LMFDB - Embedded newform 576.2.bb.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.d.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-3.73205 + 1.00000i) q^{5} +(0.633975 - 0.366025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-3.73205 + 1.00000i) q^{5} +(0.633975 - 0.366025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(0.767949 - 2.86603i) q^{11} +(-1.63397 - 6.09808i) q^{13} +(-4.73205 + 4.73205i) q^{15} -2.26795 q^{17} +(0.633975 - 0.633975i) q^{19} +(0.633975 - 1.09808i) q^{21} +(1.09808 + 0.633975i) q^{23} +(8.59808 - 4.96410i) q^{25} -5.19615i q^{27} +(-2.36603 - 0.633975i) q^{29} +(3.73205 - 6.46410i) q^{31} +(-1.33013 - 4.96410i) q^{33} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-7.73205 - 7.73205i) q^{39} +(-2.59808 - 1.50000i) q^{41} +(-0.330127 + 1.23205i) q^{43} +(-3.00000 + 11.1962i) q^{45} +(4.83013 + 8.36603i) q^{47} +(-3.23205 + 5.59808i) q^{49} +(-3.40192 + 1.96410i) q^{51} +(-0.535898 - 0.535898i) q^{53} +11.4641i q^{55} +(0.401924 - 1.50000i) q^{57} +(-4.96410 + 1.33013i) q^{59} +(-3.00000 - 0.803848i) q^{61} -2.19615i q^{63} +(12.1962 + 21.1244i) q^{65} +(-1.40192 - 5.23205i) q^{67} +2.19615 q^{69} -10.9282i q^{71} +9.73205i q^{73} +(8.59808 - 14.8923i) q^{75} +(-0.562178 - 2.09808i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(1.36603 + 0.366025i) q^{83} +(8.46410 - 2.26795i) q^{85} +(-4.09808 + 1.09808i) q^{87} +2.00000i q^{89} +(-3.26795 - 3.26795i) q^{91} -12.9282i q^{93} +(-1.73205 + 3.00000i) q^{95} +(-4.13397 - 7.16025i) q^{97} +(-6.29423 - 6.29423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 8 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 8 * q^5 + 6 * q^7 + 6 * q^9	$ 4 q + 6 q^{3} - 8 q^{5} + 6 q^{7} + 6 q^{9} + 10 q^{11} - 10 q^{13} - 12 q^{15} - 16 q^{17} + 6 q^{19} + 6 q^{21} - 6 q^{23} + 24 q^{25} - 6 q^{29} + 8 q^{31} + 12 q^{33} - 8 q^{35} + 12 q^{37} - 24 q^{39} + 16 q^{43} - 12 q^{45} + 2 q^{47} - 6 q^{49} - 24 q^{51} - 16 q^{53} + 12 q^{57} - 6 q^{59} - 12 q^{61} + 28 q^{65} - 16 q^{67} - 12 q^{69} + 24 q^{75} + 22 q^{77} + 24 q^{79} - 18 q^{81} + 2 q^{83} + 20 q^{85} - 6 q^{87} - 20 q^{91} - 20 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 8 * q^5 + 6 * q^7 + 6 * q^9 + 10 * q^11 - 10 * q^13 - 12 * q^15 - 16 * q^17 + 6 * q^19 + 6 * q^21 - 6 * q^23 + 24 * q^25 - 6 * q^29 + 8 * q^31 + 12 * q^33 - 8 * q^35 + 12 * q^37 - 24 * q^39 + 16 * q^43 - 12 * q^45 + 2 * q^47 - 6 * q^49 - 24 * q^51 - 16 * q^53 + 12 * q^57 - 6 * q^59 - 12 * q^61 + 28 * q^65 - 16 * q^67 - 12 * q^69 + 24 * q^75 + 22 * q^77 + 24 * q^79 - 18 * q^81 + 2 * q^83 + 20 * q^85 - 6 * q^87 - 20 * q^91 - 20 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$		0			0
$5$	−3.73205	+	1.00000i	−1.66902	+	0.447214i	−0.964847	−	0.262811i	$-0.915350\pi$
$5$	−3.73205	+	1.00000i	−1.66902	+	0.447214i	−0.704177	+	0.710025i	$0.748684\pi$
$6$		0			0
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	−0.375382	−	0.926870i	$-0.622489\pi$
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	0.615002	+	0.788526i	$0.289155\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	0.767949	−	2.86603i	0.231545	−	0.864139i	−0.748130	−	0.663552i	$-0.769048\pi$
$11$	0.767949	−	2.86603i	0.231545	−	0.864139i	0.979676	−	0.200587i	$-0.0642851\pi$
$12$		0			0
$13$	−1.63397	−	6.09808i	−0.453183	−	1.69130i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.63397	−	6.09808i	−0.453183	−	1.69130i	0.240192	−	0.970725i	$-0.422790\pi$
$14$		0			0
$15$	−4.73205	+	4.73205i	−1.22181	+	1.22181i
$16$		0			0
$17$	−2.26795			−0.550058			−0.275029	−	0.961436i	$-0.588688\pi$
$17$	−2.26795			−0.550058			−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	0.633975	−	0.633975i	0.145444	−	0.145444i	−0.630635	−	0.776079i	$-0.717206\pi$
$19$	0.633975	−	0.633975i	0.145444	−	0.145444i	0.776079	+	0.630635i	$0.217206\pi$
$20$		0			0
$21$	0.633975	−	1.09808i	0.138345	−	0.239620i
$22$		0			0
$23$	1.09808	+	0.633975i	0.228965	+	0.132193i	0.610094	−	0.792329i	$-0.291132\pi$
$23$	1.09808	+	0.633975i	0.228965	+	0.132193i	−0.381130	+	0.924522i	$0.624465\pi$
$24$		0			0
$25$	8.59808	−	4.96410i	1.71962	−	0.992820i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	−2.36603	−	0.633975i	−0.439360	−	0.117726i	0.0323566	−	0.999476i	$-0.489699\pi$
$29$	−2.36603	−	0.633975i	−0.439360	−	0.117726i	−0.471717	+	0.881750i	$0.656365\pi$
$30$		0			0
$31$	3.73205	−	6.46410i	0.670296	−	1.16099i	−0.307524	−	0.951540i	$-0.599500\pi$
$31$	3.73205	−	6.46410i	0.670296	−	1.16099i	0.977820	−	0.209447i	$-0.0671662\pi$
$32$		0			0
$33$	−1.33013	−	4.96410i	−0.231545	−	0.864139i
$34$		0			0
$35$	−2.00000	+	2.00000i	−0.338062	+	0.338062i
$36$		0			0
$37$	1.26795	+	1.26795i	0.208450	+	0.208450i	0.803608	−	0.595159i	$-0.202911\pi$
$37$	1.26795	+	1.26795i	0.208450	+	0.208450i	−0.595159	+	0.803608i	$0.702911\pi$
$38$		0			0
$39$	−7.73205	−	7.73205i	−1.23812	−	1.23812i
$40$		0			0
$41$	−2.59808	−	1.50000i	−0.405751	−	0.234261i	0.283211	−	0.959058i	$-0.408600\pi$
