LMFDB - Embedded newform 245.2.l.c.178.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(68,245)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			178.2
Root			$0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	245.178
Dual form			245.2.l.c.117.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$3$	0.578737	+	2.15988i	0.334134	+	1.24700i	0.904805	+	0.425826i	$0.140016\pi$
$3$	0.578737	+	2.15988i	0.334134	+	1.24700i	−0.570671	+	0.821179i	$0.693317\pi$
$4$		0			0
$5$	2.15988	+	0.578737i	0.965926	+	0.258819i
$5$	2.15988	+	0.578737i	0.965926	+	0.258819i
$6$			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	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$		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
$17$	−2.15988	+	0.578737i	−0.523847	+	0.140364i	−0.511045	−	0.859554i	$-0.670742\pi$
$17$	−2.15988	+	0.578737i	−0.523847	+	0.140364i	−0.0128014	+	0.999918i	$0.504075\pi$
$18$	−2.73205	+	0.732051i	−0.643951	+	0.172546i
$19$	−1.58114	−	2.73861i	−0.362738	−	0.628281i	0.625672	−	0.780086i	$-0.284825\pi$
$19$	−1.58114	−	2.73861i	−0.362738	−	0.628281i	−0.988410	+	0.151805i	$0.951491\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	0.732051	−	2.73205i	0.152643	−	0.569672i	−0.846653	−	0.532146i	$-0.821386\pi$
$23$	0.732051	−	2.73205i	0.152643	−	0.569672i	0.999296	−	0.0375258i	$-0.0119476\pi$
$24$	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	$-0.0898515\pi$
$30$	−1.83013	+	6.83013i	−0.334134	+	1.24700i
$31$	−2.73861	−	1.58114i	−0.491869	−	0.283981i	0.233480	−	0.972362i	$-0.424989\pi$
$31$	−2.73861	−	1.58114i	−0.491869	−	0.283981i	−0.725350	+	0.688381i	$0.758322\pi$
$32$		0			0
$33$	2.15988	+	0.578737i	0.375986	+	0.100745i
$34$	−3.16228			−0.542326
$35$		0			0
$36$		0			0
$37$	8.19615	+	2.19615i	1.34744	+	0.361045i	0.859189	−	0.511658i	$-0.170969\pi$
$37$	8.19615	+	2.19615i	1.34744	+	0.361045i	0.488250	+	0.872704i	$0.337635\pi$
$38$	−1.15747	−	4.31975i	−0.187767	−	0.700756i
$39$	−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
$45$	−4.31975	+	1.15747i	−0.643951	+	0.172546i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−1.73621	+	6.47963i	−0.253252	+	0.945151i	0.715802	+	0.698303i	$0.246061\pi$
$47$	−1.73621	+	6.47963i	−0.253252	+	0.945151i	−0.969054	+	0.246847i	$0.920605\pi$
$48$	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
$53$	−1.36603	+	0.366025i	−0.187638	+	0.0502775i	−0.351414	−	0.936220i	$-0.614299\pi$
$53$	−1.36603	+	0.366025i	−0.187638	+	0.0502775i	0.163776	+	0.986498i	$0.447632\pi$
$54$	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
$58$	1.09808	−	4.09808i	0.144184	−	0.538104i
$59$	−4.74342	+	8.21584i	−0.617540	+	1.06961i	0.372393	+	0.928075i	$0.378537\pi$
$59$	−4.74342	+	8.21584i	−0.617540	+	1.06961i	−0.989933	+	0.141536i	$0.954796\pi$
$60$		0			0
$61$	5.47723	−	3.16228i	0.701287	−	0.404888i	−0.106540	−	0.994308i	$-0.533977\pi$
$61$	5.47723	−	3.16228i	0.701287	−	0.404888i	0.807827	+	0.589420i	$0.200644\pi$
$62$	−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
$67$	−0.366025	−	1.36603i	−0.0447171	−	0.166887i	0.939956	−	0.341295i	$-0.110865\pi$
$67$	−0.366025	−	1.36603i	−0.0447171	−	0.166887i	−0.984673	+	0.174408i	$0.944199\pi$
$68$		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	$0.615871\pi$
$72$	5.46410	+	1.46410i	0.643951	+	0.172546i
$73$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$73$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$74$	10.3923	+	6.00000i	1.20808	+	0.697486i
$75$	−2.89368	+	10.7994i	−0.334134	+	1.24700i
$76$		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	$-0.927756\pi$
$79$	−11.2583	+	6.50000i	−1.26666	+	0.731307i	−0.292306	+	0.956325i	$0.594423\pi$
$80$	−2.31495	−	8.63950i	−0.258819	−	0.965926i
$81$	−5.50000	+	9.52628i	−0.611111	+	1.05848i
$82$	3.47242	−	12.9593i	0.383465	−	1.43111i
$83$	−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
$87$	6.47963	−	1.73621i	0.694689	−	0.186141i
$88$	−2.73205	+	0.732051i	−0.291238	+	0.0780369i
$89$	3.16228	+	5.47723i	0.335201	+	0.580585i	0.983523	−	0.180781i	$-0.0578625\pi$
$89$	3.16228	+	5.47723i	0.335201	+	0.580585i	−0.648323	+	0.761366i	$0.724529\pi$
$90$	−6.32456			−0.666667
$91$		0			0
$92$		0			0
$93$	1.83013	−	6.83013i	0.189775	−	0.708251i
$94$	−4.74342	+	8.21584i	−0.489246	+	0.847399i
$95$	−1.83013	−	6.83013i	−0.187767	−	0.700756i
$96$		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	$-0.283045\pi$
$101$	2.73861	+	1.58114i	0.272502	+	0.157329i	−0.357522	+	0.933905i	$0.616378\pi$
$102$	−1.83013	−	6.83013i	−0.181210	−	0.676283i
$103$	−15.1191	−	4.05116i	−1.48973	−	0.399173i	−0.580086	−	0.814556i	$-0.696981\pi$
$103$	−15.1191	−	4.05116i	−1.48973	−	0.399173i	−0.909647	+	0.415383i	$0.863648\pi$
$104$	6.32456			0.620174
$105$		0			0
$106$	−2.00000			−0.194257
$107$	4.09808	+	1.09808i	0.396176	+	0.106155i	0.451406	−	0.892319i	$-0.350923\pi$
$107$	4.09808	+	1.09808i	0.396176	+	0.106155i	−0.0552301	+	0.998474i	$0.517589\pi$
$108$		0			0
