LMFDB - Embedded newform 39.5.g.a.34.3

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			34.3
Root			$4.05053 + 4.05053i$ of defining polynomial
Character	$\chi$	$=$	39.34
Dual form			39.5.g.a.31.3

$q$-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 $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

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

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	−0.999919	−	0.0127141i	$-0.995953\pi$
$2$	−4.05053	−	4.05053i	−1.01263	−	1.01263i	−0.0127141	−	0.999919i	$-0.504047\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$			16.8136i			1.05085i
$5$	33.5573	+	33.5573i	1.34229	+	1.34229i	0.893772	+	0.448521i	$0.148049\pi$
$5$	33.5573	+	33.5573i	1.34229	+	1.34229i	0.448521	+	0.893772i	$0.351951\pi$
$6$	−21.0472	−	21.0472i	−0.584644	−	0.584644i
$7$	23.7132	−	23.7132i	0.483942	−	0.483942i	−0.422446	−	0.906388i	$-0.638828\pi$
$7$	23.7132	−	23.7132i	0.483942	−	0.483942i	0.906388	+	0.422446i	$0.138828\pi$
$8$	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	−0.561149	−	0.827715i	$-0.689641\pi$
$11$	32.2545	−	32.2545i	0.266566	−	0.266566i	0.827715	+	0.561149i	$0.189641\pi$
$12$			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	$0.209973\pi$
$17$			354.222i			1.22568i	−0.790206	+	0.612841i	$0.790027\pi$
$18$	−109.364	−	109.364i	−0.337544	−	0.337544i
$19$	−168.478	−	168.478i	−0.466699	−	0.466699i	0.434145	−	0.900843i	$-0.357051\pi$
$19$	−168.478	−	168.478i	−0.466699	−	0.466699i	−0.900843	+	0.434145i	$0.857051\pi$
$20$	−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	$-0.944921\pi$
$23$		−	182.161i		−	0.344349i	0.985066	−	0.172175i	$-0.0550793\pi$
$24$	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	0.0847522	−	0.996402i	$-0.472990\pi$
$31$	−876.095	−	876.095i	−0.911650	−	0.911650i	−0.996402	+	0.0847522i	$0.972990\pi$
$32$	−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	−0.664751	−	0.747065i	$-0.731462\pi$
$37$	112.687	−	112.687i	0.0823135	−	0.0823135i	0.747065	+	0.664751i	$0.231462\pi$
$38$			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	0.284415	−	0.958701i	$-0.408201\pi$
$41$	−1133.48	−	1133.48i	−0.674287	−	0.674287i	−0.958701	+	0.284415i	$0.908201\pi$
$42$	−998.190			−0.565868
$43$			411.247i			0.222416i	0.993797	+	0.111208i	$0.0354720\pi$
$43$			411.247i			0.222416i	−0.993797	+	0.111208i	$0.964528\pi$
$44$	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	−0.482772	+	0.875746i	$0.660370\pi$
$47$	−3000.97	+	3000.97i	−1.35852	+	1.35852i	−0.875746	+	0.482772i	$0.839630\pi$
$48$	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	−0.421350	−	0.906898i	$-0.638444\pi$
$59$	1690.19	−	1690.19i	0.485547	−	0.485547i	0.906898	+	0.421350i	$0.138444\pi$
$60$	−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	0.350386	−	0.936605i	$-0.386050\pi$
$67$	−2631.54	−	2631.54i	−0.586219	−	0.586219i	−0.936605	+	0.350386i	$0.886050\pi$
$68$	−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	0.736014	−	0.676966i	$-0.236706\pi$
$71$	297.661	+	297.661i	0.0590479	+	0.0590479i	−0.676966	+	0.736014i	$0.736706\pi$
$72$	88.9825	−	88.9825i	0.0171648	−	0.0171648i
$73$	2616.29	−	2616.29i	0.490953	−	0.490953i	−0.417653	−	0.908606i	$-0.637147\pi$
$73$	2616.29	−	2616.29i	0.490953	−	0.490953i	0.908606	+	0.417653i	$0.137147\pi$
