LMFDB - Embedded newform 9610.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9610,2,Mod(1,9610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9610, 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("9610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9610 = 2 \cdot 5 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9610.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:	$76.7362363425$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 310)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	9610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -3.46410 q^{7} -1.00000 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -3.46410 q^{7} -1.00000 q^{8} -2.46410 q^{9} +1.00000 q^{10} +2.73205 q^{11} -0.732051 q^{12} +1.26795 q^{13} +3.46410 q^{14} +0.732051 q^{15} +1.00000 q^{16} +4.00000 q^{17} +2.46410 q^{18} +5.46410 q^{19} -1.00000 q^{20} +2.53590 q^{21} -2.73205 q^{22} +0.535898 q^{23} +0.732051 q^{24} +1.00000 q^{25} -1.26795 q^{26} +4.00000 q^{27} -3.46410 q^{28} -0.732051 q^{29} -0.732051 q^{30} -1.00000 q^{32} -2.00000 q^{33} -4.00000 q^{34} +3.46410 q^{35} -2.46410 q^{36} +6.73205 q^{37} -5.46410 q^{38} -0.928203 q^{39} +1.00000 q^{40} -2.53590 q^{41} -2.53590 q^{42} -3.26795 q^{43} +2.73205 q^{44} +2.46410 q^{45} -0.535898 q^{46} -3.46410 q^{47} -0.732051 q^{48} +5.00000 q^{49} -1.00000 q^{50} -2.92820 q^{51} +1.26795 q^{52} +5.26795 q^{53} -4.00000 q^{54} -2.73205 q^{55} +3.46410 q^{56} -4.00000 q^{57} +0.732051 q^{58} +5.46410 q^{59} +0.732051 q^{60} -9.12436 q^{61} +8.53590 q^{63} +1.00000 q^{64} -1.26795 q^{65} +2.00000 q^{66} +8.39230 q^{67} +4.00000 q^{68} -0.392305 q^{69} -3.46410 q^{70} -13.8564 q^{71} +2.46410 q^{72} +4.39230 q^{73} -6.73205 q^{74} -0.732051 q^{75} +5.46410 q^{76} -9.46410 q^{77} +0.928203 q^{78} -17.4641 q^{79} -1.00000 q^{80} +4.46410 q^{81} +2.53590 q^{82} +4.73205 q^{83} +2.53590 q^{84} -4.00000 q^{85} +3.26795 q^{86} +0.535898 q^{87} -2.73205 q^{88} -0.928203 q^{89} -2.46410 q^{90} -4.39230 q^{91} +0.535898 q^{92} +3.46410 q^{94} -5.46410 q^{95} +0.732051 q^{96} +4.00000 q^{97} -5.00000 q^{98} -6.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{13} - 2 q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 4 q^{19} - 2 q^{20} + 12 q^{21} - 2 q^{22} + 8 q^{23} - 2 q^{24} + 2 q^{25} - 6 q^{26} + 8 q^{27} + 2 q^{29} + 2 q^{30} - 2 q^{32} - 4 q^{33} - 8 q^{34} + 2 q^{36} + 10 q^{37} - 4 q^{38} + 12 q^{39} + 2 q^{40} - 12 q^{41} - 12 q^{42} - 10 q^{43} + 2 q^{44} - 2 q^{45} - 8 q^{46} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 8 q^{51} + 6 q^{52} + 14 q^{53} - 8 q^{54} - 2 q^{55} - 8 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} + 6 q^{61} + 24 q^{63} + 2 q^{64} - 6 q^{65} + 4 q^{66} - 4 q^{67} + 8 q^{68} + 20 q^{69} - 2 q^{72} - 12 q^{73} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 12 q^{77} - 12 q^{78} - 28 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} + 6 q^{83} + 12 q^{84} - 8 q^{85} + 10 q^{86} + 8 q^{87} - 2 q^{88} + 12 q^{89} + 2 q^{90} + 12 q^{91} + 8 q^{92} - 4 q^{95} - 2 q^{96} + 8 q^{97} - 10 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^13 - 2 * q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 4 * q^19 - 2 * q^20 + 12 * q^21 - 2 * q^22 + 8 * q^23 - 2 * q^24 + 2 * q^25 - 6 * q^26 + 8 * q^27 + 2 * q^29 + 2 * q^30 - 2 * q^32 - 4 * q^33 - 8 * q^34 + 2 * q^36 + 10 * q^37 - 4 * q^38 + 12 * q^39 + 2 * q^40 - 12 * q^41 - 12 * q^42 - 10 * q^43 + 2 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 8 * q^51 + 6 * q^52 + 14 * q^53 - 8 * q^54 - 2 * q^55 - 8 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 + 6 * q^61 + 24 * q^63 + 2 * q^64 - 6 * q^65 + 4 * q^66 - 4 * q^67 + 8 * q^68 + 20 * q^69 - 2 * q^72 - 12 * q^73 - 10 * q^74 + 2 * q^75 + 4 * q^76 - 12 * q^77 - 12 * q^78 - 28 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 + 6 * q^83 + 12 * q^84 - 8 * q^85 + 10 * q^86 + 8 * q^87 - 2 * q^88 + 12 * q^89 + 2 * q^90 + 12 * q^91 + 8 * q^92 - 4 * q^95 - 2 * q^96 + 8 * q^97 - 10 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.732051	0.298858
$7$	−3.46410	−1.30931	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−3.46410	−1.30931	−0.654654	+	0.755929i	$0.727186\pi$
$8$	−1.00000	−0.353553
$9$	−2.46410	−0.821367
$10$	1.00000	0.316228
$11$	2.73205	0.823744	0.411872	−	0.911242i	$-0.364875\pi$
$11$	2.73205	0.823744	0.411872	+	0.911242i	$0.364875\pi$
$12$	−0.732051	−0.211325
$13$	1.26795	0.351666	0.175833	−	0.984420i	$-0.443738\pi$
$13$	1.26795	0.351666	0.175833	+	0.984420i	$0.443738\pi$
$14$	3.46410	0.925820
$15$	0.732051	0.189015
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	2.46410	0.580794
$19$	5.46410	1.25355	0.626775	−	0.779200i	$-0.284374\pi$
$19$	5.46410	1.25355	0.626775	+	0.779200i	$0.284374\pi$
$20$	−1.00000	−0.223607
$21$	2.53590	0.553378
$22$	−2.73205	−0.582475
$23$	0.535898	0.111743	0.0558713	−	0.998438i	$-0.482206\pi$
$23$	0.535898	0.111743	0.0558713	+	0.998438i	$0.482206\pi$
$24$	0.732051	0.149429
$25$	1.00000	0.200000
$26$	−1.26795	−0.248665
$27$	4.00000	0.769800
$28$	−3.46410	−0.654654
$29$	−0.732051	−0.135938	−0.0679692	−	0.997687i	$-0.521652\pi$
$29$	−0.732051	−0.135938	−0.0679692	+	0.997687i	$0.521652\pi$
$30$	−0.732051	−0.133654
$31$	0	0
$31$	0	0
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−4.00000	−0.685994
$35$	3.46410	0.585540
$36$	−2.46410	−0.410684
$37$	6.73205	1.10674	0.553371	−	0.832935i	$-0.313341\pi$
$37$	6.73205	1.10674	0.553371	+	0.832935i	$0.313341\pi$
$38$	−5.46410	−0.886394
$39$	−0.928203	−0.148631
$40$	1.00000	0.158114
$41$	−2.53590	−0.396041	−0.198020	−	0.980198i	$-0.563451\pi$
$41$	−2.53590	−0.396041	−0.198020	+	0.980198i	$0.563451\pi$
$42$	−2.53590	−0.391298
$43$	−3.26795	−0.498358	−0.249179	−	0.968458i	$-0.580161\pi$
$43$	−3.26795	−0.498358	−0.249179	+	0.968458i	$0.580161\pi$
$44$	2.73205	0.411872
$45$	2.46410	0.367327
