LMFDB - Embedded newform 39.5.g.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,5,Mod(31,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("39.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	39.g (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$4.03142856027$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 $ x^20 + 5446x^16 - 1452x^15 + 106320x^13 + 8376897x^12 - 1643220x^11 + 1054152x^10 + 232107192x^9 + 3337033804x^8 + 3105930144x^7 + 2297014848x^6 + 21034904256x^5 + 158658808624x^4 + 235144077504x^3 + 177846480000x^2 + 27353289600*x + 2103506496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.3
Root			$4.05053 - 4.05053i$ of defining polynomial
Character	$\chi$	$=$	39.31
Dual form			39.5.g.a.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.05053 + 4.05053i) q^{2} +5.19615 q^{3} -16.8136i q^{4} +(33.5573 - 33.5573i) q^{5} +(-21.0472 + 21.0472i) q^{6} +(23.7132 + 23.7132i) q^{7} +(3.29565 + 3.29565i) q^{8} +27.0000 q^{9} +271.850i q^{10} +(32.2545 + 32.2545i) q^{11} -87.3662i q^{12} +(72.8001 + 152.516i) q^{13} -192.102 q^{14} +(174.369 - 174.369i) q^{15} +242.320 q^{16} -354.222i q^{17} +(-109.364 + 109.364i) q^{18} +(-168.478 + 168.478i) q^{19} +(-564.221 - 564.221i) q^{20} +(123.217 + 123.217i) q^{21} -261.296 q^{22} +182.161i q^{23} +(17.1247 + 17.1247i) q^{24} -1627.19i q^{25} +(-912.650 - 322.892i) q^{26} +140.296 q^{27} +(398.704 - 398.704i) q^{28} +913.769 q^{29} +1412.58i q^{30} +(-876.095 + 876.095i) q^{31} +(-1034.25 + 1034.25i) q^{32} +(167.599 + 167.599i) q^{33} +(1434.79 + 1434.79i) q^{34} +1591.50 q^{35} -453.968i q^{36} +(112.687 + 112.687i) q^{37} -1364.85i q^{38} +(378.280 + 792.497i) q^{39} +221.186 q^{40} +(-1133.48 + 1133.48i) q^{41} -998.190 q^{42} -411.247i q^{43} +(542.315 - 542.315i) q^{44} +(906.048 - 906.048i) q^{45} +(-737.848 - 737.848i) q^{46} +(-3000.97 - 3000.97i) q^{47} +1259.13 q^{48} -1276.37i q^{49} +(6590.99 + 6590.99i) q^{50} -1840.59i q^{51} +(2564.35 - 1224.03i) q^{52} -4228.78 q^{53} +(-568.274 + 568.274i) q^{54} +2164.75 q^{55} +156.301i q^{56} +(-875.438 + 875.438i) q^{57} +(-3701.25 + 3701.25i) q^{58} +(1690.19 + 1690.19i) q^{59} +(-2931.78 - 2931.78i) q^{60} -3760.65 q^{61} -7097.31i q^{62} +(640.255 + 640.255i) q^{63} -4501.45i q^{64} +(7561.01 + 2675.06i) q^{65} -1357.73 q^{66} +(-2631.54 + 2631.54i) q^{67} -5955.76 q^{68} +946.535i q^{69} +(-6446.43 + 6446.43i) q^{70} +(297.661 - 297.661i) q^{71} +(88.9825 + 88.9825i) q^{72} +(2616.29 + 2616.29i) q^{73} -912.887 q^{74} -8455.13i q^{75} +(2832.73 + 2832.73i) q^{76} +1529.71i q^{77} +(-4742.27 - 1677.80i) q^{78} +7885.52 q^{79} +(8131.61 - 8131.61i) q^{80} +729.000 q^{81} -9182.36i q^{82} +(-4078.45 + 4078.45i) q^{83} +(2071.73 - 2071.73i) q^{84} +(-11886.7 - 11886.7i) q^{85} +(1665.77 + 1665.77i) q^{86} +4748.08 q^{87} +212.599i q^{88} +(1722.86 + 1722.86i) q^{89} +7339.96i q^{90} +(-1890.32 + 5342.96i) q^{91} +3062.78 q^{92} +(-4552.33 + 4552.33i) q^{93} +24311.0 q^{94} +11307.4i q^{95} +(-5374.15 + 5374.15i) q^{96} +(1560.33 - 1560.33i) q^{97} +(5169.99 + 5169.99i) q^{98} +(870.871 + 870.871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 24 q^{5} - 24 q^{7} + 540 q^{9} + 372 q^{11} - 224 q^{13} + 480 q^{14} - 252 q^{15} - 2328 q^{16} - 840 q^{19} + 228 q^{20} + 936 q^{21} + 3536 q^{22} - 1404 q^{24} - 828 q^{26} - 1984 q^{28} - 5064 q^{29}+ \cdots + 10044 q^{99}+O(q^{100}) $ 20 * q + 24 * q^5 - 24 * q^7 + 540 * q^9 + 372 * q^11 - 224 * q^13 + 480 * q^14 - 252 * q^15 - 2328 * q^16 - 840 * q^19 + 228 * q^20 + 936 * q^21 + 3536 * q^22 - 1404 * q^24 - 828 * q^26 - 1984 * q^28 - 5064 * q^29 + 1712 * q^31 - 7260 * q^32 - 540 * q^33 + 8040 * q^34 + 5976 * q^35 - 868 * q^37 - 2952 * q^39 + 6336 * q^40 - 6000 * q^41 + 648 * q^42 + 20868 * q^44 + 648 * q^45 - 1992 * q^46 + 1692 * q^47 + 2592 * q^48 + 8952 * q^50 - 12416 * q^52 - 18816 * q^53 - 3280 * q^55 - 9360 * q^57 + 1256 * q^58 - 6588 * q^59 + 9036 * q^60 - 5512 * q^61 - 648 * q^63 + 33048 * q^65 + 13464 * q^66 - 4704 * q^67 - 28296 * q^68 - 31096 * q^70 + 9756 * q^71 + 13692 * q^73 - 28296 * q^74 - 17072 * q^76 - 23868 * q^78 - 5056 * q^79 + 42228 * q^80 + 14580 * q^81 + 24708 * q^83 + 26496 * q^84 - 4752 * q^85 - 77424 * q^86 + 5256 * q^87 + 36000 * q^89 + 19104 * q^91 + 12912 * q^92 - 18432 * q^93 + 112832 * q^94 - 52344 * q^96 + 50012 * q^97 + 11544 * q^98 + 10044 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−4.05053	+	4.05053i	−1.01263	+	1.01263i	−0.0127141	+	0.999919i	$0.504047\pi$
$2$	−4.05053	+	4.05053i	−1.01263	+	1.01263i	−0.999919	+	0.0127141i	$0.995953\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$		−	16.8136i		−	1.05085i
$5$	33.5573	−	33.5573i	1.34229	−	1.34229i	0.448521	−	0.893772i	$-0.351951\pi$
$5$	33.5573	−	33.5573i	1.34229	−	1.34229i	0.893772	−	0.448521i	$-0.148049\pi$
$6$	−21.0472	+	21.0472i	−0.584644	+	0.584644i
$7$	23.7132	+	23.7132i	0.483942	+	0.483942i	0.906388	−	0.422446i	$-0.138828\pi$
$7$	23.7132	+	23.7132i	0.483942	+	0.483942i	−0.422446	+	0.906388i	$0.638828\pi$
$8$	3.29565	+	3.29565i	0.0514945	+	0.0514945i
$9$	27.0000			0.333333
$10$			271.850i			2.71850i
$11$	32.2545	+	32.2545i	0.266566	+	0.266566i	0.827715	−	0.561149i	$-0.189641\pi$
$11$	32.2545	+	32.2545i	0.266566	+	0.266566i	−0.561149	+	0.827715i	$0.689641\pi$
$12$		−	87.3662i		−	0.606710i
$13$	72.8001	+	152.516i	0.430770	+	0.902462i
$13$	72.8001	+	152.516i	0.430770	+	0.902462i
$14$	−192.102			−0.980111
$15$	174.369	−	174.369i	0.774974	−	0.774974i
$16$	242.320			0.946562
$17$		−	354.222i		−	1.22568i	−0.790206	−	0.612841i	$-0.790027\pi$
$17$		−	354.222i		−	1.22568i	0.790206	−	0.612841i	$-0.209973\pi$
$18$	−109.364	+	109.364i	−0.337544	+	0.337544i
$19$	−168.478	+	168.478i	−0.466699	+	0.466699i	−0.900843	−	0.434145i	$-0.857051\pi$
$19$	−168.478	+	168.478i	−0.466699	+	0.466699i	0.434145	+	0.900843i	$0.357051\pi$
$20$	−564.221	−	564.221i	−1.41055	−	1.41055i
$21$	123.217	+	123.217i	0.279404	+	0.279404i
$22$	−261.296			−0.539867
$23$			182.161i			0.344349i	0.985066	+	0.172175i	$0.0550793\pi$
$23$			182.161i			0.344349i	−0.985066	+	0.172175i	$0.944921\pi$
$24$	17.1247	+	17.1247i	0.0297304	+	0.0297304i
$25$		−	1627.19i		−	2.60350i
$26$	−912.650	−	322.892i	−1.35007	−	0.477651i
$27$	140.296			0.192450
$28$	398.704	−	398.704i	0.508551	−	0.508551i
$29$	913.769			1.08653			0.543264	−	0.839562i	$-0.317188\pi$
$29$	913.769			1.08653			0.543264	+	0.839562i	$0.317188\pi$
$30$			1412.58i			1.56953i
$31$	−876.095	+	876.095i	−0.911650	+	0.911650i	−0.996402	−	0.0847522i	$-0.972990\pi$
$31$	−876.095	+	876.095i	−0.911650	+	0.911650i	0.0847522	+	0.996402i	$0.472990\pi$
$32$	−1034.25	+	1034.25i	−1.01001	+	1.01001i
$33$	167.599	+	167.599i	0.153902	+	0.153902i
$34$	1434.79	+	1434.79i	1.24117	+	1.24117i
$35$	1591.50			1.29918
$36$		−	453.968i		−	0.350284i
$37$	112.687	+	112.687i	0.0823135	+	0.0823135i	0.747065	−	0.664751i	$-0.231462\pi$
$37$	112.687	+	112.687i	0.0823135	+	0.0823135i	−0.664751	+	0.747065i	$0.731462\pi$
$38$		−	1364.85i		−	0.945189i
$39$	378.280	+	792.497i	0.248705	+	0.521037i
$40$	221.186			0.138242
$41$	−1133.48	+	1133.48i	−0.674287	+	0.674287i	−0.958701	−	0.284415i	$-0.908201\pi$
$41$	−1133.48	+	1133.48i	−0.674287	+	0.674287i	0.284415	+	0.958701i	$0.408201\pi$
$42$	−998.190			−0.565868
$43$		−	411.247i		−	0.222416i	−0.993797	−	0.111208i	$-0.964528\pi$
$43$		−	411.247i		−	0.222416i	0.993797	−	0.111208i	$-0.0354720\pi$
$44$	542.315	−	542.315i	0.280121	−	0.280121i
$45$	906.048	−	906.048i	0.447431	−	0.447431i
$46$	−737.848	−	737.848i	−0.348700	−	0.348700i
$47$	−3000.97	−	3000.97i	−1.35852	−	1.35852i	−0.875746	−	0.482772i	$-0.839630\pi$
$47$	−3000.97	−	3000.97i	−1.35852	−	1.35852i	−0.482772	−	0.875746i	$-0.660370\pi$
$48$	1259.13			0.546498
$49$		−	1276.37i		−	0.531600i
$50$	6590.99	+	6590.99i	2.63639	+	2.63639i
$51$		−	1840.59i		−	0.707648i
$52$	2564.35	−	1224.03i	0.948354	−	0.452675i
$53$	−4228.78			−1.50544			−0.752720	−	0.658341i	$-0.771259\pi$
$53$	−4228.78			−1.50544			−0.752720	+	0.658341i	$0.771259\pi$
$54$	−568.274	+	568.274i	−0.194881	+	0.194881i
$55$	2164.75			0.715619
$56$			156.301i			0.0498407i
$57$	−875.438	+	875.438i	−0.269449	+	0.269449i
$58$	−3701.25	+	3701.25i	−1.10025	+	1.10025i
