LMFDB - Embedded newform 5566.2.a.bt.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5566,2,Mod(1,5566)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5566, 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("5566.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5566 = 2 \cdot 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5566.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:	$44.4447337650$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 14x^{8} + 50x^{7} + 85x^{6} - 188x^{5} - 248x^{4} + 186x^{3} + 260x^{2} + 52x - 4 $ x^10 - 4x^9 - 14x^8 + 50x^7 + 85x^6 - 188x^5 - 248x^4 + 186x^3 + 260x^2 + 52*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 506)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.17272$ of defining polynomial
Character	$\chi$	$=$	5566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.17272 q^{3} +1.00000 q^{4} +3.81446 q^{5} -3.17272 q^{6} +0.711206 q^{7} -1.00000 q^{8} +7.06614 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.17272 q^{3} +1.00000 q^{4} +3.81446 q^{5} -3.17272 q^{6} +0.711206 q^{7} -1.00000 q^{8} +7.06614 q^{9} -3.81446 q^{10} +3.17272 q^{12} +1.15076 q^{13} -0.711206 q^{14} +12.1022 q^{15} +1.00000 q^{16} +3.97045 q^{17} -7.06614 q^{18} -3.17585 q^{19} +3.81446 q^{20} +2.25646 q^{21} -1.00000 q^{23} -3.17272 q^{24} +9.55011 q^{25} -1.15076 q^{26} +12.9007 q^{27} +0.711206 q^{28} -6.95044 q^{29} -12.1022 q^{30} -7.06435 q^{31} -1.00000 q^{32} -3.97045 q^{34} +2.71287 q^{35} +7.06614 q^{36} -0.313872 q^{37} +3.17585 q^{38} +3.65102 q^{39} -3.81446 q^{40} +12.5218 q^{41} -2.25646 q^{42} +5.79562 q^{43} +26.9535 q^{45} +1.00000 q^{46} +1.89914 q^{47} +3.17272 q^{48} -6.49419 q^{49} -9.55011 q^{50} +12.5971 q^{51} +1.15076 q^{52} -12.3697 q^{53} -12.9007 q^{54} -0.711206 q^{56} -10.0761 q^{57} +6.95044 q^{58} -0.351370 q^{59} +12.1022 q^{60} -2.93339 q^{61} +7.06435 q^{62} +5.02548 q^{63} +1.00000 q^{64} +4.38951 q^{65} +5.39932 q^{67} +3.97045 q^{68} -3.17272 q^{69} -2.71287 q^{70} -15.0256 q^{71} -7.06614 q^{72} +11.6500 q^{73} +0.313872 q^{74} +30.2998 q^{75} -3.17585 q^{76} -3.65102 q^{78} +4.23644 q^{79} +3.81446 q^{80} +19.7319 q^{81} -12.5218 q^{82} -1.33343 q^{83} +2.25646 q^{84} +15.1451 q^{85} -5.79562 q^{86} -22.0518 q^{87} +5.08032 q^{89} -26.9535 q^{90} +0.818424 q^{91} -1.00000 q^{92} -22.4132 q^{93} -1.89914 q^{94} -12.1141 q^{95} -3.17272 q^{96} -12.7048 q^{97} +6.49419 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	$ 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.17272	1.83177	0.915885	−	0.401441i	$-0.131491\pi$
$3$	3.17272	1.83177	0.915885	+	0.401441i	$0.131491\pi$
$4$	1.00000	0.500000
$5$	3.81446	1.70588	0.852939	−	0.522010i	$-0.174818\pi$
$5$	3.81446	1.70588	0.852939	+	0.522010i	$0.174818\pi$
$6$	−3.17272	−1.29526
$7$	0.711206	0.268811	0.134405	−	0.990926i	$-0.457088\pi$
$7$	0.711206	0.268811	0.134405	+	0.990926i	$0.457088\pi$
$8$	−1.00000	−0.353553
$9$	7.06614	2.35538
$10$	−3.81446	−1.20624
$11$	0	0
$11$	0	0
$12$	3.17272	0.915885
$13$	1.15076	0.319162	0.159581	−	0.987185i	$-0.448986\pi$
$13$	1.15076	0.319162	0.159581	+	0.987185i	$0.448986\pi$
$14$	−0.711206	−0.190078
$15$	12.1022	3.12478
$16$	1.00000	0.250000
$17$	3.97045	0.962975	0.481488	−	0.876453i	$-0.340097\pi$
$17$	3.97045	0.962975	0.481488	+	0.876453i	$0.340097\pi$
$18$	−7.06614	−1.66551
$19$	−3.17585	−0.728590	−0.364295	−	0.931284i	$-0.618690\pi$
$19$	−3.17585	−0.728590	−0.364295	+	0.931284i	$0.618690\pi$
$20$	3.81446	0.852939
$21$	2.25646	0.492399
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.17272	−0.647628
$25$	9.55011	1.91002
$26$	−1.15076	−0.225682
$27$	12.9007	2.48274
$28$	0.711206	0.134405
$29$	−6.95044	−1.29066	−0.645332	−	0.763902i	$-0.723281\pi$
$29$	−6.95044	−1.29066	−0.645332	+	0.763902i	$0.723281\pi$
$30$	−12.1022	−2.20955
$31$	−7.06435	−1.26880	−0.634398	−	0.773007i	$-0.718752\pi$
$31$	−7.06435	−1.26880	−0.634398	+	0.773007i	$0.718752\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.97045	−0.680926
$35$	2.71287	0.458558
$36$	7.06614	1.17769
$37$	−0.313872	−0.0516003	−0.0258002	−	0.999667i	$-0.508213\pi$
$37$	−0.313872	−0.0516003	−0.0258002	+	0.999667i	$0.508213\pi$
$38$	3.17585	0.515191
$39$	3.65102	0.584632
$40$	−3.81446	−0.603119
$41$	12.5218	1.95557	0.977787	−	0.209603i	$-0.0672171\pi$
$41$	12.5218	1.95557	0.977787	+	0.209603i	$0.0672171\pi$
$42$	−2.25646	−0.348179
$43$	5.79562	0.883824	0.441912	−	0.897058i	$-0.354300\pi$
$43$	5.79562	0.883824	0.441912	+	0.897058i	$0.354300\pi$
$44$	0	0
$45$	26.9535	4.01799
$46$	1.00000	0.147442
$47$	1.89914	0.277018	0.138509	−	0.990361i	$-0.455769\pi$
$47$	1.89914	0.277018	0.138509	+	0.990361i	$0.455769\pi$
$48$	3.17272	0.457942
$49$	−6.49419	−0.927741
$50$	−9.55011	−1.35059
$51$	12.5971	1.76395
$52$	1.15076	0.159581
$53$	−12.3697	−1.69911	−0.849554	−	0.527501i	$-0.823129\pi$
$53$	−12.3697	−1.69911	−0.849554	+	0.527501i	$0.823129\pi$
$54$	−12.9007	−1.75557
$55$	0	0
$56$	−0.711206	−0.0950389
$57$	−10.0761	−1.33461
$58$	6.95044	0.912638
$59$	−0.351370	−0.0457445	−0.0228722	−	0.999738i	$-0.507281\pi$
$59$	−0.351370	−0.0457445	−0.0228722	+	0.999738i	$0.507281\pi$
$60$	12.1022	1.56239
$61$	−2.93339	−0.375582	−0.187791	−	0.982209i	$-0.560133\pi$
$61$	−2.93339	−0.375582	−0.187791	+	0.982209i	$0.560133\pi$
$62$	7.06435	0.897174
$63$	5.02548	0.633151
$64$	1.00000	0.125000
$65$	4.38951	0.544452
$66$	0	0
$67$	5.39932	0.659632	0.329816	−	0.944045i	$-0.393013\pi$
$67$	5.39932	0.659632	0.329816	+	0.944045i	$0.393013\pi$
$68$	3.97045	0.481488
$69$	−3.17272	−0.381950
$70$	−2.71287	−0.324250
$71$	−15.0256	−1.78322	−0.891608	−	0.452808i	$-0.850422\pi$
$71$	−15.0256	−1.78322	−0.891608	+	0.452808i	$0.850422\pi$
