LMFDB - Embedded newform 784.2.w.d.411.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(19,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 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("784.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.w (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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			411.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	784.411
Dual form			784.2.w.d.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.896575 - 3.34607i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.896575 - 3.34607i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-4.24264 + 2.44949i) q^{10} +(-1.36603 - 0.366025i) q^{11} +(-2.44949 - 2.44949i) q^{13} +(2.00000 - 3.46410i) q^{16} +(4.24264 - 2.44949i) q^{17} +(-1.09808 + 4.09808i) q^{18} +(1.79315 + 6.69213i) q^{19} +(4.89898 + 4.89898i) q^{20} +2.00000i q^{22} +(-2.00000 + 3.46410i) q^{23} +(-6.06218 + 3.50000i) q^{25} +(-2.44949 + 4.24264i) q^{26} +(-3.00000 + 3.00000i) q^{29} +(-2.44949 - 4.24264i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-4.89898 - 4.89898i) q^{34} +6.00000 q^{36} +(-6.83013 + 1.83013i) q^{37} +(8.48528 - 4.89898i) q^{38} +(4.89898 - 8.48528i) q^{40} +4.89898 q^{41} +(-5.00000 + 5.00000i) q^{43} +(2.73205 - 0.732051i) q^{44} +(-2.68973 + 10.0382i) q^{45} +(5.46410 + 1.46410i) q^{46} +(2.44949 - 4.24264i) q^{47} +(7.00000 + 7.00000i) q^{50} +(6.69213 + 1.79315i) q^{52} +(-0.366025 + 1.36603i) q^{53} +4.89898i q^{55} +(5.19615 + 3.00000i) q^{58} +(-1.79315 + 6.69213i) q^{59} +(-3.34607 + 0.896575i) q^{61} +(-4.89898 + 4.89898i) q^{62} +8.00000i q^{64} +(-6.00000 + 10.3923i) q^{65} +(1.83013 - 6.83013i) q^{67} +(-4.89898 + 8.48528i) q^{68} +2.00000 q^{71} +(-2.19615 - 8.19615i) q^{72} +(-4.89898 - 8.48528i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-9.79796 - 9.79796i) q^{76} +(3.46410 + 2.00000i) q^{79} +(-13.3843 - 3.58630i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-1.79315 - 6.69213i) q^{82} +(-12.0000 - 12.0000i) q^{85} +(8.66025 + 5.00000i) q^{86} +(-2.00000 - 3.46410i) q^{88} +14.6969 q^{90} -8.00000i q^{92} +(-6.69213 - 1.79315i) q^{94} +(20.7846 - 12.0000i) q^{95} +4.89898i q^{97} +(3.00000 + 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 q^{18} - 16 q^{23} - 24 q^{29} - 16 q^{32} + 48 q^{36} - 20 q^{37} - 40 q^{43} + 8 q^{44} + 16 q^{46} + 56 q^{50} + 4 q^{53} - 48 q^{65} - 20 q^{67} + 16 q^{71} + 24 q^{72} + 40 q^{74} + 36 q^{81} - 96 q^{85} - 16 q^{88} + 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 16 * q^8 - 4 * q^11 + 16 * q^16 + 12 * q^18 - 16 * q^23 - 24 * q^29 - 16 * q^32 + 48 * q^36 - 20 * q^37 - 40 * q^43 + 8 * q^44 + 16 * q^46 + 56 * q^50 + 4 * q^53 - 48 * q^65 - 20 * q^67 + 16 * q^71 + 24 * q^72 + 40 * q^74 + 36 * q^81 - 96 * q^85 - 16 * q^88 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	−0.896575	−	3.34607i	−0.400961	−	1.49641i	−0.811386	−	0.584511i	$-0.801286\pi$
$5$	−0.896575	−	3.34607i	−0.400961	−	1.49641i	0.410425	−	0.911894i	$-0.365380\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$	−4.24264	+	2.44949i	−1.34164	+	0.774597i
$11$	−1.36603	−	0.366025i	−0.411872	−	0.110361i	0.0469323	−	0.998898i	$-0.485055\pi$
$11$	−1.36603	−	0.366025i	−0.411872	−	0.110361i	−0.458804	+	0.888537i	$0.651722\pi$
$12$		0			0
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	0.280491	−	0.959857i	$-0.409503\pi$
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	−0.959857	+	0.280491i	$0.909503\pi$
$14$		0			0
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.112296	−	0.993675i	$-0.464180\pi$
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.916696	+	0.399586i	$0.130846\pi$
$18$	−1.09808	+	4.09808i	−0.258819	+	0.965926i
$19$	1.79315	+	6.69213i	0.411377	+	1.53528i	0.791983	+	0.610543i	$0.209049\pi$
$19$	1.79315	+	6.69213i	0.411377	+	1.53528i	−0.380606	+	0.924737i	$0.624285\pi$
$20$	4.89898	+	4.89898i	1.09545	+	1.09545i
$21$		0			0
$22$			2.00000i			0.426401i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−6.06218	+	3.50000i	−1.21244	+	0.700000i
$26$	−2.44949	+	4.24264i	−0.480384	+	0.832050i
$27$		0			0
$28$		0			0
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−2.44949	−	4.24264i	−0.439941	−	0.762001i	0.557743	−	0.830014i	$-0.311667\pi$
$31$	−2.44949	−	4.24264i	−0.439941	−	0.762001i	−0.997684	+	0.0680129i	$0.978334\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		0			0
$34$	−4.89898	−	4.89898i	−0.840168	−	0.840168i
$35$		0			0
$36$	6.00000			1.00000
$37$	−6.83013	+	1.83013i	−1.12287	+	0.300871i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	−6.83013	+	1.83013i	−1.12287	+	0.300871i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	8.48528	−	4.89898i	1.37649	−	0.794719i
$39$		0			0
$40$	4.89898	−	8.48528i	0.774597	−	1.34164i
$41$	4.89898			0.765092			0.382546	−	0.923936i	$-0.375047\pi$
$41$	4.89898			0.765092			0.382546	+	0.923936i	$0.375047\pi$
$42$		0			0
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	−0.976772	−	0.214280i	$-0.931260\pi$
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	0.214280	+	0.976772i	$0.431260\pi$
$44$	2.73205	−	0.732051i	0.411872	−	0.110361i
$45$	−2.68973	+	10.0382i	−0.400961	+	1.49641i
$46$	5.46410	+	1.46410i	0.805638	+	0.215870i
$47$	2.44949	−	4.24264i	0.357295	−	0.618853i	−0.630213	−	0.776422i	$-0.717032\pi$
$47$	2.44949	−	4.24264i	0.357295	−	0.618853i	0.987508	+	0.157569i	$0.0503658\pi$
$48$		0			0
$49$		0			0
$50$	7.00000	+	7.00000i	0.989949	+	0.989949i
$51$		0			0
$52$	6.69213	+	1.79315i	0.928032	+	0.248665i
$53$	−0.366025	+	1.36603i	−0.0502775	+	0.187638i	−0.986498	−	0.163776i	$-0.947632\pi$
$53$	−0.366025	+	1.36603i	−0.0502775	+	0.187638i	0.936220	+	0.351414i	$0.114299\pi$
$54$		0			0
$55$			4.89898i			0.660578i
$56$		0			0
$57$		0			0
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	−1.79315	+	6.69213i	−0.233448	+	0.871241i	0.745394	+	0.666624i	$0.232261\pi$
$59$	−1.79315	+	6.69213i	−0.233448	+	0.871241i	−0.978842	+	0.204617i	$0.934405\pi$
$60$		0			0
$61$	−3.34607	+	0.896575i	−0.428420	+	0.114795i	−0.466584	−	0.884477i	$-0.654516\pi$
$61$	−3.34607	+	0.896575i	−0.428420	+	0.114795i	0.0381645	+	0.999271i	$0.487849\pi$
$62$	−4.89898	+	4.89898i	−0.622171	+	0.622171i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	1.83013	−	6.83013i	0.223586	−	0.834433i	−0.759381	−	0.650647i	$-0.774498\pi$
$67$	1.83013	−	6.83013i	0.223586	−	0.834433i	0.982966	−	0.183786i	$-0.0588354\pi$
$68$	−4.89898	+	8.48528i	−0.594089	+	1.02899i
$69$		0			0
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$	−4.89898	−	8.48528i	−0.573382	−	0.993127i	−0.996215	−	0.0869195i	$-0.972298\pi$
$73$	−4.89898	−	8.48528i	−0.573382	−	0.993127i	0.422833	−	0.906208i	$-0.361036\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$		0			0
$76$	−9.79796	−	9.79796i	−1.12390	−	1.12390i
$77$		0			0
$78$		0			0
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	0.682048	−	0.731307i	$-0.261089\pi$
$79$	3.46410	+	2.00000i	0.389742	+	0.225018i	−0.292306	+	0.956325i	$0.594423\pi$