$59$	1690.19	+	1690.19i	0.485547	+	0.485547i	0.906898	−	0.421350i	$-0.138444\pi$
$59$	1690.19	+	1690.19i	0.485547	+	0.485547i	−0.421350	+	0.906898i	$0.638444\pi$
$60$	−2931.78	−	2931.78i	−0.814383	−	0.814383i
$61$	−3760.65			−1.01066			−0.505328	−	0.862928i	$-0.668628\pi$
$61$	−3760.65			−1.01066			−0.505328	+	0.862928i	$0.668628\pi$
$62$		−	7097.31i		−	1.84633i
$63$	640.255	+	640.255i	0.161314	+	0.161314i
$64$		−	4501.45i		−	1.09899i
$65$	7561.01	+	2675.06i	1.78959	+	0.633149i
$66$	−1357.73			−0.311692
$67$	−2631.54	+	2631.54i	−0.586219	+	0.586219i	−0.936605	−	0.350386i	$-0.886050\pi$
$67$	−2631.54	+	2631.54i	−0.586219	+	0.586219i	0.350386	+	0.936605i	$0.386050\pi$
$68$	−5955.76			−1.28801
$69$			946.535i			0.198810i
$70$	−6446.43	+	6446.43i	−1.31560	+	1.31560i
$71$	297.661	−	297.661i	0.0590479	−	0.0590479i	−0.676966	−	0.736014i	$-0.736706\pi$
$71$	297.661	−	297.661i	0.0590479	−	0.0590479i	0.736014	+	0.676966i	$0.236706\pi$
$72$	88.9825	+	88.9825i	0.0171648	+	0.0171648i
$73$	2616.29	+	2616.29i	0.490953	+	0.490953i	0.908606	−	0.417653i	$-0.137147\pi$
$73$	2616.29	+	2616.29i	0.490953	+	0.490953i	−0.417653	+	0.908606i	$0.637147\pi$
$74$	−912.887			−0.166707
$75$		−	8455.13i		−	1.50313i
$76$	2832.73	+	2832.73i	0.490431	+	0.490431i
$77$			1529.71i			0.258005i
$78$	−4742.27	−	1677.80i	−0.779466	−	0.275772i
$79$	7885.52			1.26350			0.631752	−	0.775171i	$-0.282336\pi$
$79$	7885.52			1.26350			0.631752	+	0.775171i	$0.282336\pi$
$80$	8131.61	−	8131.61i	1.27056	−	1.27056i
$81$	729.000			0.111111
$82$		−	9182.36i		−	1.36561i
$83$	−4078.45	+	4078.45i	−0.592024	+	0.592024i	−0.938178	−	0.346154i	$-0.887488\pi$
$83$	−4078.45	+	4078.45i	−0.592024	+	0.592024i	0.346154	+	0.938178i	$0.387488\pi$
$84$	2071.73	−	2071.73i	0.293612	−	0.293612i
$85$	−11886.7	−	11886.7i	−1.64522	−	1.64522i
$86$	1665.77	+	1665.77i	0.225226	+	0.225226i
$87$	4748.08			0.627307
$88$			212.599i			0.0274534i
$89$	1722.86	+	1722.86i	0.217505	+	0.217505i	0.807446	−	0.589941i	$-0.200849\pi$
$89$	1722.86	+	1722.86i	0.217505	+	0.217505i	−0.589941	+	0.807446i	$0.700849\pi$
$90$			7339.96i			0.906167i
$91$	−1890.32	+	5342.96i	−0.228272	+	0.645207i
$92$	3062.78			0.361860
$93$	−4552.33	+	4552.33i	−0.526341	+	0.526341i
$94$	24311.0			2.75136
$95$			11307.4i			1.25289i
$96$	−5374.15	+	5374.15i	−0.583132	+	0.583132i
$97$	1560.33	−	1560.33i	0.165834	−	0.165834i	−0.619311	−	0.785146i	$-0.712588\pi$
$97$	1560.33	−	1560.33i	0.165834	−	0.165834i	0.785146	+	0.619311i	$0.212588\pi$
$98$	5169.99	+	5169.99i	0.538316	+	0.538316i
$99$	870.871	+	870.871i	0.0888553	+	0.0888553i
$100$	−27359.0			−2.73590
$101$			9982.36i			0.978567i	0.872125	+	0.489283i	$0.162742\pi$
$101$			9982.36i			0.978567i	−0.872125	+	0.489283i	$0.837258\pi$
$102$	7455.38	+	7455.38i	0.716587	+	0.716587i
$103$		−	6.56148i		−	0.000618483i	−1.00000		0.000309241i	$-0.999902\pi$
$103$		−	6.56148i		−	0.000618483i	1.00000		0.000309241i	$-9.84346e-5\pi$
$104$	−262.716	+	742.563i	−0.0242896	+	0.0686541i
$105$	8269.68			0.750084
$106$	17128.8	−	17128.8i	1.52446	−	1.52446i
$107$	−6183.10			−0.540056			−0.270028	−	0.962853i	$-0.587033\pi$
$107$	−6183.10			−0.540056			−0.270028	+	0.962853i	$0.587033\pi$
$108$		−	2358.89i		−	0.202237i
$109$	3694.46	−	3694.46i	0.310956	−	0.310956i	−0.534324	−	0.845280i	$-0.679434\pi$
$109$	3694.46	−	3694.46i	0.310956	−	0.310956i	0.845280	+	0.534324i	$0.179434\pi$
$110$	−8768.39	+	8768.39i	−0.724660	+	0.724660i
$111$	585.540	+	585.540i	0.0475238	+	0.0475238i
$112$	5746.17	+	5746.17i	0.458081	+	0.458081i
$113$	−21267.9			−1.66559			−0.832794	−	0.553583i	$-0.813260\pi$
$113$	−21267.9			−1.66559			−0.832794	+	0.553583i	$0.813260\pi$
$114$		−	7091.98i		−	0.545705i
$115$	6112.83	+	6112.83i	0.462218	+	0.462218i
$116$		−	15363.8i		−	1.14178i
$117$	1965.60	+	4117.93i	0.143590	+	0.300821i
$118$	−13692.3			−0.983363
$119$	8399.72	−	8399.72i	0.593159	−	0.593159i
$120$	1149.32			0.0798138
$121$		−	12560.3i		−	0.857885i
$122$	15232.6	−	15232.6i	1.02342	−	1.02342i
$123$	−5889.71	+	5889.71i	−0.389300	+	0.389300i
$124$	14730.3	+	14730.3i	0.958009	+	0.958009i
$125$	−33630.8	−	33630.8i	−2.15237	−	2.15237i
$126$	−5186.75			−0.326704
$127$			26466.7i			1.64094i	0.571693	+	0.820468i	$0.306287\pi$
$127$			26466.7i			1.64094i	−0.571693	+	0.820468i	$0.693713\pi$
$128$	1685.19	+	1685.19i	0.102856	+	0.102856i
$129$		−	2136.90i		−	0.128412i
$130$	−41461.5	+	19790.7i	−2.45334	+	1.17105i
$131$	21491.7			1.25236			0.626178	−	0.779680i	$-0.284618\pi$
$131$	21491.7			1.25236			0.626178	+	0.779680i	$0.284618\pi$
$132$	2817.95	−	2817.95i	0.161728	−	0.161728i
$133$	−7990.30			−0.451710
$134$		−	21318.3i		−	1.18725i
$135$	4707.96	−	4707.96i	0.258325	−	0.258325i
$136$	1167.39	−	1167.39i	0.0631159	−	0.0631159i
$137$	−5030.14	−	5030.14i	−0.268002	−	0.268002i	0.560292	−	0.828295i	$-0.310689\pi$
$137$	−5030.14	−	5030.14i	−0.268002	−	0.268002i	−0.828295	+	0.560292i	$0.810689\pi$
$138$	−3833.97	−	3833.97i	−0.201322	−	0.201322i
$139$	12182.9			0.630554			0.315277	−	0.949000i	$-0.397903\pi$
$139$	12182.9			0.630554			0.315277	+	0.949000i	$0.397903\pi$
$140$		−	26758.9i		−	1.36525i
$141$	−15593.5	−	15593.5i	−0.784341	−	0.784341i
$142$			2411.37i			0.119588i
$143$	−2571.20	+	7267.45i	−0.125737	+	0.355394i
$144$	6542.64			0.315521
$145$	30663.7	−	30663.7i	1.45844	−	1.45844i
$146$	−21194.7			−0.994311
$147$		−	6632.23i		−	0.306920i
$148$	1894.68	−	1894.68i	0.0864994	−	0.0864994i
$149$	−10032.3	+	10032.3i	−0.451887	+	0.451887i	−0.895980	−	0.444094i	$-0.853526\pi$
$149$	−10032.3	+	10032.3i	−0.451887	+	0.451887i	0.444094	+	0.895980i	$0.353526\pi$
$150$	34247.8	+	34247.8i	1.52212	+	1.52212i
$151$	10057.5	+	10057.5i	0.441098	+	0.441098i	0.892381	−	0.451283i	$-0.149033\pi$
$151$	10057.5	+	10057.5i	0.441098	+	0.441098i	−0.451283	+	0.892381i	$0.649033\pi$
$152$	−1110.49			−0.0480649
$153$		−	9563.99i		−	0.408561i
$154$	−6196.14	−	6196.14i	−0.261264	−	0.261264i
$155$			58798.9i			2.44740i
$156$	13324.7	−	6360.27i	0.547532	−	0.261352i
$157$	8554.44			0.347050			0.173525	−	0.984829i	$-0.444484\pi$
$157$	8554.44			0.347050			0.173525	+	0.984829i	$0.444484\pi$
$158$	−31940.6	+	31940.6i	−1.27947	+	1.27947i
$159$	−21973.4			−0.869166
$160$			69413.7i			2.71147i
$161$	−4319.61	+	4319.61i	−0.166645	+	0.166645i
$162$	−2952.84	+	2952.84i	−0.112515	+	0.112515i
$163$	−1164.17	−	1164.17i	−0.0438170	−	0.0438170i	0.684859	−	0.728676i	$-0.259864\pi$
$163$	−1164.17	−	1164.17i	−0.0438170	−	0.0438170i	−0.728676	+	0.684859i	$0.759864\pi$
$164$	19057.8	+	19057.8i	0.708576	+	0.708576i
$165$	11248.4			0.413163
$166$		−	33039.8i		−	1.19901i
$167$	7534.77	+	7534.77i	0.270170	+	0.270170i	0.829169	−	0.558999i	$-0.188814\pi$
$167$	7534.77	+	7534.77i	0.270170	+	0.270170i	−0.558999	+	0.829169i	$0.688814\pi$
$168$			812.161i			0.0287756i
$169$	−17961.3	+	22206.4i	−0.628875	+	0.777506i
$170$	96295.3			3.33202
$171$	−4548.91	+	4548.91i	−0.155566	+	0.155566i
$172$	−6914.56			−0.233726
$173$		−	39158.0i		−	1.30836i	−0.756337	−	0.654182i	$-0.773013\pi$
$173$		−	39158.0i		−	1.30836i	0.756337	−	0.654182i	$-0.226987\pi$
$174$	−19232.3	+	19232.3i	−0.635232	+	0.635232i
$175$	38585.8	−	38585.8i	1.25994	−	1.25994i
$176$	7815.90	+	7815.90i	0.252321	+	0.252321i
$177$	8782.49	+	8782.49i	0.280331	+	0.280331i
$178$	−13957.0			−0.440505
$179$		−	37765.1i		−	1.17865i	−0.807897	−	0.589324i	$-0.799394\pi$
$179$		−	37765.1i		−	1.17865i	0.807897	−	0.589324i	$-0.200606\pi$
$180$	−15234.0	−	15234.0i	−0.470184	−	0.470184i
$181$		−	9590.57i		−	0.292744i	−0.989230	−	0.146372i	$-0.953240\pi$
$181$		−	9590.57i		−	0.292744i	0.989230	−	0.146372i	$-0.0467596\pi$
$182$	−13985.0	−	29298.6i	−0.422202	−	0.884513i
$183$	−19540.9			−0.583502
$184$	−600.338	+	600.338i	−0.0177321	+	0.0177321i
$185$	7562.97			0.220978
$186$		−	36878.7i		−	1.06598i
$187$	11425.2	−	11425.2i	0.326725	−	0.326725i
$188$	−50457.2	+	50457.2i	−1.42760	+	1.42760i
$189$	3326.86	+	3326.86i	0.0931347	+	0.0931347i
$190$	−45800.8	−	45800.8i	−1.26872	−	1.26872i
$191$	46392.7			1.27170			0.635848	−	0.771814i	$-0.280651\pi$
$191$	46392.7			1.27170			0.635848	+	0.771814i	$0.280651\pi$
$192$		−	23390.2i		−	0.634500i
$193$	9357.45	+	9357.45i	0.251213	+	0.251213i	0.821468	−	0.570255i	$-0.193155\pi$