$41$	−2.59808	−	1.50000i	−0.405751	−	0.234261i	−0.688963	+	0.724797i	$0.741934\pi$
$42$		0			0
$43$	−0.330127	+	1.23205i	−0.0503439	+	0.187886i	−0.986519	−	0.163649i	$-0.947674\pi$
$43$	−0.330127	+	1.23205i	−0.0503439	+	0.187886i	0.936175	+	0.351535i	$0.114340\pi$
$44$		0			0
$45$	−3.00000	+	11.1962i	−0.447214	+	1.66902i
$46$		0			0
$47$	4.83013	+	8.36603i	0.704546	+	1.22031i	0.966855	+	0.255326i	$0.0821828\pi$
$47$	4.83013	+	8.36603i	0.704546	+	1.22031i	−0.262309	+	0.964984i	$0.584484\pi$
$48$		0			0
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$		0			0
$51$	−3.40192	+	1.96410i	−0.476365	+	0.275029i
$52$		0			0
$53$	−0.535898	−	0.535898i	−0.0736113	−	0.0736113i	0.669343	−	0.742954i	$-0.266576\pi$
$53$	−0.535898	−	0.535898i	−0.0736113	−	0.0736113i	−0.742954	+	0.669343i	$0.766576\pi$
$54$		0			0
$55$			11.4641i			1.54582i
$56$		0			0
$57$	0.401924	−	1.50000i	0.0532361	−	0.198680i
$58$		0			0
$59$	−4.96410	+	1.33013i	−0.646271	+	0.173168i	−0.567042	−	0.823689i	$-0.691912\pi$
$59$	−4.96410	+	1.33013i	−0.646271	+	0.173168i	−0.0792287	+	0.996856i	$0.525246\pi$
$60$		0			0
$61$	−3.00000	−	0.803848i	−0.384111	−	0.102922i	0.0615961	−	0.998101i	$-0.480381\pi$
$61$	−3.00000	−	0.803848i	−0.384111	−	0.102922i	−0.445707	+	0.895179i	$0.647048\pi$
$62$		0			0
$63$		−	2.19615i		−	0.276689i
$64$		0			0
$65$	12.1962	+	21.1244i	1.51275	+	2.62015i
$66$		0			0
$67$	−1.40192	−	5.23205i	−0.171272	−	0.639197i	−0.997157	−	0.0753572i	$-0.975990\pi$
$67$	−1.40192	−	5.23205i	−0.171272	−	0.639197i	0.825884	−	0.563840i	$-0.190676\pi$
$68$		0			0
$69$	2.19615			0.264386
$70$		0			0
$71$		−	10.9282i		−	1.29694i	−0.761241	−	0.648470i	$-0.775409\pi$
$71$		−	10.9282i		−	1.29694i	0.761241	−	0.648470i	$-0.224591\pi$
$72$		0			0
$73$			9.73205i			1.13905i	0.821974	+	0.569525i	$0.192873\pi$
$73$			9.73205i			1.13905i	−0.821974	+	0.569525i	$0.807127\pi$
$74$		0			0
$75$	8.59808	−	14.8923i	0.992820	−	1.71962i
$76$		0			0
$77$	−0.562178	−	2.09808i	−0.0640661	−	0.239098i
$78$		0			0
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	1.36603	+	0.366025i	0.149941	+	0.0401765i	0.333009	−	0.942924i	$-0.391936\pi$
$83$	1.36603	+	0.366025i	0.149941	+	0.0401765i	−0.183068	+	0.983100i	$0.558603\pi$
$84$		0			0
$85$	8.46410	−	2.26795i	0.918061	−	0.245994i
$86$		0			0
$87$	−4.09808	+	1.09808i	−0.439360	+	0.117726i
$88$		0			0
$89$			2.00000i			0.212000i	0.994366	+	0.106000i	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$		0			0
$91$	−3.26795	−	3.26795i	−0.342574	−	0.342574i
$92$		0			0
$93$		−	12.9282i		−	1.34059i
$94$		0			0
$95$	−1.73205	+	3.00000i	−0.177705	+	0.307794i
$96$		0			0
$97$	−4.13397	−	7.16025i	−0.419742	−	0.727014i	0.576172	−	0.817329i	$-0.304546\pi$
$97$	−4.13397	−	7.16025i	−0.419742	−	0.727014i	−0.995913	+	0.0903150i	$0.971213\pi$
$98$		0			0
$99$	−6.29423	−	6.29423i	−0.632594	−	0.632594i
$100$		0			0
$101$	−2.00000	+	7.46410i	−0.199007	+	0.742706i	0.792186	+	0.610280i	$0.208943\pi$
$101$	−2.00000	+	7.46410i	−0.199007	+	0.742706i	−0.991193	+	0.132426i	$0.957723\pi$
$102$		0			0
$103$	7.90192	+	4.56218i	0.778600	+	0.449525i	0.835934	−	0.548830i	$-0.184927\pi$
$103$	7.90192	+	4.56218i	0.778600	+	0.449525i	−0.0573341	+	0.998355i	$0.518260\pi$
$104$		0			0
$105$	−1.26795	+	4.73205i	−0.123739	+	0.461801i
$106$		0			0
$107$	13.4904	+	13.4904i	1.30416	+	1.30416i	0.925558	+	0.378607i	$0.123597\pi$
$107$	13.4904	+	13.4904i	1.30416	+	1.30416i	0.378607	+	0.925558i	$0.376403\pi$
$108$		0			0
$109$	7.26795	−	7.26795i	0.696143	−	0.696143i	−0.267433	−	0.963576i	$-0.586175\pi$
$109$	7.26795	−	7.26795i	0.696143	−	0.696143i	0.963576	+	0.267433i	$0.0861754\pi$
$110$		0			0
$111$	3.00000	+	0.803848i	0.284747	+	0.0762978i
$112$		0			0
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	−0.330947	−	0.943649i	$-0.607368\pi$
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	0.982698	−	0.185216i	$-0.0592984\pi$
$114$		0			0
$115$	−4.73205	−	1.26795i	−0.441266	−	0.118237i
$116$		0			0
$117$	−18.2942	−	4.90192i	−1.69130	−	0.453183i
$118$		0			0
$119$	−1.43782	+	0.830127i	−0.131805	+	0.0760976i
$120$		0			0
$121$	1.90192	+	1.09808i	0.172902	+	0.0998251i
$122$		0			0
$123$	−5.19615			−0.468521
$124$		0			0
$125$	−13.4641	+	13.4641i	−1.20427	+	1.20427i
$126$		0			0
$127$	6.19615			0.549820			0.274910	−	0.961470i	$-0.411352\pi$
$127$	6.19615			0.549820			0.274910	+	0.961470i	$0.411352\pi$
$128$		0			0
$129$	0.571797	+	2.13397i	0.0503439	+	0.187886i
$130$		0			0
$131$	−0.830127	−	3.09808i	−0.0725285	−	0.270680i	0.920133	−	0.391606i	$-0.128080\pi$
$131$	−0.830127	−	3.09808i	−0.0725285	−	0.270680i	−0.992662	+	0.120926i	$0.961414\pi$
$132$		0			0
$133$	0.169873	−	0.633975i	0.0147299	−	0.0549726i
$134$		0			0
$135$	5.19615	+	19.3923i	0.447214	+	1.66902i
$136$		0			0
$137$	14.2583	−	8.23205i	1.21817	−	0.703312i	0.253645	−	0.967297i	$-0.418371\pi$
$137$	14.2583	−	8.23205i	1.21817	−	0.703312i	0.964527	+	0.263986i	$0.0850372\pi$
$138$		0			0
$139$	9.06218	−	2.42820i	0.768644	−	0.205958i	0.146872	−	0.989156i	$-0.453080\pi$
