LMFDB - Embedded newform 532.2.v.e.341.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(341,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("532.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.v (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 25x^{14} + 413x^{12} + 3916x^{10} + 26956x^{8} + 112304x^{6} + 333008x^{4} + 476096x^{2} + 473344 $ x^16 + 25x^14 + 413x^12 + 3916x^10 + 26956x^8 + 112304x^6 + 333008x^4 + 476096*x^2 + 473344
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.6
Root			$1.06269 - 1.84063i$ of defining polynomial
Character	$\chi$	$=$	532.341
Dual form			532.2.v.e.493.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06269 + 1.84063i) q^{3} +(2.32104 + 1.34005i) q^{5} +(-2.45626 + 0.983253i) q^{7} +(-0.758613 + 1.31396i) q^{9} +O(q^{10})$	\(q+(1.06269 + 1.84063i) q^{3} +(2.32104 + 1.34005i) q^{5} +(-2.45626 + 0.983253i) q^{7} +(-0.758613 + 1.31396i) q^{9} +(2.19765 + 3.80644i) q^{11} -6.19020 q^{13} +5.69623i q^{15} +(-0.167132 + 0.0964937i) q^{17} +(3.84464 - 2.05396i) q^{19} +(-4.42004 - 3.47618i) q^{21} +(3.19765 - 5.53849i) q^{23} +(1.09148 + 1.89050i) q^{25} +3.15145 q^{27} +5.19793i q^{29} +(1.06269 + 1.84063i) q^{31} +(-4.67083 + 8.09011i) q^{33} +(-7.01869 - 1.00935i) q^{35} +(-9.64052 - 5.56596i) q^{37} +(-6.57826 - 11.3939i) q^{39} +4.25075 q^{41} -0.235990 q^{43} +(-3.52154 + 2.03316i) q^{45} +(9.59294 + 5.53849i) q^{47} +(5.06643 - 4.83025i) q^{49} +(-0.355218 - 0.205085i) q^{51} +(1.51937 - 0.877212i) q^{53} +11.7798i q^{55} +(7.86624 + 4.89383i) q^{57} +(2.29467 + 3.97448i) q^{59} +(-2.92975 - 1.69149i) q^{61} +(0.571400 - 3.97333i) q^{63} +(-14.3677 - 8.29520i) q^{65} +(-7.76593 + 4.48366i) q^{67} +13.5924 q^{69} -5.28606i q^{71} +(3.14208 - 1.81408i) q^{73} +(-2.31981 + 4.01803i) q^{75} +(-9.14068 - 7.18875i) q^{77} +(9.71685 + 5.61003i) q^{79} +(5.62485 + 9.74253i) q^{81} -1.88357i q^{83} -0.517226 q^{85} +(-9.56746 + 5.52378i) q^{87} +(5.38977 - 9.33535i) q^{89} +(15.2047 - 6.08654i) q^{91} +(-2.25861 + 3.91203i) q^{93} +(11.6760 + 0.384686i) q^{95} +16.2423 q^{97} -6.66866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9}+O(q^{10}) $ 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9	$ 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9} - 4 q^{11} - 24 q^{17} + 21 q^{19} + 12 q^{23} + 10 q^{25} - 30 q^{35} - 12 q^{39} + 16 q^{43} + 72 q^{45} + 36 q^{47} - 34 q^{49} - 2 q^{57} - 24 q^{61} + 20 q^{63} - 36 q^{73} + 4 q^{77} - 24 q^{81} - 36 q^{85} - 48 q^{87} - 50 q^{93} + 31 q^{95} + 156 q^{99}+O(q^{100}) $ 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9 - 4 * q^11 - 24 * q^17 + 21 * q^19 + 12 * q^23 + 10 * q^25 - 30 * q^35 - 12 * q^39 + 16 * q^43 + 72 * q^45 + 36 * q^47 - 34 * q^49 - 2 * q^57 - 24 * q^61 + 20 * q^63 - 36 * q^73 + 4 * q^77 - 24 * q^81 - 36 * q^85 - 48 * q^87 - 50 * q^93 + 31 * q^95 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	1.06269	+	1.84063i	0.613543	+	1.06269i	0.990638	+	0.136514i	$0.0435898\pi$
$3$	1.06269	+	1.84063i	0.613543	+	1.06269i	−0.377095	+	0.926175i	$0.623077\pi$
$4$		0			0
$5$	2.32104	+	1.34005i	1.03800	+	0.599290i	0.919266	−	0.393636i	$-0.128783\pi$
$5$	2.32104	+	1.34005i	1.03800	+	0.599290i	0.118734	+	0.992926i	$0.462116\pi$
$6$		0			0
$7$	−2.45626	+	0.983253i	−0.928379	+	0.371635i
$7$	−2.45626	+	0.983253i	−0.928379	+	0.371635i
$8$		0			0
$9$	−0.758613	+	1.31396i	−0.252871	+	0.437986i
$10$		0			0
$11$	2.19765	+	3.80644i	0.662615	+	1.14768i	0.979926	+	0.199362i	$0.0638869\pi$
$11$	2.19765	+	3.80644i	0.662615	+	1.14768i	−0.317310	+	0.948322i	$0.602780\pi$
$12$		0			0
$13$	−6.19020			−1.71685			−0.858427	−	0.512936i	$-0.828558\pi$
$13$	−6.19020			−1.71685			−0.858427	+	0.512936i	$0.828558\pi$
$14$		0			0
$15$			5.69623i			1.47076i
$16$		0			0
$17$	−0.167132	+	0.0964937i	−0.0405354	+	0.0234032i	−0.520131	−	0.854087i	$-0.674117\pi$
$17$	−0.167132	+	0.0964937i	−0.0405354	+	0.0234032i	0.479595	+	0.877490i	$0.340783\pi$
$18$		0			0
$19$	3.84464	−	2.05396i	0.882020	−	0.471212i
$19$	3.84464	−	2.05396i	0.882020	−	0.471212i
$20$		0			0
$21$	−4.42004	−	3.47618i	−0.964533	−	0.758564i
$22$		0			0
$23$	3.19765	−	5.53849i	0.666755	−	1.15485i	−0.312051	−	0.950065i	$-0.601016\pi$
$23$	3.19765	−	5.53849i	0.666755	−	1.15485i	0.978806	−	0.204789i	$-0.0656508\pi$
$24$		0			0
$25$	1.09148	+	1.89050i	0.218296	+	0.378100i
$26$		0			0
$27$	3.15145			0.606497
$28$		0			0
$29$			5.19793i			0.965231i	0.875832	+	0.482615i	$0.160313\pi$
$29$			5.19793i			0.965231i	−0.875832	+	0.482615i	$0.839687\pi$
$30$		0			0
$31$	1.06269	+	1.84063i	0.190864	+	0.330587i	0.945537	−	0.325515i	$-0.105538\pi$
$31$	1.06269	+	1.84063i	0.190864	+	0.330587i	−0.754673	+	0.656102i	$0.772204\pi$
$32$		0			0
$33$	−4.67083	+	8.09011i	−0.813087	+	1.40831i
$34$		0			0
$35$	−7.01869	−	1.00935i	−1.18637	−	0.170611i
$36$		0			0
$37$	−9.64052	−	5.56596i	−1.58489	−	0.915038i	−0.994130	−	0.108192i	$-0.965494\pi$
$37$	−9.64052	−	5.56596i	−1.58489	−	0.915038i	−0.590762	−	0.806846i	$-0.701173\pi$
$38$		0			0
$39$	−6.57826	−	11.3939i	−1.05336	−	1.82448i
$40$		0			0
$41$	4.25075			0.663856			0.331928	−	0.943305i	$-0.392301\pi$
$41$	4.25075			0.663856			0.331928	+	0.943305i	$0.392301\pi$
$42$		0			0
$43$	−0.235990			−0.0359881			−0.0179940	−	0.999838i	$-0.505728\pi$
$43$	−0.235990			−0.0359881			−0.0179940	+	0.999838i	$0.505728\pi$
$44$		0			0
$45$	−3.52154	+	2.03316i	−0.524960	+	0.303086i
$46$		0			0
$47$	9.59294	+	5.53849i	1.39927	+	0.807871i	0.994317	−	0.106464i	$-0.0339529\pi$
$47$	9.59294	+	5.53849i	1.39927	+	0.807871i	0.404958	+	0.914335i	$0.367286\pi$
$48$		0			0
$49$	5.06643	−	4.83025i	0.723775	−	0.690036i
$50$		0			0
$51$	−0.355218	−	0.205085i	−0.0497405	−	0.0287177i
$52$		0			0
$53$	1.51937	−	0.877212i	0.208702	−	0.120494i	−0.392006	−	0.919963i	$-0.628219\pi$
$53$	1.51937	−	0.877212i	0.208702	−	0.120494i	0.600708	+	0.799468i	$0.294885\pi$
$54$		0			0
$55$			11.7798i			1.58839i
$56$		0			0
$57$	7.86624	+	4.89383i	1.04191	+	0.648204i
$58$		0			0
$59$	2.29467	+	3.97448i	0.298740	+	0.517433i	0.975848	−	0.218451i	$-0.0701002\pi$
$59$	2.29467	+	3.97448i	0.298740	+	0.517433i	−0.677108	+	0.735884i	$0.736767\pi$
$60$		0			0
$61$	−2.92975	−	1.69149i	−0.375116	−	0.216573i	0.300575	−	0.953758i	$-0.402821\pi$
$61$	−2.92975	−	1.69149i	−0.375116	−	0.216573i	−0.675691	+	0.737185i	$0.736155\pi$
$62$		0			0
$63$	0.571400	−	3.97333i	0.0719896	−	0.500592i
$64$		0			0
$65$	−14.3677	−	8.29520i	−1.78209	−	1.02889i
$66$		0			0
$67$	−7.76593	+	4.48366i	−0.948759	+	0.547766i	−0.892695	−	0.450661i	$-0.851188\pi$