$193$	9357.45	+	9357.45i	0.251213	+	0.251213i	−0.570255	+	0.821468i	$0.693155\pi$
$194$			12640.4i			0.335858i
$195$	39288.2	+	13900.0i	1.03322	+	0.365549i
$196$	−21460.5			−0.558633
$197$	−4463.00	+	4463.00i	−0.114999	+	0.114999i	−0.762265	−	0.647266i	$-0.775912\pi$
$197$	−4463.00	+	4463.00i	−0.114999	+	0.114999i	0.647266	+	0.762265i	$0.275912\pi$
$198$	−7054.98			−0.179956
$199$		−	71326.4i		−	1.80113i	−0.434726	−	0.900563i	$-0.643155\pi$
$199$		−	71326.4i		−	1.80113i	0.434726	−	0.900563i	$-0.356845\pi$
$200$	5362.65	−	5362.65i	0.134066	−	0.134066i
$201$	−13673.9	+	13673.9i	−0.338454	+	0.338454i
$202$	−40433.9	−	40433.9i	−0.990929	−	0.990929i
$203$	21668.4	+	21668.4i	0.525816	+	0.525816i
$204$	−30947.0			−0.743633
$205$			76072.9i			1.81018i
$206$	26.5775	+	26.5775i	0.000626296	+	0.000626296i
$207$			4918.34i			0.114783i
$208$	17640.9	+	36957.7i	0.407750	+	0.854236i
$209$	−10868.4			−0.248812
$210$	−33496.6	+	33496.6i	−0.759560	+	0.759560i
$211$	−45146.1			−1.01404			−0.507020	−	0.861934i	$-0.669253\pi$
$211$	−45146.1			−1.01404			−0.507020	+	0.861934i	$0.669253\pi$
$212$			71101.2i			1.58199i
$213$	1546.69	−	1546.69i	0.0340913	−	0.0340913i
$214$	25044.8	−	25044.8i	0.546878	−	0.546878i
$215$	−13800.4	−	13800.4i	−0.298548	−	0.298548i
$216$	462.367	+	462.367i	0.00991013	+	0.00991013i
$217$	−41550.0			−0.882371
$218$			29929.1i			0.629768i
$219$	13594.6	+	13594.6i	0.283452	+	0.283452i
$220$		−	36397.3i		−	0.752010i
$221$	54024.5	−	25787.4i	1.10613	−	0.527986i
$222$	−4743.50			−0.0962483
$223$	22521.9	−	22521.9i	0.452892	−	0.452892i	−0.443421	−	0.896313i	$-0.646235\pi$
$223$	22521.9	−	22521.9i	0.452892	−	0.452892i	0.896313	+	0.443421i	$0.146235\pi$
$224$	−49050.9			−0.977577
$225$		−	43934.1i		−	0.867835i
$226$	86146.3	−	86146.3i	1.68663	−	1.68663i
$227$	33678.9	−	33678.9i	0.653592	−	0.653592i	−0.300264	−	0.953856i	$-0.597075\pi$
$227$	33678.9	−	33678.9i	0.653592	−	0.653592i	0.953856	+	0.300264i	$0.0970749\pi$
$228$	14719.3	+	14719.3i	0.283151	+	0.283151i
$229$	55067.0	+	55067.0i	1.05008	+	1.05008i	0.998678	+	0.0513970i	$0.0163674\pi$
$229$	55067.0	+	55067.0i	1.05008	+	1.05008i	0.0513970	+	0.998678i	$0.483633\pi$
$230$	−49520.4			−0.936114
$231$			7948.61i			0.148959i
$232$	3011.46	+	3011.46i	0.0559502	+	0.0559502i
$233$			6668.81i			0.122839i	0.998112	+	0.0614195i	$0.0195627\pi$
$233$			6668.81i			0.122839i	−0.998112	+	0.0614195i	$0.980437\pi$
$234$	−24641.6	−	8718.09i	−0.450025	−	0.159217i
$235$	−201409.			−3.64706
$236$	28418.2	−	28418.2i	0.510239	−	0.510239i
$237$	40974.4			0.729484
$238$			68046.7i			1.20130i
$239$	−24924.8	+	24924.8i	−0.436350	+	0.436350i	−0.890782	−	0.454431i	$-0.849842\pi$
$239$	−24924.8	+	24924.8i	−0.436350	+	0.436350i	0.454431	+	0.890782i	$0.349842\pi$
$240$	42253.1	−	42253.1i	0.733560	−	0.733560i
$241$	4314.21	+	4314.21i	0.0742792	+	0.0742792i	0.743270	−	0.668991i	$-0.233274\pi$
$241$	4314.21	+	4314.21i	0.0742792	+	0.0742792i	−0.668991	+	0.743270i	$0.733274\pi$
$242$	50875.9	+	50875.9i	0.868723	+	0.868723i
$243$	3788.00			0.0641500
$244$			63230.2i			1.06205i
$245$	−42831.7	−	42831.7i	−0.713564	−	0.713564i
$246$		−	47713.0i		−	0.788435i
$247$	−37960.9	−	13430.4i	−0.622217	−	0.220138i
$248$	−5774.61			−0.0938900
$249$	−21192.3	+	21192.3i	−0.341805	+	0.341805i
$250$	272445.			4.35913
$251$			100235.i			1.59100i	0.605954	+	0.795500i	$0.292791\pi$
$251$			100235.i			1.59100i	−0.605954	+	0.795500i	$0.707209\pi$
$252$	10765.0	−	10765.0i	0.169517	−	0.169517i
$253$	−5875.50	+	5875.50i	−0.0917918	+	0.0917918i
$254$	−107204.	−	107204.i	−1.66167	−	1.66167i
$255$	−61765.3	−	61765.3i	−0.949871	−	0.949871i
$256$	58371.4			0.890676
$257$		−	14954.5i		−	0.226415i	−0.993571	−	0.113208i	$-0.963887\pi$
$257$		−	14954.5i		−	0.226415i	0.993571	−	0.113208i	$-0.0361125\pi$
$258$	8655.60	+	8655.60i	0.130034	+	0.130034i
$259$			5344.34i			0.0796700i
$260$	44977.4	−	127128.i	0.665346	−	1.88059i
$261$	24671.8			0.362176
$262$	−87052.7	+	87052.7i	−1.26818	+	1.26818i
$263$	−7574.07			−0.109501			−0.0547505	−	0.998500i	$-0.517436\pi$
$263$	−7574.07			−0.109501			−0.0547505	+	0.998500i	$0.517436\pi$
$264$			1104.70i			0.0158502i
$265$	−141907.	+	141907.i	−2.02074	+	2.02074i
$266$	32365.0	−	32365.0i	0.457417	−	0.457417i
$267$	8952.22	+	8952.22i	0.125576	+	0.125576i
$268$	44245.7	+	44245.7i	0.616030	+	0.616030i
$269$	100457.			1.38827			0.694136	−	0.719844i	$-0.255787\pi$
$269$	100457.			1.38827			0.694136	+	0.719844i	$0.255787\pi$
$270$			38139.5i			0.523176i
$271$	66620.4	+	66620.4i	0.907128	+	0.907128i	0.996040	−	0.0889115i	$-0.0283388\pi$
$271$	66620.4	+	66620.4i	0.907128	+	0.907128i	−0.0889115	+	0.996040i	$0.528339\pi$
$272$		−	85835.0i		−	1.16018i
$273$	−9822.38	+	27762.8i	−0.131793	+	0.372510i
$274$	40749.5			0.542776
$275$	52484.2	−	52484.2i	0.694005	−	0.694005i
$276$	15914.7			0.208920
$277$		−	70180.3i		−	0.914652i	−0.889299	−	0.457326i	$-0.848807\pi$
$277$		−	70180.3i		−	0.914652i	0.889299	−	0.457326i	$-0.151193\pi$
$278$	−49347.3	+	49347.3i	−0.638519	+	0.638519i
$279$	−23654.6	+	23654.6i	−0.303883	+	0.303883i
$280$	5245.03	+	5245.03i	0.0669009	+	0.0669009i
$281$	−20515.7	−	20515.7i	−0.259820	−	0.259820i	0.565161	−	0.824981i	$-0.308814\pi$
$281$	−20515.7	−	20515.7i	−0.259820	−	0.259820i	−0.824981	+	0.565161i	$0.808814\pi$
$282$	126324.			1.58850
$283$			30170.2i			0.376708i	0.982101	+	0.188354i	$0.0603153\pi$
$283$			30170.2i			0.376708i	−0.982101	+	0.188354i	$0.939685\pi$
$284$	−5004.76	−	5004.76i	−0.0620507	−	0.0620507i
$285$			58754.8i			0.723358i
$286$	−19022.3	−	39851.8i	−0.232558	−	0.487209i
$287$	−53756.6			−0.652631
$288$	−27924.9	+	27924.9i	−0.336672	+	0.336672i
$289$	−41952.2			−0.502295
$290$			248408.i			2.95373i
$291$	8107.73	−	8107.73i	0.0957444	−	0.0957444i
$292$	43989.3	−	43989.3i	0.515919	−	0.515919i
$293$	−67660.9	−	67660.9i	−0.788139	−	0.788139i	0.193050	−	0.981189i	$-0.438162\pi$
$293$	−67660.9	−	67660.9i	−0.788139	−	0.788139i	−0.981189	+	0.193050i	$0.938162\pi$
$294$	26864.0	+	26864.0i	0.310797	+	0.310797i
$295$	113437.			1.30349
$296$			742.755i			0.00847739i
$297$	4525.18	+	4525.18i	0.0513006	+	0.0513006i
$298$		−	81272.6i		−	0.915191i
$299$	−27782.4	+	13261.3i	−0.310762	+	0.148335i
$300$	−142161.			−1.57957
$301$	9751.97	−	9751.97i	0.107636	−	0.107636i
$302$	−81476.3			−0.893341
$303$			51869.9i			0.564976i
$304$	−40825.6	+	40825.6i	−0.441759	+	0.441759i
$305$	−126197.	+	126197.i	−1.35660	+	1.35660i
$306$	38739.3	+	38739.3i	0.413722	+	0.413722i
$307$	−96671.1	−	96671.1i	−1.02570	−	1.02570i	−0.999661	−	0.0260377i	$-0.991711\pi$
$307$	−96671.1	−	96671.1i	−1.02570	−	1.02570i	−0.0260377	−	0.999661i	$-0.508289\pi$
$308$	25720.0			0.271125
$309$		−	34.0945i		−	0.000357081i
$310$	−238167.	−	238167.i	−2.47832	−	2.47832i
$311$		−	70642.4i		−	0.730373i	−0.930934	−	0.365186i	$-0.881005\pi$
$311$		−	70642.4i		−	0.730373i	0.930934	−	0.365186i	$-0.118995\pi$
$312$	−1365.11	+	3858.47i	−0.0140236	+	0.0396375i
$313$	68524.0			0.699446			0.349723	−	0.936853i	$-0.386276\pi$
$313$	68524.0			0.699446			0.349723	+	0.936853i	$0.386276\pi$
$314$	−34650.0	+	34650.0i	−0.351435	+	0.351435i
$315$	42970.5			0.433061
$316$		−	132584.i		−	1.32775i
$317$	140417.	−	140417.i	1.39734	−	1.39734i	0.589760	−	0.807578i	$-0.299222\pi$
$317$	140417.	−	140417.i	1.39734	−	1.39734i	0.807578	−	0.589760i	$-0.200778\pi$
$318$	89003.9	−	89003.9i	0.880147	−	0.880147i
$319$	29473.2	+	29473.2i	0.289631	+	0.289631i
$320$	−151057.	−	151057.i	−1.47516	−	1.47516i
$321$	−32128.3			−0.311801
$322$		−	34993.4i		−	0.337501i
$323$	59678.7	+	59678.7i	0.572024	+	0.572024i
$324$		−	12257.1i		−	0.116761i
$325$	248173.	−	118460.i	2.34956	−	1.12151i
$326$	9431.05			0.0887411
$327$	19197.0	−	19197.0i	0.179530	−	0.179530i
$328$	−7471.08			−0.0694441
$329$		−	142325.i		−	1.31489i
$330$	−45561.9	+	45561.9i	−0.418383	+	0.418383i
$331$	−73424.6	+	73424.6i	−0.670171	+	0.670171i	−0.957755	−	0.287585i	$-0.907148\pi$
$331$	−73424.6	+	73424.6i	−0.670171	+	0.670171i	0.287585	+	0.957755i	$0.407148\pi$
$332$	68573.6	+	68573.6i	0.622130	+	0.622130i
$333$	3042.56	+	3042.56i	0.0274378	+	0.0274378i
$334$	−61039.7			−0.547166
$335$			176615.i			1.57376i
$336$	29858.0	+	29858.0i	0.264473	+	0.264473i
$337$			14312.2i			0.126022i	0.998013	+	0.0630111i	$0.0200703\pi$