$80$	−13.3843	−	3.58630i	−1.49641	−	0.400961i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−1.79315	−	6.69213i	−0.198020	−	0.739022i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$	−12.0000	−	12.0000i	−1.30158	−	1.30158i
$86$	8.66025	+	5.00000i	0.933859	+	0.539164i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	14.6969			1.54919
$91$		0			0
$92$		−	8.00000i		−	0.834058i
$93$		0			0
$94$	−6.69213	−	1.79315i	−0.690241	−	0.184949i
$95$	20.7846	−	12.0000i	2.13246	−	1.23117i
$96$		0			0
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$		0			0
$99$	3.00000	+	3.00000i	0.301511	+	0.301511i
$100$	7.00000	−	12.1244i	0.700000	−	1.21244i
$101$	−3.34607	−	0.896575i	−0.332946	−	0.0892126i	0.0884733	−	0.996079i	$-0.471801\pi$
$101$	−3.34607	−	0.896575i	−0.332946	−	0.0892126i	−0.421419	+	0.906866i	$0.638468\pi$
$102$		0			0
$103$	−8.48528	−	4.89898i	−0.836080	−	0.482711i	0.0198501	−	0.999803i	$-0.493681\pi$
$103$	−8.48528	−	4.89898i	−0.836080	−	0.482711i	−0.855930	+	0.517092i	$0.827014\pi$
$104$		−	9.79796i		−	0.960769i
$105$		0			0
$106$	2.00000			0.194257
$107$	1.09808	+	4.09808i	0.106155	+	0.396176i	0.998474	−	0.0552301i	$-0.0175892\pi$
$107$	1.09808	+	4.09808i	0.106155	+	0.396176i	−0.892319	+	0.451406i	$0.850923\pi$
$108$		0			0
$109$	−9.56218	−	2.56218i	−0.915891	−	0.245412i	−0.230063	−	0.973176i	$-0.573893\pi$
$109$	−9.56218	−	2.56218i	−0.915891	−	0.245412i	−0.685828	+	0.727764i	$0.740560\pi$
$110$	6.69213	−	1.79315i	0.638070	−	0.170970i
$111$		0			0
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	13.3843	+	3.58630i	1.24809	+	0.334424i
$116$	2.19615	−	8.19615i	0.203908	−	0.760994i
$117$	2.68973	+	10.0382i	0.248665	+	0.928032i
$118$	9.79796			0.901975
$119$		0			0
$120$		0			0
$121$	−7.79423	−	4.50000i	−0.708566	−	0.409091i
$122$	2.44949	+	4.24264i	0.221766	+	0.384111i
$123$		0			0
$124$	8.48528	+	4.89898i	0.762001	+	0.439941i
$125$	4.89898	+	4.89898i	0.438178	+	0.438178i
$126$		0			0
$127$		−	18.0000i		−	1.59724i	−0.601834	−	0.798621i	$-0.705563\pi$
$127$		−	18.0000i		−	1.59724i	0.601834	−	0.798621i	$-0.294437\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$		0			0
$130$	16.3923	+	4.39230i	1.43770	+	0.385231i
$131$	−3.58630	−	13.3843i	−0.313337	−	1.16939i	−0.925528	−	0.378679i	$-0.876379\pi$
$131$	−3.58630	−	13.3843i	−0.313337	−	1.16939i	0.612192	−	0.790710i	$-0.290288\pi$
$132$		0			0
$133$		0			0
$134$	−10.0000			−0.863868
$135$		0			0
$136$	13.3843	+	3.58630i	1.14769	+	0.307523i
$137$	−6.92820	+	4.00000i	−0.591916	+	0.341743i	−0.765855	−	0.643013i	$-0.777684\pi$
$137$	−6.92820	+	4.00000i	−0.591916	+	0.341743i	0.173939	+	0.984757i	$0.444351\pi$
$138$		0			0
$139$	−4.89898	−	4.89898i	−0.415526	−	0.415526i	0.468132	−	0.883658i	$-0.344927\pi$
$139$	−4.89898	−	4.89898i	−0.415526	−	0.415526i	−0.883658	+	0.468132i	$0.844927\pi$
$140$		0			0
$141$		0			0
$142$	−0.732051	−	2.73205i	−0.0614323	−	0.229269i
$143$	2.44949	+	4.24264i	0.204837	+	0.354787i
$144$	−10.3923	+	6.00000i	−0.866025	+	0.500000i
$145$	12.7279	+	7.34847i	1.05700	+	0.610257i
$146$	−9.79796	+	9.79796i	−0.810885	+	0.810885i
$147$		0			0
$148$	10.0000	−	10.0000i	0.821995	−	0.821995i
$149$	−4.09808	+	1.09808i	−0.335727	+	0.0899579i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	−4.09808	+	1.09808i	−0.335727	+	0.0899579i	0.0870170	+	0.996207i	$0.472267\pi$
$150$		0			0
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	−9.79796	+	16.9706i	−0.794719	+	1.37649i
$153$	−14.6969			−1.18818
$154$		0			0
$155$	−12.0000	+	12.0000i	−0.963863	+	0.963863i
$156$		0			0
$157$	4.48288	−	16.7303i	0.357773	−	1.33523i	−0.519187	−	0.854661i	$-0.673765\pi$
$157$	4.48288	−	16.7303i	0.357773	−	1.33523i	0.876959	−	0.480565i	$-0.159568\pi$
$158$	1.46410	−	5.46410i	0.116478	−	0.434701i
$159$		0			0
$160$			19.5959i			1.54919i
$161$		0			0
$162$	9.00000	−	9.00000i	0.707107	−	0.707107i
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	−0.204924	−	0.978778i	$-0.565695\pi$
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	0.311919	+	0.950109i	$0.399028\pi$
$164$	−8.48528	+	4.89898i	−0.662589	+	0.382546i
$165$		0			0
$166$		0			0
$167$		−	19.5959i		−	1.51638i	−0.652035	−	0.758189i	$-0.726085\pi$
$167$		−	19.5959i		−	1.51638i	0.652035	−	0.758189i	$-0.273915\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$	−12.0000	+	20.7846i	−0.920358	+	1.59411i
$171$	5.37945	−	20.0764i	0.411377	−	1.53528i
$172$	3.66025	−	13.6603i	0.279092	−	1.04158i
$173$	3.34607	−	0.896575i	0.254397	−	0.0681654i	−0.129367	−	0.991597i	$-0.541294\pi$
$173$	3.34607	−	0.896575i	0.254397	−	0.0681654i	0.383763	+	0.923431i	$0.374628\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000	+	4.00000i	−0.301511	+	0.301511i
$177$		0			0
$178$		0			0
$179$	1.09808	−	4.09808i	0.0820741	−	0.306305i	−0.912670	−	0.408697i	$-0.865983\pi$
$179$	1.09808	−	4.09808i	0.0820741	−	0.306305i	0.994744	+	0.102393i	$0.0326498\pi$
$180$	−5.37945	−	20.0764i	−0.400961	−	1.49641i
$181$	2.44949	−	2.44949i	0.182069	−	0.182069i	−0.610188	−	0.792257i	$-0.708906\pi$
$181$	2.44949	−	2.44949i	0.182069	−	0.182069i	0.792257	+	0.610188i	$0.208906\pi$
$182$		0			0
$183$		0			0
$184$	−10.9282	+	2.92820i	−0.805638	+	0.215870i
$185$	12.2474	+	21.2132i	0.900450	+	1.55963i
$186$		0			0
$187$	−6.69213	+	1.79315i	−0.489377	+	0.131128i
$188$			9.79796i			0.714590i
$189$		0			0
$190$	−24.0000	−	24.0000i	−1.74114	−	1.74114i
$191$	17.3205	+	10.0000i	1.25327	+	0.723575i	0.971757	−	0.235983i	$-0.0758311\pi$
$191$	17.3205	+	10.0000i	1.25327	+	0.723575i	0.281511	+	0.959558i	$0.409164\pi$
$192$		0			0
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$	6.69213	−	1.79315i	0.480467	−	0.128741i
$195$		0			0
$196$		0			0
$197$	−15.0000	−	15.0000i	−1.06871	−	1.06871i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$	−15.0000	−	15.0000i	−1.06871	−	1.06871i	−0.0712470	−	0.997459i	$-0.522698\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	−8.48528	+	4.89898i	−0.601506	+	0.347279i	−0.769634	−	0.638486i	$-0.779561\pi$
$199$	−8.48528	+	4.89898i	−0.601506	+	0.347279i	0.168128	+	0.985765i	$0.446228\pi$
$200$	−19.1244	−	5.12436i	−1.35230	−	0.362347i
$201$		0			0
$202$			4.89898i			0.344691i
$203$		0			0
$204$		0			0
$205$	−4.39230	−	16.3923i	−0.306772	−	1.14489i
$206$	−3.58630	+	13.3843i	−0.249869	+	0.932526i
$207$	10.3923	−	6.00000i	0.722315	−	0.417029i
$208$	−13.3843	+	3.58630i	−0.928032	+	0.248665i
$209$		−	9.79796i		−	0.677739i
$210$		0			0
$211$	1.00000	+	1.00000i	0.0688428	+	0.0688428i	0.740690	−	0.671847i	$-0.234499\pi$
$211$	1.00000	+	1.00000i	0.0688428	+	0.0688428i	−0.671847	+	0.740690i	$0.734499\pi$
$212$	−0.732051	−	2.73205i	−0.0502775	−	0.187638i
$213$		0			0
$214$	5.19615	−	3.00000i	0.355202	−	0.205076i
$215$	21.2132	+	12.2474i	1.44673	+	0.835269i
$216$		0			0
$217$		0			0
$218$			14.0000i			0.948200i
$219$		0			0
$220$	−4.89898	−	8.48528i	−0.330289	−	0.572078i
$221$	−16.3923	−	4.39230i	−1.10267	−	0.295458i
$222$		0			0
$223$	9.79796			0.656120			0.328060	−	0.944657i	$-0.393605\pi$
$223$	9.79796			0.656120			0.328060	+	0.944657i	$0.393605\pi$
$224$		0			0
$225$	21.0000			1.40000
$226$	−1.46410	−	5.46410i	−0.0973906	−	0.363467i
$227$	−26.7685	−	7.17260i	−1.77669	−	0.476062i	−0.786716	−	0.617316i	$-0.788220\pi$
$227$	−26.7685	−	7.17260i	−1.77669	−	0.476062i	−0.989974	+	0.141253i	$0.954887\pi$