$139$	9.06218	−	2.42820i	0.768644	−	0.205958i	0.621772	+	0.783198i	$0.286413\pi$
$140$		0			0
$141$	14.4904	+	8.36603i	1.22031	+	0.704546i
$142$		0			0
$143$	−18.7321			−1.56645
$144$		0			0
$145$	9.46410			0.785951
$146$		0			0
$147$			11.1962i			0.923443i
$148$		0			0
$149$	3.09808	−	0.830127i	0.253804	−	0.0680067i	−0.129674	−	0.991557i	$-0.541393\pi$
$149$	3.09808	−	0.830127i	0.253804	−	0.0680067i	0.383478	+	0.923550i	$0.374726\pi$
$150$		0			0
$151$	2.36603	−	1.36603i	0.192544	−	0.111166i	−0.400629	−	0.916240i	$-0.631208\pi$
$151$	2.36603	−	1.36603i	0.192544	−	0.111166i	0.593173	+	0.805075i	$0.297875\pi$
$152$		0			0
$153$	−3.40192	+	5.89230i	−0.275029	+	0.476365i
$154$		0			0
$155$	−7.46410	+	27.8564i	−0.599531	+	2.23748i
$156$		0			0
$157$	−1.26795	−	4.73205i	−0.101193	−	0.377659i	0.896692	−	0.442655i	$-0.145963\pi$
$157$	−1.26795	−	4.73205i	−0.101193	−	0.377659i	−0.997886	+	0.0649959i	$0.979297\pi$
$158$		0			0
$159$	−1.26795	−	0.339746i	−0.100555	−	0.0269436i
$160$		0			0
$161$	0.928203			0.0731527
$162$		0			0
$163$	7.00000	−	7.00000i	0.548282	−	0.548282i	−0.377661	−	0.925944i	$-0.623272\pi$
$163$	7.00000	−	7.00000i	0.548282	−	0.548282i	0.925944	+	0.377661i	$0.123272\pi$
$164$		0			0
$165$	9.92820	+	17.1962i	0.772910	+	1.33872i
$166$		0			0
$167$	−0.464102	−	0.267949i	−0.0359133	−	0.0207345i	0.481936	−	0.876206i	$-0.339934\pi$
$167$	−0.464102	−	0.267949i	−0.0359133	−	0.0207345i	−0.517849	+	0.855472i	$0.673267\pi$
$168$		0			0
$169$	−23.2583	+	13.4282i	−1.78910	+	1.03294i
$170$		0			0
$171$	−0.696152	−	2.59808i	−0.0532361	−	0.198680i
$172$		0			0
$173$	−12.5622	−	3.36603i	−0.955085	−	0.255914i	−0.252566	−	0.967580i	$-0.581275\pi$
$173$	−12.5622	−	3.36603i	−0.955085	−	0.255914i	−0.702519	+	0.711665i	$0.747941\pi$
$174$		0			0
$175$	3.63397	−	6.29423i	0.274703	−	0.475799i
$176$		0			0
$177$	−6.29423	+	6.29423i	−0.473103	+	0.473103i
$178$		0			0
$179$	−11.9282	+	11.9282i	−0.891556	+	0.891556i	−0.994670	−	0.103114i	$-0.967119\pi$
$179$	−11.9282	+	11.9282i	−0.891556	+	0.891556i	0.103114	+	0.994670i	$0.467119\pi$
$180$		0			0
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	0.999990	−	0.00454748i	$-0.00144751\pi$
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	−0.00454748	+	0.999990i	$0.501448\pi$
$182$		0			0
$183$	−5.19615	+	1.39230i	−0.384111	+	0.102922i
$184$		0			0
$185$	−6.00000	−	3.46410i	−0.441129	−	0.254686i
$186$		0			0
$187$	−1.74167	+	6.50000i	−0.127364	+	0.475327i
$188$		0			0
$189$	−1.90192	−	3.29423i	−0.138345	−	0.239620i
$190$		0			0
$191$	−7.02628	−	12.1699i	−0.508404	−	0.880581i	−0.999953	−	0.00973114i	$-0.996902\pi$
$191$	−7.02628	−	12.1699i	−0.508404	−	0.880581i	0.491549	−	0.870850i	$-0.336431\pi$
$192$		0			0
$193$	−9.13397	+	15.8205i	−0.657478	+	1.13879i	0.323789	+	0.946129i	$0.395043\pi$
$193$	−9.13397	+	15.8205i	−0.657478	+	1.13879i	−0.981266	+	0.192656i	$0.938290\pi$
$194$		0			0
$195$	36.5885	+	21.1244i	2.62015	+	1.51275i
$196$		0			0
$197$	−3.66025	−	3.66025i	−0.260782	−	0.260782i	0.564590	−	0.825372i	$-0.309034\pi$
$197$	−3.66025	−	3.66025i	−0.260782	−	0.260782i	−0.825372	+	0.564590i	$0.809034\pi$
$198$		0			0
$199$			0.875644i			0.0620728i	0.999518	+	0.0310364i	$0.00988078\pi$
$199$			0.875644i			0.0620728i	−0.999518	+	0.0310364i	$0.990119\pi$
$200$		0			0
$201$	−6.63397	−	6.63397i	−0.467924	−	0.467924i
$202$		0			0
$203$	−1.73205	+	0.464102i	−0.121566	+	0.0325735i
$204$		0			0
$205$	11.1962	+	3.00000i	0.781973	+	0.209529i
$206$		0			0
$207$	3.29423	−	1.90192i	0.228965	−	0.132193i
$208$		0			0
$209$	−1.33013	−	2.30385i	−0.0920068	−	0.159360i
$210$		0			0
$211$	1.09808	+	4.09808i	0.0755947	+	0.282123i	0.993367	−	0.114983i	$-0.0366812\pi$
$211$	1.09808	+	4.09808i	0.0755947	+	0.282123i	−0.917773	+	0.397106i	$0.870015\pi$
$212$		0			0
$213$	−9.46410	−	16.3923i	−0.648470	−	1.12318i
$214$		0			0
$215$		−	4.92820i		−	0.336101i
$216$		0			0
$217$		−	5.46410i		−	0.370927i
$218$		0			0
$219$	8.42820	+	14.5981i	0.569525	+	0.986447i
$220$		0			0
$221$	3.70577	+	13.8301i	0.249277	+	0.930315i
$222$		0			0
$223$	−11.0263	−	19.0981i	−0.738374	−	1.27890i	−0.953227	−	0.302255i	$-0.902260\pi$
$223$	−11.0263	−	19.0981i	−0.738374	−	1.27890i	0.214853	−	0.976646i	$-0.431073\pi$
$224$		0			0
$225$		−	29.7846i		−	1.98564i
$226$		0			0
$227$	14.4282	+	3.86603i	0.957633	+	0.256597i	0.703598	−	0.710598i	$-0.251575\pi$
$227$	14.4282	+	3.86603i	0.957633	+	0.256597i	0.254035	+	0.967195i	$0.418242\pi$
$228$		0			0
$229$	6.83013	−	1.83013i	0.451347	−	0.120938i	−0.0259823	−	0.999662i	$-0.508271\pi$
$229$	6.83013	−	1.83013i	0.451347	−	0.120938i	0.477330	+	0.878724i	$0.341605\pi$
$230$		0			0
$231$	−2.66025	−	2.66025i	−0.175032	−	0.175032i
$232$		0			0
$233$		−	7.19615i		−	0.471436i	−0.971822	−	0.235718i	$-0.924256\pi$
$233$		−	7.19615i		−	0.471436i	0.971822	−	0.235718i	$-0.0757441\pi$
$234$		0			0
$235$	−26.3923	−	26.3923i	−1.72164	−	1.72164i
$236$		0			0
$237$	18.0000	+	10.3923i	1.16923	+	0.675053i