$337$			14312.2i			0.126022i	−0.998013	+	0.0630111i	$0.979930\pi$
$338$	−17194.8	−	162700.i	−0.150509	−	1.42415i
$339$	−110511.			−0.961628
$340$	−199859.	+	199859.i	−1.72889	+	1.72889i
$341$	−56516.0			−0.486030
$342$		−	36851.0i		−	0.315063i
$343$	87202.1	−	87202.1i	0.741206	−	0.741206i
$344$	1355.33	−	1355.33i	0.0114532	−	0.0114532i
$345$	31763.2	+	31763.2i	0.266862	+	0.266862i
$346$	158611.	+	158611.i	1.32489	+	1.32489i
$347$	216160.			1.79521			0.897607	−	0.440797i	$-0.145304\pi$
$347$	216160.			1.79521			0.897607	+	0.440797i	$0.145304\pi$
$348$		−	79832.6i		−	0.659207i
$349$	−20673.5	−	20673.5i	−0.169732	−	0.169732i	0.617130	−	0.786862i	$-0.288295\pi$
$349$	−20673.5	−	20673.5i	−0.169732	−	0.169732i	−0.786862	+	0.617130i	$0.788295\pi$
$350$			312586.i			2.55172i
$351$	10213.6	+	21397.4i	0.0829017	+	0.173679i
$352$	−66718.7			−0.538471
$353$	−70477.9	+	70477.9i	−0.565592	+	0.565592i	−0.930890	−	0.365298i	$-0.880967\pi$
$353$	−70477.9	+	70477.9i	−0.565592	+	0.565592i	0.365298	+	0.930890i	$0.380967\pi$
$354$	−71147.5			−0.567745
$355$		−	19977.4i		−	0.158519i
$356$	28967.5	−	28967.5i	0.228565	−	0.228565i
$357$	43646.2	−	43646.2i	0.342460	−	0.342460i
$358$	152969.	+	152969.i	1.19354	+	1.19354i
$359$	−90432.4	−	90432.4i	−0.701674	−	0.701674i	0.263096	−	0.964770i	$-0.415256\pi$
$359$	−90432.4	−	90432.4i	−0.701674	−	0.701674i	−0.964770	+	0.263096i	$0.915256\pi$
$360$	5972.03			0.0460805
$361$			73551.2i			0.564385i
$362$	38846.9	+	38846.9i	0.296442	+	0.296442i
$363$		−	65265.2i		−	0.495300i
$364$	89834.5	+	31783.1i	0.678017	+	0.239880i
$365$	175591.			1.31801
$366$	79151.1	−	79151.1i	0.590874	−	0.590874i
$367$	−156339.			−1.16074			−0.580369	−	0.814354i	$-0.697091\pi$
$367$	−156339.			−1.16074			−0.580369	+	0.814354i	$0.697091\pi$
$368$			44141.2i			0.325948i
$369$	−30603.8	+	30603.8i	−0.224762	+	0.224762i
$370$	−30634.1	+	30634.1i	−0.223770	+	0.223770i
$371$	−100278.	−	100278.i	−0.728546	−	0.728546i
$372$	76541.1	+	76541.1i	0.553107	+	0.553107i
$373$	12154.0			0.0873580			0.0436790	−	0.999046i	$-0.486092\pi$
$373$	12154.0			0.0873580			0.0436790	+	0.999046i	$0.486092\pi$
$374$			92556.7i			0.661705i
$375$	−174751.	−	174751.i	−1.24267	−	1.24267i
$376$		−	19780.3i		−	0.139913i
$377$	66522.5	+	139364.i	0.468043	+	0.980549i
$378$	−26951.1			−0.188623
$379$	56764.9	−	56764.9i	0.395186	−	0.395186i	−0.481345	−	0.876531i	$-0.659852\pi$
$379$	56764.9	−	56764.9i	0.395186	−	0.395186i	0.876531	+	0.481345i	$0.159852\pi$
$380$	190118.			1.31661
$381$			137525.i			0.947395i
$382$	−187915.	+	187915.i	−1.28776	+	1.28776i
$383$	14158.7	−	14158.7i	0.0965218	−	0.0965218i	−0.657197	−	0.753719i	$-0.728258\pi$
$383$	14158.7	−	14158.7i	0.0965218	−	0.0965218i	0.753719	+	0.657197i	$0.228258\pi$
$384$	8756.51	+	8756.51i	0.0593839	+	0.0593839i
$385$	51333.0	+	51333.0i	0.346318	+	0.346318i
$386$	−75805.3			−0.508774
$387$		−	11103.7i		−	0.0741387i
$388$	−26234.9	−	26234.9i	−0.174267	−	0.174267i
$389$			14487.6i			0.0957405i	0.998854	+	0.0478703i	$0.0152434\pi$
$389$			14487.6i			0.0957405i	−0.998854	+	0.0478703i	$0.984757\pi$
$390$	−215440.	+	102836.i	−1.41644	+	0.676105i
$391$	64525.4			0.422063
$392$	4206.48	−	4206.48i	0.0273745	−	0.0273745i
$393$	111674.			0.723048
$394$		−	36155.0i		−	0.232904i
$395$	264617.	−	264617.i	1.69599	−	1.69599i
$396$	14642.5	−	14642.5i	0.0933738	−	0.0933738i
$397$	120415.	+	120415.i	0.764013	+	0.764013i	0.977045	−	0.213032i	$-0.0683339\pi$
$397$	120415.	+	120415.i	0.764013	+	0.764013i	−0.213032	+	0.977045i	$0.568334\pi$
$398$	288910.	+	288910.i	1.82388	+	1.82388i
$399$	−41518.8			−0.260795
$400$		−	394300.i		−	2.46438i
$401$	31598.4	+	31598.4i	0.196506	+	0.196506i	0.798500	−	0.601994i	$-0.205627\pi$
$401$	31598.4	+	31598.4i	0.196506	+	0.196506i	−0.601994	+	0.798500i	$0.705627\pi$
$402$		−	110773.i		−	0.685459i
$403$	−197398.	−	69838.8i	−1.21544	−	0.430018i
$404$	167840.			1.02833
$405$	24463.3	−	24463.3i	0.149144	−	0.149144i
$406$	−175537.			−1.06492
$407$			7269.34i			0.0438840i
$408$	6065.94	−	6065.94i	0.0364400	−	0.0364400i
$409$	16690.9	−	16690.9i	0.0997776	−	0.0997776i	−0.655456	−	0.755233i	$-0.727523\pi$
$409$	16690.9	−	16690.9i	0.0997776	−	0.0997776i	0.755233	+	0.655456i	$0.227523\pi$
$410$	−308136.	−	308136.i	−1.83305	−	1.83305i
$411$	−26137.4	−	26137.4i	−0.154731	−	0.154731i
$412$	−110.322			−0.000649934
$413$			80159.5i			0.469954i
$414$	−19921.9	−	19921.9i	−0.116233	−	0.116233i
$415$			273724.i			1.58934i
$416$	−233034.	−	82446.6i	−1.34658	−	0.476416i
$417$	63304.3			0.364050
$418$	44022.6	−	44022.6i	0.251955	−	0.251955i
$419$	−45247.7			−0.257732			−0.128866	−	0.991662i	$-0.541134\pi$
$419$	−45247.7			−0.257732			−0.128866	+	0.991662i	$0.541134\pi$
$420$		−	139043.i		−	0.788228i
$421$	95387.7	−	95387.7i	0.538181	−	0.538181i	−0.384814	−	0.922994i	$-0.625734\pi$
$421$	95387.7	−	95387.7i	0.538181	−	0.538181i	0.922994	+	0.384814i	$0.125734\pi$
$422$	182866.	−	182866.i	1.02685	−	1.02685i
$423$	−81026.1	−	81026.1i	−0.452839	−	0.452839i
$424$	−13936.6	−	13936.6i	−0.0775219	−	0.0775219i
$425$	−576386.			−3.19107
$426$			12529.8i			0.0690441i
$427$	−89176.8	−	89176.8i	−0.489098	−	0.489098i
$428$			103960.i			0.567519i
$429$	−13360.3	+	37762.8i	−0.0725943	+	0.205187i
$430$	111798.			0.604639
$431$	−120110.	+	120110.i	−0.646582	+	0.646582i	−0.952165	−	0.305583i	$-0.901149\pi$
$431$	−120110.	+	120110.i	−0.646582	+	0.646582i	0.305583	+	0.952165i	$0.401149\pi$
$432$	33996.5			0.182166
$433$		−	104909.i		−	0.559549i	−0.960066	−	0.279774i	$-0.909740\pi$
$433$		−	104909.i		−	0.559549i	0.960066	−	0.279774i	$-0.0902596\pi$
$434$	168300.	−	168300.i	0.893518	−	0.893518i
$435$	159333.	−	159333.i	0.842030	−	0.842030i
$436$	−62117.4	−	62117.4i	−0.326768	−	0.326768i
$437$	−30690.1	−	30690.1i	−0.160707	−	0.160707i
$438$	−110131.			−0.574066
$439$		−	189251.i		−	0.981997i	−0.871160	−	0.490998i	$-0.836632\pi$
$439$		−	189251.i		−	0.981997i	0.871160	−	0.490998i	$-0.163368\pi$
$440$	7134.25	+	7134.25i	0.0368505	+	0.0368505i
$441$		−	34462.1i		−	0.177200i
$442$	−114376.	+	323281.i	−0.585448	+	1.65476i
$443$	−154643.			−0.787995			−0.393998	−	0.919111i	$-0.628908\pi$
$443$	−154643.			−0.787995			−0.393998	+	0.919111i	$0.628908\pi$
$444$	9845.06	−	9845.06i	0.0499404	−	0.0499404i
$445$	115629.			0.583910
$446$			182451.i			0.917227i
$447$	−52129.6	+	52129.6i	−0.260897	+	0.260897i
$448$	106744.	−	106744.i	0.531846	−	0.531846i
$449$	54131.2	+	54131.2i	0.268507	+	0.268507i	0.828498	−	0.559992i	$-0.189196\pi$
$449$	54131.2	+	54131.2i	0.268507	+	0.268507i	−0.559992	+	0.828498i	$0.689196\pi$
$450$	177957.	+	177957.i	0.878798	+	0.878798i
$451$	−73119.3			−0.359484
$452$			357591.i			1.75029i
$453$	52260.2	+	52260.2i	0.254668	+	0.254668i
$454$			272835.i			1.32370i
$455$	115861.	+	242729.i	0.559649	+	1.17246i
$456$	−5770.28			−0.0277503
$457$	−44160.2	+	44160.2i	−0.211446	+	0.211446i	−0.804881	−	0.593436i	$-0.797771\pi$
$457$	−44160.2	+	44160.2i	−0.211446	+	0.211446i	0.593436	+	0.804881i	$0.297771\pi$
$458$	−446101.			−2.12668
$459$		−	49696.0i		−	0.235883i
$460$	102779.	−	102779.i	0.485723	−	0.485723i
$461$	−145494.	+	145494.i	−0.684610	+	0.684610i	−0.961035	−	0.276425i	$-0.910850\pi$
$461$	−145494.	+	145494.i	−0.684610	+	0.684610i	0.276425	+	0.961035i	$0.410850\pi$
$462$	−32196.1	−	32196.1i	−0.150841	−	0.150841i
$463$	−168589.	−	168589.i	−0.786443	−	0.786443i	0.194467	−	0.980909i	$-0.437702\pi$
$463$	−168589.	−	168589.i	−0.786443	−	0.786443i	−0.980909	+	0.194467i	$0.937702\pi$
$464$	221424.			1.02847
$465$			305528.i			1.41301i
$466$	−27012.2	−	27012.2i	−0.124391	−	0.124391i
$467$		−	164176.i		−	0.752793i	−0.926459	−	0.376397i	$-0.877163\pi$
$467$		−	164176.i		−	0.752793i	0.926459	−	0.376397i	$-0.122837\pi$
$468$	69237.4	−	33048.9i	0.316118	−	0.150892i
$469$	−124804.			−0.567392
$470$	815813.	−	815813.i	3.69313	−	3.69313i
$471$	44450.2			0.200369
$472$			11140.6i			0.0500061i
$473$	13264.6	−	13264.6i	0.0592885	−	0.0592885i
$474$	−165968.	+	165968.i	−0.738700	+	0.738700i
$475$	274146.	+	274146.i	1.21505	+	1.21505i
$476$	−141230.	−	141230.i	−0.623322	−	0.623322i
$477$	−114177.			−0.501813
$478$		−	201917.i		−	0.883726i
$479$	10906.2	+	10906.2i	0.0475337	+	0.0475337i	0.730474	−	0.682940i	$-0.239299\pi$