$228$		0			0
$229$	−2.68973	−	10.0382i	−0.177742	−	0.663343i	−0.996068	−	0.0885886i	$-0.971764\pi$
$229$	−2.68973	−	10.0382i	−0.177742	−	0.663343i	0.818326	−	0.574754i	$-0.194902\pi$
$230$		−	19.5959i		−	1.29212i
$231$		0			0
$232$	−12.0000			−0.787839
$233$	−3.46410	−	2.00000i	−0.226941	−	0.131024i	0.382219	−	0.924072i	$-0.375160\pi$
$233$	−3.46410	−	2.00000i	−0.226941	−	0.131024i	−0.609160	+	0.793047i	$0.708493\pi$
$234$	12.7279	−	7.34847i	0.832050	−	0.480384i
$235$	−16.3923	−	4.39230i	−1.06932	−	0.286522i
$236$	−3.58630	−	13.3843i	−0.233448	−	0.871241i
$237$		0			0
$238$		0			0
$239$		−	14.0000i		−	0.905585i	−0.891616	−	0.452792i	$-0.850428\pi$
$239$		−	14.0000i		−	0.905585i	0.891616	−	0.452792i	$-0.149572\pi$
$240$		0			0
$241$	−21.2132	+	12.2474i	−1.36646	+	0.788928i	−0.990474	−	0.137697i	$-0.956030\pi$
$241$	−21.2132	+	12.2474i	−1.36646	+	0.788928i	−0.375988	+	0.926624i	$0.622697\pi$
$242$	−3.29423	+	12.2942i	−0.211761	+	0.790303i
$243$		0			0
$244$	4.89898	−	4.89898i	0.313625	−	0.313625i
$245$		0			0
$246$		0			0
$247$	12.0000	−	20.7846i	0.763542	−	1.32249i
$248$	3.58630	−	13.3843i	0.227730	−	0.849901i
$249$		0			0
$250$	4.89898	−	8.48528i	0.309839	−	0.536656i
$251$	14.6969	+	14.6969i	0.927663	+	0.927663i	0.997555	−	0.0698920i	$-0.0222655\pi$
$251$	14.6969	+	14.6969i	0.927663	+	0.927663i	−0.0698920	+	0.997555i	$0.522265\pi$
$252$		0			0
$253$	4.00000	−	4.00000i	0.251478	−	0.251478i
$254$	−24.5885	+	6.58846i	−1.54282	+	0.413397i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−25.4558	−	14.6969i	−1.58789	−	0.916770i	−0.993654	−	0.112481i	$-0.964120\pi$
$257$	−25.4558	−	14.6969i	−1.58789	−	0.916770i	−0.594238	−	0.804289i	$-0.702546\pi$
$258$		0			0
$259$		0			0
$260$		−	24.0000i		−	1.48842i
$261$	12.2942	−	3.29423i	0.760994	−	0.203908i
$262$	−16.9706	+	9.79796i	−1.04844	+	0.605320i
$263$	13.0000	+	22.5167i	0.801614	+	1.38844i	0.918553	+	0.395298i	$0.129359\pi$
$263$	13.0000	+	22.5167i	0.801614	+	1.38844i	−0.116939	+	0.993139i	$0.537308\pi$
$264$		0			0
$265$	4.89898			0.300942
$266$		0			0
$267$		0			0
$268$	3.66025	+	13.6603i	0.223586	+	0.834433i
$269$	2.68973	−	10.0382i	0.163996	−	0.612040i	−0.834171	−	0.551506i	$-0.814053\pi$
$269$	2.68973	−	10.0382i	0.163996	−	0.612040i	0.998166	−	0.0605332i	$-0.0192801\pi$
$270$		0			0
$271$	−14.6969	+	25.4558i	−0.892775	+	1.54633i	−0.0562416	+	0.998417i	$0.517912\pi$
$271$	−14.6969	+	25.4558i	−0.892775	+	1.54633i	−0.836534	+	0.547915i	$0.815422\pi$
$272$		−	19.5959i		−	1.18818i
$273$		0			0
$274$	8.00000	+	8.00000i	0.483298	+	0.483298i
$275$	9.56218	−	2.56218i	0.576621	−	0.154505i
$276$		0			0
$277$	1.83013	−	6.83013i	0.109962	−	0.410383i	−0.888899	−	0.458103i	$-0.848529\pi$
$277$	1.83013	−	6.83013i	0.109962	−	0.410383i	0.998861	+	0.0477206i	$0.0151957\pi$
$278$	−4.89898	+	8.48528i	−0.293821	+	0.508913i
$279$			14.6969i			0.879883i
$280$		0			0
$281$			20.0000i			1.19310i	0.802576	+	0.596550i	$0.203462\pi$
$281$			20.0000i			1.19310i	−0.802576	+	0.596550i	$0.796538\pi$
$282$		0			0
$283$	−5.37945	+	20.0764i	−0.319775	+	1.19342i	0.599685	+	0.800236i	$0.295292\pi$
$283$	−5.37945	+	20.0764i	−0.319775	+	1.19342i	−0.919461	+	0.393182i	$0.871374\pi$
$284$	−3.46410	+	2.00000i	−0.205557	+	0.118678i
$285$		0			0
$286$	4.89898	−	4.89898i	0.289683	−	0.289683i
$287$		0			0
$288$	12.0000	+	12.0000i	0.707107	+	0.707107i
$289$	3.50000	−	6.06218i	0.205882	−	0.356599i
$290$	5.37945	−	20.0764i	0.315892	−	1.17893i
$291$		0			0
$292$	16.9706	+	9.79796i	0.993127	+	0.573382i
$293$	−12.2474	+	12.2474i	−0.715504	+	0.715504i	−0.967681	−	0.252177i	$-0.918853\pi$
$293$	−12.2474	+	12.2474i	−0.715504	+	0.715504i	0.252177	+	0.967681i	$0.418853\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$	−17.3205	−	10.0000i	−1.00673	−	0.581238i
$297$		0			0
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	13.3843	−	3.58630i	0.774032	−	0.207401i
$300$		0			0
$301$		0			0
$302$	−12.0000	+	12.0000i	−0.690522	+	0.690522i
$303$		0			0
$304$	26.7685	+	7.17260i	1.53528	+	0.411377i
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$	5.37945	+	20.0764i	0.307523	+	1.14769i
$307$	−4.89898	+	4.89898i	−0.279600	+	0.279600i	−0.832949	−	0.553350i	$-0.813349\pi$
$307$	−4.89898	+	4.89898i	−0.279600	+	0.279600i	0.553350	+	0.832949i	$0.313349\pi$
$308$		0			0
$309$		0			0
$310$	20.7846	+	12.0000i	1.18049	+	0.681554i
$311$	21.2132	−	12.2474i	1.20289	−	0.694489i	0.241694	−	0.970353i	$-0.422297\pi$
$311$	21.2132	−	12.2474i	1.20289	−	0.694489i	0.961197	+	0.275864i	$0.0889638\pi$
$312$		0			0
$313$	7.34847	−	12.7279i	0.415360	−	0.719425i	−0.580106	−	0.814541i	$-0.696989\pi$
$313$	7.34847	−	12.7279i	0.415360	−	0.719425i	0.995466	+	0.0951162i	$0.0303223\pi$
$314$	−24.4949			−1.38233
$315$		0			0
$316$	−8.00000			−0.450035
$317$	4.75833	+	17.7583i	0.267254	+	0.997407i	0.960856	+	0.277048i	$0.0893562\pi$
$317$	4.75833	+	17.7583i	0.267254	+	0.997407i	−0.693602	+	0.720359i	$0.743977\pi$
$318$		0			0
$319$	5.19615	−	3.00000i	0.290929	−	0.167968i
$320$	26.7685	−	7.17260i	1.49641	−	0.400961i
$321$		0			0
$322$		0			0
$323$	24.0000	+	24.0000i	1.33540	+	1.33540i
$324$	−15.5885	−	9.00000i	−0.866025	−	0.500000i
$325$	23.4225	+	6.27603i	1.29924	+	0.348131i
$326$	−1.00000	−	1.73205i	−0.0553849	−	0.0959294i
$327$		0			0
$328$	9.79796	+	9.79796i	0.541002	+	0.541002i
$329$		0			0
$330$		0			0
$331$	−6.95448	−	25.9545i	−0.382253	−	1.42659i	−0.842452	−	0.538772i	$-0.818889\pi$
$331$	−6.95448	−	25.9545i	−0.382253	−	1.42659i	0.460199	−	0.887816i	$-0.347778\pi$
$332$		0			0
$333$	20.4904	+	5.49038i	1.12287	+	0.300871i
$334$	−26.7685	+	7.17260i	−1.46471	+	0.392467i
$335$	−24.4949			−1.33830
$336$		0			0
$337$	28.0000			1.52526			0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000			1.52526			0.762629	+	0.646837i	$0.223908\pi$
$338$	−1.36603	+	0.366025i	−0.0743020	+	0.0199092i
$339$		0			0
$340$	32.7846	+	8.78461i	1.77800	+	0.476412i
$341$	1.79315	+	6.69213i	0.0971046	+	0.362399i
$342$	−29.3939			−1.58944
$343$		0			0
$344$	−20.0000			−1.07833
$345$		0			0
$346$	−2.44949	−	4.24264i	−0.131685	−	0.228086i
$347$	−4.09808	−	1.09808i	−0.219996	−	0.0589478i	0.147137	−	0.989116i	$-0.452994\pi$
$347$	−4.09808	−	1.09808i	−0.219996	−	0.0589478i	−0.367133	+	0.930168i	$0.619661\pi$
$348$		0			0
$349$	7.34847	+	7.34847i	0.393355	+	0.393355i	0.875881	−	0.482527i	$-0.160281\pi$
$349$	7.34847	+	7.34847i	0.393355	+	0.393355i	−0.482527	+	0.875881i	$0.660281\pi$
$350$		0			0
$351$		0			0
$352$	6.92820	+	4.00000i	0.369274	+	0.213201i
$353$	8.48528	−	4.89898i	0.451626	−	0.260746i	−0.256891	−	0.966440i	$-0.582698\pi$
$353$	8.48528	−	4.89898i	0.451626	−	0.260746i	0.708517	+	0.705694i	$0.249365\pi$
$354$		0			0
$355$	−1.79315	−	6.69213i	−0.0951706	−	0.355181i
$356$		0			0
$357$		0			0
$358$	−6.00000			−0.317110
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$	−25.4558	+	14.6969i	−1.34164	+	0.774597i
$361$	−25.1147	+	14.5000i	−1.32183	+	0.763158i
$362$	−4.24264	−	2.44949i	−0.222988	−	0.128742i
$363$		0			0
$364$		0			0
$365$	−24.0000	+	24.0000i	−1.25622	+	1.25622i
$366$		0			0
$367$	14.6969	+	25.4558i	0.767174	+	1.32878i	0.939090	+	0.343673i	$0.111671\pi$