$238$		0			0
$239$	13.0981	−	22.6865i	0.847244	−	1.46747i	−0.0364139	−	0.999337i	$-0.511593\pi$
$239$	13.0981	−	22.6865i	0.847244	−	1.46747i	0.883658	−	0.468133i	$-0.155073\pi$
$240$		0			0
$241$	−6.40192	−	11.0885i	−0.412384	−	0.714270i	0.582766	−	0.812640i	$-0.301971\pi$
$241$	−6.40192	−	11.0885i	−0.412384	−	0.714270i	−0.995150	+	0.0983699i	$0.968637\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$		0			0
$245$	6.46410	−	24.1244i	0.412976	−	1.54125i
$246$		0			0
$247$	−4.90192	−	2.83013i	−0.311902	−	0.180077i
$248$		0			0
$249$	2.36603	−	0.633975i	0.149941	−	0.0401765i
$250$		0			0
$251$	−2.83013	−	2.83013i	−0.178636	−	0.178636i	0.612125	−	0.790761i	$-0.290315\pi$
$251$	−2.83013	−	2.83013i	−0.178636	−	0.178636i	−0.790761	+	0.612125i	$0.790315\pi$
$252$		0			0
$253$	2.66025	−	2.66025i	0.167249	−	0.167249i
$254$		0			0
$255$	10.7321	−	10.7321i	0.672067	−	0.672067i
$256$		0			0
$257$	−4.42820	+	7.66987i	−0.276224	+	0.478434i	−0.970443	−	0.241330i	$-0.922416\pi$
$257$	−4.42820	+	7.66987i	−0.276224	+	0.478434i	0.694219	+	0.719763i	$0.255750\pi$
$258$		0			0
$259$	1.26795	+	0.339746i	0.0787865	+	0.0211108i
$260$		0			0
$261$	−5.19615	+	5.19615i	−0.321634	+	0.321634i
$262$		0			0
$263$	23.4904	−	13.5622i	1.44848	−	0.836280i	0.450088	−	0.892984i	$-0.351393\pi$
$263$	23.4904	−	13.5622i	1.44848	−	0.836280i	0.998391	+	0.0567045i	$0.0180593\pi$
$264$		0			0
$265$	2.53590	+	1.46410i	0.155779	+	0.0899390i
$266$		0			0
$267$	1.73205	+	3.00000i	0.106000	+	0.183597i
$268$		0			0
$269$	4.73205	−	4.73205i	0.288518	−	0.288518i	−0.547976	−	0.836494i	$-0.684601\pi$
$269$	4.73205	−	4.73205i	0.288518	−	0.288518i	0.836494	+	0.547976i	$0.184601\pi$
$270$		0			0
$271$	−20.3923			−1.23874			−0.619372	−	0.785098i	$-0.712613\pi$
$271$	−20.3923			−1.23874			−0.619372	+	0.785098i	$0.712613\pi$
$272$		0			0
$273$	−7.73205	−	2.07180i	−0.467965	−	0.125391i
$274$		0			0
$275$	−7.62436	−	28.4545i	−0.459766	−	1.71587i
$276$		0			0
$277$	−4.22243	+	15.7583i	−0.253701	+	0.946826i	0.715107	+	0.699015i	$0.246378\pi$
$277$	−4.22243	+	15.7583i	−0.253701	+	0.946826i	−0.968808	+	0.247811i	$0.920289\pi$
$278$		0			0
$279$	−11.1962	−	19.3923i	−0.670296	−	1.16099i
$280$		0			0
$281$	−8.66025	+	5.00000i	−0.516627	+	0.298275i	−0.735554	−	0.677466i	$-0.763078\pi$
$281$	−8.66025	+	5.00000i	−0.516627	+	0.298275i	0.218926	+	0.975741i	$0.429745\pi$
$282$		0			0
$283$	−27.7583	+	7.43782i	−1.65006	+	0.442133i	−0.959630	−	0.281265i	$-0.909246\pi$
$283$	−27.7583	+	7.43782i	−1.65006	+	0.442133i	−0.690431	+	0.723398i	$0.742579\pi$
$284$		0			0
$285$			6.00000i			0.355409i
$286$		0			0
$287$	−2.19615			−0.129635
$288$		0			0
$289$	−11.8564			−0.697436
$290$		0			0
$291$	−12.4019	−	7.16025i	−0.727014	−	0.419742i
$292$		0			0
$293$	13.5622	−	3.63397i	0.792311	−	0.212299i	0.160106	−	0.987100i	$-0.448817\pi$
$293$	13.5622	−	3.63397i	0.792311	−	0.212299i	0.632205	+	0.774801i	$0.282150\pi$
$294$		0			0
$295$	17.1962	−	9.92820i	1.00120	−	0.578042i
$296$		0			0
$297$	−14.8923	−	3.99038i	−0.864139	−	0.231545i
$298$		0			0
$299$	2.07180	−	7.73205i	0.119815	−	0.447156i
$300$		0			0
$301$	0.241670	+	0.901924i	0.0139296	+	0.0519860i
$302$		0			0
$303$	3.46410	+	12.9282i	0.199007	+	0.742706i
$304$		0			0
$305$	12.0000			0.687118
$306$		0			0
$307$	16.0263	−	16.0263i	0.914668	−	0.914668i	−0.0819670	−	0.996635i	$-0.526120\pi$
$307$	16.0263	−	16.0263i	0.914668	−	0.914668i	0.996635	+	0.0819670i	$0.0261202\pi$
$308$		0			0
$309$	15.8038			0.899049
$310$		0			0
$311$	−13.9019	−	8.02628i	−0.788306	−	0.455129i	0.0510600	−	0.998696i	$-0.483740\pi$
$311$	−13.9019	−	8.02628i	−0.788306	−	0.455129i	−0.839366	+	0.543567i	$0.817073\pi$
$312$		0			0
$313$	24.6506	−	14.2321i	1.39334	−	0.804443i	0.399653	−	0.916666i	$-0.369131\pi$
$313$	24.6506	−	14.2321i	1.39334	−	0.804443i	0.993683	+	0.112223i	$0.0357972\pi$
$314$		0			0
$315$	2.19615	+	8.19615i	0.123739	+	0.461801i
$316$		0			0
$317$	31.4904	+	8.43782i	1.76868	+	0.473915i	0.988445	−	0.151577i	$-0.0484351\pi$
$317$	31.4904	+	8.43782i	1.76868	+	0.473915i	0.780231	+	0.625492i	$0.215102\pi$
$318$		0			0
$319$	−3.63397	+	6.29423i	−0.203464	+	0.352409i
$320$		0			0
$321$	31.9186	+	8.55256i	1.78152	+	0.477357i
$322$		0			0
$323$	−1.43782	+	1.43782i	−0.0800026	+	0.0800026i
$324$		0			0
$325$	−44.3205	−	44.3205i	−2.45846	−	2.45846i
$326$		0			0
$327$	4.60770	−	17.1962i	0.254806	−	0.950949i
$328$		0			0
$329$	6.12436	+	3.53590i	0.337647	+	0.194940i
$330$		0			0
$331$	−5.09808	+	19.0263i	−0.280216	+	1.04578i	0.672049	+	0.740506i	$0.265414\pi$
$331$	−5.09808	+	19.0263i	−0.280216	+	1.04578i	−0.952265	+	0.305273i	$0.901252\pi$
$332$		0			0
$333$	5.19615	−	1.39230i	0.284747	−	0.0762978i
$334$		0			0
$335$	10.4641	+	18.1244i	0.571715	+	0.990239i
$336$		0			0
$337$	−11.8923	+	20.5981i	−0.647815	+	1.12205i	0.335829	+	0.941923i	$0.390984\pi$
$337$	−11.8923	+	20.5981i	−0.647815	+	1.12205i	−0.983644	+	0.180126i	$0.942350\pi$
$338$		0			0
$339$		−	24.0000i		−	1.30350i