$109$	−6.06218	−	3.50000i	−0.580651	−	0.335239i	0.180741	−	0.983531i	$-0.442150\pi$
$109$	−6.06218	−	3.50000i	−0.580651	−	0.335239i	−0.761392	+	0.648292i	$0.775484\pi$
$110$	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
$117$	1.15747	−	4.31975i	0.107009	−	0.399361i
$118$	−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
$122$	8.63950	−	2.31495i	0.782184	−	0.209586i
$123$	20.4904	−	5.49038i	1.84756	−	0.495051i
$124$		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	$0.0589879\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	4.74342	−	8.21584i	0.417635	−	0.723364i
$130$	−6.83013	+	1.83013i	−0.599042	+	0.160513i
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$		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
$137$	0.732051	+	2.73205i	0.0625433	+	0.233415i	0.990121	−	0.140215i	$-0.0447795\pi$
$137$	0.732051	+	2.73205i	0.0625433	+	0.233415i	−0.927578	+	0.373630i	$0.878113\pi$
$138$	8.63950	+	2.31495i	0.735443	+	0.197061i
$139$	−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
$142$	−8.19615	−	2.19615i	−0.687806	−	0.184297i
$143$	0.578737	+	2.15988i	0.0483964	+	0.180618i
$144$	6.92820	+	4.00000i	0.577350	+	0.333333i
$145$	1.73621	−	6.47963i	0.144184	−	0.538104i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.3923	−	6.00000i	0.851371	−	0.491539i	−0.00974235	−	0.999953i	$-0.503101\pi$
$149$	10.3923	−	6.00000i	0.851371	−	0.491539i	0.861113	+	0.508413i	$0.169768\pi$
$150$	−7.90569	+	13.6931i	−0.645497	+	1.11803i
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	−0.988969	−	0.148124i	$-0.952676\pi$
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	0.622764	+	0.782410i	$0.286010\pi$
$152$	−2.31495	+	8.63950i	−0.187767	+	0.700756i
$153$	3.16228	−	3.16228i	0.255655	−	0.255655i
$154$		0			0
$155$	−5.00000	−	5.00000i	−0.401610	−	0.401610i
$156$		0			0
$157$	−8.63950	+	2.31495i	−0.689507	+	0.184753i	−0.586526	−	0.809930i	$-0.699505\pi$
$157$	−8.63950	+	2.31495i	−0.689507	+	0.184753i	−0.102981	+	0.994683i	$0.532838\pi$
$158$	−17.7583	+	4.75833i	−1.41278	+	0.378552i
$159$	−1.58114	−	2.73861i	−0.125392	−	0.217186i
$160$		0			0
$161$		0			0
$162$	−11.0000	+	11.0000i	−0.864242	+	0.864242i
$163$	2.19615	−	8.19615i	0.172016	−	0.641972i	−0.825025	−	0.565097i	$-0.808839\pi$
$163$	2.19615	−	8.19615i	0.172016	−	0.641972i	0.997041	−	0.0768756i	$-0.0244944\pi$
$164$		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
$170$	−6.83013	−	1.83013i	−0.523847	−	0.140364i
$171$	5.47723	+	3.16228i	0.418854	+	0.241825i
$172$		0			0
$173$	15.1191	+	4.05116i	1.14949	+	0.308004i	0.782759	−	0.622325i	$-0.213812\pi$
$173$	15.1191	+	4.05116i	1.14949	+	0.308004i	0.366727	+	0.930329i	$0.380478\pi$
$174$	9.48683			0.719195
$175$		0			0
$176$	−4.00000			−0.301511
$177$	−20.4904	−	5.49038i	−1.54015	−	0.412682i
$178$	2.31495	+	8.63950i	0.173513	+	0.647558i
$179$	−5.19615	−	3.00000i	−0.388379	−	0.224231i	0.293079	−	0.956088i	$-0.405320\pi$
$179$	−5.19615	−	3.00000i	−0.388379	−	0.224231i	−0.681457	+	0.731858i	$0.738654\pi$
$180$		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
$187$	−0.578737	+	2.15988i	−0.0423214	+	0.157946i
$188$		0			0
$189$		0			0
$190$		−	10.0000i		−	0.725476i
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$	−17.2790	+	4.62990i	−1.24700	+	0.334134i
$193$	10.9282	−	2.92820i	0.786629	−	0.210777i	0.156924	−	0.987611i	$-0.449842\pi$
$193$	10.9282	−	2.92820i	0.786629	−	0.210777i	0.629705	+	0.776834i	$0.283176\pi$
$194$	−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	$0.266043\pi$
$198$	−0.732051	+	2.73205i	−0.0520246	+	0.194158i
$199$	4.74342	−	8.21584i	0.336252	−	0.582405i	−0.647473	−	0.762089i	$-0.724174\pi$
$199$	4.74342	−	8.21584i	0.336252	−	0.582405i	0.983724	+	0.179683i	$0.0575073\pi$
$200$	−3.66025	−	13.6603i	−0.258819	−	0.965926i
$201$	2.73861	−	1.58114i	0.193167	−	0.111525i
$202$	3.16228	+	3.16228i	0.222497	+	0.222497i
$203$		0			0
$204$		0			0
$205$	5.49038	−	20.4904i	0.383465	−	1.43111i
$206$	−19.1703	−	11.0680i	−1.33566	−	0.771142i
$207$	1.46410	+	5.46410i	0.101762	+	0.379781i
$208$	8.63950	+	2.31495i	0.599042	+	0.160513i
$209$	−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
$213$	−3.47242	−	12.9593i	−0.237926	−	0.887954i
$214$	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
$222$	−6.94484	+	25.9185i	−0.466107	+	1.73954i
$223$	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
$227$	2.15988	−	0.578737i	0.143356	−	0.0384121i	−0.186427	−	0.982469i	$-0.559691\pi$
$227$	2.15988	−	0.578737i	0.143356	−	0.0384121i	0.329783	+	0.944057i	$0.393024\pi$
$228$		0			0
$229$	−7.90569	−	13.6931i	−0.522423	−	0.904863i	−0.999660	−	0.0260883i	$-0.991695\pi$
$229$	−7.90569	−	13.6931i	−0.522423	−	0.904863i	0.477237	−	0.878775i	$-0.341638\pi$
$230$	6.32456	−	6.32456i	0.417029	−	0.417029i
$231$		0			0
$232$	−6.00000	+	6.00000i	−0.393919	+	0.393919i
$233$	−6.58846	+	24.5885i	−0.431624	+	1.61084i	0.317394	+	0.948294i	$0.397192\pi$
$233$	−6.58846	+	24.5885i	−0.431624	+	1.61084i	−0.749018	+	0.662550i	$0.769474\pi$