$367$	14.6969	+	25.4558i	0.767174	+	1.32878i	−0.171916	+	0.985112i	$0.554996\pi$
$368$	8.00000	+	13.8564i	0.417029	+	0.722315i
$369$	−12.7279	−	7.34847i	−0.662589	−	0.382546i
$370$	24.4949	−	24.4949i	1.27343	−	1.27343i
$371$		0			0
$372$		0			0
$373$	15.0263	−	4.02628i	0.778031	−	0.208473i	0.152115	−	0.988363i	$-0.451392\pi$
$373$	15.0263	−	4.02628i	0.778031	−	0.208473i	0.625917	+	0.779890i	$0.284725\pi$
$374$	4.89898	+	8.48528i	0.253320	+	0.438763i
$375$		0			0
$376$	13.3843	−	3.58630i	0.690241	−	0.184949i
$377$	14.6969			0.756931
$378$		0			0
$379$	−23.0000	+	23.0000i	−1.18143	+	1.18143i	−0.202057	+	0.979374i	$0.564763\pi$
$379$	−23.0000	+	23.0000i	−1.18143	+	1.18143i	−0.979374	+	0.202057i	$0.935237\pi$
$380$	−24.0000	+	41.5692i	−1.23117	+	2.13246i
$381$		0			0
$382$	7.32051	−	27.3205i	0.374550	−	1.39784i
$383$	7.34847	−	12.7279i	0.375489	−	0.650366i	−0.614911	−	0.788597i	$-0.710808\pi$
$383$	7.34847	−	12.7279i	0.375489	−	0.650366i	0.990400	+	0.138230i	$0.0441414\pi$
$384$		0			0
$385$		0			0
$386$	16.0000	−	16.0000i	0.814379	−	0.814379i
$387$	20.4904	−	5.49038i	1.04158	−	0.279092i
$388$	−4.89898	−	8.48528i	−0.248708	−	0.430775i
$389$	4.75833	−	17.7583i	0.241257	−	0.900383i	−0.733971	−	0.679181i	$-0.762335\pi$
$389$	4.75833	−	17.7583i	0.241257	−	0.900383i	0.975228	−	0.221202i	$-0.0709981\pi$
$390$		0			0
$391$			19.5959i			0.991008i
$392$		0			0
$393$		0			0
$394$	−15.0000	+	25.9808i	−0.755689	+	1.30889i
$395$	3.58630	−	13.3843i	0.180446	−	0.673435i
$396$	−8.19615	−	2.19615i	−0.411872	−	0.110361i
$397$	16.7303	−	4.48288i	0.839671	−	0.224989i	0.186743	−	0.982409i	$-0.440207\pi$
$397$	16.7303	−	4.48288i	0.839671	−	0.224989i	0.652928	+	0.757420i	$0.273540\pi$
$398$	9.79796	+	9.79796i	0.491127	+	0.491127i
$399$		0			0
$400$			28.0000i			1.40000i
$401$	4.00000	−	6.92820i	0.199750	−	0.345978i	−0.748697	−	0.662912i	$-0.769320\pi$
$401$	4.00000	−	6.92820i	0.199750	−	0.345978i	0.948447	+	0.316934i	$0.102654\pi$
$402$		0			0
$403$	−4.39230	+	16.3923i	−0.218796	+	0.816559i
$404$	6.69213	−	1.79315i	0.332946	−	0.0892126i
$405$	22.0454	−	22.0454i	1.09545	−	1.09545i
$406$		0			0
$407$	10.0000			0.495682
$408$		0			0
$409$	−12.2474	−	21.2132i	−0.605597	−	1.04893i	−0.991957	−	0.126577i	$-0.959601\pi$
$409$	−12.2474	−	21.2132i	−0.605597	−	1.04893i	0.386359	−	0.922348i	$-0.373732\pi$
$410$	−20.7846	+	12.0000i	−1.02648	+	0.592638i
$411$		0			0
$412$	19.5959			0.965422
$413$		0			0
$414$	−12.0000	−	12.0000i	−0.589768	−	0.589768i
$415$		0			0
$416$	9.79796	+	16.9706i	0.480384	+	0.832050i
$417$		0			0
$418$	−13.3843	+	3.58630i	−0.654646	+	0.175412i
$419$	4.89898	−	4.89898i	0.239331	−	0.239331i	−0.577242	−	0.816573i	$-0.695871\pi$
$419$	4.89898	−	4.89898i	0.239331	−	0.239331i	0.816573	+	0.577242i	$0.195871\pi$
$420$		0			0
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	0.922383	−	0.386276i	$-0.126239\pi$
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	−0.386276	+	0.922383i	$0.626239\pi$
$422$	1.00000	−	1.73205i	0.0486792	−	0.0843149i
$423$	−12.7279	+	7.34847i	−0.618853	+	0.357295i
$424$	−3.46410	+	2.00000i	−0.168232	+	0.0971286i
$425$	−17.1464	+	29.6985i	−0.831724	+	1.44059i
$426$		0			0
$427$		0			0
$428$	−6.00000	−	6.00000i	−0.290021	−	0.290021i
$429$		0			0
$430$	8.96575	−	33.4607i	0.432367	−	1.61362i
$431$	−8.66025	+	5.00000i	−0.417150	+	0.240842i	−0.693857	−	0.720113i	$-0.744090\pi$
$431$	−8.66025	+	5.00000i	−0.417150	+	0.240842i	0.276707	+	0.960954i	$0.410757\pi$
$432$		0			0
$433$		−	14.6969i		−	0.706290i	−0.935569	−	0.353145i	$-0.885112\pi$
$433$		−	14.6969i		−	0.706290i	0.935569	−	0.353145i	$-0.114888\pi$
$434$		0			0
$435$		0			0
$436$	19.1244	−	5.12436i	0.915891	−	0.245412i
$437$	−26.7685	−	7.17260i	−1.28051	−	0.343112i
$438$		0			0
$439$	−12.7279	−	7.34847i	−0.607471	−	0.350723i	0.164504	−	0.986376i	$-0.447398\pi$
$439$	−12.7279	−	7.34847i	−0.607471	−	0.350723i	−0.771975	+	0.635653i	$0.780731\pi$
$440$	−9.79796	+	9.79796i	−0.467099	+	0.467099i
$441$		0			0
$442$			24.0000i			1.14156i
$443$	1.83013	+	6.83013i	0.0869520	+	0.324509i	0.995677	−	0.0928868i	$-0.0296095\pi$
$443$	1.83013	+	6.83013i	0.0869520	+	0.324509i	−0.908725	+	0.417396i	$0.862943\pi$
$444$		0			0
$445$		0			0
$446$	−3.58630	−	13.3843i	−0.169816	−	0.633763i
$447$		0			0
$448$		0			0
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$	−7.68653	−	28.6865i	−0.362347	−	1.35230i
$451$	−6.69213	−	1.79315i	−0.315120	−	0.0844362i
$452$	−6.92820	+	4.00000i	−0.325875	+	0.188144i
$453$		0			0
$454$			39.1918i			1.83936i
$455$		0			0
$456$		0			0
$457$	15.5885	+	9.00000i	0.729197	+	0.421002i	0.818128	−	0.575036i	$-0.195012\pi$
$457$	15.5885	+	9.00000i	0.729197	+	0.421002i	−0.0889312	+	0.996038i	$0.528345\pi$
$458$	−12.7279	+	7.34847i	−0.594737	+	0.343371i
$459$		0			0
$460$	−26.7685	+	7.17260i	−1.24809	+	0.334424i
$461$	−22.0454	−	22.0454i	−1.02676	−	1.02676i	−0.999632	−	0.0271249i	$-0.991365\pi$
$461$	−22.0454	−	22.0454i	−1.02676	−	1.02676i	−0.0271249	−	0.999632i	$-0.508635\pi$
$462$		0			0
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	4.39230	+	16.3923i	0.203908	+	0.760994i
$465$		0			0
$466$	−1.46410	+	5.46410i	−0.0678232	+	0.253120i
$467$	7.17260	+	26.7685i	0.331909	+	1.23870i	0.907182	+	0.420738i	$0.138229\pi$
$467$	7.17260	+	26.7685i	0.331909	+	1.23870i	−0.575274	+	0.817961i	$0.695104\pi$
$468$	−14.6969	−	14.6969i	−0.679366	−	0.679366i
$469$		0			0
$470$			24.0000i			1.10704i
$471$		0			0
$472$	−16.9706	+	9.79796i	−0.781133	+	0.450988i
$473$	8.66025	−	5.00000i	0.398199	−	0.229900i
$474$		0			0
$475$	−34.2929	−	34.2929i	−1.57346	−	1.57346i
$476$		0			0
$477$	3.00000	−	3.00000i	0.137361	−	0.137361i
$478$	−19.1244	+	5.12436i	−0.874728	+	0.234383i
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	−0.997530	−	0.0702467i	$-0.977621\pi$
$479$	−12.2474	−	21.2132i	−0.559600	−	0.969256i	0.437929	−	0.899009i	$-0.355712\pi$
$480$		0			0
$481$	21.2132	+	12.2474i	0.967239	+	0.558436i
$482$	24.4949	+	24.4949i	1.11571	+	1.11571i
$483$		0			0
$484$	18.0000			0.818182
$485$	16.3923	−	4.39230i	0.744336	−	0.199444i
$486$		0			0
$487$	6.00000	+	10.3923i	0.271886	+	0.470920i	0.969345	−	0.245705i	$-0.0790193\pi$
$487$	6.00000	+	10.3923i	0.271886	+	0.470920i	−0.697459	+	0.716625i	$0.745686\pi$
$488$	−8.48528	−	4.89898i	−0.384111	−	0.221766i
$489$		0			0
$490$		0			0
$491$	11.0000	−	11.0000i	0.496423	−	0.496423i	−0.413900	−	0.910323i	$-0.635834\pi$
$491$	11.0000	−	11.0000i	0.496423	−	0.496423i	0.910323	+	0.413900i	$0.135834\pi$
$492$		0			0
$493$	−5.37945	+	20.0764i	−0.242278	+	0.904195i
$494$	−32.7846	−	8.78461i	−1.47505	−	0.395238i
$495$	7.34847	−	12.7279i	0.330289	−	0.572078i
$496$	−19.5959			−0.879883
$497$		0			0
$498$		0			0
$499$	−31.4186	+	8.41858i	−1.40649	+	0.376868i	−0.880671	−	0.473729i	$-0.842908\pi$
$499$	−31.4186	+	8.41858i	−1.40649	+	0.376868i	−0.525818	+	0.850597i	$0.676241\pi$
$500$	−13.3843	−	3.58630i	−0.598562	−	0.160384i
$501$		0			0
$502$	14.6969	−	25.4558i	0.655956	−	1.13615i
$503$		−	14.6969i		−	0.655304i	−0.944798	−	0.327652i	$-0.893743\pi$
$503$		−	14.6969i		−	0.655304i	0.944798	−	0.327652i	$-0.106257\pi$
$504$		0			0
$505$			12.0000i			0.533993i
$506$	−6.92820	−	4.00000i	−0.307996	−	0.177822i