$74$	−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	0.346154	−	0.938178i	$-0.387488\pi$
$83$	−4078.45	−	4078.45i	−0.592024	−	0.592024i	−0.938178	+	0.346154i	$0.887488\pi$
$84$	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	−0.589941	−	0.807446i	$-0.700849\pi$
$89$	1722.86	−	1722.86i	0.217505	−	0.217505i	0.807446	+	0.589941i	$0.200849\pi$
$90$		−	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	0.785146	−	0.619311i	$-0.212588\pi$
$97$	1560.33	+	1560.33i	0.165834	+	0.165834i	−0.619311	+	0.785146i	$0.712588\pi$
$98$	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	$-0.837258\pi$
$101$		−	9982.36i		−	0.978567i	0.872125	−	0.489283i	$-0.162742\pi$
$102$	7455.38	−	7455.38i	0.716587	−	0.716587i
$103$			6.56148i			0.000618483i	1.00000		0.000309241i	$9.84346e-5\pi$
$103$			6.56148i			0.000618483i	−1.00000		0.000309241i	$0.999902\pi$
$104$	−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	0.845280	−	0.534324i	$-0.179434\pi$
$109$	3694.46	+	3694.46i	0.310956	+	0.310956i	−0.534324	+	0.845280i	$0.679434\pi$
$110$	−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	$-0.693713\pi$
$127$		−	26466.7i		−	1.64094i	0.571693	−	0.820468i	$-0.306287\pi$
$128$	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	−0.828295	−	0.560292i	$-0.810689\pi$
$137$	−5030.14	+	5030.14i	−0.268002	+	0.268002i	0.560292	+	0.828295i	$0.310689\pi$
$138$	−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	0.444094	−	0.895980i	$-0.353526\pi$
$149$	−10032.3	−	10032.3i	−0.451887	−	0.451887i	−0.895980	+	0.444094i	$0.853526\pi$
$150$	34247.8	−	34247.8i	1.52212	−	1.52212i
$151$	10057.5	−	10057.5i	0.441098	−	0.441098i	−0.451283	−	0.892381i	$-0.649033\pi$
$151$	10057.5	−	10057.5i	0.441098	−	0.441098i	0.892381	+	0.451283i	$0.149033\pi$
$152$	−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	−0.728676	−	0.684859i	$-0.759864\pi$
$163$	−1164.17	+	1164.17i	−0.0438170	+	0.0438170i	0.684859	+	0.728676i	$0.259864\pi$
$164$	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	−0.558999	−	0.829169i	$-0.688814\pi$
$167$	7534.77	−	7534.77i	0.270170	−	0.270170i	0.829169	+	0.558999i	$0.188814\pi$
$168$		−	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	$0.226987\pi$
$173$			39158.0i			1.30836i	−0.756337	+	0.654182i	$0.773013\pi$
$174$	−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	$0.200606\pi$
$179$			37765.1i			1.17865i	−0.807897	+	0.589324i	$0.799394\pi$
$180$	−15234.0	+	15234.0i	−0.470184	+	0.470184i
$181$			9590.57i			0.292744i	0.989230	+	0.146372i	$0.0467596\pi$
$181$			9590.57i			0.292744i	−0.989230	+	0.146372i	$0.953240\pi$
$182$	−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	−0.570255	−	0.821468i	$-0.693155\pi$
$193$	9357.45	−	9357.45i	0.251213	−	0.251213i	0.821468	+	0.570255i	$0.193155\pi$
$194$		−	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	0.647266	−	0.762265i	$-0.275912\pi$
$197$	−4463.00	−	4463.00i	−0.114999	−	0.114999i	−0.762265	+	0.647266i	$0.775912\pi$
$198$	−7054.98			−0.179956
$199$			71326.4i			1.80113i	0.434726	+	0.900563i	$0.356845\pi$
$199$			71326.4i			1.80113i	−0.434726	+	0.900563i	$0.643155\pi$
$200$	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	0.896313	−	0.443421i	$-0.146235\pi$
$223$	22521.9	+	22521.9i	0.452892	+	0.452892i	−0.443421	+	0.896313i	$0.646235\pi$