$46$	−0.535898	−0.0790139
$47$	−3.46410	−0.505291	−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410	−0.505291	−0.252646	+	0.967559i	$0.581301\pi$
$48$	−0.732051	−0.105662
$49$	5.00000	0.714286
$50$	−1.00000	−0.141421
$51$	−2.92820	−0.410030
$52$	1.26795	0.175833
$53$	5.26795	0.723608	0.361804	−	0.932254i	$-0.382161\pi$
$53$	5.26795	0.723608	0.361804	+	0.932254i	$0.382161\pi$
$54$	−4.00000	−0.544331
$55$	−2.73205	−0.368390
$56$	3.46410	0.462910
$57$	−4.00000	−0.529813
$58$	0.732051	0.0961230
$59$	5.46410	0.711365	0.355683	−	0.934607i	$-0.384248\pi$
$59$	5.46410	0.711365	0.355683	+	0.934607i	$0.384248\pi$
$60$	0.732051	0.0945074
$61$	−9.12436	−1.16825	−0.584127	−	0.811662i	$-0.698563\pi$
$61$	−9.12436	−1.16825	−0.584127	+	0.811662i	$0.698563\pi$
$62$	0	0
$63$	8.53590	1.07542
$64$	1.00000	0.125000
$65$	−1.26795	−0.157270
$66$	2.00000	0.246183
$67$	8.39230	1.02528	0.512642	−	0.858603i	$-0.328667\pi$
$67$	8.39230	1.02528	0.512642	+	0.858603i	$0.328667\pi$
$68$	4.00000	0.485071
$69$	−0.392305	−0.0472280
$70$	−3.46410	−0.414039
$71$	−13.8564	−1.64445	−0.822226	−	0.569160i	$-0.807268\pi$
$71$	−13.8564	−1.64445	−0.822226	+	0.569160i	$0.807268\pi$
$72$	2.46410	0.290397
$73$	4.39230	0.514080	0.257040	−	0.966401i	$-0.417253\pi$
$73$	4.39230	0.514080	0.257040	+	0.966401i	$0.417253\pi$
$74$	−6.73205	−0.782585
$75$	−0.732051	−0.0845299
$76$	5.46410	0.626775
$77$	−9.46410	−1.07853
$78$	0.928203	0.105098
$79$	−17.4641	−1.96486	−0.982432	−	0.186618i	$-0.940247\pi$
$79$	−17.4641	−1.96486	−0.982432	+	0.186618i	$0.940247\pi$
$80$	−1.00000	−0.111803
$81$	4.46410	0.496011
$82$	2.53590	0.280043
$83$	4.73205	0.519410	0.259705	−	0.965688i	$-0.416375\pi$
$83$	4.73205	0.519410	0.259705	+	0.965688i	$0.416375\pi$
$84$	2.53590	0.276689
$85$	−4.00000	−0.433861
$86$	3.26795	0.352392
$87$	0.535898	0.0574543
$88$	−2.73205	−0.291238
$89$	−0.928203	−0.0983893	−0.0491947	−	0.998789i	$-0.515665\pi$
$89$	−0.928203	−0.0983893	−0.0491947	+	0.998789i	$0.515665\pi$
$90$	−2.46410	−0.259739
$91$	−4.39230	−0.460439
$92$	0.535898	0.0558713
$93$	0	0
$94$	3.46410	0.357295
$95$	−5.46410	−0.560605
$96$	0.732051	0.0747146
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	−5.00000	−0.505076
$99$	−6.73205	−0.676597
$100$	1.00000	0.100000
$101$	−16.9282	−1.68442	−0.842210	−	0.539150i	$-0.818745\pi$
$101$	−16.9282	−1.68442	−0.842210	+	0.539150i	$0.818745\pi$
$102$	2.92820	0.289935
$103$	2.92820	0.288524	0.144262	−	0.989539i	$-0.453919\pi$
$103$	2.92820	0.288524	0.144262	+	0.989539i	$0.453919\pi$
$104$	−1.26795	−0.124333
$105$	−2.53590	−0.247478
$106$	−5.26795	−0.511668
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	4.00000	0.384900
$109$	−15.4641	−1.48119	−0.740596	−	0.671950i	$-0.765457\pi$
$109$	−15.4641	−1.48119	−0.740596	+	0.671950i	$0.765457\pi$
$110$	2.73205	0.260491
$111$	−4.92820	−0.467764
$112$	−3.46410	−0.327327
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	4.00000	0.374634
$115$	−0.535898	−0.0499728
$116$	−0.732051	−0.0679692
$117$	−3.12436	−0.288847
$118$	−5.46410	−0.503011
$119$	−13.8564	−1.27021
$120$	−0.732051	−0.0668268
$121$	−3.53590	−0.321445
$122$	9.12436	0.826080
$123$	1.85641	0.167387
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	−8.53590	−0.760438
$127$	15.8564	1.40703	0.703514	−	0.710681i	$-0.251613\pi$
$127$	15.8564	1.40703	0.703514	+	0.710681i	$0.251613\pi$
$128$	−1.00000	−0.0883883
$129$	2.39230	0.210631
$130$	1.26795	0.111207
$131$	12.3923	1.08272	0.541360	−	0.840791i	$-0.317909\pi$
$131$	12.3923	1.08272	0.541360	+	0.840791i	$0.317909\pi$
$132$	−2.00000	−0.174078
$133$	−18.9282	−1.64128
$134$	−8.39230	−0.724985
$135$	−4.00000	−0.344265
$136$	−4.00000	−0.342997
$137$	20.7846	1.77575	0.887875	−	0.460086i	$-0.152181\pi$
$137$	20.7846	1.77575	0.887875	+	0.460086i	$0.152181\pi$
$138$	0.392305	0.0333952
$139$	−13.6603	−1.15865	−0.579324	−	0.815097i	$-0.696683\pi$
$139$	−13.6603	−1.15865	−0.579324	+	0.815097i	$0.696683\pi$
$140$	3.46410	0.292770
$141$	2.53590	0.213561
$142$	13.8564	1.16280
$143$	3.46410	0.289683
$144$	−2.46410	−0.205342
$145$	0.732051	0.0607935
$146$	−4.39230	−0.363510
$147$	−3.66025	−0.301893
$148$	6.73205	0.553371
$149$	−13.3205	−1.09126	−0.545629	−	0.838027i	$-0.683709\pi$
$149$	−13.3205	−1.09126	−0.545629	+	0.838027i	$0.683709\pi$
$150$	0.732051	0.0597717
$151$	−1.46410	−0.119147	−0.0595734	−	0.998224i	$-0.518974\pi$
$151$	−1.46410	−0.119147	−0.0595734	+	0.998224i	$0.518974\pi$
$152$	−5.46410	−0.443197
$153$	−9.85641	−0.796843
$154$	9.46410	0.762639
$155$	0	0
$156$	−0.928203	−0.0743157
$157$	−19.8564	−1.58471	−0.792357	−	0.610058i	$-0.791146\pi$
$157$	−19.8564	−1.58471	−0.792357	+	0.610058i	$0.791146\pi$
$158$	17.4641	1.38937
$159$	−3.85641	−0.305833
$160$	1.00000	0.0790569
$161$	−1.85641	−0.146305
$162$	−4.46410	−0.350733
$163$	−9.46410	−0.741286	−0.370643	−	0.928775i	$-0.620863\pi$
$163$	−9.46410	−0.741286	−0.370643	+	0.928775i	$0.620863\pi$
$164$	−2.53590	−0.198020
$165$	2.00000	0.155700
$166$	−4.73205	−0.367278
$167$	−17.3205	−1.34030	−0.670151	−	0.742225i	$-0.733770\pi$
$167$	−17.3205	−1.34030	−0.670151	+	0.742225i	$0.733770\pi$
$168$	−2.53590	−0.195649
$169$	−11.3923	−0.876331
$170$	4.00000	0.306786
$171$	−13.4641	−1.02963
$172$	−3.26795	−0.249179
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−0.535898	−0.0406264
$175$	−3.46410	−0.261861
$176$	2.73205	0.205936
$177$	−4.00000	−0.300658
$178$	0.928203	0.0695718
$179$	14.7321	1.10113	0.550563	−	0.834794i	$-0.314413\pi$
$179$	14.7321	1.10113	0.550563	+	0.834794i	$0.314413\pi$
$180$	2.46410	0.183663
$181$	9.12436	0.678208	0.339104	−	0.940749i	$-0.389876\pi$
$181$	9.12436	0.678208	0.339104	+	0.940749i	$0.389876\pi$
$182$	4.39230	0.325579
$183$	6.67949	0.493762
$184$	−0.535898	−0.0395070
$185$	−6.73205	−0.494950
$186$	0	0
$187$	10.9282	0.799149
$188$	−3.46410	−0.252646
$189$	−13.8564	−1.00791
$190$	5.46410	0.396408
$191$	−2.00000	−0.144715	−0.0723575	−	0.997379i	$-0.523052\pi$