$72$	−7.06614	−0.832753
$73$	11.6500	1.36353	0.681766	−	0.731570i	$-0.261212\pi$
$73$	11.6500	1.36353	0.681766	+	0.731570i	$0.261212\pi$
$74$	0.313872	0.0364869
$75$	30.2998	3.49872
$76$	−3.17585	−0.364295
$77$	0	0
$78$	−3.65102	−0.413397
$79$	4.23644	0.476637	0.238319	−	0.971187i	$-0.423404\pi$
$79$	4.23644	0.476637	0.238319	+	0.971187i	$0.423404\pi$
$80$	3.81446	0.426470
$81$	19.7319	2.19243
$82$	−12.5218	−1.38280
$83$	−1.33343	−0.146363	−0.0731813	−	0.997319i	$-0.523315\pi$
$83$	−1.33343	−0.146363	−0.0731813	+	0.997319i	$0.523315\pi$
$84$	2.25646	0.246200
$85$	15.1451	1.64272
$86$	−5.79562	−0.624958
$87$	−22.0518	−2.36420
$88$	0	0
$89$	5.08032	0.538513	0.269256	−	0.963069i	$-0.413222\pi$
$89$	5.08032	0.538513	0.269256	+	0.963069i	$0.413222\pi$
$90$	−26.9535	−2.84115
$91$	0.818424	0.0857942
$92$	−1.00000	−0.104257
$93$	−22.4132	−2.32414
$94$	−1.89914	−0.195881
$95$	−12.1141	−1.24289
$96$	−3.17272	−0.323814
$97$	−12.7048	−1.28998	−0.644989	−	0.764192i	$-0.723138\pi$
$97$	−12.7048	−1.28998	−0.644989	+	0.764192i	$0.723138\pi$
$98$	6.49419	0.656012
$99$	0	0
$100$	9.55011	0.955011
$101$	−6.72620	−0.669282	−0.334641	−	0.942346i	$-0.608615\pi$
$101$	−6.72620	−0.669282	−0.334641	+	0.942346i	$0.608615\pi$
$102$	−12.5971	−1.24730
$103$	2.41524	0.237981	0.118991	−	0.992895i	$-0.462034\pi$
$103$	2.41524	0.237981	0.118991	+	0.992895i	$0.462034\pi$
$104$	−1.15076	−0.112841
$105$	8.60716	0.839973
$106$	12.3697	1.20145
$107$	−14.6146	−1.41285	−0.706424	−	0.707789i	$-0.749693\pi$
$107$	−14.6146	−1.41285	−0.706424	+	0.707789i	$0.749693\pi$
$108$	12.9007	1.24137
$109$	−12.7537	−1.22159	−0.610793	−	0.791790i	$-0.709149\pi$
$109$	−12.7537	−1.22159	−0.610793	+	0.791790i	$0.709149\pi$
$110$	0	0
$111$	−0.995829	−0.0945199
$112$	0.711206	0.0672027
$113$	5.47302	0.514859	0.257429	−	0.966297i	$-0.417125\pi$
$113$	5.47302	0.514859	0.257429	+	0.966297i	$0.417125\pi$
$114$	10.0761	0.943711
$115$	−3.81446	−0.355700
$116$	−6.95044	−0.645332
$117$	8.13140	0.751748
$118$	0.351370	0.0323462
$119$	2.82381	0.258858
$120$	−12.1022	−1.10478
$121$	0	0
$122$	2.93339	0.265576
$123$	39.7281	3.58216
$124$	−7.06435	−0.634398
$125$	17.3562	1.55239
$126$	−5.02548	−0.447706
$127$	−8.44567	−0.749432	−0.374716	−	0.927140i	$-0.622260\pi$
$127$	−8.44567	−0.749432	−0.374716	+	0.927140i	$0.622260\pi$
$128$	−1.00000	−0.0883883
$129$	18.3879	1.61896
$130$	−4.38951	−0.384986
$131$	−8.37860	−0.732041	−0.366021	−	0.930607i	$-0.619280\pi$
$131$	−8.37860	−0.732041	−0.366021	+	0.930607i	$0.619280\pi$
$132$	0	0
$133$	−2.25868	−0.195853
$134$	−5.39932	−0.466430
$135$	49.2093	4.23526
$136$	−3.97045	−0.340463
$137$	21.8913	1.87030	0.935148	−	0.354257i	$-0.115266\pi$
$137$	21.8913	1.87030	0.935148	+	0.354257i	$0.115266\pi$
$138$	3.17272	0.270080
$139$	22.7190	1.92700	0.963500	−	0.267709i	$-0.0862666\pi$
$139$	22.7190	1.92700	0.963500	+	0.267709i	$0.0862666\pi$
$140$	2.71287	0.229279
$141$	6.02543	0.507433
$142$	15.0256	1.26092
$143$	0	0
$144$	7.06614	0.588845
$145$	−26.5122	−2.20172
$146$	−11.6500	−0.964163
$147$	−20.6042	−1.69941
$148$	−0.313872	−0.0258002
$149$	−7.14195	−0.585091	−0.292546	−	0.956252i	$-0.594502\pi$
$149$	−7.14195	−0.585091	−0.292546	+	0.956252i	$0.594502\pi$
$150$	−30.2998	−2.47397
$151$	−3.15393	−0.256663	−0.128332	−	0.991731i	$-0.540962\pi$
$151$	−3.15393	−0.256663	−0.128332	+	0.991731i	$0.540962\pi$
$152$	3.17585	0.257595
$153$	28.0557	2.26817
$154$	0	0
$155$	−26.9467	−2.16441
$156$	3.65102	0.292316
$157$	17.1260	1.36681	0.683403	−	0.730041i	$-0.260499\pi$
$157$	17.1260	1.36681	0.683403	+	0.730041i	$0.260499\pi$
$158$	−4.23644	−0.337033
$159$	−39.2456	−3.11238
$160$	−3.81446	−0.301560
$161$	−0.711206	−0.0560509
$162$	−19.7319	−1.55029
$163$	9.03957	0.708034	0.354017	−	0.935239i	$-0.384815\pi$
$163$	9.03957	0.708034	0.354017	+	0.935239i	$0.384815\pi$
$164$	12.5218	0.977787
$165$	0	0
$166$	1.33343	0.103494
$167$	−7.18634	−0.556096	−0.278048	−	0.960567i	$-0.589687\pi$
$167$	−7.18634	−0.556096	−0.278048	+	0.960567i	$0.589687\pi$
$168$	−2.25646	−0.174089
$169$	−11.6758	−0.898135
$170$	−15.1451	−1.16158
$171$	−22.4410	−1.71611
$172$	5.79562	0.441912
$173$	11.3625	0.863874	0.431937	−	0.901904i	$-0.357830\pi$
$173$	11.3625	0.863874	0.431937	+	0.901904i	$0.357830\pi$
$174$	22.0518	1.67174
$175$	6.79210	0.513434
$176$	0	0
$177$	−1.11480	−0.0837934
$178$	−5.08032	−0.380786
$179$	12.5491	0.937961	0.468980	−	0.883209i	$-0.344622\pi$
$179$	12.5491	0.937961	0.468980	+	0.883209i	$0.344622\pi$
$180$	26.9535	2.00900
$181$	0.139453	0.0103654	0.00518272	−	0.999987i	$-0.498350\pi$
$181$	0.139453	0.0103654	0.00518272	+	0.999987i	$0.498350\pi$
$182$	−0.818424	−0.0606657
$183$	−9.30681	−0.687979
$184$	1.00000	0.0737210
$185$	−1.19725	−0.0880239
$186$	22.4132	1.64342
$187$	0	0
$188$	1.89914	0.138509
$189$	9.17507	0.667388
$190$	12.1141	0.878853
$191$	−12.9039	−0.933696	−0.466848	−	0.884338i	$-0.654610\pi$
$191$	−12.9039	−0.933696	−0.466848	+	0.884338i	$0.654610\pi$
$192$	3.17272	0.228971
$193$	−23.7470	−1.70935	−0.854674	−	0.519166i	$-0.826243\pi$
$193$	−23.7470	−1.70935	−0.854674	+	0.519166i	$0.826243\pi$
$194$	12.7048	0.912152
$195$	13.9267	0.997311
$196$	−6.49419	−0.463870
$197$	17.4582	1.24385	0.621924	−	0.783077i	$-0.286351\pi$
$197$	17.4582	1.24385	0.621924	+	0.783077i	$0.286351\pi$
$198$	0	0
$199$	4.39149	0.311304	0.155652	−	0.987812i	$-0.450252\pi$
$199$	4.39149	0.311304	0.155652	+	0.987812i	$0.450252\pi$
$200$	−9.55011	−0.675295
$201$	17.1305	1.20829
$202$	6.72620	0.473254
$203$	−4.94320	−0.346944
$204$	12.5971	0.881974
$205$	47.7638	3.33597
$206$	−2.41524	−0.168278
$207$	−7.06614	−0.491131
$208$	1.15076	0.0797905
$209$	0	0
$210$	−8.60716	−0.593951
$211$	−17.7499	−1.22196	−0.610978	−	0.791648i	$-0.709224\pi$