$224$	−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	0.953856	−	0.300264i	$-0.0970749\pi$
$227$	33678.9	+	33678.9i	0.653592	+	0.653592i	−0.300264	+	0.953856i	$0.597075\pi$
$228$	14719.3	−	14719.3i	0.283151	−	0.283151i
$229$	55067.0	−	55067.0i	1.05008	−	1.05008i	0.0513970	−	0.998678i	$-0.483633\pi$
$229$	55067.0	−	55067.0i	1.05008	−	1.05008i	0.998678	−	0.0513970i	$-0.0163674\pi$
$230$	−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	$-0.980437\pi$
$233$		−	6668.81i		−	0.122839i	0.998112	−	0.0614195i	$-0.0195627\pi$
$234$	−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	0.454431	−	0.890782i	$-0.349842\pi$
$239$	−24924.8	−	24924.8i	−0.436350	−	0.436350i	−0.890782	+	0.454431i	$0.849842\pi$
$240$	42253.1	+	42253.1i	0.733560	+	0.733560i
$241$	4314.21	−	4314.21i	0.0742792	−	0.0742792i	−0.668991	−	0.743270i	$-0.733274\pi$
$241$	4314.21	−	4314.21i	0.0742792	−	0.0742792i	0.743270	+	0.668991i	$0.233274\pi$
$242$	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	$-0.707209\pi$
$251$		−	100235.i		−	1.59100i	0.605954	−	0.795500i	$-0.292791\pi$
$252$	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	$0.0361125\pi$
$257$			14954.5i			0.226415i	−0.993571	+	0.113208i	$0.963887\pi$
$258$	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	−0.0889115	−	0.996040i	$-0.528339\pi$
$271$	66620.4	−	66620.4i	0.907128	−	0.907128i	0.996040	+	0.0889115i	$0.0283388\pi$
$272$			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	$0.151193\pi$
$277$			70180.3i			0.914652i	−0.889299	+	0.457326i	$0.848807\pi$
$278$	−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	−0.824981	−	0.565161i	$-0.808814\pi$
$281$	−20515.7	+	20515.7i	−0.259820	+	0.259820i	0.565161	+	0.824981i	$0.308814\pi$
$282$	126324.			1.58850
$283$		−	30170.2i		−	0.376708i	−0.982101	−	0.188354i	$-0.939685\pi$
$283$		−	30170.2i		−	0.376708i	0.982101	−	0.188354i	$-0.0603153\pi$
$284$	−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	−0.981189	−	0.193050i	$-0.938162\pi$
$293$	−67660.9	+	67660.9i	−0.788139	+	0.788139i	0.193050	+	0.981189i	$0.438162\pi$
$294$	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	−0.0260377	+	0.999661i	$0.508289\pi$
$307$	−96671.1	+	96671.1i	−1.02570	+	1.02570i	−0.999661	+	0.0260377i	$0.991711\pi$
$308$	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	$0.118995\pi$
$311$			70642.4i			0.730373i	−0.930934	+	0.365186i	$0.881005\pi$
$312$	−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	0.807578	+	0.589760i	$0.200778\pi$
$317$	140417.	+	140417.i	1.39734	+	1.39734i	0.589760	+	0.807578i	$0.299222\pi$
$318$	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	0.287585	−	0.957755i	$-0.407148\pi$
$331$	−73424.6	−	73424.6i	−0.670171	−	0.670171i	−0.957755	+	0.287585i	$0.907148\pi$
$332$	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	$-0.979930\pi$
$337$		−	14312.2i		−	0.126022i	0.998013	−	0.0630111i	$-0.0200703\pi$
$338$	−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	−0.786862	−	0.617130i	$-0.788295\pi$
$349$	−20673.5	+	20673.5i	−0.169732	+	0.169732i	0.617130	+	0.786862i	$0.288295\pi$
$350$		−	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	0.365298	−	0.930890i	$-0.380967\pi$
$353$	−70477.9	−	70477.9i	−0.565592	−	0.565592i	−0.930890	+	0.365298i	$0.880967\pi$
$354$	−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	−0.964770	−	0.263096i	$-0.915256\pi$