$67$	−7.76593	+	4.48366i	−0.948759	+	0.547766i	−0.0560640	+	0.998427i	$0.517855\pi$
$68$		0			0
$69$	13.5924			1.63633
$70$		0			0
$71$		−	5.28606i		−	0.627340i	−0.949532	−	0.313670i	$-0.898441\pi$
$71$		−	5.28606i		−	0.627340i	0.949532	−	0.313670i	$-0.101559\pi$
$72$		0			0
$73$	3.14208	−	1.81408i	0.367752	−	0.212322i	−0.304724	−	0.952441i	$-0.598564\pi$
$73$	3.14208	−	1.81408i	0.367752	−	0.212322i	0.672476	+	0.740119i	$0.265231\pi$
$74$		0			0
$75$	−2.31981	+	4.01803i	−0.267868	+	0.463962i
$76$		0			0
$77$	−9.14068	−	7.18875i	−1.04168	−	0.819235i
$78$		0			0
$79$	9.71685	+	5.61003i	1.09323	+	0.631177i	0.934435	−	0.356134i	$-0.115905\pi$
$79$	9.71685	+	5.61003i	1.09323	+	0.631177i	0.158796	+	0.987311i	$0.449239\pi$
$80$		0			0
$81$	5.62485	+	9.74253i	0.624984	+	1.08250i
$82$		0			0
$83$		−	1.88357i		−	0.206749i	−0.994643	−	0.103374i	$-0.967036\pi$
$83$		−	1.88357i		−	0.206749i	0.994643	−	0.103374i	$-0.0329640\pi$
$84$		0			0
$85$	−0.517226			−0.0561011
$86$		0			0
$87$	−9.56746	+	5.52378i	−1.02574	+	0.592211i
$88$		0			0
$89$	5.38977	−	9.33535i	0.571314	−	0.989545i	−0.425117	−	0.905138i	$-0.639767\pi$
$89$	5.38977	−	9.33535i	0.571314	−	0.989545i	0.996431	−	0.0844071i	$-0.0268996\pi$
$90$		0			0
$91$	15.2047	−	6.08654i	1.59389	−	0.638042i
$92$		0			0
$93$	−2.25861	+	3.91203i	−0.234207	+	0.405659i
$94$		0			0
$95$	11.6760	+	0.384686i	1.19793	+	0.0394679i
$96$		0			0
$97$	16.2423			1.64916			0.824578	−	0.565749i	$-0.191413\pi$
$97$	16.2423			1.64916			0.824578	+	0.565749i	$0.191413\pi$
$98$		0			0
$99$	−6.66866			−0.670225
$100$		0			0
$101$	−14.8796	+	8.59076i	−1.48058	+	0.854813i	−0.999758	−	0.0220056i	$-0.992995\pi$
$101$	−14.8796	+	8.59076i	−1.48058	+	0.854813i	−0.480822	+	0.876818i	$0.659661\pi$
$102$		0			0
$103$	4.42004	−	7.65574i	0.435520	−	0.754343i	−0.561818	−	0.827261i	$-0.689898\pi$
$103$	4.42004	−	7.65574i	0.435520	−	0.754343i	0.997338	+	0.0729183i	$0.0232312\pi$
$104$		0			0
$105$	−5.60084	−	13.9914i	−0.546586	−	1.36542i
$106$		0			0
$107$	−13.9362	−	8.04604i	−1.34726	−	0.777840i	−0.359399	−	0.933184i	$-0.617018\pi$
$107$	−13.9362	−	8.04604i	−1.34726	−	0.777840i	−0.987860	+	0.155344i	$0.950351\pi$
$108$		0			0
$109$	7.76593	−	4.48366i	0.743841	−	0.429457i	−0.0796231	−	0.996825i	$-0.525372\pi$
$109$	7.76593	−	4.48366i	0.743841	−	0.429457i	0.823464	+	0.567368i	$0.192038\pi$
$110$		0			0
$111$		−	23.6595i		−	2.24566i
$112$		0			0
$113$		−	7.68841i		−	0.723265i	−0.932321	−	0.361632i	$-0.882220\pi$
$113$		−	7.68841i		−	0.723265i	0.932321	−	0.361632i	$-0.117780\pi$
$114$		0			0
$115$	14.8437	−	8.57003i	1.38418	−	0.799159i
$116$		0			0
$117$	4.69597	−	8.13366i	0.434142	−	0.751957i
$118$		0			0
$119$	0.315642	−	0.401346i	0.0289348	−	0.0367914i
$120$		0			0
$121$	−4.15930	+	7.20413i	−0.378119	+	0.654921i
$122$		0			0
$123$	4.51723	+	7.82407i	0.407305	+	0.705472i
$124$		0			0
$125$		−	7.54996i		−	0.675289i
$126$		0			0
$127$			3.27109i			0.290262i	0.989412	+	0.145131i	$0.0463604\pi$
$127$			3.27109i			0.290262i	−0.989412	+	0.145131i	$0.953640\pi$
$128$		0			0
$129$	−0.250784	−	0.434370i	−0.0220803	−	0.0382441i
$130$		0			0
$131$	−2.95480	−	1.70595i	−0.258162	−	0.149050i	0.365334	−	0.930877i	$-0.380955\pi$
$131$	−2.95480	−	1.70595i	−0.258162	−	0.149050i	−0.623496	+	0.781827i	$0.714288\pi$
$132$		0			0
$133$	−7.42386	+	8.82532i	−0.643731	+	0.765252i
$134$		0			0
$135$	7.31464	+	4.22311i	0.629544	+	0.363468i
$136$		0			0
$137$	−7.14208	−	12.3704i	−0.610189	−	1.05688i	−0.991208	−	0.132311i	$-0.957760\pi$
$137$	−7.14208	−	12.3704i	−0.610189	−	1.05688i	0.381019	−	0.924567i	$-0.375573\pi$
$138$		0			0
$139$		−	11.8320i		−	1.00358i	−0.864989	−	0.501790i	$-0.832675\pi$
$139$		−	11.8320i		−	1.00358i	0.864989	−	0.501790i	$-0.167325\pi$
$140$		0			0
$141$			23.5427i			1.98266i
$142$		0			0
$143$	−13.6039	−	23.5626i	−1.13761	−	1.97040i
$144$		0			0
$145$	−6.96550	+	12.0646i	−0.578453	+	1.00191i
$146$		0			0
$147$	14.2747	+	4.19237i	1.17736	+	0.345781i
$148$		0			0
$149$	0.355492	−	0.615729i	0.0291230	−	0.0504425i	−0.851097	−	0.525009i	$-0.824062\pi$
$149$	0.355492	−	0.615729i	0.0291230	−	0.0504425i	0.880220	+	0.474567i	$0.157395\pi$
$150$		0			0
$151$	−9.35829	+	5.40301i	−0.761567	+	0.439691i	−0.829858	−	0.557975i	$-0.811579\pi$
$151$	−9.35829	+	5.40301i	−0.761567	+	0.439691i	0.0682911	+	0.997665i	$0.478245\pi$
$152$		0			0
$153$		−	0.292805i		−	0.0236719i
$154$		0			0
$155$			5.69623i			0.457532i
$156$		0			0
$157$	−10.3781	+	5.99178i	−0.828260	+	0.478196i	−0.853257	−	0.521491i	$-0.825376\pi$
$157$	−10.3781	+	5.99178i	−0.828260	+	0.478196i	0.0249966	+	0.999688i	$0.492043\pi$
$158$		0			0
$159$	3.22924	+	1.86440i	0.256096	+	0.147857i
$160$		0			0
$161$	−2.40852	+	16.7481i	−0.189818	+	1.31993i
$162$		0			0
$163$	9.26947	−	16.0552i	0.726041	−	1.25754i	−0.232503	−	0.972596i	$-0.574692\pi$
$163$	9.26947	−	16.0552i	0.726041	−	1.25754i	0.958544	−	0.284944i	$-0.0919751\pi$
$164$		0			0
$165$	−21.6823	+	12.5183i	−1.68797	+	0.974549i
$166$		0			0
$167$	21.9080			1.69529			0.847646	−	0.530563i	$-0.178019\pi$
$167$	21.9080			1.69529			0.847646	+	0.530563i	$0.178019\pi$
$168$		0			0
$169$	25.3186			1.94759
$170$		0			0
$171$	−0.217773	+	6.60985i	−0.0166535	+	0.505468i
$172$		0			0
$173$	6.35949	−	11.0150i	0.483503	−	0.837452i	−0.516317	−	0.856397i	$-0.672697\pi$
$173$	6.35949	−	11.0150i	0.483503	−	0.837452i	0.999821	+	0.0189451i	$0.00603077\pi$
$174$		0			0
$175$	−4.53980	−	3.57036i	−0.343177	−	0.269894i
$176$		0			0
$177$	−4.87703	+	8.44727i	−0.366580	+	0.634936i
$178$		0			0
$179$	−6.02091	+	3.47618i	−0.450024	+	0.259822i	−0.707840	−	0.706372i	$-0.750330\pi$
$179$	−6.02091	+	3.47618i	−0.450024	+	0.259822i	0.257816	+	0.966194i	$0.416997\pi$
$180$		0			0
$181$	−7.62808			−0.566991			−0.283496	−	0.958974i	$-0.591494\pi$
$181$	−7.62808			−0.566991			−0.283496	+	0.958974i	$0.591494\pi$
$182$		0			0
$183$		−	7.19011i		−	0.531508i
$184$		0			0
$185$	−14.9174	−	25.8376i	−1.09675	−	1.89962i
$186$		0			0
$187$	−0.734594	−	0.424118i	−0.0537188	−	0.0310146i
$188$		0			0
$189$	−7.74079	+	3.09868i	−0.563059	+	0.225395i
$190$		0			0
$191$	−5.85938	+	10.1487i	−0.423970	+	0.734338i	−0.996324	−	0.0856693i	$-0.972697\pi$
$191$	−5.85938	+	10.1487i	−0.423970	+	0.734338i	0.572354	+	0.820007i	$0.306030\pi$
$192$		0			0
$193$	−11.3855	+	6.57344i	−0.819549	+	0.473167i	−0.850261	−	0.526361i	$-0.823556\pi$
$193$	−11.3855	+	6.57344i	−0.819549	+	0.473167i	0.0307119	+	0.999528i	$0.490223\pi$
$194$		0			0
$195$		−	35.2608i		−	2.52508i
$196$		0			0
$197$	−4.32940			−0.308457			−0.154229	−	0.988035i	$-0.549289\pi$
$197$	−4.32940			−0.308457			−0.154229	+	0.988035i	$0.549289\pi$
