0.101784	+	0.994807i	$0.467545\pi$
$224$	14.6226	0.977015
$225$	10.3060	0.687064
$226$	27.5637	1.83351
$227$	−3.26183	−0.216495	−0.108248	−	0.994124i	$-0.534524\pi$
$227$	−3.26183	−0.216495	−0.108248	+	0.994124i	$0.534524\pi$
$228$	2.67136	0.176915
$229$	−12.5503	−0.829347	−0.414674	−	0.909970i	$-0.636104\pi$
$229$	−12.5503	−0.829347	−0.414674	+	0.909970i	$0.636104\pi$
$230$	−13.1056	−0.864155
$231$	0	0
$232$	14.8103	0.972341
$233$	16.4838	1.07989	0.539946	−	0.841700i	$-0.318445\pi$
$233$	16.4838	1.07989	0.539946	+	0.841700i	$0.318445\pi$
$234$	−7.57364	−0.495104
$235$	−4.56278	−0.297643
$236$	−63.8779	−4.15810
$237$	−0.447492	−0.0290677
$238$	25.2213	1.63485
$239$	11.5700	0.748401	0.374201	−	0.927348i	$-0.377917\pi$
$239$	11.5700	0.748401	0.374201	+	0.927348i	$0.377917\pi$
$240$	−0.658511	−0.0425067
$241$	−14.7766	−0.951842	−0.475921	−	0.879488i	$-0.657885\pi$
$241$	−14.7766	−0.951842	−0.475921	+	0.879488i	$0.657885\pi$
$242$	0	0
$243$	2.16372	0.138803
$244$	−11.5668	−0.740489
$245$	−4.65858	−0.297626
$246$	−0.628746	−0.0400874
$247$	7.55280	0.480573
$248$	−27.3530	−1.73692
$249$	−0.244882	−0.0155188
$250$	26.6553	1.68583
$251$	8.64320	0.545554	0.272777	−	0.962077i	$-0.412058\pi$
$251$	8.64320	0.545554	0.272777	+	0.962077i	$0.412058\pi$
$252$	−43.1605	−2.71886
$253$	0	0
$254$	−27.8776	−1.74920
$255$	−0.305177	−0.0191109
$256$	−30.6802	−1.91751
$257$	24.7182	1.54188	0.770938	−	0.636910i	$-0.219788\pi$
$257$	24.7182	1.54188	0.770938	+	0.636910i	$0.219788\pi$
$258$	−1.40309	−0.0873525
$259$	7.39859	0.459726
$260$	−5.49187	−0.340591
$261$	−7.29894	−0.451793
$262$	−4.39858	−0.271745
$263$	18.0241	1.11141	0.555706	−	0.831379i	$-0.312448\pi$
$263$	18.0241	1.11141	0.555706	+	0.831379i	$0.312448\pi$
$264$	0	0
$265$	−9.90105	−0.608216
$266$	62.6024	3.83840
$267$	−1.38684	−0.0848730
$268$	−44.9996	−2.74879
$269$	−27.9512	−1.70422	−0.852108	−	0.523366i	$-0.824676\pi$
$269$	−27.9512	−1.70422	−0.852108	+	0.523366i	$0.824676\pi$
$270$	1.52079	0.0925525
$271$	−17.4756	−1.06156	−0.530782	−	0.847508i	$-0.678102\pi$
$271$	−17.4756	−1.06156	−0.530782	+	0.847508i	$0.678102\pi$
$272$	19.9793	1.21142
$273$	0.263299	0.0159356
$274$	16.7007	1.00892
$275$	0	0
$276$	1.46818	0.0883739
$277$	13.9375	0.837426	0.418713	−	0.908119i	$-0.362481\pi$
$277$	13.9375	0.837426	0.418713	+	0.908119i	$0.362481\pi$
$278$	35.3658	2.12110
$279$	13.4804	0.807048
$280$	−24.8332	−1.48407
$281$	−6.62406	−0.395158	−0.197579	−	0.980287i	$-0.563308\pi$
$281$	−6.62406	−0.395158	−0.197579	+	0.980287i	$0.563308\pi$
$282$	0.743453	0.0442720
$283$	−15.6101	−0.927925	−0.463963	−	0.885855i	$-0.653573\pi$
$283$	−15.6101	−0.927925	−0.463963	+	0.885855i	$0.653573\pi$
$284$	58.6436	3.47986
$285$	−0.757487	−0.0448697
$286$	0	0
$287$	−10.1306	−0.597988
$288$	−13.3613	−0.787320
$289$	−7.74091	−0.455348
$290$	−7.69796	−0.452040
$291$	−0.606088	−0.0355295
$292$	23.6804	1.38579
$293$	18.5394	1.08309	0.541543	−	0.840673i	$-0.317841\pi$
$293$	18.5394	1.08309	0.541543	+	0.840673i	$0.317841\pi$
$294$	0.759062	0.0442694
$295$	18.1131	1.05459
$296$	13.7175	0.797312
$297$	0	0
$298$	29.1943	1.69118
$299$	4.15102	0.240059
$300$	−1.21766	−0.0703019
$301$	−22.6070	−1.30305
$302$	44.1220	2.53894
$303$	0.0870804	0.00500264
$304$	49.5911	2.84425
$305$	3.27987	0.187805
$306$	−23.0456	−1.31743
$307$	−15.8266	−0.903274	−0.451637	−	0.892202i	$-0.649160\pi$
$307$	−15.8266	−0.903274	−0.451637	+	0.892202i	$0.649160\pi$
$308$	0	0
$309$	−1.57315	−0.0894933
$310$	14.2173	0.807489
$311$	9.66457	0.548028	0.274014	−	0.961726i	$-0.411649\pi$
$311$	9.66457	0.548028	0.274014	+	0.961726i	$0.411649\pi$
$312$	0.488173	0.0276374
$313$	−17.2964	−0.977651	−0.488826	−	0.872381i	$-0.662575\pi$
$313$	−17.2964	−0.977651	−0.488826	+	0.872381i	$0.662575\pi$
$314$	3.22016	0.181724
$315$	12.2385	0.689564
$316$	−24.5041	−1.37846
$317$	−29.6415	−1.66483	−0.832415	−	0.554153i	$-0.813042\pi$
$317$	−29.6415	−1.66483	−0.832415	+	0.554153i	$0.813042\pi$