$507$		0			0
$508$	18.0000	+	31.1769i	0.798621	+	1.38325i
$509$	−10.0382	+	2.68973i	−0.444935	+	0.119220i	−0.474329	−	0.880348i	$-0.657309\pi$
$509$	−10.0382	+	2.68973i	−0.444935	+	0.119220i	0.0293934	+	0.999568i	$0.490642\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−10.7589	+	40.1528i	−0.474555	+	1.77106i
$515$	−8.78461	+	32.7846i	−0.387096	+	1.44466i
$516$		0			0
$517$	−4.89898	+	4.89898i	−0.215457	+	0.215457i
$518$		0			0
$519$		0			0
$520$	−32.7846	+	8.78461i	−1.43770	+	0.385231i
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	0.807367	−	0.590049i	$-0.200892\pi$
$521$	−2.44949	−	4.24264i	−0.107314	−	0.185873i	−0.914681	+	0.404176i	$0.867558\pi$
$522$	−9.00000	−	15.5885i	−0.393919	−	0.682288i
$523$	20.0764	−	5.37945i	0.877879	−	0.235227i	0.208387	−	0.978046i	$-0.433179\pi$
$523$	20.0764	−	5.37945i	0.877879	−	0.235227i	0.669492	+	0.742819i	$0.266512\pi$
$524$	19.5959	+	19.5959i	0.856052	+	0.856052i
$525$		0			0
$526$	26.0000	−	26.0000i	1.13365	−	1.13365i
$527$	−20.7846	−	12.0000i	−0.905392	−	0.522728i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−1.79315	−	6.69213i	−0.0778895	−	0.290688i
$531$	14.6969	−	14.6969i	0.637793	−	0.637793i
$532$		0			0
$533$	−12.0000	−	12.0000i	−0.519778	−	0.519778i
$534$		0			0
$535$	12.7279	−	7.34847i	0.550276	−	0.317702i
$536$	17.3205	−	10.0000i	0.748132	−	0.431934i
$537$		0			0
$538$	−14.6969			−0.633630
$539$		0			0
$540$		0			0
$541$	−10.6147	−	39.6147i	−0.456363	−	1.70317i	−0.684049	−	0.729436i	$-0.739783\pi$
$541$	−10.6147	−	39.6147i	−0.456363	−	1.70317i	0.227686	−	0.973735i	$-0.426884\pi$
$542$	40.1528	+	10.7589i	1.72471	+	0.462135i
$543$		0			0
$544$	−26.7685	+	7.17260i	−1.14769	+	0.307523i
$545$			34.2929i			1.46894i
$546$		0			0
$547$	−5.00000	−	5.00000i	−0.213785	−	0.213785i	0.592088	−	0.805873i	$-0.298304\pi$
$547$	−5.00000	−	5.00000i	−0.213785	−	0.213785i	−0.805873	+	0.592088i	$0.798304\pi$
$548$	8.00000	−	13.8564i	0.341743	−	0.591916i
$549$	10.0382	+	2.68973i	0.428420	+	0.114795i
$550$	−7.00000	−	12.1244i	−0.298481	−	0.516984i
$551$	−25.4558	−	14.6969i	−1.08446	−	0.626111i
$552$		0			0
$553$		0			0
$554$	−10.0000			−0.424859
$555$		0			0
$556$	13.3843	+	3.58630i	0.567619	+	0.152093i
$557$	−4.09808	−	1.09808i	−0.173641	−	0.0465270i	0.170951	−	0.985280i	$-0.445316\pi$
$557$	−4.09808	−	1.09808i	−0.173641	−	0.0465270i	−0.344592	+	0.938753i	$0.611983\pi$
$558$	20.0764	−	5.37945i	0.849901	−	0.227730i
$559$	24.4949			1.03602
$560$		0			0
$561$		0			0
$562$	27.3205	−	7.32051i	1.15245	−	0.308797i
$563$	33.4607	+	8.96575i	1.41020	+	0.377862i	0.881996	−	0.471257i	$-0.156200\pi$
$563$	33.4607	+	8.96575i	1.41020	+	0.377862i	0.528202	+	0.849118i	$0.322866\pi$
$564$		0			0
$565$	−3.58630	−	13.3843i	−0.150877	−	0.563080i
$566$	29.3939			1.23552
$567$		0			0
$568$	4.00000	+	4.00000i	0.167836	+	0.167836i
$569$	12.1244	+	7.00000i	0.508279	+	0.293455i	0.732126	−	0.681169i	$-0.238528\pi$
$569$	12.1244	+	7.00000i	0.508279	+	0.293455i	−0.223847	+	0.974624i	$0.571861\pi$
$570$		0			0
$571$	−42.3468	−	11.3468i	−1.77216	−	0.474848i	−0.783040	−	0.621972i	$-0.786332\pi$
$571$	−42.3468	−	11.3468i	−1.77216	−	0.474848i	−0.989118	+	0.147123i	$0.952999\pi$
$572$	−8.48528	−	4.89898i	−0.354787	−	0.204837i
$573$		0			0
$574$		0			0
$575$		−	28.0000i		−	1.16768i
$576$	12.0000	−	20.7846i	0.500000	−	0.866025i
$577$	25.4558	−	14.6969i	1.05974	−	0.611842i	0.134380	−	0.990930i	$-0.457096\pi$
$577$	25.4558	−	14.6969i	1.05974	−	0.611842i	0.925361	+	0.379088i	$0.123762\pi$
$578$	−9.56218	−	2.56218i	−0.397734	−	0.106573i
$579$		0			0
$580$	−29.3939			−1.22051
$581$		0			0
$582$		0			0
$583$	1.00000	−	1.73205i	0.0414158	−	0.0717342i
$584$	7.17260	−	26.7685i	0.296804	−	1.10769i
$585$	31.1769	−	18.0000i	1.28901	−	0.744208i
$586$	21.2132	+	12.2474i	0.876309	+	0.505937i
$587$	24.4949	+	24.4949i	1.01101	+	1.01101i	0.999939	+	0.0110739i	$0.00352501\pi$
$587$	24.4949	+	24.4949i	1.01101	+	1.01101i	0.0110739	+	0.999939i	$0.496475\pi$
$588$		0			0
$589$	24.0000	−	24.0000i	0.988903	−	0.988903i
$590$	−8.78461	−	32.7846i	−0.361657	−	1.34972i
$591$		0			0
$592$	−7.32051	+	27.3205i	−0.300871	+	1.12287i
$593$	33.9411	+	19.5959i	1.39379	+	0.804708i	0.993733	−	0.111780i	$-0.0356552\pi$
$593$	33.9411	+	19.5959i	1.39379	+	0.804708i	0.400062	+	0.916488i	$0.368989\pi$
$594$		0			0
$595$		0			0
$596$	6.00000	−	6.00000i	0.245770	−	0.245770i
$597$		0			0
$598$	−9.79796	−	16.9706i	−0.400668	−	0.693978i
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	0.745613	−	0.666379i	$-0.232157\pi$
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	−0.949908	+	0.312531i	$0.898823\pi$
$600$		0			0
$601$	−19.5959			−0.799334			−0.399667	−	0.916660i	$-0.630874\pi$
$601$	−19.5959			−0.799334			−0.399667	+	0.916660i	$0.630874\pi$
$602$		0			0
$603$	−15.0000	+	15.0000i	−0.610847	+	0.610847i
$604$	20.7846	+	12.0000i	0.845714	+	0.488273i
$605$	−8.06918	+	30.1146i	−0.328059	+	1.22433i
$606$		0			0
$607$	14.6969	−	25.4558i	0.596530	−	1.03322i	−0.396799	−	0.917906i	$-0.629879\pi$
$607$	14.6969	−	25.4558i	0.596530	−	1.03322i	0.993329	−	0.115315i	$-0.0367878\pi$
$608$		−	39.1918i		−	1.58944i
$609$		0			0
$610$	12.0000	−	12.0000i	0.485866	−	0.485866i
$611$	−16.3923	+	4.39230i	−0.663162	+	0.177694i
$612$	25.4558	−	14.6969i	1.02899	−	0.594089i
$613$	6.95448	−	25.9545i	0.280889	−	1.04829i	−0.670902	−	0.741546i	$-0.734093\pi$
$613$	6.95448	−	25.9545i	0.280889	−	1.04829i	0.951791	−	0.306746i	$-0.0992402\pi$
$614$	8.48528	+	4.89898i	0.342438	+	0.197707i
$615$		0			0
$616$		0			0
$617$			2.00000i			0.0805170i	0.999189	+	0.0402585i	$0.0128181\pi$
$617$			2.00000i			0.0805170i	−0.999189	+	0.0402585i	$0.987182\pi$
$618$		0			0
$619$	−1.79315	+	6.69213i	−0.0720728	+	0.268979i	−0.992554	−	0.121808i	$-0.961131\pi$
$619$	−1.79315	+	6.69213i	−0.0720728	+	0.268979i	0.920481	+	0.390788i	$0.127797\pi$
$620$	8.78461	−	32.7846i	0.352798	−	1.31666i
$621$		0			0
$622$	−24.4949	−	24.4949i	−0.982156	−	0.982156i
$623$		0			0
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−20.0764	−	5.37945i	−0.802414	−	0.215006i
$627$		0			0
$628$	8.96575	+	33.4607i	0.357773	+	1.33523i
$629$	−24.4949	+	24.4949i	−0.976676	+	0.976676i
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	2.92820	+	10.9282i	0.116478	+	0.434701i
$633$		0			0
$634$	22.5167	−	13.0000i	0.894251	−	0.516296i
$635$	−60.2292	+	16.1384i	−2.39012	+	0.640431i
$636$		0			0
$637$		0			0
$638$	−6.00000	−	6.00000i	−0.237542	−	0.237542i
$639$	−5.19615	−	3.00000i	−0.205557	−	0.118678i
$640$	−19.5959	−	33.9411i	−0.774597	−	1.34164i
$641$	−16.0000	−	27.7128i	−0.631962	−	1.09459i	−0.987150	−	0.159795i	$-0.948917\pi$
$641$	−16.0000	−	27.7128i	−0.631962	−	1.09459i	0.355188	−	0.934795i	$-0.384417\pi$
$642$		0			0
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$	24.0000	−	41.5692i	0.944267	−	1.63552i
$647$	−16.9706	+	9.79796i	−0.667182	+	0.385198i	−0.795008	−	0.606599i	$-0.792533\pi$
$647$	−16.9706	+	9.79796i	−0.667182	+	0.385198i	0.127826	+	0.991797i	$0.459200\pi$
$648$	−6.58846	+	24.5885i	−0.258819	+	0.965926i
$649$	4.89898	−	8.48528i	0.192302	−	0.333076i
$650$		−	34.2929i		−	1.34508i
$651$		0			0