$198$		0			0
$199$	13.2202	−	7.63270i	0.937157	−	0.541068i	0.0480889	−	0.998843i	$-0.484687\pi$
$199$	13.2202	−	7.63270i	0.937157	−	0.541068i	0.889068	+	0.457775i	$0.151354\pi$
$200$		0			0
$201$	−16.5055	−	9.52947i	−1.16421	−	0.672157i
$202$		0			0
$203$	−5.11088	−	12.7675i	−0.358713	−	0.896100i
$204$		0			0
$205$	9.86616	+	5.69623i	0.689083	+	0.397842i
$206$		0			0
$207$	4.85155	+	8.40314i	0.337206	+	0.584058i
$208$		0			0
$209$	16.2674	+	10.1205i	1.12524	+	0.700048i
$210$		0			0
$211$			28.1325i			1.93672i	0.249558	+	0.968360i	$0.419715\pi$
$211$			28.1325i			1.93672i	−0.249558	+	0.968360i	$0.580285\pi$
$212$		0			0
$213$	9.72969	−	5.61744i	0.666667	−	0.384900i
$214$		0			0
$215$	−0.547741	−	0.316239i	−0.0373556	−	0.0215673i
$216$		0			0
$217$	−4.42004	−	3.47618i	−0.300052	−	0.235978i
$218$		0			0
$219$	6.67810	+	3.85560i	0.451264	+	0.260537i
$220$		0			0
$221$	1.03458	−	0.597315i	0.0695934	−	0.0401798i
$222$		0			0
$223$	−2.46396			−0.164999			−0.0824994	−	0.996591i	$-0.526290\pi$
$223$	−2.46396			−0.164999			−0.0824994	+	0.996591i	$0.526290\pi$
$224$		0			0
$225$	−3.31205			−0.220803
$226$		0			0
$227$	0.343747	+	0.595388i	0.0228153	+	0.0395173i	0.877208	−	0.480111i	$-0.159404\pi$
$227$	0.343747	+	0.595388i	0.0228153	+	0.0395173i	−0.854392	+	0.519628i	$0.826070\pi$
$228$		0			0
$229$	−12.1671	−	7.02470i	−0.804027	−	0.464205i	0.0408505	−	0.999165i	$-0.486993\pi$
$229$	−12.1671	−	7.02470i	−0.804027	−	0.464205i	−0.844877	+	0.534960i	$0.820327\pi$
$230$		0			0
$231$	3.51814	−	24.4640i	0.231477	−	1.60961i
$232$		0			0
$233$	−1.16713	+	2.02153i	−0.0764614	+	0.132435i	−0.901721	−	0.432319i	$-0.857696\pi$
$233$	−1.16713	+	2.02153i	−0.0764614	+	0.132435i	0.825259	+	0.564754i	$0.191029\pi$
$234$		0			0
$235$	14.8437	+	25.7101i	0.968298	+	1.67714i
$236$		0			0
$237$			23.8468i			1.54902i
$238$		0			0
$239$	−18.0080			−1.16484			−0.582420	−	0.812888i	$-0.697894\pi$
$239$	−18.0080			−1.16484			−0.582420	+	0.812888i	$0.697894\pi$
$240$		0			0
$241$	2.92581	+	5.06765i	0.188468	+	0.326436i	0.944740	−	0.327822i	$-0.106314\pi$
$241$	2.92581	+	5.06765i	0.188468	+	0.326436i	−0.756272	+	0.654258i	$0.772981\pi$
$242$		0			0
$243$	−7.22775	+	12.5188i	−0.463660	+	0.803083i
$244$		0			0
$245$	18.2322	−	4.42192i	1.16481	−	0.282506i
$246$		0			0
$247$	−23.7991	+	12.7145i	−1.51430	+	0.809001i
$248$		0			0
$249$	3.46696	−	2.00165i	0.219709	−	0.126849i
$250$		0			0
$251$			25.0471i			1.58096i	0.612490	+	0.790478i	$0.290168\pi$
$251$			25.0471i			1.58096i	−0.612490	+	0.790478i	$0.709832\pi$
$252$		0			0
$253$	28.1092			1.76721
$254$		0			0
$255$	−0.549650	−	0.952022i	−0.0344204	−	0.0596180i
$256$		0			0
$257$	−11.8223	+	20.4767i	−0.737452	+	1.27730i	0.216188	+	0.976352i	$0.430638\pi$
$257$	−11.8223	+	20.4767i	−0.737452	+	1.27730i	−0.953639	+	0.300952i	$0.902696\pi$
$258$		0			0
$259$	29.1524	+	4.19237i	1.81144	+	0.260501i
$260$		0			0
$261$	−6.82985	−	3.94322i	−0.422757	−	0.244079i
$262$		0			0
$263$	−10.4749	−	18.1431i	−0.645913	−	1.11875i	−0.984090	−	0.177671i	$-0.943144\pi$
$263$	−10.4749	−	18.1431i	−0.645913	−	1.11875i	0.338177	−	0.941083i	$-0.390190\pi$
$264$		0			0
$265$	4.70204			0.288844
$266$		0			0
$267$	22.9106			1.40210
$268$		0			0
$269$	4.61448	+	7.99251i	0.281350	+	0.487312i	0.971717	−	0.236147i	$-0.0758846\pi$
$269$	4.61448	+	7.99251i	0.281350	+	0.487312i	−0.690368	+	0.723459i	$0.742551\pi$
$270$		0			0
$271$	−12.7867	−	7.38240i	−0.776737	−	0.448449i	0.0585359	−	0.998285i	$-0.481357\pi$
$271$	−12.7867	−	7.38240i	−0.776737	−	0.448449i	−0.835272	+	0.549836i	$0.814690\pi$
$272$		0			0
$273$	27.3610	+	21.5182i	1.65596	+	1.30234i
$274$		0			0
$275$	−4.79738	+	8.30931i	−0.289293	+	0.501070i
$276$		0			0
$277$	−14.3624	−	24.8764i	−0.862954	−	1.49468i	−0.869065	−	0.494698i	$-0.835279\pi$
$277$	−14.3624	−	24.8764i	−0.862954	−	1.49468i	0.00611105	−	0.999981i	$-0.498055\pi$
$278$		0			0
$279$	−3.22468			−0.193056
$280$		0			0
$281$		−	18.0843i		−	1.07882i	−0.842044	−	0.539408i	$-0.818648\pi$
$281$		−	18.0843i		−	1.07882i	0.842044	−	0.539408i	$-0.181352\pi$
$282$		0			0
$283$	−10.0611	+	5.80880i	−0.598073	+	0.345297i	−0.768283	−	0.640110i	$-0.778889\pi$
$283$	−10.0611	+	5.80880i	−0.598073	+	0.345297i	0.170210	+	0.985408i	$0.445555\pi$
$284$		0			0
$285$	11.6999	+	21.8999i	0.693040	+	1.29724i
$286$		0			0
$287$	−10.4410	+	4.17957i	−0.616310	+	0.246712i
$288$		0			0
$289$	−8.48138	+	14.6902i	−0.498905	+	0.864128i
$290$		0			0
$291$	17.2605	+	29.8961i	1.01183	+	1.75254i
$292$		0			0
$293$	4.25075			0.248332			0.124166	−	0.992261i	$-0.460375\pi$
$293$	4.25075			0.248332			0.124166	+	0.992261i	$0.460375\pi$
$294$		0			0
$295$			12.2999i			0.716128i
$296$		0			0
$297$	6.92578	+	11.9958i	0.401875	+	0.696067i
$298$		0			0
$299$	−19.7941	+	34.2844i	−1.14472	+	1.98272i
$300$		0			0
$301$	0.579652	−	0.232038i	0.0334106	−	0.0133744i
$302$		0			0
$303$	−31.6248	−	18.2586i	−1.81680	−	1.04893i
$304$		0			0
$305$	−4.53337	−	7.85203i	−0.259580	−	0.449606i
$306$		0			0
$307$	−1.43788			−0.0820643			−0.0410321	−	0.999158i	$-0.513065\pi$
$307$	−1.43788			−0.0820643			−0.0410321	+	0.999158i	$0.513065\pi$
$308$		0			0
$309$	18.7885			1.06884
$310$		0			0
$311$	−1.12211	+	0.647849i	−0.0636289	+	0.0367361i	−0.531477	−	0.847073i	$-0.678363\pi$
$311$	−1.12211	+	0.647849i	−0.0636289	+	0.0367361i	0.467848	+	0.883809i	$0.345029\pi$
$312$		0			0
$313$	5.38315	+	3.10796i	0.304274	+	0.175672i	0.644361	−	0.764721i	$-0.277123\pi$
$313$	5.38315	+	3.10796i	0.304274	+	0.175672i	−0.340087	+	0.940394i	$0.610457\pi$
$314$		0			0
$315$	6.65071	−	8.45654i	0.374725	−	0.476472i
$316$		0			0
$317$	−1.81801	−	1.04963i	−0.102109	−	0.0589529i	0.448076	−	0.893996i	$-0.352110\pi$
$317$	−1.81801	−	1.04963i	−0.102109	−	0.0589529i	−0.550185	+	0.835043i	$0.685443\pi$
$318$		0			0
$319$	−19.7856	+	11.4232i	−1.10778	+	0.639577i
$320$		0			0
$321$		−	34.2017i		−	1.90896i
$322$		0			0
$323$	−0.444367	+	0.714266i	−0.0247252	+	0.0397428i
$324$		0			0
$325$	−6.75649	−	11.7026i	−0.374783	−	0.649143i
$326$		0			0
$327$	16.5055	+	9.52947i	0.912758	+	0.526981i
$328$		0			0
$329$	−29.0085	−	4.17168i	−1.59929	−	0.229992i
$330$		0			0
$331$	6.02091	+	3.47618i	0.330939	+	0.191068i	0.656258	−	0.754537i	$-0.272138\pi$
$331$	6.02091	+	3.47618i	0.330939	+	0.191068i	−0.325319	+	0.945604i	$0.605472\pi$
$332$		0			0
$333$	14.6269	−	8.44482i	0.801547	−	0.462773i
$334$		0			0
$335$	−24.0334			−1.31308
$336$		0			0
$337$			17.6088i			0.959210i	0.877485	+	0.479605i	$0.159220\pi$
$337$			17.6088i			0.959210i	−0.877485	+	0.479605i	$0.840780\pi$
$338$		0			0