$318$	1.61326	0.0904672
$319$	0	0
$320$	2.29559	0.128328
$321$	−1.07448	−0.0599714
$322$	34.4062	1.91738
$323$	22.9822	1.27877
$324$	39.3522	2.18623
$325$	−3.44273	−0.190968
$326$	44.8173	2.48220
$327$	−0.746563	−0.0412850
$328$	−18.7827	−1.03710
$329$	11.9787	0.660410
$330$	0	0
$331$	−7.04956	−0.387479	−0.193739	−	0.981053i	$-0.562062\pi$
$331$	−7.04956	−0.387479	−0.193739	+	0.981053i	$0.562062\pi$
$332$	−13.4094	−0.735937
$333$	−6.76038	−0.370467
$334$	−35.2676	−1.92976
$335$	12.7600	0.697155
$336$	1.72880	0.0943137
$337$	7.47920	0.407418	0.203709	−	0.979031i	$-0.434700\pi$
$337$	7.47920	0.407418	0.203709	+	0.979031i	$0.434700\pi$
$338$	2.52999	0.137614
$339$	0.875594	0.0475557
$340$	−16.7111	−0.906285
$341$	0	0
$342$	−57.2022	−3.09314
$343$	−10.7028	−0.577895
$344$	−41.9149	−2.25990
$345$	−0.416314	−0.0224136
$346$	17.5609	0.944077
$347$	1.53473	0.0823887	0.0411943	−	0.999151i	$-0.486884\pi$
$347$	1.53473	0.0823887	0.0411943	+	0.999151i	$0.486884\pi$
$348$	0.862380	0.0462284
$349$	10.7499	0.575431	0.287715	−	0.957716i	$-0.407104\pi$
$349$	10.7499	0.575431	0.287715	+	0.957716i	$0.407104\pi$
$350$	−28.5355	−1.52529
$351$	−0.481692	−0.0257108
$352$	0	0
$353$	2.12628	0.113170	0.0565851	−	0.998398i	$-0.481979\pi$
$353$	2.12628	0.113170	0.0565851	+	0.998398i	$0.481979\pi$
$354$	−2.95133	−0.156861
$355$	−16.6289	−0.882570
$356$	−75.9414	−4.02488
$357$	0.801185	0.0424032
$358$	23.0982	1.22078
$359$	4.36958	0.230618	0.115309	−	0.993330i	$-0.463214\pi$
$359$	4.36958	0.230618	0.115309	+	0.993330i	$0.463214\pi$
$360$	22.6911	1.19592
$361$	38.0449	2.00236
$362$	12.5986	0.662166
$363$	0	0
$364$	14.4179	0.755703
$365$	−6.71478	−0.351468
$366$	−0.534416	−0.0279344
$367$	1.19419	0.0623360	0.0311680	−	0.999514i	$-0.490077\pi$
$367$	1.19419	0.0623360	0.0311680	+	0.999514i	$0.490077\pi$
$368$	27.2552	1.42078
$369$	9.25668	0.481884
$370$	−7.12996	−0.370669
$371$	25.9934	1.34951
$372$	−1.59272	−0.0825789
$373$	4.57972	0.237129	0.118564	−	0.992946i	$-0.462171\pi$
$373$	4.57972	0.237129	0.118564	+	0.992946i	$0.462171\pi$
$374$	0	0
$375$	0.846740	0.0437255
$376$	22.2094	1.14536
$377$	2.43823	0.125575
$378$	−3.99256	−0.205355
$379$	12.8382	0.659454	0.329727	−	0.944076i	$-0.393043\pi$
$379$	12.8382	0.659454	0.329727	+	0.944076i	$0.393043\pi$
$380$	−41.4790	−2.12783
$381$	−0.885567	−0.0453690
$382$	24.1004	1.23309
$383$	−2.93004	−0.149718	−0.0748590	−	0.997194i	$-0.523851\pi$
$383$	−2.93004	−0.149718	−0.0748590	+	0.997194i	$0.523851\pi$
$384$	−1.09147	−0.0556987
$385$	0	0
$386$	−51.0296	−2.59734
$387$	20.6569	1.05005
$388$	−33.1886	−1.68489
$389$	16.2689	0.824867	0.412434	−	0.910988i	$-0.364679\pi$
$389$	16.2689	0.824867	0.412434	+	0.910988i	$0.364679\pi$
$390$	−0.253739	−0.0128486
$391$	12.6310	0.638778
$392$	22.6757	1.14530
$393$	−0.139727	−0.00704827
$394$	−38.3630	−1.93270
$395$	6.94834	0.349609
$396$	0	0
$397$	31.0984	1.56078	0.780392	−	0.625291i	$-0.215020\pi$
$397$	31.0984	1.56078	0.780392	+	0.625291i	$0.215020\pi$
$398$	−0.984348	−0.0493409
$399$	1.98864	0.0995567
$400$	−22.6047	−1.13024
$401$	27.9118	1.39385	0.696925	−	0.717144i	$-0.254551\pi$
$401$	27.9118	1.39385	0.696925	+	0.717144i	$0.254551\pi$
$402$	−2.07910	−0.103696
$403$	−4.50315	−0.224318
$404$	4.76841	0.237237
$405$	−11.1587	−0.554478
$406$	20.2096	1.00298
$407$	0	0
$408$	1.48545	0.0735407
$409$	−20.9532	−1.03607	−0.518034	−	0.855360i	$-0.673336\pi$
$409$	−20.9532	−1.03607	−0.518034	+	0.855360i	$0.673336\pi$
$410$	9.76273	0.482147
$411$	0.530518	0.0261685
$412$	−86.1435	−4.24399
$413$	−47.5527	−2.33992
$414$	−31.4383	−1.54511
$415$	3.80236	0.186650
$416$	4.46336	0.218834
$417$	1.12344	0.0550150
$418$	0	0
$419$	−3.95756	−0.193339	−0.0966697	−	0.995317i	$-0.530819\pi$
$419$	−3.95756	−0.193339	−0.0966697	+	0.995317i	$0.530819\pi$
$420$	−1.44600	−0.0705577
$421$	0.432112	0.0210598	0.0105299	−	0.999945i	$-0.496648\pi$
$421$	0.432112	0.0210598	0.0105299	+	0.999945i	$0.496648\pi$