$191$	−2.00000	−0.144715	−0.0723575	+	0.997379i	$0.523052\pi$
$192$	−0.732051	−0.0528312
$193$	15.8564	1.14137	0.570685	−	0.821169i	$-0.306678\pi$
$193$	15.8564	1.14137	0.570685	+	0.821169i	$0.306678\pi$
$194$	−4.00000	−0.287183
$195$	0.928203	0.0664700
$196$	5.00000	0.357143
$197$	−21.2679	−1.51528	−0.757639	−	0.652673i	$-0.773647\pi$
$197$	−21.2679	−1.51528	−0.757639	+	0.652673i	$0.773647\pi$
$198$	6.73205	0.478426
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	−1.00000	−0.0707107
$201$	−6.14359	−0.433336
$202$	16.9282	1.19106
$203$	2.53590	0.177985
$204$	−2.92820	−0.205015
$205$	2.53590	0.177115
$206$	−2.92820	−0.204018
$207$	−1.32051	−0.0917817
$208$	1.26795	0.0879165
$209$	14.9282	1.03261
$210$	2.53590	0.174994
$211$	26.9282	1.85381	0.926907	−	0.375291i	$-0.122457\pi$
$211$	26.9282	1.85381	0.926907	+	0.375291i	$0.122457\pi$
$212$	5.26795	0.361804
$213$	10.1436	0.695028
$214$	−4.00000	−0.273434
$215$	3.26795	0.222872
$216$	−4.00000	−0.272166
$217$	0	0
$218$	15.4641	1.04736
$219$	−3.21539	−0.217276
$220$	−2.73205	−0.184195
$221$	5.07180	0.341166
$222$	4.92820	0.330759
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	3.46410	0.231455
$225$	−2.46410	−0.164273
$226$	−8.00000	−0.532152
$227$	−13.4641	−0.893644	−0.446822	−	0.894623i	$-0.647444\pi$
$227$	−13.4641	−0.893644	−0.446822	+	0.894623i	$0.647444\pi$
$228$	−4.00000	−0.264906
$229$	24.0526	1.58944	0.794719	−	0.606978i	$-0.207618\pi$
$229$	24.0526	1.58944	0.794719	+	0.606978i	$0.207618\pi$
$230$	0.535898	0.0353361
$231$	6.92820	0.455842
$232$	0.732051	0.0480615
$233$	24.7846	1.62369	0.811847	−	0.583870i	$-0.198462\pi$
$233$	24.7846	1.62369	0.811847	+	0.583870i	$0.198462\pi$
$234$	3.12436	0.204246
$235$	3.46410	0.225973
$236$	5.46410	0.355683
$237$	12.7846	0.830450
$238$	13.8564	0.898177
$239$	9.46410	0.612182	0.306091	−	0.952002i	$-0.400979\pi$
$239$	9.46410	0.612182	0.306091	+	0.952002i	$0.400979\pi$
$240$	0.732051	0.0472537
$241$	20.2487	1.30433	0.652167	−	0.758075i	$-0.273860\pi$
$241$	20.2487	1.30433	0.652167	+	0.758075i	$0.273860\pi$
$242$	3.53590	0.227296
$243$	−15.2679	−0.979439
$244$	−9.12436	−0.584127
$245$	−5.00000	−0.319438
$246$	−1.85641	−0.118360
$247$	6.92820	0.440831
$248$	0	0
$249$	−3.46410	−0.219529
$250$	1.00000	0.0632456
$251$	20.9808	1.32429	0.662147	−	0.749374i	$-0.269645\pi$
$251$	20.9808	1.32429	0.662147	+	0.749374i	$0.269645\pi$
$252$	8.53590	0.537711
$253$	1.46410	0.0920473
$254$	−15.8564	−0.994919
$255$	2.92820	0.183371
$256$	1.00000	0.0625000
$257$	16.9282	1.05595	0.527976	−	0.849259i	$-0.322951\pi$
$257$	16.9282	1.05595	0.527976	+	0.849259i	$0.322951\pi$
$258$	−2.39230	−0.148938
$259$	−23.3205	−1.44907
$260$	−1.26795	−0.0786349
$261$	1.80385	0.111655
$262$	−12.3923	−0.765599
$263$	−26.7846	−1.65161	−0.825805	−	0.563956i	$-0.809279\pi$
$263$	−26.7846	−1.65161	−0.825805	+	0.563956i	$0.809279\pi$
$264$	2.00000	0.123091
$265$	−5.26795	−0.323608
$266$	18.9282	1.16056
$267$	0.679492	0.0415842
$268$	8.39230	0.512642
$269$	0.339746	0.0207147	0.0103573	−	0.999946i	$-0.496703\pi$
$269$	0.339746	0.0207147	0.0103573	+	0.999946i	$0.496703\pi$
$270$	4.00000	0.243432
$271$	5.46410	0.331921	0.165960	−	0.986132i	$-0.446928\pi$
$271$	5.46410	0.331921	0.165960	+	0.986132i	$0.446928\pi$
$272$	4.00000	0.242536
$273$	3.21539	0.194604
$274$	−20.7846	−1.25564
$275$	2.73205	0.164749
$276$	−0.392305	−0.0236140
$277$	27.1244	1.62974	0.814872	−	0.579641i	$-0.196807\pi$
$277$	27.1244	1.62974	0.814872	+	0.579641i	$0.196807\pi$
$278$	13.6603	0.819288
$279$	0	0
$280$	−3.46410	−0.207020
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	−2.53590	−0.151011
$283$	9.46410	0.562582	0.281291	−	0.959622i	$-0.409237\pi$
$283$	9.46410	0.562582	0.281291	+	0.959622i	$0.409237\pi$
$284$	−13.8564	−0.822226
$285$	4.00000	0.236940
$286$	−3.46410	−0.204837
$287$	8.78461	0.518539
$288$	2.46410	0.145199
$289$	−1.00000	−0.0588235
$290$	−0.732051	−0.0429875
$291$	−2.92820	−0.171654
$292$	4.39230	0.257040
$293$	−17.3205	−1.01187	−0.505937	−	0.862570i	$-0.668853\pi$
$293$	−17.3205	−1.01187	−0.505937	+	0.862570i	$0.668853\pi$
$294$	3.66025	0.213470
$295$	−5.46410	−0.318132
$296$	−6.73205	−0.391293
$297$	10.9282	0.634119
$298$	13.3205	0.771636
$299$	0.679492	0.0392960
$300$	−0.732051	−0.0422650
$301$	11.3205	0.652503
$302$	1.46410	0.0842496
$303$	12.3923	0.711919
$304$	5.46410	0.313388
$305$	9.12436	0.522459
$306$	9.85641	0.563453
$307$	−24.7846	−1.41453	−0.707266	−	0.706947i	$-0.750072\pi$
$307$	−24.7846	−1.41453	−0.707266	+	0.706947i	$0.750072\pi$
$308$	−9.46410	−0.539267
$309$	−2.14359	−0.121945
$310$	0	0
$311$	13.0718	0.741234	0.370617	−	0.928786i	$-0.379146\pi$
$311$	13.0718	0.741234	0.370617	+	0.928786i	$0.379146\pi$
$312$	0.928203	0.0525492
$313$	−28.7846	−1.62700	−0.813501	−	0.581563i	$-0.802441\pi$
$313$	−28.7846	−1.62700	−0.813501	+	0.581563i	$0.802441\pi$
$314$	19.8564	1.12056
$315$	−8.53590	−0.480943
$316$	−17.4641	−0.982432
$317$	23.4641	1.31788	0.658938	−	0.752198i	$-0.271006\pi$
$317$	23.4641	1.31788	0.658938	+	0.752198i	$0.271006\pi$
$318$	3.85641	0.216257
$319$	−2.00000	−0.111979
$320$	−1.00000	−0.0559017
$321$	−2.92820	−0.163436
$322$	1.85641	0.103453
$323$	21.8564	1.21612
$324$	4.46410	0.248006
$325$	1.26795	0.0703332
$326$	9.46410	0.524168
$327$	11.3205	0.626026
$328$	2.53590	0.140022
$329$	12.0000	0.661581
$330$	−2.00000	−0.110096
$331$	13.2679	0.729272	0.364636	−	0.931150i	$-0.381193\pi$
$331$	13.2679	0.729272	0.364636	+	0.931150i	$0.381193\pi$
$332$	4.73205	0.259705
$333$	−16.5885	−0.909042
$334$	17.3205	0.947736
$335$	−8.39230	−0.458521
$336$	2.53590	0.138345
$337$	11.6077	0.632311	0.316156	−	0.948707i	$-0.397608\pi$
$337$	11.6077	0.632311	0.316156	+	0.948707i	$0.397608\pi$
$338$	11.3923	0.619660
$339$	−5.85641	−0.318076
$340$	−4.00000	−0.216930
$341$	0	0
$342$	13.4641	0.728055
$343$	6.92820	0.374088
$344$	3.26795	0.176196