$652$	−2.00000	+	2.00000i	−0.0783260	+	0.0783260i
$653$	5.49038	+	20.4904i	0.214855	+	0.801851i	0.986217	+	0.165454i	$0.0529090\pi$
$653$	5.49038	+	20.4904i	0.214855	+	0.801851i	−0.771362	+	0.636396i	$0.780424\pi$
$654$		0			0
$655$	−41.5692	+	24.0000i	−1.62424	+	0.937758i
$656$	9.79796	−	16.9706i	0.382546	−	0.662589i
$657$			29.3939i			1.14676i
$658$		0			0
$659$	−27.0000	−	27.0000i	−1.05177	−	1.05177i	−0.998585	−	0.0531861i	$-0.983062\pi$
$659$	−27.0000	−	27.0000i	−1.05177	−	1.05177i	−0.0531861	−	0.998585i	$-0.516938\pi$
$660$		0			0
$661$	−3.34607	−	0.896575i	−0.130147	−	0.0348727i	0.193158	−	0.981168i	$-0.438127\pi$
$661$	−3.34607	−	0.896575i	−0.130147	−	0.0348727i	−0.323304	+	0.946295i	$0.604794\pi$
$662$	−32.9090	+	19.0000i	−1.27904	+	0.738456i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		−	30.0000i		−	1.16248i
$667$	−4.39230	−	16.3923i	−0.170071	−	0.634713i
$668$	19.5959	+	33.9411i	0.758189	+	1.31322i
$669$		0			0
$670$	8.96575	+	33.4607i	0.346377	+	1.29270i
$671$	4.89898			0.189123
$672$		0			0
$673$	−6.00000			−0.231283			−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000			−0.231283			−0.115642	+	0.993291i	$0.536892\pi$
$674$	−10.2487	−	38.2487i	−0.394766	−	1.47329i
$675$		0			0
$676$	1.00000	+	1.73205i	0.0384615	+	0.0666173i
$677$	2.68973	+	10.0382i	0.103375	+	0.385799i	0.998156	−	0.0607058i	$-0.0193352\pi$
$677$	2.68973	+	10.0382i	0.103375	+	0.385799i	−0.894781	+	0.446505i	$0.852668\pi$
$678$		0			0
$679$		0			0
$680$		−	48.0000i		−	1.84072i
$681$		0			0
$682$	8.48528	−	4.89898i	0.324918	−	0.187592i
$683$	34.1506	+	9.15064i	1.30674	+	0.350139i	0.843994	−	0.536353i	$-0.180198\pi$
$683$	34.1506	+	9.15064i	1.30674	+	0.350139i	0.462744	+	0.886492i	$0.346865\pi$
$684$	10.7589	+	40.1528i	0.411377	+	1.53528i
$685$	19.5959	+	19.5959i	0.748722	+	0.748722i
$686$		0			0
$687$		0			0
$688$	7.32051	+	27.3205i	0.279092	+	1.04158i
$689$	4.24264	−	2.44949i	0.161632	−	0.0933181i
$690$		0			0
$691$	−3.58630	−	13.3843i	−0.136429	−	0.509161i	−0.999988	−	0.00491275i	$-0.998436\pi$
$691$	−3.58630	−	13.3843i	−0.136429	−	0.509161i	0.863559	−	0.504249i	$-0.168230\pi$
$692$	−4.89898	+	4.89898i	−0.186231	+	0.186231i
$693$		0			0
$694$			6.00000i			0.227757i
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		0			0
$697$	20.7846	−	12.0000i	0.787273	−	0.454532i
$698$	7.34847	−	12.7279i	0.278144	−	0.481759i
$699$		0			0
$700$		0			0
$701$	−29.0000	+	29.0000i	−1.09531	+	1.09531i	−0.100364	+	0.994951i	$0.532001\pi$
$701$	−29.0000	+	29.0000i	−1.09531	+	1.09531i	−0.994951	+	0.100364i	$0.967999\pi$
$702$		0			0
$703$	−24.4949	−	42.4264i	−0.923843	−	1.60014i
$704$	2.92820	−	10.9282i	0.110361	−	0.411872i
$705$		0			0
$706$	−9.79796	−	9.79796i	−0.368751	−	0.368751i
$707$		0			0
$708$		0			0
$709$	−31.4186	+	8.41858i	−1.17995	+	0.316167i	−0.794906	−	0.606732i	$-0.792480\pi$
$709$	−31.4186	+	8.41858i	−1.17995	+	0.316167i	−0.385043	+	0.922899i	$0.625813\pi$
$710$	−8.48528	+	4.89898i	−0.318447	+	0.183855i
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$		0			0
$713$	19.5959			0.733873
$714$		0			0
$715$	12.0000	−	12.0000i	0.448775	−	0.448775i
$716$	2.19615	+	8.19615i	0.0820741	+	0.306305i
$717$		0			0
$718$	27.3205	+	7.32051i	1.01959	+	0.273199i
$719$	−12.2474	+	21.2132i	−0.456753	+	0.791119i	−0.998787	−	0.0492373i	$-0.984321\pi$
$719$	−12.2474	+	21.2132i	−0.456753	+	0.791119i	0.542034	+	0.840356i	$0.317654\pi$
$720$	29.3939	+	29.3939i	1.09545	+	1.09545i
$721$		0			0
$722$	29.0000	+	29.0000i	1.07927	+	1.07927i
$723$		0			0
$724$	−1.79315	+	6.69213i	−0.0666419	+	0.248711i
$725$	7.68653	−	28.6865i	0.285471	−	1.06539i
$726$		0			0
$727$		−	19.5959i		−	0.726772i	−0.931639	−	0.363386i	$-0.881621\pi$
$727$		−	19.5959i		−	0.726772i	0.931639	−	0.363386i	$-0.118379\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	41.5692	+	24.0000i	1.53855	+	0.888280i
$731$	−8.96575	+	33.4607i	−0.331610	+	1.23759i
$732$		0			0
$733$	−30.1146	+	8.06918i	−1.11231	+	0.298042i	−0.767767	−	0.640729i	$-0.778632\pi$
$733$	−30.1146	+	8.06918i	−1.11231	+	0.298042i	−0.344541	+	0.938771i	$0.611965\pi$
$734$	29.3939	−	29.3939i	1.08495	−	1.08495i
$735$		0			0
$736$	16.0000	−	16.0000i	0.589768	−	0.589768i
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$	−5.37945	+	20.0764i	−0.198020	+	0.739022i
$739$	−6.22243	+	23.2224i	−0.228896	+	0.854251i	0.751910	+	0.659265i	$0.229133\pi$
$739$	−6.22243	+	23.2224i	−0.228896	+	0.854251i	−0.980806	+	0.194986i	$0.937534\pi$
$740$	−42.4264	−	24.4949i	−1.55963	−	0.900450i
$741$		0			0
$742$		0			0
$743$	4.00000			0.146746			0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000			0.146746			0.0733729	+	0.997305i	$0.476624\pi$
$744$		0			0
$745$	7.34847	+	12.7279i	0.269227	+	0.466315i
$746$	−11.0000	−	19.0526i	−0.402739	−	0.697564i
$747$		0			0
$748$	9.79796	−	9.79796i	0.358249	−	0.358249i
$749$		0			0
$750$		0			0
$751$	−8.66025	−	5.00000i	−0.316017	−	0.182453i	0.333599	−	0.942715i	$-0.391737\pi$
$751$	−8.66025	−	5.00000i	−0.316017	−	0.182453i	−0.649616	+	0.760263i	$0.725070\pi$
$752$	−9.79796	−	16.9706i	−0.357295	−	0.618853i
$753$		0			0
$754$	−5.37945	−	20.0764i	−0.195908	−	0.731139i
$755$	−29.3939	+	29.3939i	−1.06975	+	1.06975i
$756$		0			0
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	0.610380	−	0.792108i	$-0.291017\pi$
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	−0.792108	+	0.610380i	$0.791017\pi$
$758$	39.8372	+	23.0000i	1.44695	+	0.835398i
$759$		0			0
$760$	65.5692	+	17.5692i	2.37845	+	0.637303i
$761$	22.0454	−	38.1838i	0.799145	−	1.38416i	−0.121028	−	0.992649i	$-0.538619\pi$
$761$	22.0454	−	38.1838i	0.799145	−	1.38416i	0.920173	−	0.391511i	$-0.128048\pi$
$762$		0			0
$763$		0			0
$764$	−40.0000			−1.44715
$765$	13.1769	+	49.1769i	0.476412	+	1.77800i
$766$	−20.0764	−	5.37945i	−0.725390	−	0.194368i
$767$	20.7846	−	12.0000i	0.750489	−	0.433295i
$768$		0			0
$769$		−	34.2929i		−	1.23663i	−0.785930	−	0.618316i	$-0.787815\pi$
$769$		−	34.2929i		−	1.23663i	0.785930	−	0.618316i	$-0.212185\pi$
$770$		0			0
$771$		0			0
$772$	−27.7128	−	16.0000i	−0.997406	−	0.575853i
$773$	−16.7303	−	4.48288i	−0.601748	−	0.161238i	−0.0549312	−	0.998490i	$-0.517494\pi$
$773$	−16.7303	−	4.48288i	−0.601748	−	0.161238i	−0.546817	+	0.837252i	$0.684161\pi$
$774$	−15.0000	−	25.9808i	−0.539164	−	0.933859i
$775$	29.6985	+	17.1464i	1.06680	+	0.615918i
$776$	−9.79796	+	9.79796i	−0.351726	+	0.351726i
$777$		0			0
$778$	−26.0000			−0.932145
$779$	8.78461	+	32.7846i	0.314741	+	1.17463i
$780$		0			0
$781$	−2.73205	−	0.732051i	−0.0977605	−	0.0261948i
$782$	26.7685	−	7.17260i	0.957240	−	0.256492i
$783$		0			0
$784$		0			0
$785$	−60.0000			−2.14149
$786$		0			0
$787$	6.69213	+	1.79315i	0.238549	+	0.0639189i	0.376113	−	0.926574i	$-0.377261\pi$
$787$	6.69213	+	1.79315i	0.238549	+	0.0639189i	−0.137564	+	0.990493i	$0.543927\pi$
$788$	40.9808	+	10.9808i	1.45988	+	0.391173i
$789$		0			0
$790$	−19.5959			−0.697191
$791$		0			0
$792$			12.0000i			0.426401i
$793$	10.3923	+	6.00000i	0.369042	+	0.213066i
$794$	−12.2474	−	21.2132i	−0.434646	−	0.752828i
$795$		0			0
$796$	9.79796	−	16.9706i	0.347279	−	0.601506i
$797$	−12.2474	−	12.2474i	−0.433827	−	0.433827i	0.456101	−	0.889928i	$-0.349246\pi$