$422$	−35.9500	−1.75002
$423$	−10.9454	−0.532186
$424$	48.1934	2.34048
$425$	−10.4758	−0.508151
$426$	2.70949	0.131275
$427$	−8.61069	−0.416700
$428$	−58.8369	−2.84399
$429$	0	0
$430$	21.7862	1.05062
$431$	−9.45609	−0.455484	−0.227742	−	0.973722i	$-0.573134\pi$
$431$	−9.45609	−0.455484	−0.227742	+	0.973722i	$0.573134\pi$
$432$	−3.16275	−0.152168
$433$	−38.9251	−1.87062	−0.935310	−	0.353828i	$-0.884880\pi$
$433$	−38.9251	−1.87062	−0.935310	+	0.353828i	$0.884880\pi$
$434$	−37.3249	−1.79165
$435$	−0.244535	−0.0117246
$436$	−40.8808	−1.95784
$437$	31.3518	1.49976
$438$	1.09410	0.0522779
$439$	19.3922	0.925540	0.462770	−	0.886478i	$-0.346856\pi$
$439$	19.3922	0.925540	0.462770	+	0.886478i	$0.346856\pi$
$440$	0	0
$441$	−11.1753	−0.532155
$442$	7.69846	0.366178
$443$	0.903990	0.0429499	0.0214749	−	0.999769i	$-0.493164\pi$
$443$	0.903990	0.0429499	0.0214749	+	0.999769i	$0.493164\pi$
$444$	0.798749	0.0379069
$445$	21.5338	1.02080
$446$	7.69096	0.364177
$447$	0.927392	0.0438641
$448$	−6.02665	−0.284733
$449$	33.8321	1.59664	0.798319	−	0.602235i	$-0.205723\pi$
$449$	33.8321	1.59664	0.798319	+	0.602235i	$0.205723\pi$
$450$	26.0740	1.22914
$451$	0	0
$452$	47.9464	2.25521
$453$	1.40159	0.0658525
$454$	−8.25241	−0.387305
$455$	−4.08832	−0.191663
$456$	3.68708	0.172663
$457$	18.9041	0.884294	0.442147	−	0.896943i	$-0.354217\pi$
$457$	18.9041	0.884294	0.442147	+	0.896943i	$0.354217\pi$
$458$	−31.7522	−1.48368
$459$	−1.46573	−0.0684143
$460$	−22.7968	−1.06291
$461$	24.9625	1.16262	0.581309	−	0.813683i	$-0.302541\pi$
$461$	24.9625	1.16262	0.581309	+	0.813683i	$0.302541\pi$
$462$	0	0
$463$	8.38527	0.389696	0.194848	−	0.980833i	$-0.437579\pi$
$463$	8.38527	0.389696	0.194848	+	0.980833i	$0.437579\pi$
$464$	16.0092	0.743209
$465$	0.451631	0.0209439
$466$	41.7040	1.93190
$467$	−11.9301	−0.552058	−0.276029	−	0.961149i	$-0.589019\pi$
$467$	−11.9301	−0.552058	−0.276029	+	0.961149i	$0.589019\pi$
$468$	−13.1742	−0.608977
$469$	−33.4991	−1.54685
$470$	−11.5438	−0.532477
$471$	0.102292	0.00471338
$472$	−88.1659	−4.05816
$473$	0	0
$474$	−1.13215	−0.0520014
$475$	−26.0023	−1.19307
$476$	43.8718	2.01086
$477$	−23.7512	−1.08749
$478$	29.2720	1.33887
$479$	10.1184	0.462320	0.231160	−	0.972916i	$-0.425748\pi$
$479$	10.1184	0.462320	0.231160	+	0.972916i	$0.425748\pi$
$480$	−0.447641	−0.0204319
$481$	2.25832	0.102971
$482$	−37.3846	−1.70282
$483$	1.09296	0.0497313
$484$	0	0
$485$	9.41091	0.427327
$486$	5.47420	0.248315
$487$	−22.9433	−1.03966	−0.519831	−	0.854269i	$-0.674005\pi$
$487$	−22.9433	−1.03966	−0.519831	+	0.854269i	$0.674005\pi$
$488$	−15.9648	−0.722692
$489$	1.42368	0.0643810
$490$	−11.7862	−0.532446
$491$	29.9003	1.34938	0.674691	−	0.738101i	$-0.264277\pi$
$491$	29.9003	1.34938	0.674691	+	0.738101i	$0.264277\pi$
$492$	−1.09369	−0.0493074
$493$	7.41922	0.334145
$494$	19.1086	0.859734
$495$	0	0
$496$	−29.5673	−1.32761
$497$	43.6561	1.95824
$498$	−0.619550	−0.0277627
$499$	9.80634	0.438992	0.219496	−	0.975613i	$-0.429559\pi$
$499$	9.80634	0.438992	0.219496	+	0.975613i	$0.429559\pi$
$500$	46.3664	2.07357
$501$	−1.12032	−0.0500522
$502$	21.8673	0.975983
$503$	−12.4710	−0.556053	−0.278027	−	0.960573i	$-0.589680\pi$
$503$	−12.4710	−0.556053	−0.278027	+	0.960573i	$0.589680\pi$
$504$	−59.5712	−2.65351
$505$	−1.35212	−0.0601687
$506$	0	0
$507$	0.0803684	0.00356929
$508$	−48.4925	−2.15151
$509$	−26.3559	−1.16821	−0.584103	−	0.811680i	$-0.698553\pi$
$509$	−26.3559	−1.16821	−0.584103	+	0.811680i	$0.698553\pi$
$510$	−0.772095	−0.0341889
$511$	17.6284	0.779835
$512$	−50.4592	−2.23000
$513$	−3.63812	−0.160627
$514$	62.5368	2.75838
$515$	24.4267	1.07637
$516$	−2.44064	−0.107443
$517$	0	0
$518$	18.7184	0.822439
$519$	0.557842	0.0244866
$520$	−7.58001	−0.332405
$521$	8.94194	0.391754	0.195877	−	0.980629i	$-0.437245\pi$
$521$	8.94194	0.391754	0.195877	+	0.980629i	$0.437245\pi$
$522$	−18.4663	−0.808247
$523$	35.3218	1.54451	0.772257	−	0.635310i	$-0.219128\pi$