$479$	10906.2	+	10906.2i	0.0475337	+	0.0475337i	−0.682940	+	0.730474i	$0.739299\pi$
$480$			360684.i			1.56547i
$481$	−8982.97	+	25390.3i	−0.0388267	+	0.109743i
$482$	−34949.7			−0.150435
$483$	−22445.3	+	22445.3i	−0.0962126	+	0.0962126i
$484$	−211184.			−0.901510
$485$		−	104721.i		−	0.445196i
$486$	−15343.4	+	15343.4i	−0.0649605	+	0.0649605i
$487$	225502.	−	225502.i	0.950808	−	0.950808i	−0.0480379	−	0.998846i	$-0.515297\pi$
$487$	225502.	−	225502.i	0.950808	−	0.950808i	0.998846	+	0.0480379i	$0.0152968\pi$
$488$	−12393.8	−	12393.8i	−0.0520432	−	0.0520432i
$489$	−6049.23	−	6049.23i	−0.0252978	−	0.0252978i
$490$	346982.			1.44516
$491$			311585.i			1.29245i	0.763147	+	0.646225i	$0.223653\pi$
$491$			311585.i			1.29245i	−0.763147	+	0.646225i	$0.776347\pi$
$492$	99027.5	+	99027.5i	0.409096	+	0.409096i
$493$		−	323677.i		−	1.33174i
$494$	208162.	−	99361.4i	0.852997	−	0.407159i
$495$	58448.2			0.238540
$496$	−212295.	+	212295.i	−0.862933	+	0.862933i
$497$	14116.9			0.0571516
$498$		−	171680.i		−	0.692247i
$499$	1928.12	−	1928.12i	0.00774341	−	0.00774341i	−0.703224	−	0.710968i	$-0.748257\pi$
$499$	1928.12	−	1928.12i	0.00774341	−	0.00774341i	0.710968	+	0.703224i	$0.248257\pi$
$500$	−565456.	+	565456.i	−2.26183	+	2.26183i
$501$	39151.8	+	39151.8i	0.155983	+	0.155983i
$502$	−406003.	−	406003.i	−1.61110	−	1.61110i
$503$	−185299.			−0.732382			−0.366191	−	0.930540i	$-0.619338\pi$
$503$	−185299.			−0.732382			−0.366191	+	0.930540i	$0.619338\pi$
$504$			4220.11i			0.0166136i
$505$	334981.	+	334981.i	1.31352	+	1.31352i
$506$		−	47597.8i		−	0.185903i
$507$	−93329.6	+	115388.i	−0.363081	+	0.448894i
$508$	445001.			1.72438
$509$	103850.	−	103850.i	0.400841	−	0.400841i	−0.477688	−	0.878529i	$-0.658525\pi$
$509$	103850.	−	103850.i	0.400841	−	0.400841i	0.878529	+	0.477688i	$0.158525\pi$
$510$	500365.			1.92374
$511$			124081.i			0.475186i
$512$	−263398.	+	263398.i	−1.00478	+	1.00478i
$513$	−23636.8	+	23636.8i	−0.0898162	+	0.0898162i
$514$	60573.7	+	60573.7i	0.229276	+	0.229276i
$515$	−220.186	−	220.186i	−0.000830185	−	0.000830185i
$516$	−35929.1			−0.134942
$517$		−	193589.i		−	0.724269i
$518$	−21647.4	−	21647.4i	−0.0806765	−	0.0806765i
$519$		−	203471.i		−	0.755384i
$520$	16102.4	+	33734.5i	0.0595503	+	0.124758i
$521$	200788.			0.739712			0.369856	−	0.929089i	$-0.379407\pi$
$521$	200788.			0.739712			0.369856	+	0.929089i	$0.379407\pi$
$522$	−99933.8	+	99933.8i	−0.366751	+	0.366751i
$523$	−9411.84			−0.0344089			−0.0172045	−	0.999852i	$-0.505477\pi$
$523$	−9411.84			−0.0344089			−0.0172045	+	0.999852i	$0.505477\pi$
$524$		−	361353.i		−	1.31604i
$525$	200498.	−	200498.i	0.727429	−	0.727429i
$526$	30679.0	−	30679.0i	0.110884	−	0.110884i
$527$	310332.	+	310332.i	1.11739	+	1.11739i
$528$	40612.6	+	40612.6i	0.145678	+	0.145678i
$529$	246658.			0.881424
$530$		−	1.14959e6i		−	4.09254i
$531$	45635.1	+	45635.1i	0.161849	+	0.161849i
$532$			134346.i			0.474681i
$533$	−255390.	−	90356.1i	−0.898980	−	0.318056i
$534$	−72522.5			−0.254326
$535$	−207488.	+	207488.i	−0.724913	+	0.724913i
$536$	−17345.3			−0.0603742
$537$		−	196233.i		−	0.680493i
$538$	−406904.	+	406904.i	−1.40581	+	1.40581i
$539$	41168.7	−	41168.7i	0.141707	−	0.141707i
$540$	−79158.0	−	79158.0i	−0.271461	−	0.271461i
$541$	−16197.1	−	16197.1i	−0.0553406	−	0.0553406i	0.678895	−	0.734235i	$-0.262459\pi$
$541$	−16197.1	−	16197.1i	−0.0553406	−	0.0553406i	−0.734235	+	0.678895i	$0.762459\pi$
$542$	−539696.			−1.83718
$543$		−	49834.1i		−	0.169016i
$544$	366356.	+	366356.i	1.23796	+	1.23796i
$545$		−	247953.i		−	0.834788i
$546$	−72668.3	−	152240.i	−0.243759	−	0.510674i
$547$	−211628.			−0.707292			−0.353646	−	0.935379i	$-0.615058\pi$
$547$	−211628.			−0.707292			−0.353646	+	0.935379i	$0.615058\pi$
$548$	−84574.9	+	84574.9i	−0.281631	+	0.281631i
$549$	−101537.			−0.336885
$550$			425178.i			1.40555i
$551$	−153950.	+	153950.i	−0.507081	+	0.507081i
$552$	−3119.45	+	3119.45i	−0.0102376	+	0.0102376i
$553$	186991.	+	186991.i	0.611462	+	0.611462i
$554$	284268.	+	284268.i	0.926207	+	0.926207i
$555$	39298.3			0.127582
$556$		−	204839.i		−	0.662619i
$557$	−143135.	−	143135.i	−0.461354	−	0.461354i	0.437745	−	0.899099i	$-0.355777\pi$
$557$	−143135.	−	143135.i	−0.461354	−	0.461354i	−0.899099	+	0.437745i	$0.855777\pi$
$558$		−	191627.i		−	0.615445i
$559$	62721.8	−	29938.8i	0.200722	−	0.0958101i
$560$	385652.			1.22976
$561$	59367.3	−	59367.3i	0.188635	−	0.188635i
$562$	166199.			0.526206
$563$			230941.i			0.728592i	0.931283	+	0.364296i	$0.118690\pi$
$563$			230941.i			0.728592i	−0.931283	+	0.364296i	$0.881310\pi$
$564$	−262183.	+	262183.i	−0.824226	+	0.824226i
$565$	−713694.	+	713694.i	−2.23571	+	2.23571i
$566$	−122205.	−	122205.i	−0.381467	−	0.381467i
$567$	17286.9	+	17286.9i	0.0537713	+	0.0537713i
$568$	1961.97			0.00608129
$569$			243018.i			0.750609i	0.926902	+	0.375305i	$0.122462\pi$
$569$			243018.i			0.750609i	−0.926902	+	0.375305i	$0.877538\pi$
$570$	−237988.	−	237988.i	−0.732497	−	0.732497i
$571$			229921.i			0.705189i	0.935776	+	0.352595i	$0.114701\pi$
$571$			229921.i			0.705189i	−0.935776	+	0.352595i	$0.885299\pi$
$572$	122192.	+	43231.2i	0.373467	+	0.132131i
$573$	241064.			0.734214
$574$	217743.	−	217743.i	0.660876	−	0.660876i
$575$	296410.			0.896515
$576$		−	121539.i		−	0.366329i
$577$	−45748.5	+	45748.5i	−0.137412	+	0.137412i	−0.772467	−	0.635055i	$-0.780977\pi$
$577$	−45748.5	+	45748.5i	−0.137412	+	0.137412i	0.635055	+	0.772467i	$0.280977\pi$
$578$	169929.	−	169929.i	0.508641	−	0.508641i
$579$	48622.7	+	48622.7i	0.145038	+	0.145038i
$580$	−515568.	−	515568.i	−1.53260	−	1.53260i
$581$	−193426.			−0.573010
$582$			65681.3i			0.193908i
$583$	−136397.	−	136397.i	−0.401299	−	0.401299i
$584$			17244.7i			0.0505628i
$585$	204147.	+	72226.5i	0.596529	+	0.211050i
$586$	548126.			1.59619
$587$	−183355.	+	183355.i	−0.532127	+	0.532127i	−0.921205	−	0.389078i	$-0.872794\pi$
$587$	−183355.	+	183355.i	−0.532127	+	0.532127i	0.389078	+	0.921205i	$0.372794\pi$
$588$	−111512.			−0.322527
$589$		−	295206.i		−	0.850931i
$590$	−459479.	+	459479.i	−1.31996	+	1.31996i
$591$	−23190.4	+	23190.4i	−0.0663947	+	0.0663947i
$592$	27306.4	+	27306.4i	0.0779149	+	0.0779149i
$593$	−83397.8	−	83397.8i	−0.237162	−	0.237162i	0.578512	−	0.815674i	$-0.303634\pi$
$593$	−83397.8	−	83397.8i	−0.237162	−	0.237162i	−0.815674	+	0.578512i	$0.803634\pi$
$594$	−36658.8			−0.103897
$595$		−	563745.i		−	1.59239i
$596$	168680.	+	168680.i	0.474866	+	0.474866i
$597$		−	370623.i		−	1.03988i
$598$	58818.3	−	166249.i	0.164479	−	0.464897i
$599$	−217649.			−0.606601			−0.303300	−	0.952895i	$-0.598089\pi$
$599$	−217649.			−0.606601			−0.303300	+	0.952895i	$0.598089\pi$
$600$	27865.1	−	27865.1i	0.0774031	−	0.0774031i
$601$	−441379.			−1.22197			−0.610987	−	0.791640i	$-0.709227\pi$
$601$	−441379.			−1.22197			−0.610987	+	0.791640i	$0.709227\pi$
$602$			79001.4i			0.217993i
$603$	−71051.5	+	71051.5i	−0.195406	+	0.195406i
$604$	169103.	−	169103.i	0.463529	−	0.463529i
$605$	−421490.	−	421490.i	−1.15153	−	1.15153i
$606$	−210101.	−	210101.i	−0.572113	−	0.572113i
$607$	−283335.			−0.768993			−0.384497	−	0.923126i	$-0.625625\pi$
$607$	−283335.			−0.768993			−0.384497	+	0.923126i	$0.625625\pi$
$608$		−	348499.i		−	0.942745i
$609$	112592.	+	112592.i	0.303580	+	0.303580i
$610$		−	1.02233e6i		−	2.74747i
$611$	239225.	−	676166.i	0.640802	−	1.81122i
$612$	−160805.			−0.429337
$613$	482403.	−	482403.i	1.28377	−	1.28377i	0.345272	−	0.938503i	$-0.387787\pi$
$613$	482403.	−	482403.i	1.28377	−	1.28377i	0.938503	−	0.345272i	$-0.112213\pi$
$614$	783139.			2.07731
$615$			395286.i			1.04511i
$616$	−5041.39	+	5041.39i	−0.0132858	+	0.0132858i
$617$	136398.	−	136398.i	0.358293	−	0.358293i	−0.504890	−	0.863184i	$-0.668467\pi$
$617$	136398.	−	136398.i	0.358293	−	0.358293i	0.863184	+	0.504890i	$0.168467\pi$
$618$	138.101	+	138.101i	0.000361592	+	0.000361592i
$619$	130340.	+	130340.i	0.340170	+	0.340170i	0.856431	−	0.516261i	$-0.172677\pi$
$619$	130340.	+	130340.i	0.340170	+	0.340170i	−0.516261	+	0.856431i	$0.672677\pi$
$620$	988623.			2.57186
$621$			25556.5i			0.0662701i
$622$	286139.	+	286139.i	0.739600	+	0.739600i
$623$			81708.7i			0.210519i
$624$	91664.8	+	192038.i	0.235415	+	0.493193i
$625$	−1.24013e6			−3.17473
$626$	−277559.	+	277559.i	−0.708282	+	0.708282i