$359$	−90432.4	+	90432.4i	−0.701674	+	0.701674i	0.263096	+	0.964770i	$0.415256\pi$
$360$	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	0.876531	−	0.481345i	$-0.159852\pi$
$379$	56764.9	+	56764.9i	0.395186	+	0.395186i	−0.481345	+	0.876531i	$0.659852\pi$
$380$	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	0.753719	−	0.657197i	$-0.228258\pi$
$383$	14158.7	+	14158.7i	0.0965218	+	0.0965218i	−0.657197	+	0.753719i	$0.728258\pi$
$384$	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	$-0.984757\pi$
$389$		−	14487.6i		−	0.0957405i	0.998854	−	0.0478703i	$-0.0152434\pi$
$390$	−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	−0.213032	−	0.977045i	$-0.568334\pi$
$397$	120415.	−	120415.i	0.764013	−	0.764013i	0.977045	+	0.213032i	$0.0683339\pi$
$398$	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	−0.601994	−	0.798500i	$-0.705627\pi$
$401$	31598.4	−	31598.4i	0.196506	−	0.196506i	0.798500	+	0.601994i	$0.205627\pi$
$402$			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	0.755233	−	0.655456i	$-0.227523\pi$
$409$	16690.9	+	16690.9i	0.0997776	+	0.0997776i	−0.655456	+	0.755233i	$0.727523\pi$
$410$	−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	0.922994	−	0.384814i	$-0.125734\pi$
$421$	95387.7	+	95387.7i	0.538181	+	0.538181i	−0.384814	+	0.922994i	$0.625734\pi$
$422$	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	0.305583	−	0.952165i	$-0.401149\pi$
$431$	−120110.	−	120110.i	−0.646582	−	0.646582i	−0.952165	+	0.305583i	$0.901149\pi$
$432$	33996.5			0.182166
$433$			104909.i			0.559549i	0.960066	+	0.279774i	$0.0902596\pi$
$433$			104909.i			0.559549i	−0.960066	+	0.279774i	$0.909740\pi$
$434$	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	$0.163368\pi$
$439$			189251.i			0.981997i	−0.871160	+	0.490998i	$0.836632\pi$
$440$	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	−0.559992	−	0.828498i	$-0.689196\pi$
$449$	54131.2	−	54131.2i	0.268507	−	0.268507i	0.828498	+	0.559992i	$0.189196\pi$
$450$	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	0.593436	−	0.804881i	$-0.297771\pi$
$457$	−44160.2	−	44160.2i	−0.211446	−	0.211446i	−0.804881	+	0.593436i	$0.797771\pi$
$458$	−446101.			−2.12668
$459$			49696.0i			0.235883i
$460$	102779.	+	102779.i	0.485723	+	0.485723i
$461$	−145494.	−	145494.i	−0.684610	−	0.684610i	0.276425	−	0.961035i	$-0.410850\pi$
$461$	−145494.	−	145494.i	−0.684610	−	0.684610i	−0.961035	+	0.276425i	$0.910850\pi$
$462$	−32196.1	+	32196.1i	−0.150841	+	0.150841i
$463$	−168589.	+	168589.i	−0.786443	+	0.786443i	−0.980909	−	0.194467i	$-0.937702\pi$
$463$	−168589.	+	168589.i	−0.786443	+	0.786443i	0.194467	+	0.980909i	$0.437702\pi$
$464$	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	$0.122837\pi$
$467$			164176.i			0.752793i	−0.926459	+	0.376397i	$0.877163\pi$
$468$	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	−0.682940	−	0.730474i	$-0.739299\pi$
$479$	10906.2	−	10906.2i	0.0475337	−	0.0475337i	0.730474	+	0.682940i	$0.239299\pi$
$480$		−	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	0.998846	−	0.0480379i	$-0.0152968\pi$
$487$	225502.	+	225502.i	0.950808	+	0.950808i	−0.0480379	+	0.998846i	$0.515297\pi$
$488$	−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	$-0.776347\pi$
$491$		−	311585.i		−	1.29245i	0.763147	−	0.646225i	$-0.223653\pi$