$339$	14.1515	−	8.17039i	0.768605	−	0.443754i
$340$		0			0
$341$	−4.67083	+	8.09011i	−0.252940	+	0.438104i
$342$		0			0
$343$	−7.69511	+	16.8459i	−0.415497	+	0.909595i
$344$		0			0
$345$	31.5485	+	18.2145i	1.69851	+	0.980638i
$346$		0			0
$347$	−3.29992	−	5.71563i	−0.177149	−	0.306831i	0.763754	−	0.645508i	$-0.223354\pi$
$347$	−3.29992	−	5.71563i	−0.177149	−	0.306831i	−0.940903	+	0.338676i	$0.890021\pi$
$348$		0			0
$349$			10.6273i			0.568864i	0.958696	+	0.284432i	$0.0918049\pi$
$349$			10.6273i			0.568864i	−0.958696	+	0.284432i	$0.908195\pi$
$350$		0			0
$351$	−19.5081			−1.04127
$352$		0			0
$353$	18.2510	−	10.5372i	0.971401	−	0.560838i	0.0717377	−	0.997424i	$-0.477146\pi$
$353$	18.2510	−	10.5372i	0.971401	−	0.560838i	0.899663	+	0.436585i	$0.143812\pi$
$354$		0			0
$355$	7.08360	−	12.2692i	0.375958	−	0.651179i
$356$		0			0
$357$	1.07416	+	0.154474i	0.0568505	+	0.00817561i
$358$		0			0
$359$	−14.0865	+	24.3985i	−0.743458	+	1.28771i	0.207454	+	0.978245i	$0.433482\pi$
$359$	−14.0865	+	24.3985i	−0.743458	+	1.28771i	−0.950912	+	0.309461i	$0.899851\pi$
$360$		0			0
$361$	10.5625	−	15.7935i	0.555919	−	0.831236i
$362$		0			0
$363$	−17.6802			−0.927969
$364$		0			0
$365$	9.72385			0.508969
$366$		0			0
$367$	18.1476	−	10.4775i	0.947297	−	0.546922i	0.0550569	−	0.998483i	$-0.482466\pi$
$367$	18.1476	−	10.4775i	0.947297	−	0.546922i	0.892240	+	0.451561i	$0.149133\pi$
$368$		0			0
$369$	−3.22468	+	5.58531i	−0.167870	+	0.290759i
$370$		0			0
$371$	−2.86946	+	3.64859i	−0.148975	+	0.189425i
$372$		0			0
$373$	−0.0565878	−	0.0326710i	−0.00293000	−	0.00169164i	0.498534	−	0.866870i	$-0.333872\pi$
$373$	−0.0565878	−	0.0326710i	−0.00293000	−	0.00169164i	−0.501464	+	0.865178i	$0.667205\pi$
$374$		0			0
$375$	13.8967	−	8.02325i	0.717621	−	0.414319i
$376$		0			0
$377$		−	32.1762i		−	1.65716i
$378$		0			0
$379$			7.77655i			0.399454i	0.979852	+	0.199727i	$0.0640056\pi$
$379$			7.77655i			0.399454i	−0.979852	+	0.199727i	$0.935994\pi$
$380$		0			0
$381$	−6.02087	+	3.47615i	−0.308458	+	0.178089i
$382$		0			0
$383$	0.375194	−	0.649855i	0.0191715	−	0.0332060i	−0.856280	−	0.516511i	$-0.827230\pi$
$383$	0.375194	−	0.649855i	0.0191715	−	0.0332060i	0.875452	+	0.483305i	$0.160564\pi$
$384$		0			0
$385$	−11.5826	−	28.9344i	−0.590302	−	1.47463i
$386$		0			0
$387$	0.179025	−	0.310080i	0.00910035	−	0.0157623i
$388$		0			0
$389$	−2.67356	−	4.63075i	−0.135555	−	0.234788i	0.790254	−	0.612779i	$-0.209948\pi$
$389$	−2.67356	−	4.63075i	−0.135555	−	0.234788i	−0.925809	+	0.377991i	$0.876615\pi$
$390$		0			0
$391$			1.23421i			0.0624167i
$392$		0			0
$393$		−	7.25159i		−	0.365795i
$394$		0			0
$395$	15.0355	+	26.0422i	0.756516	+	1.31032i
$396$		0			0
$397$	−31.0906	−	17.9502i	−1.56039	−	0.900892i	−0.997217	−	0.0745541i	$-0.976247\pi$
$397$	−31.0906	−	17.9502i	−1.56039	−	0.900892i	−0.563174	−	0.826338i	$-0.690420\pi$
$398$		0			0
$399$	−24.1334	−	4.28602i	−1.20818	−	0.214569i
$400$		0			0
$401$	−12.3970	−	7.15744i	−0.619079	−	0.357425i	0.157431	−	0.987530i	$-0.449679\pi$
$401$	−12.3970	−	7.15744i	−0.619079	−	0.357425i	−0.776510	+	0.630105i	$0.783012\pi$
$402$		0			0
$403$	−6.57826	−	11.3939i	−0.327686	−	0.567569i
$404$		0			0
$405$			30.1504i			1.49818i
$406$		0			0
$407$		−	48.9280i		−	2.42527i
$408$		0			0
$409$	−3.88703	−	6.73253i	−0.192201	−	0.332902i	0.753778	−	0.657129i	$-0.228229\pi$
$409$	−3.88703	−	6.73253i	−0.192201	−	0.332902i	−0.945979	+	0.324227i	$0.894896\pi$
$410$		0			0
$411$	15.1796	−	26.2918i	0.748755	−	1.29688i
$412$		0			0
$413$	−9.54422	−	7.50612i	−0.469640	−	0.369352i
$414$		0			0
$415$	2.52408	−	4.37184i	0.123902	−	0.214605i
$416$		0			0
$417$	21.7784	−	12.5738i	1.06649	−	0.615740i
$418$		0			0
$419$		−	23.3271i		−	1.13960i	−0.821783	−	0.569801i	$-0.807020\pi$
$419$		−	23.3271i		−	1.13960i	0.821783	−	0.569801i	$-0.192980\pi$
$420$		0			0
$421$			16.0693i			0.783169i	0.920142	+	0.391585i	$0.128073\pi$
$421$			16.0693i			0.783169i	−0.920142	+	0.391585i	$0.871927\pi$
$422$		0			0
$423$	−14.5547	+	8.40314i	−0.707672	+	0.408575i
$424$		0			0
$425$	−0.364843	−	0.210642i	−0.0176975	−	0.0102176i
$426$		0			0
$427$	8.85938	+	1.27406i	0.428736	+	0.0616560i
$428$		0			0
$429$	28.9134	−	50.0794i	1.39595	−	2.41786i
$430$		0			0
$431$	−24.0615	+	13.8919i	−1.15900	+	0.669149i	−0.951064	−	0.308993i	$-0.900008\pi$
$431$	−24.0615	+	13.8919i	−1.15900	+	0.669149i	−0.207936	+	0.978142i	$0.566675\pi$
$432$		0			0
$433$	−39.5652			−1.90138			−0.950692	−	0.310138i	$-0.899625\pi$
$433$	−39.5652			−1.90138			−0.950692	+	0.310138i	$0.899625\pi$
$434$		0			0
$435$	−29.6086			−1.41962
$436$		0			0
$437$	0.917941	−	27.8613i	0.0439111	−	1.33279i
$438$		0			0
$439$	15.1681	−	26.2720i	0.723936	−	1.25389i	−0.235475	−	0.971880i	$-0.575665\pi$
$439$	15.1681	−	26.2720i	0.723936	−	1.25389i	0.959411	−	0.282013i	$-0.0910021\pi$
$440$		0			0
$441$	2.50328	+	10.3214i	0.119204	+	0.491493i
$442$		0			0
$443$	−14.4593	+	25.0442i	−0.686982	+	1.18989i	0.285828	+	0.958281i	$0.407731\pi$
$443$	−14.4593	+	25.0442i	−0.686982	+	1.18989i	−0.972810	+	0.231606i	$0.925602\pi$
$444$		0			0
$445$	25.0197	−	14.4451i	1.18605	−	0.684766i
$446$		0			0
$447$	1.51111			0.0714729
$448$		0			0
$449$		−	5.69238i		−	0.268640i	−0.990938	−	0.134320i	$-0.957115\pi$
$449$		−	5.69238i		−	0.268640i	0.990938	−	0.134320i	$-0.0428850\pi$
$450$		0			0
$451$	9.34166	+	16.1802i	0.439881	+	0.761897i
$452$		0			0
$453$	−19.8899	−	11.4834i	−0.934509	−	0.539539i
$454$		0			0
$455$	43.4471	+	6.24807i	2.03683	+	0.292914i
$456$		0			0
$457$	1.84227	−	3.19090i	0.0861776	−	0.149264i	−0.819715	−	0.572772i	$-0.805868\pi$
$457$	1.84227	−	3.19090i	0.0861776	−	0.149264i	0.905892	+	0.423508i	$0.139201\pi$
$458$		0			0
$459$	−0.526708	+	0.304095i	−0.0245846	+	0.0141939i
$460$		0			0
$461$		−	24.9477i		−	1.16193i	−0.813928	−	0.580966i	$-0.802675\pi$
$461$		−	24.9477i		−	1.16193i	0.813928	−	0.580966i	$-0.197325\pi$
$462$		0			0
$463$	−8.44054			−0.392265			−0.196133	−	0.980577i	$-0.562838\pi$
$463$	−8.44054			−0.392265			−0.196133	+	0.980577i	$0.562838\pi$
$464$		0			0
$465$	−10.4847	+	6.05332i	−0.486214	+	0.280716i
$466$		0			0
$467$	8.26655	+	4.77270i	0.382530	+	0.220854i	0.678919	−	0.734214i	$-0.262449\pi$
$467$	8.26655	+	4.77270i	0.382530	+	0.220854i	−0.296388	+	0.955068i	$0.595782\pi$
$468$		0			0
$469$	14.6666	−	18.6489i	0.677239	−	0.861127i
$470$		0			0
$471$	−22.0573	−	12.7348i	−1.01635	−	0.586788i
$472$		0			0
$473$	−0.518622	−	0.898280i	−0.0238463	−	0.0413029i
$474$		0			0
$475$	8.07937	+	5.02643i	0.370707	+	0.230628i
$476$		0			0
$477$			2.66186i			0.121878i
$478$		0			0