$523$	35.3218	1.54451	0.772257	+	0.635310i	$0.219128\pi$
$524$	−7.65124	−0.334246
$525$	−0.906467	−0.0395615
$526$	45.6008	1.98829
$527$	−13.7025	−0.596891
$528$	0	0
$529$	−5.76907	−0.250829
$530$	−25.0496	−1.08808
$531$	43.4508	1.88560
$532$	108.895	4.72122
$533$	−3.09222	−0.133939
$534$	−3.50869	−0.151836
$535$	16.6837	0.721299
$536$	−62.1096	−2.68272
$537$	0.733742	0.0316633
$538$	−70.7164	−3.04880
$539$	0	0
$540$	2.64539	0.113839
$541$	38.1030	1.63818	0.819089	−	0.573667i	$-0.194480\pi$
$541$	38.1030	1.63818	0.819089	+	0.573667i	$0.194480\pi$
$542$	−44.2131	−1.89911
$543$	0.400209	0.0171746
$544$	13.5815	0.582300
$545$	11.5921	0.496552
$546$	0.666144	0.0285083
$547$	8.30808	0.355228	0.177614	−	0.984100i	$-0.443162\pi$
$547$	8.30808	0.355228	0.177614	+	0.984100i	$0.443162\pi$
$548$	29.0505	1.24097
$549$	7.86792	0.335795
$550$	0	0
$551$	18.4155	0.784525
$552$	2.02641	0.0862499
$553$	−18.2416	−0.775711
$554$	35.2619	1.49814
$555$	−0.226492	−0.00961405
$556$	61.5180	2.60894
$557$	27.7483	1.17574	0.587868	−	0.808957i	$-0.299968\pi$
$557$	27.7483	1.17574	0.587868	+	0.808957i	$0.299968\pi$
$558$	34.1052	1.44379
$559$	−6.90049	−0.291860
$560$	−26.8436	−1.13435
$561$	0	0
$562$	−16.7588	−0.706929
$563$	−5.58475	−0.235369	−0.117685	−	0.993051i	$-0.537547\pi$
$563$	−5.58475	−0.235369	−0.117685	+	0.993051i	$0.537547\pi$
$564$	1.29322	0.0544544
$565$	−13.5956	−0.571972
$566$	−39.4935	−1.66004
$567$	29.2950	1.23027
$568$	80.9413	3.39622
$569$	8.25572	0.346098	0.173049	−	0.984913i	$-0.444638\pi$
$569$	8.25572	0.346098	0.173049	+	0.984913i	$0.444638\pi$
$570$	−1.91644	−0.0802708
$571$	18.1674	0.760283	0.380141	−	0.924928i	$-0.375875\pi$
$571$	18.1674	0.760283	0.380141	+	0.924928i	$0.375875\pi$
$572$	0	0
$573$	0.765581	0.0319826
$574$	−25.6302	−1.06979
$575$	−14.2908	−0.595969
$576$	5.50679	0.229450
$577$	−23.1561	−0.964000	−0.482000	−	0.876171i	$-0.660089\pi$
$577$	−23.1561	−0.964000	−0.482000	+	0.876171i	$0.660089\pi$
$578$	−19.5845	−0.814606
$579$	−1.62102	−0.0673673
$580$	−13.3904	−0.556007
$581$	−9.98238	−0.414139
$582$	−1.53340	−0.0635614
$583$	0	0
$584$	32.6842	1.35248
$585$	3.73566	0.154450
$586$	46.9046	1.93761
$587$	19.9179	0.822100	0.411050	−	0.911613i	$-0.365162\pi$
$587$	19.9179	0.822100	0.411050	+	0.911613i	$0.365162\pi$
$588$	1.32037	0.0544512
$589$	−34.0114	−1.40142
$590$	45.8261	1.88663
$591$	−1.21865	−0.0501286
$592$	14.8280	0.609426
$593$	−6.55107	−0.269020	−0.134510	−	0.990912i	$-0.542946\pi$
$593$	−6.55107	−0.269020	−0.134510	+	0.990912i	$0.542946\pi$
$594$	0	0
$595$	−12.4402	−0.510000
$596$	50.7828	2.08014
$597$	−0.0312691	−0.00127976
$598$	10.5020	0.429461
$599$	−10.9521	−0.447489	−0.223744	−	0.974648i	$-0.571828\pi$
$599$	−10.9521	−0.447489	−0.223744	+	0.974648i	$0.571828\pi$
$600$	−1.68065	−0.0686122
$601$	−3.16157	−0.128963	−0.0644815	−	0.997919i	$-0.520539\pi$
$601$	−3.16157	−0.128963	−0.0644815	+	0.997919i	$0.520539\pi$
$602$	−57.1956	−2.33112
$603$	30.6094	1.24651
$604$	76.7493	3.12289
$605$	0	0
$606$	0.220313	0.00894959
$607$	19.8957	0.807540	0.403770	−	0.914861i	$-0.367700\pi$
$607$	19.8957	0.807540	0.403770	+	0.914861i	$0.367700\pi$
$608$	33.7109	1.36716
$609$	0.641982	0.0260144
$610$	8.29805	0.335978
$611$	3.65635	0.147920
$612$	−40.0874	−1.62044
$613$	42.0589	1.69874	0.849371	−	0.527796i	$-0.176981\pi$
$613$	42.0589	1.69874	0.849371	+	0.527796i	$0.176981\pi$
$614$	−40.0413	−1.61594
$615$	0.310125	0.0125055
$616$	0	0
$617$	−11.6799	−0.470216	−0.235108	−	0.971969i	$-0.575544\pi$
$617$	−11.6799	−0.470216	−0.235108	+	0.971969i	$0.575544\pi$
$618$	−3.98006	−0.160101
$619$	3.99167	0.160439	0.0802193	−	0.996777i	$-0.474438\pi$
$619$	3.99167	0.160439	0.0802193	+	0.996777i	$0.474438\pi$
$620$	24.7307	0.993209
$621$	−1.99951	−0.0802375
$622$	24.4513	0.980408
$623$	−56.5331	−2.26495
$624$	0.527693	0.0211246
$625$	4.06607	0.162643
$626$	−43.7598	−1.74899
$627$	0	0
$628$	5.60139	0.223520
$629$	6.87179	0.273996
$630$	30.9635	1.23361
