LMFDB - Embedded newform 704.2.u.c.63.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [704,2,Mod(63,704)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("704.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(704, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.u (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			63.3
Root			$-0.544389 - 1.30524i$ of defining polynomial
Character	$\chi$	$=$	704.63
Dual form			704.2.u.c.447.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.704424 - 0.228881i) q^{3} +(-1.09089 - 0.792578i) q^{5} +(-0.503194 + 1.54867i) q^{7} +(-1.98322 + 1.44090i) q^{9} +(-3.29726 + 0.357912i) q^{11} +(2.09089 + 2.87786i) q^{13} +(-0.949856 - 0.308627i) q^{15} +(-0.0411247 + 0.0566033i) q^{17} +(2.45716 + 7.56236i) q^{19} +1.20609i q^{21} +5.30988i q^{23} +(-0.983224 - 3.02605i) q^{25} +(-2.37331 + 3.26658i) q^{27} +(-3.74364 - 1.21638i) q^{29} +(2.17121 + 2.98842i) q^{31} +(-2.24075 + 1.00680i) q^{33} +(1.77637 - 1.29061i) q^{35} +(2.12561 - 6.54194i) q^{37} +(2.13156 + 1.54867i) q^{39} +(5.50305 - 1.78805i) q^{41} +1.89516 q^{43} +3.30550 q^{45} +(-9.32545 + 3.03002i) q^{47} +(3.51794 + 2.55593i) q^{49} +(-0.0160138 + 0.0492854i) q^{51} +(-3.14518 + 2.28511i) q^{53} +(3.88062 + 2.22289i) q^{55} +(3.46177 + 4.76471i) q^{57} +(-4.62366 - 1.50232i) q^{59} +(-0.791173 + 1.08896i) q^{61} +(-1.23353 - 3.79641i) q^{63} -4.79662i q^{65} +4.91303i q^{67} +(1.21533 + 3.74041i) q^{69} +(4.10014 - 5.64335i) q^{71} +(-9.62677 - 3.12793i) q^{73} +(-1.38521 - 1.90658i) q^{75} +(1.10487 - 5.28646i) q^{77} +(-4.85779 + 3.52939i) q^{79} +(1.34841 - 4.14999i) q^{81} +(2.92211 + 2.12304i) q^{83} +(0.0897250 - 0.0291534i) q^{85} -2.91552 q^{87} -5.39711 q^{89} +(-5.50899 + 1.78998i) q^{91} +(2.21345 + 1.60816i) q^{93} +(3.31327 - 10.1972i) q^{95} +(-5.92705 + 4.30625i) q^{97} +(6.02348 - 5.46083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} - 10 q^{9} + 10 q^{13} - 10 q^{17} + 6 q^{25} + 10 q^{29} - 12 q^{33} - 18 q^{37} + 10 q^{41} - 40 q^{45} + 6 q^{49} - 38 q^{53} + 10 q^{61} + 16 q^{69} - 30 q^{73} - 2 q^{77} - 4 q^{81}+ \cdots - 68 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 - 10 * q^9 + 10 * q^13 - 10 * q^17 + 6 * q^25 + 10 * q^29 - 12 * q^33 - 18 * q^37 + 10 * q^41 - 40 * q^45 + 6 * q^49 - 38 * q^53 + 10 * q^61 + 16 * q^69 - 30 * q^73 - 2 * q^77 - 4 * q^81 + 50 * q^85 - 36 * q^89 + 38 * q^93 - 68 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$-1$

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			0
$2$		0			0
$3$	0.704424	−	0.228881i	0.406700	−	0.132145i	−0.0985210	−	0.995135i	$-0.531411\pi$
$3$	0.704424	−	0.228881i	0.406700	−	0.132145i	0.505221	+	0.862990i	$0.331411\pi$
$4$		0			0
$5$	−1.09089	−	0.792578i	−0.487861	−	0.354452i	0.316500	−	0.948592i	$-0.397492\pi$
$5$	−1.09089	−	0.792578i	−0.487861	−	0.354452i	−0.804361	+	0.594141i	$0.797492\pi$
$6$		0			0
$7$	−0.503194	+	1.54867i	−0.190189	+	0.585343i	−0.999999	−	0.00134995i	$-0.999570\pi$
$7$	−0.503194	+	1.54867i	−0.190189	+	0.585343i	0.809810	+	0.586693i	$0.199570\pi$
$8$		0			0
$9$	−1.98322	+	1.44090i	−0.661075	+	0.480299i
$10$		0			0
$11$	−3.29726	+	0.357912i	−0.994160	+	0.107915i
$11$	−3.29726	+	0.357912i	−0.994160	+	0.107915i
$12$		0			0
$13$	2.09089	+	2.87786i	0.579909	+	0.798176i	0.993685	−	0.112203i	$-0.0357906\pi$
$13$	2.09089	+	2.87786i	0.579909	+	0.798176i	−0.413777	+	0.910378i	$0.635791\pi$
$14$		0			0
$15$	−0.949856	−	0.308627i	−0.245252	−	0.0796871i
$16$		0			0
$17$	−0.0411247	+	0.0566033i	−0.00997420	+	0.0137283i	−0.813975	−	0.580900i	$-0.802701\pi$
$17$	−0.0411247	+	0.0566033i	−0.00997420	+	0.0137283i	0.804001	+	0.594628i	$0.202701\pi$
$18$		0			0
$19$	2.45716	+	7.56236i	0.563711	+	1.73493i	0.671749	+	0.740778i	$0.265543\pi$
$19$	2.45716	+	7.56236i	0.563711	+	1.73493i	−0.108038	+	0.994147i	$0.534457\pi$
$20$		0			0
$21$			1.20609i			0.263191i
$22$		0			0
$23$			5.30988i			1.10719i	0.832787	+	0.553593i	$0.186744\pi$
$23$			5.30988i			1.10719i	−0.832787	+	0.553593i	$0.813256\pi$
$24$		0			0
$25$	−0.983224	−	3.02605i	−0.196645	−	0.605210i
$26$		0			0
$27$	−2.37331	+	3.26658i	−0.456744	+	0.628654i
$28$		0			0
$29$	−3.74364	−	1.21638i	−0.695177	−	0.225877i	−0.0599489	−	0.998201i	$-0.519094\pi$
$29$	−3.74364	−	1.21638i	−0.695177	−	0.225877i	−0.635228	+	0.772325i	$0.719094\pi$
$30$		0			0
$31$	2.17121	+	2.98842i	0.389961	+	0.536735i	0.958189	−	0.286136i	$-0.0923708\pi$
$31$	2.17121	+	2.98842i	0.389961	+	0.536735i	−0.568228	+	0.822871i	$0.692371\pi$
$32$		0			0
$33$	−2.24075	+	1.00680i	−0.390064	+	0.175262i
$34$		0			0
$35$	1.77637	−	1.29061i	0.300262	−	0.218153i
$36$		0			0
$37$	2.12561	−	6.54194i	0.349448	−	1.07549i	−0.609712	−	0.792623i	$-0.708715\pi$
$37$	2.12561	−	6.54194i	0.349448	−	1.07549i	0.959159	−	0.282866i	$-0.0912852\pi$
$38$		0			0
$39$	2.13156	+	1.54867i	0.341323	+	0.247986i
$40$		0			0
$41$	5.50305	−	1.78805i	0.859432	−	0.279246i	0.154041	−	0.988065i	$-0.450771\pi$
$41$	5.50305	−	1.78805i	0.859432	−	0.279246i	0.705391	+	0.708818i	$0.250771\pi$
$42$		0			0
$43$	1.89516			0.289009			0.144505	−	0.989504i	$-0.453841\pi$
$43$	1.89516			0.289009			0.144505	+	0.989504i	$0.453841\pi$
$44$		0			0
$45$	3.30550			0.492755
$46$		0			0
$47$	−9.32545	+	3.03002i	−1.36026	+	0.441974i	−0.896129	−	0.443794i	$-0.853632\pi$
$47$	−9.32545	+	3.03002i	−1.36026	+	0.441974i	−0.464128	+	0.885768i	$0.653632\pi$
$48$		0			0
$49$	3.51794	+	2.55593i	0.502563	+	0.365133i
$50$		0			0
$51$	−0.0160138	+	0.0492854i	−0.00224238	+	0.00690134i
$52$		0			0
$53$	−3.14518	+	2.28511i	−0.432023	+	0.313883i	−0.782457	−	0.622704i	$-0.786034\pi$
$53$	−3.14518	+	2.28511i	−0.432023	+	0.313883i	0.350434	+	0.936587i	$0.386034\pi$
$54$		0			0
$55$	3.88062	+	2.22289i	0.523262	+	0.299734i
$56$		0			0
$57$	3.46177	+	4.76471i	0.458522	+	0.631102i
$58$		0			0
$59$	−4.62366	−	1.50232i	−0.601950	−	0.195585i	−0.00783982	−	0.999969i	$-0.502496\pi$
$59$	−4.62366	−	1.50232i	−0.601950	−	0.195585i	−0.594110	+	0.804384i	$0.702496\pi$
$60$		0			0
$61$	−0.791173	+	1.08896i	−0.101299	+	0.139427i	−0.856657	−	0.515886i	$-0.827463\pi$
$61$	−0.791173	+	1.08896i	−0.101299	+	0.139427i	0.755358	+	0.655312i	$0.227463\pi$
$62$		0			0
$63$	−1.23353	−	3.79641i	−0.155410	−	0.478303i
$64$		0			0
$65$		−	4.79662i		−	0.594948i
$66$		0			0
$67$			4.91303i			0.600223i	0.953904	+	0.300111i	$0.0970238\pi$
$67$			4.91303i			0.600223i	−0.953904	+	0.300111i	$0.902976\pi$
$68$		0			0
$69$	1.21533	+	3.74041i	0.146309	+	0.450292i
$70$		0			0
$71$	4.10014	−	5.64335i	0.486597	−	0.669743i	−0.493159	−	0.869939i	$-0.664158\pi$
$71$	4.10014	−	5.64335i	0.486597	−	0.669743i	0.979756	+	0.200196i	$0.0641580\pi$
$72$		0			0
$73$	−9.62677	−	3.12793i	−1.12673	−	0.366096i	−0.314397	−	0.949292i	$-0.601802\pi$
$73$	−9.62677	−	3.12793i	−1.12673	−	0.366096i	−0.812332	+	0.583195i	$0.801802\pi$
$74$		0			0