$340$		0			0
$341$	−15.6603	−	15.6603i	−0.848050	−	0.848050i
$342$		0			0
$343$			9.85641i			0.532196i
$344$		0			0
$345$	−8.19615	+	2.19615i	−0.441266	+	0.118237i
$346$		0			0
$347$	24.7224	−	6.62436i	1.32717	−	0.355614i	0.475510	−	0.879710i	$-0.342263\pi$
$347$	24.7224	−	6.62436i	1.32717	−	0.355614i	0.851659	+	0.524096i	$0.175597\pi$
$348$		0			0
$349$	−7.73205	−	2.07180i	−0.413887	−	0.110901i	0.0458657	−	0.998948i	$-0.485395\pi$
$349$	−7.73205	−	2.07180i	−0.413887	−	0.110901i	−0.459753	+	0.888047i	$0.652062\pi$
$350$		0			0
$351$	−31.6865	+	8.49038i	−1.69130	+	0.453183i
$352$		0			0
$353$	−10.1603	−	17.5981i	−0.540776	−	0.936651i	−0.998860	−	0.0477421i	$-0.984797\pi$
$353$	−10.1603	−	17.5981i	−0.540776	−	0.936651i	0.458084	−	0.888909i	$-0.348536\pi$
$354$		0			0
$355$	10.9282	+	40.7846i	0.580009	+	2.16462i
$356$		0			0
$357$	−1.43782	+	2.49038i	−0.0760976	+	0.131805i
$358$		0			0
$359$			14.7321i			0.777528i	0.921337	+	0.388764i	$0.127098\pi$
$359$			14.7321i			0.777528i	−0.921337	+	0.388764i	$0.872902\pi$
$360$		0			0
$361$			18.1962i			0.957692i
$362$		0			0
$363$	3.80385			0.199650
$364$		0			0
$365$	−9.73205	−	36.3205i	−0.509399	−	1.90110i
$366$		0			0
$367$	10.1244	+	17.5359i	0.528487	+	0.915366i	0.999448	+	0.0332125i	$0.0105738\pi$
$367$	10.1244	+	17.5359i	0.528487	+	0.915366i	−0.470961	+	0.882154i	$0.656093\pi$
$368$		0			0
$369$	−7.79423	+	4.50000i	−0.405751	+	0.234261i
$370$		0			0
$371$	−0.535898	−	0.143594i	−0.0278225	−	0.00745501i
$372$		0			0
$373$	−5.63397	+	1.50962i	−0.291716	+	0.0781651i	−0.401709	−	0.915767i	$-0.631584\pi$
$373$	−5.63397	+	1.50962i	−0.291716	+	0.0781651i	0.109993	+	0.993932i	$0.464917\pi$
$374$		0			0
$375$	−8.53590	+	31.8564i	−0.440792	+	1.64506i
$376$		0			0
$377$			15.4641i			0.796442i
$378$		0			0
$379$	18.7583	+	18.7583i	0.963551	+	0.963551i	0.999359	−	0.0358080i	$-0.0114005\pi$
$379$	18.7583	+	18.7583i	0.963551	+	0.963551i	−0.0358080	+	0.999359i	$0.511400\pi$
$380$		0			0
$381$	9.29423	−	5.36603i	0.476158	−	0.274910i
$382$		0			0
$383$	3.26795	−	5.66025i	0.166984	−	0.289225i	−0.770374	−	0.637593i	$-0.779930\pi$
$383$	3.26795	−	5.66025i	0.166984	−	0.289225i	0.937358	+	0.348367i	$0.113264\pi$
$384$		0			0
$385$	4.19615	+	7.26795i	0.213856	+	0.370409i
$386$		0			0
$387$	2.70577	+	2.70577i	0.137542	+	0.137542i
$388$		0			0
$389$	−2.75833	+	10.2942i	−0.139853	+	0.521938i	0.860078	+	0.510163i	$0.170415\pi$
$389$	−2.75833	+	10.2942i	−0.139853	+	0.521938i	−0.999931	+	0.0117752i	$0.996252\pi$
$390$		0			0
$391$	−2.49038	−	1.43782i	−0.125944	−	0.0727138i
$392$		0			0
$393$	−3.92820	−	3.92820i	−0.198152	−	0.198152i
$394$		0			0
$395$	−32.7846	−	32.7846i	−1.64957	−	1.64957i
$396$		0			0
$397$	−12.7321	+	12.7321i	−0.639003	+	0.639003i	−0.950310	−	0.311306i	$-0.899233\pi$
$397$	−12.7321	+	12.7321i	−0.639003	+	0.639003i	0.311306	+	0.950310i	$0.399233\pi$
$398$		0			0
$399$	−0.294229	−	1.09808i	−0.0147299	−	0.0549726i
$400$		0			0
$401$	13.7942	−	23.8923i	0.688851	−	1.19312i	−0.283359	−	0.959014i	$-0.591449\pi$
$401$	13.7942	−	23.8923i	0.688851	−	1.19312i	0.972210	−	0.234111i	$-0.0752179\pi$
$402$		0			0
$403$	−45.5167	−	12.1962i	−2.26735	−	0.607534i
$404$		0			0
$405$	24.5885	+	24.5885i	1.22181	+	1.22181i
$406$		0			0
$407$	4.60770	−	2.66025i	0.228395	−	0.131864i
$408$		0			0
$409$	−26.1340	−	15.0885i	−1.29224	−	0.746076i	−0.313191	−	0.949690i	$-0.601398\pi$
$409$	−26.1340	−	15.0885i	−1.29224	−	0.746076i	−0.979051	+	0.203614i	$0.934731\pi$
$410$		0			0
$411$	14.2583	−	24.6962i	0.703312	−	1.21817i
$412$		0			0
$413$	−2.66025	+	2.66025i	−0.130903	+	0.130903i
$414$		0			0
$415$	−5.46410			−0.268222
$416$		0			0
$417$	11.4904	−	11.4904i	0.562686	−	0.562686i
$418$		0			0
$419$	8.36603	+	31.2224i	0.408707	+	1.52532i	0.797115	+	0.603828i	$0.206359\pi$
$419$	8.36603	+	31.2224i	0.408707	+	1.52532i	−0.388408	+	0.921488i	$0.626975\pi$
$420$		0			0
$421$	0.588457	−	2.19615i	0.0286797	−	0.107034i	−0.950102	−	0.311938i	$-0.899022\pi$
$421$	0.588457	−	2.19615i	0.0286797	−	0.107034i	0.978782	+	0.204905i	$0.0656884\pi$
$422$		0			0
$423$	28.9808			1.40909
$424$		0			0
$425$	−19.5000	+	11.2583i	−0.945889	+	0.546109i
$426$		0			0
$427$	−2.19615	+	0.588457i	−0.106279	+	0.0284774i
$428$		0			0
$429$	−28.0981	+	16.2224i	−1.35659	+	0.783226i
$430$		0			0
$431$	5.80385			0.279562			0.139781	−	0.990182i	$-0.455360\pi$
$431$	5.80385			0.279562			0.139781	+	0.990182i	$0.455360\pi$
$432$		0			0
$433$	−2.26795			−0.108991			−0.0544953	−	0.998514i	$-0.517355\pi$
$433$	−2.26795			−0.108991			−0.0544953	+	0.998514i	$0.517355\pi$
$434$		0			0
$435$	14.1962	−	8.19615i	0.680653	−	0.392975i
$436$		0			0
$437$	1.09808	−	0.294229i	0.0525281	−	0.0140749i
$438$		0			0
$439$	4.85641	−	2.80385i	0.231784	−	0.133820i	−0.379611	−	0.925146i	$-0.623942\pi$
$439$	4.85641	−	2.80385i	0.231784	−	0.133820i	0.611395	+	0.791326i	$0.290609\pi$
$440$		0			0
$441$	9.69615	+	16.7942i	0.461722	+	0.799725i
$442$		0			0
$443$	5.25833	−	19.6244i	0.249831	−	0.932381i	−0.721063	−	0.692870i	$-0.756346\pi$