$211$	−17.7499	−1.22196	−0.610978	+	0.791648i	$0.709224\pi$
$212$	−12.3697	−0.849554
$213$	−47.6721	−3.26644
$214$	14.6146	0.999035
$215$	22.1072	1.50770
$216$	−12.9007	−0.877783
$217$	−5.02421	−0.341066
$218$	12.7537	0.863792
$219$	36.9622	2.49768
$220$	0	0
$221$	4.56902	0.307345
$222$	0.995829	0.0668357
$223$	3.64330	0.243973	0.121987	−	0.992532i	$-0.461074\pi$
$223$	3.64330	0.243973	0.121987	+	0.992532i	$0.461074\pi$
$224$	−0.711206	−0.0475195
$225$	67.4824	4.49883
$226$	−5.47302	−0.364060
$227$	−6.60404	−0.438326	−0.219163	−	0.975688i	$-0.570333\pi$
$227$	−6.60404	−0.438326	−0.219163	+	0.975688i	$0.570333\pi$
$228$	−10.0761	−0.667304
$229$	2.51386	0.166120	0.0830602	−	0.996545i	$-0.473531\pi$
$229$	2.51386	0.166120	0.0830602	+	0.996545i	$0.473531\pi$
$230$	3.81446	0.251518
$231$	0	0
$232$	6.95044	0.456319
$233$	11.6951	0.766173	0.383087	−	0.923712i	$-0.374861\pi$
$233$	11.6951	0.766173	0.383087	+	0.923712i	$0.374861\pi$
$234$	−8.13140	−0.531566
$235$	7.24418	0.472558
$236$	−0.351370	−0.0228722
$237$	13.4410	0.873089
$238$	−2.82381	−0.183040
$239$	4.09405	0.264822	0.132411	−	0.991195i	$-0.457728\pi$
$239$	4.09405	0.264822	0.132411	+	0.991195i	$0.457728\pi$
$240$	12.1022	0.781194
$241$	−7.67288	−0.494254	−0.247127	−	0.968983i	$-0.579486\pi$
$241$	−7.67288	−0.494254	−0.247127	+	0.968983i	$0.579486\pi$
$242$	0	0
$243$	23.9017	1.53329
$244$	−2.93339	−0.187791
$245$	−24.7718	−1.58261
$246$	−39.7281	−2.53297
$247$	−3.65463	−0.232538
$248$	7.06435	0.448587
$249$	−4.23059	−0.268103
$250$	−17.3562	−1.09770
$251$	−12.6758	−0.800087	−0.400043	−	0.916496i	$-0.631005\pi$
$251$	−12.6758	−0.800087	−0.400043	+	0.916496i	$0.631005\pi$
$252$	5.02548	0.316576
$253$	0	0
$254$	8.44567	0.529929
$255$	48.0512	3.00908
$256$	1.00000	0.0625000
$257$	11.0101	0.686790	0.343395	−	0.939191i	$-0.388423\pi$
$257$	11.0101	0.686790	0.343395	+	0.939191i	$0.388423\pi$
$258$	−18.3879	−1.14478
$259$	−0.223228	−0.0138707
$260$	4.38951	0.272226
$261$	−49.1128	−3.04001
$262$	8.37860	0.517631
$263$	−18.7605	−1.15682	−0.578411	−	0.815746i	$-0.696327\pi$
$263$	−18.7605	−1.15682	−0.578411	+	0.815746i	$0.696327\pi$
$264$	0	0
$265$	−47.1837	−2.89847
$266$	2.25868	0.138489
$267$	16.1184	0.986431
$268$	5.39932	0.329816
$269$	−23.9601	−1.46087	−0.730436	−	0.682981i	$-0.760683\pi$
$269$	−23.9601	−1.46087	−0.730436	+	0.682981i	$0.760683\pi$
$270$	−49.2093	−2.99478
$271$	6.72570	0.408557	0.204278	−	0.978913i	$-0.434515\pi$
$271$	6.72570	0.408557	0.204278	+	0.978913i	$0.434515\pi$
$272$	3.97045	0.240744
$273$	2.59663	0.157155
$274$	−21.8913	−1.32250
$275$	0	0
$276$	−3.17272	−0.190975
$277$	−5.78858	−0.347802	−0.173901	−	0.984763i	$-0.555637\pi$
$277$	−5.78858	−0.347802	−0.173901	+	0.984763i	$0.555637\pi$
$278$	−22.7190	−1.36259
$279$	−49.9177	−2.98850
$280$	−2.71287	−0.162125
$281$	11.0390	0.658529	0.329265	−	0.944238i	$-0.393199\pi$
$281$	11.0390	0.658529	0.329265	+	0.944238i	$0.393199\pi$
$282$	−6.02543	−0.358809
$283$	−12.6676	−0.753010	−0.376505	−	0.926415i	$-0.622874\pi$
$283$	−12.6676	−0.753010	−0.376505	+	0.926415i	$0.622874\pi$
$284$	−15.0256	−0.891608
$285$	−38.4348	−2.27668
$286$	0	0
$287$	8.90557	0.525679
$288$	−7.06614	−0.416376
$289$	−1.23554	−0.0726786
$290$	26.5122	1.55685
$291$	−40.3088	−2.36294
$292$	11.6500	0.681766
$293$	−14.1243	−0.825151	−0.412576	−	0.910923i	$-0.635371\pi$
$293$	−14.1243	−0.825151	−0.412576	+	0.910923i	$0.635371\pi$
$294$	20.6042	1.20166
$295$	−1.34029	−0.0780345
$296$	0.313872	0.0182435
$297$	0	0
$298$	7.14195	0.413722
$299$	−1.15076	−0.0665499
$300$	30.2998	1.74936
$301$	4.12188	0.237581
$302$	3.15393	0.181488
$303$	−21.3403	−1.22597
$304$	−3.17585	−0.182147
$305$	−11.1893	−0.640697
$306$	−28.0557	−1.60384
$307$	−17.5888	−1.00384	−0.501922	−	0.864913i	$-0.667373\pi$
$307$	−17.5888	−1.00384	−0.501922	+	0.864913i	$0.667373\pi$
$308$	0	0
$309$	7.66289	0.435927
$310$	26.9467	1.53047
$311$	15.1279	0.857822	0.428911	−	0.903347i	$-0.358897\pi$
$311$	15.1279	0.857822	0.428911	+	0.903347i	$0.358897\pi$
$312$	−3.65102	−0.206698
$313$	30.4935	1.72359	0.861796	−	0.507255i	$-0.169340\pi$
$313$	30.4935	1.72359	0.861796	+	0.507255i	$0.169340\pi$
$314$	−17.1260	−0.966478
$315$	19.1695	1.08008
$316$	4.23644	0.238319
$317$	21.2377	1.19283	0.596415	−	0.802676i	$-0.296591\pi$
$317$	21.2377	1.19283	0.596415	+	0.802676i	$0.296591\pi$
$318$	39.2456	2.20078
$319$	0	0
$320$	3.81446	0.213235
$321$	−46.3681	−2.58801
$322$	0.711206	0.0396340
$323$	−12.6095	−0.701614
$324$	19.7319	1.09622
$325$	10.9898	0.609607
$326$	−9.03957	−0.500656
$327$	−40.4640	−2.23766
$328$	−12.5218	−0.691400
$329$	1.35068	0.0744653
$330$	0	0
$331$	−9.03028	−0.496349	−0.248174	−	0.968715i	$-0.579831\pi$
$331$	−9.03028	−0.496349	−0.248174	+	0.968715i	$0.579831\pi$
$332$	−1.33343	−0.0731813
$333$	−2.21787	−0.121538
$334$	7.18634	0.393219
$335$	20.5955	1.12525
$336$	2.25646	0.123100
$337$	18.9785	1.03382	0.516911	−	0.856039i	$-0.327082\pi$
$337$	18.9785	1.03382	0.516911	+	0.856039i	$0.327082\pi$
$338$	11.6758	0.635078
$339$	17.3644	0.943103
$340$	15.1451	0.821359
$341$	0	0
$342$	22.4410	1.21347
$343$	−9.59715	−0.518197
$344$	−5.79562	−0.312479
$345$	−12.1022	−0.651561
$346$	−11.3625	−0.610851
$347$	13.7868	0.740113	0.370057	−	0.929009i	$-0.379338\pi$
$347$	13.7868	0.740113	0.370057	+	0.929009i	$0.379338\pi$
$348$	−22.0518	−1.18210
$349$	−15.1332	−0.810063	−0.405032	−	0.914303i	$-0.632740\pi$
$349$	−15.1332	−0.810063	−0.405032	+	0.914303i	$0.632740\pi$
$350$	−6.79210	−0.363053
$351$	14.8456	0.792398
$352$	0	0
$353$	13.4377	0.715215	0.357607	−	0.933872i	$-0.383593\pi$
$353$	13.4377	0.715215	0.357607	+	0.933872i	$0.383593\pi$
$354$	1.11480	0.0592508
$355$	−57.3147	−3.04195