$234$	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	$-0.636487\pi$
$241$	−21.9089	−	12.6491i	−1.41128	−	0.814801i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	3.66025	+	13.6603i	0.235290	+	0.878114i
$243$	−17.2790	−	4.62990i	−1.10845	−	0.297008i
$244$		0			0
$245$		0			0
$246$	30.0000			1.91273
$247$	6.83013	+	1.83013i	0.434591	+	0.116448i
$248$	2.31495	+	8.63950i	0.146999	+	0.548609i
$249$	−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
$255$	−2.89368	−	10.7994i	−0.181210	−	0.676283i
$256$		0			0
$257$	4.62990	−	17.2790i	0.288805	−	1.07783i	−0.657209	−	0.753709i	$-0.728263\pi$
$257$	4.62990	−	17.2790i	0.288805	−	1.07783i	0.946014	−	0.324126i	$-0.105070\pi$
$258$	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
$263$	−9.56218	+	2.56218i	−0.589629	+	0.157991i	−0.541284	−	0.840840i	$-0.682061\pi$
$263$	−9.56218	+	2.56218i	−0.589629	+	0.157991i	−0.0483454	+	0.998831i	$0.515395\pi$
$264$	−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	−0.417238	−	0.908797i	$-0.637002\pi$
$269$	9.48683	−	16.4317i	0.578422	−	1.00186i	0.995661	−	0.0930598i	$-0.0296648\pi$
$270$	1.83013	+	6.83013i	0.111378	+	0.415668i
$271$	−10.9545	+	6.32456i	−0.665436	+	0.384189i	−0.794345	−	0.607467i	$-0.792186\pi$
$271$	−10.9545	+	6.32456i	−0.665436	+	0.384189i	0.128909	+	0.991656i	$0.458852\pi$
$272$	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
$277$	−6.58846	−	24.5885i	−0.395862	−	1.47738i	−0.820307	−	0.571923i	$-0.806197\pi$
$277$	−6.58846	−	24.5885i	−0.395862	−	1.47738i	0.424445	−	0.905454i	$-0.360469\pi$
$278$	−25.9185	−	6.94484i	−1.55449	−	0.416524i
$279$	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	$0.413489\pi$
$282$	−20.4904	−	5.49038i	−1.22018	−	0.326947i
$283$	−1.73621	−	6.47963i	−0.103207	−	0.385174i	0.894929	−	0.446209i	$-0.147226\pi$
$283$	−1.73621	−	6.47963i	−0.103207	−	0.385174i	−0.998136	+	0.0610356i	$0.980560\pi$
$284$		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
$297$	2.15988	−	0.578737i	0.125329	−	0.0335817i
$298$	16.3923	−	4.39230i	0.949581	−	0.254439i
$299$	3.16228	+	5.47723i	0.182879	+	0.316756i
$300$		0			0
$301$		0			0
$302$	−9.00000	+	9.00000i	−0.517892	+	0.517892i
$303$	−1.83013	+	6.83013i	−0.105138	+	0.392381i
$304$	−6.32456	+	10.9545i	−0.362738	+	0.628281i
$305$	13.6603	−	3.66025i	0.782184	−	0.209586i
$306$	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	$-0.117368\pi$
$311$	19.1703	+	11.0680i	1.08705	+	0.627607i	0.154259	+	0.988031i	$0.450701\pi$
$312$	3.66025	+	13.6603i	0.207221	+	0.773360i
$313$	19.4389	+	5.20863i	1.09875	+	0.294409i	0.762256	−	0.647276i	$-0.224092\pi$
$313$	19.4389	+	5.20863i	1.09875	+	0.294409i	0.336495	+	0.941685i	$0.390759\pi$
$314$	−12.6491			−0.713831
$315$		0			0
$316$		0			0
$317$	−25.9545	−	6.95448i	−1.45775	−	0.390603i	−0.559037	−	0.829143i	$-0.688829\pi$
$317$	−25.9545	−	6.95448i	−1.45775	−	0.390603i	−0.898712	+	0.438540i	$0.855496\pi$
$318$	−1.15747	−	4.31975i	−0.0649079	−	0.242240i
$319$	−2.59808	−	1.50000i	−0.145464	−	0.0839839i
$320$	−4.62990	+	17.2790i	−0.258819	+	0.965926i
$321$			9.48683i			0.529503i
$322$		0			0
$323$	5.00000	+	5.00000i	0.278207	+	0.278207i
$324$		0			0
$325$	−10.7994	+	2.89368i	−0.599042	+	0.160513i
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$	4.05116	−	15.1191i	0.224030	−	0.836090i
$328$	−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	0.936618	−	0.350352i	$-0.113938\pi$
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	−0.771723	+	0.635959i	$0.780605\pi$
$332$		0			0
$333$	−16.3923	+	4.39230i	−0.898293	+	0.240697i
$334$	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	$0.349709\pi$
$338$	−2.92820	+	10.9282i	−0.159273	+	0.594416i
$339$	−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
$345$	13.6603	+	3.66025i	0.735443	+	0.197061i
$346$	19.1703	+	11.0680i	1.03060	+	0.595018i
$347$	8.78461	+	32.7846i	0.471583	+	1.75997i	0.634086	+	0.773262i	$0.281376\pi$
$347$	8.78461	+	32.7846i	0.471583	+	1.75997i	−0.162504	+	0.986708i	$0.551957\pi$
$348$		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
$353$	5.20863	+	19.4389i	0.277228	+	1.03463i	0.954334	+	0.298742i	$0.0965670\pi$
$353$	5.20863	+	19.4389i	0.277228	+	1.03463i	−0.677106	+	0.735885i	$0.736766\pi$
$354$	−25.9808	−	15.0000i	−1.38086	−	0.797241i
$355$	−12.9593	−	3.47242i	−0.687806	−	0.184297i
$356$		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	$-0.469501\pi$
$359$	19.0526	−	11.0000i	1.00556	−	0.580558i	0.909887	+	0.414855i	$0.136168\pi$
$360$	10.9545	+	6.32456i	0.577350	+	0.333333i
$361$	4.50000	−	7.79423i	0.236842	−	0.410223i
$362$	8.10232	−	30.2383i	0.425848	−	1.58929i
$363$	−15.8114	+	15.8114i	−0.829883	+	0.829883i
$364$		0			0
$365$		0			0
$366$	10.0000	+	17.3205i	0.522708	+	0.905357i
$367$	23.7586	−	6.36611i	1.24019	−	0.332308i	0.421651	−	0.906758i	$-0.361451\pi$
$367$	23.7586	−	6.36611i	1.24019	−	0.332308i	0.818540	+	0.574450i	$0.194784\pi$