$345$	0.392305	0.0211210
$346$	2.00000	0.107521
$347$	20.0526	1.07648	0.538239	−	0.842792i	$-0.319090\pi$
$347$	20.0526	1.07648	0.538239	+	0.842792i	$0.319090\pi$
$348$	0.535898	0.0287272
$349$	−28.5359	−1.52749	−0.763746	−	0.645517i	$-0.776642\pi$
$349$	−28.5359	−1.52749	−0.763746	+	0.645517i	$0.776642\pi$
$350$	3.46410	0.185164
$351$	5.07180	0.270712
$352$	−2.73205	−0.145619
$353$	16.3923	0.872474	0.436237	−	0.899832i	$-0.356311\pi$
$353$	16.3923	0.872474	0.436237	+	0.899832i	$0.356311\pi$
$354$	4.00000	0.212598
$355$	13.8564	0.735422
$356$	−0.928203	−0.0491947
$357$	10.1436	0.536856
$358$	−14.7321	−0.778613
$359$	−32.9282	−1.73788	−0.868942	−	0.494914i	$-0.835200\pi$
$359$	−32.9282	−1.73788	−0.868942	+	0.494914i	$0.835200\pi$
$360$	−2.46410	−0.129870
$361$	10.8564	0.571390
$362$	−9.12436	−0.479565
$363$	2.58846	0.135859
$364$	−4.39230	−0.230219
$365$	−4.39230	−0.229904
$366$	−6.67949	−0.349143
$367$	28.5359	1.48956	0.744781	−	0.667309i	$-0.232554\pi$
$367$	28.5359	1.48956	0.744781	+	0.667309i	$0.232554\pi$
$368$	0.535898	0.0279356
$369$	6.24871	0.325295
$370$	6.73205	0.349983
$371$	−18.2487	−0.947426
$372$	0	0
$373$	9.32051	0.482598	0.241299	−	0.970451i	$-0.422427\pi$
$373$	9.32051	0.482598	0.241299	+	0.970451i	$0.422427\pi$
$374$	−10.9282	−0.565084
$375$	0.732051	0.0378029
$376$	3.46410	0.178647
$377$	−0.928203	−0.0478049
$378$	13.8564	0.712697
$379$	−7.32051	−0.376029	−0.188015	−	0.982166i	$-0.560205\pi$
$379$	−7.32051	−0.376029	−0.188015	+	0.982166i	$0.560205\pi$
$380$	−5.46410	−0.280302
$381$	−11.6077	−0.594680
$382$	2.00000	0.102329
$383$	2.00000	0.102195	0.0510976	−	0.998694i	$-0.483728\pi$
$383$	2.00000	0.102195	0.0510976	+	0.998694i	$0.483728\pi$
$384$	0.732051	0.0373573
$385$	9.46410	0.482335
$386$	−15.8564	−0.807070
$387$	8.05256	0.409335
$388$	4.00000	0.203069
$389$	−26.1962	−1.32820	−0.664099	−	0.747645i	$-0.731185\pi$
$389$	−26.1962	−1.32820	−0.664099	+	0.747645i	$0.731185\pi$
$390$	−0.928203	−0.0470014
$391$	2.14359	0.108406
$392$	−5.00000	−0.252538
$393$	−9.07180	−0.457612
$394$	21.2679	1.07146
$395$	17.4641	0.878714
$396$	−6.73205	−0.338298
$397$	16.2487	0.815499	0.407750	−	0.913094i	$-0.366314\pi$
$397$	16.2487	0.815499	0.407750	+	0.913094i	$0.366314\pi$
$398$	−20.0000	−1.00251
$399$	13.8564	0.693688
$400$	1.00000	0.0500000
$401$	7.46410	0.372739	0.186370	−	0.982480i	$-0.440328\pi$
$401$	7.46410	0.372739	0.186370	+	0.982480i	$0.440328\pi$
$402$	6.14359	0.306415
$403$	0	0
$404$	−16.9282	−0.842210
$405$	−4.46410	−0.221823
$406$	−2.53590	−0.125855
$407$	18.3923	0.911673
$408$	2.92820	0.144968
$409$	8.53590	0.422073	0.211037	−	0.977478i	$-0.432316\pi$
$409$	8.53590	0.422073	0.211037	+	0.977478i	$0.432316\pi$
$410$	−2.53590	−0.125239
$411$	−15.2154	−0.750520
$412$	2.92820	0.144262
$413$	−18.9282	−0.931396
$414$	1.32051	0.0648994
$415$	−4.73205	−0.232287
$416$	−1.26795	−0.0621663
$417$	10.0000	0.489702
$418$	−14.9282	−0.730162
$419$	−4.39230	−0.214578	−0.107289	−	0.994228i	$-0.534217\pi$
$419$	−4.39230	−0.214578	−0.107289	+	0.994228i	$0.534217\pi$
$420$	−2.53590	−0.123739
$421$	32.2487	1.57171	0.785853	−	0.618413i	$-0.212224\pi$
$421$	32.2487	1.57171	0.785853	+	0.618413i	$0.212224\pi$
$422$	−26.9282	−1.31084
$423$	8.53590	0.415030
$424$	−5.26795	−0.255834
$425$	4.00000	0.194029
$426$	−10.1436	−0.491459
$427$	31.6077	1.52960
$428$	4.00000	0.193347
$429$	−2.53590	−0.122434
$430$	−3.26795	−0.157595
$431$	26.7846	1.29017	0.645085	−	0.764111i	$-0.276822\pi$
$431$	26.7846	1.29017	0.645085	+	0.764111i	$0.276822\pi$
$432$	4.00000	0.192450
$433$	−16.7846	−0.806617	−0.403308	−	0.915064i	$-0.632140\pi$
$433$	−16.7846	−0.806617	−0.403308	+	0.915064i	$0.632140\pi$
$434$	0	0
$435$	−0.535898	−0.0256944
$436$	−15.4641	−0.740596
$437$	2.92820	0.140075
$438$	3.21539	0.153637
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	2.73205	0.130245
$441$	−12.3205	−0.586691
$442$	−5.07180	−0.241241
$443$	−34.9282	−1.65949	−0.829745	−	0.558143i	$-0.811514\pi$
$443$	−34.9282	−1.65949	−0.829745	+	0.558143i	$0.811514\pi$
$444$	−4.92820	−0.233882
$445$	0.928203	0.0440011
$446$	10.0000	0.473514
$447$	9.75129	0.461220
$448$	−3.46410	−0.163663
$449$	−29.3205	−1.38372	−0.691860	−	0.722032i	$-0.743209\pi$
$449$	−29.3205	−1.38372	−0.691860	+	0.722032i	$0.743209\pi$
$450$	2.46410	0.116159
$451$	−6.92820	−0.326236
$452$	8.00000	0.376288
$453$	1.07180	0.0503574
$454$	13.4641	0.631902
$455$	4.39230	0.205914
$456$	4.00000	0.187317
$457$	−14.9282	−0.698312	−0.349156	−	0.937065i	$-0.613532\pi$
$457$	−14.9282	−0.698312	−0.349156	+	0.937065i	$0.613532\pi$
$458$	−24.0526	−1.12390
$459$	16.0000	0.746816
$460$	−0.535898	−0.0249864
$461$	27.2679	1.27000	0.634998	−	0.772514i	$-0.281001\pi$
$461$	27.2679	1.27000	0.634998	+	0.772514i	$0.281001\pi$
$462$	−6.92820	−0.322329
$463$	10.3923	0.482971	0.241486	−	0.970404i	$-0.422365\pi$
$463$	10.3923	0.482971	0.241486	+	0.970404i	$0.422365\pi$
$464$	−0.732051	−0.0339846
$465$	0	0
$466$	−24.7846	−1.14812
$467$	6.14359	0.284292	0.142146	−	0.989846i	$-0.454600\pi$
$467$	6.14359	0.284292	0.142146	+	0.989846i	$0.454600\pi$
$468$	−3.12436	−0.144423
$469$	−29.0718	−1.34241
$470$	−3.46410	−0.159787
$471$	14.5359	0.669779
$472$	−5.46410	−0.251506
$473$	−8.92820	−0.410519
$474$	−12.7846	−0.587217
$475$	5.46410	0.250710
$476$	−13.8564	−0.635107
$477$	−12.9808	−0.594348
$478$	−9.46410	−0.432878
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	−0.732051	−0.0334134
$481$	8.53590	0.389203
$482$	−20.2487	−0.922304
$483$	1.35898	0.0618359
$484$	−3.53590	−0.160723
$485$	−4.00000	−0.181631
$486$	15.2679	0.692568
$487$	10.0000	0.453143	0.226572	−	0.973995i	$-0.427248\pi$
$487$	10.0000	0.453143	0.226572	+	0.973995i	$0.427248\pi$
$488$	9.12436	0.413040
$489$	6.92820	0.313304
$490$	5.00000	0.225877
$491$	−18.7321	−0.845366	−0.422683	−	0.906278i	$-0.638912\pi$
$491$	−18.7321	−0.845366	−0.422683	+	0.906278i	$0.638912\pi$
$492$	1.85641	0.0836933