$356$	5.08032	0.269256
$357$	8.95914	0.474168
$358$	−12.5491	−0.663238
$359$	−26.3963	−1.39314	−0.696572	−	0.717487i	$-0.745292\pi$
$359$	−26.3963	−1.39314	−0.696572	+	0.717487i	$0.745292\pi$
$360$	−26.9535	−1.42057
$361$	−8.91399	−0.469157
$362$	−0.139453	−0.00732948
$363$	0	0
$364$	0.818424	0.0428971
$365$	44.4386	2.32602
$366$	9.30681	0.486475
$367$	4.24241	0.221452	0.110726	−	0.993851i	$-0.464682\pi$
$367$	4.24241	0.221452	0.110726	+	0.993851i	$0.464682\pi$
$368$	−1.00000	−0.0521286
$369$	88.4806	4.60612
$370$	1.19725	0.0622423
$371$	−8.79740	−0.456738
$372$	−22.4132	−1.16207
$373$	27.8321	1.44109	0.720547	−	0.693407i	$-0.243891\pi$
$373$	27.8321	1.44109	0.720547	+	0.693407i	$0.243891\pi$
$374$	0	0
$375$	55.0664	2.84361
$376$	−1.89914	−0.0979405
$377$	−7.99826	−0.411931
$378$	−9.17507	−0.471915
$379$	−33.8342	−1.73795	−0.868973	−	0.494860i	$-0.835219\pi$
$379$	−33.8342	−1.73795	−0.868973	+	0.494860i	$0.835219\pi$
$380$	−12.1141	−0.621443
$381$	−26.7957	−1.37279
$382$	12.9039	0.660222
$383$	−4.67567	−0.238916	−0.119458	−	0.992839i	$-0.538116\pi$
$383$	−4.67567	−0.238916	−0.119458	+	0.992839i	$0.538116\pi$
$384$	−3.17272	−0.161907
$385$	0	0
$386$	23.7470	1.20869
$387$	40.9527	2.08174
$388$	−12.7048	−0.644989
$389$	−7.97709	−0.404455	−0.202227	−	0.979339i	$-0.564818\pi$
$389$	−7.97709	−0.404455	−0.202227	+	0.979339i	$0.564818\pi$
$390$	−13.9267	−0.705205
$391$	−3.97045	−0.200794
$392$	6.49419	0.328006
$393$	−26.5829	−1.34093
$394$	−17.4582	−0.879534
$395$	16.1597	0.813085
$396$	0	0
$397$	−20.0989	−1.00873	−0.504367	−	0.863489i	$-0.668274\pi$
$397$	−20.0989	−1.00873	−0.504367	+	0.863489i	$0.668274\pi$
$398$	−4.39149	−0.220126
$399$	−7.16616	−0.358757
$400$	9.55011	0.477505
$401$	−30.5883	−1.52751	−0.763753	−	0.645509i	$-0.776645\pi$
$401$	−30.5883	−1.52751	−0.763753	+	0.645509i	$0.776645\pi$
$402$	−17.1305	−0.854392
$403$	−8.12935	−0.404952
$404$	−6.72620	−0.334641
$405$	75.2666	3.74003
$406$	4.94320	0.245327
$407$	0	0
$408$	−12.5971	−0.623650
$409$	3.23108	0.159767	0.0798834	−	0.996804i	$-0.474545\pi$
$409$	3.23108	0.159767	0.0798834	+	0.996804i	$0.474545\pi$
$410$	−47.7638	−2.35889
$411$	69.4548	3.42595
$412$	2.41524	0.118991
$413$	−0.249897	−0.0122966
$414$	7.06614	0.347282
$415$	−5.08630	−0.249677
$416$	−1.15076	−0.0564204
$417$	72.0810	3.52982
$418$	0	0
$419$	22.9090	1.11918	0.559588	−	0.828771i	$-0.310959\pi$
$419$	22.9090	1.11918	0.559588	+	0.828771i	$0.310959\pi$
$420$	8.60716	0.419987
$421$	22.5484	1.09894	0.549471	−	0.835513i	$-0.314829\pi$
$421$	22.5484	1.09894	0.549471	+	0.835513i	$0.314829\pi$
$422$	17.7499	0.864053
$423$	13.4196	0.652482
$424$	12.3697	0.600726
$425$	37.9182	1.83930
$426$	47.6721	2.30972
$427$	−2.08624	−0.100960
$428$	−14.6146	−0.706424
$429$	0	0
$430$	−22.1072	−1.06610
$431$	28.7033	1.38259	0.691295	−	0.722573i	$-0.257040\pi$
$431$	28.7033	1.38259	0.691295	+	0.722573i	$0.257040\pi$
$432$	12.9007	0.620686
$433$	−20.7090	−0.995211	−0.497605	−	0.867404i	$-0.665787\pi$
$433$	−20.7090	−0.995211	−0.497605	+	0.867404i	$0.665787\pi$
$434$	5.02421	0.241170
$435$	−84.1157	−4.03304
$436$	−12.7537	−0.610793
$437$	3.17585	0.151921
$438$	−36.9622	−1.76612
$439$	−16.1709	−0.771793	−0.385896	−	0.922542i	$-0.626108\pi$
$439$	−16.1709	−0.771793	−0.385896	+	0.922542i	$0.626108\pi$
$440$	0	0
$441$	−45.8888	−2.18518
$442$	−4.56902	−0.217326
$443$	−39.1046	−1.85792	−0.928958	−	0.370186i	$-0.879294\pi$
$443$	−39.1046	−1.85792	−0.928958	+	0.370186i	$0.879294\pi$
$444$	−0.995829	−0.0472599
$445$	19.3787	0.918637
$446$	−3.64330	−0.172515
$447$	−22.6594	−1.07175
$448$	0.711206	0.0336013
$449$	−3.19276	−0.150676	−0.0753378	−	0.997158i	$-0.524003\pi$
$449$	−3.19276	−0.150676	−0.0753378	+	0.997158i	$0.524003\pi$
$450$	−67.4824	−3.18115
$451$	0	0
$452$	5.47302	0.257429
$453$	−10.0065	−0.470148
$454$	6.60404	0.309943
$455$	3.12185	0.146354
$456$	10.0761	0.471855
$457$	37.5416	1.75612	0.878060	−	0.478551i	$-0.158838\pi$
$457$	37.5416	1.75612	0.878060	+	0.478551i	$0.158838\pi$
$458$	−2.51386	−0.117465
$459$	51.2216	2.39082
$460$	−3.81446	−0.177850
$461$	−13.4911	−0.628343	−0.314171	−	0.949366i	$-0.601727\pi$
$461$	−13.4911	−0.628343	−0.314171	+	0.949366i	$0.601727\pi$
$462$	0	0
$463$	42.1844	1.96047	0.980237	−	0.197825i	$-0.0633879\pi$
$463$	42.1844	1.96047	0.980237	+	0.197825i	$0.0633879\pi$
$464$	−6.95044	−0.322666
$465$	−85.4943	−3.96470
$466$	−11.6951	−0.541766
$467$	−3.62080	−0.167551	−0.0837754	−	0.996485i	$-0.526698\pi$
$467$	−3.62080	−0.167551	−0.0837754	+	0.996485i	$0.526698\pi$
$468$	8.13140	0.375874
$469$	3.84003	0.177316
$470$	−7.24418	−0.334149
$471$	54.3361	2.50367
$472$	0.351370	0.0161731
$473$	0	0
$474$	−13.4410	−0.617367
$475$	−30.3297	−1.39162
$476$	2.82381	0.129429
$477$	−87.4060	−4.00205
$478$	−4.09405	−0.187258
$479$	−36.0090	−1.64529	−0.822646	−	0.568554i	$-0.807503\pi$
$479$	−36.0090	−1.64529	−0.822646	+	0.568554i	$0.807503\pi$
$480$	−12.1022	−0.552388
$481$	−0.361191	−0.0164689
$482$	7.67288	0.349490
$483$	−2.25646	−0.102672
$484$	0	0
$485$	−48.4620	−2.20054
$486$	−23.9017	−1.08420
$487$	−6.68812	−0.303068	−0.151534	−	0.988452i	$-0.548421\pi$
$487$	−6.68812	−0.303068	−0.151534	+	0.988452i	$0.548421\pi$
$488$	2.93339	0.132788
$489$	28.6800	1.29696
$490$	24.7718	1.11908
$491$	20.4104	0.921107	0.460553	−	0.887632i	$-0.347651\pi$
$491$	20.4104	0.921107	0.460553	+	0.887632i	$0.347651\pi$
$492$	39.7281	1.79108
$493$	−27.5964	−1.24288
$494$	3.65463	0.164429
$495$	0	0
$496$	−7.06435	−0.317199
$497$	−10.6863	−0.479347
$498$	4.23059	0.189577
$499$	9.65857	0.432377	0.216189	−	0.976352i	$-0.430637\pi$
$499$	9.65857	0.432377	0.216189	+	0.976352i	$0.430637\pi$
$500$	17.3562	0.776193
$501$	−22.8002	−1.01864
$502$	12.6758	0.565747