$368$	−10.9282	+	2.92820i	−0.569672	+	0.152643i
$369$	9.48683	+	16.4317i	0.493865	+	0.855399i
$370$	18.9737	+	18.9737i	0.986394	+	0.986394i
$371$		0			0
$372$		0			0
$373$	4.39230	−	16.3923i	0.227425	−	0.848761i	−0.753994	−	0.656882i	$-0.771875\pi$
$373$	4.39230	−	16.3923i	0.227425	−	0.848761i	0.981418	−	0.191880i	$-0.0614583\pi$
$374$	−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
$382$	1.09808	+	4.09808i	0.0561825	+	0.209676i
$383$	21.5988	+	5.78737i	1.10364	+	0.295721i	0.764248	−	0.644922i	$-0.223110\pi$
$383$	21.5988	+	5.78737i	1.10364	+	0.295721i	0.339397	+	0.940643i	$0.389777\pi$
$384$	−25.2982			−1.29099
$385$		0			0
$386$	16.0000			0.814379
$387$	8.19615	+	2.19615i	0.416634	+	0.111637i
$388$		0			0
$389$	19.9186	+	11.5000i	1.00991	+	0.583073i	0.911166	−	0.412039i	$-0.135183\pi$
$389$	19.9186	+	11.5000i	1.00991	+	0.583073i	0.0987463	+	0.995113i	$0.468517\pi$
$390$	−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
$395$	−28.0784	+	7.52358i	−1.41278	+	0.378552i
$396$		0			0
$397$	−8.68105	+	32.3981i	−0.435690	+	1.62602i	0.303721	+	0.952761i	$0.401771\pi$
$397$	−8.68105	+	32.3981i	−0.435690	+	1.62602i	−0.739411	+	0.673255i	$0.764896\pi$
$398$	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	0.878240	−	0.478220i	$-0.158718\pi$
$401$	0.500000	+	0.866025i	0.0249688	+	0.0432472i	−0.853271	+	0.521468i	$0.825385\pi$
$402$	4.31975	−	1.15747i	0.215450	−	0.0577296i
$403$	6.83013	−	1.83013i	0.340233	−	0.0911651i
$404$		0			0
$405$	−17.3925	+	17.3925i	−0.864242	+	0.864242i
$406$		0			0
$407$	6.00000	−	6.00000i	0.297409	−	0.297409i
$408$	−3.66025	+	13.6603i	−0.181210	+	0.676283i
$409$	−1.58114	+	2.73861i	−0.0781823	+	0.135416i	−0.902466	−	0.430762i	$-0.858245\pi$
$409$	−1.58114	+	2.73861i	−0.0781823	+	0.135416i	0.824283	+	0.566177i	$0.191578\pi$
$410$	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
$417$	−10.9808	−	40.9808i	−0.537730	−	2.00684i
$418$	−4.31975	−	1.15747i	−0.211286	−	0.0566139i
$419$	−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	$0.346772\pi$
$422$	23.2224	+	6.22243i	1.13045	+	0.302903i
$423$	−3.47242	−	12.9593i	−0.168835	−	0.630101i
$424$	3.46410	+	2.00000i	0.168232	+	0.0971286i
$425$	−10.7994	−	2.89368i	−0.523847	−	0.140364i
$426$		−	18.9737i		−	0.919277i
$427$		0			0
$428$		0			0
$429$	−4.33013	+	2.50000i	−0.209061	+	0.120701i
$430$	−3.47242	−	12.9593i	−0.167455	−	0.624951i
$431$	11.5000	−	19.9186i	0.553936	−	0.959444i	−0.444050	−	0.896002i	$-0.646459\pi$
$431$	11.5000	−	19.9186i	0.553936	−	0.959444i	0.997985	−	0.0634424i	$-0.0202079\pi$
$432$	2.31495	−	8.63950i	0.111378	−	0.415668i
$433$	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
$437$	−8.63950	+	2.31495i	−0.413283	+	0.110739i
$438$		0			0
$439$	6.32456	+	10.9545i	0.301855	+	0.522827i	0.976556	−	0.215263i	$-0.0690610\pi$
$439$	6.32456	+	10.9545i	0.301855	+	0.522827i	−0.674701	+	0.738091i	$0.735728\pi$
$440$	−6.32456			−0.301511
$441$		0			0
$442$	5.00000	−	5.00000i	0.237826	−	0.237826i
$443$	0.366025	−	1.36603i	0.0173904	−	0.0649018i	−0.956685	−	0.291124i	$-0.905971\pi$
$443$	0.366025	−	1.36603i	0.0173904	−	0.0649018i	0.974076	+	0.226222i	$0.0726375\pi$
$444$		0			0
$445$	3.66025	+	13.6603i	0.173513	+	0.647558i
$446$	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	$0.868614\pi$
$450$	−13.6603	−	3.66025i	−0.643951	−	0.172546i
$451$	−8.21584	−	4.74342i	−0.386869	−	0.223359i
$452$		0			0
$453$	−19.4389	−	5.20863i	−0.913318	−	0.244723i
$454$	3.16228			0.148413
$455$		0			0
$456$	−20.0000			−0.936586
$457$	1.36603	+	0.366025i	0.0639000	+	0.0171219i	0.290627	−	0.956836i	$-0.406136\pi$
$457$	1.36603	+	0.366025i	0.0639000	+	0.0171219i	−0.226727	+	0.973958i	$0.572803\pi$
$458$	−5.78737	−	21.5988i	−0.270426	−	1.00924i
$459$	−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
$467$	−4.05116	+	15.1191i	−0.187465	+	0.699630i	0.806624	+	0.591065i	$0.201292\pi$
$467$	−4.05116	+	15.1191i	−0.187465	+	0.699630i	−0.994089	+	0.108565i	$0.965374\pi$
$468$		0			0
$469$		0			0
$470$	−15.0000	+	15.0000i	−0.691898	+	0.691898i
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$	25.9185	−	6.94484i	1.19300	−	0.319662i
$473$	−4.09808	+	1.09808i	−0.188430	+	0.0504896i
$474$	−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
$478$	6.95448	−	25.9545i	0.318091	−	1.18713i
$479$	3.16228	−	5.47723i	0.144488	−	0.250261i	−0.784694	−	0.619884i	$-0.787180\pi$
$479$	3.16228	−	5.47723i	0.144488	−	0.250261i	0.929182	+	0.369623i	$0.120513\pi$
$480$		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
$487$	1.46410	+	5.46410i	0.0663448	+	0.247602i	0.991132	−	0.132883i	$-0.0424236\pi$
$487$	1.46410	+	5.46410i	0.0663448	+	0.247602i	−0.924787	+	0.380485i	$0.875757\pi$
$488$	−17.2790	−	4.62990i	−0.782184	−	0.209586i
$489$	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
$493$	1.73621	+	6.47963i	0.0781950	+	0.291828i
$494$	8.66025	+	5.00000i	0.389643	+	0.224961i
$495$	−1.15747	+	4.31975i	−0.0520246	+	0.194158i
$496$			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	$-0.806490\pi$