$627$	−56473.6			−0.143652
$628$		−	143831.i		−	0.364698i
$629$	39916.3	−	39916.3i	0.100890	−	0.100890i
$630$	−174054.	+	174054.i	−0.438532	+	0.438532i
$631$	−145847.	−	145847.i	−0.366302	−	0.366302i	0.499825	−	0.866127i	$-0.333398\pi$
$631$	−145847.	−	145847.i	−0.366302	−	0.366302i	−0.866127	+	0.499825i	$0.833398\pi$
$632$	25987.9	+	25987.9i	0.0650635	+	0.0650635i
$633$	−234586.			−0.585456
$634$			1.13753e6i			2.82998i
$635$	888150.	+	888150.i	2.20262	+	2.20262i
$636$			369453.i			0.913365i
$637$	194667.	−	92920.0i	0.479749	−	0.228997i
$638$	−238764.			−0.586580
$639$	8036.84	−	8036.84i	0.0196826	−	0.0196826i
$640$	113101.			0.276126
$641$			207974.i			0.506165i	0.967445	+	0.253083i	$0.0814445\pi$
$641$			207974.i			0.506165i	−0.967445	+	0.253083i	$0.918556\pi$
$642$	130137.	−	130137.i	0.315740	−	0.315740i
$643$	−30795.0	+	30795.0i	−0.0744831	+	0.0744831i	−0.743367	−	0.668884i	$-0.766772\pi$
$643$	−30795.0	+	30795.0i	−0.0744831	+	0.0744831i	0.668884	+	0.743367i	$0.266772\pi$
$644$	72628.3	+	72628.3i	0.175119	+	0.175119i
$645$	−71708.8	−	71708.8i	−0.172367	−	0.172367i
$646$	−483461.			−1.15850
$647$			216754.i			0.517795i	0.965905	+	0.258898i	$0.0833592\pi$
$647$			216754.i			0.517795i	−0.965905	+	0.258898i	$0.916641\pi$
$648$	2402.53	+	2402.53i	0.00572161	+	0.00572161i
$649$			109032.i			0.258861i
$650$	−525407.	+	1.48506e6i	−1.24357	+	3.51492i
$651$	−215900.			−0.509437
$652$	−19574.0	+	19574.0i	−0.0460452	+	0.0460452i
$653$	622399.			1.45963			0.729815	−	0.683645i	$-0.239606\pi$
$653$	622399.			1.45963			0.729815	+	0.683645i	$0.239606\pi$
$654$			155516.i			0.363597i
$655$	721203.	−	721203.i	1.68103	−	1.68103i
$656$	−274664.	+	274664.i	−0.638254	+	0.638254i
$657$	70639.8	+	70639.8i	0.163651	+	0.163651i
$658$	576491.	+	576491.i	1.33150	+	1.33150i
$659$	127164.			0.292814			0.146407	−	0.989224i	$-0.453229\pi$
$659$	127164.			0.292814			0.146407	+	0.989224i	$0.453229\pi$
$660$		−	189126.i		−	0.434173i
$661$	512043.	+	512043.i	1.17194	+	1.17194i	0.981748	+	0.190187i	$0.0609095\pi$
$661$	512043.	+	512043.i	1.17194	+	1.17194i	0.190187	+	0.981748i	$0.439091\pi$
$662$		−	594817.i		−	1.35727i
$663$	280720.	−	133995.i	0.638625	−	0.304833i
$664$	−26882.3			−0.0609720
$665$	−268133.	+	268133.i	−0.606328	+	0.606328i
$666$	−24647.9			−0.0555690
$667$			166453.i			0.374145i
$668$	126687.	−	126687.i	0.283909	−	0.283909i
$669$	117027.	−	117027.i	0.261477	−	0.261477i
$670$	−715384.	−	715384.i	−1.59364	−	1.59364i
$671$	−121298.	−	121298.i	−0.269406	−	0.269406i
$672$	−254876.			−0.564404
$673$		−	70363.7i		−	0.155353i	−0.996979	−	0.0776763i	$-0.975250\pi$
$673$		−	70363.7i		−	0.155353i	0.996979	−	0.0776763i	$-0.0247501\pi$
$674$	−57972.1	−	57972.1i	−0.127614	−	0.127614i
$675$		−	228288.i		−	0.501045i
$676$	373370.	+	301995.i	0.817044	+	0.660855i
$677$	289817.			0.632334			0.316167	−	0.948704i	$-0.397604\pi$
$677$	289817.			0.632334			0.316167	+	0.948704i	$0.397604\pi$
$678$	447629.	−	447629.i	0.973776	−	0.973776i
$679$	74000.9			0.160508
$680$		−	78349.1i		−	0.169440i
$681$	175001.	−	175001.i	0.377351	−	0.377351i
$682$	228920.	−	228920.i	0.492170	−	0.492170i
$683$	126812.	+	126812.i	0.271844	+	0.271844i	0.829842	−	0.557998i	$-0.188430\pi$
$683$	126812.	+	126812.i	0.271844	+	0.271844i	−0.557998	+	0.829842i	$0.688430\pi$
$684$	76483.7	+	76483.7i	0.163477	+	0.163477i
$685$	−337596.			−0.719476
$686$			706430.i			1.50114i
$687$	286137.	+	286137.i	0.606261	+	0.606261i
$688$		−	99653.4i		−	0.210531i
$689$	−307856.	−	644957.i	−0.648498	−	1.35860i
$690$	−257316.			−0.540466
$691$	512067.	−	512067.i	1.07243	−	1.07243i	0.0752718	−	0.997163i	$-0.476018\pi$
$691$	512067.	−	512067.i	1.07243	−	1.07243i	0.997163	−	0.0752718i	$-0.0239824\pi$
$692$	−658388.			−1.37490
$693$			41302.2i			0.0860016i
$694$	−875563.	+	875563.i	−1.81789	+	1.81789i
$695$	408827.	−	408827.i	0.846388	−	0.846388i
$696$	15648.0	+	15648.0i	0.0323029	+	0.0323029i
$697$	401502.	+	401502.i	0.826461	+	0.826461i
$698$	167478.			0.343753
$699$			34652.1i			0.0709211i
$700$	−648768.	−	648768.i	−1.32402	−	1.32402i
$701$			718609.i			1.46237i	0.682181	+	0.731184i	$0.261032\pi$
$701$			718609.i			1.46237i	−0.682181	+	0.731184i	$0.738968\pi$
$702$	−128041.	−	45300.5i	−0.259822	−	0.0919240i
$703$	−37970.7			−0.0768312
$704$	145192.	−	145192.i	0.292952	−	0.292952i
$705$	−1.04655e6			−2.10563
$706$		−	570946.i		−	1.14547i
$707$	−236713.	+	236713.i	−0.473570	+	0.473570i
$708$	147666.	−	147666.i	0.294586	−	0.294586i
$709$	−360756.	−	360756.i	−0.717664	−	0.717664i	0.250462	−	0.968126i	$-0.419417\pi$
$709$	−360756.	−	360756.i	−0.717664	−	0.717664i	−0.968126	+	0.250462i	$0.919417\pi$
$710$	80919.1	+	80919.1i	0.160522	+	0.160522i
$711$	212909.			0.421168
$712$			11355.9i			0.0224006i
$713$	−159590.	−	159590.i	−0.313926	−	0.313926i
$714$			353581.i			0.693573i
$715$	157594.	+	330159.i	0.308267	+	0.645819i
$716$	−634968.			−1.23858
$717$	−129513.	+	129513.i	−0.251927	+	0.251927i
$718$	732599.			1.42108
$719$		−	756213.i		−	1.46280i	−0.681946	−	0.731402i	$-0.738866\pi$
$719$		−	756213.i		−	1.46280i	0.681946	−	0.731402i	$-0.261134\pi$
$720$	219553.	−	219553.i	0.423521	−	0.423521i
$721$	155.593	−	155.593i	0.000299310	−	0.000299310i
$722$	−297921.	−	297921.i	−0.571515	−	0.571515i
$723$	22417.3	+	22417.3i	0.0428851	+	0.0428851i
$724$	−161252.			−0.307630
$725$		−	1.48688e6i		−	2.82878i
$726$	264359.	+	264359.i	0.501557	+	0.501557i
$727$			2488.50i			0.00470835i	0.999997	+	0.00235417i	$0.000749357\pi$
$727$			2488.50i			0.00470835i	−0.999997	+	0.00235417i	$0.999251\pi$
$728$	−23838.3	+	11378.7i	−0.0449794	+	0.0214699i
$729$	19683.0			0.0370370
$730$	−711239.	+	711239.i	−1.33466	+	1.33466i
$731$	−145673.			−0.272611
$732$			328554.i			0.613174i
$733$	269312.	−	269312.i	0.501243	−	0.501243i	−0.410581	−	0.911824i	$-0.634674\pi$
$733$	269312.	−	269312.i	0.501243	−	0.501243i	0.911824	+	0.410581i	$0.134674\pi$
$734$	633254.	−	633254.i	1.17540	−	1.17540i
$735$	−222560.	−	222560.i	−0.411976	−	0.411976i
$736$	−188401.	−	188401.i	−0.347798	−	0.347798i
$737$	−169758.			−0.312532
$738$		−	247924.i		−	0.455203i
$739$	−710849.	−	710849.i	−1.30163	−	1.30163i	−0.927291	−	0.374342i	$-0.877869\pi$
$739$	−710849.	−	710849.i	−1.30163	−	1.30163i	−0.374342	−	0.927291i	$-0.622131\pi$
$740$		−	127161.i		−	0.232215i
$741$	−197250.	−	69786.4i	−0.359237	−	0.127097i
$742$	812357.			1.47550
$743$	−516575.	+	516575.i	−0.935741	+	0.935741i	−0.998057	−	0.0623154i	$-0.980152\pi$
$743$	−516575.	+	516575.i	−0.935741	+	0.935741i	0.0623154	+	0.998057i	$0.480152\pi$
$744$	−30005.7			−0.0542074
$745$			673317.i			1.21313i
$746$	−49230.3	+	49230.3i	−0.0884616	+	0.0884616i
$747$	−110118.	+	110118.i	−0.197341	+	0.197341i
$748$	−192100.	−	192100.i	−0.343340	−	0.343340i
$749$	−146621.	−	146621.i	−0.261356	−	0.261356i
$750$	1.41567e6			2.51674
$751$			628582.i			1.11450i	0.830343	+	0.557252i	$0.188144\pi$
$751$			628582.i			1.11450i	−0.830343	+	0.557252i	$0.811856\pi$
$752$	−727194.	−	727194.i	−1.28592	−	1.28592i
$753$			520834.i			0.918564i
$754$	−833952.	−	295049.i	−1.46689	−	0.518981i
$755$	675004.			1.18417
$756$	55936.7	−	55936.7i	0.0978708	−	0.0978708i
$757$	874918.			1.52678			0.763389	−	0.645940i	$-0.223534\pi$
$757$	874918.			1.52678			0.763389	+	0.645940i	$0.223534\pi$
$758$			459856.i			0.800357i
$759$	−30530.0	+	30530.0i	−0.0529960	+	0.0529960i
$760$	−37265.1	+	37265.1i	−0.0645171	+	0.0645171i
$761$	176909.	+	176909.i	0.305479	+	0.305479i	0.843153	−	0.537674i	$-0.180697\pi$
$761$	176909.	+	176909.i	0.305479	+	0.305479i	−0.537674	+	0.843153i	$0.680697\pi$
$762$	−557049.	−	557049.i	−0.959363	−	0.959363i
$763$	175215.			0.300969
$764$		−	780031.i		−	1.33636i
$765$	−320942.	−	320942.i	−0.548408	−	0.548408i
$766$			114700.i			0.195482i
$767$	−134735.	+	380827.i	−0.229029	+	0.647347i
$768$	303306.			0.514232
$769$	64761.1	−	64761.1i	0.109512	−	0.109512i	−0.650228	−	0.759740i	$-0.725326\pi$
$769$	64761.1	−	64761.1i	0.109512	−	0.109512i	0.759740	+	0.650228i	$0.225326\pi$
$770$	−415852.			−0.701387
$771$		−	77705.8i		−	0.130721i
$772$	157333.	−	157333.i	0.263988	−	0.263988i
$773$	65728.0	−	65728.0i	0.110000	−	0.110000i	−0.649965	−	0.759964i	$-0.725216\pi$
