LMFDB - Embedded newform 245.2.l.c.68.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(68,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.68"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.1
Root			$-2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	245.68
Dual form			245.2.l.c.227.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(-2.15988 - 0.578737i) q^{3} +(-0.578737 - 2.15988i) q^{5} +3.16228i q^{6} +(-2.00000 - 2.00000i) q^{8} +(1.73205 + 1.00000i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.58114 + 1.58114i) q^{13} +5.00000i q^{15} +(-2.00000 + 3.46410i) q^{16} +(0.578737 - 2.15988i) q^{17} +(0.732051 - 2.73205i) q^{18} +(-1.58114 + 2.73861i) q^{19} +(1.00000 - 1.00000i) q^{22} +(-2.73205 + 0.732051i) q^{23} +(3.16228 + 5.47723i) q^{24} +(-4.33013 + 2.50000i) q^{25} +(2.73861 + 1.58114i) q^{26} +(1.58114 + 1.58114i) q^{27} -3.00000i q^{29} +(6.83013 - 1.83013i) q^{30} +(2.73861 - 1.58114i) q^{31} +(-0.578737 - 2.15988i) q^{33} -3.16228 q^{34} +(-2.19615 - 8.19615i) q^{37} +(4.31975 + 1.15747i) q^{38} +(4.33013 - 2.50000i) q^{39} +(-3.16228 + 5.47723i) q^{40} -9.48683i q^{41} +(-3.00000 - 3.00000i) q^{43} +(1.15747 - 4.31975i) q^{45} +(2.00000 + 3.46410i) q^{46} +(6.47963 - 1.73621i) q^{47} +(6.32456 - 6.32456i) q^{48} +(5.00000 + 5.00000i) q^{50} +(-2.50000 + 4.33013i) q^{51} +(0.366025 - 1.36603i) q^{53} +(1.58114 - 2.73861i) q^{54} +(1.58114 - 1.58114i) q^{55} +(5.00000 - 5.00000i) q^{57} +(-4.09808 + 1.09808i) q^{58} +(-4.74342 - 8.21584i) q^{59} +(-5.47723 - 3.16228i) q^{61} +(-3.16228 - 3.16228i) q^{62} +8.00000i q^{64} +(4.33013 + 2.50000i) q^{65} +(-2.73861 + 1.58114i) q^{66} +(1.36603 + 0.366025i) q^{67} +6.32456 q^{69} -6.00000 q^{71} +(-1.46410 - 5.46410i) q^{72} +(-10.3923 + 6.00000i) q^{74} +(10.7994 - 2.89368i) q^{75} +(-5.00000 - 5.00000i) q^{78} +(11.2583 + 6.50000i) q^{79} +(8.63950 + 2.31495i) q^{80} +(-5.50000 - 9.52628i) q^{81} +(-12.9593 + 3.47242i) q^{82} +(-3.16228 + 3.16228i) q^{83} -5.00000 q^{85} +(-3.00000 + 5.19615i) q^{86} +(-1.73621 + 6.47963i) q^{87} +(0.732051 - 2.73205i) q^{88} +(3.16228 - 5.47723i) q^{89} -6.32456 q^{90} +(-6.83013 + 1.83013i) q^{93} +(-4.74342 - 8.21584i) q^{94} +(6.83013 + 1.83013i) q^{95} +(-1.58114 - 1.58114i) q^{97} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 16 q^{8} + 4 q^{11} - 16 q^{16} - 8 q^{18} + 8 q^{22} - 8 q^{23} + 20 q^{30} + 24 q^{37} - 24 q^{43} + 16 q^{46} + 40 q^{50} - 20 q^{51} - 4 q^{53} + 40 q^{57} - 12 q^{58} + 4 q^{67} - 48 q^{71}+ \cdots + 20 q^{95}+O(q^{100}) $ 8 * q + 4 * q^2 - 16 * q^8 + 4 * q^11 - 16 * q^16 - 8 * q^18 + 8 * q^22 - 8 * q^23 + 20 * q^30 + 24 * q^37 - 24 * q^43 + 16 * q^46 + 40 * q^50 - 20 * q^51 - 4 * q^53 + 40 * q^57 - 12 * q^58 + 4 * q^67 - 48 * q^71 + 16 * q^72 - 40 * q^78 - 44 * q^81 - 40 * q^85 - 24 * q^86 - 8 * q^88 - 20 * q^93 + 20 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$3$	−2.15988	−	0.578737i	−1.24700	−	0.334134i	−0.425826	−	0.904805i	$-0.640016\pi$
$3$	−2.15988	−	0.578737i	−1.24700	−	0.334134i	−0.821179	+	0.570671i	$0.806683\pi$
$4$		0			0
$5$	−0.578737	−	2.15988i	−0.258819	−	0.965926i
$5$	−0.578737	−	2.15988i	−0.258819	−	0.965926i
$6$			3.16228i			1.29099i
$7$		0			0
$7$		0			0
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	1.73205	+	1.00000i	0.577350	+	0.333333i
$10$	−2.73861	+	1.58114i	−0.866025	+	0.500000i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	−1.58114	+	1.58114i	−0.438529	+	0.438529i	−0.891517	−	0.452988i	$-0.850358\pi$
$13$	−1.58114	+	1.58114i	−0.438529	+	0.438529i	0.452988	+	0.891517i	$0.350358\pi$
$14$		0			0
$15$			5.00000i			1.29099i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	0.578737	−	2.15988i	0.140364	−	0.523847i	−0.859554	−	0.511045i	$-0.829258\pi$
$17$	0.578737	−	2.15988i	0.140364	−	0.523847i	0.999918	−	0.0128014i	$-0.00407493\pi$
$18$	0.732051	−	2.73205i	0.172546	−	0.643951i
$19$	−1.58114	+	2.73861i	−0.362738	+	0.628281i	−0.988410	−	0.151805i	$-0.951491\pi$
$19$	−1.58114	+	2.73861i	−0.362738	+	0.628281i	0.625672	+	0.780086i	$0.284825\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−2.73205	+	0.732051i	−0.569672	+	0.152643i	−0.532146	−	0.846653i	$-0.678614\pi$
$23$	−2.73205	+	0.732051i	−0.569672	+	0.152643i	−0.0375258	+	0.999296i	$0.511948\pi$
$24$	3.16228	+	5.47723i	0.645497	+	1.11803i
$25$	−4.33013	+	2.50000i	−0.866025	+	0.500000i
$26$	2.73861	+	1.58114i	0.537086	+	0.310087i
$27$	1.58114	+	1.58114i	0.304290	+	0.304290i
$28$		0			0
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	6.83013	−	1.83013i	1.24700	−	0.334134i
$31$	2.73861	−	1.58114i	0.491869	−	0.283981i	−0.233480	−	0.972362i	$-0.575011\pi$
$31$	2.73861	−	1.58114i	0.491869	−	0.283981i	0.725350	+	0.688381i	$0.241678\pi$
$32$		0			0
$33$	−0.578737	−	2.15988i	−0.100745	−	0.375986i
$34$	−3.16228			−0.542326
$35$		0			0
$36$		0			0
$37$	−2.19615	−	8.19615i	−0.361045	−	1.34744i	−0.872704	−	0.488250i	$-0.837635\pi$
$37$	−2.19615	−	8.19615i	−0.361045	−	1.34744i	0.511658	−	0.859189i	$-0.329031\pi$
$38$	4.31975	+	1.15747i	0.700756	+	0.187767i
$39$	4.33013	−	2.50000i	0.693375	−	0.400320i
$40$	−3.16228	+	5.47723i	−0.500000	+	0.866025i
$41$		−	9.48683i		−	1.48159i	−0.671729	−	0.740797i	$-0.734448\pi$
$41$		−	9.48683i		−	1.48159i	0.671729	−	0.740797i	$-0.265552\pi$
$42$		0			0
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	0.440337	−	0.897833i	$-0.354859\pi$
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	−0.897833	+	0.440337i	$0.854859\pi$
$44$		0			0
$45$	1.15747	−	4.31975i	0.172546	−	0.643951i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	6.47963	−	1.73621i	0.945151	−	0.253252i	0.246847	−	0.969054i	$-0.420605\pi$
$47$	6.47963	−	1.73621i	0.945151	−	0.253252i	0.698303	+	0.715802i	$0.253939\pi$
$48$	6.32456	−	6.32456i	0.912871	−	0.912871i
$49$		0			0
$50$	5.00000	+	5.00000i	0.707107	+	0.707107i
$51$	−2.50000	+	4.33013i	−0.350070	+	0.606339i
$52$		0			0
$53$	0.366025	−	1.36603i	0.0502775	−	0.187638i	−0.936220	−	0.351414i	$-0.885701\pi$
$53$	0.366025	−	1.36603i	0.0502775	−	0.187638i	0.986498	+	0.163776i	$0.0523675\pi$
$54$	1.58114	−	2.73861i	0.215166	−	0.372678i
$55$	1.58114	−	1.58114i	0.213201	−	0.213201i
$56$		0			0
$57$	5.00000	−	5.00000i	0.662266	−	0.662266i
$58$	−4.09808	+	1.09808i	−0.538104	+	0.144184i
$59$	−4.74342	−	8.21584i	−0.617540	−	1.06961i	−0.989933	−	0.141536i	$-0.954796\pi$
$59$	−4.74342	−	8.21584i	−0.617540	−	1.06961i	0.372393	−	0.928075i	$-0.378537\pi$
$60$		0			0
$61$	−5.47723	−	3.16228i	−0.701287	−	0.404888i	0.106540	−	0.994308i	$-0.466023\pi$
$61$	−5.47723	−	3.16228i	−0.701287	−	0.404888i	−0.807827	+	0.589420i	$0.799356\pi$
$62$	−3.16228	−	3.16228i	−0.401610	−	0.401610i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	4.33013	+	2.50000i	0.537086	+	0.310087i
$66$	−2.73861	+	1.58114i	−0.337100	+	0.194625i
$67$	1.36603	+	0.366025i	0.166887	+	0.0447171i	0.341295	−	0.939956i	$-0.389135\pi$
$67$	1.36603	+	0.366025i	0.166887	+	0.0447171i	−0.174408	+	0.984673i	$0.555801\pi$
$68$		0			0
$69$	6.32456			0.761387
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.46410	−	5.46410i	−0.172546	−	0.643951i
$73$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$73$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$74$	−10.3923	+	6.00000i	−1.20808	+	0.697486i
$75$	10.7994	−	2.89368i	1.24700	−	0.334134i
$76$		0			0
$77$		0			0
$78$	−5.00000	−	5.00000i	−0.566139	−	0.566139i
$79$	11.2583	+	6.50000i	1.26666	+	0.731307i	0.974355	−	0.225018i	$-0.0722440\pi$
$79$	11.2583	+	6.50000i	1.26666	+	0.731307i	0.292306	+	0.956325i	$0.405577\pi$
$80$	8.63950	+	2.31495i	0.965926	+	0.258819i