$631$	46.1728	1.83811	0.919055	−	0.394130i	$-0.128954\pi$
$631$	46.1728	1.83811	0.919055	+	0.394130i	$0.128954\pi$
$632$	−33.8211	−1.34533
$633$	−1.14200	−0.0453903
$634$	−74.9927	−2.97834
$635$	13.7505	0.545671
$636$	2.80623	0.111274
$637$	3.73312	0.147912
$638$	0	0
$639$	−39.8903	−1.57803
$640$	16.9475	0.669911
$641$	−19.3134	−0.762833	−0.381416	−	0.924403i	$-0.624564\pi$
$641$	−19.3134	−0.762833	−0.381416	+	0.924403i	$0.624564\pi$
$642$	−2.71842	−0.107287
$643$	5.27894	0.208181	0.104091	−	0.994568i	$-0.466807\pi$
$643$	5.27894	0.208181	0.104091	+	0.994568i	$0.466807\pi$
$644$	59.8489	2.35838
$645$	0.692065	0.0272501
$646$	58.1449	2.28768
$647$	10.6881	0.420192	0.210096	−	0.977681i	$-0.432622\pi$
$647$	10.6881	0.420192	0.210096	+	0.977681i	$0.432622\pi$
$648$	54.3148	2.13369
$649$	0	0
$650$	−8.71009	−0.341638
$651$	−1.18567	−0.0464702
$652$	77.9588	3.05310
$653$	5.46610	0.213905	0.106952	−	0.994264i	$-0.465891\pi$
$653$	5.46610	0.213905	0.106952	+	0.994264i	$0.465891\pi$
$654$	−1.88880	−0.0738579
$655$	2.16958	0.0847724
$656$	−20.3033	−0.792709
$657$	−16.1078	−0.628424
$658$	30.3062	1.18146
$659$	−29.6542	−1.15516	−0.577582	−	0.816332i	$-0.696004\pi$
$659$	−29.6542	−1.15516	−0.577582	+	0.816332i	$0.696004\pi$
$660$	0	0
$661$	23.8353	0.927084	0.463542	−	0.886075i	$-0.346578\pi$
$661$	23.8353	0.927084	0.463542	+	0.886075i	$0.346578\pi$
$662$	−17.8353	−0.693190
$663$	0.244551	0.00949758
$664$	−18.5080	−0.718250
$665$	−30.8783	−1.19741
$666$	−17.1037	−0.662756
$667$	10.1211	0.391891
$668$	−61.3472	−2.37360
$669$	0.244313	0.00944568
$670$	32.2828	1.24719
$671$	0	0
$672$	1.17520	0.0453342
$673$	−26.8864	−1.03639	−0.518197	−	0.855261i	$-0.673397\pi$
$673$	−26.8864	−1.03639	−0.518197	+	0.855261i	$0.673397\pi$
$674$	18.9223	0.728861
$675$	1.65834	0.0638293
$676$	4.40087	0.169264
$677$	6.11603	0.235058	0.117529	−	0.993069i	$-0.462503\pi$
$677$	6.11603	0.235058	0.117529	+	0.993069i	$0.462503\pi$
$678$	2.21525	0.0850761
$679$	−24.7066	−0.948152
$680$	−23.0650	−0.884503
$681$	−0.262148	−0.0100455
$682$	0	0
$683$	30.5930	1.17061	0.585304	−	0.810814i	$-0.300975\pi$
$683$	30.5930	1.17061	0.585304	+	0.810814i	$0.300975\pi$
$684$	−99.5021	−3.80456
$685$	−8.23752	−0.314739
$686$	−27.0779	−1.03384
$687$	−1.00865	−0.0384823
$688$	−45.3081	−1.72735
$689$	7.93413	0.302266
$690$	−1.05327	−0.0400974
$691$	36.0479	1.37133	0.685663	−	0.727919i	$-0.259512\pi$
$691$	36.0479	1.37133	0.685663	+	0.727919i	$0.259512\pi$
$692$	30.5467	1.16121
$693$	0	0
$694$	3.88286	0.147391
$695$	−17.4440	−0.661687
$696$	1.19028	0.0451173
$697$	−9.40923	−0.356400
$698$	27.1973	1.02943
$699$	1.32478	0.0501078
$700$	−49.6369	−1.87610
$701$	−24.5791	−0.928339	−0.464169	−	0.885747i	$-0.653647\pi$
$701$	−24.5791	−0.928339	−0.464169	+	0.885747i	$0.653647\pi$
$702$	−1.21868	−0.0459960
$703$	17.0567	0.643304
$704$	0	0
$705$	−0.366704	−0.0138109
$706$	5.37946	0.202459
$707$	3.54975	0.133502
$708$	−5.13377	−0.192939
$709$	14.4080	0.541102	0.270551	−	0.962706i	$-0.412794\pi$
$709$	14.4080	0.541102	0.270551	+	0.962706i	$0.412794\pi$
$710$	−42.0710	−1.57890
$711$	16.6680	0.625100
$712$	−104.816	−3.92815
$713$	−18.6926	−0.700045
$714$	2.02699	0.0758583
$715$	0	0
$716$	40.1787	1.50155
$717$	0.929863	0.0347264
$718$	11.0550	0.412569
$719$	5.45468	0.203425	0.101713	−	0.994814i	$-0.467568\pi$
$719$	5.45468	0.203425	0.101713	+	0.994814i	$0.467568\pi$
$720$	24.5280	0.914105
$721$	−64.1279	−2.38825
$722$	96.2533	3.58218
$723$	−1.18757	−0.0441662
$724$	21.9149	0.814462
$725$	−8.39417	−0.311752
$726$	0	0
$727$	9.26097	0.343470	0.171735	−	0.985143i	$-0.445063\pi$
$727$	9.26097	0.343470	0.171735	+	0.985143i	$0.445063\pi$
$728$	19.8999	0.737540
$729$	−26.6518	−0.987105
$730$	−16.9884	−0.628767
$731$	−20.9973	−0.776614
$732$	−0.929606	−0.0343592
$733$	−35.9220	−1.32681	−0.663404	−	0.748261i	$-0.730889\pi$
$733$	−35.9220	−1.32681	−0.663404	+	0.748261i	$0.730889\pi$
$734$	3.02128	0.111518
$735$	−0.374403	−0.0138101