$492$	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	0.710968	−	0.703224i	$-0.248257\pi$
$499$	1928.12	+	1928.12i	0.00774341	+	0.00774341i	−0.703224	+	0.710968i	$0.748257\pi$
$500$	−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	0.878529	−	0.477688i	$-0.158525\pi$
$509$	103850.	+	103850.i	0.400841	+	0.400841i	−0.477688	+	0.878529i	$0.658525\pi$
$510$	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	−0.734235	−	0.678895i	$-0.762459\pi$
$541$	−16197.1	+	16197.1i	−0.0553406	+	0.0553406i	0.678895	+	0.734235i	$0.262459\pi$
$542$	−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	−0.899099	−	0.437745i	$-0.855777\pi$
$557$	−143135.	+	143135.i	−0.461354	+	0.461354i	0.437745	+	0.899099i	$0.355777\pi$
$558$			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	$-0.881310\pi$
$563$		−	230941.i		−	0.728592i	0.931283	−	0.364296i	$-0.118690\pi$
$564$	−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	$-0.877538\pi$
$569$		−	243018.i		−	0.750609i	0.926902	−	0.375305i	$-0.122462\pi$
$570$	−237988.	+	237988.i	−0.732497	+	0.732497i
$571$		−	229921.i		−	0.705189i	−0.935776	−	0.352595i	$-0.885299\pi$
$571$		−	229921.i		−	0.705189i	0.935776	−	0.352595i	$-0.114701\pi$
$572$	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	0.635055	−	0.772467i	$-0.280977\pi$
$577$	−45748.5	−	45748.5i	−0.137412	−	0.137412i	−0.772467	+	0.635055i	$0.780977\pi$
$578$	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	0.389078	−	0.921205i	$-0.372794\pi$
$587$	−183355.	−	183355.i	−0.532127	−	0.532127i	−0.921205	+	0.389078i	$0.872794\pi$
$588$	−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	−0.815674	−	0.578512i	$-0.803634\pi$
$593$	−83397.8	+	83397.8i	−0.237162	+	0.237162i	0.578512	+	0.815674i	$0.303634\pi$
$594$	−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	0.938503	+	0.345272i	$0.112213\pi$
$613$	482403.	+	482403.i	1.28377	+	1.28377i	0.345272	+	0.938503i	$0.387787\pi$
$614$	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	0.863184	−	0.504890i	$-0.168467\pi$
$617$	136398.	+	136398.i	0.358293	+	0.358293i	−0.504890	+	0.863184i	$0.668467\pi$
$618$	138.101	−	138.101i	0.000361592	−	0.000361592i
$619$	130340.	−	130340.i	0.340170	−	0.340170i	−0.516261	−	0.856431i	$-0.672677\pi$
$619$	130340.	−	130340.i	0.340170	−	0.340170i	0.856431	+	0.516261i	$0.172677\pi$
$620$	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	−0.866127	−	0.499825i	$-0.833398\pi$
$631$	−145847.	+	145847.i	−0.366302	+	0.366302i	0.499825	+	0.866127i	$0.333398\pi$
$632$	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	$-0.918556\pi$
$641$		−	207974.i		−	0.506165i	0.967445	−	0.253083i	$-0.0814445\pi$
$642$	130137.	+	130137.i	0.315740	+	0.315740i
$643$	−30795.0	−	30795.0i	−0.0744831	−	0.0744831i	0.668884	−	0.743367i	$-0.266772\pi$
$643$	−30795.0	−	30795.0i	−0.0744831	−	0.0744831i	−0.743367	+	0.668884i	$0.766772\pi$
$644$	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	$-0.916641\pi$
$647$		−	216754.i		−	0.517795i	0.965905	−	0.258898i	$-0.0833592\pi$
$648$	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	0.190187	−	0.981748i	$-0.439091\pi$
$661$	512043.	−	512043.i	1.17194	−	1.17194i	0.981748	−	0.190187i	$-0.0609095\pi$
$662$			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	$0.0247501\pi$