$503$	27.8643	1.24241	0.621204	−	0.783649i	$-0.286644\pi$
$503$	27.8643	1.24241	0.621204	+	0.783649i	$0.286644\pi$
$504$	−5.02548	−0.223853
$505$	−25.6568	−1.14171
$506$	0	0
$507$	−37.0439	−1.64518
$508$	−8.44567	−0.374716
$509$	14.3457	0.635860	0.317930	−	0.948114i	$-0.397012\pi$
$509$	14.3457	0.635860	0.317930	+	0.948114i	$0.397012\pi$
$510$	−48.0512	−2.12774
$511$	8.28557	0.366532
$512$	−1.00000	−0.0441942
$513$	−40.9707	−1.80890
$514$	−11.0101	−0.485634
$515$	9.21286	0.405967
$516$	18.3879	0.809481
$517$	0	0
$518$	0.223228	0.00980808
$519$	36.0500	1.58242
$520$	−4.38951	−0.192493
$521$	−17.1778	−0.752571	−0.376286	−	0.926504i	$-0.622799\pi$
$521$	−17.1778	−0.752571	−0.376286	+	0.926504i	$0.622799\pi$
$522$	49.1128	2.14961
$523$	−12.8199	−0.560575	−0.280287	−	0.959916i	$-0.590430\pi$
$523$	−12.8199	−0.560575	−0.280287	+	0.959916i	$0.590430\pi$
$524$	−8.37860	−0.366021
$525$	21.5494	0.940493
$526$	18.7605	0.817996
$527$	−28.0487	−1.22182
$528$	0	0
$529$	1.00000	0.0434783
$530$	47.1837	2.04953
$531$	−2.48283	−0.107746
$532$	−2.25868	−0.0979263
$533$	14.4095	0.624145
$534$	−16.1184	−0.697512
$535$	−55.7469	−2.41015
$536$	−5.39932	−0.233215
$537$	39.8146	1.71813
$538$	23.9601	1.03299
$539$	0	0
$540$	49.2093	2.11763
$541$	−4.72820	−0.203281	−0.101641	−	0.994821i	$-0.532409\pi$
$541$	−4.72820	−0.203281	−0.101641	+	0.994821i	$0.532409\pi$
$542$	−6.72570	−0.288893
$543$	0.442444	0.0189871
$544$	−3.97045	−0.170232
$545$	−48.6486	−2.08388
$546$	−2.59663	−0.111126
$547$	−30.4488	−1.30190	−0.650948	−	0.759122i	$-0.725629\pi$
$547$	−30.4488	−1.30190	−0.650948	+	0.759122i	$0.725629\pi$
$548$	21.8913	0.935148
$549$	−20.7277	−0.884638
$550$	0	0
$551$	22.0735	0.940365
$552$	3.17272	0.135040
$553$	3.01298	0.128125
$554$	5.78858	0.245933
$555$	−3.79855	−0.161239
$556$	22.7190	0.963500
$557$	18.8725	0.799653	0.399827	−	0.916591i	$-0.369070\pi$
$557$	18.8725	0.799653	0.399827	+	0.916591i	$0.369070\pi$
$558$	49.9177	2.11319
$559$	6.66935	0.282083
$560$	2.71287	0.114640
$561$	0	0
$562$	−11.0390	−0.465650
$563$	−25.0059	−1.05387	−0.526936	−	0.849905i	$-0.676659\pi$
$563$	−25.0059	−1.05387	−0.526936	+	0.849905i	$0.676659\pi$
$564$	6.02543	0.253716
$565$	20.8766	0.878287
$566$	12.6676	0.532458
$567$	14.0335	0.589350
$568$	15.0256	0.630462
$569$	23.8832	1.00124	0.500618	−	0.865668i	$-0.333106\pi$
$569$	23.8832	1.00124	0.500618	+	0.865668i	$0.333106\pi$
$570$	38.4348	1.60986
$571$	−12.7877	−0.535148	−0.267574	−	0.963537i	$-0.586222\pi$
$571$	−12.7877	−0.535148	−0.267574	+	0.963537i	$0.586222\pi$
$572$	0	0
$573$	−40.9405	−1.71032
$574$	−8.90557	−0.371711
$575$	−9.55011	−0.398267
$576$	7.06614	0.294422
$577$	−25.6520	−1.06791	−0.533953	−	0.845514i	$-0.679294\pi$
$577$	−25.6520	−1.06791	−0.533953	+	0.845514i	$0.679294\pi$
$578$	1.23554	0.0513915
$579$	−75.3426	−3.13113
$580$	−26.5122	−1.10086
$581$	−0.948341	−0.0393438
$582$	40.3088	1.67085
$583$	0	0
$584$	−11.6500	−0.482081
$585$	31.0169	1.28239
$586$	14.1243	0.583470
$587$	−0.256572	−0.0105898	−0.00529492	−	0.999986i	$-0.501685\pi$
$587$	−0.256572	−0.0105898	−0.00529492	+	0.999986i	$0.501685\pi$
$588$	−20.6042	−0.849704
$589$	22.4353	0.924431
$590$	1.34029	0.0551787
$591$	55.3901	2.27844
$592$	−0.313872	−0.0129001
$593$	23.3373	0.958350	0.479175	−	0.877719i	$-0.340936\pi$
$593$	23.3373	0.958350	0.479175	+	0.877719i	$0.340936\pi$
$594$	0	0
$595$	10.7713	0.441580
$596$	−7.14195	−0.292546
$597$	13.9330	0.570238
$598$	1.15076	0.0470579
$599$	−18.7128	−0.764583	−0.382291	−	0.924042i	$-0.624865\pi$
$599$	−18.7128	−0.764583	−0.382291	+	0.924042i	$0.624865\pi$
$600$	−30.2998	−1.23698
$601$	26.3124	1.07331	0.536653	−	0.843803i	$-0.319688\pi$
$601$	26.3124	1.07331	0.536653	+	0.843803i	$0.319688\pi$
$602$	−4.12188	−0.167995
$603$	38.1523	1.55368
$604$	−3.15393	−0.128332
$605$	0	0
$606$	21.3403	0.866892
$607$	−22.0750	−0.895998	−0.447999	−	0.894034i	$-0.647863\pi$
$607$	−22.0750	−0.895998	−0.447999	+	0.894034i	$0.647863\pi$
$608$	3.17585	0.128798
$609$	−15.6834	−0.635522
$610$	11.1893	0.453041
$611$	2.18544	0.0884136
$612$	28.0557	1.13409
$613$	19.7279	0.796803	0.398402	−	0.917211i	$-0.369565\pi$
$613$	19.7279	0.796803	0.398402	+	0.917211i	$0.369565\pi$
$614$	17.5888	0.709825
$615$	151.541	6.11073
$616$	0	0
$617$	33.3093	1.34098	0.670492	−	0.741917i	$-0.266083\pi$
$617$	33.3093	1.34098	0.670492	+	0.741917i	$0.266083\pi$
$618$	−7.66289	−0.308247
$619$	1.25889	0.0505992	0.0252996	−	0.999680i	$-0.491946\pi$
$619$	1.25889	0.0505992	0.0252996	+	0.999680i	$0.491946\pi$
$620$	−26.9467	−1.08221
$621$	−12.9007	−0.517688
$622$	−15.1279	−0.606572
$623$	3.61315	0.144758
$624$	3.65102	0.146158
$625$	18.4540	0.738161
$626$	−30.4935	−1.21876
$627$	0	0
$628$	17.1260	0.683403
$629$	−1.24621	−0.0496898
$630$	−19.1695	−0.763731
$631$	20.9616	0.834469	0.417235	−	0.908799i	$-0.362999\pi$
$631$	20.9616	0.834469	0.417235	+	0.908799i	$0.362999\pi$
$632$	−4.23644	−0.168517
$633$	−56.3155	−2.23834
$634$	−21.2377	−0.843459
$635$	−32.2157	−1.27844
$636$	−39.2456	−1.55619
$637$	−7.47322	−0.296100
$638$	0	0
$639$	−106.173	−4.20015
$640$	−3.81446	−0.150780
$641$	−11.7887	−0.465627	−0.232813	−	0.972521i	$-0.574793\pi$
$641$	−11.7887	−0.465627	−0.232813	+	0.972521i	$0.574793\pi$
$642$	46.3681	1.83000
$643$	19.2587	0.759487	0.379744	−	0.925092i	$-0.376012\pi$
$643$	19.2587	0.759487	0.379744	+	0.925092i	$0.376012\pi$
$644$	−0.711206	−0.0280254
$645$	70.1398	2.76175
$646$	12.6095	0.496116
$647$	−1.10917	−0.0436060	−0.0218030	−	0.999762i	$-0.506941\pi$
$647$	−1.10917	−0.0436060	−0.0218030	+	0.999762i	$0.506941\pi$
$648$	−19.7319	−0.775143
$649$	0	0
$650$	−10.9898	−0.431057
$651$	−15.9404	−0.624754
$652$	9.03957	0.354017