$736$	18.5275	0.682932
$737$	0	0
$738$	23.4194	0.862078
$739$	40.0365	1.47277	0.736383	−	0.676565i	$-0.236532\pi$
$739$	40.0365	1.47277	0.736383	+	0.676565i	$0.236532\pi$
$740$	−12.4024	−0.455922
$741$	0.607007	0.0222990
$742$	65.7631	2.41424
$743$	−23.6293	−0.866873	−0.433437	−	0.901184i	$-0.642699\pi$
$743$	−23.6293	−0.866873	−0.433437	+	0.901184i	$0.642699\pi$
$744$	−2.19832	−0.0805942
$745$	−14.3999	−0.527571
$746$	11.5867	0.424218
$747$	9.12129	0.333731
$748$	0	0
$749$	−43.8000	−1.60042
$750$	2.14225	0.0782238
$751$	−8.85058	−0.322962	−0.161481	−	0.986876i	$-0.551627\pi$
$751$	−8.85058	−0.322962	−0.161481	+	0.986876i	$0.551627\pi$
$752$	24.0073	0.875457
$753$	0.694641	0.0253141
$754$	6.16870	0.224651
$755$	−21.7629	−0.792035
$756$	−6.94497	−0.252586
$757$	−0.273477	−0.00993970	−0.00496985	−	0.999988i	$-0.501582\pi$
$757$	−0.273477	−0.00993970	−0.00496985	+	0.999988i	$0.501582\pi$
$758$	32.4806	1.17975
$759$	0	0
$760$	−57.2503	−2.07669
$761$	10.5124	0.381074	0.190537	−	0.981680i	$-0.438977\pi$
$761$	10.5124	0.381074	0.190537	+	0.981680i	$0.438977\pi$
$762$	−2.24048	−0.0811640
$763$	−30.4329	−1.10175
$764$	41.9222	1.51669
$765$	11.3671	0.410979
$766$	−7.41298	−0.267842
$767$	−14.5148	−0.524100
$768$	−2.46572	−0.0889741
$769$	35.1105	1.26612	0.633059	−	0.774104i	$-0.281799\pi$
$769$	35.1105	1.26612	0.633059	+	0.774104i	$0.281799\pi$
$770$	0	0
$771$	1.98656	0.0715442
$772$	−88.7649	−3.19472
$773$	−8.29986	−0.298525	−0.149263	−	0.988798i	$-0.547690\pi$
$773$	−8.29986	−0.298525	−0.149263	+	0.988798i	$0.547690\pi$
$774$	52.2618	1.87851
$775$	15.5031	0.556889
$776$	−45.8077	−1.64440
$777$	0.594613	0.0213316
$778$	41.1603	1.47567
$779$	−23.3549	−0.836777
$780$	−0.441373	−0.0158037
$781$	0	0
$782$	31.9564	1.14276
$783$	−1.17447	−0.0419723
$784$	24.5114	0.875407
$785$	−1.58832	−0.0566897
$786$	−0.353507	−0.0126092
$787$	−50.7152	−1.80780	−0.903901	−	0.427742i	$-0.859309\pi$
$787$	−50.7152	−1.80780	−0.903901	+	0.427742i	$0.859309\pi$
$788$	−66.7317	−2.37722
$789$	1.44857	0.0515704
$790$	17.5793	0.625442
$791$	35.6928	1.26909
$792$	0	0
$793$	−2.62830	−0.0933336
$794$	78.6787	2.79220
$795$	−0.795732	−0.0282217
$796$	−1.71225	−0.0606892
$797$	−36.4542	−1.29127	−0.645637	−	0.763645i	$-0.723408\pi$
$797$	−36.4542	−1.29127	−0.645637	+	0.763645i	$0.723408\pi$
$798$	5.03126	0.178105
$799$	11.1258	0.393603
$800$	−15.3662	−0.543276
$801$	51.6565	1.82519
$802$	70.6168	2.49356
$803$	0	0
$804$	−3.61655	−0.127546
$805$	−16.9707	−0.598138
$806$	−11.3929	−0.401299
$807$	−2.24640	−0.0790769
$808$	6.58147	0.231535
$809$	−40.7772	−1.43365	−0.716825	−	0.697254i	$-0.754405\pi$
$809$	−40.7772	−1.43365	−0.716825	+	0.697254i	$0.754405\pi$
$810$	−28.2313	−0.991948
$811$	−20.7362	−0.728145	−0.364072	−	0.931371i	$-0.618614\pi$
$811$	−20.7362	−0.728145	−0.364072	+	0.931371i	$0.618614\pi$
$812$	35.1541	1.23367
$813$	−1.40448	−0.0492574
$814$	0	0
$815$	−22.1059	−0.774336
$816$	1.60570	0.0562108
$817$	−52.1181	−1.82338
$818$	−53.0114	−1.85350
$819$	−9.80727	−0.342694
$820$	16.9821	0.593039
$821$	25.9947	0.907223	0.453611	−	0.891200i	$-0.350135\pi$
$821$	25.9947	0.907223	0.453611	+	0.891200i	$0.350135\pi$
$822$	1.34221	0.0468149
$823$	−23.3787	−0.814932	−0.407466	−	0.913220i	$-0.633587\pi$
$823$	−23.3787	−0.814932	−0.407466	+	0.913220i	$0.633587\pi$
$824$	−118.897	−4.14199
$825$	0	0
$826$	−120.308	−4.18605
$827$	−16.2931	−0.566568	−0.283284	−	0.959036i	$-0.591424\pi$
$827$	−16.2931	−0.566568	−0.283284	+	0.959036i	$0.591424\pi$
$828$	−54.6863	−1.90048
$829$	23.0389	0.800173	0.400086	−	0.916477i	$-0.368980\pi$
$829$	23.0389	0.800173	0.400086	+	0.916477i	$0.368980\pi$
$830$	9.61994	0.333913
$831$	1.12014	0.0388572
$832$	−1.83956	−0.0637752
$833$	11.3594	0.393581
$834$	2.84229	0.0984205
$835$	17.3955	0.601998
$836$	0	0
$837$	2.16913	0.0749761
$838$	−10.0126	−0.345880
$839$	12.5602	0.433626	0.216813	−	0.976213i	$-0.430434\pi$
$839$	12.5602	0.433626	0.216813	+	0.976213i	$0.430434\pi$