$493$	−2.92820	−0.131880
$494$	−6.92820	−0.311715
$495$	6.73205	0.302583
$496$	0	0
$497$	48.0000	2.15309
$498$	3.46410	0.155230
$499$	−19.1244	−0.856124	−0.428062	−	0.903749i	$-0.640803\pi$
$499$	−19.1244	−0.856124	−0.428062	+	0.903749i	$0.640803\pi$
$500$	−1.00000	−0.0447214
$501$	12.6795	0.566478
$502$	−20.9808	−0.936417
$503$	30.6410	1.36622	0.683108	−	0.730318i	$-0.260628\pi$
$503$	30.6410	1.36622	0.683108	+	0.730318i	$0.260628\pi$
$504$	−8.53590	−0.380219
$505$	16.9282	0.753295
$506$	−1.46410	−0.0650873
$507$	8.33975	0.370381
$508$	15.8564	0.703514
$509$	12.3397	0.546950	0.273475	−	0.961879i	$-0.411827\pi$
$509$	12.3397	0.546950	0.273475	+	0.961879i	$0.411827\pi$
$510$	−2.92820	−0.129663
$511$	−15.2154	−0.673089
$512$	−1.00000	−0.0441942
$513$	21.8564	0.964984
$514$	−16.9282	−0.746671
$515$	−2.92820	−0.129032
$516$	2.39230	0.105315
$517$	−9.46410	−0.416231
$518$	23.3205	1.02464
$519$	1.46410	0.0642669
$520$	1.26795	0.0556033
$521$	4.92820	0.215909	0.107954	−	0.994156i	$-0.465570\pi$
$521$	4.92820	0.215909	0.107954	+	0.994156i	$0.465570\pi$
$522$	−1.80385	−0.0789523
$523$	30.1962	1.32039	0.660193	−	0.751096i	$-0.270475\pi$
$523$	30.1962	1.32039	0.660193	+	0.751096i	$0.270475\pi$
$524$	12.3923	0.541360
$525$	2.53590	0.110676
$526$	26.7846	1.16786
$527$	0	0
$528$	−2.00000	−0.0870388
$529$	−22.7128	−0.987514
$530$	5.26795	0.228825
$531$	−13.4641	−0.584292
$532$	−18.9282	−0.820642
$533$	−3.21539	−0.139274
$534$	−0.679492	−0.0294045
$535$	−4.00000	−0.172935
$536$	−8.39230	−0.362492
$537$	−10.7846	−0.465390
$538$	−0.339746	−0.0146475
$539$	13.6603	0.588389
$540$	−4.00000	−0.172133
$541$	−21.3205	−0.916640	−0.458320	−	0.888787i	$-0.651549\pi$
$541$	−21.3205	−0.916640	−0.458320	+	0.888787i	$0.651549\pi$
$542$	−5.46410	−0.234703
$543$	−6.67949	−0.286644
$544$	−4.00000	−0.171499
$545$	15.4641	0.662409
$546$	−3.21539	−0.137606
$547$	−31.3205	−1.33917	−0.669584	−	0.742736i	$-0.733528\pi$
$547$	−31.3205	−1.33917	−0.669584	+	0.742736i	$0.733528\pi$
$548$	20.7846	0.887875
$549$	22.4833	0.959566
$550$	−2.73205	−0.116495
$551$	−4.00000	−0.170406
$552$	0.392305	0.0166976
$553$	60.4974	2.57261
$554$	−27.1244	−1.15240
$555$	4.92820	0.209191
$556$	−13.6603	−0.579324
$557$	−27.1244	−1.14930	−0.574648	−	0.818401i	$-0.694861\pi$
$557$	−27.1244	−1.14930	−0.574648	+	0.818401i	$0.694861\pi$
$558$	0	0
$559$	−4.14359	−0.175255
$560$	3.46410	0.146385
$561$	−8.00000	−0.337760
$562$	−10.0000	−0.421825
$563$	7.60770	0.320626	0.160313	−	0.987066i	$-0.448750\pi$
$563$	7.60770	0.320626	0.160313	+	0.987066i	$0.448750\pi$
$564$	2.53590	0.106781
$565$	−8.00000	−0.336563
$566$	−9.46410	−0.397806
$567$	−15.4641	−0.649431
$568$	13.8564	0.581402
$569$	−29.3205	−1.22918	−0.614590	−	0.788847i	$-0.710678\pi$
$569$	−29.3205	−1.22918	−0.614590	+	0.788847i	$0.710678\pi$
$570$	−4.00000	−0.167542
$571$	−28.5885	−1.19639	−0.598195	−	0.801351i	$-0.704115\pi$
$571$	−28.5885	−1.19639	−0.598195	+	0.801351i	$0.704115\pi$
$572$	3.46410	0.144841
$573$	1.46410	0.0611637
$574$	−8.78461	−0.366663
$575$	0.535898	0.0223485
$576$	−2.46410	−0.102671
$577$	−18.9282	−0.787991	−0.393996	−	0.919112i	$-0.628908\pi$
$577$	−18.9282	−0.787991	−0.393996	+	0.919112i	$0.628908\pi$
$578$	1.00000	0.0415945
$579$	−11.6077	−0.482399
$580$	0.732051	0.0303968
$581$	−16.3923	−0.680067
$582$	2.92820	0.121378
$583$	14.3923	0.596068
$584$	−4.39230	−0.181755
$585$	3.12436	0.129176
$586$	17.3205	0.715504
$587$	24.0526	0.992755	0.496378	−	0.868107i	$-0.334663\pi$
$587$	24.0526	0.992755	0.496378	+	0.868107i	$0.334663\pi$
$588$	−3.66025	−0.150946
$589$	0	0
$590$	5.46410	0.224954
$591$	15.5692	0.640432
$592$	6.73205	0.276686
$593$	8.00000	0.328521	0.164260	−	0.986417i	$-0.447476\pi$
$593$	8.00000	0.328521	0.164260	+	0.986417i	$0.447476\pi$
$594$	−10.9282	−0.448390
$595$	13.8564	0.568057
$596$	−13.3205	−0.545629
$597$	−14.6410	−0.599217
$598$	−0.679492	−0.0277865
$599$	27.8564	1.13818	0.569091	−	0.822275i	$-0.307295\pi$
$599$	27.8564	1.13818	0.569091	+	0.822275i	$0.307295\pi$
$600$	0.732051	0.0298858
$601$	−28.9282	−1.18001	−0.590003	−	0.807401i	$-0.700873\pi$
$601$	−28.9282	−1.18001	−0.590003	+	0.807401i	$0.700873\pi$
$602$	−11.3205	−0.461389
$603$	−20.6795	−0.842134
$604$	−1.46410	−0.0595734
$605$	3.53590	0.143755
$606$	−12.3923	−0.503403
$607$	12.0000	0.487065	0.243532	−	0.969893i	$-0.421694\pi$
$607$	12.0000	0.487065	0.243532	+	0.969893i	$0.421694\pi$
$608$	−5.46410	−0.221599
$609$	−1.85641	−0.0752254
$610$	−9.12436	−0.369434
$611$	−4.39230	−0.177694
$612$	−9.85641	−0.398422
$613$	−16.5885	−0.670001	−0.335001	−	0.942218i	$-0.608737\pi$
$613$	−16.5885	−0.670001	−0.335001	+	0.942218i	$0.608737\pi$
$614$	24.7846	1.00023
$615$	−1.85641	−0.0748575
$616$	9.46410	0.381320
$617$	35.8564	1.44352	0.721762	−	0.692141i	$-0.243332\pi$
$617$	35.8564	1.44352	0.721762	+	0.692141i	$0.243332\pi$
$618$	2.14359	0.0862280
$619$	0.196152	0.00788403	0.00394202	−	0.999992i	$-0.498745\pi$
$619$	0.196152	0.00788403	0.00394202	+	0.999992i	$0.498745\pi$
$620$	0	0
$621$	2.14359	0.0860194
$622$	−13.0718	−0.524131
$623$	3.21539	0.128822
$624$	−0.928203	−0.0371579
$625$	1.00000	0.0400000
$626$	28.7846	1.15046
$627$	−10.9282	−0.436430
$628$	−19.8564	−0.792357
$629$	26.9282	1.07370
$630$	8.53590	0.340078
$631$	−0.392305	−0.0156174	−0.00780870	−	0.999970i	$-0.502486\pi$
$631$	−0.392305	−0.0156174	−0.00780870	+	0.999970i	$0.502486\pi$
$632$	17.4641	0.694685
$633$	−19.7128	−0.783514
$634$	−23.4641	−0.931879
$635$	−15.8564	−0.629242
$636$	−3.85641	−0.152916
$637$	6.33975	0.251190
$638$	2.00000	0.0791808
$639$	34.1436	1.35070
$640$	1.00000	0.0395285
$641$	3.46410	0.136824	0.0684119	−	0.997657i	$-0.478207\pi$
$641$	3.46410	0.136824	0.0684119	+	0.997657i	$0.478207\pi$
$642$	2.92820	0.115567
$643$	−28.3397	−1.11761	−0.558805	−	0.829299i	$-0.688740\pi$
$643$	−28.3397	−1.11761	−0.558805	+	0.829299i	$0.688740\pi$
$644$	−1.85641	−0.0731527