$653$	−2.13726	−0.0836375	−0.0418188	−	0.999125i	$-0.513315\pi$
$653$	−2.13726	−0.0836375	−0.0418188	+	0.999125i	$0.513315\pi$
$654$	40.4640	1.58227
$655$	−31.9598	−1.24877
$656$	12.5218	0.488893
$657$	82.3207	3.21164
$658$	−1.35068	−0.0526549
$659$	−1.93861	−0.0755175	−0.0377587	−	0.999287i	$-0.512022\pi$
$659$	−1.93861	−0.0755175	−0.0377587	+	0.999287i	$0.512022\pi$
$660$	0	0
$661$	30.8610	1.20035	0.600177	−	0.799867i	$-0.295097\pi$
$661$	30.8610	1.20035	0.600177	+	0.799867i	$0.295097\pi$
$662$	9.03028	0.350972
$663$	14.4962	0.562986
$664$	1.33343	0.0517470
$665$	−8.61566	−0.334101
$666$	2.21787	0.0859406
$667$	6.95044	0.269122
$668$	−7.18634	−0.278048
$669$	11.5592	0.446903
$670$	−20.5955	−0.795673
$671$	0	0
$672$	−2.25646	−0.0870447
$673$	29.7711	1.14759	0.573795	−	0.818999i	$-0.305470\pi$
$673$	29.7711	1.14759	0.573795	+	0.818999i	$0.305470\pi$
$674$	−18.9785	−0.731023
$675$	123.203	4.74209
$676$	−11.6758	−0.449068
$677$	2.86232	0.110008	0.0550039	−	0.998486i	$-0.482483\pi$
$677$	2.86232	0.110008	0.0550039	+	0.998486i	$0.482483\pi$
$678$	−17.3644	−0.666874
$679$	−9.03573	−0.346760
$680$	−15.1451	−0.580789
$681$	−20.9528	−0.802912
$682$	0	0
$683$	−23.5420	−0.900810	−0.450405	−	0.892824i	$-0.648720\pi$
$683$	−23.5420	−0.900810	−0.450405	+	0.892824i	$0.648720\pi$
$684$	−22.4410	−0.858053
$685$	83.5033	3.19050
$686$	9.59715	0.366421
$687$	7.97576	0.304294
$688$	5.79562	0.220956
$689$	−14.2345	−0.542291
$690$	12.1022	0.460723
$691$	−7.69225	−0.292627	−0.146314	−	0.989238i	$-0.546741\pi$
$691$	−7.69225	−0.292627	−0.146314	+	0.989238i	$0.546741\pi$
$692$	11.3625	0.431937
$693$	0	0
$694$	−13.7868	−0.523339
$695$	86.6607	3.28723
$696$	22.0518	0.835871
$697$	49.7171	1.88317
$698$	15.1332	0.572801
$699$	37.1053	1.40345
$700$	6.79210	0.256717
$701$	−18.1698	−0.686263	−0.343131	−	0.939287i	$-0.611488\pi$
$701$	−18.1698	−0.686263	−0.343131	+	0.939287i	$0.611488\pi$
$702$	−14.8456	−0.560310
$703$	0.996811	0.0375955
$704$	0	0
$705$	22.9838	0.865618
$706$	−13.4377	−0.505733
$707$	−4.78372	−0.179910
$708$	−1.11480	−0.0418967
$709$	10.4565	0.392701	0.196351	−	0.980534i	$-0.437091\pi$
$709$	10.4565	0.392701	0.196351	+	0.980534i	$0.437091\pi$
$710$	57.3147	2.15098
$711$	29.9353	1.12266
$712$	−5.08032	−0.190393
$713$	7.06435	0.264562
$714$	−8.95914	−0.335288
$715$	0	0
$716$	12.5491	0.468980
$717$	12.9893	0.485093
$718$	26.3963	0.985101
$719$	27.2235	1.01526	0.507632	−	0.861574i	$-0.330521\pi$
$719$	27.2235	1.01526	0.507632	+	0.861574i	$0.330521\pi$
$720$	26.9535	1.00450
$721$	1.71774	0.0639719
$722$	8.91399	0.331744
$723$	−24.3439	−0.905359
$724$	0.139453	0.00518272
$725$	−66.3775	−2.46520
$726$	0	0
$727$	8.11347	0.300912	0.150456	−	0.988617i	$-0.451926\pi$
$727$	8.11347	0.300912	0.150456	+	0.988617i	$0.451926\pi$
$728$	−0.818424	−0.0303328
$729$	16.6375	0.616202
$730$	−44.4386	−1.64474
$731$	23.0112	0.851101
$732$	−9.30681	−0.343990
$733$	26.2690	0.970266	0.485133	−	0.874440i	$-0.338771\pi$
$733$	26.2690	0.970266	0.485133	+	0.874440i	$0.338771\pi$
$734$	−4.24241	−0.156590
$735$	−78.5940	−2.89898
$736$	1.00000	0.0368605
$737$	0	0
$738$	−88.4806	−3.25702
$739$	−1.85031	−0.0680648	−0.0340324	−	0.999421i	$-0.510835\pi$
$739$	−1.85031	−0.0680648	−0.0340324	+	0.999421i	$0.510835\pi$
$740$	−1.19725	−0.0440119
$741$	−11.5951	−0.425956
$742$	8.79740	0.322963
$743$	50.3564	1.84740	0.923698	−	0.383122i	$-0.125151\pi$
$743$	50.3564	1.84740	0.923698	+	0.383122i	$0.125151\pi$
$744$	22.4132	0.821708
$745$	−27.2427	−0.998094
$746$	−27.8321	−1.01901
$747$	−9.42218	−0.344740
$748$	0	0
$749$	−10.3940	−0.379789
$750$	−55.0664	−2.01074
$751$	26.0232	0.949601	0.474800	−	0.880094i	$-0.342520\pi$
$751$	26.0232	0.949601	0.474800	+	0.880094i	$0.342520\pi$
$752$	1.89914	0.0692544
$753$	−40.2166	−1.46557
$754$	7.99826	0.291279
$755$	−12.0305	−0.437837
$756$	9.17507	0.333694
$757$	−14.3277	−0.520749	−0.260375	−	0.965508i	$-0.583846\pi$
$757$	−14.3277	−0.520749	−0.260375	+	0.965508i	$0.583846\pi$
$758$	33.8342	1.22891
$759$	0	0
$760$	12.1141	0.439426
$761$	34.9843	1.26818	0.634090	−	0.773260i	$-0.281375\pi$
$761$	34.9843	1.26818	0.634090	+	0.773260i	$0.281375\pi$
$762$	26.7957	0.970707
$763$	−9.07053	−0.328375
$764$	−12.9039	−0.466848
$765$	107.018	3.86923
$766$	4.67567	0.168939
$767$	−0.404341	−0.0145999
$768$	3.17272	0.114486
$769$	−41.7546	−1.50571	−0.752855	−	0.658187i	$-0.771324\pi$
$769$	−41.7546	−1.50571	−0.752855	+	0.658187i	$0.771324\pi$
$770$	0	0
$771$	34.9319	1.25804
$772$	−23.7470	−0.854674
$773$	4.13901	0.148870	0.0744349	−	0.997226i	$-0.476285\pi$
$773$	4.13901	0.148870	0.0744349	+	0.997226i	$0.476285\pi$
$774$	−40.9527	−1.47201
$775$	−67.4653	−2.42343
$776$	12.7048	0.456076
$777$	−0.708240	−0.0254080
$778$	7.97709	0.285993
$779$	−39.7673	−1.42481
$780$	13.9267	0.498655
$781$	0	0
$782$	3.97045	0.141983
$783$	−89.6657	−3.20439
$784$	−6.49419	−0.231935
$785$	65.3266	2.33161
$786$	26.5829	0.948181
$787$	−2.00799	−0.0715770	−0.0357885	−	0.999359i	$-0.511394\pi$
$787$	−2.00799	−0.0715770	−0.0357885	+	0.999359i	$0.511394\pi$
$788$	17.4582	0.621924
$789$	−59.5218	−2.11903
$790$	−16.1597	−0.574938
$791$	3.89245	0.138400
$792$	0	0
$793$	−3.37561	−0.119871
$794$	20.0989	0.713283
$795$	−149.701	−5.30933
$796$	4.39149	0.155652
$797$	12.8367	0.454698	0.227349	−	0.973813i	$-0.426994\pi$
$797$	12.8367	0.454698	0.227349	+	0.973813i	$0.426994\pi$
$798$	7.16616	0.253679
$799$	7.54043	0.266761
$800$	−9.55011	−0.337647
$801$	35.8982	1.26840
$802$	30.5883	1.08011
$803$	0	0
$804$	17.1305	0.604147
$805$	−2.71287	−0.0956160
$806$	8.12935	0.286344
$807$	−76.0186	−2.67598
$808$	6.72620	0.236627
$809$	12.3664	0.434779	0.217390	−	0.976085i	$-0.430246\pi$
$809$	12.3664	0.434779	0.217390	+	0.976085i	$0.430246\pi$