$75$	−1.38521	−	1.90658i	−0.159951	−	0.220153i
$76$		0			0
$77$	1.10487	−	5.28646i	0.125912	−	0.602449i
$78$		0			0
$79$	−4.85779	+	3.52939i	−0.546544	+	0.397088i	−0.826510	−	0.562923i	$-0.809677\pi$
$79$	−4.85779	+	3.52939i	−0.546544	+	0.397088i	0.279966	+	0.960010i	$0.409677\pi$
$80$		0			0
$81$	1.34841	−	4.14999i	0.149824	−	0.461110i
$82$		0			0
$83$	2.92211	+	2.12304i	0.320744	+	0.233034i	0.736493	−	0.676446i	$-0.236481\pi$
$83$	2.92211	+	2.12304i	0.320744	+	0.233034i	−0.415749	+	0.909479i	$0.636481\pi$
$84$		0			0
$85$	0.0897250	−	0.0291534i	0.00973205	−	0.00316213i
$86$		0			0
$87$	−2.91552			−0.312576
$88$		0			0
$89$	−5.39711			−0.572093			−0.286046	−	0.958216i	$-0.592341\pi$
$89$	−5.39711			−0.572093			−0.286046	+	0.958216i	$0.592341\pi$
$90$		0			0
$91$	−5.50899	+	1.78998i	−0.577499	+	0.187641i
$92$		0			0
$93$	2.21345	+	1.60816i	0.229524	+	0.166759i
$94$		0			0
$95$	3.31327	−	10.1972i	0.339934	−	1.04621i
$96$		0			0
$97$	−5.92705	+	4.30625i	−0.601801	+	0.437234i	−0.846518	−	0.532361i	$-0.821305\pi$
$97$	−5.92705	+	4.30625i	−0.601801	+	0.437234i	0.244717	+	0.969595i	$0.421305\pi$
$98$		0			0
$99$	6.02348	−	5.46083i	0.605383	−	0.548834i
$100$		0			0
$101$	5.62667	+	7.74445i	0.559875	+	0.770602i	0.991311	−	0.131542i	$-0.0419928\pi$
$101$	5.62667	+	7.74445i	0.559875	+	0.770602i	−0.431436	+	0.902144i	$0.641993\pi$
$102$		0			0
$103$	9.81631	+	3.18951i	0.967230	+	0.314272i	0.749697	−	0.661781i	$-0.230199\pi$
$103$	9.81631	+	3.18951i	0.967230	+	0.314272i	0.217533	+	0.976053i	$0.430199\pi$
$104$		0			0
$105$	0.955923	−	1.31571i	0.0932885	−	0.128401i
$106$		0			0
$107$	−3.42303	−	10.5350i	−0.330917	−	1.01846i	−0.968699	−	0.248240i	$-0.920148\pi$
$107$	−3.42303	−	10.5350i	−0.330917	−	1.01846i	0.637782	−	0.770217i	$-0.279852\pi$
$108$		0			0
$109$		−	8.95933i		−	0.858149i	−0.903269	−	0.429074i	$-0.858840\pi$
$109$		−	8.95933i		−	0.858149i	0.903269	−	0.429074i	$-0.141160\pi$
$110$		0			0
$111$		−	5.09482i		−	0.483579i
$112$		0			0
$113$	3.40631	+	10.4836i	0.320439	+	0.986210i	0.973457	+	0.228868i	$0.0735025\pi$
$113$	3.40631	+	10.4836i	0.320439	+	0.986210i	−0.653018	+	0.757342i	$0.726498\pi$
$114$		0			0
$115$	4.20849	−	5.79249i	0.392444	−	0.540153i
$116$		0			0
$117$	−8.29341	−	2.69469i	−0.766726	−	0.249124i
$118$		0			0
$119$	−0.0669662	−	0.0921710i	−0.00613878	−	0.00844931i
$120$		0			0
$121$	10.7438	−	2.36026i	0.976709	−	0.214569i
$122$		0			0
$123$	3.46723	−	2.51909i	0.312630	−	0.227139i
$124$		0			0
$125$	−3.40921	+	10.4925i	−0.304929	+	0.938474i
$126$		0			0
$127$	−8.32668	−	6.04969i	−0.738874	−	0.536823i	0.153485	−	0.988151i	$-0.450950\pi$
$127$	−8.32668	−	6.04969i	−0.738874	−	0.536823i	−0.892358	+	0.451328i	$0.850950\pi$
$128$		0			0
$129$	1.33500	−	0.433767i	0.117540	−	0.0381910i
$130$		0			0
$131$	1.86768			0.163180			0.0815901	−	0.996666i	$-0.474000\pi$
$131$	1.86768			0.163180			0.0815901	+	0.996666i	$0.474000\pi$
$132$		0			0
$133$	−12.9480			−1.12274
$134$		0			0
$135$	5.17804	−	1.68245i	0.445655	−	0.144802i
$136$		0			0
$137$	1.01489	+	0.737362i	0.0867080	+	0.0629971i	0.630295	−	0.776356i	$-0.282934\pi$
$137$	1.01489	+	0.737362i	0.0867080	+	0.0629971i	−0.543587	+	0.839353i	$0.682934\pi$
$138$		0			0
$139$	1.94407	−	5.98323i	0.164894	−	0.507491i	−0.834135	−	0.551561i	$-0.814032\pi$
$139$	1.94407	−	5.98323i	0.164894	−	0.507491i	0.999028	+	0.0440698i	$0.0140324\pi$
$140$		0			0
$141$	−5.87556	+	4.26884i	−0.494811	+	0.359501i
$142$		0			0
$143$	−7.92422	−	8.74070i	−0.662657	−	0.730934i
$144$		0			0
$145$	3.11982	+	4.29407i	0.259087	+	0.356603i
$146$		0			0
$147$	3.06313	+	0.995271i	0.252643	+	0.0820886i
$148$		0			0
$149$	10.0839	−	13.8792i	0.826102	−	1.13703i	−0.162534	−	0.986703i	$-0.551967\pi$
$149$	10.0839	−	13.8792i	0.826102	−	1.13703i	0.988636	−	0.150329i	$-0.0480332\pi$
$150$		0			0
$151$	3.75712	+	11.5632i	0.305750	+	0.941002i	0.979396	+	0.201948i	$0.0647271\pi$
$151$	3.75712	+	11.5632i	0.305750	+	0.941002i	−0.673646	+	0.739054i	$0.735273\pi$
$152$		0			0
$153$		−	0.171513i		−	0.0138660i
$154$		0			0
$155$		−	4.98089i		−	0.400074i
$156$		0			0
$157$	1.63833	+	5.04225i	0.130753	+	0.402415i	0.994905	−	0.100815i	$-0.0321449\pi$
$157$	1.63833	+	5.04225i	0.130753	+	0.402415i	−0.864153	+	0.503230i	$0.832145\pi$
$158$		0			0
$159$	−1.69252	+	2.32956i	−0.134226	+	0.184746i
$160$		0			0
$161$	−8.22325	−	2.67190i	−0.648083	−	0.210575i
$162$		0			0
$163$	5.91168	+	8.13673i	0.463039	+	0.637318i	0.975135	−	0.221610i	$-0.0711311\pi$
$163$	5.91168	+	8.13673i	0.463039	+	0.637318i	−0.512097	+	0.858928i	$0.671131\pi$
$164$		0			0
$165$	3.24238	+	0.677657i	0.252419	+	0.0527555i
$166$		0			0
$167$	17.7237	−	12.8770i	1.37150	−	0.996451i	0.373879	−	0.927478i	$-0.378028\pi$
$167$	17.7237	−	12.8770i	1.37150	−	0.996451i	0.997618	−	0.0689735i	$-0.0219724\pi$
$168$		0			0
$169$	0.106946	−	0.329146i	0.00822661	−	0.0253189i
$170$		0			0
$171$	−15.7697	−	11.4573i	−1.20594	−	0.876165i
$172$		0			0
$173$	11.2531	−	3.65635i	0.855557	−	0.277987i	0.151785	−	0.988413i	$-0.451498\pi$
$173$	11.2531	−	3.65635i	0.855557	−	0.277987i	0.703772	+	0.710426i	$0.251498\pi$
$174$		0			0
$175$	5.18111			0.391655
$176$		0			0
$177$	−3.60087			−0.270658
$178$		0			0
$179$	0.887979	−	0.288522i	0.0663707	−	0.0215651i	−0.275643	−	0.961260i	$-0.588891\pi$
$179$	0.887979	−	0.288522i	0.0663707	−	0.0215651i	0.342014	+	0.939695i	$0.388891\pi$
$180$		0			0
$181$	15.2414	+	11.0736i	1.13289	+	0.823091i	0.986113	−	0.166079i	$-0.0531106\pi$
$181$	15.2414	+	11.0736i	1.13289	+	0.823091i	0.146775	+	0.989170i	$0.453111\pi$
$182$		0			0
$183$	−0.308080	+	0.948172i	−0.0227739	+	0.0700909i
$184$		0			0
$185$	−7.50380	+	5.45183i	−0.551691	+	0.400827i
$186$		0			0
$187$	0.115340	−	0.201355i	0.00843447	−	0.0147245i
$188$		0			0
$189$	−3.86463	−	5.31920i	−0.281110	−	0.386915i
$190$		0			0
$191$	−19.4435	−	6.31757i	−1.40688	−	0.457124i	−0.495472	−	0.868624i	$-0.665005\pi$
$191$	−19.4435	−	6.31757i	−1.40688	−	0.457124i	−0.911410	+	0.411500i	$0.865005\pi$
$192$		0			0
$193$	10.1927	−	14.0291i	0.733690	−	1.00984i	−0.265267	−	0.964175i	$-0.585460\pi$
$193$	10.1927	−	14.0291i	0.733690	−	1.00984i	0.998957	−	0.0456628i	$-0.0145400\pi$
$194$		0			0
$195$	−1.09786	−	3.37886i	−0.0786192	−	0.241965i
$196$		0			0
$197$		−	3.49133i		−	0.248747i	−0.992235	−	0.124374i	$-0.960308\pi$
$197$		−	3.49133i		−	0.248747i	0.992235	−	0.124374i	$-0.0396921\pi$
$198$		0			0
$199$		−	11.2660i		−	0.798625i	−0.916815	−	0.399313i	$-0.869249\pi$
$199$		−	11.2660i		−	0.798625i	0.916815	−	0.399313i	$-0.130751\pi$
$200$		0			0
$201$	1.12450	+	3.46086i	0.0793162	+	0.244110i
$202$		0			0
$203$	3.76755	−	5.18559i	0.264430	−	0.363957i
$204$		0			0
$205$	−7.42039	−	2.41103i	−0.518262	−	0.168394i
$206$		0			0
$207$	−7.65098	−	10.5307i	−0.531780	−	0.731932i
$208$		0			0
$209$	−10.8086	−	24.0556i	−0.747643	−	1.66396i
$210$		0			0