$645$	−2.39230	−0.0941969
$646$	−21.8564	−0.859929
$647$	−18.0000	−0.707653	−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000	−0.707653	−0.353827	+	0.935311i	$0.615120\pi$
$648$	−4.46410	−0.175366
$649$	14.9282	0.585983
$650$	−1.26795	−0.0497331
$651$	0	0
$652$	−9.46410	−0.370643
$653$	−12.9282	−0.505920	−0.252960	−	0.967477i	$-0.581404\pi$
$653$	−12.9282	−0.505920	−0.252960	+	0.967477i	$0.581404\pi$
$654$	−11.3205	−0.442667
$655$	−12.3923	−0.484207
$656$	−2.53590	−0.0990102
$657$	−10.8231	−0.422249
$658$	−12.0000	−0.467809
$659$	21.4641	0.836123	0.418061	−	0.908419i	$-0.362710\pi$
$659$	21.4641	0.836123	0.418061	+	0.908419i	$0.362710\pi$
$660$	2.00000	0.0778499
$661$	32.2487	1.25433	0.627165	−	0.778887i	$-0.284215\pi$
$661$	32.2487	1.25433	0.627165	+	0.778887i	$0.284215\pi$
$662$	−13.2679	−0.515673
$663$	−3.71281	−0.144194
$664$	−4.73205	−0.183639
$665$	18.9282	0.734004
$666$	16.5885	0.642790
$667$	−0.392305	−0.0151901
$668$	−17.3205	−0.670151
$669$	7.32051	0.283027
$670$	8.39230	0.324223
$671$	−24.9282	−0.962343
$672$	−2.53590	−0.0978244
$673$	−36.7846	−1.41794	−0.708971	−	0.705237i	$-0.750840\pi$
$673$	−36.7846	−1.41794	−0.708971	+	0.705237i	$0.750840\pi$
$674$	−11.6077	−0.447112
$675$	4.00000	0.153960
$676$	−11.3923	−0.438166
$677$	10.0526	0.386351	0.193176	−	0.981164i	$-0.438121\pi$
$677$	10.0526	0.386351	0.193176	+	0.981164i	$0.438121\pi$
$678$	5.85641	0.224914
$679$	−13.8564	−0.531760
$680$	4.00000	0.153393
$681$	9.85641	0.377698
$682$	0	0
$683$	15.7128	0.601234	0.300617	−	0.953745i	$-0.402807\pi$
$683$	15.7128	0.601234	0.300617	+	0.953745i	$0.402807\pi$
$684$	−13.4641	−0.514813
$685$	−20.7846	−0.794139
$686$	−6.92820	−0.264520
$687$	−17.6077	−0.671775
$688$	−3.26795	−0.124589
$689$	6.67949	0.254468
$690$	−0.392305	−0.0149348
$691$	−4.78461	−0.182015	−0.0910076	−	0.995850i	$-0.529009\pi$
$691$	−4.78461	−0.182015	−0.0910076	+	0.995850i	$0.529009\pi$
$692$	−2.00000	−0.0760286
$693$	23.3205	0.885873
$694$	−20.0526	−0.761185
$695$	13.6603	0.518163
$696$	−0.535898	−0.0203132
$697$	−10.1436	−0.384216
$698$	28.5359	1.08010
$699$	−18.1436	−0.686254
$700$	−3.46410	−0.130931
$701$	40.9282	1.54584	0.772918	−	0.634505i	$-0.218796\pi$
$701$	40.9282	1.54584	0.772918	+	0.634505i	$0.218796\pi$
$702$	−5.07180	−0.191423
$703$	36.7846	1.38736
$704$	2.73205	0.102968
$705$	−2.53590	−0.0955075
$706$	−16.3923	−0.616933
$707$	58.6410	2.20542
$708$	−4.00000	−0.150329
$709$	8.05256	0.302420	0.151210	−	0.988502i	$-0.451683\pi$
$709$	8.05256	0.302420	0.151210	+	0.988502i	$0.451683\pi$
$710$	−13.8564	−0.520022
$711$	43.0333	1.61388
$712$	0.928203	0.0347859
$713$	0	0
$714$	−10.1436	−0.379614
$715$	−3.46410	−0.129550
$716$	14.7321	0.550563
$717$	−6.92820	−0.258738
$718$	32.9282	1.22887
$719$	25.8564	0.964281	0.482141	−	0.876094i	$-0.339859\pi$
$719$	25.8564	0.964281	0.482141	+	0.876094i	$0.339859\pi$
$720$	2.46410	0.0918316
$721$	−10.1436	−0.377767
$722$	−10.8564	−0.404034
$723$	−14.8231	−0.551276
$724$	9.12436	0.339104
$725$	−0.732051	−0.0271877
$726$	−2.58846	−0.0960667
$727$	36.7846	1.36427	0.682133	−	0.731228i	$-0.261053\pi$
$727$	36.7846	1.36427	0.682133	+	0.731228i	$0.261053\pi$
$728$	4.39230	0.162790
$729$	−2.21539	−0.0820515
$730$	4.39230	0.162566
$731$	−13.0718	−0.483478
$732$	6.67949	0.246881
$733$	−17.6077	−0.650355	−0.325178	−	0.945653i	$-0.605424\pi$
$733$	−17.6077	−0.650355	−0.325178	+	0.945653i	$0.605424\pi$
$734$	−28.5359	−1.05328
$735$	3.66025	0.135011
$736$	−0.535898	−0.0197535
$737$	22.9282	0.844571
$738$	−6.24871	−0.230018
$739$	−23.8038	−0.875639	−0.437819	−	0.899063i	$-0.644249\pi$
$739$	−23.8038	−0.875639	−0.437819	+	0.899063i	$0.644249\pi$
$740$	−6.73205	−0.247475
$741$	−5.07180	−0.186317
$742$	18.2487	0.669931
$743$	21.7128	0.796566	0.398283	−	0.917263i	$-0.369606\pi$
$743$	21.7128	0.796566	0.398283	+	0.917263i	$0.369606\pi$
$744$	0	0
$745$	13.3205	0.488026
$746$	−9.32051	−0.341248
$747$	−11.6603	−0.426626
$748$	10.9282	0.399575
$749$	−13.8564	−0.506302
$750$	−0.732051	−0.0267307
$751$	−7.85641	−0.286684	−0.143342	−	0.989673i	$-0.545785\pi$
$751$	−7.85641	−0.286684	−0.143342	+	0.989673i	$0.545785\pi$
$752$	−3.46410	−0.126323
$753$	−15.3590	−0.559712
$754$	0.928203	0.0338032
$755$	1.46410	0.0532841
$756$	−13.8564	−0.503953
$757$	−14.4449	−0.525008	−0.262504	−	0.964931i	$-0.584548\pi$
$757$	−14.4449	−0.525008	−0.262504	+	0.964931i	$0.584548\pi$
$758$	7.32051	0.265893
$759$	−1.07180	−0.0389038
$760$	5.46410	0.198204
$761$	−0.535898	−0.0194263	−0.00971315	−	0.999953i	$-0.503092\pi$
$761$	−0.535898	−0.0194263	−0.00971315	+	0.999953i	$0.503092\pi$
$762$	11.6077	0.420502
$763$	53.5692	1.93934
$764$	−2.00000	−0.0723575
$765$	9.85641	0.356359
$766$	−2.00000	−0.0722629
$767$	6.92820	0.250163
$768$	−0.732051	−0.0264156
$769$	39.3205	1.41793	0.708967	−	0.705242i	$-0.249162\pi$
$769$	39.3205	1.41793	0.708967	+	0.705242i	$0.249162\pi$
$770$	−9.46410	−0.341063
$771$	−12.3923	−0.446298
$772$	15.8564	0.570685
$773$	47.5167	1.70906	0.854528	−	0.519406i	$-0.173847\pi$
$773$	47.5167	1.70906	0.854528	+	0.519406i	$0.173847\pi$
$774$	−8.05256	−0.289443
$775$	0	0
$776$	−4.00000	−0.143592
$777$	17.0718	0.612447
$778$	26.1962	0.939178
$779$	−13.8564	−0.496457
$780$	0.928203	0.0332350
$781$	−37.8564	−1.35461
$782$	−2.14359	−0.0766547
$783$	−2.92820	−0.104645
$784$	5.00000	0.178571
$785$	19.8564	0.708706
$786$	9.07180	0.323580
$787$	7.66025	0.273059	0.136529	−	0.990636i	$-0.456405\pi$
$787$	7.66025	0.273059	0.136529	+	0.990636i	$0.456405\pi$
$788$	−21.2679	−0.757639
$789$	19.6077	0.698052
$790$	−17.4641	−0.621345
$791$	−27.7128	−0.985354
$792$	6.73205	0.239213
$793$	−11.5692	−0.410835
$794$	−16.2487	−0.576645
$795$	3.85641	0.136773
$796$	20.0000	0.708881
$797$	−42.8372	−1.51737	−0.758685	−	0.651457i	$-0.774158\pi$
$797$	−42.8372	−1.51737	−0.758685	+	0.651457i	$0.774158\pi$
$798$	−13.8564	−0.490511
$799$	−13.8564	−0.490204