$810$	−75.2666	−2.64460
$811$	4.98949	0.175205	0.0876023	−	0.996156i	$-0.472080\pi$
$811$	4.98949	0.175205	0.0876023	+	0.996156i	$0.472080\pi$
$812$	−4.94320	−0.173472
$813$	21.3387	0.748382
$814$	0	0
$815$	34.4811	1.20782
$816$	12.5971	0.440987
$817$	−18.4060	−0.643945
$818$	−3.23108	−0.112972
$819$	5.78310	0.202078
$820$	47.7638	1.66799
$821$	0.314056	0.0109606	0.00548032	−	0.999985i	$-0.498256\pi$
$821$	0.314056	0.0109606	0.00548032	+	0.999985i	$0.498256\pi$
$822$	−69.4548	−2.42251
$823$	16.1600	0.563301	0.281650	−	0.959517i	$-0.409118\pi$
$823$	16.1600	0.563301	0.281650	+	0.959517i	$0.409118\pi$
$824$	−2.41524	−0.0841390
$825$	0	0
$826$	0.249897	0.00869501
$827$	6.16336	0.214321	0.107160	−	0.994242i	$-0.465824\pi$
$827$	6.16336	0.214321	0.107160	+	0.994242i	$0.465824\pi$
$828$	−7.06614	−0.245565
$829$	−16.2850	−0.565600	−0.282800	−	0.959179i	$-0.591263\pi$
$829$	−16.2850	−0.565600	−0.282800	+	0.959179i	$0.591263\pi$
$830$	5.08630	0.176548
$831$	−18.3655	−0.637093
$832$	1.15076	0.0398953
$833$	−25.7848	−0.893392
$834$	−72.0810	−2.49596
$835$	−27.4120	−0.948632
$836$	0	0
$837$	−91.1352	−3.15009
$838$	−22.9090	−0.791377
$839$	53.9399	1.86221	0.931107	−	0.364746i	$-0.118844\pi$
$839$	53.9399	1.86221	0.931107	+	0.364746i	$0.118844\pi$
$840$	−8.60716	−0.296975
$841$	19.3086	0.665815
$842$	−22.5484	−0.777070
$843$	35.0235	1.20627
$844$	−17.7499	−0.610978
$845$	−44.5367	−1.53211
$846$	−13.4196	−0.461374
$847$	0	0
$848$	−12.3697	−0.424777
$849$	−40.1907	−1.37934
$850$	−37.9182	−1.30058
$851$	0.313872	0.0107594
$852$	−47.6721	−1.63322
$853$	−56.0131	−1.91785	−0.958926	−	0.283656i	$-0.908453\pi$
$853$	−56.0131	−1.91785	−0.958926	+	0.283656i	$0.908453\pi$
$854$	2.08624	0.0713898
$855$	−85.6003	−2.92747
$856$	14.6146	0.499517
$857$	29.5820	1.01050	0.505250	−	0.862973i	$-0.331400\pi$
$857$	29.5820	1.01050	0.505250	+	0.862973i	$0.331400\pi$
$858$	0	0
$859$	27.0568	0.923168	0.461584	−	0.887097i	$-0.347281\pi$
$859$	27.0568	0.923168	0.461584	+	0.887097i	$0.347281\pi$
$860$	22.1072	0.753848
$861$	28.2548	0.962923
$862$	−28.7033	−0.977639
$863$	−3.63795	−0.123837	−0.0619187	−	0.998081i	$-0.519722\pi$
$863$	−3.63795	−0.123837	−0.0619187	+	0.998081i	$0.519722\pi$
$864$	−12.9007	−0.438891
$865$	43.3418	1.47366
$866$	20.7090	0.703720
$867$	−3.92001	−0.133130
$868$	−5.02421	−0.170533
$869$	0	0
$870$	84.1157	2.85179
$871$	6.21329	0.210529
$872$	12.7537	0.431896
$873$	−89.7739	−3.03839
$874$	−3.17585	−0.107425
$875$	12.3438	0.417298
$876$	36.9622	1.24884
$877$	−9.55880	−0.322778	−0.161389	−	0.986891i	$-0.551597\pi$
$877$	−9.55880	−0.322778	−0.161389	+	0.986891i	$0.551597\pi$
$878$	16.1709	0.545740
$879$	−44.8125	−1.51149
$880$	0	0
$881$	36.3450	1.22449	0.612247	−	0.790666i	$-0.290266\pi$
$881$	36.3450	1.22449	0.612247	+	0.790666i	$0.290266\pi$
$882$	45.8888	1.54516
$883$	−9.43559	−0.317533	−0.158766	−	0.987316i	$-0.550752\pi$
$883$	−9.43559	−0.317533	−0.158766	+	0.987316i	$0.550752\pi$
$884$	4.56902	0.153673
$885$	−4.25235	−0.142941
$886$	39.1046	1.31374
$887$	43.5409	1.46196	0.730981	−	0.682398i	$-0.239063\pi$
$887$	43.5409	1.46196	0.730981	+	0.682398i	$0.239063\pi$
$888$	0.995829	0.0334178
$889$	−6.00661	−0.201455
$890$	−19.3787	−0.649574
$891$	0	0
$892$	3.64330	0.121987
$893$	−6.03137	−0.201832
$894$	22.6594	0.757843
$895$	47.8679	1.60005
$896$	−0.711206	−0.0237597
$897$	−3.65102	−0.121904
$898$	3.19276	0.106544
$899$	49.1004	1.63759
$900$	67.4824	2.24941
$901$	−49.1132	−1.63620
$902$	0	0
$903$	13.0776	0.435194
$904$	−5.47302	−0.182030
$905$	0.531937	0.0176822
$906$	10.0065	0.332445
$907$	−23.2055	−0.770526	−0.385263	−	0.922807i	$-0.625889\pi$
$907$	−23.2055	−0.770526	−0.385263	+	0.922807i	$0.625889\pi$
$908$	−6.60404	−0.219163
$909$	−47.5283	−1.57641
$910$	−3.12185	−0.103488
$911$	25.6601	0.850158	0.425079	−	0.905156i	$-0.360246\pi$
$911$	25.6601	0.850158	0.425079	+	0.905156i	$0.360246\pi$
$912$	−10.0761	−0.333652
$913$	0	0
$914$	−37.5416	−1.24176
$915$	−35.5005	−1.17361
$916$	2.51386	0.0830602
$917$	−5.95891	−0.196781
$918$	−51.2216	−1.69057
$919$	23.4593	0.773851	0.386925	−	0.922111i	$-0.373537\pi$
$919$	23.4593	0.773851	0.386925	+	0.922111i	$0.373537\pi$
$920$	3.81446	0.125759
$921$	−55.8042	−1.83881
$922$	13.4911	0.444305
$923$	−17.2908	−0.569135
$924$	0	0
$925$	−2.99752	−0.0985577
$926$	−42.1844	−1.38626
$927$	17.0665	0.560536
$928$	6.95044	0.228159
$929$	51.9317	1.70382	0.851912	−	0.523685i	$-0.175443\pi$
$929$	51.9317	1.70382	0.851912	+	0.523685i	$0.175443\pi$
$930$	85.4943	2.80347
$931$	20.6245	0.675942
$932$	11.6951	0.383087
$933$	47.9964	1.57133
$934$	3.62080	0.118476
$935$	0	0
$936$	−8.13140	−0.265783
$937$	−6.99626	−0.228558	−0.114279	−	0.993449i	$-0.536456\pi$
$937$	−6.99626	−0.228558	−0.114279	+	0.993449i	$0.536456\pi$
$938$	−3.84003	−0.125381
$939$	96.7471	3.15722
$940$	7.24418	0.236279
$941$	40.1896	1.31014	0.655072	−	0.755566i	$-0.272638\pi$
$941$	40.1896	1.31014	0.655072	+	0.755566i	$0.272638\pi$
$942$	−54.3361	−1.77036
$943$	−12.5218	−0.407765
$944$	−0.351370	−0.0114361
$945$	34.9979	1.13848
$946$	0	0
$947$	−4.06805	−0.132194	−0.0660969	−	0.997813i	$-0.521055\pi$
$947$	−4.06805	−0.132194	−0.0660969	+	0.997813i	$0.521055\pi$
$948$	13.4410	0.436545
$949$	13.4063	0.435188
$950$	30.3297	0.984025
$951$	67.3814	2.18499
$952$	−2.82381	−0.0915201
$953$	−23.7349	−0.768848	−0.384424	−	0.923157i	$-0.625600\pi$
$953$	−23.7349	−0.768848	−0.384424	+	0.923157i	$0.625600\pi$
$954$	87.4060	2.82987
$955$	−49.2215	−1.59277
$956$	4.09405	0.132411
$957$	0	0
$958$	36.0090	1.16340
$959$	15.5692	0.502756
$960$	12.1022	0.390597
$961$	18.9051	0.609842
$962$	0.361191	0.0116453
$963$	−103.269	−3.32780
$964$	−7.67288	−0.247127
$965$	−90.5820	−2.91594
$966$	2.25646	0.0726003