$81$	−5.50000	−	9.52628i	−0.611111	−	1.05848i
$82$	−12.9593	+	3.47242i	−1.43111	+	0.383465i
$83$	−3.16228	+	3.16228i	−0.347105	+	0.347105i	−0.859030	−	0.511925i	$-0.828933\pi$
$83$	−3.16228	+	3.16228i	−0.347105	+	0.347105i	0.511925	+	0.859030i	$0.328933\pi$
$84$		0			0
$85$	−5.00000			−0.542326
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$	−1.73621	+	6.47963i	−0.186141	+	0.694689i
$88$	0.732051	−	2.73205i	0.0780369	−	0.291238i
$89$	3.16228	−	5.47723i	0.335201	−	0.580585i	−0.648323	−	0.761366i	$-0.724529\pi$
$89$	3.16228	−	5.47723i	0.335201	−	0.580585i	0.983523	+	0.180781i	$0.0578625\pi$
$90$	−6.32456			−0.666667
$91$		0			0
$92$		0			0
$93$	−6.83013	+	1.83013i	−0.708251	+	0.189775i
$94$	−4.74342	−	8.21584i	−0.489246	−	0.847399i
$95$	6.83013	+	1.83013i	0.700756	+	0.187767i
$96$		0			0
$97$	−1.58114	−	1.58114i	−0.160540	−	0.160540i	0.622266	−	0.782806i	$-0.286212\pi$
$97$	−1.58114	−	1.58114i	−0.160540	−	0.160540i	−0.782806	+	0.622266i	$0.786212\pi$
$98$		0			0
$99$			2.00000i			0.201008i
$100$		0			0
$101$	−2.73861	+	1.58114i	−0.272502	+	0.157329i	−0.630024	−	0.776576i	$-0.716955\pi$
$101$	−2.73861	+	1.58114i	−0.272502	+	0.157329i	0.357522	+	0.933905i	$0.383622\pi$
$102$	6.83013	+	1.83013i	0.676283	+	0.181210i
$103$	4.05116	+	15.1191i	0.399173	+	1.48973i	0.814556	+	0.580086i	$0.196981\pi$
$103$	4.05116	+	15.1191i	0.399173	+	1.48973i	−0.415383	+	0.909647i	$0.636352\pi$
$104$	6.32456			0.620174
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−1.09808	−	4.09808i	−0.106155	−	0.396176i	0.892319	−	0.451406i	$-0.149077\pi$
$107$	−1.09808	−	4.09808i	−0.106155	−	0.396176i	−0.998474	+	0.0552301i	$0.982411\pi$
$108$		0			0
$109$	6.06218	−	3.50000i	0.580651	−	0.335239i	−0.180741	−	0.983531i	$-0.557850\pi$
$109$	6.06218	−	3.50000i	0.580651	−	0.335239i	0.761392	+	0.648292i	$0.224516\pi$
$110$	−2.73861	−	1.58114i	−0.261116	−	0.150756i
$111$			18.9737i			1.80090i
$112$		0			0
$113$	12.0000	+	12.0000i	1.12887	+	1.12887i	0.990362	+	0.138503i	$0.0442291\pi$
$113$	12.0000	+	12.0000i	1.12887	+	1.12887i	0.138503	+	0.990362i	$0.455771\pi$
$114$	−8.66025	−	5.00000i	−0.811107	−	0.468293i
$115$	3.16228	+	5.47723i	0.294884	+	0.510754i
$116$		0			0
$117$	−4.31975	+	1.15747i	−0.399361	+	0.107009i
$118$	−9.48683	+	9.48683i	−0.873334	+	0.873334i
$119$		0			0
$120$	10.0000	−	10.0000i	0.912871	−	0.912871i
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−2.31495	+	8.63950i	−0.209586	+	0.782184i
$123$	−5.49038	+	20.4904i	−0.495051	+	1.84756i
$124$		0			0
$125$	7.90569	+	7.90569i	0.707107	+	0.707107i
$126$		0			0
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$	4.74342	+	8.21584i	0.417635	+	0.723364i
$130$	1.83013	−	6.83013i	0.160513	−	0.599042i
$131$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$131$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$132$		0			0
$133$		0			0
$134$		−	2.00000i		−	0.172774i
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$	−5.47723	+	3.16228i	−0.469668	+	0.271163i
$137$	−2.73205	−	0.732051i	−0.233415	−	0.0625433i	0.140215	−	0.990121i	$-0.455220\pi$
$137$	−2.73205	−	0.732051i	−0.233415	−	0.0625433i	−0.373630	+	0.927578i	$0.621887\pi$
$138$	−2.31495	−	8.63950i	−0.197061	−	0.735443i
$139$	−18.9737			−1.60933			−0.804663	−	0.593732i	$-0.797654\pi$
$139$	−18.9737			−1.60933			−0.804663	+	0.593732i	$0.797654\pi$
$140$		0			0
$141$	−15.0000			−1.26323
$142$	2.19615	+	8.19615i	0.184297	+	0.687806i
$143$	−2.15988	−	0.578737i	−0.180618	−	0.0483964i
$144$	−6.92820	+	4.00000i	−0.577350	+	0.333333i
$145$	−6.47963	+	1.73621i	−0.538104	+	0.144184i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.3923	−	6.00000i	−0.851371	−	0.491539i	0.00974235	−	0.999953i	$-0.496899\pi$
$149$	−10.3923	−	6.00000i	−0.851371	−	0.491539i	−0.861113	+	0.508413i	$0.830232\pi$
$150$	−7.90569	−	13.6931i	−0.645497	−	1.11803i
$151$	−4.50000	−	7.79423i	−0.366205	−	0.634285i	0.622764	−	0.782410i	$-0.286010\pi$
$151$	−4.50000	−	7.79423i	−0.366205	−	0.634285i	−0.988969	+	0.148124i	$0.952676\pi$
$152$	8.63950	−	2.31495i	0.700756	−	0.187767i
$153$	3.16228	−	3.16228i	0.255655	−	0.255655i
$154$		0			0
$155$	−5.00000	−	5.00000i	−0.401610	−	0.401610i
$156$		0			0
$157$	2.31495	−	8.63950i	0.184753	−	0.689507i	−0.809930	−	0.586526i	$-0.800495\pi$
$157$	2.31495	−	8.63950i	0.184753	−	0.689507i	0.994683	−	0.102981i	$-0.0328382\pi$
$158$	4.75833	−	17.7583i	0.378552	−	1.41278i
$159$	−1.58114	+	2.73861i	−0.125392	+	0.217186i
$160$		0			0
$161$		0			0
$162$	−11.0000	+	11.0000i	−0.864242	+	0.864242i
$163$	−8.19615	+	2.19615i	−0.641972	+	0.172016i	−0.565097	−	0.825025i	$-0.691161\pi$
$163$	−8.19615	+	2.19615i	−0.641972	+	0.172016i	−0.0768756	+	0.997041i	$0.524494\pi$
$164$		0			0
$165$	−4.33013	+	2.50000i	−0.337100	+	0.194625i
$166$	5.47723	+	3.16228i	0.425115	+	0.245440i
$167$	11.0680	+	11.0680i	0.856465	+	0.856465i	0.990920	−	0.134454i	$-0.0429282\pi$
$167$	11.0680	+	11.0680i	0.856465	+	0.856465i	−0.134454	+	0.990920i	$0.542928\pi$
$168$		0			0
$169$			8.00000i			0.615385i
$170$	1.83013	+	6.83013i	0.140364	+	0.523847i
$171$	−5.47723	+	3.16228i	−0.418854	+	0.241825i
$172$		0			0
$173$	−4.05116	−	15.1191i	−0.308004	−	1.14949i	−0.930329	−	0.366727i	$-0.880478\pi$
$173$	−4.05116	−	15.1191i	−0.308004	−	1.14949i	0.622325	−	0.782759i	$-0.286188\pi$
$174$	9.48683			0.719195
$175$		0			0
$176$	−4.00000			−0.301511
$177$	5.49038	+	20.4904i	0.412682	+	1.54015i
$178$	−8.63950	−	2.31495i	−0.647558	−	0.173513i
$179$	5.19615	−	3.00000i	0.388379	−	0.224231i	−0.293079	−	0.956088i	$-0.594680\pi$
$179$	5.19615	−	3.00000i	0.388379	−	0.224231i	0.681457	+	0.731858i	$0.261346\pi$
$180$		0			0
$181$		−	22.1359i		−	1.64535i	−0.568511	−	0.822676i	$-0.692480\pi$
$181$		−	22.1359i		−	1.64535i	0.568511	−	0.822676i	$-0.307520\pi$
$182$		0			0
$183$	10.0000	+	10.0000i	0.739221	+	0.739221i
$184$	6.92820	+	4.00000i	0.510754	+	0.294884i
$185$	−16.4317	+	9.48683i	−1.20808	+	0.697486i
$186$	5.00000	+	8.66025i	0.366618	+	0.635001i
$187$	2.15988	−	0.578737i	0.157946	−	0.0423214i
$188$		0			0
$189$		0			0
$190$		−	10.0000i		−	0.725476i
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	−0.806641	−	0.591041i	$-0.798717\pi$
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	0.915177	+	0.403051i	$0.132050\pi$
$192$	4.62990	−	17.2790i	0.334134	−	1.24700i
$193$	−2.92820	+	10.9282i	−0.210777	+	0.786629i	0.776834	+	0.629705i	$0.216824\pi$
$193$	−2.92820	+	10.9282i	−0.210777	+	0.786629i	−0.987611	+	0.156924i	$0.949842\pi$
$194$	−1.58114	+	2.73861i	−0.113519	+	0.196621i
$195$	−7.90569	−	7.90569i	−0.566139	−	0.566139i
$196$		0			0
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	−0.741832	−	0.670585i	$-0.766043\pi$
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	0.670585	+	0.741832i	$0.266043\pi$
$198$	2.73205	−	0.732051i	0.194158	−	0.0520246i
$199$	4.74342	+	8.21584i	0.336252	+	0.582405i	0.983724	−	0.179683i	$-0.0575073\pi$
$199$	4.74342	+	8.21584i	0.336252	+	0.582405i	−0.647473	+	0.762089i	$0.724174\pi$
$200$	13.6603	+	3.66025i	0.965926	+	0.258819i
$201$	−2.73861	−	1.58114i	−0.193167	−	0.111525i
$202$	3.16228	+	3.16228i	0.222497	+	0.222497i
$203$		0			0
$204$		0			0
$205$	−20.4904	+	5.49038i	−1.43111	+	0.383465i
$206$	19.1703	−	11.0680i	1.33566	−	0.771142i
$207$	−5.46410	−	1.46410i	−0.379781	−	0.101762i
$208$	−2.31495	−	8.63950i	−0.160513	−	0.599042i
$209$	−3.16228			−0.218739
$210$		0			0
$211$	17.0000			1.17033			0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000			1.17033			0.585164	+	0.810915i	$0.301030\pi$
$212$		0			0
$213$	12.9593	+	3.47242i	0.887954	+	0.237926i
$214$	−5.19615	+	3.00000i	−0.355202	+	0.205076i