$499$	−16.4545	+	9.50000i	−0.736604	+	0.425278i	0.0842294	+	0.996446i	$0.473157\pi$
$500$		0			0
$501$	−17.5000	+	30.3109i	−0.781842	+	1.35419i
$502$	−4.62990	+	17.2790i	−0.206642	+	0.771200i
$503$	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
$507$	−17.2790	+	4.62990i	−0.767388	+	0.205621i
$508$		0			0
$509$	−9.48683	−	16.4317i	−0.420496	−	0.728321i	0.575492	−	0.817808i	$-0.304811\pi$
$509$	−9.48683	−	16.4317i	−0.420496	−	0.728321i	−0.995988	+	0.0894865i	$0.971477\pi$
$510$		−	15.8114i		−	0.700140i
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	1.83013	−	6.83013i	0.0808021	−	0.301557i
$514$	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
$520$	13.6603	+	3.66025i	0.599042	+	0.160513i
$521$	−35.6020	−	20.5548i	−1.55975	−	0.900522i	−0.997280	−	0.0737049i	$-0.976518\pi$
$521$	−35.6020	−	20.5548i	−1.55975	−	0.900522i	−0.562470	−	0.826817i	$-0.690149\pi$
$522$	2.19615	+	8.19615i	0.0961230	+	0.358736i
$523$	25.9185	+	6.94484i	1.13334	+	0.303677i	0.776269	−	0.630402i	$-0.217110\pi$
$523$	25.9185	+	6.94484i	1.13334	+	0.303677i	0.357068	+	0.934078i	$0.383776\pi$
$524$		0			0
$525$		0			0
$526$	−14.0000			−0.610429
$527$	6.83013	+	1.83013i	0.297525	+	0.0797216i
$528$	−2.31495	−	8.63950i	−0.100745	−	0.375986i
$529$	12.9904	+	7.50000i	0.564799	+	0.326087i
$530$	−4.31975	−	1.15747i	−0.187638	−	0.0502775i
$531$		−	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
$537$	3.47242	−	12.9593i	0.149846	−	0.559233i
$538$	18.9737	−	18.9737i	0.818013	−	0.818013i
$539$		0			0
$540$		0			0
$541$	−4.50000	−	7.79423i	−0.193470	−	0.335100i	0.752928	−	0.658103i	$-0.228641\pi$
$541$	−4.50000	−	7.79423i	−0.193470	−	0.335100i	−0.946398	+	0.323003i	$0.895308\pi$
$542$	−17.2790	+	4.62990i	−0.742197	+	0.198871i
$543$	47.8109	−	12.8109i	2.05176	−	0.549768i
$544$		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
$550$	6.83013	−	1.83013i	0.291238	−	0.0780369i
$551$	−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
$555$	−10.9808	+	40.9808i	−0.466107	+	1.73954i
$556$		0			0
$557$	−2.19615	−	8.19615i	−0.0930540	−	0.347282i	0.903663	−	0.428244i	$-0.140868\pi$
$557$	−2.19615	−	8.19615i	−0.0930540	−	0.347282i	−0.996717	+	0.0809616i	$0.974201\pi$
$558$	8.63950	+	2.31495i	0.365739	+	0.0979996i
$559$	9.48683			0.401250
$560$		0			0
$561$	−5.00000			−0.211100
$562$	12.2942	+	3.29423i	0.518601	+	0.138959i
$563$	3.47242	+	12.9593i	0.146345	+	0.546167i	0.999692	+	0.0248236i	$0.00790242\pi$
$563$	3.47242	+	12.9593i	0.146345	+	0.546167i	−0.853347	+	0.521344i	$0.825431\pi$
$564$		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	$-0.432637\pi$
$569$	27.7128	−	16.0000i	1.16178	−	0.670755i	0.951730	+	0.306935i	$0.0993036\pi$
$570$	21.5988	−	5.78737i	0.904672	−	0.242406i
$571$	13.0000	−	22.5167i	0.544033	−	0.942293i	−0.454634	−	0.890678i	$-0.650230\pi$
$571$	13.0000	−	22.5167i	0.544033	−	0.942293i	0.998667	−	0.0516146i	$-0.0164367\pi$
$572$		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
$577$	−28.0784	+	7.52358i	−1.16892	+	0.313211i	−0.790522	−	0.612433i	$-0.790191\pi$
$577$	−28.0784	+	7.52358i	−1.16892	+	0.313211i	−0.378396	+	0.925644i	$0.623524\pi$
$578$	−16.3923	+	4.39230i	−0.681830	+	0.182696i
$579$	12.6491	+	21.9089i	0.525679	+	0.910503i
$580$		0			0
$581$		0			0
$582$	5.00000	−	5.00000i	0.207257	−	0.207257i
$583$	−0.366025	+	1.36603i	−0.0151592	+	0.0565750i
$584$		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
$592$	−8.78461	−	32.7846i	−0.361045	−	1.34744i
$593$	−28.0784	−	7.52358i	−1.15304	−	0.308956i	−0.368858	−	0.929486i	$-0.620251\pi$
$593$	−28.0784	−	7.52358i	−1.15304	−	0.308956i	−0.784183	+	0.620529i	$0.786918\pi$
$594$	3.16228			0.129750
$595$		0			0
$596$		0			0
$597$	20.4904	+	5.49038i	0.838615	+	0.224706i
$598$	2.31495	+	8.63950i	0.0946653	+	0.353296i
$599$	11.2583	+	6.50000i	0.460003	+	0.265583i	0.712045	−	0.702133i	$-0.247769\pi$
$599$	11.2583	+	6.50000i	0.460003	+	0.265583i	−0.252043	+	0.967716i	$0.581102\pi$
$600$	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
$605$	5.78737	+	21.5988i	0.235290	+	0.878114i
$606$	−5.00000	+	8.66025i	−0.203111	+	0.351799i
$607$	5.20863	−	19.4389i	0.211412	−	0.789000i	−0.775987	−	0.630749i	$-0.782748\pi$
$607$	5.20863	−	19.4389i	0.211412	−	0.789000i	0.987399	−	0.158251i	$-0.0505855\pi$
$608$		0			0
$609$		0			0
$610$	20.0000			0.809776
$611$	−7.50000	−	12.9904i	−0.303418	−	0.525535i
$612$		0			0
$613$	−23.2224	+	6.22243i	−0.937945	+	0.251322i	−0.695239	−	0.718778i	$-0.744702\pi$
$613$	−23.2224	+	6.22243i	−0.937945	+	0.251322i	−0.242706	+	0.970100i	$0.578035\pi$
$614$	−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	$0.213676\pi$
$618$	12.8109	−	47.8109i	0.515330	−	1.92324i
$619$	12.6491	−	21.9089i	0.508411	−	0.880593i	−0.491542	−	0.870854i	$-0.663567\pi$
$619$	12.6491	−	21.9089i	0.508411	−	0.880593i	0.999953	−	0.00973920i	$-0.00310013\pi$
$620$		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