$967$	46.0832	1.48194	0.740968	−	0.671540i	$-0.234367\pi$
$967$	46.0832	1.48194	0.740968	+	0.671540i	$0.234367\pi$
$968$	0	0
$969$	−40.0065	−1.28519
$970$	48.4620	1.55602
$971$	4.04568	0.129832	0.0649160	−	0.997891i	$-0.479322\pi$
$971$	4.04568	0.129832	0.0649160	+	0.997891i	$0.479322\pi$
$972$	23.9017	0.766646
$973$	16.1579	0.517998
$974$	6.68812	0.214301
$975$	34.8677	1.11666
$976$	−2.93339	−0.0938954
$977$	50.4946	1.61547	0.807733	−	0.589548i	$-0.200694\pi$
$977$	50.4946	1.61547	0.807733	+	0.589548i	$0.200694\pi$
$978$	−28.6800	−0.917086
$979$	0	0
$980$	−24.7718	−0.791307
$981$	−90.1196	−2.87730
$982$	−20.4104	−0.651321
$983$	−3.85903	−0.123084	−0.0615420	−	0.998104i	$-0.519602\pi$
$983$	−3.85903	−0.123084	−0.0615420	+	0.998104i	$0.519602\pi$
$984$	−39.7281	−1.26648
$985$	66.5938	2.12185
$986$	27.5964	0.878847
$987$	4.28532	0.136403
$988$	−3.65463	−0.116269
$989$	−5.79562	−0.184290
$990$	0	0
$991$	−27.6195	−0.877362	−0.438681	−	0.898643i	$-0.644554\pi$
$991$	−27.6195	−0.877362	−0.438681	+	0.898643i	$0.644554\pi$
$992$	7.06435	0.224293
$993$	−28.6505	−0.909197
$994$	10.6863	0.338950
$995$	16.7512	0.531048
$996$	−4.23059	−0.134051
$997$	11.1570	0.353346	0.176673	−	0.984270i	$-0.443467\pi$
$997$	11.1570	0.353346	0.176673	+	0.984270i	$0.443467\pi$
$998$	−9.65857	−0.305737
$999$	−4.04918	−0.128110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5566.2.a.bt.1.10		10
11.7	odd	10		506.2.e.h.93.1	✓	20
11.8	odd	10		506.2.e.h.185.1	yes	20
11.10	odd	2		5566.2.a.bu.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
506.2.e.h.93.1	✓	20	11.7	odd	10
506.2.e.h.185.1	yes	20	11.8	odd	10
5566.2.a.bt.1.10		10	1.1	even	1	trivial
5566.2.a.bu.1.10		10	11.10	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:	\( N \)	\(=\)	\( 5566 = 2 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5566.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.17272 q^{3} +1.00000 q^{4} +3.81446 q^{5} -3.17272 q^{6} +0.711206 q^{7} -1.00000 q^{8} +7.06614 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.17272 q^{3} +1.00000 q^{4} +3.81446 q^{5} -3.17272 q^{6} +0.711206 q^{7} -1.00000 q^{8} +7.06614 q^{9} -3.81446 q^{10} +3.17272 q^{12} +1.15076 q^{13} -0.711206 q^{14} +12.1022 q^{15} +1.00000 q^{16} +3.97045 q^{17} -7.06614 q^{18} -3.17585 q^{19} +3.81446 q^{20} +2.25646 q^{21} -1.00000 q^{23} -3.17272 q^{24} +9.55011 q^{25} -1.15076 q^{26} +12.9007 q^{27} +0.711206 q^{28} -6.95044 q^{29} -12.1022 q^{30} -7.06435 q^{31} -1.00000 q^{32} -3.97045 q^{34} +2.71287 q^{35} +7.06614 q^{36} -0.313872 q^{37} +3.17585 q^{38} +3.65102 q^{39} -3.81446 q^{40} +12.5218 q^{41} -2.25646 q^{42} +5.79562 q^{43} +26.9535 q^{45} +1.00000 q^{46} +1.89914 q^{47} +3.17272 q^{48} -6.49419 q^{49} -9.55011 q^{50} +12.5971 q^{51} +1.15076 q^{52} -12.3697 q^{53} -12.9007 q^{54} -0.711206 q^{56} -10.0761 q^{57} +6.95044 q^{58} -0.351370 q^{59} +12.1022 q^{60} -2.93339 q^{61} +7.06435 q^{62} +5.02548 q^{63} +1.00000 q^{64} +4.38951 q^{65} +5.39932 q^{67} +3.97045 q^{68} -3.17272 q^{69} -2.71287 q^{70} -15.0256 q^{71} -7.06614 q^{72} +11.6500 q^{73} +0.313872 q^{74} +30.2998 q^{75} -3.17585 q^{76} -3.65102 q^{78} +4.23644 q^{79} +3.81446 q^{80} +19.7319 q^{81} -12.5218 q^{82} -1.33343 q^{83} +2.25646 q^{84} +15.1451 q^{85} -5.79562 q^{86} -22.0518 q^{87} +5.08032 q^{89} -26.9535 q^{90} +0.818424 q^{91} -1.00000 q^{92} -22.4132 q^{93} -1.89914 q^{94} -12.1141 q^{95} -3.17272 q^{96} -12.7048 q^{97} +6.49419 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9	\( 10 q - 10 q^{2} + 6 q^{3} + 10 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} - 10 q^{8} + 16 q^{9} - 12 q^{10} + 6 q^{12} + 3 q^{13} + 4 q^{14} + 6 q^{15} + 10 q^{16} + 4 q^{17} - 16 q^{18} - 8 q^{19} + 12 q^{20} - 8 q^{21} - 10 q^{23} - 6 q^{24} + 34 q^{25} - 3 q^{26} + 12 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 10 q^{32} - 4 q^{34} - 8 q^{35} + 16 q^{36} + 18 q^{37} + 8 q^{38} - 29 q^{39} - 12 q^{40} - 3 q^{41} + 8 q^{42} - 4 q^{43} + 72 q^{45} + 10 q^{46} + 42 q^{47} + 6 q^{48} + 12 q^{49} - 34 q^{50} - 18 q^{51} + 3 q^{52} + 11 q^{53} - 12 q^{54} + 4 q^{56} - 16 q^{57} - 15 q^{58} + 54 q^{59} + 6 q^{60} - 6 q^{61} + 10 q^{64} + 31 q^{65} + 24 q^{67} + 4 q^{68} - 6 q^{69} + 8 q^{70} + 37 q^{71} - 16 q^{72} + 42 q^{73} - 18 q^{74} - 12 q^{75} - 8 q^{76} + 29 q^{78} - 37 q^{79} + 12 q^{80} + 10 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 20 q^{85} + 4 q^{86} - 15 q^{87} + 63 q^{89} - 72 q^{90} + 11 q^{91} - 10 q^{92} + 8 q^{93} - 42 q^{94} + 30 q^{95} - 6 q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 6 * q^3 + 10 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 - 10 * q^8 + 16 * q^9 - 12 * q^10 + 6 * q^12 + 3 * q^13 + 4 * q^14 + 6 * q^15 + 10 * q^16 + 4 * q^17 - 16 * q^18 - 8 * q^19 + 12 * q^20 - 8 * q^21 - 10 * q^23 - 6 * q^24 + 34 * q^25 - 3 * q^26 + 12 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 10 * q^32 - 4 * q^34 - 8 * q^35 + 16 * q^36 + 18 * q^37 + 8 * q^38 - 29 * q^39 - 12 * q^40 - 3 * q^41 + 8 * q^42 - 4 * q^43 + 72 * q^45 + 10 * q^46 + 42 * q^47 + 6 * q^48 + 12 * q^49 - 34 * q^50 - 18 * q^51 + 3 * q^52 + 11 * q^53 - 12 * q^54 + 4 * q^56 - 16 * q^57 - 15 * q^58 + 54 * q^59 + 6 * q^60 - 6 * q^61 + 10 * q^64 + 31 * q^65 + 24 * q^67 + 4 * q^68 - 6 * q^69 + 8 * q^70 + 37 * q^71 - 16 * q^72 + 42 * q^73 - 18 * q^74 - 12 * q^75 - 8 * q^76 + 29 * q^78 - 37 * q^79 + 12 * q^80 + 10 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 20 * q^85 + 4 * q^86 - 15 * q^87 + 63 * q^89 - 72 * q^90 + 11 * q^91 - 10 * q^92 + 8 * q^93 - 42 * q^94 + 30 * q^95 - 6 * q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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