$215$	−4.74342	+	8.21584i	−0.323498	+	0.560316i
$216$		−	6.32456i		−	0.430331i
$217$		0			0
$218$	−7.00000	−	7.00000i	−0.474100	−	0.474100i
$219$		0			0
$220$		0			0
$221$	2.50000	+	4.33013i	0.168168	+	0.291276i
$222$	25.9185	−	6.94484i	1.73954	−	0.466107i
$223$	14.2302	−	14.2302i	0.952928	−	0.952928i	−0.0460129	−	0.998941i	$-0.514652\pi$
$223$	14.2302	−	14.2302i	0.952928	−	0.952928i	0.998941	+	0.0460129i	$0.0146515\pi$
$224$		0			0
$225$	−10.0000			−0.666667
$226$	12.0000	−	20.7846i	0.798228	−	1.38257i
$227$	−0.578737	+	2.15988i	−0.0384121	+	0.143356i	−0.982469	−	0.186427i	$-0.940309\pi$
$227$	−0.578737	+	2.15988i	−0.0384121	+	0.143356i	0.944057	+	0.329783i	$0.106976\pi$
$228$		0			0
$229$	−7.90569	+	13.6931i	−0.522423	+	0.904863i	0.477237	+	0.878775i	$0.341638\pi$
$229$	−7.90569	+	13.6931i	−0.522423	+	0.904863i	−0.999660	+	0.0260883i	$0.991695\pi$
$230$	6.32456	−	6.32456i	0.417029	−	0.417029i
$231$		0			0
$232$	−6.00000	+	6.00000i	−0.393919	+	0.393919i
$233$	24.5885	−	6.58846i	1.61084	−	0.431624i	0.662550	−	0.749018i	$-0.269474\pi$
$233$	24.5885	−	6.58846i	1.61084	−	0.431624i	0.948294	+	0.317394i	$0.102808\pi$
$234$	3.16228	+	5.47723i	0.206725	+	0.358057i
$235$	−7.50000	−	12.9904i	−0.489246	−	0.847399i
$236$		0			0
$237$	−20.5548	−	20.5548i	−1.33518	−	1.33518i
$238$		0			0
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$	−17.3205	−	10.0000i	−1.11803	−	0.645497i
$241$	21.9089	−	12.6491i	1.41128	−	0.814801i	0.415768	−	0.909471i	$-0.363513\pi$
$241$	21.9089	−	12.6491i	1.41128	−	0.814801i	0.995509	+	0.0946700i	$0.0301796\pi$
$242$	−13.6603	−	3.66025i	−0.878114	−	0.235290i
$243$	4.62990	+	17.2790i	0.297008	+	1.10845i
$244$		0			0
$245$		0			0
$246$	30.0000			1.91273
$247$	−1.83013	−	6.83013i	−0.116448	−	0.434591i
$248$	−8.63950	−	2.31495i	−0.548609	−	0.146999i
$249$	8.66025	−	5.00000i	0.548821	−	0.316862i
$250$	7.90569	−	13.6931i	0.500000	−	0.866025i
$251$			12.6491i			0.798405i	0.916863	+	0.399202i	$0.130713\pi$
$251$			12.6491i			0.798405i	−0.916863	+	0.399202i	$0.869287\pi$
$252$		0			0
$253$	−2.00000	−	2.00000i	−0.125739	−	0.125739i
$254$	−15.5885	−	9.00000i	−0.978107	−	0.564710i
$255$	10.7994	+	2.89368i	0.676283	+	0.181210i
$256$		0			0
$257$	−17.2790	+	4.62990i	−1.07783	+	0.288805i	−0.753709	−	0.657209i	$-0.771737\pi$
$257$	−17.2790	+	4.62990i	−1.07783	+	0.288805i	−0.324126	+	0.946014i	$0.605070\pi$
$258$	9.48683	−	9.48683i	0.590624	−	0.590624i
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	2.56218	−	9.56218i	0.157991	−	0.589629i	−0.840840	−	0.541284i	$-0.817939\pi$
$263$	2.56218	−	9.56218i	0.157991	−	0.589629i	0.998831	−	0.0483454i	$-0.0153948\pi$
$264$	−3.16228	+	5.47723i	−0.194625	+	0.337100i
$265$	−3.16228			−0.194257
$266$		0			0
$267$	−10.0000	+	10.0000i	−0.611990	+	0.611990i
$268$		0			0
$269$	9.48683	+	16.4317i	0.578422	+	1.00186i	0.995661	+	0.0930598i	$0.0296648\pi$
$269$	9.48683	+	16.4317i	0.578422	+	1.00186i	−0.417238	+	0.908797i	$0.637002\pi$
$270$	−6.83013	−	1.83013i	−0.415668	−	0.111378i
$271$	10.9545	+	6.32456i	0.665436	+	0.384189i	0.794345	−	0.607467i	$-0.207814\pi$
$271$	10.9545	+	6.32456i	0.665436	+	0.384189i	−0.128909	+	0.991656i	$0.541148\pi$
$272$	6.32456	+	6.32456i	0.383482	+	0.383482i
$273$		0			0
$274$			4.00000i			0.241649i
$275$	−4.33013	−	2.50000i	−0.261116	−	0.150756i
$276$		0			0
$277$	24.5885	+	6.58846i	1.47738	+	0.395862i	0.905454	−	0.424445i	$-0.139531\pi$
$277$	24.5885	+	6.58846i	1.47738	+	0.395862i	0.571923	+	0.820307i	$0.306197\pi$
$278$	6.94484	+	25.9185i	0.416524	+	1.55449i
$279$	6.32456			0.378641
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	5.49038	+	20.4904i	0.326947	+	1.22018i
$283$	6.47963	+	1.73621i	0.385174	+	0.103207i	0.446209	−	0.894929i	$-0.352774\pi$
$283$	6.47963	+	1.73621i	0.385174	+	0.103207i	−0.0610356	+	0.998136i	$0.519440\pi$
$284$		0			0
$285$	−13.6931	−	7.90569i	−0.811107	−	0.468293i
$286$			3.16228i			0.186989i
$287$		0			0
$288$		0			0
$289$	10.3923	+	6.00000i	0.611312	+	0.352941i
$290$	4.74342	+	8.21584i	0.278543	+	0.482451i
$291$	2.50000	+	4.33013i	0.146553	+	0.253837i
$292$		0			0
$293$	−7.90569	+	7.90569i	−0.461856	+	0.461856i	−0.899263	−	0.437408i	$-0.855897\pi$
$293$	−7.90569	+	7.90569i	−0.461856	+	0.461856i	0.437408	+	0.899263i	$0.355897\pi$
$294$		0			0
$295$	−15.0000	+	15.0000i	−0.873334	+	0.873334i
$296$	−12.0000	+	20.7846i	−0.697486	+	1.20808i
$297$	−0.578737	+	2.15988i	−0.0335817	+	0.125329i
$298$	−4.39230	+	16.3923i	−0.254439	+	0.949581i
$299$	3.16228	−	5.47723i	0.182879	−	0.316756i
$300$		0			0
$301$		0			0
$302$	−9.00000	+	9.00000i	−0.517892	+	0.517892i
$303$	6.83013	−	1.83013i	0.392381	−	0.105138i
$304$	−6.32456	−	10.9545i	−0.362738	−	0.628281i
$305$	−3.66025	+	13.6603i	−0.209586	+	0.782184i
$306$	−5.47723	−	3.16228i	−0.313112	−	0.180775i
$307$	−4.74342	−	4.74342i	−0.270721	−	0.270721i	0.558669	−	0.829390i	$-0.311312\pi$
$307$	−4.74342	−	4.74342i	−0.270721	−	0.270721i	−0.829390	+	0.558669i	$0.811312\pi$
$308$		0			0
$309$		−	35.0000i		−	1.99108i
$310$	−5.00000	+	8.66025i	−0.283981	+	0.491869i
$311$	−19.1703	+	11.0680i	−1.08705	+	0.627607i	−0.932789	−	0.360423i	$-0.882632\pi$
$311$	−19.1703	+	11.0680i	−1.08705	+	0.627607i	−0.154259	+	0.988031i	$0.549299\pi$
$312$	−13.6603	−	3.66025i	−0.773360	−	0.207221i
$313$	−5.20863	−	19.4389i	−0.294409	−	1.09875i	−0.941685	−	0.336495i	$-0.890759\pi$
$313$	−5.20863	−	19.4389i	−0.294409	−	1.09875i	0.647276	−	0.762256i	$-0.275908\pi$
$314$	−12.6491			−0.713831
$315$		0			0
$316$		0			0
$317$	6.95448	+	25.9545i	0.390603	+	1.45775i	0.829143	+	0.559037i	$0.188829\pi$
$317$	6.95448	+	25.9545i	0.390603	+	1.45775i	−0.438540	+	0.898712i	$0.644504\pi$
$318$	4.31975	+	1.15747i	0.242240	+	0.0649079i
$319$	2.59808	−	1.50000i	0.145464	−	0.0839839i
$320$	17.2790	−	4.62990i	0.965926	−	0.258819i
$321$			9.48683i			0.529503i
$322$		0			0
$323$	5.00000	+	5.00000i	0.278207	+	0.278207i
$324$		0			0
$325$	2.89368	−	10.7994i	0.160513	−	0.599042i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	−15.1191	+	4.05116i	−0.836090	+	0.224030i
$328$	−18.9737	+	18.9737i	−1.04765	+	1.04765i
$329$		0			0
$330$	5.00000	+	5.00000i	0.275241	+	0.275241i
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	−0.771723	−	0.635959i	$-0.780605\pi$
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	0.936618	+	0.350352i	$0.113938\pi$
$332$		0			0
$333$	4.39230	−	16.3923i	0.240697	−	0.898293i
$334$	11.0680	−	19.1703i	0.605612	−	1.04895i
$335$		−	3.16228i		−	0.172774i
$336$		0			0
$337$	−8.00000	+	8.00000i	−0.435788	+	0.435788i	−0.890592	−	0.454804i	$-0.849709\pi$
$337$	−8.00000	+	8.00000i	−0.435788	+	0.435788i	0.454804	+	0.890592i	$0.349709\pi$
$338$	10.9282	−	2.92820i	0.594416	−	0.159273i
$339$	−18.9737	−	32.8634i	−1.03051	−	1.78489i
$340$		0			0
$341$	2.73861	+	1.58114i	0.148304	+	0.0856235i
$342$	6.32456	+	6.32456i	0.341993	+	0.341993i
$343$		0			0
$344$			12.0000i			0.646997i
$345$	−3.66025	−	13.6603i	−0.197061	−	0.735443i
$346$	−19.1703	+	11.0680i	−1.03060	+	0.595018i
$347$	−32.7846	−	8.78461i	−1.75997	−	0.471583i	−0.773262	−	0.634086i	$-0.781376\pi$
$347$	−32.7846	−	8.78461i	−1.75997	−	0.471583i	−0.986708	+	0.162504i	$0.948043\pi$
$348$		0			0
$349$	34.7851			1.86200			0.931001	−	0.365018i	$-0.118937\pi$
$349$	34.7851			1.86200			0.931001	+	0.365018i	$0.118937\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$		0			0
$353$	−19.4389	−	5.20863i	−1.03463	−	0.277228i	−0.298742	−	0.954334i	$-0.596567\pi$
$353$	−19.4389	−	5.20863i	−1.03463	−	0.277228i	−0.735885	+	0.677106i	$0.763234\pi$
$354$	25.9808	−	15.0000i	1.38086	−	0.797241i
$355$	3.47242	+	12.9593i	0.184297	+	0.687806i
$356$		0			0
$357$		0			0