$627$	−1.83013	−	6.83013i	−0.0730882	−	0.272769i
$628$		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	$0.711670\pi$
$632$	35.5167	+	9.51666i	1.41278	+	0.378552i
$633$	9.83853	+	36.7179i	0.391046	+	1.45941i
$634$	−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	−0.00587459	+	0.999983i	$0.501870\pi$
$641$	−22.0000	+	38.1051i	−0.868948	+	1.50506i	−0.863073	+	0.505079i	$0.831463\pi$
$642$	−3.47242	+	12.9593i	−0.137046	+	0.511461i
$643$	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
$647$	−17.2790	+	4.62990i	−0.679308	+	0.182020i	−0.581944	−	0.813229i	$-0.697708\pi$
$647$	−17.2790	+	4.62990i	−0.679308	+	0.182020i	−0.0973638	+	0.995249i	$0.531041\pi$
$648$	30.0526	−	8.05256i	1.18058	−	0.316334i
$649$	4.74342	+	8.21584i	0.186195	+	0.322500i
$650$	−15.8114			−0.620174
$651$		0			0
$652$		0			0
$653$	−6.95448	+	25.9545i	−0.272150	+	1.01568i	0.685577	+	0.728000i	$0.259550\pi$
$653$	−6.95448	+	25.9545i	−0.272150	+	1.01568i	−0.957727	+	0.287678i	$0.907117\pi$
$654$	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	$-0.254218\pi$
$661$	10.9545	+	6.32456i	0.426079	+	0.245997i	−0.271596	+	0.962411i	$0.587551\pi$
$662$	2.19615	+	8.19615i	0.0853559	+	0.318553i
$663$	10.7994	+	2.89368i	0.419413	+	0.112381i
$664$	12.6491			0.490881
$665$		0			0
$666$	−24.0000			−0.929981
$667$	−8.19615	−	2.19615i	−0.317356	−	0.0850354i
$668$		0			0
$669$	38.9711	+	22.5000i	1.50671	+	0.869900i
$670$	1.15747	−	4.31975i	0.0447171	−	0.166887i
$671$		−	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
$675$	2.89368	+	10.7994i	0.111378	+	0.415668i
$676$		0			0
$677$	−5.20863	+	19.4389i	−0.200184	+	0.747097i	0.790680	+	0.612230i	$0.209727\pi$
$677$	−5.20863	+	19.4389i	−0.200184	+	0.747097i	−0.990864	+	0.134867i	$0.956939\pi$
$678$	−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
$682$	−4.31975	+	1.15747i	−0.165412	+	0.0443220i
$683$	−43.7128	+	11.7128i	−1.67262	+	0.448178i	−0.965816	−	0.259227i	$-0.916532\pi$
$683$	−43.7128	+	11.7128i	−1.67262	+	0.448178i	−0.706808	+	0.707406i	$0.749865\pi$
$684$		0			0
$685$			6.32456i			0.241649i
$686$		0			0
$687$	25.0000	−	25.0000i	0.953809	−	0.953809i
$688$	−4.39230	+	16.3923i	−0.167455	+	0.624951i
$689$	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	$-0.461239\pi$
$691$	27.3861	−	15.8114i	1.04182	−	0.601494i	0.920348	+	0.391102i	$0.127906\pi$
$692$		0			0
$693$		0			0
$694$			48.0000i			1.82206i
$695$	−40.9808	−	10.9808i	−1.55449	−	0.416524i
$696$	−16.4317	−	9.48683i	−0.622841	−	0.359597i
$697$	5.49038	+	20.4904i	0.207963	+	0.776129i
$698$	47.5173	+	12.7322i	1.79856	+	0.481921i
$699$	−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	$0.578953\pi$
$702$	−6.83013	−	1.83013i	−0.257787	−	0.0690737i
$703$	−6.94484	−	25.9185i	−0.261930	−	0.977535i
$704$	6.92820	+	4.00000i	0.261116	+	0.150756i
$705$	−32.3981	−	8.68105i	−1.22018	−	0.326947i
$706$			28.4605i			1.07113i
$707$		0			0
$708$		0			0
$709$	−7.79423	+	4.50000i	−0.292718	+	0.169001i	−0.639167	−	0.769068i	$-0.720721\pi$
$709$	−7.79423	+	4.50000i	−0.292718	+	0.169001i	0.346449	+	0.938069i	$0.387387\pi$
$710$	−16.4317	−	9.48683i	−0.616670	−	0.356034i
$711$	13.0000	−	22.5167i	0.487538	−	0.844441i
$712$	4.62990	−	17.2790i	0.173513	−	0.647558i
$713$	−6.32456	+	6.32456i	−0.236856	+	0.236856i
$714$		0			0
$715$			5.00000i			0.186989i
$716$		0			0
$717$	41.0376	−	10.9960i	1.53258	−	0.410653i
$718$	30.0526	−	8.05256i	1.12155	−	0.300519i
$719$	−15.8114	−	27.3861i	−0.589665	−	1.02133i	−0.994276	−	0.106841i	$-0.965926\pi$
$719$	−15.8114	−	27.3861i	−0.589665	−	1.02133i	0.404611	−	0.914489i	$-0.367407\pi$
$720$	12.6491	+	12.6491i	0.471405	+	0.471405i
$721$		0			0
$722$	9.00000	−	9.00000i	0.334945	−	0.334945i
$723$	14.6410	−	54.6410i	0.544505	−	2.03212i
$724$		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
$733$	−23.7586	−	6.36611i	−0.877545	−	0.235138i	−0.208197	−	0.978087i	$-0.566760\pi$
$733$	−23.7586	−	6.36611i	−0.877545	−	0.235138i	−0.669348	+	0.742949i	$0.733426\pi$
$734$	34.7851			1.28394
$735$		0			0
$736$		0			0
$737$	−1.36603	−	0.366025i	−0.0503182	−	0.0134827i
$738$	6.94484	+	25.9185i	0.255643	+	0.954074i
$739$	−32.0429	−	18.5000i	−1.17872	−	0.680534i	−0.223001	−	0.974818i	$-0.571585\pi$
$739$	−32.0429	−	18.5000i	−1.17872	−	0.680534i	−0.955718	+	0.294285i	$0.904919\pi$
$740$		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
$745$	25.9185	−	6.94484i	0.949581	−	0.254439i
$746$	12.0000	−	20.7846i	0.439351	−	0.760979i
$747$	2.31495	−	8.63950i	0.0846995	−	0.316103i
$748$		0			0
$749$		0			0
$750$	−25.0000	+	25.0000i	−0.912871	+	0.912871i
$751$	−18.5000	−	32.0429i	−0.675075	−	1.16926i	−0.976447	−	0.215757i	$-0.930778\pi$
$751$	−18.5000	−	32.0429i	−0.675075	−	1.16926i	0.301373	−	0.953506i	$-0.402555\pi$
$752$	25.9185	−	6.94484i	0.945151	−	0.253252i
$753$	−27.3205	+	7.32051i	−0.995615	+	0.266774i
$754$	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	$0.384892\pi$
$758$	2.92820	−	10.9282i	0.106357	−	0.396930i