$211$	−2.21909	+	1.61227i	−0.152769	+	0.110993i	−0.661544	−	0.749906i	$-0.730098\pi$
$211$	−2.21909	+	1.61227i	−0.152769	+	0.110993i	0.508775	+	0.860899i	$0.330098\pi$
$212$		0			0
$213$	1.59658	−	4.91376i	0.109396	−	0.336685i
$214$		0			0
$215$	−2.06741	−	1.50206i	−0.140996	−	0.102440i
$216$		0			0
$217$	−5.72061	+	1.85874i	−0.388341	+	0.126180i
$218$		0			0
$219$	−7.49726			−0.506618
$220$		0			0
$221$	−0.248884			−0.0167417
$222$		0			0
$223$	22.5646	−	7.33167i	1.51103	−	0.490965i	0.567821	−	0.823152i	$-0.307787\pi$
$223$	22.5646	−	7.33167i	1.51103	−	0.490965i	0.943213	+	0.332187i	$0.107787\pi$
$224$		0			0
$225$	6.31018	+	4.58462i	0.420679	+	0.305641i
$226$		0			0
$227$	0.247473	−	0.761643i	0.0164254	−	0.0505520i	−0.942508	−	0.334184i	$-0.891539\pi$
$227$	0.247473	−	0.761643i	0.0164254	−	0.0505520i	0.958933	+	0.283632i	$0.0915394\pi$
$228$		0			0
$229$	−19.0839	+	13.8652i	−1.26110	+	0.916241i	−0.998811	−	0.0487497i	$-0.984476\pi$
$229$	−19.0839	+	13.8652i	−1.26110	+	0.916241i	−0.262286	+	0.964990i	$0.584476\pi$
$230$		0			0
$231$	−0.431676	−	3.97680i	−0.0284022	−	0.261654i
$232$		0			0
$233$	10.2812	+	14.1509i	0.673547	+	0.927058i	0.999834	−	0.0182127i	$-0.00579761\pi$
$233$	10.2812	+	14.1509i	0.673547	+	0.927058i	−0.326287	+	0.945271i	$0.605798\pi$
$234$		0			0
$235$	12.5746	+	4.08572i	0.820274	+	0.266523i
$236$		0			0
$237$	−2.61413	+	3.59805i	−0.169806	+	0.233718i
$238$		0			0
$239$	2.06577	+	6.35778i	0.133623	+	0.411251i	0.995373	−	0.0960826i	$-0.0306313\pi$
$239$	2.06577	+	6.35778i	0.133623	+	0.411251i	−0.861750	+	0.507333i	$0.830631\pi$
$240$		0			0
$241$		−	4.28655i		−	0.276121i	−0.990424	−	0.138061i	$-0.955913\pi$
$241$		−	4.28655i		−	0.276121i	0.990424	−	0.138061i	$-0.0440868\pi$
$242$		0			0
$243$		−	15.3451i		−	0.984391i
$244$		0			0
$245$	−1.81191	−	5.57648i	−0.115759	−	0.356268i
$246$		0			0
$247$	−16.6258	+	22.8834i	−1.05787	+	1.45604i
$248$		0			0
$249$	2.54433	+	0.826703i	0.161240	+	0.0523902i
$250$		0			0
$251$	−2.87878	−	3.96230i	−0.181707	−	0.250098i	0.708441	−	0.705770i	$-0.249399\pi$
$251$	−2.87878	−	3.96230i	−0.181707	−	0.250098i	−0.890148	+	0.455672i	$0.849399\pi$
$252$		0			0
$253$	−1.90047	−	17.5080i	−0.119482	−	1.10072i
$254$		0			0
$255$	0.0565318	−	0.0410728i	0.00354016	−	0.00257208i
$256$		0			0
$257$	−3.82696	+	11.7782i	−0.238719	+	0.734702i	0.757887	+	0.652386i	$0.226232\pi$
$257$	−3.82696	+	11.7782i	−0.238719	+	0.734702i	−0.996606	+	0.0823161i	$0.973768\pi$
$258$		0			0
$259$	9.06173	+	6.58373i	0.563068	+	0.409093i
$260$		0			0
$261$	9.17716	−	2.98184i	0.568052	−	0.184571i
$262$		0			0
$263$	16.9489			1.04511			0.522556	−	0.852605i	$-0.324979\pi$
$263$	16.9489			1.04511			0.522556	+	0.852605i	$0.324979\pi$
$264$		0			0
$265$	5.24217			0.322024
$266$		0			0
$267$	−3.80186	+	1.23530i	−0.232670	+	0.0755990i
$268$		0			0
$269$	3.19947	+	2.32455i	0.195075	+	0.141730i	0.681035	−	0.732251i	$-0.261530\pi$
$269$	3.19947	+	2.32455i	0.195075	+	0.141730i	−0.485960	+	0.873981i	$0.661530\pi$
$270$		0			0
$271$	−7.33528	+	22.5757i	−0.445587	+	1.37137i	0.436252	+	0.899824i	$0.356305\pi$
$271$	−7.33528	+	22.5757i	−0.445587	+	1.37137i	−0.881839	+	0.471550i	$0.843695\pi$
$272$		0			0
$273$	−3.47097	+	2.52181i	−0.210073	+	0.152627i
$274$		0			0
$275$	4.32500	+	9.62576i	0.260807	+	0.580455i
$276$		0			0
$277$	8.82329	+	12.1442i	0.530140	+	0.729675i	0.987152	−	0.159786i	$-0.0510803\pi$
$277$	8.82329	+	12.1442i	0.530140	+	0.729675i	−0.457012	+	0.889461i	$0.651080\pi$
$278$		0			0
$279$	−8.61200	−	2.79821i	−0.515587	−	0.167524i
$280$		0			0
$281$	3.37468	−	4.64485i	0.201317	−	0.277089i	−0.696408	−	0.717647i	$-0.745219\pi$
$281$	3.37468	−	4.64485i	0.201317	−	0.277089i	0.897724	+	0.440558i	$0.145219\pi$
$282$		0			0
$283$	3.45938	+	10.6469i	0.205639	+	0.632890i	0.999687	+	0.0250353i	$0.00796982\pi$
$283$	3.45938	+	10.6469i	0.205639	+	0.632890i	−0.794048	+	0.607855i	$0.792030\pi$
$284$		0			0
$285$		−	7.94150i		−	0.470414i
$286$		0			0
$287$			9.42215i			0.556172i
$288$		0			0
$289$	5.25178	+	16.1633i	0.308928	+	0.950783i
$290$		0			0
$291$	−3.18954	+	4.39002i	−0.186974	+	0.257348i
$292$		0			0
$293$	−5.04336	−	1.63869i	−0.294636	−	0.0957331i	0.157969	−	0.987444i	$-0.449505\pi$
$293$	−5.04336	−	1.63869i	−0.294636	−	0.0957331i	−0.452605	+	0.891711i	$0.649505\pi$
$294$		0			0
$295$	3.85320	+	5.30348i	0.224342	+	0.308780i
$296$		0			0
$297$	6.65627	−	11.6202i	0.386236	−	0.674272i
$298$		0			0
$299$	−15.2811	+	11.1024i	−0.883729	+	0.642066i
$300$		0			0
$301$	−0.953632	+	2.93498i	−0.0549664	+	0.169169i
$302$		0			0
$303$	5.73613	+	4.16754i	0.329532	+	0.239419i
$304$		0			0
$305$	1.72617	−	0.560865i	0.0988400	−	0.0321150i
$306$		0			0
$307$	−2.27014			−0.129564			−0.0647820	−	0.997899i	$-0.520635\pi$
$307$	−2.27014			−0.129564			−0.0647820	+	0.997899i	$0.520635\pi$
$308$		0			0
$309$	7.64487			0.434901
$310$		0			0
$311$	−19.1795	+	6.23180i	−1.08757	+	0.353373i	−0.797307	−	0.603574i	$-0.793743\pi$
$311$	−19.1795	+	6.23180i	−1.08757	+	0.353373i	−0.290263	+	0.956947i	$0.593743\pi$
$312$		0			0
$313$	−1.24741	−	0.906296i	−0.0705078	−	0.0512269i	0.551973	−	0.833862i	$-0.313875\pi$
$313$	−1.24741	−	0.906296i	−0.0705078	−	0.0512269i	−0.622481	+	0.782635i	$0.713875\pi$
$314$		0			0
$315$	−1.66331	+	5.11913i	−0.0937168	+	0.288431i
$316$		0			0
$317$	−13.6418	+	9.91136i	−0.766201	+	0.556678i	−0.900806	−	0.434222i	$-0.857023\pi$
$317$	−13.6418	+	9.91136i	−0.766201	+	0.556678i	0.134605	+	0.990899i	$0.457023\pi$
$318$		0			0
$319$	12.7791	+	2.67083i	0.715492	+	0.149538i
$320$		0			0
$321$	−4.82253	−	6.63765i	−0.269167	−	0.370477i
$322$		0			0
$323$	−0.529105	−	0.171917i	−0.0294402	−	0.00956569i
$324$		0			0
$325$	6.65275	−	9.15673i	0.369028	−	0.507924i
$326$		0			0
$327$	−2.05062	−	6.31117i	−0.113400	−	0.349009i
$328$		0			0
$329$		−	15.9667i		−	0.880275i
$330$		0			0
$331$			33.9735i			1.86735i	0.358115	+	0.933677i	$0.383419\pi$
$331$			33.9735i			1.86735i	−0.358115	+	0.933677i	$0.616581\pi$
$332$		0			0
$333$	5.21071	+	16.0369i	0.285545	+	0.878818i
$334$		0			0
$335$	3.89396	−	5.35958i	0.212750	−	0.292825i
$336$		0			0
$337$	−16.2590	−	5.28286i	−0.885683	−	0.287776i	−0.169368	−	0.985553i	$-0.554173\pi$
$337$	−16.2590	−	5.28286i	−0.885683	−	0.287776i	−0.716315	+	0.697777i	$0.754173\pi$
$338$		0			0
$339$	4.79898	+	6.60523i	0.260645	+	0.358747i
$340$		0			0
$341$	−8.22863	−	9.07647i	−0.445605	−	0.491518i
$342$		0			0
$343$	−14.9502	+	10.8619i	−0.807232	+	0.586489i
$344$		0			0
$345$	1.63877	−	5.04362i	0.0882284	−	0.271539i
$346$		0			0
$347$	−2.02180	−	1.46893i	−0.108536	−	0.0788561i	0.532193	−	0.846623i	$-0.321368\pi$
$347$	−2.02180	−	1.46893i	−0.108536	−	0.0788561i	−0.640729	+	0.767767i	$0.721368\pi$
$348$		0			0
$349$	6.66811	−	2.16660i	0.356936	−	0.115975i	−0.125060	−	0.992149i	$-0.539912\pi$
$349$	6.66811	−	2.16660i	0.356936	−	0.115975i	0.481995	+	0.876174i	$0.339912\pi$
$350$		0			0