$479$	1.33329	−	0.769777i	0.0609197	−	0.0351720i	−0.469231	−	0.883076i	$-0.655469\pi$
$479$	1.33329	−	0.769777i	0.0609197	−	0.0351720i	0.530150	+	0.847904i	$0.322135\pi$
$480$		0			0
$481$	59.6768	+	34.4544i	2.72103	+	1.57099i
$482$		0			0
$483$	−33.3865	+	13.3648i	−1.51914	+	0.608118i
$484$		0			0
$485$	37.6990	+	21.7655i	1.71182	+	0.988322i
$486$		0			0
$487$	−31.1136	+	17.9635i	−1.40989	+	0.814002i	−0.995377	−	0.0960401i	$-0.969382\pi$
$487$	−31.1136	+	17.9635i	−1.40989	+	0.814002i	−0.414516	+	0.910042i	$0.636049\pi$
$488$		0			0
$489$	39.4022			1.78183
$490$		0			0
$491$	−2.83778			−0.128067			−0.0640335	−	0.997948i	$-0.520396\pi$
$491$	−2.83778			−0.128067			−0.0640335	+	0.997948i	$0.520396\pi$
$492$		0			0
$493$	−0.501567	−	0.868740i	−0.0225894	−	0.0391261i
$494$		0			0
$495$	−15.4782	−	8.93635i	−0.695694	−	0.401659i
$496$		0			0
$497$	5.19754	+	12.9839i	0.233141	+	0.582409i
$498$		0			0
$499$	2.98131	−	5.16379i	0.133462	−	0.231163i	−0.791547	−	0.611108i	$-0.790724\pi$
$499$	2.98131	−	5.16379i	0.133462	−	0.231163i	0.925009	+	0.379946i	$0.124057\pi$
$500$		0			0
$501$	23.2814	+	40.3245i	1.04013	+	1.80157i
$502$		0			0
$503$			38.3879i			1.71163i	0.517280	+	0.855816i	$0.326945\pi$
$503$			38.3879i			1.71163i	−0.517280	+	0.855816i	$0.673055\pi$
$504$		0			0
$505$	−46.0483			−2.04912
$506$		0			0
$507$	26.9058	+	46.6022i	1.19493	+	2.06968i
$508$		0			0
$509$	14.6666	−	25.4032i	0.650084	−	1.12598i	−0.333018	−	0.942921i	$-0.608067\pi$
$509$	14.6666	−	25.4032i	0.650084	−	1.12598i	0.983102	−	0.183058i	$-0.0585997\pi$
$510$		0			0
$511$	−5.93406	+	7.54531i	−0.262507	+	0.333785i
$512$		0			0
$513$	12.1162	−	6.47297i	0.534943	−	0.285789i
$514$		0			0
$515$	20.5182	−	11.8462i	0.904139	−	0.522005i
$516$		0			0
$517$			48.6866i			2.14123i
$518$		0			0
$519$	27.0326			1.18660
$520$		0			0
$521$	1.85796	+	3.21807i	0.0813985	+	0.140986i	0.903851	−	0.427848i	$-0.140728\pi$
$521$	1.85796	+	3.21807i	0.0813985	+	0.140986i	−0.822452	+	0.568834i	$0.807395\pi$
$522$		0			0
$523$	5.64055	−	9.76972i	0.246644	−	0.427200i	−0.715948	−	0.698153i	$-0.754005\pi$
$523$	5.64055	−	9.76972i	0.246644	−	0.427200i	0.962593	+	0.270953i	$0.0873388\pi$
$524$		0			0
$525$	1.74732	−	12.1503i	0.0762592	−	0.530282i
$526$		0			0
$527$	−0.355218	−	0.205085i	−0.0154736	−	0.00893366i
$528$		0			0
$529$	−8.94989	−	15.5017i	−0.389126	−	0.673986i
$530$		0			0
$531$	−6.96306			−0.302171
$532$		0			0
$533$	−26.3130			−1.13974
$534$		0			0
$535$	−21.5642	−	37.3504i	−0.932303	−	1.61480i
$536$		0			0
$537$	−12.7967	−	7.38818i	−0.552219	−	0.318824i
$538$		0			0
$539$	29.5203	+	8.66985i	1.27153	+	0.373437i
$540$		0			0
$541$	5.62085	−	9.73560i	0.241659	−	0.418566i	−0.719528	−	0.694464i	$-0.755642\pi$
$541$	5.62085	−	9.73560i	0.241659	−	0.418566i	0.961187	+	0.275898i	$0.0889751\pi$
$542$		0			0
$543$	−8.10628	−	14.0405i	−0.347874	−	0.602535i
$544$		0			0
$545$	24.0334			1.02948
$546$		0			0
$547$		−	19.3376i		−	0.826815i	−0.910546	−	0.413407i	$-0.864339\pi$
$547$		−	19.3376i		−	0.826815i	0.910546	−	0.413407i	$-0.135661\pi$
$548$		0			0
$549$	4.44509	−	2.56637i	0.189712	−	0.109530i
$550$		0			0
$551$	10.6764	+	19.9841i	0.454828	+	0.851353i
$552$		0			0
$553$	−29.3832	−	4.22556i	−1.24950	−	0.179689i
$554$		0			0
$555$	31.7050	−	54.9147i	1.34580	−	2.33100i
$556$		0			0
$557$	−6.33183	−	10.9671i	−0.268288	−	0.464689i	0.700132	−	0.714014i	$-0.253125\pi$
$557$	−6.33183	−	10.9671i	−0.268288	−	0.464689i	−0.968420	+	0.249325i	$0.919791\pi$
$558$		0			0
$559$	1.46082			0.0617863
$560$		0			0
$561$		−	1.80282i		−	0.0761152i
$562$		0			0
$563$	8.65082	+	14.9837i	0.364589	+	0.631486i	0.988710	−	0.149841i	$-0.0478763\pi$
$563$	8.65082	+	14.9837i	0.364589	+	0.631486i	−0.624121	+	0.781327i	$0.714543\pi$
$564$		0			0
$565$	10.3029	−	17.8451i	0.433445	−	0.750749i
$566$		0			0
$567$	−23.3955	−	18.3995i	−0.982517	−	0.772708i
$568$		0			0
$569$	21.0826	+	12.1721i	0.883831	+	0.510280i	0.871920	−	0.489649i	$-0.162875\pi$
$569$	21.0826	+	12.1721i	0.883831	+	0.510280i	0.0119111	+	0.999929i	$0.496208\pi$
$570$		0			0
$571$	−11.6274	−	20.1392i	−0.486591	−	0.842801i	0.513290	−	0.858215i	$-0.328427\pi$
$571$	−11.6274	−	20.1392i	−0.486591	−	0.842801i	−0.999881	+	0.0154145i	$0.995093\pi$
$572$		0			0
$573$	−24.9068			−1.04050
$574$		0			0
$575$	13.9607			0.582201
$576$		0			0
$577$	−13.7340	+	7.92936i	−0.571756	+	0.330103i	−0.757850	−	0.652428i	$-0.773750\pi$
$577$	−13.7340	+	7.92936i	−0.571756	+	0.330103i	0.186094	+	0.982532i	$0.440417\pi$
$578$		0			0
$579$	−24.1986	−	13.9710i	−1.00566	−	0.580617i
$580$		0			0
$581$	1.85203	+	4.62654i	0.0768350	+	0.191941i
$582$		0			0
$583$	6.67810	+	3.85560i	0.276579	+	0.159683i
$584$		0			0
$585$	21.7991	−	12.5857i	0.901280	−	0.520354i
$586$		0			0
$587$			21.6534i			0.893730i	0.894601	+	0.446865i	$0.147460\pi$
$587$			21.6534i			0.893730i	−0.894601	+	0.446865i	$0.852540\pi$
$588$		0			0
$589$	7.86624	+	4.89383i	0.324123	+	0.201647i
$590$		0			0
$591$	−4.60081	−	7.96883i	−0.189252	−	0.327794i
$592$		0			0
$593$	−3.35670	−	1.93799i	−0.137843	−	0.0795838i	0.429492	−	0.903070i	$-0.358692\pi$
$593$	−3.35670	−	1.93799i	−0.137843	−	0.0795838i	−0.567336	+	0.823487i	$0.692026\pi$
$594$		0			0
$595$	1.27044	−	0.508564i	0.0520831	−	0.0208491i
$596$		0			0
$597$	28.0980	+	16.2224i	1.14997	+	0.663937i
$598$		0			0
$599$	35.6915	−	20.6065i	1.45831	−	0.841958i	0.459386	−	0.888237i	$-0.348069\pi$
$599$	35.6915	−	20.6065i	1.45831	−	0.841958i	0.998929	+	0.0462782i	$0.0147361\pi$
$600$		0			0
$601$	−1.92244			−0.0784180			−0.0392090	−	0.999231i	$-0.512484\pi$
$601$	−1.92244			−0.0784180			−0.0392090	+	0.999231i	$0.512484\pi$
$602$		0			0
$603$		−	13.6055i		−	0.554057i
$604$		0			0
$605$	−19.3078	+	11.1474i	−0.784974	+	0.453205i
$606$		0			0
$607$	17.8798	−	30.9687i	0.725718	−	1.25698i	−0.232960	−	0.972486i	$-0.574841\pi$
$607$	17.8798	−	30.9687i	0.725718	−	1.25698i	0.958678	−	0.284494i	$-0.0918255\pi$
$608$		0			0
$609$	18.0689	−	22.9751i	0.732189	−	0.930997i
$610$		0			0
$611$	−59.3822	−	34.2844i	−2.40235	−	1.38700i
$612$		0			0
$613$	4.79355	+	8.30268i	0.193610	+	0.335342i	0.946444	−	0.322868i	$-0.104647\pi$
$613$	4.79355	+	8.30268i	0.193610	+	0.335342i	−0.752834	+	0.658210i	$0.771314\pi$
$614$		0			0
$615$			24.2133i			0.976374i
$616$		0			0
$617$	5.70019			0.229481			0.114740	−	0.993396i	$-0.463396\pi$
$617$	5.70019			0.229481			0.114740	+	0.993396i	$0.463396\pi$
$618$		0			0
$619$	−15.6825	+	9.05429i	−0.630333	+	0.363923i	−0.780881	−	0.624680i	$-0.785229\pi$
$619$	−15.6825	+	9.05429i	−0.630333	+	0.363923i	0.150548	+	0.988603i	$0.451896\pi$
$620$		0			0