$443$	5.25833	−	19.6244i	0.249831	−	0.932381i	0.970894	−	0.239511i	$-0.0769873\pi$
$444$		0			0
$445$	−2.00000	−	7.46410i	−0.0948091	−	0.353832i
$446$		0			0
$447$	3.92820	−	3.92820i	0.185798	−	0.185798i
$448$		0			0
$449$	−20.6603			−0.975018			−0.487509	−	0.873118i	$-0.662094\pi$
$449$	−20.6603			−0.975018			−0.487509	+	0.873118i	$0.662094\pi$
$450$		0			0
$451$	−6.29423	+	6.29423i	−0.296384	+	0.296384i
$452$		0			0
$453$	2.36603	−	4.09808i	0.111166	−	0.192544i
$454$		0			0
$455$	15.4641	+	8.92820i	0.724968	+	0.418561i
$456$		0			0
$457$	20.2583	−	11.6962i	0.947645	−	0.547123i	0.0552962	−	0.998470i	$-0.482390\pi$
$457$	20.2583	−	11.6962i	0.947645	−	0.547123i	0.892348	+	0.451347i	$0.149056\pi$
$458$		0			0
$459$			11.7846i			0.550058i
$460$		0			0
$461$	2.56218	+	0.686533i	0.119333	+	0.0319751i	0.317991	−	0.948094i	$-0.396992\pi$
$461$	2.56218	+	0.686533i	0.119333	+	0.0319751i	−0.198659	+	0.980069i	$0.563658\pi$
$462$		0			0
$463$	9.19615	−	15.9282i	0.427381	−	0.740246i	−0.569258	−	0.822159i	$-0.692769\pi$
$463$	9.19615	−	15.9282i	0.427381	−	0.740246i	0.996640	+	0.0819125i	$0.0261028\pi$
$464$		0			0
$465$	12.9282	+	48.2487i	0.599531	+	2.23748i
$466$		0			0
$467$	−4.36603	+	4.36603i	−0.202036	+	0.202036i	−0.800872	−	0.598836i	$-0.795630\pi$
$467$	−4.36603	+	4.36603i	−0.202036	+	0.202036i	0.598836	+	0.800872i	$0.295630\pi$
$468$		0			0
$469$	−2.80385	−	2.80385i	−0.129470	−	0.129470i
$470$		0			0
$471$	−6.00000	−	6.00000i	−0.276465	−	0.276465i
$472$		0			0
$473$	3.27757	+	1.89230i	0.150703	+	0.0870083i
$474$		0			0
$475$	2.30385	−	8.59808i	0.105708	−	0.394507i
$476$		0			0
$477$	−2.19615	+	0.588457i	−0.100555	+	0.0269436i
$478$		0			0
$479$	−12.8301	−	22.2224i	−0.586223	−	1.01537i	−0.994722	−	0.102610i	$-0.967281\pi$
$479$	−12.8301	−	22.2224i	−0.586223	−	1.01537i	0.408498	−	0.912759i	$-0.366053\pi$
$480$		0			0
$481$	5.66025	−	9.80385i	0.258085	−	0.447017i
$482$		0			0
$483$	1.39230	−	0.803848i	0.0633521	−	0.0365763i
$484$		0			0
$485$	22.5885	+	22.5885i	1.02569	+	1.02569i
$486$		0			0
$487$			16.1962i			0.733918i	0.930237	+	0.366959i	$0.119601\pi$
$487$			16.1962i			0.733918i	−0.930237	+	0.366959i	$0.880399\pi$
$488$		0			0
$489$	4.43782	−	16.5622i	0.200685	−	0.748968i
$490$		0			0
$491$	25.7224	−	6.89230i	1.16084	−	0.311045i	0.373537	−	0.927615i	$-0.378145\pi$
$491$	25.7224	−	6.89230i	1.16084	−	0.311045i	0.787300	+	0.616570i	$0.211478\pi$
$492$		0			0
$493$	5.36603	+	1.43782i	0.241674	+	0.0647563i
$494$		0			0
$495$	29.7846	+	17.1962i	1.33872	+	0.772910i
$496$		0			0
$497$	−4.00000	−	6.92820i	−0.179425	−	0.310772i
$498$		0			0
$499$	1.69615	+	6.33013i	0.0759302	+	0.283375i	0.993443	−	0.114332i	$-0.0364727\pi$
$499$	1.69615	+	6.33013i	0.0759302	+	0.283375i	−0.917512	+	0.397707i	$0.869806\pi$
$500$		0			0
$501$	−0.928203			−0.0414691
$502$		0			0
$503$			27.7128i			1.23565i	0.786314	+	0.617827i	$0.211987\pi$
$503$			27.7128i			1.23565i	−0.786314	+	0.617827i	$0.788013\pi$
$504$		0			0
$505$		−	29.8564i		−	1.32859i
$506$		0			0
$507$	−23.2583	+	40.2846i	−1.03294	+	1.78910i
$508$		0			0
$509$	−4.53590	−	16.9282i	−0.201050	−	0.750329i	−0.990617	−	0.136665i	$-0.956362\pi$
$509$	−4.53590	−	16.9282i	−0.201050	−	0.750329i	0.789567	−	0.613664i	$-0.210305\pi$
$510$		0			0
$511$	3.56218	+	6.16987i	0.157581	+	0.272939i
$512$		0			0
$513$	−3.29423	−	3.29423i	−0.145444	−	0.145444i
$514$		0			0
$515$	−34.0526	−	9.12436i	−1.50054	−	0.402067i
$516$		0			0
$517$	27.6865	−	7.41858i	1.21765	−	0.326269i
$518$		0			0
$519$	−21.7583	+	5.83013i	−0.955085	+	0.255914i
$520$		0			0
$521$		−	13.0000i		−	0.569540i	−0.958596	−	0.284770i	$-0.908083\pi$
$521$		−	13.0000i		−	0.569540i	0.958596	−	0.284770i	$-0.0919173\pi$
$522$		0			0
$523$	14.4641	+	14.4641i	0.632471	+	0.632471i	0.948687	−	0.316216i	$-0.102412\pi$
$523$	14.4641	+	14.4641i	0.632471	+	0.632471i	−0.316216	+	0.948687i	$0.602412\pi$
$524$		0			0
$525$		−	12.5885i		−	0.549405i
$526$		0			0
$527$	−8.46410	+	14.6603i	−0.368702	+	0.638611i
$528$		0			0
$529$	−10.6962	−	18.5263i	−0.465050	−	0.805490i
$530$		0			0
$531$	−3.99038	+	14.8923i	−0.173168	+	0.646271i
$532$		0			0
$533$	−4.90192	+	18.2942i	−0.212326	+	0.792411i
$534$		0			0
$535$	−63.8372	−	36.8564i	−2.75992	−	1.59344i
$536$		0			0
$537$	−7.56218	+	28.2224i	−0.326332	+	1.21789i
$538$		0			0
$539$	13.5622	+	13.5622i	0.584164	+	0.584164i
$540$		0			0
$541$	−8.19615	+	8.19615i	−0.352380	+	0.352380i	−0.860994	−	0.508614i	$-0.830158\pi$
$541$	−8.19615	+	8.19615i	−0.352380	+	0.352380i	0.508614	+	0.860994i	$0.330158\pi$
$542$		0			0
$543$	31.6865	+	8.49038i	1.35980	+	0.364357i
$544$		0			0
$545$	−19.8564	+	34.3923i	−0.850555	+	1.47320i
$546$		0			0
$547$	31.2583	+	8.37564i	1.33651	+	0.358117i	0.855138	−	0.518400i	$-0.173472\pi$
$547$	31.2583	+	8.37564i	1.33651	+	0.358117i	0.481371	+	0.876517i	$0.340139\pi$
$548$		0			0
$549$	−6.58846	+	6.58846i	−0.281189	+	0.281189i
$550$		0			0
$551$	−1.90192	+	1.09808i	−0.0810247	+	0.0467796i