$351$	−14.3631			−0.766646
$352$		0			0
$353$	17.9431			0.955017			0.477509	−	0.878627i	$-0.341540\pi$
$353$	17.9431			0.955017			0.477509	+	0.878627i	$0.341540\pi$
$354$		0			0
$355$	−8.94560	+	2.90660i	−0.474783	+	0.154266i
$356$		0			0
$357$	−0.0682688	−	0.0496002i	−0.00361317	−	0.00262512i
$358$		0			0
$359$	2.99112	−	9.20572i	0.157865	−	0.485859i	−0.840575	−	0.541696i	$-0.817783\pi$
$359$	2.99112	−	9.20572i	0.157865	−	0.485859i	0.998440	+	0.0558363i	$0.0177825\pi$
$360$		0			0
$361$	−35.7804	+	25.9960i	−1.88318	+	1.36821i
$362$		0			0
$363$	7.02797	−	4.12168i	0.368873	−	0.216332i
$364$		0			0
$365$	8.02262	+	11.0422i	0.419923	+	0.577975i
$366$		0			0
$367$	29.4325	+	9.56319i	1.53636	+	0.499194i	0.950370	−	0.311122i	$-0.100705\pi$
$367$	29.4325	+	9.56319i	1.53636	+	0.499194i	0.585992	+	0.810317i	$0.300705\pi$
$368$		0			0
$369$	−8.33739	+	11.4754i	−0.434027	+	0.597387i
$370$		0			0
$371$	−1.95624	−	6.02070i	−0.101563	−	0.312579i
$372$		0			0
$373$			4.92658i			0.255088i	0.991833	+	0.127544i	$0.0407095\pi$
$373$			4.92658i			0.255088i	−0.991833	+	0.127544i	$0.959291\pi$
$374$		0			0
$375$			8.17145i			0.421972i
$376$		0			0
$377$	−4.32696	−	13.3170i	−0.222850	−	0.685861i
$378$		0			0
$379$	−2.36592	+	3.25642i	−0.121529	+	0.167271i	−0.865447	−	0.501000i	$-0.832965\pi$
$379$	−2.36592	+	3.25642i	−0.121529	+	0.167271i	0.743918	+	0.668271i	$0.232965\pi$
$380$		0			0
$381$	−7.25018	−	2.35573i	−0.371438	−	0.120688i
$382$		0			0
$383$	7.04690	+	9.69922i	0.360080	+	0.495607i	0.950171	−	0.311729i	$-0.100908\pi$
$383$	7.04690	+	9.69922i	0.360080	+	0.495607i	−0.590091	+	0.807337i	$0.700908\pi$
$384$		0			0
$385$	−5.39523	+	4.89125i	−0.274966	+	0.249281i
$386$		0			0
$387$	−3.75853	+	2.73073i	−0.191057	+	0.138811i
$388$		0			0
$389$	−4.24498	+	13.0647i	−0.215229	+	0.662407i	0.783908	+	0.620877i	$0.213223\pi$
$389$	−4.24498	+	13.0647i	−0.215229	+	0.662407i	−0.999137	+	0.0415304i	$0.986777\pi$
$390$		0			0
$391$	−0.300556	−	0.218367i	−0.0151998	−	0.0110433i
$392$		0			0
$393$	1.31564	−	0.427478i	0.0663654	−	0.0215634i
$394$		0			0
$395$	8.09663			0.407386
$396$		0			0
$397$	12.1547			0.610027			0.305014	−	0.952348i	$-0.401339\pi$
$397$	12.1547			0.610027			0.305014	+	0.952348i	$0.401339\pi$
$398$		0			0
$399$	−9.12092	+	2.96357i	−0.456617	+	0.148364i
$400$		0			0
$401$	23.2839	+	16.9167i	1.16274	+	0.844782i	0.990122	−	0.140207i	$-0.0447768\pi$
$401$	23.2839	+	16.9167i	1.16274	+	0.844782i	0.172620	+	0.984989i	$0.444777\pi$
$402$		0			0
$403$	−4.06049	+	12.4969i	−0.202267	+	0.622515i
$404$		0			0
$405$	−4.76016	+	3.45846i	−0.236534	+	0.171852i
$406$		0			0
$407$	−4.66723	+	22.3312i	−0.231346	+	1.10692i
$408$		0			0
$409$	11.1416	+	15.3351i	0.550917	+	0.758272i	0.990136	−	0.140108i	$-0.0447449\pi$
$409$	11.1416	+	15.3351i	0.550917	+	0.758272i	−0.439219	+	0.898380i	$0.644745\pi$
$410$		0			0
$411$	0.883682	+	0.287126i	0.0435888	+	0.0141629i
$412$		0			0
$413$	4.65320	−	6.40457i	0.228969	−	0.315149i
$414$		0			0
$415$	−1.50503	−	4.63200i	−0.0738790	−	0.227376i
$416$		0			0
$417$		−	4.65970i		−	0.228186i
$418$		0			0
$419$		−	15.3705i		−	0.750898i	−0.926843	−	0.375449i	$-0.877488\pi$
$419$		−	15.3705i		−	0.750898i	0.926843	−	0.375449i	$-0.122512\pi$
$420$		0			0
$421$	−5.97047	−	18.3752i	−0.290983	−	0.895553i	−0.984541	−	0.175153i	$-0.943958\pi$
$421$	−5.97047	−	18.3752i	−0.290983	−	0.895553i	0.693558	−	0.720400i	$-0.256042\pi$
$422$		0			0
$423$	14.1285	−	19.4462i	0.686952	−	0.945508i
$424$		0			0
$425$	0.211719	+	0.0687918i	0.0102699	+	0.00333689i
$426$		0			0
$427$	−1.28832	−	1.77322i	−0.0623463	−	0.0858123i
$428$		0			0
$429$	−7.58260	−	4.34345i	−0.366091	−	0.209704i
$430$		0			0
$431$	−21.9276	+	15.9313i	−1.05621	+	0.767385i	−0.973384	−	0.229179i	$-0.926396\pi$
$431$	−21.9276	+	15.9313i	−1.05621	+	0.767385i	−0.0828305	+	0.996564i	$0.526396\pi$
$432$		0			0
$433$	1.34612	−	4.14294i	0.0646905	−	0.199097i	−0.913487	−	0.406868i	$-0.866621\pi$
$433$	1.34612	−	4.14294i	0.0646905	−	0.199097i	0.978177	+	0.207771i	$0.0666209\pi$
$434$		0			0
$435$	3.18051	+	2.31078i	0.152494	+	0.110793i
$436$		0			0
$437$	−40.1552	+	13.0472i	−1.92088	+	0.624133i
$438$		0			0
$439$	−24.0996			−1.15021			−0.575105	−	0.818080i	$-0.695039\pi$
$439$	−24.0996			−1.15021			−0.575105	+	0.818080i	$0.695039\pi$
$440$		0			0
$441$	−10.6597			−0.507605
$442$		0			0
$443$	21.9169	−	7.12124i	1.04130	−	0.338340i	0.262054	−	0.965053i	$-0.415600\pi$
$443$	21.9169	−	7.12124i	1.04130	−	0.338340i	0.779250	+	0.626713i	$0.215600\pi$
$444$		0			0
$445$	5.88765	+	4.27763i	0.279102	+	0.202779i
$446$		0			0
$447$	3.92662	−	12.0849i	0.185723	−	0.571595i
$448$		0			0
$449$	3.05281	−	2.21800i	0.144071	−	0.104674i	−0.513415	−	0.858140i	$-0.671620\pi$
$449$	3.05281	−	2.21800i	0.144071	−	0.104674i	0.657486	+	0.753467i	$0.271620\pi$
$450$		0			0
$451$	−17.5050	+	7.86527i	−0.824278	+	0.370361i
$452$		0			0
$453$	5.29321	+	7.28548i	0.248697	+	0.342302i
$454$		0			0
$455$	7.42839	+	2.41363i	0.348248	+	0.113153i
$456$		0			0
$457$	20.7236	−	28.5236i	0.969409	−	1.33428i	0.0270646	−	0.999634i	$-0.491384\pi$
$457$	20.7236	−	28.5236i	0.969409	−	1.33428i	0.942345	−	0.334644i	$-0.108616\pi$
$458$		0			0
$459$	−0.0872976	−	0.268674i	−0.00407470	−	0.0125406i
$460$		0			0
$461$		−	38.5074i		−	1.79347i	−0.442571	−	0.896734i	$-0.645933\pi$
$461$		−	38.5074i		−	1.79347i	0.442571	−	0.896734i	$-0.354067\pi$
$462$		0			0
$463$			10.7672i			0.500394i	0.968195	+	0.250197i	$0.0804954\pi$
$463$			10.7672i			0.500394i	−0.968195	+	0.250197i	$0.919505\pi$
$464$		0			0
$465$	−1.14003	−	3.50866i	−0.0528677	−	0.162710i
$466$		0			0
$467$	−12.1553	+	16.7304i	−0.562481	+	0.774189i	−0.991639	−	0.129040i	$-0.958810\pi$
$467$	−12.1553	+	16.7304i	−0.562481	+	0.774189i	0.429158	+	0.903229i	$0.358810\pi$
$468$		0			0
$469$	−7.60867	−	2.47221i	−0.351336	−	0.114156i
$470$		0			0
$471$	2.30815	+	3.17690i	0.106354	+	0.146384i
$472$		0			0
$473$	−6.24883	+	0.678301i	−0.287321	+	0.0311883i
$474$		0			0
$475$	20.4682	−	14.8710i	0.939144	−	0.682328i
$476$		0			0
$477$	2.94499	−	9.06375i	0.134842	−	0.415001i
$478$		0			0
$479$	9.23398	+	6.70888i	0.421911	+	0.306536i	0.778406	−	0.627761i	$-0.216028\pi$
$479$	9.23398	+	6.70888i	0.421911	+	0.306536i	−0.356495	+	0.934297i	$0.616028\pi$
$480$		0			0
$481$	23.2712	−	7.56128i	1.06108	−	0.344765i
$482$		0			0
$483$	−6.40421			−0.291401
$484$		0			0
$485$	9.87880			0.448573
$486$		0			0
$487$	−3.80894	+	1.23760i	−0.172600	+	0.0560810i	−0.394042	−	0.919092i	$-0.628924\pi$
$487$	−3.80894	+	1.23760i	−0.172600	+	0.0560810i	0.221442	+	0.975173i	$0.428924\pi$
$488$		0			0
$489$	6.02668	+	4.37864i	0.272536	+	0.198009i
$490$		0			0
$491$	−3.45914	+	10.6461i	−0.156109	+	0.480454i	−0.998272	−	0.0587698i	$-0.981282\pi$
$491$	−3.45914	+	10.6461i	−0.156109	+	0.480454i	0.842163	+	0.539223i	$0.181282\pi$
$492$		0			0
$493$	0.222807	−	0.161879i	0.0100347	−	0.00729066i