$621$	10.0772	−	17.4543i	0.404385	−	0.700416i
$622$		0			0
$623$	−4.05966	+	28.2296i	−0.162647	+	1.13099i
$624$		0			0
$625$	15.5747	−	26.9762i	0.622990	−	1.07905i
$626$		0			0
$627$	−1.34084	+	40.6972i	−0.0535482	+	1.62529i
$628$		0			0
$629$	2.14832			0.0856591
$630$		0			0
$631$	−17.9448			−0.714372			−0.357186	−	0.934033i	$-0.616264\pi$
$631$	−17.9448			−0.714372			−0.357186	+	0.934033i	$0.616264\pi$
$632$		0			0
$633$	−51.7815	+	29.8961i	−2.05813	+	1.18826i
$634$		0			0
$635$	−4.38343	+	7.59233i	−0.173951	+	0.301292i
$636$		0			0
$637$	−31.3622	+	29.9002i	−1.24262	+	1.18469i
$638$		0			0
$639$	6.94566	+	4.01008i	0.274766	+	0.158636i
$640$		0			0
$641$	7.02998	−	4.05876i	0.277667	−	0.160311i	−0.354700	−	0.934980i	$-0.615417\pi$
$641$	7.02998	−	4.05876i	0.277667	−	0.160311i	0.632367	+	0.774669i	$0.282083\pi$
$642$		0			0
$643$		−	7.02235i		−	0.276935i	−0.990367	−	0.138467i	$-0.955782\pi$
$643$		−	7.02235i		−	0.276935i	0.990367	−	0.138467i	$-0.0442176\pi$
$644$		0			0
$645$		−	1.34425i		−	0.0529299i
$646$		0			0
$647$	39.1279	−	22.5905i	1.53828	−	0.888124i	0.539336	−	0.842091i	$-0.318675\pi$
$647$	39.1279	−	22.5905i	1.53828	−	0.888124i	0.998940	−	0.0460332i	$-0.0146580\pi$
$648$		0			0
$649$	−10.0857	+	17.4690i	−0.395900	+	0.685719i
$650$		0			0
$651$	1.70122	−	11.8298i	0.0666762	−	0.463645i
$652$		0			0
$653$	−19.0002	+	32.9093i	−0.743534	+	1.28784i	0.207342	+	0.978268i	$0.433519\pi$
$653$	−19.0002	+	32.9093i	−0.743534	+	1.28784i	−0.950876	+	0.309571i	$0.899815\pi$
$654$		0			0
$655$	−4.57214	−	7.91918i	−0.178648	−	0.309428i
$656$		0			0
$657$			5.50474i			0.214760i
$658$		0			0
$659$		−	27.7185i		−	1.07976i	−0.841743	−	0.539879i	$-0.818470\pi$
$659$		−	27.7185i		−	1.07976i	0.841743	−	0.539879i	$-0.181530\pi$
$660$		0			0
$661$	−0.257089	−	0.445291i	−0.00999959	−	0.0173198i	0.860982	−	0.508635i	$-0.169850\pi$
$661$	−0.257089	−	0.445291i	−0.00999959	−	0.0173198i	−0.870982	+	0.491315i	$0.836516\pi$
$662$		0			0
$663$	2.19887	+	1.26952i	0.0853972	+	0.0493041i
$664$		0			0
$665$	−29.0575	+	10.5355i	−1.12680	+	0.408551i
$666$		0			0
$667$	28.7887	+	16.6211i	1.11470	+	0.643573i
$668$		0			0
$669$	−2.61842	−	4.53524i	−0.101234	−	0.175342i
$670$		0			0
$671$		−	14.8692i		−	0.574019i
$672$		0			0
$673$			33.6563i			1.29735i	0.761063	+	0.648677i	$0.224678\pi$
$673$			33.6563i			1.29735i	−0.761063	+	0.648677i	$0.775322\pi$
$674$		0			0
$675$	3.43975	+	5.95782i	0.132396	+	0.229317i
$676$		0			0
$677$	−7.76593	+	13.4510i	−0.298469	+	0.516963i	−0.975786	−	0.218728i	$-0.929809\pi$
$677$	−7.76593	+	13.4510i	−0.298469	+	0.516963i	0.677317	+	0.735691i	$0.263143\pi$
$678$		0			0
$679$	−39.8953	+	15.9703i	−1.53104	+	0.612883i
$680$		0			0
$681$	−0.730593	+	1.26542i	−0.0279964	+	0.0484911i
$682$		0			0
$683$	−9.92275	+	5.72890i	−0.379684	+	0.219210i	−0.677681	−	0.735356i	$-0.737015\pi$
$683$	−9.92275	+	5.72890i	−0.379684	+	0.219210i	0.297997	+	0.954567i	$0.403681\pi$
$684$		0			0
$685$		−	38.2830i		−	1.46272i
$686$		0			0
$687$		−	29.8603i		−	1.13924i
$688$		0			0
$689$	−9.40524	+	5.43012i	−0.358311	+	0.206871i
$690$		0			0
$691$	23.6825	+	13.6731i	0.900926	+	0.520150i	0.877501	−	0.479575i	$-0.159209\pi$
$691$	23.6825	+	13.6731i	0.900926	+	0.520150i	0.0234258	+	0.999726i	$0.492543\pi$
$692$		0			0
$693$	16.3800	−	6.55698i	0.622223	−	0.249079i
$694$		0			0
$695$	15.8556	−	27.4626i	0.601435	−	1.04172i
$696$		0			0
$697$	−0.710437	+	0.410171i	−0.0269097	+	0.0155363i
$698$		0			0
$699$	−4.96119			−0.187649
$700$		0			0
$701$	−5.25736			−0.198568			−0.0992838	−	0.995059i	$-0.531655\pi$
$701$	−5.25736			−0.198568			−0.0992838	+	0.995059i	$0.531655\pi$
$702$		0			0
$703$	−48.4966	−	1.59781i	−1.82908	−	0.0602624i
$704$		0			0
$705$	−31.5485	+	54.6436i	−1.18819	+	2.05800i
$706$		0			0
$707$	28.1014	−	35.7316i	1.05686	−	1.34383i
$708$		0			0
$709$	10.6779	−	18.4946i	0.401016	−	0.694580i	−0.592833	−	0.805326i	$-0.701990\pi$
$709$	10.6779	−	18.4946i	0.401016	−	0.694580i	0.993849	+	0.110745i	$0.0353238\pi$
$710$		0			0
$711$	−14.7427	+	8.51168i	−0.552893	+	0.319213i
$712$		0			0
$713$	13.5924			0.509040
$714$		0			0
$715$		−	72.9197i		−	2.72704i
$716$		0			0
$717$	−19.1369	−	33.1461i	−0.714680	−	1.23786i
$718$		0			0
$719$	−17.9951	−	10.3895i	−0.671104	−	0.387462i	0.125391	−	0.992107i	$-0.459981\pi$
$719$	−17.9951	−	10.3895i	−0.671104	−	0.387462i	−0.796495	+	0.604646i	$0.793315\pi$
$720$		0			0
$721$	−3.32925	+	23.1505i	−0.123988	+	0.862170i
$722$		0			0
$723$	−6.21845	+	10.7707i	−0.231267	+	0.400566i
$724$		0			0
$725$	−9.82669	+	5.67344i	−0.364954	+	0.210706i
$726$		0			0
$727$			30.9769i			1.14887i	0.818550	+	0.574435i	$0.194778\pi$
$727$			30.9769i			1.14887i	−0.818550	+	0.574435i	$0.805222\pi$
$728$		0			0
$729$	3.02573			0.112064
$730$		0			0
$731$	0.0394414	−	0.0227715i	0.00145879	−	0.000842235i
$732$		0			0
$733$	33.4286	+	19.3000i	1.23471	+	0.712863i	0.968009	−	0.250916i	$-0.0807317\pi$
$733$	33.4286	+	19.3000i	1.23471	+	0.712863i	0.266705	+	0.963778i	$0.414065\pi$
$734$		0			0
$735$	27.5142	+	28.8595i	1.01488	+	1.06450i
$736$		0			0
$737$	−34.1335	−	19.7070i	−1.25733	−	0.725917i
$738$		0			0
$739$	2.74818	+	4.75999i	0.101093	+	0.175099i	0.912135	−	0.409889i	$-0.134433\pi$
$739$	2.74818	+	4.75999i	0.101093	+	0.175099i	−0.811042	+	0.584988i	$0.801099\pi$
$740$		0			0
$741$	−48.6936	−	30.2938i	−1.78880	−	1.11287i
$742$		0			0
$743$			20.0111i			0.734136i	0.930194	+	0.367068i	$0.119638\pi$
$743$			20.0111i			0.734136i	−0.930194	+	0.367068i	$0.880362\pi$
$744$		0			0
$745$	1.65022	−	0.952755i	0.0604594	−	0.0349062i
$746$		0			0
$747$	2.47493	+	1.42890i	0.0905529	+	0.0522808i
$748$		0			0
$749$	42.1421	+	6.06041i	1.53984	+	0.221443i
$750$		0			0
$751$	−16.0397	−	9.26054i	−0.585298	−	0.337922i	0.177938	−	0.984042i	$-0.443057\pi$
$751$	−16.0397	−	9.26054i	−0.585298	−	0.337922i	−0.763236	+	0.646120i	$0.776391\pi$
$752$		0			0
$753$	−46.1024	+	26.6172i	−1.68006	+	0.969985i
$754$		0			0
$755$	−28.9613			−1.05401
$756$		0			0
$757$	49.9050			1.81383			0.906914	−	0.421316i	$-0.138432\pi$
$757$	49.9050			1.81383			0.906914	+	0.421316i	$0.138432\pi$
$758$		0			0
$759$	29.8713	+	51.7386i	1.08426	+	1.87799i
$760$		0			0
$761$	11.8885	+	6.86383i	0.430958	+	0.248814i	0.699755	−	0.714383i	$-0.253293\pi$
$761$	11.8885	+	6.86383i	0.430958	+	0.248814i	−0.268797	+	0.963197i	$0.586626\pi$
$762$		0			0
$763$	−14.6666	+	18.6489i	−0.530965	+	0.675136i
$764$		0			0
$765$	0.392375	−	0.679613i	0.0141863	−	0.0245715i
$766$		0			0
$767$	−14.2045	−	24.6028i	−0.512893	−	0.888357i
$768$		0			0
$769$			25.3198i			0.913057i	0.889709	+	0.456528i	$0.150907\pi$