$552$		0			0
$553$	7.60770	+	4.39230i	0.323512	+	0.186780i
$554$		0			0
$555$	−12.0000			−0.509372
$556$		0			0
$557$	−25.1962	+	25.1962i	−1.06760	+	1.06760i	−0.0700519	+	0.997543i	$0.522316\pi$
$557$	−25.1962	+	25.1962i	−1.06760	+	1.06760i	−0.997543	+	0.0700519i	$0.977684\pi$
$558$		0			0
$559$	8.05256			0.340587
$560$		0			0
$561$	3.01666	+	11.2583i	0.127364	+	0.475327i
$562$		0			0
$563$	−1.00962	−	3.76795i	−0.0425504	−	0.158800i	0.941382	−	0.337343i	$-0.109528\pi$
$563$	−1.00962	−	3.76795i	−0.0425504	−	0.158800i	−0.983932	+	0.178543i	$0.942862\pi$
$564$		0			0
$565$	−13.8564	+	51.7128i	−0.582943	+	2.17557i
$566$		0			0
$567$	−5.70577	−	3.29423i	−0.239620	−	0.138345i
$568$		0			0
$569$	23.5981	−	13.6244i	0.989283	−	0.571163i	0.0842230	−	0.996447i	$-0.473159\pi$
$569$	23.5981	−	13.6244i	0.989283	−	0.571163i	0.905060	+	0.425284i	$0.139826\pi$
$570$		0			0
$571$	19.8923	−	5.33013i	0.832467	−	0.223059i	0.182677	−	0.983173i	$-0.441524\pi$
$571$	19.8923	−	5.33013i	0.832467	−	0.223059i	0.649790	+	0.760114i	$0.274857\pi$
$572$		0			0
$573$	−21.0788	−	12.1699i	−0.880581	−	0.508404i
$574$		0			0
$575$	12.5885			0.524975
$576$		0			0
$577$	35.7846			1.48973			0.744866	−	0.667214i	$-0.232513\pi$
$577$	35.7846			1.48973			0.744866	+	0.667214i	$0.232513\pi$
$578$		0			0
$579$			31.6410i			1.31496i
$580$		0			0
$581$	1.00000	−	0.267949i	0.0414870	−	0.0111164i
$582$		0			0
$583$	−1.94744	+	1.12436i	−0.0806548	+	0.0465661i
$584$		0			0
$585$	73.1769			3.02549
$586$		0			0
$587$	1.00962	−	3.76795i	0.0416714	−	0.155520i	−0.941955	−	0.335739i	$-0.891014\pi$
$587$	1.00962	−	3.76795i	0.0416714	−	0.155520i	0.983626	+	0.180219i	$0.0576807\pi$
$588$		0			0
$589$	−1.73205	−	6.46410i	−0.0713679	−	0.266349i
$590$		0			0
$591$	−8.66025	−	2.32051i	−0.356235	−	0.0954529i
$592$		0			0
$593$	10.5359			0.432657			0.216329	−	0.976321i	$-0.430592\pi$
$593$	10.5359			0.432657			0.216329	+	0.976321i	$0.430592\pi$
$594$		0			0
$595$	4.53590	−	4.53590i	0.185954	−	0.185954i
$596$		0			0
$597$	0.758330	+	1.31347i	0.0310364	+	0.0537566i
$598$		0			0
$599$	−23.3205	−	13.4641i	−0.952850	−	0.550128i	−0.0588850	−	0.998265i	$-0.518755\pi$
$599$	−23.3205	−	13.4641i	−0.952850	−	0.550128i	−0.893965	+	0.448136i	$0.852088\pi$
$600$		0			0
$601$	−17.5526	+	10.1340i	−0.715984	+	0.413373i	−0.813273	−	0.581883i	$-0.802316\pi$
$601$	−17.5526	+	10.1340i	−0.715984	+	0.413373i	0.0972889	+	0.995256i	$0.468983\pi$
$602$		0			0
$603$	−15.6962	−	4.20577i	−0.639197	−	0.171272i
$604$		0			0
$605$	−8.19615	−	2.19615i	−0.333221	−	0.0892863i
$606$		0			0
$607$	−22.5885	+	39.1244i	−0.916837	+	1.58801i	−0.112648	+	0.993635i	$0.535933\pi$
$607$	−22.5885	+	39.1244i	−0.916837	+	1.58801i	−0.804189	+	0.594374i	$0.797400\pi$
$608$		0			0
$609$	−2.19615	+	2.19615i	−0.0889926	+	0.0889926i
$610$		0			0
$611$	43.1244	−	43.1244i	1.74462	−	1.74462i
$612$		0			0
$613$	1.66025	+	1.66025i	0.0670570	+	0.0670570i	0.739840	−	0.672783i	$-0.234901\pi$
$613$	1.66025	+	1.66025i	0.0670570	+	0.0670570i	−0.672783	+	0.739840i	$0.734901\pi$
$614$		0			0
$615$	19.3923	−	5.19615i	0.781973	−	0.209529i
$616$		0			0
$617$	3.91154	+	2.25833i	0.157473	+	0.0909170i	0.576666	−	0.816980i	$-0.304354\pi$
$617$	3.91154	+	2.25833i	0.157473	+	0.0909170i	−0.419193	+	0.907897i	$0.637687\pi$
$618$		0			0
$619$	10.4019	−	38.8205i	0.418089	−	1.56033i	−0.360479	−	0.932767i	$-0.617387\pi$
$619$	10.4019	−	38.8205i	0.418089	−	1.56033i	0.778568	−	0.627561i	$-0.215947\pi$
$620$		0			0
$621$	3.29423	−	5.70577i	0.132193	−	0.228965i
$622$		0			0
$623$	0.732051	+	1.26795i	0.0293290	+	0.0507993i
$624$		0			0
$625$	11.9641	−	20.7224i	0.478564	−	0.828897i
$626$		0			0
$627$	−3.99038	−	2.30385i	−0.159360	−	0.0920068i
$628$		0			0
$629$	−2.87564	−	2.87564i	−0.114659	−	0.114659i
$630$		0			0
$631$			38.3923i			1.52837i	0.644995	+	0.764187i	$0.276859\pi$
$631$			38.3923i			1.52837i	−0.644995	+	0.764187i	$0.723141\pi$
$632$		0			0
$633$	5.19615	+	5.19615i	0.206529	+	0.206529i
$634$		0			0
$635$	−23.1244	+	6.19615i	−0.917662	+	0.245887i
$636$		0			0
$637$	39.4186	+	10.5622i	1.56182	+	0.418489i
$638$		0			0
$639$	−28.3923	−	16.3923i	−1.12318	−	0.648470i
$640$		0			0
$641$	−4.20577	−	7.28461i	−0.166118	−	0.287725i	0.770934	−	0.636915i	$-0.219790\pi$
$641$	−4.20577	−	7.28461i	−0.166118	−	0.287725i	−0.937052	+	0.349191i	$0.886457\pi$
$642$		0			0
$643$	−12.2321	−	45.6506i	−0.482385	−	1.80029i	−0.591558	−	0.806263i	$-0.701487\pi$
$643$	−12.2321	−	45.6506i	−0.482385	−	1.80029i	0.109173	−	0.994023i	$-0.465180\pi$
$644$		0			0
$645$	−4.26795	−	7.39230i	−0.168050	−	0.291072i
$646$		0			0
$647$			13.2679i			0.521617i	0.965391	+	0.260808i	$0.0839891\pi$
$647$			13.2679i			0.521617i	−0.965391	+	0.260808i	$0.916011\pi$
$648$		0			0
$649$			15.2487i			0.598564i
$650$		0			0
$651$	−4.73205	−	8.19615i	−0.185464	−	0.321233i
$652$		0			0
$653$	−1.50962	−	5.63397i	−0.0590760	−	0.220474i	0.930077	−	0.367365i	$-0.119740\pi$
$653$	−1.50962	−	5.63397i	−0.0590760	−	0.220474i	−0.989153	+	0.146891i	$0.953073\pi$