$673$			70363.7i			0.155353i	−0.996979	+	0.0776763i	$0.975250\pi$
$674$	−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	−0.557998	−	0.829842i	$-0.688430\pi$
$683$	126812.	−	126812.i	0.271844	−	0.271844i	0.829842	+	0.557998i	$0.188430\pi$
$684$	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	0.997163	+	0.0752718i	$0.0239824\pi$
$691$	512067.	+	512067.i	1.07243	+	1.07243i	0.0752718	+	0.997163i	$0.476018\pi$
$692$	−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	$-0.738968\pi$
$701$		−	718609.i		−	1.46237i	0.682181	−	0.731184i	$-0.261032\pi$
$702$	−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	−0.968126	−	0.250462i	$-0.919417\pi$
$709$	−360756.	+	360756.i	−0.717664	+	0.717664i	0.250462	+	0.968126i	$0.419417\pi$
$710$	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	$0.261134\pi$
$719$			756213.i			1.46280i	−0.681946	+	0.731402i	$0.738866\pi$
$720$	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	$-0.999251\pi$
$727$		−	2488.50i		−	0.00470835i	0.999997	−	0.00235417i	$-0.000749357\pi$
$728$	−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	0.911824	−	0.410581i	$-0.134674\pi$
$733$	269312.	+	269312.i	0.501243	+	0.501243i	−0.410581	+	0.911824i	$0.634674\pi$
$734$	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	−0.374342	+	0.927291i	$0.622131\pi$
$739$	−710849.	+	710849.i	−1.30163	+	1.30163i	−0.927291	+	0.374342i	$0.877869\pi$
$740$			127161.i			0.232215i
$741$	−197250.	+	69786.4i	−0.359237	+	0.127097i
$742$	812357.			1.47550
$743$	−516575.	−	516575.i	−0.935741	−	0.935741i	0.0623154	−	0.998057i	$-0.480152\pi$
$743$	−516575.	−	516575.i	−0.935741	−	0.935741i	−0.998057	+	0.0623154i	$0.980152\pi$
$744$	−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	$-0.811856\pi$
$751$		−	628582.i		−	1.11450i	0.830343	−	0.557252i	$-0.188144\pi$
$752$	−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	−0.537674	−	0.843153i	$-0.680697\pi$
$761$	176909.	−	176909.i	0.305479	−	0.305479i	0.843153	+	0.537674i	$0.180697\pi$
$762$	−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	0.759740	−	0.650228i	$-0.225326\pi$
$769$	64761.1	+	64761.1i	0.109512	+	0.109512i	−0.650228	+	0.759740i	$0.725326\pi$
$770$	−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	0.759964	−	0.649965i	$-0.225216\pi$
$773$	65728.0	+	65728.0i	0.110000	+	0.110000i	−0.649965	+	0.759964i	$0.725216\pi$
$774$	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	0.528420	−	0.848983i	$-0.322785\pi$
$787$	853121.	−	853121.i	1.37740	−	1.37740i	0.848983	−	0.528420i	$-0.177215\pi$
$788$	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	$-0.933224\pi$
$797$		−	264563.i		−	0.416498i	0.978076	−	0.208249i	$-0.0667765\pi$
$798$	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	0.817446	−	0.576005i	$-0.195389\pi$
$811$	158801.	+	158801.i	0.241442	+	0.241442i	−0.576005	+	0.817446i	$0.695389\pi$
$812$	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	0.988877	−	0.148735i	$-0.0475203\pi$
$821$	566290.	+	566290.i	0.840142	+	0.840142i	−0.148735	+	0.988877i	$0.547520\pi$
$822$	211740.			0.313372
$823$			664034.i			0.980371i	0.871618	+	0.490186i	$0.163071\pi$
$823$			664034.i			0.980371i	−0.871618	+	0.490186i	$0.836929\pi$
$824$	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	−0.0159954	+	0.999872i	$0.505092\pi$
$827$	−694781.	+	694781.i	−1.01587	+	1.01587i	−0.999872	+	0.0159954i	$0.994908\pi$