$769$			25.3198i			0.913057i	−0.889709	+	0.456528i	$0.849093\pi$
$770$		0			0
$771$	−50.2535			−1.80983
$772$		0			0
$773$	1.51087	+	2.61690i	0.0543422	+	0.0941235i	0.891917	−	0.452199i	$-0.149360\pi$
$773$	1.51087	+	2.61690i	0.0543422	+	0.0941235i	−0.837575	+	0.546323i	$0.816027\pi$
$774$		0			0
$775$	−2.31981	+	4.01803i	−0.0833300	+	0.144332i
$776$		0			0
$777$	23.2633	+	58.1139i	0.834566	+	2.08483i
$778$		0			0
$779$	16.3426	−	8.73089i	0.585535	−	0.312817i
$780$		0			0
$781$	20.1211	−	11.6169i	0.719988	−	0.415685i
$782$		0			0
$783$			16.3810i			0.585410i
$784$		0			0
$785$	−32.1172			−1.14631
$786$		0			0
$787$	0.149315	+	0.258622i	0.00532251	+	0.00921887i	0.868674	−	0.495383i	$-0.164972\pi$
$787$	0.149315	+	0.258622i	0.00532251	+	0.00921887i	−0.863352	+	0.504602i	$0.831639\pi$
$788$		0			0
$789$	22.2632	−	38.5610i	0.792591	−	1.37281i
$790$		0			0
$791$	7.55965	+	18.8847i	0.268790	+	0.671464i
$792$		0			0
$793$	18.1357	+	10.4707i	0.644018	+	0.371824i
$794$		0			0
$795$	4.99680	+	8.65471i	0.177218	+	0.306951i
$796$		0			0
$797$	6.85036			0.242652			0.121326	−	0.992613i	$-0.461285\pi$
$797$	6.85036			0.242652			0.121326	+	0.992613i	$0.461285\pi$
$798$		0			0
$799$	−2.13772			−0.0756269
$800$		0			0
$801$	8.17750	+	14.1638i	0.288938	+	0.500455i
$802$		0			0
$803$	13.8104	+	7.97341i	0.487357	+	0.281376i
$804$		0			0
$805$	−28.0335	+	35.6454i	−0.988053	+	1.25633i
$806$		0			0
$807$	−9.80750	+	16.9871i	−0.345240	+	0.597974i
$808$		0			0
$809$	3.45097	+	5.97726i	0.121330	+	0.210149i	0.920292	−	0.391231i	$-0.127951\pi$
$809$	3.45097	+	5.97726i	0.121330	+	0.210149i	−0.798963	+	0.601381i	$0.794617\pi$
$810$		0			0
$811$	−7.67789			−0.269607			−0.134804	−	0.990872i	$-0.543040\pi$
$811$	−7.67789			−0.269607			−0.134804	+	0.990872i	$0.543040\pi$
$812$		0			0
$813$		−	31.3808i		−	1.10057i
$814$		0			0
$815$	43.0296	−	24.8432i	1.50726	−	0.870218i
$816$		0			0
$817$	−0.907295	+	0.484714i	−0.0317422	+	0.0169580i
$818$		0			0
$819$	−3.53708	+	24.5957i	−0.123596	+	0.859443i
$820$		0			0
$821$	16.0675	−	27.8297i	0.560758	−	0.971262i	−0.436672	−	0.899621i	$-0.643843\pi$
$821$	16.0675	−	27.8297i	0.560758	−	0.971262i	0.997430	−	0.0716411i	$-0.0228236\pi$
$822$		0			0
$823$	22.5881	+	39.1237i	0.787371	+	1.36377i	0.927572	+	0.373644i	$0.121892\pi$
$823$	22.5881	+	39.1237i	0.787371	+	1.36377i	−0.140201	+	0.990123i	$0.544775\pi$
$824$		0			0
$825$	−20.3925			−0.709975
$826$		0			0
$827$			31.2965i			1.08829i	0.838993	+	0.544143i	$0.183145\pi$
$827$			31.2965i			1.08829i	−0.838993	+	0.544143i	$0.816855\pi$
$828$		0			0
$829$	23.3625	+	40.4650i	0.811413	+	1.40541i	0.911875	+	0.410468i	$0.134635\pi$
$829$	23.3625	+	40.4650i	0.811413	+	1.40541i	−0.100461	+	0.994941i	$0.532032\pi$
$830$		0			0
$831$	30.5255	−	52.8718i	1.05892	−	1.83410i
$832$		0			0
$833$	−0.380673	+	1.29617i	−0.0131895	+	0.0449095i
$834$		0			0
$835$	50.8493	+	29.3579i	1.75971	+	1.01597i
$836$		0			0
$837$	3.34901	+	5.80066i	0.115759	+	0.200500i
$838$		0			0
$839$	1.04902			0.0362161			0.0181081	−	0.999836i	$-0.494236\pi$
$839$	1.04902			0.0362161			0.0181081	+	0.999836i	$0.494236\pi$
$840$		0			0
$841$	1.98155			0.0683294
$842$		0			0
$843$	33.2864	−	19.2179i	1.14645	−	0.661901i
$844$		0			0
$845$	58.7655	+	33.9283i	2.02159	+	1.16717i
$846$		0			0
$847$	3.13285	−	21.7849i	0.107646	−	0.748537i
$848$		0			0
$849$	−21.3837	−	12.3459i	−0.733887	−	0.423710i
$850$		0			0
$851$	−61.6540	+	35.5959i	−2.11347	+	1.22021i
$852$		0			0
$853$			25.1341i			0.860574i	0.902692	+	0.430287i	$0.141588\pi$
$853$			25.1341i			0.860574i	−0.902692	+	0.430287i	$0.858412\pi$
$854$		0			0
$855$	−9.36301	+	15.0499i	−0.320208	+	0.514695i
$856$		0			0
$857$	−26.5140	−	45.9235i	−0.905700	−	1.56872i	−0.819975	−	0.572399i	$-0.806013\pi$
$857$	−26.5140	−	45.9235i	−0.905700	−	1.56872i	−0.0857243	−	0.996319i	$-0.527320\pi$
$858$		0			0
$859$	−33.3216	−	19.2383i	−1.13692	−	0.656401i	−0.191254	−	0.981541i	$-0.561255\pi$
$859$	−33.3216	−	19.2383i	−1.13692	−	0.656401i	−0.945666	+	0.325140i	$0.894589\pi$
$860$		0			0
$861$	−18.7885	−	14.7764i	−0.640311	−	0.503577i
$862$		0			0
$863$	34.7907	+	20.0864i	1.18429	+	0.683750i	0.957003	−	0.290078i	$-0.0936811\pi$
$863$	34.7907	+	20.0864i	1.18429	+	0.683750i	0.227287	+	0.973828i	$0.427014\pi$
$864$		0			0
$865$	29.5213	−	17.0441i	1.00375	−	0.579517i
$866$		0			0
$867$	−36.0522			−1.22440
$868$		0			0
$869$			49.3154i			1.67291i
$870$		0			0
$871$	48.0727	−	27.7548i	1.62888	−	0.940435i
$872$		0			0
$873$	−12.3216	+	21.3417i	−0.417024	+	0.722306i
$874$		0			0
$875$	7.42352	+	18.5447i	0.250961	+	0.626924i
$876$		0			0
$877$	−0.790102	−	0.456166i	−0.0266799	−	0.0154036i	0.486601	−	0.873624i	$-0.338237\pi$
$877$	−0.790102	−	0.456166i	−0.0266799	−	0.0154036i	−0.513281	+	0.858221i	$0.671570\pi$
$878$		0			0
$879$	4.51723	+	7.82407i	0.152362	+	0.263899i
$880$		0			0
$881$			33.8036i			1.13887i	0.822035	+	0.569436i	$0.192839\pi$
$881$			33.8036i			1.13887i	−0.822035	+	0.569436i	$0.807161\pi$
$882$		0			0
$883$	2.32617			0.0782817			0.0391409	−	0.999234i	$-0.487538\pi$
$883$	2.32617			0.0782817			0.0391409	+	0.999234i	$0.487538\pi$
$884$		0			0
$885$	−22.6396	+	13.0710i	−0.761021	+	0.439376i
$886$		0			0
$887$	−21.1954	+	36.7114i	−0.711670	+	1.23265i	0.252560	+	0.967581i	$0.418728\pi$
$887$	−21.1954	+	36.7114i	−0.711670	+	1.23265i	−0.964230	+	0.265068i	$0.914606\pi$
$888$		0			0
$889$	−3.21631	−	8.03465i	−0.107872	−	0.269473i
$890$		0			0
$891$	−24.7229	+	42.8213i	−0.828248	+	1.43457i
$892$		0			0
$893$	48.2572	+	1.58992i	1.61487	+	0.0532047i
$894$		0			0
$895$	−18.6330			−0.622833
$896$		0			0
$897$	−84.1398			−2.80934
$898$		0			0
$899$	−9.56746	+	5.52378i	−0.319093	+	0.184228i
$900$		0			0
$901$	−0.169291	+	0.293220i	−0.00563989	+	0.00976858i
$902$		0			0
$903$	1.04308	+	0.820342i	0.0347117	+	0.0272993i
$904$		0			0
$905$	−17.7051	−	10.2220i	−0.588537	−	0.339792i
$906$		0			0
$907$	6.52545	−	3.76747i	0.216674	−	0.125097i	−0.387735	−	0.921771i	$-0.626743\pi$
$907$	6.52545	−	3.76747i	0.216674	−	0.125097i	0.604409	+	0.796674i	$0.293409\pi$
$908$		0			0
$909$		−	26.0683i		−	0.864630i
$910$		0			0
$911$		−	44.6565i		−	1.47954i	−0.672862	−	0.739768i	$-0.734935\pi$
$911$		−	44.6565i		−	1.47954i	0.672862	−	0.739768i	$-0.265065\pi$
$912$		0			0
$913$	7.16969	−	4.13942i	0.237282	−	0.136995i
$914$		0			0
$915$	9.63512	−	16.6885i	0.318527	−	0.551705i
$916$		0			0
$917$	8.93514	+	1.28495i	0.295064	+	0.0424329i
$918$		0			0
$919$	9.32758	−	16.1558i	0.307689	−	0.532932i	−0.670168	−	0.742210i	$-0.733778\pi$