$840$	−1.99581	−0.0688619
$841$	−23.0550	−0.795001
$842$	1.09324	0.0376756
$843$	−0.532365	−0.0183356
$844$	−62.5343	−2.15252
$845$	−1.24791	−0.0429292
$846$	−27.6919	−0.952068
$847$	0	0
$848$	52.0949	1.78895
$849$	−1.25456	−0.0430564
$850$	−26.5037	−0.909070
$851$	9.37433	0.321348
$852$	4.71309	0.161468
$853$	−44.4245	−1.52107	−0.760533	−	0.649299i	$-0.775062\pi$
$853$	−44.4245	−1.52107	−0.760533	+	0.649299i	$0.775062\pi$
$854$	−21.7850	−0.745467
$855$	28.2147	0.964922
$856$	−81.2081	−2.77563
$857$	15.4929	0.529227	0.264614	−	0.964355i	$-0.414756\pi$
$857$	15.4929	0.529227	0.264614	+	0.964355i	$0.414756\pi$
$858$	0	0
$859$	−11.1682	−0.381055	−0.190528	−	0.981682i	$-0.561020\pi$
$859$	−11.1682	−0.381055	−0.190528	+	0.981682i	$0.561020\pi$
$860$	37.8966	1.29226
$861$	−0.814177	−0.0277471
$862$	−23.9239	−0.814850
$863$	−23.0883	−0.785933	−0.392967	−	0.919553i	$-0.628551\pi$
$863$	−23.0883	−0.785933	−0.392967	+	0.919553i	$0.628551\pi$
$864$	−2.14996	−0.0731433
$865$	−8.66179	−0.294510
$866$	−98.4803	−3.34650
$867$	−0.622125	−0.0211285
$868$	−64.9259	−2.20373
$869$	0	0
$870$	−0.618673	−0.0209750
$871$	−10.2252	−0.346466
$872$	−56.4247	−1.91078
$873$	22.5754	0.764061
$874$	79.3199	2.68304
$875$	34.5166	1.16687
$876$	1.90316	0.0643017
$877$	4.82322	0.162869	0.0814343	−	0.996679i	$-0.474050\pi$
$877$	4.82322	0.162869	0.0814343	+	0.996679i	$0.474050\pi$
$878$	49.0622	1.65577
$879$	1.48998	0.0502559
$880$	0	0
$881$	4.26489	0.143688	0.0718439	−	0.997416i	$-0.477112\pi$
$881$	4.26489	0.143688	0.0718439	+	0.997416i	$0.477112\pi$
$882$	−28.2733	−0.952013
$883$	38.3785	1.29154	0.645770	−	0.763532i	$-0.276537\pi$
$883$	38.3785	1.29154	0.645770	+	0.763532i	$0.276537\pi$
$884$	13.3913	0.450398
$885$	1.45572	0.0489337
$886$	2.28709	0.0768363
$887$	−55.2454	−1.85496	−0.927480	−	0.373872i	$-0.878030\pi$
$887$	−55.2454	−1.85496	−0.927480	+	0.373872i	$0.878030\pi$
$888$	1.10245	0.0369959
$889$	−36.0993	−1.21073
$890$	54.4805	1.82619
$891$	0	0
$892$	13.3783	0.447937
$893$	27.6157	0.924125
$894$	2.34630	0.0784719
$895$	−11.3930	−0.380827
$896$	−44.4927	−1.48640
$897$	0.333611	0.0111389
$898$	85.5951	2.85635
$899$	−10.9797	−0.366194
$900$	45.3552	1.51184
$901$	24.1426	0.804306
$902$	0	0
$903$	−1.81689	−0.0604623
$904$	66.1768	2.20101
$905$	−6.21417	−0.206566
$906$	3.54602	0.117809
$907$	43.7830	1.45379	0.726895	−	0.686749i	$-0.240963\pi$
$907$	43.7830	1.45379	0.726895	+	0.686749i	$0.240963\pi$
$908$	−14.3549	−0.476384
$909$	−3.24354	−0.107582
$910$	−10.3434	−0.342881
$911$	−26.8560	−0.889781	−0.444890	−	0.895585i	$-0.646757\pi$
$911$	−26.8560	−0.889781	−0.444890	+	0.895585i	$0.646757\pi$
$912$	3.98556	0.131975
$913$	0	0
$914$	47.8271	1.58198
$915$	0.263598	0.00871428
$916$	−55.2323	−1.82493
$917$	−5.69582	−0.188093
$918$	−3.70828	−0.122391
$919$	41.2597	1.36103	0.680515	−	0.732734i	$-0.261756\pi$
$919$	41.2597	1.36103	0.680515	+	0.732734i	$0.261756\pi$
$920$	−31.4647	−1.03736
$921$	−1.27196	−0.0419126
$922$	63.1549	2.07989
$923$	13.3254	0.438612
$924$	0	0
$925$	−7.77480	−0.255634
$926$	21.2147	0.697158
$927$	58.5962	1.92455
$928$	10.8827	0.357242
$929$	−29.2549	−0.959823	−0.479912	−	0.877317i	$-0.659331\pi$
$929$	−29.2549	−0.959823	−0.479912	+	0.877317i	$0.659331\pi$
$930$	1.14262	0.0374681
$931$	28.1956	0.924072
$932$	72.5432	2.37623
$933$	0.776727	0.0254289
$934$	−30.1830	−0.987618
$935$	0	0
$936$	−18.1833	−0.594341
$937$	2.70999	0.0885316	0.0442658	−	0.999020i	$-0.485905\pi$
$937$	2.70999	0.0885316	0.0442658	+	0.999020i	$0.485905\pi$
$938$	−84.7525	−2.76727
$939$	−1.39009	−0.0453637
$940$	−20.0802	−0.654945
$941$	59.5001	1.93965	0.969824	−	0.243806i	$-0.0783960\pi$
$941$	59.5001	1.93965	0.969824	+	0.243806i	$0.0783960\pi$
$942$	0.258799	0.00843213
$943$	−12.8358	−0.417993
$944$	−95.3033	−3.10186
$945$	1.96931	0.0640616
$946$	0	0
$947$	36.9507	1.20074	0.600369	−	0.799723i	$-0.295020\pi$
$947$	36.9507	1.20074	0.600369	+	0.799723i	$0.295020\pi$