$828$	82695.2			0.120620
$829$			1.07123e6i			1.55874i	0.626564	+	0.779370i	$0.284461\pi$
$829$			1.07123e6i			1.55874i	−0.626564	+	0.779370i	$0.715539\pi$
$830$	−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	0.00959972	−	0.999954i	$-0.496944\pi$
$839$	710646.	−	710646.i	1.00955	−	1.00955i	0.999954	−	0.00959972i	$-0.00305573\pi$
$840$	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	−0.999932	−	0.0116445i	$-0.996293\pi$
$853$	−719087.	+	719087.i	−0.988288	+	0.988288i	0.0116445	+	0.999932i	$0.496293\pi$
$854$	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	$-0.859916\pi$
$857$		−	625779.i		−	0.852038i	0.904714	−	0.426019i	$-0.140084\pi$
$858$	−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	0.517497	−	0.855685i	$-0.326864\pi$
$863$	−251871.	−	251871.i	−0.338187	−	0.338187i	−0.855685	+	0.517497i	$0.826864\pi$
$864$	−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	0.849946	−	0.526869i	$-0.176634\pi$
$877$	248488.	+	248488.i	0.323077	+	0.323077i	−0.526869	+	0.849946i	$0.676634\pi$
$878$	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	$-0.773379\pi$
$881$		−	1.01415e6i		−	1.30662i	0.757089	−	0.653312i	$-0.226621\pi$
$882$	139590.	−	139590.i	0.179439	−	0.179439i
$883$		−	1.21924e6i		−	1.56375i	−0.623433	−	0.781877i	$-0.714263\pi$
$883$		−	1.21924e6i		−	1.56375i	0.623433	−	0.781877i	$-0.285737\pi$
$884$	−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	$-0.673742\pi$
$907$		−	1.40623e6i		−	1.70940i	0.519124	−	0.854699i	$-0.326258\pi$
$908$	−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	0.980846	−	0.194783i	$-0.0624001\pi$
$929$	678405.	+	678405.i	0.786064	+	0.786064i	−0.194783	+	0.980846i	$0.562400\pi$
$930$	−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	0.930302	−	0.366795i	$-0.119545\pi$
$941$	498975.	+	498975.i	0.563507	+	0.563507i	−0.366795	+	0.930302i	$0.619545\pi$
$942$	−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	−0.974522	−	0.224293i	$-0.927993\pi$
$947$	−672812.	+	672812.i	−0.750228	+	0.750228i	0.224293	+	0.974522i	$0.427993\pi$
$948$			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	$-0.960249\pi$
$953$		−	226250.i		−	0.249117i	0.992212	−	0.124558i	$-0.0397514\pi$
$954$	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	0.266315	−	0.963886i	$-0.414194\pi$
$967$	−652291.	−	652291.i	−0.697571	−	0.697571i	−0.963886	+	0.266315i	$0.914194\pi$
$968$	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	0.139013	−	0.990291i	$-0.455607\pi$
$977$	−812569.	−	812569.i	−0.851278	−	0.851278i	−0.990291	+	0.139013i	$0.955607\pi$
$978$	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	0.509898	−	0.860235i	$-0.329683\pi$
$983$	1.32394e6	−	1.32394e6i	1.37013	−	1.37013i	0.860235	−	0.509898i	$-0.170317\pi$
$984$	−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.34.3	yes	20
3.2	odd	2		117.5.j.b.73.8		20
13.5	odd	4	inner	39.5.g.a.31.3	✓	20
39.5	even	4		117.5.j.b.109.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.5.g.a.31.3	✓	20	13.5	odd	4	inner
39.5.g.a.34.3	yes	20	1.1	even	1	trivial
117.5.j.b.73.8		20	3.2	odd	2
117.5.j.b.109.8		20	39.5	even	4

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

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Database

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