$358$	−6.00000	−	6.00000i	−0.317110	−	0.317110i
$359$	−19.0526	−	11.0000i	−1.00556	−	0.580558i	−0.0956683	−	0.995413i	$-0.530499\pi$
$359$	−19.0526	−	11.0000i	−1.00556	−	0.580558i	−0.909887	+	0.414855i	$0.863832\pi$
$360$	−10.9545	+	6.32456i	−0.577350	+	0.333333i
$361$	4.50000	+	7.79423i	0.236842	+	0.410223i
$362$	−30.2383	+	8.10232i	−1.58929	+	0.425848i
$363$	−15.8114	+	15.8114i	−0.829883	+	0.829883i
$364$		0			0
$365$		0			0
$366$	10.0000	−	17.3205i	0.522708	−	0.905357i
$367$	−6.36611	+	23.7586i	−0.332308	+	1.24019i	0.574450	+	0.818540i	$0.305216\pi$
$367$	−6.36611	+	23.7586i	−0.332308	+	1.24019i	−0.906758	+	0.421651i	$0.861451\pi$
$368$	2.92820	−	10.9282i	0.152643	−	0.569672i
$369$	9.48683	−	16.4317i	0.493865	−	0.855399i
$370$	18.9737	+	18.9737i	0.986394	+	0.986394i
$371$		0			0
$372$		0			0
$373$	−16.3923	+	4.39230i	−0.848761	+	0.227425i	−0.656882	−	0.753994i	$-0.728125\pi$
$373$	−16.3923	+	4.39230i	−0.848761	+	0.227425i	−0.191880	+	0.981418i	$0.561458\pi$
$374$	−1.58114	−	2.73861i	−0.0817587	−	0.141610i
$375$	−12.5000	−	21.6506i	−0.645497	−	1.11803i
$376$	−16.4317	−	9.48683i	−0.847399	−	0.489246i
$377$	4.74342	+	4.74342i	0.244298	+	0.244298i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$	−24.6475	+	14.2302i	−1.26273	+	0.729038i
$382$	−4.09808	−	1.09808i	−0.209676	−	0.0561825i
$383$	−5.78737	−	21.5988i	−0.295721	−	1.10364i	−0.940643	−	0.339397i	$-0.889777\pi$
$383$	−5.78737	−	21.5988i	−0.295721	−	1.10364i	0.644922	−	0.764248i	$-0.276890\pi$
$384$	−25.2982			−1.29099
$385$		0			0
$386$	16.0000			0.814379
$387$	−2.19615	−	8.19615i	−0.111637	−	0.416634i
$388$		0			0
$389$	−19.9186	+	11.5000i	−1.00991	+	0.583073i	−0.911166	−	0.412039i	$-0.864817\pi$
$389$	−19.9186	+	11.5000i	−1.00991	+	0.583073i	−0.0987463	+	0.995113i	$0.531483\pi$
$390$	−7.90569	+	13.6931i	−0.400320	+	0.693375i
$391$			6.32456i			0.319847i
$392$		0			0
$393$		0			0
$394$	1.73205	+	1.00000i	0.0872595	+	0.0503793i
$395$	7.52358	−	28.0784i	0.378552	−	1.41278i
$396$		0			0
$397$	32.3981	−	8.68105i	1.62602	−	0.435690i	0.673255	−	0.739411i	$-0.264896\pi$
$397$	32.3981	−	8.68105i	1.62602	−	0.435690i	0.952761	+	0.303721i	$0.0982290\pi$
$398$	9.48683	−	9.48683i	0.475532	−	0.475532i
$399$		0			0
$400$		−	20.0000i		−	1.00000i
$401$	0.500000	−	0.866025i	0.0249688	−	0.0432472i	−0.853271	−	0.521468i	$-0.825385\pi$
$401$	0.500000	−	0.866025i	0.0249688	−	0.0432472i	0.878240	+	0.478220i	$0.158718\pi$
$402$	−1.15747	+	4.31975i	−0.0577296	+	0.215450i
$403$	−1.83013	+	6.83013i	−0.0911651	+	0.340233i
$404$		0			0
$405$	−17.3925	+	17.3925i	−0.864242	+	0.864242i
$406$		0			0
$407$	6.00000	−	6.00000i	0.297409	−	0.297409i
$408$	13.6603	−	3.66025i	0.676283	−	0.181210i
$409$	−1.58114	−	2.73861i	−0.0781823	−	0.135416i	0.824283	−	0.566177i	$-0.191578\pi$
$409$	−1.58114	−	2.73861i	−0.0781823	−	0.135416i	−0.902466	+	0.430762i	$0.858245\pi$
$410$	15.0000	+	25.9808i	0.740797	+	1.28310i
$411$	5.47723	+	3.16228i	0.270172	+	0.155984i
$412$		0			0
$413$		0			0
$414$			8.00000i			0.393179i
$415$	8.66025	+	5.00000i	0.425115	+	0.245440i
$416$		0			0
$417$	40.9808	+	10.9808i	2.00684	+	0.537730i
$418$	1.15747	+	4.31975i	0.0566139	+	0.211286i
$419$	−15.8114			−0.772437			−0.386218	−	0.922407i	$-0.626219\pi$
$419$	−15.8114			−0.772437			−0.386218	+	0.922407i	$0.626219\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−6.22243	−	23.2224i	−0.302903	−	1.13045i
$423$	12.9593	+	3.47242i	0.630101	+	0.168835i
$424$	−3.46410	+	2.00000i	−0.168232	+	0.0971286i
$425$	2.89368	+	10.7994i	0.140364	+	0.523847i
$426$		−	18.9737i		−	0.919277i
$427$		0			0
$428$		0			0
$429$	4.33013	+	2.50000i	0.209061	+	0.120701i
$430$	12.9593	+	3.47242i	0.624951	+	0.167455i
$431$	11.5000	+	19.9186i	0.553936	+	0.959444i	0.997985	+	0.0634424i	$0.0202079\pi$
$431$	11.5000	+	19.9186i	0.553936	+	0.959444i	−0.444050	+	0.896002i	$0.646459\pi$
$432$	−8.63950	+	2.31495i	−0.415668	+	0.111378i
$433$	9.48683	−	9.48683i	0.455908	−	0.455908i	−0.441402	−	0.897310i	$-0.645519\pi$
$433$	9.48683	−	9.48683i	0.455908	−	0.455908i	0.897310	+	0.441402i	$0.145519\pi$
$434$		0			0
$435$	15.0000			0.719195
$436$		0			0
$437$	2.31495	−	8.63950i	0.110739	−	0.413283i
$438$		0			0
$439$	6.32456	−	10.9545i	0.301855	−	0.522827i	−0.674701	−	0.738091i	$-0.735728\pi$
$439$	6.32456	−	10.9545i	0.301855	−	0.522827i	0.976556	+	0.215263i	$0.0690610\pi$
$440$	−6.32456			−0.301511
$441$		0			0
$442$	5.00000	−	5.00000i	0.237826	−	0.237826i
$443$	−1.36603	+	0.366025i	−0.0649018	+	0.0173904i	−0.291124	−	0.956685i	$-0.594029\pi$
$443$	−1.36603	+	0.366025i	−0.0649018	+	0.0173904i	0.226222	+	0.974076i	$0.427363\pi$
$444$		0			0
$445$	−13.6603	−	3.66025i	−0.647558	−	0.173513i
$446$	−24.6475	−	14.2302i	−1.16709	−	0.673822i
$447$	18.9737	+	18.9737i	0.897424	+	0.897424i
$448$		0			0
$449$			17.0000i			0.802280i	0.916017	+	0.401140i	$0.131386\pi$
$449$			17.0000i			0.802280i	−0.916017	+	0.401140i	$0.868614\pi$
$450$	3.66025	+	13.6603i	0.172546	+	0.643951i
$451$	8.21584	−	4.74342i	0.386869	−	0.223359i
$452$		0			0
$453$	5.20863	+	19.4389i	0.244723	+	0.913318i
$454$	3.16228			0.148413
$455$		0			0
$456$	−20.0000			−0.936586
$457$	−0.366025	−	1.36603i	−0.0171219	−	0.0639000i	0.956836	−	0.290627i	$-0.0938640\pi$
$457$	−0.366025	−	1.36603i	−0.0171219	−	0.0639000i	−0.973958	+	0.226727i	$0.927197\pi$
$458$	21.5988	+	5.78737i	1.00924	+	0.270426i
$459$	4.33013	−	2.50000i	0.202113	−	0.116690i
$460$		0			0
$461$		−	6.32456i		−	0.294564i	−0.989095	−	0.147282i	$-0.952948\pi$
$461$		−	6.32456i		−	0.294564i	0.989095	−	0.147282i	$-0.0470525\pi$
$462$		0			0
$463$	−4.00000	−	4.00000i	−0.185896	−	0.185896i	0.608023	−	0.793919i	$-0.291963\pi$
$463$	−4.00000	−	4.00000i	−0.185896	−	0.185896i	−0.793919	+	0.608023i	$0.791963\pi$
$464$	10.3923	+	6.00000i	0.482451	+	0.278543i
$465$	7.90569	+	13.6931i	0.366618	+	0.635001i
$466$	−18.0000	−	31.1769i	−0.833834	−	1.44424i
$467$	15.1191	−	4.05116i	0.699630	−	0.187465i	0.108565	−	0.994089i	$-0.465374\pi$
$467$	15.1191	−	4.05116i	0.699630	−	0.187465i	0.591065	+	0.806624i	$0.298708\pi$
$468$		0			0
$469$		0			0
$470$	−15.0000	+	15.0000i	−0.691898	+	0.691898i
$471$	−10.0000	+	17.3205i	−0.460776	+	0.798087i
$472$	−6.94484	+	25.9185i	−0.319662	+	1.19300i
$473$	1.09808	−	4.09808i	0.0504896	−	0.188430i
$474$	−20.5548	+	35.6020i	−0.944113	+	1.63525i
$475$		−	15.8114i		−	0.725476i
$476$		0			0
$477$	2.00000	−	2.00000i	0.0915737	−	0.0915737i
$478$	−25.9545	+	6.95448i	−1.18713	+	0.318091i
$479$	3.16228	+	5.47723i	0.144488	+	0.250261i	0.929182	−	0.369623i	$-0.120513\pi$
$479$	3.16228	+	5.47723i	0.144488	+	0.250261i	−0.784694	+	0.619884i	$0.787180\pi$
$480$		0			0
$481$	16.4317	+	9.48683i	0.749220	+	0.432562i
$482$	−25.2982	−	25.2982i	−1.15230	−	1.15230i
$483$		0			0
$484$		0			0
$485$	−2.50000	+	4.33013i	−0.113519	+	0.196621i
$486$	21.9089	−	12.6491i	0.993808	−	0.573775i
$487$	−5.46410	−	1.46410i	−0.247602	−	0.0663448i	0.132883	−	0.991132i	$-0.457576\pi$
$487$	−5.46410	−	1.46410i	−0.247602	−	0.0663448i	−0.380485	+	0.924787i	$0.624243\pi$
$488$	4.62990	+	17.2790i	0.209586	+	0.782184i
$489$	18.9737			0.858019
$490$		0			0
$491$	−41.0000			−1.85030			−0.925152	−	0.379597i	$-0.876063\pi$
$491$	−41.0000			−1.85030			−0.925152	+	0.379597i	$0.876063\pi$
$492$		0			0
$493$	−6.47963	−	1.73621i	−0.291828	−	0.0781950i
$494$	−8.66025	+	5.00000i	−0.389643	+	0.224961i
$495$	4.31975	−	1.15747i	0.194158	−	0.0520246i
$496$			12.6491i			0.567962i
$497$		0			0
$498$	−10.0000	−	10.0000i	−0.448111	−	0.448111i
$499$	16.4545	+	9.50000i	0.736604	+	0.425278i	0.820833	−	0.571168i	$-0.193510\pi$
$499$	16.4545	+	9.50000i	0.736604	+	0.425278i	−0.0842294	+	0.996446i	$0.526843\pi$