$494$		0			0
$495$	−10.8991	+	1.18308i	−0.489877	+	0.0531755i
$496$		0			0
$497$	6.67654	+	9.18946i	0.299484	+	0.412204i
$498$		0			0
$499$	−37.4389	−	12.1646i	−1.67599	−	0.544564i	−0.691867	−	0.722025i	$-0.743211\pi$
$499$	−37.4389	−	12.1646i	−1.67599	−	0.544564i	−0.984128	+	0.177462i	$0.943211\pi$
$500$		0			0
$501$	9.53767	−	13.1275i	0.426112	−	0.586492i
$502$		0			0
$503$	−5.97544	−	18.3905i	−0.266432	−	0.819993i	−0.991360	−	0.131168i	$-0.958127\pi$
$503$	−5.97544	−	18.3905i	−0.266432	−	0.819993i	0.724928	−	0.688824i	$-0.241873\pi$
$504$		0			0
$505$		−	12.9079i		−	0.574395i
$506$		0			0
$507$		−	0.256336i		−	0.0113843i
$508$		0			0
$509$	13.2867	+	40.8921i	0.588920	+	1.81251i	0.582921	+	0.812529i	$0.301910\pi$
$509$	13.2867	+	40.8921i	0.588920	+	1.81251i	0.00599915	+	0.999982i	$0.498090\pi$
$510$		0			0
$511$	9.68826	−	13.3347i	0.428583	−	0.589895i
$512$		0			0
$513$	−30.5347	−	9.92132i	−1.34814	−	0.438037i
$514$		0			0
$515$	−8.18058	−	11.2596i	−0.360479	−	0.496157i
$516$		0			0
$517$	29.6639	−	13.3285i	1.30462	−	0.586185i
$518$		0			0
$519$	7.09009	−	5.15125i	0.311220	−	0.226115i
$520$		0			0
$521$	−4.55221	+	14.0103i	−0.199436	+	0.613801i	0.800460	+	0.599386i	$0.204589\pi$
$521$	−4.55221	+	14.0103i	−0.199436	+	0.613801i	−0.999896	+	0.0144150i	$0.995411\pi$
$522$		0			0
$523$	32.7270	+	23.7776i	1.43105	+	1.03972i	0.989819	+	0.142329i	$0.0454591\pi$
$523$	32.7270	+	23.7776i	1.43105	+	1.03972i	0.441234	+	0.897392i	$0.354541\pi$
$524$		0			0
$525$	3.64970	−	1.18586i	0.159286	−	0.0517552i
$526$		0			0
$527$	−0.258445			−0.0112580
$528$		0			0
$529$	−5.19479			−0.225860
$530$		0			0
$531$	11.3344	−	3.68278i	0.491873	−	0.159819i
$532$		0			0
$533$	16.6520	+	12.0984i	0.721280	+	0.524040i
$534$		0			0
$535$	−4.61566	+	14.2055i	−0.199552	+	0.614159i
$536$		0			0
$537$	0.559477	−	0.406484i	0.0241432	−	0.0175411i
$538$		0			0
$539$	−12.5144	−	7.16845i	−0.539031	−	0.308767i
$540$		0			0
$541$	9.83661	+	13.5389i	0.422909	+	0.582084i	0.966307	−	0.257391i	$-0.0828627\pi$
$541$	9.83661	+	13.5389i	0.422909	+	0.582084i	−0.543399	+	0.839475i	$0.682863\pi$
$542$		0			0
$543$	13.2710	+	4.31200i	0.569512	+	0.185046i
$544$		0			0
$545$	−7.10097	+	9.77365i	−0.304172	+	0.418657i
$546$		0			0
$547$	2.87078	+	8.83536i	0.122746	+	0.377773i	0.993484	−	0.113975i	$-0.0363583\pi$
$547$	2.87078	+	8.83536i	0.122746	+	0.377773i	−0.870738	+	0.491747i	$0.836358\pi$
$548$		0			0
$549$		−	3.29964i		−	0.140825i
$550$		0			0
$551$		−	31.2996i		−	1.33341i
$552$		0			0
$553$	−3.02146	−	9.29909i	−0.128485	−	0.395437i
$554$		0			0
$555$	−4.03804	+	5.55788i	−0.171405	+	0.235919i
$556$		0			0
$557$	−12.6129	−	4.09818i	−0.534425	−	0.173645i	0.0293567	−	0.999569i	$-0.490654\pi$
$557$	−12.6129	−	4.09818i	−0.534425	−	0.173645i	−0.563782	+	0.825924i	$0.690654\pi$
$558$		0			0
$559$	3.96257	+	5.45401i	0.167599	+	0.230680i
$560$		0			0
$561$	0.0351618	−	0.168238i	0.00148453	−	0.00710302i
$562$		0			0
$563$	19.0155	−	13.8156i	0.801408	−	0.582257i	−0.109919	−	0.993941i	$-0.535059\pi$
$563$	19.0155	−	13.8156i	0.801408	−	0.582257i	0.911327	+	0.411684i	$0.135059\pi$
$564$		0			0
$565$	4.59312	−	14.1362i	0.193234	−	0.594713i
$566$		0			0
$567$	5.74846	+	4.17650i	0.241413	+	0.175396i
$568$		0			0
$569$	−12.2494	+	3.98008i	−0.513523	+	0.166854i	−0.554304	−	0.832315i	$-0.687015\pi$
$569$	−12.2494	+	3.98008i	−0.513523	+	0.166854i	0.0407811	+	0.999168i	$0.487015\pi$
$570$		0			0
$571$	20.4261			0.854806			0.427403	−	0.904061i	$-0.359429\pi$
$571$	20.4261			0.854806			0.427403	+	0.904061i	$0.359429\pi$
$572$		0			0
$573$	−15.1424			−0.632585
$574$		0			0
$575$	16.0680	−	5.22080i	0.670080	−	0.217722i
$576$		0			0
$577$	−5.53777	−	4.02342i	−0.230540	−	0.167497i	0.466518	−	0.884512i	$-0.345508\pi$
$577$	−5.53777	−	4.02342i	−0.230540	−	0.167497i	−0.697058	+	0.717014i	$0.745508\pi$
$578$		0			0
$579$	3.96902	−	12.2154i	0.164947	−	0.507654i
$580$		0			0
$581$	−4.75828	+	3.45709i	−0.197407	+	0.143424i
$582$		0			0
$583$	9.55259	−	8.66028i	0.395628	−	0.358672i
$584$		0			0
$585$	6.91144	+	9.51278i	0.285753	+	0.393305i
$586$		0			0
$587$	−0.607533	−	0.197399i	−0.0250756	−	0.00814754i	0.296452	−	0.955048i	$-0.404196\pi$
$587$	−0.607533	−	0.197399i	−0.0250756	−	0.00814754i	−0.321528	+	0.946900i	$0.604196\pi$
$588$		0			0
$589$	−17.2645	+	23.7625i	−0.711370	+	0.979117i
$590$		0			0
$591$	−0.799100	−	2.45938i	−0.0328706	−	0.101165i
$592$		0			0
$593$		−	17.0480i		−	0.700077i	−0.936735	−	0.350039i	$-0.886168\pi$
$593$		−	17.0480i		−	0.700077i	0.936735	−	0.350039i	$-0.113832\pi$
$594$		0			0
$595$			0.153624i			0.00629799i
$596$		0			0
$597$	−2.57858	−	7.93604i	−0.105534	−	0.324801i
$598$		0			0
$599$	1.16656	−	1.60564i	0.0476645	−	0.0656045i	−0.784519	−	0.620104i	$-0.787090\pi$
$599$	1.16656	−	1.60564i	0.0476645	−	0.0656045i	0.832184	+	0.554500i	$0.187090\pi$
$600$		0			0
$601$	15.6571	+	5.08729i	0.638665	+	0.207515i	0.610410	−	0.792086i	$-0.291005\pi$
$601$	15.6571	+	5.08729i	0.638665	+	0.207515i	0.0282553	+	0.999601i	$0.491005\pi$
$602$		0			0
$603$	−7.07917	−	9.74365i	−0.288286	−	0.396792i
$604$		0			0
$605$	−13.5910	−	5.94052i	−0.552552	−	0.241516i
$606$		0			0
$607$	23.2353	−	16.8814i	0.943091	−	0.685196i	−0.00607141	−	0.999982i	$-0.501933\pi$
$607$	23.2353	−	16.8814i	0.943091	−	0.685196i	0.949163	+	0.314786i	$0.101933\pi$
$608$		0			0
$609$	1.46707	−	4.51518i	0.0594487	−	0.182964i
$610$		0			0
$611$	−28.2185	−	20.5019i	−1.14160	−	0.829419i
$612$		0			0
$613$	−6.32812	+	2.05613i	−0.255590	+	0.0830464i	−0.434010	−	0.900908i	$-0.642902\pi$
$613$	−6.32812	+	2.05613i	−0.255590	+	0.0830464i	0.178419	+	0.983955i	$0.442902\pi$
$614$		0			0
$615$	−5.77894			−0.233029
$616$		0			0
$617$	−17.8948			−0.720416			−0.360208	−	0.932872i	$-0.617294\pi$
$617$	−17.8948			−0.720416			−0.360208	+	0.932872i	$0.617294\pi$
$618$		0			0
$619$	22.1005	−	7.18088i	0.888293	−	0.288624i	0.170897	−	0.985289i	$-0.445334\pi$
$619$	22.1005	−	7.18088i	0.888293	−	0.288624i	0.717397	+	0.696665i	$0.245334\pi$
$620$		0			0
$621$	−17.3452	−	12.6020i	−0.696037	−	0.505700i
$622$		0			0
$623$	2.71579	−	8.35835i	0.108806	−	0.334870i
$624$		0			0
$625$	−0.835407	+	0.606959i	−0.0334163	+	0.0242784i
$626$		0			0
$627$	−13.1197	−	14.4715i	−0.523950	−	0.577935i
$628$		0			0
$629$	0.282881	+	0.389352i	0.0112792	+	0.0155245i
$630$		0			0
$631$	−44.0545	−	14.3142i	−1.75378	−	0.569838i	−0.757255	−	0.653119i	$-0.773460\pi$
$631$	−44.0545	−	14.3142i	−1.75378	−	0.569838i	−0.996526	+	0.0832806i	$0.973460\pi$
$632$		0			0
$633$	−1.19417	+	1.64363i	−0.0474639	+	0.0653284i
$634$		0			0
$635$	4.28864	+	13.1991i	0.170190	+	0.523790i
$636$		0			0
$637$			15.4683i			0.612877i
$638$		0			0
$639$			17.0999i			0.676462i
$640$		0			0
$641$	8.39773	+	25.8456i	0.331691	+	1.02084i	0.968329	+	0.249676i	$0.0803242\pi$
$641$	8.39773	+	25.8456i	0.331691	+	1.02084i	−0.636639	+	0.771162i	$0.719676\pi$