$797$	−12.2474	−	12.2474i	−0.433827	−	0.433827i	−0.889928	+	0.456101i	$0.849246\pi$
$798$		0			0
$799$		−	24.0000i		−	0.849059i
$800$	38.2487	−	10.2487i	1.35230	−	0.362347i
$801$		0			0
$802$	−10.9282	−	2.92820i	−0.385888	−	0.103398i
$803$	3.58630	+	13.3843i	0.126558	+	0.472320i
$804$		0			0
$805$		0			0
$806$	24.0000			0.845364
$807$		0			0
$808$	−4.89898	−	8.48528i	−0.172345	−	0.298511i
$809$	39.8372	−	23.0000i	1.40060	−	0.808637i	0.406146	−	0.913808i	$-0.366872\pi$
$809$	39.8372	−	23.0000i	1.40060	−	0.808637i	0.994454	+	0.105171i	$0.0335391\pi$
$810$	−38.1838	−	22.0454i	−1.34164	−	0.774597i
$811$	14.6969	+	14.6969i	0.516079	+	0.516079i	0.916383	−	0.400303i	$-0.131095\pi$
$811$	14.6969	+	14.6969i	0.516079	+	0.516079i	−0.400303	+	0.916383i	$0.631095\pi$
$812$		0			0
$813$		0			0
$814$	−3.66025	−	13.6603i	−0.128292	−	0.478792i
$815$	−2.44949	−	4.24264i	−0.0858019	−	0.148613i
$816$		0			0
$817$	−42.4264	−	24.4949i	−1.48431	−	0.856968i
$818$	−24.4949	+	24.4949i	−0.856444	+	0.856444i
$819$		0			0
$820$	24.0000	+	24.0000i	0.838116	+	0.838116i
$821$	25.9545	−	6.95448i	0.905818	−	0.242713i	0.224305	−	0.974519i	$-0.427989\pi$
$821$	25.9545	−	6.95448i	0.905818	−	0.242713i	0.681513	+	0.731806i	$0.261322\pi$
$822$		0			0
$823$	3.00000	+	5.19615i	0.104573	+	0.181126i	0.913564	−	0.406695i	$-0.133319\pi$
$823$	3.00000	+	5.19615i	0.104573	+	0.181126i	−0.808990	+	0.587822i	$0.799986\pi$
$824$	−7.17260	−	26.7685i	−0.249869	−	0.932526i
$825$		0			0
$826$		0			0
$827$	33.0000	−	33.0000i	1.14752	−	1.14752i	0.160484	−	0.987038i	$-0.448695\pi$
$827$	33.0000	−	33.0000i	1.14752	−	1.14752i	0.987038	−	0.160484i	$-0.0513055\pi$
$828$	−12.0000	+	20.7846i	−0.417029	+	0.722315i
$829$	2.68973	−	10.0382i	0.0934181	−	0.348641i	−0.903357	−	0.428890i	$-0.858905\pi$
$829$	2.68973	−	10.0382i	0.0934181	−	0.348641i	0.996775	+	0.0802489i	$0.0255715\pi$
$830$		0			0
$831$		0			0
$832$	19.5959	−	19.5959i	0.679366	−	0.679366i
$833$		0			0
$834$		0			0
$835$	−65.5692	+	17.5692i	−2.26912	+	0.608008i
$836$	9.79796	+	16.9706i	0.338869	+	0.586939i
$837$		0			0
$838$	−8.48528	−	4.89898i	−0.293119	−	0.169232i
$839$		−	9.79796i		−	0.338263i	−0.985593	−	0.169132i	$-0.945904\pi$
$839$		−	9.79796i		−	0.338263i	0.985593	−	0.169132i	$-0.0540963\pi$
$840$		0			0
$841$			11.0000i			0.379310i
$842$	11.0000	−	19.0526i	0.379085	−	0.656595i
$843$		0			0
$844$	−2.73205	−	0.732051i	−0.0940411	−	0.0251982i
$845$	−3.34607	+	0.896575i	−0.115108	+	0.0308431i
$846$	14.6969	+	14.6969i	0.505291	+	0.505291i
$847$		0			0
$848$	4.00000	+	4.00000i	0.137361	+	0.137361i
$849$		0			0
$850$	46.8449	+	12.5521i	1.60677	+	0.430532i
$851$	7.32051	−	27.3205i	0.250944	−	0.936535i
$852$		0			0
$853$	12.2474	−	12.2474i	0.419345	−	0.419345i	−0.465633	−	0.884978i	$-0.654173\pi$
$853$	12.2474	−	12.2474i	0.419345	−	0.419345i	0.884978	+	0.465633i	$0.154173\pi$
$854$		0			0
$855$	−72.0000			−2.46235
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	2.44949	+	4.24264i	0.0836730	+	0.144926i	0.904825	−	0.425784i	$-0.140002\pi$
$857$	2.44949	+	4.24264i	0.0836730	+	0.144926i	−0.821152	+	0.570710i	$0.806668\pi$
$858$		0			0
$859$	40.1528	−	10.7589i	1.37000	−	0.367089i	0.502518	−	0.864567i	$-0.332407\pi$
$859$	40.1528	−	10.7589i	1.37000	−	0.367089i	0.867477	+	0.497477i	$0.165740\pi$
$860$	−48.9898			−1.67054
$861$		0			0
$862$	10.0000	+	10.0000i	0.340601	+	0.340601i
$863$	−3.46410	−	2.00000i	−0.117919	−	0.0680808i	0.439880	−	0.898056i	$-0.355021\pi$
$863$	−3.46410	−	2.00000i	−0.117919	−	0.0680808i	−0.557800	+	0.829976i	$0.688354\pi$
$864$		0			0
$865$	−6.00000	−	10.3923i	−0.204006	−	0.353349i
$866$	−20.0764	+	5.37945i	−0.682224	+	0.182801i
$867$		0			0
$868$		0			0
$869$	−4.00000	−	4.00000i	−0.135691	−	0.135691i
$870$		0			0
$871$	−21.2132	+	12.2474i	−0.718782	+	0.414989i
$872$	−14.0000	−	24.2487i	−0.474100	−	0.821165i
$873$	7.34847	−	12.7279i	0.248708	−	0.430775i
$874$			39.1918i			1.32568i
$875$		0			0
$876$		0			0
$877$	4.75833	+	17.7583i	0.160677	+	0.599656i	0.998552	+	0.0537936i	$0.0171313\pi$
$877$	4.75833	+	17.7583i	0.160677	+	0.599656i	−0.837875	+	0.545863i	$0.816202\pi$
$878$	−5.37945	+	20.0764i	−0.181548	+	0.677545i
$879$		0			0
$880$	16.9706	+	9.79796i	0.572078	+	0.330289i
$881$		−	48.9898i		−	1.65051i	−0.564762	−	0.825254i	$-0.691032\pi$
$881$		−	48.9898i		−	1.65051i	0.564762	−	0.825254i	$-0.308968\pi$
$882$		0			0
$883$	−31.0000	−	31.0000i	−1.04323	−	1.04323i	−0.999022	−	0.0442108i	$-0.985923\pi$
$883$	−31.0000	−	31.0000i	−1.04323	−	1.04323i	−0.0442108	−	0.999022i	$-0.514077\pi$
$884$	32.7846	−	8.78461i	1.10267	−	0.295458i
$885$		0			0
$886$	8.66025	−	5.00000i	0.290947	−	0.167978i
$887$	16.9706	+	9.79796i	0.569816	+	0.328983i	0.757076	−	0.653327i	$-0.226627\pi$
$887$	16.9706	+	9.79796i	0.569816	+	0.328983i	−0.187260	+	0.982310i	$0.559961\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−3.29423	−	12.2942i	−0.110361	−	0.411872i
$892$	−16.9706	+	9.79796i	−0.568216	+	0.328060i
$893$	32.7846	+	8.78461i	1.09710	+	0.293966i
$894$		0			0
$895$	−14.6969			−0.491264
$896$		0			0
$897$		0			0
$898$	−3.66025	−	13.6603i	−0.122144	−	0.455849i
$899$	20.0764	+	5.37945i	0.669585	+	0.179415i
$900$	−36.3731	+	21.0000i	−1.21244	+	0.700000i
$901$	1.79315	+	6.69213i	0.0597385	+	0.222947i
$902$			9.79796i			0.326236i
$903$		0			0
$904$	8.00000	+	8.00000i	0.266076	+	0.266076i
$905$	−10.3923	−	6.00000i	−0.345452	−	0.199447i
$906$		0			0
$907$	9.56218	+	2.56218i	0.317507	+	0.0850757i	0.414053	−	0.910253i	$-0.364113\pi$
$907$	9.56218	+	2.56218i	0.317507	+	0.0850757i	−0.0965460	+	0.995329i	$0.530780\pi$
$908$	53.5370	−	14.3452i	1.77669	−	0.476062i
$909$	7.34847	+	7.34847i	0.243733	+	0.243733i
$910$		0			0
$911$			50.0000i			1.65657i	0.560304	+	0.828287i	$0.310684\pi$
$911$			50.0000i			1.65657i	−0.560304	+	0.828287i	$0.689316\pi$
$912$		0			0
$913$		0			0
$914$	6.58846	−	24.5885i	0.217927	−	0.813314i
$915$		0			0
$916$	14.6969	+	14.6969i	0.485601	+	0.485601i
$917$		0			0
$918$		0			0
$919$	5.00000	−	8.66025i	0.164935	−	0.285675i	−0.771697	−	0.635990i	$-0.780592\pi$
$919$	5.00000	−	8.66025i	0.164935	−	0.285675i	0.936632	+	0.350315i	$0.113925\pi$
$920$	19.5959	+	33.9411i	0.646058	+	1.11901i
$921$		0			0
$922$	−22.0454	+	38.1838i	−0.726027	+	1.25752i
$923$	−4.89898	−	4.89898i	−0.161252	−	0.161252i
$924$		0			0
$925$	35.0000	−	35.0000i	1.15079	−	1.15079i
$926$	5.46410	−	1.46410i	0.179562	−	0.0481134i
$927$	14.6969	+	25.4558i	0.482711	+	0.836080i
$928$	20.7846	−	12.0000i	0.682288	−	0.393919i
$929$	29.6985	+	17.1464i	0.974376	+	0.562556i	0.900567	−	0.434716i	$-0.143151\pi$
$929$	29.6985	+	17.1464i	0.974376	+	0.562556i	0.0738083	+	0.997272i	$0.476485\pi$
$930$		0			0
$931$		0			0
$932$	8.00000			0.262049
$933$		0			0
$934$	33.9411	−	19.5959i	1.11059	−	0.641198i
$935$	12.0000	+	20.7846i	0.392442	+	0.679729i
$936$	−14.6969	+	25.4558i	−0.480384	+	0.832050i
$937$	−29.3939			−0.960256			−0.480128	−	0.877198i	$-0.659410\pi$
$937$	−29.3939			−0.960256			−0.480128	+	0.877198i	$0.659410\pi$
$938$		0			0
$939$		0			0
$940$	32.7846	−	8.78461i	1.06932	−	0.286522i
$941$	9.86233	−	36.8067i	0.321503	−	1.19986i	−0.596278	−	0.802778i	$-0.703354\pi$