$948$	−1.96935	−0.0639616
$949$	5.38084	0.174669
$950$	−65.7856	−2.13437
$951$	−2.38224	−0.0772493
$952$	60.5530	1.96253
$953$	−2.56877	−0.0832105	−0.0416053	−	0.999134i	$-0.513247\pi$
$953$	−2.56877	−0.0832105	−0.0416053	+	0.999134i	$0.513247\pi$
$954$	−60.0903	−1.94549
$955$	−11.8874	−0.384667
$956$	50.9181	1.64681
$957$	0	0
$958$	25.5994	0.827080
$959$	21.6261	0.698342
$960$	0.184493	0.00595449
$961$	−10.7216	−0.345859
$962$	5.71354	0.184212
$963$	40.0217	1.28968
$964$	−65.0298	−2.09447
$965$	25.1701	0.810253
$966$	2.76517	0.0889680
$967$	30.7435	0.988643	0.494322	−	0.869279i	$-0.335416\pi$
$967$	30.7435	0.988643	0.494322	+	0.869279i	$0.335416\pi$
$968$	0	0
$969$	1.84705	0.0593357
$970$	23.8095	0.764478
$971$	37.6815	1.20926	0.604628	−	0.796508i	$-0.293322\pi$
$971$	37.6815	1.20926	0.604628	+	0.796508i	$0.293322\pi$
$972$	9.52226	0.305427
$973$	45.7959	1.46815
$974$	−58.0465	−1.85993
$975$	−0.276687	−0.00886108
$976$	−17.2572	−0.552390
$977$	−31.4933	−1.00756	−0.503781	−	0.863832i	$-0.668058\pi$
$977$	−31.4933	−1.00756	−0.503781	+	0.863832i	$0.668058\pi$
$978$	3.60190	0.115176
$979$	0	0
$980$	−20.5018	−0.654907
$981$	27.8078	0.887834
$982$	75.6476	2.41401
$983$	40.4825	1.29119	0.645596	−	0.763679i	$-0.276609\pi$
$983$	40.4825	1.29119	0.645596	+	0.763679i	$0.276609\pi$
$984$	−1.50954	−0.0481223
$985$	18.9223	0.602916
$986$	18.7706	0.597777
$987$	0.962713	0.0306435
$988$	33.2389	1.05747
$989$	−28.6440	−0.910828
$990$	0	0
$991$	−46.4809	−1.47651	−0.738257	−	0.674520i	$-0.764351\pi$
$991$	−46.4809	−1.47651	−0.738257	+	0.674520i	$0.764351\pi$
$992$	−20.0992	−0.638150
$993$	−0.566562	−0.0179793
$994$	110.450	3.50325
$995$	0.485524	0.0153922
$996$	−1.07769	−0.0341480
$997$	−16.6114	−0.526089	−0.263045	−	0.964784i	$-0.584727\pi$
$997$	−16.6114	−0.526089	−0.263045	+	0.964784i	$0.584727\pi$
$998$	24.8100	0.785346
$999$	−1.08781	−0.0344169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.2.a.s.1.14		14
11.5	even	5		143.2.h.c.14.1	✓	28
11.9	even	5		143.2.h.c.92.1	yes	28
11.10	odd	2		1573.2.a.r.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.1	✓	28	11.5	even	5
143.2.h.c.92.1	yes	28	11.9	even	5
1573.2.a.r.1.1		14	11.10	odd	2
1573.2.a.s.1.14		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+2.52999 q^{2} +0.0803684 q^{3} +4.40087 q^{4} -1.24791 q^{5} +0.203332 q^{6} +3.27614 q^{7} +6.07419 q^{8} -2.99354 q^{9} +O(q^{10})\)	\(q+2.52999 q^{2} +0.0803684 q^{3} +4.40087 q^{4} -1.24791 q^{5} +0.203332 q^{6} +3.27614 q^{7} +6.07419 q^{8} -2.99354 q^{9} -3.15719 q^{10} +0.353691 q^{12} +1.00000 q^{13} +8.28863 q^{14} -0.100292 q^{15} +6.56592 q^{16} +3.04287 q^{17} -7.57364 q^{18} +7.55280 q^{19} -5.49187 q^{20} +0.263299 q^{21} +4.15102 q^{23} +0.488173 q^{24} -3.44273 q^{25} +2.52999 q^{26} -0.481692 q^{27} +14.4179 q^{28} +2.43823 q^{29} -0.253739 q^{30} -4.50315 q^{31} +4.46336 q^{32} +7.69846 q^{34} -4.08832 q^{35} -13.1742 q^{36} +2.25832 q^{37} +19.1086 q^{38} +0.0803684 q^{39} -7.58001 q^{40} -3.09222 q^{41} +0.666144 q^{42} -6.90049 q^{43} +3.73566 q^{45} +10.5020 q^{46} +3.65635 q^{47} +0.527693 q^{48} +3.73312 q^{49} -8.71009 q^{50} +0.244551 q^{51} +4.40087 q^{52} +7.93413 q^{53} -1.21868 q^{54} +19.8999 q^{56} +0.607007 q^{57} +6.16870 q^{58} -14.5148 q^{59} -0.441373 q^{60} -2.62830 q^{61} -11.3929 q^{62} -9.80727 q^{63} -1.83956 q^{64} -1.24791 q^{65} -10.2252 q^{67} +13.3913 q^{68} +0.333611 q^{69} -10.3434 q^{70} +13.3254 q^{71} -18.1833 q^{72} +5.38084 q^{73} +5.71354 q^{74} -0.276687 q^{75} +33.2389 q^{76} +0.203332 q^{78} -5.56800 q^{79} -8.19365 q^{80} +8.94191 q^{81} -7.82329 q^{82} -3.04699 q^{83} +1.15874 q^{84} -3.79722 q^{85} -17.4582 q^{86} +0.195957 q^{87} -17.2560 q^{89} +9.45119 q^{90} +3.27614 q^{91} +18.2681 q^{92} -0.361911 q^{93} +9.25055 q^{94} -9.42518 q^{95} +0.358714 q^{96} -7.54136 q^{97} +9.44478 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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