$773$	65728.0	−	65728.0i	0.110000	−	0.110000i	0.759964	+	0.649965i	$0.225216\pi$
$774$	44975.8	+	44975.8i	0.0750753	+	0.0750753i
$775$	1.42557e6	+	1.42557e6i	2.37348	+	2.37348i
$776$	10284.6			0.0170791
$777$			27770.0i			0.0459975i
$778$	−58682.3	−	58682.3i	−0.0969501	−	0.0969501i
$779$		−	381932.i		−	0.629377i
$780$	233709.	−	660577.i	0.384138	−	1.08576i
$781$	19201.8			0.0314803
$782$	−261362.	+	261362.i	−0.427395	+	0.427395i
$783$	128198.			0.209102
$784$		−	309290.i		−	0.503193i
$785$	287064.	−	287064.i	0.465843	−	0.465843i
$786$	−452339.	+	452339.i	−0.732182	+	0.732182i
$787$	853121.	+	853121.i	1.37740	+	1.37740i	0.848983	+	0.528420i	$0.177215\pi$
$787$	853121.	+	853121.i	1.37740	+	1.37740i	0.528420	+	0.848983i	$0.322785\pi$
$788$	75039.2	+	75039.2i	0.120847	+	0.120847i
$789$	−39356.0			−0.0632204
$790$			2.14368e6i			3.43484i
$791$	−504329.	−	504329.i	−0.806048	−	0.806048i
$792$			5740.17i			0.00915112i
$793$	−273775.	−	573559.i	−0.435360	−	0.912078i
$794$	−975493.			−1.54733
$795$	−737369.	+	737369.i	−1.16668	+	1.16668i
$796$	−1.19926e6			−1.89272
$797$			264563.i			0.416498i	0.978076	+	0.208249i	$0.0667765\pi$
$797$			264563.i			0.416498i	−0.978076	+	0.208249i	$0.933224\pi$
$798$	168173.	−	168173.i	0.264090	−	0.264090i
$799$	−1.06301e6	+	1.06301e6i	−1.66511	+	1.66511i
$800$	1.68293e6	+	1.68293e6i	2.62958	+	2.62958i
$801$	46517.1	+	46517.1i	0.0725016	+	0.0725016i
$802$	−255980.			−0.397977
$803$			168774.i			0.261743i
$804$	229908.	+	229908.i	0.355665	+	0.355665i
$805$			289909.i			0.447373i
$806$	1.08245e6	−	516685.i	1.66625	−	0.795345i
$807$	521989.			0.801520
$808$	−32898.4	+	32898.4i	−0.0503908	+	0.0503908i
$809$	−903066.			−1.37982			−0.689910	−	0.723895i	$-0.742350\pi$
$809$	−903066.			−1.37982			−0.689910	+	0.723895i	$0.742350\pi$
$810$			198179.i			0.302056i
$811$	158801.	−	158801.i	0.241442	−	0.241442i	−0.576005	−	0.817446i	$-0.695389\pi$
$811$	158801.	−	158801.i	0.241442	−	0.241442i	0.817446	+	0.576005i	$0.195389\pi$
$812$	364324.	−	364324.i	0.552555	−	0.552555i
$813$	346170.	+	346170.i	0.523731	+	0.523731i
$814$	−29444.7	−	29444.7i	−0.0444384	−	0.0444384i
$815$	−78133.2			−0.117631
$816$		−	446012.i		−	0.669832i
$817$	69286.2	+	69286.2i	0.103801	+	0.103801i
$818$			135214.i			0.202076i
$819$	−51038.6	+	144260.i	−0.0760905	+	0.215069i
$820$	1.27906e6			1.90223
$821$	566290.	−	566290.i	0.840142	−	0.840142i	−0.148735	−	0.988877i	$-0.547520\pi$
$821$	566290.	−	566290.i	0.840142	−	0.840142i	0.988877	+	0.148735i	$0.0475203\pi$
$822$	211740.			0.313372
$823$		−	664034.i		−	0.980371i	−0.871618	−	0.490186i	$-0.836929\pi$
$823$		−	664034.i		−	0.980371i	0.871618	−	0.490186i	$-0.163071\pi$
$824$	21.6244	−	21.6244i	3.18485e−5	−	3.18485e-5i
$825$	272716.	−	272716.i	0.400684	−	0.400684i
$826$	−324689.	−	324689.i	−0.475891	−	0.475891i
$827$	−694781.	−	694781.i	−1.01587	−	1.01587i	−0.999872	−	0.0159954i	$-0.994908\pi$
$827$	−694781.	−	694781.i	−1.01587	−	1.01587i	−0.0159954	−	0.999872i	$-0.505092\pi$
$828$	82695.2			0.120620
$829$		−	1.07123e6i		−	1.55874i	−0.626564	−	0.779370i	$-0.715539\pi$
$829$		−	1.07123e6i		−	1.55874i	0.626564	−	0.779370i	$-0.284461\pi$
$830$	−1.10873e6	−	1.10873e6i	−1.60942	−	1.60942i
$831$		−	364668.i		−	0.528074i
$832$	686543.	−	327706.i	0.991794	−	0.473410i
$833$	−452119.			−0.651573
$834$	−256416.	+	256416.i	−0.368649	+	0.368649i
$835$	505694.			0.725295
$836$			182737.i			0.261465i
$837$	−122913.	+	122913.i	−0.175447	+	0.175447i
$838$	183277.	−	183277.i	0.260988	−	0.260988i
$839$	710646.	+	710646.i	1.00955	+	1.00955i	0.999954	+	0.00959972i	$0.00305573\pi$
$839$	710646.	+	710646.i	1.00955	+	1.00955i	0.00959972	+	0.999954i	$0.496944\pi$
$840$	27254.0	+	27254.0i	0.0386252	+	0.0386252i
$841$	127693.			0.180541
$842$			772742.i			1.08996i
$843$	−106603.	−	106603.i	−0.150007	−	0.150007i
$844$			759070.i			1.06561i
$845$	142453.	+	1.34792e6i	0.199507	+	1.88778i
$846$	656398.			0.917120
$847$	297844.	−	297844.i	0.415167	−	0.415167i
$848$	−1.02472e6			−1.42499
$849$			156769.i			0.217493i
$850$	2.33467e6	−	2.33467e6i	3.23138	−	3.23138i
$851$	−20527.2	+	20527.2i	−0.0283446	+	0.0283446i
$852$	−26005.5	−	26005.5i	−0.0358250	−	0.0358250i
$853$	−719087.	−	719087.i	−0.988288	−	0.988288i	0.0116445	−	0.999932i	$-0.496293\pi$
$853$	−719087.	−	719087.i	−0.988288	−	0.988288i	−0.999932	+	0.0116445i	$0.996293\pi$
$854$	722427.			0.990555
$855$			305299.i			0.417631i
$856$	−20377.3	−	20377.3i	−0.0278099	−	0.0278099i
$857$			625779.i			0.852038i	0.904714	+	0.426019i	$0.140084\pi$
$857$			625779.i			0.852038i	−0.904714	+	0.426019i	$0.859916\pi$
$858$	−98843.0	−	207076.i	−0.134268	−	0.281290i
$859$	−1.38660e6			−1.87917			−0.939585	−	0.342315i	$-0.888789\pi$
$859$	−1.38660e6			−1.87917			−0.939585	+	0.342315i	$0.888789\pi$
$860$	−232034.	+	232034.i	−0.313729	+	0.313729i
$861$	−279327.			−0.376797
$862$		−	973017.i		−	1.30950i
$863$	−251871.	+	251871.i	−0.338187	+	0.338187i	−0.855685	−	0.517497i	$-0.826864\pi$
$863$	−251871.	+	251871.i	−0.338187	+	0.338187i	0.517497	+	0.855685i	$0.326864\pi$
$864$	−145102.	+	145102.i	−0.194377	+	0.194377i
$865$	−1.31404e6	−	1.31404e6i	−1.75621	−	1.75621i
$866$	424938.	+	424938.i	0.566618	+	0.566618i
$867$	−217990.			−0.290000
$868$			698606.i			0.927242i
$869$	254343.	+	254343.i	0.336807	+	0.336807i
$870$			1.29077e6i			1.70533i
$871$	−592928.	−	209776.i	−0.781566	−	0.276515i
$872$	24351.3			0.0320250
$873$	42129.0	−	42129.0i	0.0552781	−	0.0552781i
$874$	248623.			0.325475
$875$		−	1.59499e6i		−	2.08325i
$876$	228575.	−	228575.i	0.297866	−	0.297866i
$877$	248488.	−	248488.i	0.323077	−	0.323077i	−0.526869	−	0.849946i	$-0.676634\pi$
$877$	248488.	−	248488.i	0.323077	−	0.323077i	0.849946	+	0.526869i	$0.176634\pi$
$878$	766569.	+	766569.i	0.994403	+	0.994403i
$879$	−351577.	−	351577.i	−0.455032	−	0.455032i
$880$	524562.			0.677378
$881$			1.01415e6i			1.30662i	0.757089	+	0.653312i	$0.226621\pi$
$881$			1.01415e6i			1.30662i	−0.757089	+	0.653312i	$0.773379\pi$
$882$	139590.	+	139590.i	0.179439	+	0.179439i
$883$			1.21924e6i			1.56375i	0.623433	+	0.781877i	$0.285737\pi$
$883$			1.21924e6i			1.56375i	−0.623433	+	0.781877i	$0.714263\pi$
$884$	−433580.	−	908349.i	−0.554836	−	1.16238i
$885$	589434.			0.752573
$886$	626388.	−	626388.i	0.797950	−	0.797950i
$887$	904300.			1.14938			0.574692	−	0.818370i	$-0.305122\pi$
$887$	904300.			1.14938			0.574692	+	0.818370i	$0.305122\pi$
$888$			3859.47i			0.00489443i
$889$	−627608.	+	627608.i	−0.794118	+	0.794118i
$890$	−468359.	+	468359.i	−0.591287	+	0.591287i
$891$	23513.5	+	23513.5i	0.0296184	+	0.0296184i
$892$	−378674.	−	378674.i	−0.475923	−	0.475923i
$893$	1.01120e6			1.26804
$894$		−	422305.i		−	0.528386i
$895$	−1.26729e6	−	1.26729e6i	−1.58209	−	1.58209i
$896$			79922.4i			0.0995526i
$897$	−144362.	+	68907.8i	−0.179419	+	0.0856414i
$898$	−438520.			−0.543797
$899$	−800549.	+	800549.i	−0.990532	+	0.990532i
$900$	−738692.			−0.911966
$901$			1.49793e6i			1.84519i
$902$	296172.	−	296172.i	0.364025	−	0.364025i
$903$	50672.7	−	50672.7i	0.0621439	−	0.0621439i
$904$	−70091.5	−	70091.5i	−0.0857687	−	0.0857687i
$905$	−321834.	−	321834.i	−0.392948	−	0.392948i
$906$	−423363.			−0.515771
$907$			1.40623e6i			1.70940i	0.519124	+	0.854699i	$0.326258\pi$
$907$			1.40623e6i			1.70940i	−0.519124	+	0.854699i	$0.673742\pi$
$908$	−566265.	−	566265.i	−0.686828	−	0.686828i
$909$			269524.i			0.326189i
$910$	−1.45248e6	−	513883.i	−1.75400	−	0.620557i
$911$	−320928.			−0.386697			−0.193348	−	0.981130i	$-0.561935\pi$
$911$	−320928.			−0.386697			−0.193348	+	0.981130i	$0.561935\pi$
$912$	−212136.	+	212136.i	−0.255050	+	0.255050i
$913$	−263097.			−0.315627
$914$		−	357745.i		−	0.428234i
$915$	−655741.	+	655741.i	−0.783231	+	0.783231i
$916$	925876.	−	925876.i	1.10347	−	1.10347i
$917$	509635.	+	509635.i	0.606067	+	0.606067i
$918$	201295.	+	201295.i	0.238862	+	0.238862i
$919$	−824931.			−0.976757			−0.488378	−	0.872632i	$-0.662411\pi$
$919$	−824931.			−0.976757			−0.488378	+	0.872632i	$0.662411\pi$
$920$			40291.5i			0.0476034i
$921$	−502318.	−	502318.i	−0.592187	−	0.592187i
$922$		−	1.17866e6i		−	1.38652i
$923$	67067.8	+	23728.3i	0.0787246	+	0.0278525i
$924$	133645.			0.156534
$925$	183364.	−	183364.i	0.214304	−	0.214304i
$926$	1.36575e6			1.59276
$927$		−	177.160i		−	0.000206161i