$759$	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	$-0.515043\pi$
$761$	21.9089	−	12.6491i	0.794197	−	0.458530i	0.841438	+	0.540354i	$0.181710\pi$
$762$	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
$767$	−5.49038	−	20.4904i	−0.198246	−	0.739865i
$768$		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
$773$	−13.3110	−	49.6771i	−0.478762	−	1.78676i	−0.606644	−	0.794973i	$-0.707485\pi$
$773$	−13.3110	−	49.6771i	−0.478762	−	1.78676i	0.127883	−	0.991789i	$-0.459182\pi$
$774$	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
$782$	−2.31495	+	8.63950i	−0.0827824	+	0.308948i
$783$	4.74342	−	4.74342i	0.169516	−	0.169516i
$784$		0			0
$785$	−20.0000			−0.713831
$786$		0			0
$787$	−23.7586	+	6.36611i	−0.846904	+	0.226927i	−0.656075	−	0.754696i	$-0.727784\pi$
$787$	−23.7586	+	6.36611i	−0.846904	+	0.226927i	−0.190829	+	0.981623i	$0.561118\pi$
$788$		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
$793$	−3.66025	+	13.6603i	−0.129979	+	0.485090i
$794$	−23.7171	+	41.0792i	−0.841688	+	1.45785i
$795$	−1.83013	−	6.83013i	−0.0649079	−	0.242240i
$796$		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
$802$	0.366025	+	1.36603i	0.0129248	+	0.0482360i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	10.0000			0.352235
$807$	40.9808	+	10.9808i	1.44259	+	0.386541i
$808$	−2.31495	−	8.63950i	−0.0814396	−	0.303937i
$809$	2.59808	+	1.50000i	0.0913435	+	0.0527372i	0.544976	−	0.838452i	$-0.316539\pi$
$809$	2.59808	+	1.50000i	0.0913435	+	0.0527372i	−0.453632	+	0.891189i	$0.649872\pi$
$810$	−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
$817$	−3.47242	+	12.9593i	−0.121485	+	0.453387i
$818$	−3.16228	+	3.16228i	−0.110566	+	0.110566i
$819$		0			0
$820$		0			0
$821$	11.5000	+	19.9186i	0.401353	+	0.695163i	0.993889	−	0.110380i	$-0.0352068\pi$
$821$	11.5000	+	19.9186i	0.401353	+	0.695163i	−0.592537	+	0.805543i	$0.701873\pi$
$822$	−8.63950	+	2.31495i	−0.301337	+	0.0807431i
$823$	4.09808	−	1.09808i	0.142850	−	0.0382765i	−0.186686	−	0.982420i	$-0.559775\pi$
$823$	4.09808	−	1.09808i	0.142850	−	0.0382765i	0.329535	+	0.944143i	$0.393108\pi$
$824$	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	−0.999978	−	0.00664181i	$-0.997886\pi$
$829$	−14.2302	+	24.6475i	−0.494237	+	0.856044i	0.505741	+	0.862685i	$0.331219\pi$
$830$	−13.6603	+	3.66025i	−0.474154	+	0.127049i
$831$	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
$837$	−1.83013	−	6.83013i	−0.0632584	−	0.236084i
$838$	−21.5988	−	5.78737i	−0.746117	−	0.199921i
$839$	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
$842$	25.9545	+	6.95448i	0.894451	+	0.239667i
$843$	5.20863	+	19.4389i	0.179395	+	0.669511i
$844$		0			0
$845$	−4.62990	+	17.2790i	−0.159273	+	0.594416i
$846$		−	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
$857$	43.1975	−	11.5747i	1.47560	−	0.395386i	0.570752	−	0.821122i	$-0.306652\pi$
$857$	43.1975	−	11.5747i	1.47560	−	0.395386i	0.904847	+	0.425737i	$0.139985\pi$
$858$	−6.83013	+	1.83013i	−0.233177	+	0.0624795i
$859$	−6.32456	−	10.9545i	−0.215791	−	0.373761i	0.737726	−	0.675100i	$-0.235900\pi$
$859$	−6.32456	−	10.9545i	−0.215791	−	0.373761i	−0.953517	+	0.301339i	$0.902566\pi$
$860$		0			0
$861$		0			0
$862$	23.0000	−	23.0000i	0.783383	−	0.783383i
$863$	−4.75833	+	17.7583i	−0.161975	+	0.604501i	0.836431	+	0.548072i	$0.184638\pi$
$863$	−4.75833	+	17.7583i	−0.161975	+	0.604501i	−0.998407	+	0.0564286i	$0.982029\pi$
$864$		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
$870$	20.4904	+	5.49038i	0.694689	+	0.186141i
$871$	2.73861	+	1.58114i	0.0927944	+	0.0535748i
$872$	5.12436	+	19.1244i	0.173533	+	0.647632i
$873$	4.31975	+	1.15747i	0.146201	+	0.0391746i
$874$	−12.6491			−0.427863
$875$		0			0
$876$		0			0
$877$	−23.2224	−	6.22243i	−0.784166	−	0.210117i	−0.155545	−	0.987829i	$-0.549713\pi$
$877$	−23.2224	−	6.22243i	−0.784166	−	0.210117i	−0.628621	+	0.777712i	$0.716380\pi$
$878$	4.62990	+	17.2790i	0.156251	+	0.583138i
$879$	−21.6506	−	12.5000i	−0.730258	−	0.421615i
$880$	−8.63950	−	2.31495i	−0.291238	−	0.0780369i
$881$			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
$887$	1.15747	−	4.31975i	0.0388642	−	0.145043i	−0.943767	−	0.330610i	$-0.892746\pi$
$887$	1.15747	−	4.31975i	0.0388642	−	0.145043i	0.982632	+	0.185567i	$0.0594122\pi$
$888$	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
$893$	20.4904	−	5.49038i	0.685684	−	0.183729i
$894$	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
$898$	−6.22243	+	23.2224i	−0.207645	+	0.774943i
$899$	−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
$905$	12.8109	−	47.8109i	0.425848	−	1.58929i
$906$	−24.6475	−	14.2302i	−0.818859	−	0.472768i
$907$	8.05256	+	30.0526i	0.267381	+	0.997879i	0.960777	+	0.277322i	$0.0894470\pi$
$907$	8.05256	+	30.0526i	0.267381	+	0.997879i	−0.693396	+	0.720557i	$0.743886\pi$
$908$		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	$0.147496\pi$
$912$	−27.3205	−	7.32051i	−0.904672	−	0.242406i
$913$	1.15747	+	4.31975i	0.0383068	+	0.142963i