$642$		0			0
$643$	18.2352	−	25.0987i	0.719128	−	0.989794i	−0.280425	−	0.959876i	$-0.590475\pi$
$643$	18.2352	−	25.0987i	0.719128	−	0.989794i	0.999552	−	0.0299182i	$-0.00952467\pi$
$644$		0			0
$645$	−1.80013	−	0.584897i	−0.0708800	−	0.0230303i
$646$		0			0
$647$	−24.7877	−	34.1173i	−0.974505	−	1.34129i	−0.939738	−	0.341895i	$-0.888931\pi$
$647$	−24.7877	−	34.1173i	−0.974505	−	1.34129i	−0.0347664	−	0.999395i	$-0.511069\pi$
$648$		0			0
$649$	15.7831	+	3.29867i	0.619541	+	0.129484i
$650$		0			0
$651$	−3.60431	+	2.61868i	−0.141264	+	0.102634i
$652$		0			0
$653$	1.25077	−	3.84947i	0.0489464	−	0.150641i	−0.923596	−	0.383367i	$-0.874764\pi$
$653$	1.25077	−	3.84947i	0.0489464	−	0.150641i	0.972542	+	0.232726i	$0.0747644\pi$
$654$		0			0
$655$	−2.03744	−	1.48028i	−0.0796093	−	0.0578395i
$656$		0			0
$657$	23.5991	−	7.66780i	0.920687	−	0.299149i
$658$		0			0
$659$	−6.46292			−0.251760			−0.125880	−	0.992045i	$-0.540175\pi$
$659$	−6.46292			−0.251760			−0.125880	+	0.992045i	$0.540175\pi$
$660$		0			0
$661$	−26.6232			−1.03552			−0.517761	−	0.855525i	$-0.673234\pi$
$661$	−26.6232			−1.03552			−0.517761	+	0.855525i	$0.673234\pi$
$662$		0			0
$663$	−0.175320	+	0.0569648i	−0.00680885	+	0.00221233i
$664$		0			0
$665$	14.1249	+	10.2623i	0.547740	+	0.397956i
$666$		0			0
$667$	6.45884	−	19.8783i	0.250087	−	0.769690i
$668$		0			0
$669$	14.2169	−	10.3292i	0.549659	−	0.399350i
$670$		0			0
$671$	2.21895	−	3.87374i	0.0856616	−	0.149544i
$672$		0			0
$673$	−4.89033	−	6.73096i	−0.188508	−	0.259460i	0.704294	−	0.709909i	$-0.251264\pi$
$673$	−4.89033	−	6.73096i	−0.188508	−	0.259460i	−0.892802	+	0.450449i	$0.851264\pi$
$674$		0			0
$675$	12.2183	+	3.96998i	0.470284	+	0.152805i
$676$		0			0
$677$	8.97132	−	12.3480i	0.344796	−	0.474571i	−0.601039	−	0.799220i	$-0.705246\pi$
$677$	8.97132	−	12.3480i	0.344796	−	0.474571i	0.945834	+	0.324649i	$0.105246\pi$
$678$		0			0
$679$	−3.68652	−	11.3459i	−0.141476	−	0.435417i
$680$		0			0
$681$		−	0.593162i		−	0.0227300i
$682$		0			0
$683$		−	32.9156i		−	1.25948i	−0.776806	−	0.629740i	$-0.783161\pi$
$683$		−	32.9156i		−	1.25948i	0.776806	−	0.629740i	$-0.216839\pi$
$684$		0			0
$685$	−0.522718	−	1.60876i	−0.0199720	−	0.0614676i
$686$		0			0
$687$	−10.2696	+	14.1349i	−0.391811	+	0.539282i
$688$		0			0
$689$	−13.1524	−	4.27349i	−0.501068	−	0.162807i
$690$		0			0
$691$	−26.7545	−	36.8244i	−1.01779	−	1.40087i	−0.913742	−	0.406294i	$-0.866821\pi$
$691$	−26.7545	−	36.8244i	−1.01779	−	1.40087i	−0.104047	−	0.994572i	$-0.533179\pi$
$692$		0			0
$693$	5.42604	+	12.0762i	0.206118	+	0.458739i
$694$		0			0
$695$	−6.86294	+	4.98622i	−0.260326	+	0.189138i
$696$		0			0
$697$	−0.125102	+	0.385024i	−0.00473857	+	0.0145838i
$698$		0			0
$699$	10.4812	+	7.61507i	0.396437	+	0.288028i
$700$		0			0
$701$	47.6330	−	15.4769i	1.79907	−	0.584555i	0.799210	−	0.601052i	$-0.205252\pi$
$701$	47.6330	−	15.4769i	1.79907	−	0.584555i	0.999864	+	0.0164975i	$0.00525154\pi$
$702$		0			0
$703$	54.6955			2.06288
$704$		0			0
$705$	9.79298			0.368825
$706$		0			0
$707$	−14.8249	+	4.81691i	−0.557548	+	0.181158i
$708$		0			0
$709$	−6.87556	−	4.99539i	−0.258217	−	0.187606i	0.451144	−	0.892451i	$-0.351016\pi$
$709$	−6.87556	−	4.99539i	−0.258217	−	0.187606i	−0.709361	+	0.704846i	$0.751016\pi$
$710$		0			0
$711$	4.54860	−	13.9991i	0.170586	−	0.525009i
$712$		0			0
$713$	−15.8681	+	11.5289i	−0.594266	+	0.431759i
$714$		0			0
$715$	1.71677	+	15.8157i	0.0642036	+	0.591474i
$716$		0			0
$717$	2.91036	+	4.00576i	0.108689	+	0.149598i
$718$		0			0
$719$	−6.94019	−	2.25500i	−0.258825	−	0.0840974i	0.176730	−	0.984259i	$-0.443448\pi$
$719$	−6.94019	−	2.25500i	−0.258825	−	0.0840974i	−0.435555	+	0.900162i	$0.643448\pi$
$720$		0			0
$721$	−9.87901	+	13.5973i	−0.367914	+	0.506390i
$722$		0			0
$723$	−0.981112	−	3.01955i	−0.0364879	−	0.112298i
$724$		0			0
$725$			12.5244i			0.465146i
$726$		0			0
$727$			1.85004i			0.0686140i	0.999411	+	0.0343070i	$0.0109224\pi$
$727$			1.85004i			0.0686140i	−0.999411	+	0.0343070i	$0.989078\pi$
$728$		0			0
$729$	0.533026	+	1.64049i	0.0197417	+	0.0607587i
$730$		0			0
$731$	−0.0779378	+	0.107272i	−0.00288264	+	0.00396761i
$732$		0			0
$733$	−17.9690	−	5.83849i	−0.663701	−	0.215650i	−0.0422555	−	0.999107i	$-0.513454\pi$
$733$	−17.9690	−	5.83849i	−0.663701	−	0.215650i	−0.621446	+	0.783457i	$0.713454\pi$
$734$		0			0
$735$	−2.55271	−	3.51350i	−0.0941580	−	0.129597i
$736$		0			0
$737$	−1.75843	−	16.1995i	−0.0647728	−	0.596717i
$738$		0			0
$739$	−12.7166	+	9.23916i	−0.467788	+	0.339868i	−0.796579	−	0.604535i	$-0.793359\pi$
$739$	−12.7166	+	9.23916i	−0.467788	+	0.339868i	0.328791	+	0.944403i	$0.393359\pi$
$740$		0			0
$741$	−6.47402	+	19.9250i	−0.237829	+	0.731963i
$742$		0			0
$743$	4.69746	+	3.41290i	0.172333	+	0.125207i	0.670608	−	0.741812i	$-0.266033\pi$
$743$	4.69746	+	3.41290i	0.172333	+	0.125207i	−0.498275	+	0.867019i	$0.666033\pi$
$744$		0			0
$745$	−22.0008	+	7.14848i	−0.806045	+	0.261900i
$746$		0			0
$747$	−8.85428			−0.323961
$748$		0			0
$749$	18.0377			0.659083
$750$		0			0
$751$	2.85643	−	0.928110i	0.104233	−	0.0338672i	−0.256436	−	0.966561i	$-0.582548\pi$
$751$	2.85643	−	0.928110i	0.104233	−	0.0338672i	0.360669	+	0.932694i	$0.382548\pi$
$752$		0			0
$753$	−2.93478	−	2.13224i	−0.106949	−	0.0777033i
$754$		0			0
$755$	5.06615	−	15.5920i	0.184376	−	0.567451i
$756$		0			0
$757$	−21.1049	+	15.3336i	−0.767071	+	0.557310i	−0.901071	−	0.433672i	$-0.857218\pi$
$757$	−21.1049	+	15.3336i	−0.767071	+	0.557310i	0.134000	+	0.990981i	$0.457218\pi$
$758$		0			0
$759$	−5.34600	−	11.8981i	−0.194047	−	0.431874i
$760$		0			0
$761$	−18.7813	−	25.8502i	−0.680820	−	0.937068i	0.319123	−	0.947713i	$-0.396612\pi$
$761$	−18.7813	−	25.8502i	−0.680820	−	0.937068i	−0.999943	+	0.0106450i	$0.996612\pi$
$762$		0			0
$763$	13.8751	+	4.50828i	0.502311	+	0.163211i
$764$		0			0
$765$	−0.135938	+	0.187102i	−0.00491484	+	0.00676470i
$766$		0			0
$767$	−5.34410	−	16.4474i	−0.192964	−	0.593883i
$768$		0			0
$769$			22.3560i			0.806176i	0.915161	+	0.403088i	$0.132063\pi$
$769$			22.3560i			0.806176i	−0.915161	+	0.403088i	$0.867937\pi$
$770$		0			0
$771$			9.17275i			0.330348i
$772$		0			0
$773$	−1.56889	−	4.82855i	−0.0564291	−	0.173671i	0.918869	−	0.394562i	$-0.129104\pi$
$773$	−1.56889	−	4.82855i	−0.0564291	−	0.173671i	−0.975299	+	0.220891i	$0.929104\pi$
$774$		0			0
$775$	6.90832	−	9.50848i	0.248154	−	0.341555i
$776$		0			0
$777$	7.89020	+	2.56368i	0.283059	+	0.0919715i
$778$		0			0
$779$	27.0438	+	37.2225i	0.968943	+	1.33364i
$780$		0			0
$781$	−11.4994	+	20.0751i	−0.411480	+	0.718343i
$782$		0			0
$783$	12.8582	−	9.34206i	0.459516	−	0.333858i
$784$		0			0
$785$	2.20914	−	6.79904i	0.0788476	−	0.242668i
$786$		0			0
$787$	−2.38155	−	1.73029i	−0.0848930	−	0.0616783i	0.544529	−	0.838742i	$-0.316708\pi$
$787$	−2.38155	−	1.73029i	−0.0848930	−	0.0616783i	−0.629422	+	0.777064i	$0.716708\pi$