$800$	−1.00000	−0.0353553
$801$	2.28719	0.0808138
$802$	−7.46410	−0.263567
$803$	12.0000	0.423471
$804$	−6.14359	−0.216668
$805$	1.85641	0.0654297
$806$	0	0
$807$	−0.248711	−0.00875505
$808$	16.9282	0.595532
$809$	16.2487	0.571274	0.285637	−	0.958338i	$-0.407795\pi$
$809$	16.2487	0.571274	0.285637	+	0.958338i	$0.407795\pi$
$810$	4.46410	0.156853
$811$	−16.3923	−0.575612	−0.287806	−	0.957689i	$-0.592926\pi$
$811$	−16.3923	−0.575612	−0.287806	+	0.957689i	$0.592926\pi$
$812$	2.53590	0.0889926
$813$	−4.00000	−0.140286
$814$	−18.3923	−0.644650
$815$	9.46410	0.331513
$816$	−2.92820	−0.102508
$817$	−17.8564	−0.624717
$818$	−8.53590	−0.298451
$819$	10.8231	0.378189
$820$	2.53590	0.0885574
$821$	−9.51666	−0.332134	−0.166067	−	0.986114i	$-0.553107\pi$
$821$	−9.51666	−0.332134	−0.166067	+	0.986114i	$0.553107\pi$
$822$	15.2154	0.530698
$823$	51.8564	1.80760	0.903800	−	0.427954i	$-0.140766\pi$
$823$	51.8564	1.80760	0.903800	+	0.427954i	$0.140766\pi$
$824$	−2.92820	−0.102009
$825$	−2.00000	−0.0696311
$826$	18.9282	0.658596
$827$	33.5167	1.16549	0.582744	−	0.812656i	$-0.301979\pi$
$827$	33.5167	1.16549	0.582744	+	0.812656i	$0.301979\pi$
$828$	−1.32051	−0.0458908
$829$	25.1244	0.872605	0.436302	−	0.899800i	$-0.356288\pi$
$829$	25.1244	0.872605	0.436302	+	0.899800i	$0.356288\pi$
$830$	4.73205	0.164252
$831$	−19.8564	−0.688811
$832$	1.26795	0.0439582
$833$	20.0000	0.692959
$834$	−10.0000	−0.346272
$835$	17.3205	0.599401
$836$	14.9282	0.516303
$837$	0	0
$838$	4.39230	0.151730
$839$	−5.21539	−0.180055	−0.0900276	−	0.995939i	$-0.528696\pi$
$839$	−5.21539	−0.180055	−0.0900276	+	0.995939i	$0.528696\pi$
$840$	2.53590	0.0874968
$841$	−28.4641	−0.981521
$842$	−32.2487	−1.11136
$843$	−7.32051	−0.252132
$844$	26.9282	0.926907
$845$	11.3923	0.391907
$846$	−8.53590	−0.293470
$847$	12.2487	0.420871
$848$	5.26795	0.180902
$849$	−6.92820	−0.237775
$850$	−4.00000	−0.137199
$851$	3.60770	0.123670
$852$	10.1436	0.347514
$853$	−51.8564	−1.77553	−0.887765	−	0.460297i	$-0.847743\pi$
$853$	−51.8564	−1.77553	−0.887765	+	0.460297i	$0.847743\pi$
$854$	−31.6077	−1.08159
$855$	13.4641	0.460463
$856$	−4.00000	−0.136717
$857$	−24.9282	−0.851531	−0.425766	−	0.904833i	$-0.639995\pi$
$857$	−24.9282	−0.851531	−0.425766	+	0.904833i	$0.639995\pi$
$858$	2.53590	0.0865741
$859$	38.4449	1.31172	0.655861	−	0.754882i	$-0.272306\pi$
$859$	38.4449	1.31172	0.655861	+	0.754882i	$0.272306\pi$
$860$	3.26795	0.111436
$861$	−6.43078	−0.219160
$862$	−26.7846	−0.912287
$863$	4.14359	0.141050	0.0705248	−	0.997510i	$-0.477533\pi$
$863$	4.14359	0.141050	0.0705248	+	0.997510i	$0.477533\pi$
$864$	−4.00000	−0.136083
$865$	2.00000	0.0680020
$866$	16.7846	0.570364
$867$	0.732051	0.0248617
$868$	0	0
$869$	−47.7128	−1.61855
$870$	0.535898	0.0181687
$871$	10.6410	0.360557
$872$	15.4641	0.523681
$873$	−9.85641	−0.333589
$874$	−2.92820	−0.0990480
$875$	3.46410	0.117108
$876$	−3.21539	−0.108638
$877$	10.6795	0.360621	0.180310	−	0.983610i	$-0.442290\pi$
$877$	10.6795	0.360621	0.180310	+	0.983610i	$0.442290\pi$
$878$	−22.0000	−0.742464
$879$	12.6795	0.427669
$880$	−2.73205	−0.0920974
$881$	47.5692	1.60265	0.801324	−	0.598231i	$-0.204129\pi$
$881$	47.5692	1.60265	0.801324	+	0.598231i	$0.204129\pi$
$882$	12.3205	0.414853
$883$	19.6603	0.661620	0.330810	−	0.943697i	$-0.392678\pi$
$883$	19.6603	0.661620	0.330810	+	0.943697i	$0.392678\pi$
$884$	5.07180	0.170583
$885$	4.00000	0.134459
$886$	34.9282	1.17344
$887$	26.1051	0.876524	0.438262	−	0.898847i	$-0.355594\pi$
$887$	26.1051	0.876524	0.438262	+	0.898847i	$0.355594\pi$
$888$	4.92820	0.165380
$889$	−54.9282	−1.84223
$890$	−0.928203	−0.0311134
$891$	12.1962	0.408586
$892$	−10.0000	−0.334825
$893$	−18.9282	−0.633408
$894$	−9.75129	−0.326132
$895$	−14.7321	−0.492438
$896$	3.46410	0.115728
$897$	−0.497423	−0.0166085
$898$	29.3205	0.978438
$899$	0	0
$900$	−2.46410	−0.0821367
$901$	21.0718	0.702003
$902$	6.92820	0.230684
$903$	−8.28719	−0.275780
$904$	−8.00000	−0.266076
$905$	−9.12436	−0.303304
$906$	−1.07180	−0.0356081
$907$	17.8564	0.592912	0.296456	−	0.955046i	$-0.404195\pi$
$907$	17.8564	0.592912	0.296456	+	0.955046i	$0.404195\pi$
$908$	−13.4641	−0.446822
$909$	41.7128	1.38353
$910$	−4.39230	−0.145603
$911$	17.0718	0.565614	0.282807	−	0.959177i	$-0.408734\pi$
$911$	17.0718	0.565614	0.282807	+	0.959177i	$0.408734\pi$
$912$	−4.00000	−0.132453
$913$	12.9282	0.427861
$914$	14.9282	0.493781
$915$	−6.67949	−0.220817
$916$	24.0526	0.794719
$917$	−42.9282	−1.41761
$918$	−16.0000	−0.528079
$919$	0.784610	0.0258819	0.0129409	−	0.999916i	$-0.495881\pi$
$919$	0.784610	0.0258819	0.0129409	+	0.999916i	$0.495881\pi$
$920$	0.535898	0.0176680
$921$	18.1436	0.597852
$922$	−27.2679	−0.898022
$923$	−17.5692	−0.578298
$924$	6.92820	0.227921
$925$	6.73205	0.221348
$926$	−10.3923	−0.341512
$927$	−7.21539	−0.236985
$928$	0.732051	0.0240307
$929$	1.60770	0.0527468	0.0263734	−	0.999652i	$-0.491604\pi$
$929$	1.60770	0.0527468	0.0263734	+	0.999652i	$0.491604\pi$
$930$	0	0
$931$	27.3205	0.895393
$932$	24.7846	0.811847
$933$	−9.56922	−0.313282
$934$	−6.14359	−0.201025
$935$	−10.9282	−0.357390
$936$	3.12436	0.102123
$937$	−19.0718	−0.623048	−0.311524	−	0.950238i	$-0.600840\pi$
$937$	−19.0718	−0.623048	−0.311524	+	0.950238i	$0.600840\pi$
$938$	29.0718	0.949228
$939$	21.0718	0.687652
$940$	3.46410	0.112987
$941$	54.5885	1.77953	0.889766	−	0.456416i	$-0.150867\pi$
$941$	54.5885	1.77953	0.889766	+	0.456416i	$0.150867\pi$
$942$	−14.5359	−0.473605
$943$	−1.35898	−0.0442546
$944$	5.46410	0.177841
$945$	13.8564	0.450749
$946$	8.92820	0.290281
$947$	10.1962	0.331330	0.165665	−	0.986182i	$-0.447023\pi$
$947$	10.1962	0.331330	0.165665	+	0.986182i	$0.447023\pi$
$948$	12.7846	0.415225
$949$	5.56922	0.180785
$950$	−5.46410	−0.177279
$951$	−17.1769	−0.557000
$952$	13.8564	0.449089
$953$	−30.9282	−1.00186	−0.500931	−	0.865487i	$-0.667009\pi$
$953$	−30.9282	−1.00186	−0.500931	+	0.865487i	$0.667009\pi$
$954$	12.9808	0.420268