$500$		0			0
$501$	−17.5000	−	30.3109i	−0.781842	−	1.35419i
$502$	17.2790	−	4.62990i	0.771200	−	0.206642i
$503$	7.90569	−	7.90569i	0.352497	−	0.352497i	−0.508541	−	0.861038i	$-0.669815\pi$
$503$	7.90569	−	7.90569i	0.352497	−	0.352497i	0.861038	+	0.508541i	$0.169815\pi$
$504$		0			0
$505$	5.00000	+	5.00000i	0.222497	+	0.222497i
$506$	−2.00000	+	3.46410i	−0.0889108	+	0.153998i
$507$	4.62990	−	17.2790i	0.205621	−	0.767388i
$508$		0			0
$509$	−9.48683	+	16.4317i	−0.420496	+	0.728321i	−0.995988	−	0.0894865i	$-0.971477\pi$
$509$	−9.48683	+	16.4317i	−0.420496	+	0.728321i	0.575492	+	0.817808i	$0.304811\pi$
$510$		−	15.8114i		−	0.700140i
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−6.83013	+	1.83013i	−0.301557	+	0.0808021i
$514$	12.6491	+	21.9089i	0.557928	+	0.966360i
$515$	30.3109	−	17.5000i	1.33566	−	0.771142i
$516$		0			0
$517$	4.74342	+	4.74342i	0.208615	+	0.208615i
$518$		0			0
$519$			35.0000i			1.53633i
$520$	−3.66025	−	13.6603i	−0.160513	−	0.599042i
$521$	35.6020	−	20.5548i	1.55975	−	0.900522i	0.562470	−	0.826817i	$-0.309851\pi$
$521$	35.6020	−	20.5548i	1.55975	−	0.900522i	0.997280	−	0.0737049i	$-0.0234823\pi$
$522$	−8.19615	−	2.19615i	−0.358736	−	0.0961230i
$523$	−6.94484	−	25.9185i	−0.303677	−	1.13334i	−0.934078	−	0.357068i	$-0.883776\pi$
$523$	−6.94484	−	25.9185i	−0.303677	−	1.13334i	0.630402	−	0.776269i	$-0.282890\pi$
$524$		0			0
$525$		0			0
$526$	−14.0000			−0.610429
$527$	−1.83013	−	6.83013i	−0.0797216	−	0.297525i
$528$	8.63950	+	2.31495i	0.375986	+	0.100745i
$529$	−12.9904	+	7.50000i	−0.564799	+	0.326087i
$530$	1.15747	+	4.31975i	0.0502775	+	0.187638i
$531$		−	18.9737i		−	0.823387i
$532$		0			0
$533$	15.0000	+	15.0000i	0.649722	+	0.649722i
$534$	17.3205	+	10.0000i	0.749532	+	0.432742i
$535$	−8.21584	+	4.74342i	−0.355202	+	0.205076i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−12.9593	+	3.47242i	−0.559233	+	0.149846i
$538$	18.9737	−	18.9737i	0.818013	−	0.818013i
$539$		0			0
$540$		0			0
$541$	−4.50000	+	7.79423i	−0.193470	+	0.335100i	−0.946398	−	0.323003i	$-0.895308\pi$
$541$	−4.50000	+	7.79423i	−0.193470	+	0.335100i	0.752928	+	0.658103i	$0.228641\pi$
$542$	4.62990	−	17.2790i	0.198871	−	0.742197i
$543$	−12.8109	+	47.8109i	−0.549768	+	2.05176i
$544$		0			0
$545$	−11.0680	−	11.0680i	−0.474100	−	0.474100i
$546$		0			0
$547$	14.0000	−	14.0000i	0.598597	−	0.598597i	−0.341342	−	0.939939i	$-0.610882\pi$
$547$	14.0000	−	14.0000i	0.598597	−	0.598597i	0.939939	+	0.341342i	$0.110882\pi$
$548$		0			0
$549$	−6.32456	−	10.9545i	−0.269925	−	0.467525i
$550$	−1.83013	+	6.83013i	−0.0780369	+	0.291238i
$551$	8.21584	+	4.74342i	0.350006	+	0.202076i
$552$	−12.6491	−	12.6491i	−0.538382	−	0.538382i
$553$		0			0
$554$		−	36.0000i		−	1.52949i
$555$	40.9808	−	10.9808i	1.73954	−	0.466107i
$556$		0			0
$557$	8.19615	+	2.19615i	0.347282	+	0.0930540i	0.428244	−	0.903663i	$-0.359132\pi$
$557$	8.19615	+	2.19615i	0.347282	+	0.0930540i	−0.0809616	+	0.996717i	$0.525799\pi$
$558$	−2.31495	−	8.63950i	−0.0979996	−	0.365739i
$559$	9.48683			0.401250
$560$		0			0
$561$	−5.00000			−0.211100
$562$	−3.29423	−	12.2942i	−0.138959	−	0.518601i
$563$	−12.9593	−	3.47242i	−0.546167	−	0.146345i	−0.0248236	−	0.999692i	$-0.507902\pi$
$563$	−12.9593	−	3.47242i	−0.546167	−	0.146345i	−0.521344	+	0.853347i	$0.674569\pi$
$564$		0			0
$565$	18.9737	−	32.8634i	0.798228	−	1.38257i
$566$		−	9.48683i		−	0.398761i
$567$		0			0
$568$	12.0000	+	12.0000i	0.503509	+	0.503509i
$569$	−27.7128	−	16.0000i	−1.16178	−	0.670755i	−0.210051	−	0.977690i	$-0.567363\pi$
$569$	−27.7128	−	16.0000i	−1.16178	−	0.670755i	−0.951730	+	0.306935i	$0.900696\pi$
$570$	−5.78737	+	21.5988i	−0.242406	+	0.904672i
$571$	13.0000	+	22.5167i	0.544033	+	0.942293i	0.998667	+	0.0516146i	$0.0164367\pi$
$571$	13.0000	+	22.5167i	0.544033	+	0.942293i	−0.454634	+	0.890678i	$0.650230\pi$
$572$		0			0
$573$	−4.74342	+	4.74342i	−0.198159	+	0.198159i
$574$		0			0
$575$	10.0000	−	10.0000i	0.417029	−	0.417029i
$576$	−8.00000	+	13.8564i	−0.333333	+	0.577350i
$577$	7.52358	−	28.0784i	0.313211	−	1.16892i	−0.612433	−	0.790522i	$-0.709809\pi$
$577$	7.52358	−	28.0784i	0.313211	−	1.16892i	0.925644	−	0.378396i	$-0.123524\pi$
$578$	4.39230	−	16.3923i	0.182696	−	0.681830i
$579$	12.6491	−	21.9089i	0.525679	−	0.910503i
$580$		0			0
$581$		0			0
$582$	5.00000	−	5.00000i	0.207257	−	0.207257i
$583$	1.36603	−	0.366025i	0.0565750	−	0.0151592i
$584$		0			0
$585$	5.00000	+	8.66025i	0.206725	+	0.358057i
$586$	13.6931	+	7.90569i	0.565655	+	0.326581i
$587$	−15.8114	−	15.8114i	−0.652606	−	0.652606i	0.301014	−	0.953620i	$-0.402675\pi$
$587$	−15.8114	−	15.8114i	−0.652606	−	0.652606i	−0.953620	+	0.301014i	$0.902675\pi$
$588$		0			0
$589$			10.0000i			0.412043i
$590$	25.9808	+	15.0000i	1.06961	+	0.617540i
$591$	2.73861	−	1.58114i	0.112651	−	0.0650394i
$592$	32.7846	+	8.78461i	1.34744	+	0.361045i
$593$	7.52358	+	28.0784i	0.308956	+	1.15304i	0.929486	+	0.368858i	$0.120251\pi$
$593$	7.52358	+	28.0784i	0.308956	+	1.15304i	−0.620529	+	0.784183i	$0.713082\pi$
$594$	3.16228			0.129750
$595$		0			0
$596$		0			0
$597$	−5.49038	−	20.4904i	−0.224706	−	0.838615i
$598$	−8.63950	−	2.31495i	−0.353296	−	0.0946653i
$599$	−11.2583	+	6.50000i	−0.460003	+	0.265583i	−0.712045	−	0.702133i	$-0.752231\pi$
$599$	−11.2583	+	6.50000i	−0.460003	+	0.265583i	0.252043	+	0.967716i	$0.418898\pi$
$600$	−27.3861	−	15.8114i	−1.11803	−	0.645497i
$601$			22.1359i			0.902944i	0.892285	+	0.451472i	$0.149101\pi$
$601$			22.1359i			0.902944i	−0.892285	+	0.451472i	$0.850899\pi$
$602$		0			0
$603$	2.00000	+	2.00000i	0.0814463	+	0.0814463i
$604$		0			0
$605$	−21.5988	−	5.78737i	−0.878114	−	0.235290i
$606$	−5.00000	−	8.66025i	−0.203111	−	0.351799i
$607$	−19.4389	+	5.20863i	−0.789000	+	0.211412i	−0.630749	−	0.775987i	$-0.717252\pi$
$607$	−19.4389	+	5.20863i	−0.789000	+	0.211412i	−0.158251	+	0.987399i	$0.550586\pi$
$608$		0			0
$609$		0			0
$610$	20.0000			0.809776
$611$	−7.50000	+	12.9904i	−0.303418	+	0.525535i
$612$		0			0
$613$	6.22243	−	23.2224i	0.251322	−	0.937945i	−0.718778	−	0.695239i	$-0.755298\pi$
$613$	6.22243	−	23.2224i	0.251322	−	0.937945i	0.970100	−	0.242706i	$-0.0780350\pi$
$614$	−4.74342	+	8.21584i	−0.191429	+	0.331564i
$615$	47.4342			1.91273
$616$		0			0
$617$	4.00000	−	4.00000i	0.161034	−	0.161034i	−0.621991	−	0.783025i	$-0.713676\pi$
$617$	4.00000	−	4.00000i	0.161034	−	0.161034i	0.783025	+	0.621991i	$0.213676\pi$
$618$	−47.8109	+	12.8109i	−1.92324	+	0.515330i
$619$	12.6491	+	21.9089i	0.508411	+	0.880593i	0.999953	+	0.00973920i	$0.00310013\pi$
$619$	12.6491	+	21.9089i	0.508411	+	0.880593i	−0.491542	+	0.870854i	$0.663567\pi$
$620$		0			0
$621$	−5.47723	−	3.16228i	−0.219793	−	0.126898i
$622$	22.1359	+	22.1359i	0.887570	+	0.887570i
$623$		0			0
$624$			20.0000i			0.800641i
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	−24.6475	+	14.2302i	−0.985113	+	0.568755i
$627$	6.83013	+	1.83013i	0.272769	+	0.0730882i
$628$		0			0
$629$	−18.9737			−0.756530
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$	−9.51666	−	35.5167i	−0.378552	−	1.41278i
$633$	−36.7179	−	9.83853i	−1.45941	−	0.391046i
$634$	32.9090	−	19.0000i	1.30698	−	0.754586i
$635$	−24.6475	−	14.2302i	−0.978107	−	0.564710i
$636$		0			0
$637$		0			0
$638$	−3.00000	−	3.00000i	−0.118771	−	0.118771i
$639$	−10.3923	−	6.00000i	−0.411113	−	0.237356i
$640$	−12.6491	−	21.9089i	−0.500000	−	0.866025i
$641$	−22.0000	−	38.1051i	−0.868948	−	1.50506i	−0.863073	−	0.505079i	$-0.831463\pi$
$641$	−22.0000	−	38.1051i	−0.868948	−	1.50506i	−0.00587459	−	0.999983i	$-0.501870\pi$
$642$	12.9593	−	3.47242i	0.511461	−	0.137046i