$788$		0			0
$789$	11.9392	−	3.87928i	0.425046	−	0.138106i
$790$		0			0
$791$	−17.9496			−0.638215
$792$		0			0
$793$	−4.78812			−0.170031
$794$		0			0
$795$	3.69271	−	1.19983i	0.130967	−	0.0425537i
$796$		0			0
$797$	6.06111	+	4.40365i	0.214695	+	0.155985i	0.689936	−	0.723871i	$-0.257639\pi$
$797$	6.06111	+	4.40365i	0.214695	+	0.155985i	−0.475240	+	0.879856i	$0.657639\pi$
$798$		0			0
$799$	0.211997	−	0.652460i	0.00749992	−	0.0230824i
$800$		0			0
$801$	10.7037	−	7.77668i	0.378196	−	0.274775i
$802$		0			0
$803$	32.8615	+	6.86804i	1.15966	+	0.242368i
$804$		0			0
$805$	6.85298	+	9.43231i	0.241536	+	0.332445i
$806$		0			0
$807$	2.78583	+	0.905170i	0.0980658	+	0.0318635i
$808$		0			0
$809$	23.4091	−	32.2199i	0.823022	−	1.13279i	−0.166160	−	0.986099i	$-0.553137\pi$
$809$	23.4091	−	32.2199i	0.823022	−	1.13279i	0.989182	−	0.146694i	$-0.0468631\pi$
$810$		0			0
$811$	−13.1790	−	40.5607i	−0.462777	−	1.42428i	−0.861757	−	0.507321i	$-0.830636\pi$
$811$	−13.1790	−	40.5607i	−0.462777	−	1.42428i	0.398981	−	0.916959i	$-0.369364\pi$
$812$		0			0
$813$			17.5818i			0.616619i
$814$		0			0
$815$		−	13.5617i		−	0.475047i
$816$		0			0
$817$	4.65671	+	14.3319i	0.162918	+	0.501409i
$818$		0			0
$819$	8.34638	−	11.4878i	0.291646	−	0.401416i
$820$		0			0
$821$	18.3658	+	5.96742i	0.640972	+	0.208264i	0.611429	−	0.791299i	$-0.290595\pi$
$821$	18.3658	+	5.96742i	0.640972	+	0.208264i	0.0295426	+	0.999564i	$0.490595\pi$
$822$		0			0
$823$	−5.83041	−	8.02487i	−0.203235	−	0.279729i	0.695218	−	0.718799i	$-0.255308\pi$
$823$	−5.83041	−	8.02487i	−0.203235	−	0.279729i	−0.898453	+	0.439070i	$0.855308\pi$
$824$		0			0
$825$	5.24979	+	5.79071i	0.182774	+	0.201607i
$826$		0			0
$827$	−35.2981	+	25.6455i	−1.22743	+	0.891783i	−0.996695	−	0.0812332i	$-0.974114\pi$
$827$	−35.2981	+	25.6455i	−1.22743	+	0.891783i	−0.230738	+	0.973016i	$0.574114\pi$
$828$		0			0
$829$	8.69871	−	26.7719i	0.302119	−	0.929826i	−0.678618	−	0.734491i	$-0.737421\pi$
$829$	8.69871	−	26.7719i	0.302119	−	0.929826i	0.980737	−	0.195335i	$-0.0625793\pi$
$830$		0			0
$831$	8.99492	+	6.53519i	0.312030	+	0.226703i
$832$		0			0
$833$	−0.289348	+	0.0940150i	−0.0100253	+	0.00325743i
$834$		0			0
$835$	−29.5406			−1.02229
$836$		0			0
$837$	−14.9149			−0.515533
$838$		0			0
$839$	33.2421	−	10.8010i	1.14764	−	0.372892i	0.327388	−	0.944890i	$-0.393831\pi$
$839$	33.2421	−	10.8010i	1.14764	−	0.372892i	0.820255	+	0.571998i	$0.193831\pi$
$840$		0			0
$841$	−10.9262	−	7.93837i	−0.376767	−	0.273737i
$842$		0			0
$843$	1.31409	−	4.04435i	0.0452596	−	0.139295i
$844$		0			0
$845$	−0.377540	+	0.274299i	−0.0129878	+	0.00943617i
$846$		0			0
$847$	−1.75095	+	17.8263i	−0.0601634	+	0.612518i
$848$		0			0
$849$	4.87374	+	6.70812i	0.167266	+	0.230222i
$850$		0			0
$851$	34.7369	+	11.2867i	1.19077	+	0.386903i
$852$		0			0
$853$	15.9973	−	22.0183i	0.547736	−	0.753894i	−0.441967	−	0.897031i	$-0.645719\pi$
$853$	15.9973	−	22.0183i	0.547736	−	0.753894i	0.989703	+	0.143138i	$0.0457191\pi$
$854$		0			0
$855$	8.12215	+	24.9974i	0.277772	+	0.854893i
$856$		0			0
$857$			37.5541i			1.28282i	0.767197	+	0.641412i	$0.221651\pi$
$857$			37.5541i			1.28282i	−0.767197	+	0.641412i	$0.778349\pi$
$858$		0			0
$859$			4.50293i			0.153638i	0.997045	+	0.0768190i	$0.0244764\pi$
$859$			4.50293i			0.153638i	−0.997045	+	0.0768190i	$0.975524\pi$
$860$		0			0
$861$	2.15655	+	6.63719i	0.0734952	+	0.226195i
$862$		0			0
$863$	−10.6014	+	14.5915i	−0.360875	+	0.496702i	−0.950392	−	0.311054i	$-0.899318\pi$
$863$	−10.6014	+	14.5915i	−0.360875	+	0.496702i	0.589517	+	0.807756i	$0.299318\pi$
$864$		0			0
$865$	−15.1738	−	4.93028i	−0.515926	−	0.167634i
$866$		0			0
$867$	7.39896	+	10.1838i	0.251282	+	0.345860i
$868$		0			0
$869$	14.7542	−	13.3760i	0.500501	−	0.453749i
$870$		0			0
$871$	−14.1390	+	10.2726i	−0.479083	+	0.348074i
$872$		0			0
$873$	5.54980	−	17.0805i	0.187832	−	0.578089i
$874$		0			0
$875$	−14.5339	−	10.5595i	−0.491335	−	0.356976i
$876$		0			0
$877$	12.9541	−	4.20903i	0.437428	−	0.142129i	−0.0820206	−	0.996631i	$-0.526137\pi$
$877$	12.9541	−	4.20903i	0.437428	−	0.142129i	0.519449	+	0.854502i	$0.326137\pi$
$878$		0			0
$879$	−3.92773			−0.132479
$880$		0			0
$881$	5.44549			0.183463			0.0917317	−	0.995784i	$-0.470760\pi$
$881$	5.44549			0.183463			0.0917317	+	0.995784i	$0.470760\pi$
$882$		0			0
$883$	−26.8480	+	8.72345i	−0.903508	+	0.293568i	−0.723684	−	0.690131i	$-0.757553\pi$
$883$	−26.8480	+	8.72345i	−0.903508	+	0.293568i	−0.179824	+	0.983699i	$0.557553\pi$
$884$		0			0
$885$	3.92816	+	2.85397i	0.132044	+	0.0959352i
$886$		0			0
$887$	−13.1145	+	40.3623i	−0.440342	+	1.35523i	0.447171	+	0.894449i	$0.352432\pi$
$887$	−13.1145	+	40.3623i	−0.440342	+	1.35523i	−0.887512	+	0.460784i	$0.847568\pi$
$888$		0			0
$889$	13.5589	−	9.85113i	0.454751	−	0.330396i
$890$		0			0
$891$	−2.96073	+	14.1662i	−0.0991883	+	0.474586i
$892$		0			0
$893$	−45.8283	−	63.0772i	−1.53358	−	2.11080i
$894$		0			0
$895$	−1.19736	−	0.389047i	−0.0400234	−	0.0130044i
$896$		0			0
$897$	−8.22325	+	11.3183i	−0.274566	+	0.377908i
$898$		0			0
$899$	−4.49318	−	13.8286i	−0.149856	−	0.461209i
$900$		0			0
$901$		−	0.272002i		−	0.00906169i
$902$		0			0
$903$			2.28574i			0.0760646i
$904$		0			0
$905$	−7.85008	−	24.1601i	−0.260946	−	0.803108i
$906$		0			0
$907$	20.3902	−	28.0647i	0.677046	−	0.931873i	−0.322848	−	0.946451i	$-0.604640\pi$
$907$	20.3902	−	28.0647i	0.677046	−	0.931873i	0.999894	+	0.0145776i	$0.00464034\pi$
$908$		0			0
$909$	−22.3179	−	7.25153i	−0.740238	−	0.240518i
$910$		0			0
$911$	17.4380	+	24.0014i	0.577748	+	0.795202i	0.993446	−	0.114300i	$-0.0364627\pi$
$911$	17.4380	+	24.0014i	0.577748	+	0.795202i	−0.415698	+	0.909503i	$0.636463\pi$
$912$		0			0
$913$	−10.3948	−	5.95434i	−0.344018	−	0.197060i
$914$		0			0
$915$	1.08758	−	0.790174i	0.0359543	−	0.0261224i
$916$		0			0
$917$	−0.939807	+	2.89243i	−0.0310352	+	0.0955164i
$918$		0			0
$919$	−17.4823	−	12.7016i	−0.576687	−	0.418988i	0.260841	−	0.965382i	$-0.416000\pi$
$919$	−17.4823	−	12.7016i	−0.576687	−	0.418988i	−0.837528	+	0.546394i	$0.816000\pi$
$920$		0			0
$921$	−1.59915	+	0.519594i	−0.0526936	+	0.0171212i
$922$		0			0
$923$	24.8137			0.816754
$924$		0			0
$925$	−21.8862			−0.719614
$926$		0			0
$927$	−24.0637	+	7.81877i	−0.790356	+	0.256802i
$928$		0			0
$929$	−38.2024	−	27.7557i	−1.25338	−	0.910635i	−0.254968	−	0.966949i	$-0.582065\pi$
$929$	−38.2024	−	27.7557i	−1.25338	−	0.910635i	−0.998413	+	0.0563145i	$0.982065\pi$
$930$		0			0
$931$	−10.6848	+	32.8843i	−0.350179	+	1.07774i
$932$		0			0
$933$	−12.0842	+	8.77967i	−0.395618	+	0.287433i
$934$		0			0
$935$	−0.285412	+	0.128240i	−0.00933397	+	0.00419390i
$936$		0			0
$937$	27.2659	+	37.5283i	0.890738	+	1.22600i	0.973329	+	0.229412i	$0.0736804\pi$
$937$	27.2659	+	37.5283i	0.890738	+	1.22600i	−0.0825914	+	0.996583i	$0.526320\pi$
$938$		0			0
$939$	−1.08614	−	0.352908i	−0.0354449	−	0.0115167i