$928$	−945070.	+	945070.i	−1.09741	+	1.09741i
$929$	678405.	−	678405.i	0.786064	−	0.786064i	−0.194783	−	0.980846i	$-0.562400\pi$
$929$	678405.	−	678405.i	0.786064	−	0.786064i	0.980846	+	0.194783i	$0.0624001\pi$
$930$	−1.23755e6	−	1.23755e6i	−1.43086	−	1.43086i
$931$	215041.	+	215041.i	0.248097	+	0.248097i
$932$	112127.			0.129086
$933$		−	367069.i		−	0.421681i
$934$	665000.	+	665000.i	0.762303	+	0.762303i
$935$		−	766802.i		−	0.877122i
$936$	−7093.33	+	20049.2i	−0.00809652	+	0.0228847i
$937$	1.11931e6			1.27488			0.637441	−	0.770499i	$-0.279993\pi$
$937$	1.11931e6			1.27488			0.637441	+	0.770499i	$0.279993\pi$
$938$	505523.	−	505523.i	0.574560	−	0.574560i
$939$	356061.			0.403825
$940$			3.38642e6i			3.83252i
$941$	498975.	−	498975.i	0.563507	−	0.563507i	−0.366795	−	0.930302i	$-0.619545\pi$
$941$	498975.	−	498975.i	0.563507	−	0.563507i	0.930302	+	0.366795i	$0.119545\pi$
$942$	−180047.	+	180047.i	−0.202901	+	0.202901i
$943$	−206475.	−	206475.i	−0.232190	−	0.232190i
$944$	409567.	+	409567.i	0.459601	+	0.459601i
$945$	223281.			0.250028
$946$			107457.i			0.120075i
$947$	−672812.	−	672812.i	−0.750228	−	0.750228i	0.224293	−	0.974522i	$-0.427993\pi$
$947$	−672812.	−	672812.i	−0.750228	−	0.750228i	−0.974522	+	0.224293i	$0.927993\pi$
$948$		−	688928.i		−	0.766580i
$949$	−208560.	+	589492.i	−0.231579	+	0.654554i
$950$	−2.22087e6			−2.46080
$951$	729629.	−	729629.i	0.806754	−	0.806754i
$952$	55365.1			0.0610889
$953$			226250.i			0.249117i	0.992212	+	0.124558i	$0.0397514\pi$
$953$			226250.i			0.249117i	−0.992212	+	0.124558i	$0.960249\pi$
$954$	462478.	−	462478.i	0.508153	−	0.508153i
$955$	1.55682e6	−	1.55682e6i	1.70699	−	1.70699i
$956$	419076.	+	419076.i	0.458540	+	0.458540i
$957$	153147.	+	153147.i	0.167219	+	0.167219i
$958$	−88351.7			−0.0962684
$959$		−	238561.i		−	0.259395i
$960$	−784913.	−	784913.i	−0.851686	−	0.851686i
$961$		−	611566.i		−	0.662211i
$962$	−66458.2	−	139230.i	−0.0718123	−	0.150447i
$963$	−166944.			−0.180019
$964$	72537.6	−	72537.6i	0.0780565	−	0.0780565i
$965$	628022.			0.674404
$966$		−	181831.i		−	0.194856i
$967$	−652291.	+	652291.i	−0.697571	+	0.697571i	−0.963886	−	0.266315i	$-0.914194\pi$
$967$	−652291.	+	652291.i	−0.697571	+	0.697571i	0.266315	+	0.963886i	$0.414194\pi$
$968$	41394.3	−	41394.3i	0.0441764	−	0.0441764i
$969$	310100.	+	310100.i	0.330258	+	0.330258i
$970$	424177.	+	424177.i	0.450821	+	0.450821i
$971$	330964.			0.351028			0.175514	−	0.984477i	$-0.443841\pi$
$971$	330964.			0.351028			0.175514	+	0.984477i	$0.443841\pi$
$972$		−	63690.0i		−	0.0674122i
$973$	288896.	+	288896.i	0.305151	+	0.305151i
$974$			1.82681e6i			1.92564i
$975$	1.28954e6	−	615534.i	1.35652	−	0.647504i
$976$	−911280.			−0.956648
$977$	−812569.	+	812569.i	−0.851278	+	0.851278i	−0.990291	−	0.139013i	$-0.955607\pi$
$977$	−812569.	+	812569.i	−0.851278	+	0.851278i	0.139013	+	0.990291i	$0.455607\pi$
$978$	49005.2			0.0512347
$979$			111140.i			0.115959i
$980$	−720156.	+	720156.i	−0.749850	+	0.749850i
$981$	99750.5	−	99750.5i	0.103652	−	0.103652i
$982$	−1.26209e6	−	1.26209e6i	−1.30878	−	1.30878i
$983$	1.32394e6	+	1.32394e6i	1.37013	+	1.37013i	0.860235	+	0.509898i	$0.170317\pi$
$983$	1.32394e6	+	1.32394e6i	1.37013	+	1.37013i	0.509898	+	0.860235i	$0.329683\pi$
$984$	−38820.9			−0.0400936
$985$			299533.i			0.308725i
$986$	1.31107e6	+	1.31107e6i	1.34856	+	1.34856i
$987$		−	739541.i		−	0.759151i
$988$	−225814.	+	638260.i	−0.231333	+	0.653858i
$989$	74913.1			0.0765888
$990$	−236746.	+	236746.i	−0.241553	+	0.241553i
$991$	−424185.			−0.431925			−0.215962	−	0.976402i	$-0.569289\pi$
$991$	−424185.			−0.431925			−0.215962	+	0.976402i	$0.569289\pi$
$992$		−	1.81221e6i		−	1.84156i
$993$	−381525.	+	381525.i	−0.386923	+	0.386923i
$994$	−57181.2	+	57181.2i	−0.0578736	+	0.0578736i
$995$	−2.39352e6	−	2.39352e6i	−2.41764	−	2.41764i
$996$	356319.	+	356319.i	0.359187	+	0.359187i
$997$	1.53487e6			1.54412			0.772060	−	0.635549i	$-0.219226\pi$
$997$	1.53487e6			1.54412			0.772060	+	0.635549i	$0.219226\pi$
$998$			15619.8i			0.0156825i
$999$	15809.6	+	15809.6i	0.0158413	+	0.0158413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.5.g.a.31.3	✓	20
3.2	odd	2		117.5.j.b.109.8		20
13.8	odd	4	inner	39.5.g.a.34.3	yes	20
39.8	even	4		117.5.j.b.73.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.5.g.a.31.3	✓	20	1.1	even	1	trivial
39.5.g.a.34.3	yes	20	13.8	odd	4	inner
117.5.j.b.73.8		20	39.8	even	4
117.5.j.b.109.8		20	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	39.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.05053 + 4.05053i) q^{2} +5.19615 q^{3} -16.8136i q^{4} +(33.5573 - 33.5573i) q^{5} +(-21.0472 + 21.0472i) q^{6} +(23.7132 + 23.7132i) q^{7} +(3.29565 + 3.29565i) q^{8} +27.0000 q^{9} +271.850i q^{10} +(32.2545 + 32.2545i) q^{11} -87.3662i q^{12} +(72.8001 + 152.516i) q^{13} -192.102 q^{14} +(174.369 - 174.369i) q^{15} +242.320 q^{16} -354.222i q^{17} +(-109.364 + 109.364i) q^{18} +(-168.478 + 168.478i) q^{19} +(-564.221 - 564.221i) q^{20} +(123.217 + 123.217i) q^{21} -261.296 q^{22} +182.161i q^{23} +(17.1247 + 17.1247i) q^{24} -1627.19i q^{25} +(-912.650 - 322.892i) q^{26} +140.296 q^{27} +(398.704 - 398.704i) q^{28} +913.769 q^{29} +1412.58i q^{30} +(-876.095 + 876.095i) q^{31} +(-1034.25 + 1034.25i) q^{32} +(167.599 + 167.599i) q^{33} +(1434.79 + 1434.79i) q^{34} +1591.50 q^{35} -453.968i q^{36} +(112.687 + 112.687i) q^{37} -1364.85i q^{38} +(378.280 + 792.497i) q^{39} +221.186 q^{40} +(-1133.48 + 1133.48i) q^{41} -998.190 q^{42} -411.247i q^{43} +(542.315 - 542.315i) q^{44} +(906.048 - 906.048i) q^{45} +(-737.848 - 737.848i) q^{46} +(-3000.97 - 3000.97i) q^{47} +1259.13 q^{48} -1276.37i q^{49} +(6590.99 + 6590.99i) q^{50} -1840.59i q^{51} +(2564.35 - 1224.03i) q^{52} -4228.78 q^{53} +(-568.274 + 568.274i) q^{54} +2164.75 q^{55} +156.301i q^{56} +(-875.438 + 875.438i) q^{57} +(-3701.25 + 3701.25i) q^{58} +(1690.19 + 1690.19i) q^{59} +(-2931.78 - 2931.78i) q^{60} -3760.65 q^{61} -7097.31i q^{62} +(640.255 + 640.255i) q^{63} -4501.45i q^{64} +(7561.01 + 2675.06i) q^{65} -1357.73 q^{66} +(-2631.54 + 2631.54i) q^{67} -5955.76 q^{68} +946.535i q^{69} +(-6446.43 + 6446.43i) q^{70} +(297.661 - 297.661i) q^{71} +(88.9825 + 88.9825i) q^{72} +(2616.29 + 2616.29i) q^{73} -912.887 q^{74} -8455.13i q^{75} +(2832.73 + 2832.73i) q^{76} +1529.71i q^{77} +(-4742.27 - 1677.80i) q^{78} +7885.52 q^{79} +(8131.61 - 8131.61i) q^{80} +729.000 q^{81} -9182.36i q^{82} +(-4078.45 + 4078.45i) q^{83} +(2071.73 - 2071.73i) q^{84} +(-11886.7 - 11886.7i) q^{85} +(1665.77 + 1665.77i) q^{86} +4748.08 q^{87} +212.599i q^{88} +(1722.86 + 1722.86i) q^{89} +7339.96i q^{90} +(-1890.32 + 5342.96i) q^{91} +3062.78 q^{92} +(-4552.33 + 4552.33i) q^{93} +24311.0 q^{94} +11307.4i q^{95} +(-5374.15 + 5374.15i) q^{96} +(1560.33 - 1560.33i) q^{97} +(5169.99 + 5169.99i) q^{98} +(870.871 + 870.871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{5} - 24 q^{7} + 540 q^{9} + 372 q^{11} - 224 q^{13} + 480 q^{14} - 252 q^{15} - 2328 q^{16} - 840 q^{19} + 228 q^{20} + 936 q^{21} + 3536 q^{22} - 1404 q^{24} - 828 q^{26} - 1984 q^{28} - 5064 q^{29}+ \cdots + 10044 q^{99}+O(q^{100}) \) 20 * q + 24 * q^5 - 24 * q^7 + 540 * q^9 + 372 * q^11 - 224 * q^13 + 480 * q^14 - 252 * q^15 - 2328 * q^16 - 840 * q^19 + 228 * q^20 + 936 * q^21 + 3536 * q^22 - 1404 * q^24 - 828 * q^26 - 1984 * q^28 - 5064 * q^29 + 1712 * q^31 - 7260 * q^32 - 540 * q^33 + 8040 * q^34 + 5976 * q^35 - 868 * q^37 - 2952 * q^39 + 6336 * q^40 - 6000 * q^41 + 648 * q^42 + 20868 * q^44 + 648 * q^45 - 1992 * q^46 + 1692 * q^47 + 2592 * q^48 + 8952 * q^50 - 12416 * q^52 - 18816 * q^53 - 3280 * q^55 - 9360 * q^57 + 1256 * q^58 - 6588 * q^59 + 9036 * q^60 - 5512 * q^61 - 648 * q^63 + 33048 * q^65 + 13464 * q^66 - 4704 * q^67 - 28296 * q^68 - 31096 * q^70 + 9756 * q^71 + 13692 * q^73 - 28296 * q^74 - 17072 * q^76 - 23868 * q^78 - 5056 * q^79 + 42228 * q^80 + 14580 * q^81 + 24708 * q^83 + 26496 * q^84 - 4752 * q^85 - 77424 * q^86 + 5256 * q^87 + 36000 * q^89 + 19104 * q^91 + 12912 * q^92 - 18432 * q^93 + 112832 * q^94 - 52344 * q^96 + 50012 * q^97 + 11544 * q^98 + 10044 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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