$919$	9.32758	−	16.1558i	0.307689	−	0.532932i	0.977856	+	0.209277i	$0.0671112\pi$
$920$		0			0
$921$	−1.52802	−	2.64661i	−0.0503500	−	0.0872087i
$922$		0			0
$923$			32.7218i			1.07705i
$924$		0			0
$925$		−	24.3006i		−	0.798997i
$926$		0			0
$927$	6.70621	+	11.6155i	0.220261	+	0.381503i
$928$		0			0
$929$	28.7163	+	16.5794i	0.942152	+	0.543952i	0.890634	−	0.454720i	$-0.150261\pi$
$929$	28.7163	+	16.5794i	0.942152	+	0.543952i	0.0515177	+	0.998672i	$0.483594\pi$
$930$		0			0
$931$	9.55742	−	28.9768i	0.313232	−	0.949677i
$932$		0			0
$933$	−2.38490	−	1.37692i	−0.0780782	−	0.0450784i
$934$		0			0
$935$	−1.13668	−	1.96879i	−0.0371734	−	0.0643863i
$936$		0			0
$937$		−	19.1539i		−	0.625731i	−0.949797	−	0.312866i	$-0.898711\pi$
$937$		−	19.1539i		−	0.625731i	0.949797	−	0.312866i	$-0.101289\pi$
$938$		0			0
$939$			13.2112i			0.431131i
$940$		0			0
$941$	−15.2977	−	26.4964i	−0.498691	−	0.863758i	0.501308	−	0.865269i	$-0.332852\pi$
$941$	−15.2977	−	26.4964i	−0.498691	−	0.863758i	−0.999999	+	0.00151068i	$0.999519\pi$
$942$		0			0
$943$	13.5924	−	23.5427i	0.442630	−	0.766657i
$944$		0			0
$945$	−22.1191	−	3.18092i	−0.719533	−	0.103475i
$946$		0			0
$947$	−9.80521	+	16.9831i	−0.318626	+	0.551877i	−0.980202	−	0.198002i	$-0.936555\pi$
$947$	−9.80521	+	16.9831i	−0.318626	+	0.551877i	0.661575	+	0.749879i	$0.269888\pi$
$948$		0			0
$949$	−19.4501	+	11.2295i	−0.631377	+	0.364526i
$950$		0			0
$951$		−	4.46170i		−	0.144681i
$952$		0			0
$953$		−	34.7013i		−	1.12409i	−0.827108	−	0.562043i	$-0.810016\pi$
$953$		−	34.7013i		−	1.12409i	0.827108	−	0.562043i	$-0.189984\pi$
$954$		0			0
$955$	−27.1997	+	15.7038i	−0.880162	+	0.508162i
$956$		0			0
$957$	−42.0518	−	24.2786i	−1.35934	−	0.784816i
$958$		0			0
$959$	29.7061	+	23.3626i	0.959259	+	0.754416i
$960$		0			0
$961$	13.2414	−	22.9348i	0.427142	−	0.739831i
$962$		0			0
$963$	21.1443	−	12.2077i	0.681366	−	0.393387i
$964$		0			0
$965$	−35.2350			−1.13426
$966$		0			0
$967$	25.4434			0.818203			0.409102	−	0.912489i	$-0.365842\pi$
$967$	25.4434			0.818203			0.409102	+	0.912489i	$0.365842\pi$
$968$		0			0
$969$	−1.78692	−	0.0588734i	−0.0574042	−	0.00189129i
$970$		0			0
$971$	−14.2747	+	24.7246i	−0.458098	+	0.793449i	−0.998860	−	0.0477262i	$-0.984803\pi$
$971$	−14.2747	+	24.7246i	−0.458098	+	0.793449i	0.540762	+	0.841175i	$0.318136\pi$
$972$		0			0
$973$	11.6339	+	29.0626i	0.372965	+	0.931703i
$974$		0			0
$975$	14.3601	−	24.8724i	0.459891	−	0.796554i
$976$		0			0
$977$	23.2723	−	13.4363i	0.744546	−	0.429864i	−0.0791739	−	0.996861i	$-0.525228\pi$
$977$	23.2723	−	13.4363i	0.744546	−	0.429864i	0.823720	+	0.566997i	$0.191895\pi$
$978$		0			0
$979$	47.3792			1.51425
$980$		0			0
$981$			13.6055i			0.434389i
$982$		0			0
$983$	23.6364	+	40.9394i	0.753883	+	1.30576i	0.945928	+	0.324378i	$0.105155\pi$
$983$	23.6364	+	40.9394i	0.753883	+	1.30576i	−0.192045	+	0.981386i	$0.561512\pi$
$984$		0			0
$985$	−10.0487	−	5.80163i	−0.320179	−	0.184855i
$986$		0			0
$987$	−23.1485	−	57.8271i	−0.736824	−	1.84066i
$988$		0			0
$989$	−0.754612	+	1.30703i	−0.0239953	+	0.0415610i
$990$		0			0
$991$	22.1172	−	12.7694i	0.702577	−	0.405633i	−0.105730	−	0.994395i	$-0.533718\pi$
$991$	22.1172	−	12.7694i	0.702577	−	0.405633i	0.808306	+	0.588762i	$0.200384\pi$
$992$		0			0
$993$			14.7764i			0.468914i
$994$		0			0
$995$	40.9129			1.29703
$996$		0			0
$997$	15.7484	−	9.09234i	0.498757	−	0.287957i	−0.229443	−	0.973322i	$-0.573691\pi$
$997$	15.7484	−	9.09234i	0.498757	−	0.287957i	0.728200	+	0.685365i	$0.240357\pi$
$998$		0			0
$999$	−30.3817	−	17.5409i	−0.961233	−	0.554968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.v.e.341.6	yes	16
7.2	even	3		3724.2.g.f.1861.5		16
7.3	odd	6	inner	532.2.v.e.493.3	yes	16
7.5	odd	6		3724.2.g.f.1861.12		16
19.18	odd	2	inner	532.2.v.e.341.3	✓	16
133.37	odd	6		3724.2.g.f.1861.11		16
133.75	even	6		3724.2.g.f.1861.6		16
133.94	even	6	inner	532.2.v.e.493.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.v.e.341.3	✓	16	19.18	odd	2	inner
532.2.v.e.341.6	yes	16	1.1	even	1	trivial
532.2.v.e.493.3	yes	16	7.3	odd	6	inner
532.2.v.e.493.6	yes	16	133.94	even	6	inner
3724.2.g.f.1861.5		16	7.2	even	3
3724.2.g.f.1861.6		16	133.75	even	6
3724.2.g.f.1861.11		16	133.37	odd	6
3724.2.g.f.1861.12		16	7.5	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:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06269 + 1.84063i) q^{3} +(2.32104 + 1.34005i) q^{5} +(-2.45626 + 0.983253i) q^{7} +(-0.758613 + 1.31396i) q^{9} +O(q^{10})\)	\(q+(1.06269 + 1.84063i) q^{3} +(2.32104 + 1.34005i) q^{5} +(-2.45626 + 0.983253i) q^{7} +(-0.758613 + 1.31396i) q^{9} +(2.19765 + 3.80644i) q^{11} -6.19020 q^{13} +5.69623i q^{15} +(-0.167132 + 0.0964937i) q^{17} +(3.84464 - 2.05396i) q^{19} +(-4.42004 - 3.47618i) q^{21} +(3.19765 - 5.53849i) q^{23} +(1.09148 + 1.89050i) q^{25} +3.15145 q^{27} +5.19793i q^{29} +(1.06269 + 1.84063i) q^{31} +(-4.67083 + 8.09011i) q^{33} +(-7.01869 - 1.00935i) q^{35} +(-9.64052 - 5.56596i) q^{37} +(-6.57826 - 11.3939i) q^{39} +4.25075 q^{41} -0.235990 q^{43} +(-3.52154 + 2.03316i) q^{45} +(9.59294 + 5.53849i) q^{47} +(5.06643 - 4.83025i) q^{49} +(-0.355218 - 0.205085i) q^{51} +(1.51937 - 0.877212i) q^{53} +11.7798i q^{55} +(7.86624 + 4.89383i) q^{57} +(2.29467 + 3.97448i) q^{59} +(-2.92975 - 1.69149i) q^{61} +(0.571400 - 3.97333i) q^{63} +(-14.3677 - 8.29520i) q^{65} +(-7.76593 + 4.48366i) q^{67} +13.5924 q^{69} -5.28606i q^{71} +(3.14208 - 1.81408i) q^{73} +(-2.31981 + 4.01803i) q^{75} +(-9.14068 - 7.18875i) q^{77} +(9.71685 + 5.61003i) q^{79} +(5.62485 + 9.74253i) q^{81} -1.88357i q^{83} -0.517226 q^{85} +(-9.56746 + 5.52378i) q^{87} +(5.38977 - 9.33535i) q^{89} +(15.2047 - 6.08654i) q^{91} +(-2.25861 + 3.91203i) q^{93} +(11.6760 + 0.384686i) q^{95} +16.2423 q^{97} -6.66866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9}+O(q^{10}) \) 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9	\( 16 q - 6 q^{5} - 14 q^{7} - 26 q^{9} - 4 q^{11} - 24 q^{17} + 21 q^{19} + 12 q^{23} + 10 q^{25} - 30 q^{35} - 12 q^{39} + 16 q^{43} + 72 q^{45} + 36 q^{47} - 34 q^{49} - 2 q^{57} - 24 q^{61} + 20 q^{63} - 36 q^{73} + 4 q^{77} - 24 q^{81} - 36 q^{85} - 48 q^{87} - 50 q^{93} + 31 q^{95} + 156 q^{99}+O(q^{100}) \) 16 * q - 6 * q^5 - 14 * q^7 - 26 * q^9 - 4 * q^11 - 24 * q^17 + 21 * q^19 + 12 * q^23 + 10 * q^25 - 30 * q^35 - 12 * q^39 + 16 * q^43 + 72 * q^45 + 36 * q^47 - 34 * q^49 - 2 * q^57 - 24 * q^61 + 20 * q^63 - 36 * q^73 + 4 * q^77 - 24 * q^81 - 36 * q^85 - 48 * q^87 - 50 * q^93 + 31 * q^95 + 156 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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