$940$		0			0
$941$	−23.1708	+	31.8919i	−0.755347	+	1.03965i	0.242240	+	0.970216i	$0.422118\pi$
$941$	−23.1708	+	31.8919i	−0.755347	+	1.03965i	−0.997587	+	0.0694293i	$0.977882\pi$
$942$		0			0
$943$	9.49432	+	29.2205i	0.309178	+	0.951551i
$944$		0			0
$945$			8.86568i			0.288401i
$946$		0			0
$947$			24.9488i			0.810725i	0.914156	+	0.405363i	$0.132855\pi$
$947$			24.9488i			0.810725i	−0.914156	+	0.405363i	$0.867145\pi$
$948$		0			0
$949$	−11.1268	−	34.2447i	−0.361190	−	1.11163i
$950$		0			0
$951$	−7.34110	+	10.1042i	−0.238052	+	0.327650i
$952$		0			0
$953$	38.9090	+	12.6423i	1.26039	+	0.409524i	0.861632	−	0.507534i	$-0.169443\pi$
$953$	38.9090	+	12.6423i	1.26039	+	0.409524i	0.398754	+	0.917058i	$0.369443\pi$
$954$		0			0
$955$	16.2035	+	22.3023i	0.524334	+	0.721684i
$956$		0			0
$957$	9.61321	−	1.04350i	0.310751	−	0.0337316i
$958$		0			0
$959$	−1.65262	+	1.20070i	−0.0533658	+	0.0387725i
$960$		0			0
$961$	5.36305	−	16.5058i	0.173002	−	0.532445i
$962$		0			0
$963$	21.9685	+	15.9610i	0.707925	+	0.514337i
$964$		0			0
$965$	−22.2383	+	7.22567i	−0.715877	+	0.232603i
$966$		0			0
$967$	−23.6696			−0.761164			−0.380582	−	0.924747i	$-0.624276\pi$
$967$	−23.6696			−0.761164			−0.380582	+	0.924747i	$0.624276\pi$
$968$		0			0
$969$	−0.412063			−0.0132374
$970$		0			0
$971$	−51.2925	+	16.6659i	−1.64606	+	0.534836i	−0.977880	−	0.209168i	$-0.932924\pi$
$971$	−51.2925	+	16.6659i	−1.64606	+	0.534836i	−0.668176	+	0.744004i	$0.732924\pi$
$972$		0			0
$973$	8.28781	+	6.02145i	0.265695	+	0.193039i
$974$		0			0
$975$	2.59056	−	7.97291i	0.0829642	−	0.255338i
$976$		0			0
$977$	7.76321	−	5.64030i	0.248367	−	0.180449i	−0.456636	−	0.889654i	$-0.650946\pi$
$977$	7.76321	−	5.64030i	0.248367	−	0.180449i	0.705003	+	0.709204i	$0.250946\pi$
$978$		0			0
$979$	17.7957	−	1.93169i	0.568752	−	0.0617371i
$980$		0			0
$981$	12.9095	+	17.7684i	0.412168	+	0.567300i
$982$		0			0
$983$	33.5747	+	10.9091i	1.07087	+	0.347945i	0.790824	−	0.612043i	$-0.209652\pi$
$983$	33.5747	+	10.9091i	1.07087	+	0.347945i	0.280041	+	0.959988i	$0.409652\pi$
$984$		0			0
$985$	−2.76715	+	3.80866i	−0.0881688	+	0.121354i
$986$		0			0
$987$	−3.65449	−	11.2474i	−0.116324	−	0.358007i
$988$		0			0
$989$			10.0631i			0.319987i
$990$		0			0
$991$		−	17.8021i		−	0.565502i	−0.959193	−	0.282751i	$-0.908753\pi$
$991$		−	17.8021i		−	0.565502i	0.959193	−	0.282751i	$-0.0912471\pi$
$992$		0			0
$993$	7.77591	+	23.9318i	0.246761	+	0.759452i
$994$		0			0
$995$	−8.92918	+	12.2900i	−0.283074	+	0.389618i
$996$		0			0
$997$	59.8586	+	19.4492i	1.89574	+	0.615963i	0.973144	+	0.230197i	$0.0739370\pi$
$997$	59.8586	+	19.4492i	1.89574	+	0.615963i	0.922596	+	0.385766i	$0.126063\pi$
$998$		0			0
$999$	16.3251	+	22.4695i	0.516503	+	0.710905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.u.c.63.3		16
4.3	odd	2	inner	704.2.u.c.63.2		16
8.3	odd	2		44.2.g.a.19.1	yes	16
8.5	even	2		44.2.g.a.19.3	yes	16
11.7	odd	10	inner	704.2.u.c.447.2		16
24.5	odd	2		396.2.r.a.19.2		16
24.11	even	2		396.2.r.a.19.4		16
44.7	even	10	inner	704.2.u.c.447.3		16
88.3	odd	10		484.2.g.j.215.2		16
88.5	even	10		484.2.g.f.475.3		16
88.13	odd	10		484.2.c.d.483.13		16
88.19	even	10		484.2.g.f.215.3		16
88.21	odd	2		484.2.g.i.239.2		16
88.27	odd	10		484.2.g.f.475.4		16
88.29	odd	10		44.2.g.a.7.1	✓	16
88.35	even	10		484.2.c.d.483.3		16
88.37	even	10		484.2.g.i.403.4		16
88.43	even	2		484.2.g.i.239.4		16
88.51	even	10		44.2.g.a.7.3	yes	16
88.53	even	10		484.2.c.d.483.4		16
88.59	odd	10		484.2.g.i.403.2		16
88.61	odd	10		484.2.g.j.475.2		16
88.69	even	10		484.2.g.j.215.1		16
88.75	odd	10		484.2.c.d.483.14		16
88.83	even	10		484.2.g.j.475.1		16
88.85	odd	10		484.2.g.f.215.4		16
264.29	even	10		396.2.r.a.271.4		16
264.227	odd	10		396.2.r.a.271.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.7.1	✓	16	88.29	odd	10
44.2.g.a.7.3	yes	16	88.51	even	10
44.2.g.a.19.1	yes	16	8.3	odd	2
44.2.g.a.19.3	yes	16	8.5	even	2
396.2.r.a.19.2		16	24.5	odd	2
396.2.r.a.19.4		16	24.11	even	2
396.2.r.a.271.2		16	264.227	odd	10
396.2.r.a.271.4		16	264.29	even	10
484.2.c.d.483.3		16	88.35	even	10
484.2.c.d.483.4		16	88.53	even	10
484.2.c.d.483.13		16	88.13	odd	10
484.2.c.d.483.14		16	88.75	odd	10
484.2.g.f.215.3		16	88.19	even	10
484.2.g.f.215.4		16	88.85	odd	10
484.2.g.f.475.3		16	88.5	even	10
484.2.g.f.475.4		16	88.27	odd	10
484.2.g.i.239.2		16	88.21	odd	2
484.2.g.i.239.4		16	88.43	even	2
484.2.g.i.403.2		16	88.59	odd	10
484.2.g.i.403.4		16	88.37	even	10
484.2.g.j.215.1		16	88.69	even	10
484.2.g.j.215.2		16	88.3	odd	10
484.2.g.j.475.1		16	88.83	even	10
484.2.g.j.475.2		16	88.61	odd	10
704.2.u.c.63.2		16	4.3	odd	2	inner
704.2.u.c.63.3		16	1.1	even	1	trivial
704.2.u.c.447.2		16	11.7	odd	10	inner
704.2.u.c.447.3		16	44.7	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.u (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.704424 - 0.228881i) q^{3} +(-1.09089 - 0.792578i) q^{5} +(-0.503194 + 1.54867i) q^{7} +(-1.98322 + 1.44090i) q^{9} +(-3.29726 + 0.357912i) q^{11} +(2.09089 + 2.87786i) q^{13} +(-0.949856 - 0.308627i) q^{15} +(-0.0411247 + 0.0566033i) q^{17} +(2.45716 + 7.56236i) q^{19} +1.20609i q^{21} +5.30988i q^{23} +(-0.983224 - 3.02605i) q^{25} +(-2.37331 + 3.26658i) q^{27} +(-3.74364 - 1.21638i) q^{29} +(2.17121 + 2.98842i) q^{31} +(-2.24075 + 1.00680i) q^{33} +(1.77637 - 1.29061i) q^{35} +(2.12561 - 6.54194i) q^{37} +(2.13156 + 1.54867i) q^{39} +(5.50305 - 1.78805i) q^{41} +1.89516 q^{43} +3.30550 q^{45} +(-9.32545 + 3.03002i) q^{47} +(3.51794 + 2.55593i) q^{49} +(-0.0160138 + 0.0492854i) q^{51} +(-3.14518 + 2.28511i) q^{53} +(3.88062 + 2.22289i) q^{55} +(3.46177 + 4.76471i) q^{57} +(-4.62366 - 1.50232i) q^{59} +(-0.791173 + 1.08896i) q^{61} +(-1.23353 - 3.79641i) q^{63} -4.79662i q^{65} +4.91303i q^{67} +(1.21533 + 3.74041i) q^{69} +(4.10014 - 5.64335i) q^{71} +(-9.62677 - 3.12793i) q^{73} +(-1.38521 - 1.90658i) q^{75} +(1.10487 - 5.28646i) q^{77} +(-4.85779 + 3.52939i) q^{79} +(1.34841 - 4.14999i) q^{81} +(2.92211 + 2.12304i) q^{83} +(0.0897250 - 0.0291534i) q^{85} -2.91552 q^{87} -5.39711 q^{89} +(-5.50899 + 1.78998i) q^{91} +(2.21345 + 1.60816i) q^{93} +(3.31327 - 10.1972i) q^{95} +(-5.92705 + 4.30625i) q^{97} +(6.02348 - 5.46083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} - 10 q^{9} + 10 q^{13} - 10 q^{17} + 6 q^{25} + 10 q^{29} - 12 q^{33} - 18 q^{37} + 10 q^{41} - 40 q^{45} + 6 q^{49} - 38 q^{53} + 10 q^{61} + 16 q^{69} - 30 q^{73} - 2 q^{77} - 4 q^{81}+ \cdots - 68 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 - 10 * q^9 + 10 * q^13 - 10 * q^17 + 6 * q^25 + 10 * q^29 - 12 * q^33 - 18 * q^37 + 10 * q^41 - 40 * q^45 + 6 * q^49 - 38 * q^53 + 10 * q^61 + 16 * q^69 - 30 * q^73 - 2 * q^77 - 4 * q^81 + 50 * q^85 - 36 * q^89 + 38 * q^93 - 68 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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