$914$	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	$-0.519755\pi$
$919$	23.3827	−	13.5000i	0.771324	−	0.445324i	0.833347	+	0.552751i	$0.186422\pi$
$920$	−17.2790	+	4.62990i	−0.569672	+	0.152643i
$921$	7.50000	−	12.9904i	0.247133	−	0.428048i
$922$	2.31495	−	8.63950i	0.0762387	−	0.284527i
$923$	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
$927$	30.2383	−	8.10232i	0.993155	−	0.266115i
$928$		0			0
$929$	−1.58114	−	2.73861i	−0.0518755	−	0.0898510i	0.838922	−	0.544252i	$-0.183187\pi$
$929$	−1.58114	−	2.73861i	−0.0518755	−	0.0898510i	−0.890797	+	0.454401i	$0.849853\pi$
$930$	15.8114	−	15.8114i	0.518476	−	0.518476i
$931$		0			0
$932$		0			0
$933$	−12.8109	+	47.8109i	−0.419410	+	1.56526i
$934$	−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	$-0.121064\pi$
$941$	32.8634	+	18.9737i	1.07131	+	0.618524i	0.142774	+	0.989755i	$0.454398\pi$
$942$	−7.32051	−	27.3205i	−0.238515	−	0.890150i
$943$	−25.9185	−	6.94484i	−0.844023	−	0.226155i
$944$	37.9473			1.23508
$945$		0			0
$946$	−6.00000			−0.195077
$947$	−9.56218	−	2.56218i	−0.310729	−	0.0832596i	0.100085	−	0.994979i	$-0.468089\pi$
$947$	−9.56218	−	2.56218i	−0.310729	−	0.0832596i	−0.410814	+	0.911719i	$0.634755\pi$
$948$		0			0
$949$		0			0
$950$	5.78737	−	21.5988i	0.187767	−	0.700756i
$951$		−	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
$955$	1.73621	+	6.47963i	0.0561825	+	0.209676i
$956$		0			0
$957$	1.73621	−	6.47963i	0.0561237	−	0.209457i
$958$	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
$962$	−25.9185	+	6.94484i	−0.835646	+	0.223911i
$963$	−8.19615	+	2.19615i	−0.264117	+	0.0707700i
$964$		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	$0.979867\pi$
$968$	7.32051	−	27.3205i	0.235290	−	0.878114i
$969$	−7.90569	+	13.6931i	−0.253967	+	0.439885i
$970$	−1.83013	−	6.83013i	−0.0587618	−	0.219302i
$971$	−30.1247	+	17.3925i	−0.966749	+	0.558153i	−0.898244	−	0.439498i	$-0.855156\pi$
$971$	−30.1247	+	17.3925i	−0.966749	+	0.558153i	−0.0685054	+	0.997651i	$0.521823\pi$
$972$		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
$977$	−0.366025	−	1.36603i	−0.0117102	−	0.0437030i	0.959824	−	0.280604i	$-0.0905349\pi$
$977$	−0.366025	−	1.36603i	−0.0117102	−	0.0437030i	−0.971534	+	0.236901i	$0.923868\pi$
$978$	25.9185	+	6.94484i	0.828783	+	0.222072i
$979$	6.32456			0.202134
$980$		0			0
$981$	14.0000			0.446986
$982$	−56.0070	−	15.0070i	−1.78726	−	0.478894i
$983$	−7.52358	−	28.0784i	−0.239965	−	0.895561i	−0.975848	−	0.218452i	$-0.929899\pi$
$983$	−7.52358	−	28.0784i	−0.239965	−	0.895561i	0.735883	−	0.677109i	$-0.236767\pi$
$984$	−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	−0.896042	−	0.443969i	$-0.853570\pi$
$991$	−2.00000	+	3.46410i	−0.0635321	+	0.110041i	0.832510	+	0.554010i	$0.186903\pi$
$992$		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
$997$	−19.4389	+	5.20863i	−0.615636	+	0.164959i	−0.553143	−	0.833086i	$-0.686572\pi$
$997$	−19.4389	+	5.20863i	−0.615636	+	0.164959i	−0.0624926	+	0.998045i	$0.519905\pi$
$998$	−25.9545	+	6.95448i	−0.821575	+	0.220140i
$999$	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.178.2		8
5.2	odd	4	inner	245.2.l.c.227.2		8
7.2	even	3	inner	245.2.l.c.68.1		8
7.3	odd	6		35.2.f.a.13.1	✓	4
7.4	even	3		35.2.f.a.13.2	yes	4
7.5	odd	6	inner	245.2.l.c.68.2		8
7.6	odd	2	inner	245.2.l.c.178.1		8
21.11	odd	6		315.2.p.c.118.2		4
21.17	even	6		315.2.p.c.118.1		4
28.3	even	6		560.2.bj.a.433.2		4
28.11	odd	6		560.2.bj.a.433.1		4
35.2	odd	12	inner	245.2.l.c.117.1		8
35.3	even	12		175.2.f.c.132.1		4
35.4	even	6		175.2.f.c.118.1		4
35.12	even	12	inner	245.2.l.c.117.2		8
35.17	even	12		35.2.f.a.27.2	yes	4
35.18	odd	12		175.2.f.c.132.2		4
35.24	odd	6		175.2.f.c.118.2		4
35.27	even	4	inner	245.2.l.c.227.1		8
35.32	odd	12		35.2.f.a.27.1	yes	4
105.17	odd	12		315.2.p.c.307.2		4
105.32	even	12		315.2.p.c.307.1		4
140.67	even	12		560.2.bj.a.97.2		4
140.87	odd	12		560.2.bj.a.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.f.a.13.1	✓	4	7.3	odd	6
35.2.f.a.13.2	yes	4	7.4	even	3
35.2.f.a.27.1	yes	4	35.32	odd	12
35.2.f.a.27.2	yes	4	35.17	even	12
175.2.f.c.118.1		4	35.4	even	6
175.2.f.c.118.2		4	35.24	odd	6
175.2.f.c.132.1		4	35.3	even	12
175.2.f.c.132.2		4	35.18	odd	12
245.2.l.c.68.1		8	7.2	even	3	inner
245.2.l.c.68.2		8	7.5	odd	6	inner
245.2.l.c.117.1		8	35.2	odd	12	inner
245.2.l.c.117.2		8	35.12	even	12	inner
245.2.l.c.178.1		8	7.6	odd	2	inner
245.2.l.c.178.2		8	1.1	even	1	trivial
245.2.l.c.227.1		8	35.27	even	4	inner
245.2.l.c.227.2		8	5.2	odd	4	inner
315.2.p.c.118.1		4	21.17	even	6
315.2.p.c.118.2		4	21.11	odd	6
315.2.p.c.307.1		4	105.32	even	12
315.2.p.c.307.2		4	105.17	odd	12
560.2.bj.a.97.1		4	140.87	odd	12
560.2.bj.a.97.2		4	140.67	even	12
560.2.bj.a.433.1		4	28.11	odd	6
560.2.bj.a.433.2		4	28.3	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 $\F_{q}$

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

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

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