$941$	9.86233	−	36.8067i	0.321503	−	1.19986i	0.917781	−	0.397087i	$-0.129979\pi$
$942$		0			0
$943$	−9.79796	+	16.9706i	−0.319065	+	0.552638i
$944$	19.5959	+	19.5959i	0.637793	+	0.637793i
$945$		0			0
$946$	−10.0000	−	10.0000i	−0.325128	−	0.325128i
$947$	20.4904	−	5.49038i	0.665848	−	0.178413i	0.0899642	−	0.995945i	$-0.471325\pi$
$947$	20.4904	−	5.49038i	0.665848	−	0.178413i	0.575884	+	0.817532i	$0.304658\pi$
$948$		0			0
$949$	−8.78461	+	32.7846i	−0.285160	+	1.06423i
$950$	−34.2929	+	59.3970i	−1.11261	+	1.92709i
$951$		0			0
$952$		0			0
$953$		−	16.0000i		−	0.518291i	−0.965838	−	0.259145i	$-0.916559\pi$
$953$		−	16.0000i		−	0.518291i	0.965838	−	0.259145i	$-0.0834409\pi$
$954$	−5.19615	−	3.00000i	−0.168232	−	0.0971286i
$955$	17.9315	−	66.9213i	0.580250	−	2.16552i
$956$	14.0000	+	24.2487i	0.452792	+	0.784259i
$957$		0			0
$958$	−24.4949	+	24.4949i	−0.791394	+	0.791394i
$959$		0			0
$960$		0			0
$961$	3.50000	−	6.06218i	0.112903	−	0.195554i
$962$	8.96575	−	33.4607i	0.289068	−	1.07881i
$963$	3.29423	−	12.2942i	0.106155	−	0.396176i
$964$	24.4949	−	42.4264i	0.788928	−	1.36646i
$965$	39.1918	−	39.1918i	1.26163	−	1.26163i
$966$		0			0
$967$	28.0000			0.900419			0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000			0.900419			0.450210	+	0.892923i	$0.351349\pi$
$968$	−6.58846	−	24.5885i	−0.211761	−	0.790303i
$969$		0			0
$970$	−12.0000	−	20.7846i	−0.385297	−	0.667354i
$971$	13.3843	−	3.58630i	0.429521	−	0.115090i	−0.0375801	−	0.999294i	$-0.511965\pi$
$971$	13.3843	−	3.58630i	0.429521	−	0.115090i	0.467101	+	0.884204i	$0.345298\pi$
$972$		0			0
$973$		0			0
$974$	12.0000	−	12.0000i	0.384505	−	0.384505i
$975$		0			0
$976$	−3.58630	+	13.3843i	−0.114795	+	0.428420i
$977$	−19.0000	−	32.9090i	−0.607864	−	1.05285i	−0.991592	−	0.129405i	$-0.958693\pi$
$977$	−19.0000	−	32.9090i	−0.607864	−	1.05285i	0.383728	−	0.923446i	$-0.374640\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	21.0000	+	21.0000i	0.670478	+	0.670478i
$982$	−19.0526	−	11.0000i	−0.607992	−	0.351024i
$983$	8.48528	−	4.89898i	0.270638	−	0.156253i	−0.358539	−	0.933515i	$-0.616725\pi$
$983$	8.48528	−	4.89898i	0.270638	−	0.156253i	0.629178	+	0.777261i	$0.283392\pi$
$984$		0			0
$985$	−36.7423	+	63.6396i	−1.17071	+	2.02773i
$986$	29.3939			0.936092
$987$		0			0
$988$			48.0000i			1.52708i
$989$	−7.32051	−	27.3205i	−0.232779	−	0.868742i
$990$	−20.0764	−	5.37945i	−0.638070	−	0.170970i
$991$	−51.9615	+	30.0000i	−1.65061	+	0.952981i	−0.673792	+	0.738921i	$0.735336\pi$
$991$	−51.9615	+	30.0000i	−1.65061	+	0.952981i	−0.976820	+	0.214060i	$0.931331\pi$
$992$	7.17260	+	26.7685i	0.227730	+	0.849901i
$993$		0			0
$994$		0			0
$995$	24.0000	+	24.0000i	0.760851	+	0.760851i
$996$		0			0
$997$	−10.0382	−	2.68973i	−0.317913	−	0.0851845i	0.0963340	−	0.995349i	$-0.469288\pi$
$997$	−10.0382	−	2.68973i	−0.317913	−	0.0851845i	−0.414247	+	0.910165i	$0.635955\pi$
$998$	23.0000	+	39.8372i	0.728052	+	1.26102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.d.411.1		8
7.2	even	3		112.2.j.a.27.1	✓	4
7.3	odd	6	inner	784.2.w.d.619.1		8
7.4	even	3	inner	784.2.w.d.619.2		8
7.5	odd	6		112.2.j.a.27.2	yes	4
7.6	odd	2	inner	784.2.w.d.411.2		8
16.3	odd	4	inner	784.2.w.d.19.1		8
28.19	even	6		448.2.j.b.335.2		4
28.23	odd	6		448.2.j.b.335.1		4
56.5	odd	6		896.2.j.b.671.1		4
56.19	even	6		896.2.j.e.671.1		4
56.37	even	6		896.2.j.b.671.2		4
56.51	odd	6		896.2.j.e.671.2		4
112.3	even	12	inner	784.2.w.d.227.1		8
112.5	odd	12		896.2.j.e.223.2		4
112.19	even	12		112.2.j.a.83.1	yes	4
112.37	even	12		896.2.j.e.223.1		4
112.51	odd	12		112.2.j.a.83.2	yes	4
112.61	odd	12		448.2.j.b.111.1		4
112.67	odd	12	inner	784.2.w.d.227.2		8
112.75	even	12		896.2.j.b.223.2		4
112.83	even	4	inner	784.2.w.d.19.2		8
112.93	even	12		448.2.j.b.111.2		4
112.107	odd	12		896.2.j.b.223.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.j.a.27.1	✓	4	7.2	even	3
112.2.j.a.27.2	yes	4	7.5	odd	6
112.2.j.a.83.1	yes	4	112.19	even	12
112.2.j.a.83.2	yes	4	112.51	odd	12
448.2.j.b.111.1		4	112.61	odd	12
448.2.j.b.111.2		4	112.93	even	12
448.2.j.b.335.1		4	28.23	odd	6
448.2.j.b.335.2		4	28.19	even	6
784.2.w.d.19.1		8	16.3	odd	4	inner
784.2.w.d.19.2		8	112.83	even	4	inner
784.2.w.d.227.1		8	112.3	even	12	inner
784.2.w.d.227.2		8	112.67	odd	12	inner
784.2.w.d.411.1		8	1.1	even	1	trivial
784.2.w.d.411.2		8	7.6	odd	2	inner
784.2.w.d.619.1		8	7.3	odd	6	inner
784.2.w.d.619.2		8	7.4	even	3	inner
896.2.j.b.223.1		4	112.107	odd	12
896.2.j.b.223.2		4	112.75	even	12
896.2.j.b.671.1		4	56.5	odd	6
896.2.j.b.671.2		4	56.37	even	6
896.2.j.e.223.1		4	112.37	even	12
896.2.j.e.223.2		4	112.5	odd	12
896.2.j.e.671.1		4	56.19	even	6
896.2.j.e.671.2		4	56.51	odd	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.896575 - 3.34607i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.896575 - 3.34607i) q^{5} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-4.24264 + 2.44949i) q^{10} +(-1.36603 - 0.366025i) q^{11} +(-2.44949 - 2.44949i) q^{13} +(2.00000 - 3.46410i) q^{16} +(4.24264 - 2.44949i) q^{17} +(-1.09808 + 4.09808i) q^{18} +(1.79315 + 6.69213i) q^{19} +(4.89898 + 4.89898i) q^{20} +2.00000i q^{22} +(-2.00000 + 3.46410i) q^{23} +(-6.06218 + 3.50000i) q^{25} +(-2.44949 + 4.24264i) q^{26} +(-3.00000 + 3.00000i) q^{29} +(-2.44949 - 4.24264i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-4.89898 - 4.89898i) q^{34} +6.00000 q^{36} +(-6.83013 + 1.83013i) q^{37} +(8.48528 - 4.89898i) q^{38} +(4.89898 - 8.48528i) q^{40} +4.89898 q^{41} +(-5.00000 + 5.00000i) q^{43} +(2.73205 - 0.732051i) q^{44} +(-2.68973 + 10.0382i) q^{45} +(5.46410 + 1.46410i) q^{46} +(2.44949 - 4.24264i) q^{47} +(7.00000 + 7.00000i) q^{50} +(6.69213 + 1.79315i) q^{52} +(-0.366025 + 1.36603i) q^{53} +4.89898i q^{55} +(5.19615 + 3.00000i) q^{58} +(-1.79315 + 6.69213i) q^{59} +(-3.34607 + 0.896575i) q^{61} +(-4.89898 + 4.89898i) q^{62} +8.00000i q^{64} +(-6.00000 + 10.3923i) q^{65} +(1.83013 - 6.83013i) q^{67} +(-4.89898 + 8.48528i) q^{68} +2.00000 q^{71} +(-2.19615 - 8.19615i) q^{72} +(-4.89898 - 8.48528i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-9.79796 - 9.79796i) q^{76} +(3.46410 + 2.00000i) q^{79} +(-13.3843 - 3.58630i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-1.79315 - 6.69213i) q^{82} +(-12.0000 - 12.0000i) q^{85} +(8.66025 + 5.00000i) q^{86} +(-2.00000 - 3.46410i) q^{88} +14.6969 q^{90} -8.00000i q^{92} +(-6.69213 - 1.79315i) q^{94} +(20.7846 - 12.0000i) q^{95} +4.89898i q^{97} +(3.00000 + 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 16 * q^8	\( 8 q + 4 q^{2} + 16 q^{8} - 4 q^{11} + 16 q^{16} + 12 q^{18} - 16 q^{23} - 24 q^{29} - 16 q^{32} + 48 q^{36} - 20 q^{37} - 40 q^{43} + 8 q^{44} + 16 q^{46} + 56 q^{50} + 4 q^{53} - 48 q^{65} - 20 q^{67} + 16 q^{71} + 24 q^{72} + 40 q^{74} + 36 q^{81} - 96 q^{85} - 16 q^{88} + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 16 * q^8 - 4 * q^11 + 16 * q^16 + 12 * q^18 - 16 * q^23 - 24 * q^29 - 16 * q^32 + 48 * q^36 - 20 * q^37 - 40 * q^43 + 8 * q^44 + 16 * q^46 + 56 * q^50 + 4 * q^53 - 48 * q^65 - 20 * q^67 + 16 * q^71 + 24 * q^72 + 40 * q^74 + 36 * q^81 - 96 * q^85 - 16 * q^88 + 24 * q^99

Introduction

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