$643$	4.74342	−	4.74342i	0.187062	−	0.187062i	−0.607363	−	0.794425i	$-0.707772\pi$
$643$	4.74342	−	4.74342i	0.187062	−	0.187062i	0.794425	+	0.607363i	$0.207772\pi$
$644$		0			0
$645$	15.0000	−	15.0000i	0.590624	−	0.590624i
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	4.62990	−	17.2790i	0.182020	−	0.679308i	−0.813229	−	0.581944i	$-0.802292\pi$
$647$	4.62990	−	17.2790i	0.182020	−	0.679308i	0.995249	−	0.0973638i	$-0.0310411\pi$
$648$	−8.05256	+	30.0526i	−0.316334	+	1.18058i
$649$	4.74342	−	8.21584i	0.186195	−	0.322500i
$650$	−15.8114			−0.620174
$651$		0			0
$652$		0			0
$653$	25.9545	−	6.95448i	1.01568	−	0.272150i	0.287678	−	0.957727i	$-0.407117\pi$
$653$	25.9545	−	6.95448i	1.01568	−	0.272150i	0.728000	+	0.685577i	$0.240450\pi$
$654$	11.0680	+	19.1703i	0.432792	+	0.749618i
$655$		0			0
$656$	32.8634	+	18.9737i	1.28310	+	0.740797i
$657$		0			0
$658$		0			0
$659$			1.00000i			0.0389545i	0.999810	+	0.0194772i	$0.00620019\pi$
$659$			1.00000i			0.0389545i	−0.999810	+	0.0194772i	$0.993800\pi$
$660$		0			0
$661$	−10.9545	+	6.32456i	−0.426079	+	0.245997i	−0.697675	−	0.716415i	$-0.745782\pi$
$661$	−10.9545	+	6.32456i	−0.426079	+	0.245997i	0.271596	+	0.962411i	$0.412449\pi$
$662$	−8.19615	−	2.19615i	−0.318553	−	0.0853559i
$663$	−2.89368	−	10.7994i	−0.112381	−	0.419413i
$664$	12.6491			0.490881
$665$		0			0
$666$	−24.0000			−0.929981
$667$	2.19615	+	8.19615i	0.0850354	+	0.317356i
$668$		0			0
$669$	−38.9711	+	22.5000i	−1.50671	+	0.869900i
$670$	−4.31975	+	1.15747i	−0.166887	+	0.0447171i
$671$		−	6.32456i		−	0.244157i
$672$		0			0
$673$	−24.0000	−	24.0000i	−0.925132	−	0.925132i	0.0722542	−	0.997386i	$-0.476981\pi$
$673$	−24.0000	−	24.0000i	−0.925132	−	0.925132i	−0.997386	+	0.0722542i	$0.976981\pi$
$674$	13.8564	+	8.00000i	0.533729	+	0.308148i
$675$	−10.7994	−	2.89368i	−0.415668	−	0.111378i
$676$		0			0
$677$	19.4389	−	5.20863i	0.747097	−	0.200184i	0.134867	−	0.990864i	$-0.456939\pi$
$677$	19.4389	−	5.20863i	0.747097	−	0.200184i	0.612230	+	0.790680i	$0.290273\pi$
$678$	−37.9473	+	37.9473i	−1.45736	+	1.45736i
$679$		0			0
$680$	10.0000	+	10.0000i	0.383482	+	0.383482i
$681$	2.50000	−	4.33013i	0.0958002	−	0.165931i
$682$	1.15747	−	4.31975i	0.0443220	−	0.165412i
$683$	11.7128	−	43.7128i	0.448178	−	1.67262i	−0.259227	−	0.965816i	$-0.583468\pi$
$683$	11.7128	−	43.7128i	0.448178	−	1.67262i	0.707406	−	0.706808i	$-0.249865\pi$
$684$		0			0
$685$			6.32456i			0.241649i
$686$		0			0
$687$	25.0000	−	25.0000i	0.953809	−	0.953809i
$688$	16.3923	−	4.39230i	0.624951	−	0.167455i
$689$	1.58114	+	2.73861i	0.0602366	+	0.104333i
$690$	−17.3205	+	10.0000i	−0.659380	+	0.380693i
$691$	−27.3861	−	15.8114i	−1.04182	−	0.601494i	−0.121470	−	0.992595i	$-0.538761\pi$
$691$	−27.3861	−	15.8114i	−1.04182	−	0.601494i	−0.920348	+	0.391102i	$0.872094\pi$
$692$		0			0
$693$		0			0
$694$			48.0000i			1.82206i
$695$	10.9808	+	40.9808i	0.416524	+	1.55449i
$696$	16.4317	−	9.48683i	0.622841	−	0.359597i
$697$	−20.4904	−	5.49038i	−0.776129	−	0.207963i
$698$	−12.7322	−	47.5173i	−0.481921	−	1.79856i
$699$	−56.9210			−2.15295
$700$		0			0
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$	1.83013	+	6.83013i	0.0690737	+	0.257787i
$703$	25.9185	+	6.94484i	0.977535	+	0.261930i
$704$	−6.92820	+	4.00000i	−0.261116	+	0.150756i
$705$	8.68105	+	32.3981i	0.326947	+	1.22018i
$706$			28.4605i			1.07113i
$707$		0			0
$708$		0			0
$709$	7.79423	+	4.50000i	0.292718	+	0.169001i	0.639167	−	0.769068i	$-0.279279\pi$
$709$	7.79423	+	4.50000i	0.292718	+	0.169001i	−0.346449	+	0.938069i	$0.612613\pi$
$710$	16.4317	−	9.48683i	0.616670	−	0.356034i
$711$	13.0000	+	22.5167i	0.487538	+	0.844441i
$712$	−17.2790	+	4.62990i	−0.647558	+	0.173513i
$713$	−6.32456	+	6.32456i	−0.236856	+	0.236856i
$714$		0			0
$715$			5.00000i			0.186989i
$716$		0			0
$717$	−10.9960	+	41.0376i	−0.410653	+	1.53258i
$718$	−8.05256	+	30.0526i	−0.300519	+	1.12155i
$719$	−15.8114	+	27.3861i	−0.589665	+	1.02133i	0.404611	+	0.914489i	$0.367407\pi$
$719$	−15.8114	+	27.3861i	−0.589665	+	1.02133i	−0.994276	+	0.106841i	$0.965926\pi$
$720$	12.6491	+	12.6491i	0.471405	+	0.471405i
$721$		0			0
$722$	9.00000	−	9.00000i	0.334945	−	0.334945i
$723$	−54.6410	+	14.6410i	−2.03212	+	0.544505i
$724$		0			0
$725$	7.50000	+	12.9904i	0.278543	+	0.482451i
$726$	27.3861	+	15.8114i	1.01639	+	0.586816i
$727$	9.48683	+	9.48683i	0.351847	+	0.351847i	0.860796	−	0.508949i	$-0.169966\pi$
$727$	9.48683	+	9.48683i	0.351847	+	0.351847i	−0.508949	+	0.860796i	$0.669966\pi$
$728$		0			0
$729$		−	7.00000i		−	0.259259i
$730$		0			0
$731$	−8.21584	+	4.74342i	−0.303874	+	0.175442i
$732$		0			0
$733$	6.36611	+	23.7586i	0.235138	+	0.877545i	0.978087	+	0.208197i	$0.0667597\pi$
$733$	6.36611	+	23.7586i	0.235138	+	0.877545i	−0.742949	+	0.669348i	$0.766574\pi$
$734$	34.7851			1.28394
$735$		0			0
$736$		0			0
$737$	0.366025	+	1.36603i	0.0134827	+	0.0503182i
$738$	−25.9185	−	6.94484i	−0.954074	−	0.255643i
$739$	32.0429	−	18.5000i	1.17872	−	0.680534i	0.223001	−	0.974818i	$-0.428415\pi$
$739$	32.0429	−	18.5000i	1.17872	−	0.680534i	0.955718	+	0.294285i	$0.0950814\pi$
$740$		0			0
$741$			15.8114i			0.580846i
$742$		0			0
$743$	−9.00000	−	9.00000i	−0.330178	−	0.330178i	0.522476	−	0.852654i	$-0.325008\pi$
$743$	−9.00000	−	9.00000i	−0.330178	−	0.330178i	−0.852654	+	0.522476i	$0.825008\pi$
$744$	17.3205	+	10.0000i	0.635001	+	0.366618i
$745$	−6.94484	+	25.9185i	−0.254439	+	0.949581i
$746$	12.0000	+	20.7846i	0.439351	+	0.760979i
$747$	−8.63950	+	2.31495i	−0.316103	+	0.0846995i
$748$		0			0
$749$		0			0
$750$	−25.0000	+	25.0000i	−0.912871	+	0.912871i
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	0.301373	+	0.953506i	$0.402555\pi$
$751$	−18.5000	+	32.0429i	−0.675075	+	1.16926i	−0.976447	+	0.215757i	$0.930778\pi$
$752$	−6.94484	+	25.9185i	−0.253252	+	0.945151i
$753$	7.32051	−	27.3205i	0.266774	−	0.995615i
$754$	4.74342	−	8.21584i	0.172745	−	0.299203i
$755$	−14.2302	+	14.2302i	−0.517892	+	0.517892i
$756$		0			0
$757$	−16.0000	+	16.0000i	−0.581530	+	0.581530i	−0.935324	−	0.353794i	$-0.884892\pi$
$757$	−16.0000	+	16.0000i	−0.581530	+	0.581530i	0.353794	+	0.935324i	$0.384892\pi$
$758$	−10.9282	+	2.92820i	−0.396930	+	0.106357i
$759$	3.16228	+	5.47723i	0.114783	+	0.198811i
$760$	−10.0000	−	17.3205i	−0.362738	−	0.628281i
$761$	−21.9089	−	12.6491i	−0.794197	−	0.458530i	0.0472409	−	0.998884i	$-0.484957\pi$
$761$	−21.9089	−	12.6491i	−0.794197	−	0.458530i	−0.841438	+	0.540354i	$0.818290\pi$
$762$	28.4605	+	28.4605i	1.03102	+	1.03102i
$763$		0			0
$764$		0			0
$765$	−8.66025	−	5.00000i	−0.313112	−	0.180775i
$766$	−27.3861	+	15.8114i	−0.989501	+	0.571289i
$767$	20.4904	+	5.49038i	0.739865	+	0.198246i
$768$		0			0
$769$	−22.1359			−0.798243			−0.399121	−	0.916898i	$-0.630685\pi$
$769$	−22.1359			−0.798243			−0.399121	+	0.916898i	$0.630685\pi$
$770$		0			0
$771$	40.0000			1.44056
$772$		0			0
$773$	49.6771	+	13.3110i	1.78676	+	0.478762i	0.991789	−	0.127883i	$-0.0408181\pi$
$773$	49.6771	+	13.3110i	1.78676	+	0.478762i	0.794973	+	0.606644i	$0.207485\pi$
$774$	−10.3923	+	6.00000i	−0.373544	+	0.215666i
$775$	−7.90569	+	13.6931i	−0.283981	+	0.491869i
$776$			6.32456i			0.227038i
$777$		0			0
$778$	23.0000	+	23.0000i	0.824590	+	0.824590i
$779$	25.9808	+	15.0000i	0.930857	+	0.537431i
$780$		0			0
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$	8.63950	−	2.31495i	0.308948	−	0.0827824i
$783$	4.74342	−	4.74342i	0.169516	−	0.169516i
$784$		0			0
$785$	−20.0000			−0.713831
$786$		0			0
$787$	6.36611	−	23.7586i	0.226927	−	0.846904i	−0.754696	−	0.656075i	$-0.772216\pi$
$787$	6.36611	−	23.7586i	0.226927	−	0.846904i	0.981623	−	0.190829i	$-0.0611177\pi$
$788$		0			0