$955$	2.00000	0.0647185
$956$	9.46410	0.306091
$957$	1.46410	0.0473277
$958$	0	0
$959$	−72.0000	−2.32500
$960$	0.732051	0.0236268
$961$	0	0
$962$	−8.53590	−0.275208
$963$	−9.85641	−0.317618
$964$	20.2487	0.652167
$965$	−15.8564	−0.510436
$966$	−1.35898	−0.0437246
$967$	12.1436	0.390512	0.195256	−	0.980752i	$-0.437446\pi$
$967$	12.1436	0.390512	0.195256	+	0.980752i	$0.437446\pi$
$968$	3.53590	0.113648
$969$	−16.0000	−0.513994
$970$	4.00000	0.128432
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	−15.2679	−0.489720
$973$	47.3205	1.51703
$974$	−10.0000	−0.320421
$975$	−0.928203	−0.0297263
$976$	−9.12436	−0.292064
$977$	42.7846	1.36880	0.684400	−	0.729106i	$-0.260064\pi$
$977$	42.7846	1.36880	0.684400	+	0.729106i	$0.260064\pi$
$978$	−6.92820	−0.221540
$979$	−2.53590	−0.0810477
$980$	−5.00000	−0.159719
$981$	38.1051	1.21660
$982$	18.7321	0.597764
$983$	37.7128	1.20285	0.601426	−	0.798929i	$-0.294599\pi$
$983$	37.7128	1.20285	0.601426	+	0.798929i	$0.294599\pi$
$984$	−1.85641	−0.0591801
$985$	21.2679	0.677653
$986$	2.92820	0.0932530
$987$	−8.78461	−0.279617
$988$	6.92820	0.220416
$989$	−1.75129	−0.0556877
$990$	−6.73205	−0.213959
$991$	−13.0718	−0.415239	−0.207620	−	0.978210i	$-0.566572\pi$
$991$	−13.0718	−0.415239	−0.207620	+	0.978210i	$0.566572\pi$
$992$	0	0
$993$	−9.71281	−0.308227
$994$	−48.0000	−1.52247
$995$	−20.0000	−0.634043
$996$	−3.46410	−0.109764
$997$	−23.1769	−0.734020	−0.367010	−	0.930217i	$-0.619619\pi$
$997$	−23.1769	−0.734020	−0.367010	+	0.930217i	$0.619619\pi$
$998$	19.1244	0.605371
$999$	26.9282	0.851971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9610.2.a.j.1.1		2
31.30	odd	2		310.2.a.c.1.2	✓	2
93.92	even	2		2790.2.a.bh.1.1		2
124.123	even	2		2480.2.a.s.1.1		2
155.92	even	4		1550.2.b.h.249.1		4
155.123	even	4		1550.2.b.h.249.4		4
155.154	odd	2		1550.2.a.j.1.1		2
248.61	odd	2		9920.2.a.bt.1.1		2
248.123	even	2		9920.2.a.bl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.a.c.1.2	✓	2	31.30	odd	2
1550.2.a.j.1.1		2	155.154	odd	2
1550.2.b.h.249.1		4	155.92	even	4
1550.2.b.h.249.4		4	155.123	even	4
2480.2.a.s.1.1		2	124.123	even	2
2790.2.a.bh.1.1		2	93.92	even	2
9610.2.a.j.1.1		2	1.1	even	1	trivial
9920.2.a.bl.1.2		2	248.123	even	2
9920.2.a.bt.1.1		2	248.61	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:	\( N \)	\(=\)	\( 9610 = 2 \cdot 5 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -3.46410 q^{7} -1.00000 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -3.46410 q^{7} -1.00000 q^{8} -2.46410 q^{9} +1.00000 q^{10} +2.73205 q^{11} -0.732051 q^{12} +1.26795 q^{13} +3.46410 q^{14} +0.732051 q^{15} +1.00000 q^{16} +4.00000 q^{17} +2.46410 q^{18} +5.46410 q^{19} -1.00000 q^{20} +2.53590 q^{21} -2.73205 q^{22} +0.535898 q^{23} +0.732051 q^{24} +1.00000 q^{25} -1.26795 q^{26} +4.00000 q^{27} -3.46410 q^{28} -0.732051 q^{29} -0.732051 q^{30} -1.00000 q^{32} -2.00000 q^{33} -4.00000 q^{34} +3.46410 q^{35} -2.46410 q^{36} +6.73205 q^{37} -5.46410 q^{38} -0.928203 q^{39} +1.00000 q^{40} -2.53590 q^{41} -2.53590 q^{42} -3.26795 q^{43} +2.73205 q^{44} +2.46410 q^{45} -0.535898 q^{46} -3.46410 q^{47} -0.732051 q^{48} +5.00000 q^{49} -1.00000 q^{50} -2.92820 q^{51} +1.26795 q^{52} +5.26795 q^{53} -4.00000 q^{54} -2.73205 q^{55} +3.46410 q^{56} -4.00000 q^{57} +0.732051 q^{58} +5.46410 q^{59} +0.732051 q^{60} -9.12436 q^{61} +8.53590 q^{63} +1.00000 q^{64} -1.26795 q^{65} +2.00000 q^{66} +8.39230 q^{67} +4.00000 q^{68} -0.392305 q^{69} -3.46410 q^{70} -13.8564 q^{71} +2.46410 q^{72} +4.39230 q^{73} -6.73205 q^{74} -0.732051 q^{75} +5.46410 q^{76} -9.46410 q^{77} +0.928203 q^{78} -17.4641 q^{79} -1.00000 q^{80} +4.46410 q^{81} +2.53590 q^{82} +4.73205 q^{83} +2.53590 q^{84} -4.00000 q^{85} +3.26795 q^{86} +0.535898 q^{87} -2.73205 q^{88} -0.928203 q^{89} -2.46410 q^{90} -4.39230 q^{91} +0.535898 q^{92} +3.46410 q^{94} -5.46410 q^{95} +0.732051 q^{96} +4.00000 q^{97} -5.00000 q^{98} -6.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{13} - 2 q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 4 q^{19} - 2 q^{20} + 12 q^{21} - 2 q^{22} + 8 q^{23} - 2 q^{24} + 2 q^{25} - 6 q^{26} + 8 q^{27} + 2 q^{29} + 2 q^{30} - 2 q^{32} - 4 q^{33} - 8 q^{34} + 2 q^{36} + 10 q^{37} - 4 q^{38} + 12 q^{39} + 2 q^{40} - 12 q^{41} - 12 q^{42} - 10 q^{43} + 2 q^{44} - 2 q^{45} - 8 q^{46} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 8 q^{51} + 6 q^{52} + 14 q^{53} - 8 q^{54} - 2 q^{55} - 8 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} + 6 q^{61} + 24 q^{63} + 2 q^{64} - 6 q^{65} + 4 q^{66} - 4 q^{67} + 8 q^{68} + 20 q^{69} - 2 q^{72} - 12 q^{73} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 12 q^{77} - 12 q^{78} - 28 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} + 6 q^{83} + 12 q^{84} - 8 q^{85} + 10 q^{86} + 8 q^{87} - 2 q^{88} + 12 q^{89} + 2 q^{90} + 12 q^{91} + 8 q^{92} - 4 q^{95} - 2 q^{96} + 8 q^{97} - 10 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^13 - 2 * q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 4 * q^19 - 2 * q^20 + 12 * q^21 - 2 * q^22 + 8 * q^23 - 2 * q^24 + 2 * q^25 - 6 * q^26 + 8 * q^27 + 2 * q^29 + 2 * q^30 - 2 * q^32 - 4 * q^33 - 8 * q^34 + 2 * q^36 + 10 * q^37 - 4 * q^38 + 12 * q^39 + 2 * q^40 - 12 * q^41 - 12 * q^42 - 10 * q^43 + 2 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 8 * q^51 + 6 * q^52 + 14 * q^53 - 8 * q^54 - 2 * q^55 - 8 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 + 6 * q^61 + 24 * q^63 + 2 * q^64 - 6 * q^65 + 4 * q^66 - 4 * q^67 + 8 * q^68 + 20 * q^69 - 2 * q^72 - 12 * q^73 - 10 * q^74 + 2 * q^75 + 4 * q^76 - 12 * q^77 - 12 * q^78 - 28 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 + 6 * q^83 + 12 * q^84 - 8 * q^85 + 10 * q^86 + 8 * q^87 - 2 * q^88 + 12 * q^89 + 2 * q^90 + 12 * q^91 + 8 * q^92 - 4 * q^95 - 2 * q^96 + 8 * q^97 - 10 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more