$789$	−11.0680	+	19.1703i	−0.394030	+	0.682480i
$790$	−41.1096			−1.46261
$791$		0			0
$792$	4.00000	−	4.00000i	0.142134	−	0.142134i
$793$	13.6603	−	3.66025i	0.485090	−	0.129979i
$794$	−23.7171	−	41.0792i	−0.841688	−	1.45785i
$795$	6.83013	+	1.83013i	0.242240	+	0.0649079i
$796$		0			0
$797$	1.58114	+	1.58114i	0.0560068	+	0.0560068i	0.734555	−	0.678549i	$-0.237391\pi$
$797$	1.58114	+	1.58114i	0.0560068	+	0.0560068i	−0.678549	+	0.734555i	$0.737391\pi$
$798$		0			0
$799$		−	15.0000i		−	0.530662i
$800$		0			0
$801$	10.9545	−	6.32456i	0.387056	−	0.223467i
$802$	−1.36603	−	0.366025i	−0.0482360	−	0.0129248i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	10.0000			0.352235
$807$	−10.9808	−	40.9808i	−0.386541	−	1.44259i
$808$	8.63950	+	2.31495i	0.303937	+	0.0814396i
$809$	−2.59808	+	1.50000i	−0.0913435	+	0.0527372i	−0.544976	−	0.838452i	$-0.683461\pi$
$809$	−2.59808	+	1.50000i	−0.0913435	+	0.0527372i	0.453632	+	0.891189i	$0.350128\pi$
$810$	30.1247	+	17.3925i	1.05848	+	0.611111i
$811$		−	37.9473i		−	1.33251i	−0.745724	−	0.666256i	$-0.767896\pi$
$811$		−	37.9473i		−	1.33251i	0.745724	−	0.666256i	$-0.232104\pi$
$812$		0			0
$813$	−20.0000	−	20.0000i	−0.701431	−	0.701431i
$814$	−10.3923	−	6.00000i	−0.364250	−	0.210300i
$815$	9.48683	+	16.4317i	0.332309	+	0.575577i
$816$	−10.0000	−	17.3205i	−0.350070	−	0.606339i
$817$	12.9593	−	3.47242i	0.453387	−	0.121485i
$818$	−3.16228	+	3.16228i	−0.110566	+	0.110566i
$819$		0			0
$820$		0			0
$821$	11.5000	−	19.9186i	0.401353	−	0.695163i	−0.592537	−	0.805543i	$-0.701873\pi$
$821$	11.5000	−	19.9186i	0.401353	−	0.695163i	0.993889	+	0.110380i	$0.0352068\pi$
$822$	2.31495	−	8.63950i	0.0807431	−	0.301337i
$823$	−1.09808	+	4.09808i	−0.0382765	+	0.142850i	−0.982420	−	0.186686i	$-0.940225\pi$
$823$	−1.09808	+	4.09808i	−0.0382765	+	0.142850i	0.944143	+	0.329535i	$0.106892\pi$
$824$	22.1359	−	38.3406i	0.771142	−	1.33566i
$825$	7.90569	+	7.90569i	0.275241	+	0.275241i
$826$		0			0
$827$	−26.0000	+	26.0000i	−0.904109	+	0.904109i	−0.995789	−	0.0916799i	$-0.970776\pi$
$827$	−26.0000	+	26.0000i	−0.904109	+	0.904109i	0.0916799	+	0.995789i	$0.470776\pi$
$828$		0			0
$829$	−14.2302	−	24.6475i	−0.494237	−	0.856044i	0.505741	−	0.862685i	$-0.331219\pi$
$829$	−14.2302	−	24.6475i	−0.494237	−	0.856044i	−0.999978	+	0.00664181i	$0.997886\pi$
$830$	3.66025	−	13.6603i	0.127049	−	0.474154i
$831$	−49.2950	−	28.4605i	−1.71003	−	0.987284i
$832$	−12.6491	−	12.6491i	−0.438529	−	0.438529i
$833$		0			0
$834$		−	60.0000i		−	2.07763i
$835$	17.5000	−	30.3109i	0.605612	−	1.04895i
$836$		0			0
$837$	6.83013	+	1.83013i	0.236084	+	0.0632584i
$838$	5.78737	+	21.5988i	0.199921	+	0.746117i
$839$	50.5964			1.74678			0.873392	−	0.487019i	$-0.161916\pi$
$839$	50.5964			1.74678			0.873392	+	0.487019i	$0.161916\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−6.95448	−	25.9545i	−0.239667	−	0.894451i
$843$	−19.4389	−	5.20863i	−0.669511	−	0.179395i
$844$		0			0
$845$	17.2790	−	4.62990i	0.594416	−	0.159273i
$846$		−	18.9737i		−	0.652328i
$847$		0			0
$848$	4.00000	+	4.00000i	0.137361	+	0.137361i
$849$	−12.9904	−	7.50000i	−0.445829	−	0.257399i
$850$	13.6931	−	7.90569i	0.469668	−	0.271163i
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$		0			0
$855$	10.0000	+	10.0000i	0.341993	+	0.341993i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−11.5747	+	43.1975i	−0.395386	+	1.47560i	0.425737	+	0.904847i	$0.360015\pi$
$857$	−11.5747	+	43.1975i	−0.395386	+	1.47560i	−0.821122	+	0.570752i	$0.806652\pi$
$858$	1.83013	−	6.83013i	0.0624795	−	0.233177i
$859$	−6.32456	+	10.9545i	−0.215791	+	0.373761i	−0.953517	−	0.301339i	$-0.902566\pi$
$859$	−6.32456	+	10.9545i	−0.215791	+	0.373761i	0.737726	+	0.675100i	$0.235900\pi$
$860$		0			0
$861$		0			0
$862$	23.0000	−	23.0000i	0.783383	−	0.783383i
$863$	17.7583	−	4.75833i	0.604501	−	0.161975i	0.0564286	−	0.998407i	$-0.482029\pi$
$863$	17.7583	−	4.75833i	0.604501	−	0.161975i	0.548072	+	0.836431i	$0.315362\pi$
$864$		0			0
$865$	−30.3109	+	17.5000i	−1.03060	+	0.595018i
$866$	−16.4317	−	9.48683i	−0.558371	−	0.322376i
$867$	−18.9737	−	18.9737i	−0.644379	−	0.644379i
$868$		0			0
$869$			13.0000i			0.440995i
$870$	−5.49038	−	20.4904i	−0.186141	−	0.694689i
$871$	−2.73861	+	1.58114i	−0.0927944	+	0.0535748i
$872$	−19.1244	−	5.12436i	−0.647632	−	0.173533i
$873$	−1.15747	−	4.31975i	−0.0391746	−	0.146201i
$874$	−12.6491			−0.427863
$875$		0			0
$876$		0			0
$877$	6.22243	+	23.2224i	0.210117	+	0.784166i	0.987829	+	0.155545i	$0.0497135\pi$
$877$	6.22243	+	23.2224i	0.210117	+	0.784166i	−0.777712	+	0.628621i	$0.783620\pi$
$878$	−17.2790	−	4.62990i	−0.583138	−	0.156251i
$879$	21.6506	−	12.5000i	0.730258	−	0.421615i
$880$	2.31495	+	8.63950i	0.0780369	+	0.291238i
$881$			37.9473i			1.27848i	0.769008	+	0.639239i	$0.220751\pi$
$881$			37.9473i			1.27848i	−0.769008	+	0.639239i	$0.779249\pi$
$882$		0			0
$883$	−18.0000	−	18.0000i	−0.605748	−	0.605748i	0.336084	−	0.941832i	$-0.390897\pi$
$883$	−18.0000	−	18.0000i	−0.605748	−	0.605748i	−0.941832	+	0.336084i	$0.890897\pi$
$884$		0			0
$885$	41.0792	−	23.7171i	1.38086	−	0.797241i
$886$	1.00000	+	1.73205i	0.0335957	+	0.0581894i
$887$	−4.31975	+	1.15747i	−0.145043	+	0.0388642i	−0.330610	−	0.943767i	$-0.607254\pi$
$887$	−4.31975	+	1.15747i	−0.145043	+	0.0388642i	0.185567	+	0.982632i	$0.440588\pi$
$888$	37.9473	−	37.9473i	1.27343	−	1.27343i
$889$		0			0
$890$			20.0000i			0.670402i
$891$	5.50000	−	9.52628i	0.184257	−	0.319142i
$892$		0			0
$893$	−5.49038	+	20.4904i	−0.183729	+	0.685684i
$894$	18.9737	−	32.8634i	0.634574	−	1.09911i
$895$	−9.48683	−	9.48683i	−0.317110	−	0.317110i
$896$		0			0
$897$	−10.0000	+	10.0000i	−0.333890	+	0.333890i
$898$	23.2224	−	6.22243i	0.774943	−	0.207645i
$899$	−4.74342	−	8.21584i	−0.158202	−	0.274014i
$900$		0			0
$901$	−2.73861	−	1.58114i	−0.0912364	−	0.0526754i
$902$	−9.48683	−	9.48683i	−0.315877	−	0.315877i
$903$		0			0
$904$		−	48.0000i		−	1.59646i
$905$	−47.8109	+	12.8109i	−1.58929	+	0.425848i
$906$	24.6475	−	14.2302i	0.818859	−	0.472768i
$907$	−30.0526	−	8.05256i	−0.997879	−	0.267381i	−0.277322	−	0.960777i	$-0.589447\pi$
$907$	−30.0526	−	8.05256i	−0.997879	−	0.267381i	−0.720557	+	0.693396i	$0.756114\pi$
$908$		0			0
$909$	−6.32456			−0.209772
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	7.32051	+	27.3205i	0.242406	+	0.904672i
$913$	−4.31975	−	1.15747i	−0.142963	−	0.0383068i
$914$	−1.73205	+	1.00000i	−0.0572911	+	0.0330771i
$915$	15.8114	−	27.3861i	0.522708	−	0.905357i
$916$		0			0
$917$		0			0
$918$	−5.00000	−	5.00000i	−0.165025	−	0.165025i
$919$	−23.3827	−	13.5000i	−0.771324	−	0.445324i	0.0620230	−	0.998075i	$-0.480245\pi$
$919$	−23.3827	−	13.5000i	−0.771324	−	0.445324i	−0.833347	+	0.552751i	$0.813578\pi$
$920$	4.62990	−	17.2790i	0.152643	−	0.569672i
$921$	7.50000	+	12.9904i	0.247133	+	0.428048i
$922$	−8.63950	+	2.31495i	−0.284527	+	0.0762387i
$923$	9.48683	−	9.48683i	0.312263	−	0.312263i
$924$		0			0
$925$	30.0000	+	30.0000i	0.986394	+	0.986394i
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$	−8.10232	+	30.2383i	−0.266115	+	0.993155i
$928$		0			0
$929$	−1.58114	+	2.73861i	−0.0518755	+	0.0898510i	−0.890797	−	0.454401i	$-0.849853\pi$
$929$	−1.58114	+	2.73861i	−0.0518755	+	0.0898510i	0.838922	+	0.544252i	$0.183187\pi$
$930$	15.8114	−	15.8114i	0.518476	−	0.518476i
$931$		0			0
$932$		0			0
$933$	47.8109	−	12.8109i	1.56526	−	0.419410i
$934$	−11.0680	−	19.1703i	−0.362155	−	0.627271i
$935$	−2.50000	−	4.33013i	−0.0817587	−	0.141610i
$936$	10.9545	+	6.32456i	0.358057	+	0.206725i
$937$	−14.2302	−	14.2302i	−0.464882	−	0.464882i	0.435370	−	0.900252i	$-0.356618\pi$
$937$	−14.2302	−	14.2302i	−0.464882	−	0.464882i	−0.900252	+	0.435370i	$0.856618\pi$
$938$		0			0
$939$			45.0000i			1.46852i
$940$		0			0
$941$	−32.8634	+	18.9737i	−1.07131	+	0.618524i	−0.928540	−	0.371231i	$-0.878936\pi$
$941$	−32.8634	+	18.9737i	−1.07131	+	0.618524i	−0.142774	+	0.989755i	$0.545602\pi$
$942$	27.3205	+	7.32051i	0.890150	+	0.238515i
$943$	6.94484	+	25.9185i	0.226155	+	0.844023i
$944$	37.9473			1.23508
$945$		0			0
$946$	−6.00000			−0.195077
$947$	2.56218	+	9.56218i	0.0832596	+	0.310729i	0.994979	−	0.100085i	$-0.0319114\pi$
$947$	2.56218	+	9.56218i	0.0832596	+	0.310729i	−0.911719	+	0.410814i	$0.865245\pi$
$948$		0			0
$949$		0			0
$950$	−21.5988	+	5.78737i	−0.700756	+	0.187767i
$951$		−	60.0833i		−	1.94833i
$952$		0			0
$953$	−3.00000	−	3.00000i	−0.0971795	−	0.0971795i	0.656846	−	0.754025i	$-0.271890\pi$
$953$	−3.00000	−	3.00000i	−0.0971795	−	0.0971795i	−0.754025	+	0.656846i	$0.771890\pi$
$954$	−3.46410	−	2.00000i	−0.112154	−	0.0647524i
$955$	−6.47963	−	1.73621i	−0.209676	−	0.0561825i
$956$		0			0
$957$	−6.47963	+	1.73621i	−0.209457	+	0.0561237i
$958$	6.32456	−	6.32456i	0.204337	−	0.204337i
$959$		0			0
$960$	−40.0000			−1.29099
$961$	−10.5000	+	18.1865i	−0.338710	+	0.586662i
$962$	6.94484	−	25.9185i	0.223911	−	0.835646i
$963$	2.19615	−	8.19615i	0.0707700	−	0.264117i
$964$		0			0
$965$	25.2982			0.814379
$966$		0			0
$967$	−33.0000	+	33.0000i	−1.06121	+	1.06121i	−0.0632081	+	0.998000i	$0.520133\pi$
$967$	−33.0000	+	33.0000i	−1.06121	+	1.06121i	−0.998000	+	0.0632081i	$0.979867\pi$
$968$	−27.3205	+	7.32051i	−0.878114	+	0.235290i
$969$	−7.90569	−	13.6931i	−0.253967	−	0.439885i
$970$	6.83013	+	1.83013i	0.219302	+	0.0587618i
$971$	30.1247	+	17.3925i	0.966749	+	0.558153i	0.898244	−	0.439498i	$-0.144844\pi$
$971$	30.1247	+	17.3925i	0.966749	+	0.558153i	0.0685054	+	0.997651i	$0.478177\pi$
$972$		0			0
$973$		0			0
$974$			8.00000i			0.256337i
$975$	−12.5000	+	21.6506i	−0.400320	+	0.693375i
$976$	21.9089	−	12.6491i	0.701287	−	0.404888i
$977$	1.36603	+	0.366025i	0.0437030	+	0.0117102i	0.280604	−	0.959824i	$-0.409465\pi$
$977$	1.36603	+	0.366025i	0.0437030	+	0.0117102i	−0.236901	+	0.971534i	$0.576132\pi$
$978$	−6.94484	−	25.9185i	−0.222072	−	0.828783i
$979$	6.32456			0.202134
$980$		0			0
$981$	14.0000			0.446986
$982$	15.0070	+	56.0070i	0.478894	+	1.78726i
$983$	28.0784	+	7.52358i	0.895561	+	0.239965i	0.677109	−	0.735883i	$-0.263233\pi$
$983$	28.0784	+	7.52358i	0.895561	+	0.239965i	0.218452	+	0.975848i	$0.429899\pi$
$984$	51.9615	−	30.0000i	1.65647	−	0.956365i
$985$	2.73861	+	1.58114i	0.0872595	+	0.0503793i
$986$			9.48683i			0.302122i
$987$		0			0
$988$		0			0
$989$	10.3923	+	6.00000i	0.330456	+	0.190789i
$990$	−3.16228	−	5.47723i	−0.100504	−	0.174078i
$991$	−2.00000	−	3.46410i	−0.0635321	−	0.110041i	0.832510	−	0.554010i	$-0.186903\pi$
$991$	−2.00000	−	3.46410i	−0.0635321	−	0.110041i	−0.896042	+	0.443969i	$0.853570\pi$
$992$		0			0
$993$	−9.48683	+	9.48683i	−0.301056	+	0.301056i
$994$		0			0
$995$	15.0000	−	15.0000i	0.475532	−	0.475532i
$996$		0			0
$997$	5.20863	−	19.4389i	0.164959	−	0.615636i	−0.833086	−	0.553143i	$-0.813428\pi$
$997$	5.20863	−	19.4389i	0.164959	−	0.615636i	0.998045	−	0.0624926i	$-0.0199050\pi$
$998$	6.95448	−	25.9545i	0.220140	−	0.821575i
$999$	9.48683	−	16.4317i	0.300150	−	0.519875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.l.c.68.1		8
5.2	odd	4	inner	245.2.l.c.117.1		8
7.2	even	3		35.2.f.a.13.2	yes	4
7.3	odd	6	inner	245.2.l.c.178.1		8
7.4	even	3	inner	245.2.l.c.178.2		8
7.5	odd	6		35.2.f.a.13.1	✓	4
7.6	odd	2	inner	245.2.l.c.68.2		8
21.2	odd	6		315.2.p.c.118.2		4
21.5	even	6		315.2.p.c.118.1		4
28.19	even	6		560.2.bj.a.433.2		4
28.23	odd	6		560.2.bj.a.433.1		4
35.2	odd	12		35.2.f.a.27.1	yes	4
35.9	even	6		175.2.f.c.118.1		4
35.12	even	12		35.2.f.a.27.2	yes	4
35.17	even	12	inner	245.2.l.c.227.1		8
35.19	odd	6		175.2.f.c.118.2		4
35.23	odd	12		175.2.f.c.132.2		4
35.27	even	4	inner	245.2.l.c.117.2		8
35.32	odd	12	inner	245.2.l.c.227.2		8
35.33	even	12		175.2.f.c.132.1		4
105.2	even	12		315.2.p.c.307.1		4
105.47	odd	12		315.2.p.c.307.2		4
140.47	odd	12		560.2.bj.a.97.1		4
140.107	even	12		560.2.bj.a.97.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.f.a.13.1	✓	4	7.5	odd	6
35.2.f.a.13.2	yes	4	7.2	even	3
35.2.f.a.27.1	yes	4	35.2	odd	12
35.2.f.a.27.2	yes	4	35.12	even	12
175.2.f.c.118.1		4	35.9	even	6
175.2.f.c.118.2		4	35.19	odd	6
175.2.f.c.132.1		4	35.33	even	12
175.2.f.c.132.2		4	35.23	odd	12
245.2.l.c.68.1		8	1.1	even	1	trivial
245.2.l.c.68.2		8	7.6	odd	2	inner
245.2.l.c.117.1		8	5.2	odd	4	inner
245.2.l.c.117.2		8	35.27	even	4	inner
245.2.l.c.178.1		8	7.3	odd	6	inner
245.2.l.c.178.2		8	7.4	even	3	inner
245.2.l.c.227.1		8	35.17	even	12	inner
245.2.l.c.227.2		8	35.32	odd	12	inner
315.2.p.c.118.1		4	21.5	even	6
315.2.p.c.118.2		4	21.2	odd	6
315.2.p.c.307.1		4	105.2	even	12
315.2.p.c.307.2		4	105.47	odd	12
560.2.bj.a.97.1		4	140.47	odd	12
560.2.bj.a.97.2		4	140.107	even	12
560.2.bj.a.433.1		4	28.23	odd	6
560.2.bj.a.433.2		4	28.19	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-2.15988 - 0.578737i) q^{3} +(-0.578737 - 2.15988i) q^{5} +3.16228i q^{6} +(-2.00000 - 2.00000i) q^{8} +(1.73205 + 1.00000i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.58114 + 1.58114i) q^{13} +5.00000i q^{15} +(-2.00000 + 3.46410i) q^{16} +(0.578737 - 2.15988i) q^{17} +(0.732051 - 2.73205i) q^{18} +(-1.58114 + 2.73861i) q^{19} +(1.00000 - 1.00000i) q^{22} +(-2.73205 + 0.732051i) q^{23} +(3.16228 + 5.47723i) q^{24} +(-4.33013 + 2.50000i) q^{25} +(2.73861 + 1.58114i) q^{26} +(1.58114 + 1.58114i) q^{27} -3.00000i q^{29} +(6.83013 - 1.83013i) q^{30} +(2.73861 - 1.58114i) q^{31} +(-0.578737 - 2.15988i) q^{33} -3.16228 q^{34} +(-2.19615 - 8.19615i) q^{37} +(4.31975 + 1.15747i) q^{38} +(4.33013 - 2.50000i) q^{39} +(-3.16228 + 5.47723i) q^{40} -9.48683i q^{41} +(-3.00000 - 3.00000i) q^{43} +(1.15747 - 4.31975i) q^{45} +(2.00000 + 3.46410i) q^{46} +(6.47963 - 1.73621i) q^{47} +(6.32456 - 6.32456i) q^{48} +(5.00000 + 5.00000i) q^{50} +(-2.50000 + 4.33013i) q^{51} +(0.366025 - 1.36603i) q^{53} +(1.58114 - 2.73861i) q^{54} +(1.58114 - 1.58114i) q^{55} +(5.00000 - 5.00000i) q^{57} +(-4.09808 + 1.09808i) q^{58} +(-4.74342 - 8.21584i) q^{59} +(-5.47723 - 3.16228i) q^{61} +(-3.16228 - 3.16228i) q^{62} +8.00000i q^{64} +(4.33013 + 2.50000i) q^{65} +(-2.73861 + 1.58114i) q^{66} +(1.36603 + 0.366025i) q^{67} +6.32456 q^{69} -6.00000 q^{71} +(-1.46410 - 5.46410i) q^{72} +(-10.3923 + 6.00000i) q^{74} +(10.7994 - 2.89368i) q^{75} +(-5.00000 - 5.00000i) q^{78} +(11.2583 + 6.50000i) q^{79} +(8.63950 + 2.31495i) q^{80} +(-5.50000 - 9.52628i) q^{81} +(-12.9593 + 3.47242i) q^{82} +(-3.16228 + 3.16228i) q^{83} -5.00000 q^{85} +(-3.00000 + 5.19615i) q^{86} +(-1.73621 + 6.47963i) q^{87} +(0.732051 - 2.73205i) q^{88} +(3.16228 - 5.47723i) q^{89} -6.32456 q^{90} +(-6.83013 + 1.83013i) q^{93} +(-4.74342 - 8.21584i) q^{94} +(6.83013 + 1.83013i) q^{95} +(-1.58114 - 1.58114i) q^{97} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 16 q^{8} + 4 q^{11} - 16 q^{16} - 8 q^{18} + 8 q^{22} - 8 q^{23} + 20 q^{30} + 24 q^{37} - 24 q^{43} + 16 q^{46} + 40 q^{50} - 20 q^{51} - 4 q^{53} + 40 q^{57} - 12 q^{58} + 4 q^{67} - 48 q^{71}+ \cdots + 20 q^{95}+O(q^{100}) \) 8 * q + 4 * q^2 - 16 * q^8 + 4 * q^11 - 16 * q^16 - 8 * q^18 + 8 * q^22 - 8 * q^23 + 20 * q^30 + 24 * q^37 - 24 * q^43 + 16 * q^46 + 40 * q^50 - 20 * q^51 - 4 * q^53 + 40 * q^57 - 12 * q^58 + 4 * q^67 - 48 * q^71 + 16 * q^72 - 40 * q^78 - 44 * q^81 - 40 * q^85 - 24 * q^86 - 8 * q^88 - 20 * q^93 + 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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