$654$		0			0
$655$	6.19615	+	10.7321i	0.242104	+	0.419336i
$656$		0			0
$657$	25.2846	+	14.5981i	0.986447	+	0.569525i
$658$		0			0
$659$	15.0263	+	4.02628i	0.585341	+	0.156842i	0.539323	−	0.842099i	$-0.318680\pi$
$659$	15.0263	+	4.02628i	0.585341	+	0.156842i	0.0460178	+	0.998941i	$0.485347\pi$
$660$		0			0
$661$	−8.19615	+	2.19615i	−0.318793	+	0.0854204i	−0.414667	−	0.909973i	$-0.636102\pi$
$661$	−8.19615	+	2.19615i	−0.318793	+	0.0854204i	0.0958740	+	0.995393i	$0.469435\pi$
$662$		0			0
$663$	17.5359	+	17.5359i	0.681038	+	0.681038i
$664$		0			0
$665$			2.53590i			0.0983379i
$666$		0			0
$667$	−2.19615	−	2.19615i	−0.0850354	−	0.0850354i
$668$		0			0
$669$	−33.0788	−	19.0981i	−1.27890	−	0.738374i
$670$		0			0
$671$	−4.60770	+	7.98076i	−0.177878	+	0.308094i
$672$		0			0
$673$	8.80385	+	15.2487i	0.339363	+	0.587795i	0.984313	−	0.176430i	$-0.0564550\pi$
$673$	8.80385	+	15.2487i	0.339363	+	0.587795i	−0.644950	+	0.764225i	$0.723122\pi$
$674$		0			0
$675$	−25.7942	−	44.6769i	−0.992820	−	1.71962i
$676$		0			0
$677$	−1.26795	+	4.73205i	−0.0487312	+	0.181867i	−0.986002	−	0.166736i	$-0.946677\pi$
$677$	−1.26795	+	4.73205i	−0.0487312	+	0.181867i	0.937270	+	0.348603i	$0.113344\pi$
$678$		0			0
$679$	−5.24167	−	3.02628i	−0.201157	−	0.116138i
$680$		0			0
$681$	24.9904	−	6.69615i	0.957633	−	0.256597i
$682$		0			0
$683$	4.70577	+	4.70577i	0.180061	+	0.180061i	0.791383	−	0.611321i	$-0.209362\pi$
$683$	4.70577	+	4.70577i	0.180061	+	0.180061i	−0.611321	+	0.791383i	$0.709362\pi$
$684$		0			0
$685$	−44.9808	+	44.9808i	−1.71863	+	1.71863i
$686$		0			0
$687$	8.66025	−	8.66025i	0.330409	−	0.330409i
$688$		0			0
$689$	−2.39230	+	4.14359i	−0.0911396	+	0.157858i
$690$		0			0
$691$	−23.4904	−	6.29423i	−0.893616	−	0.239444i	−0.217344	−	0.976095i	$-0.569739\pi$
$691$	−23.4904	−	6.29423i	−0.893616	−	0.239444i	−0.676273	+	0.736651i	$0.736406\pi$
$692$		0			0
$693$	−6.29423	−	1.68653i	−0.239098	−	0.0640661i
$694$		0			0
$695$	−31.3923	+	18.1244i	−1.19078	+	0.687496i
$696$		0			0
$697$	5.89230	+	3.40192i	0.223187	+	0.128857i
$698$		0			0
$699$	−6.23205	−	10.7942i	−0.235718	−	0.408275i
$700$		0			0
$701$	10.6603	−	10.6603i	0.402632	−	0.402632i	−0.476527	−	0.879160i	$-0.658105\pi$
$701$	10.6603	−	10.6603i	0.402632	−	0.402632i	0.879160	+	0.476527i	$0.158105\pi$
$702$		0			0
$703$	1.60770			0.0606354
$704$		0			0
$705$	−62.4449	−	16.7321i	−2.35181	−	0.630165i
$706$		0			0
$707$	1.46410	+	5.46410i	0.0550632	+	0.205499i
$708$		0			0
$709$	5.41154	−	20.1962i	0.203235	−	0.758482i	−0.786746	−	0.617277i	$-0.788236\pi$
$709$	5.41154	−	20.1962i	0.203235	−	0.758482i	0.989980	−	0.141205i	$-0.0450977\pi$
$710$		0			0
$711$	36.0000			1.35011
$712$		0			0
$713$	8.19615	−	4.73205i	0.306948	−	0.177217i
$714$		0			0
$715$	69.9090	−	18.7321i	2.61445	−	0.700539i
$716$		0			0
$717$		−	45.3731i		−	1.69449i
$718$		0			0
$719$	16.3923			0.611330			0.305665	−	0.952139i	$-0.401121\pi$
$719$	16.3923			0.611330			0.305665	+	0.952139i	$0.401121\pi$
$720$		0			0
$721$	6.67949			0.248757
$722$		0			0
$723$	−19.2058	−	11.0885i	−0.714270	−	0.412384i
$724$		0			0
$725$	−23.4904	+	6.29423i	−0.872411	+	0.233762i
$726$		0			0
$727$	31.8109	−	18.3660i	1.17980	−	0.681158i	0.223832	−	0.974628i	$-0.428143\pi$
$727$	31.8109	−	18.3660i	1.17980	−	0.681158i	0.955968	+	0.293470i	$0.0948099\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	0.748711	−	2.79423i	0.0276921	−	0.103348i
$732$		0			0
$733$	8.02628	+	29.9545i	0.296457	+	1.10639i	0.940053	+	0.341028i	$0.110775\pi$
$733$	8.02628	+	29.9545i	0.296457	+	1.10639i	−0.643596	+	0.765366i	$0.722558\pi$
$734$		0			0
$735$	−11.1962	−	41.7846i	−0.412976	−	1.54125i
$736$		0			0
$737$	−16.0718			−0.592012
$738$		0			0
$739$	−21.2224	+	21.2224i	−0.780680	+	0.780680i	−0.979945	−	0.199266i	$-0.936144\pi$
$739$	−21.2224	+	21.2224i	−0.780680	+	0.780680i	0.199266	+	0.979945i	$0.436144\pi$
$740$		0			0
$741$	−9.80385			−0.360153
$742$		0			0
$743$	2.24167	+	1.29423i	0.0822389	+	0.0474806i	0.540556	−	0.841308i	$-0.318214\pi$
$743$	2.24167	+	1.29423i	0.0822389	+	0.0474806i	−0.458317	+	0.888789i	$0.651547\pi$
$744$		0			0
$745$	−10.7321	+	6.19615i	−0.393192	+	0.227009i
$746$		0			0
$747$	3.00000	−	3.00000i	0.109764	−	0.109764i
$748$		0			0
$749$	13.4904	+	3.61474i	0.492928	+	0.132080i
$750$		0			0
$751$	−18.8564	+	32.6603i	−0.688080	+	1.19179i	0.284378	+	0.958712i	$0.408213\pi$
$751$	−18.8564	+	32.6603i	−0.688080	+	1.19179i	−0.972458	+	0.233077i	$0.925120\pi$
$752$		0			0
$753$	−6.69615	−	1.79423i	−0.244021	−	0.0653853i
$754$		0			0
$755$	−7.46410	+	7.46410i	−0.271646	+	0.271646i
$756$		0			0
$757$	−6.07180	−	6.07180i	−0.220683	−	0.220683i	0.588103	−	0.808786i	$-0.299875\pi$
$757$	−6.07180	−	6.07180i	−0.220683	−	0.220683i	−0.808786	+	0.588103i	$0.799875\pi$
$758$		0			0
$759$	1.68653	−	6.29423i	0.0612173	−	0.228466i
$760$		0			0
$761$	27.3731	+	15.8038i	0.992273	+	0.572889i	0.905953	−	0.423378i	$-0.139156\pi$
$761$	27.3731	+	15.8038i	0.992273	+	0.572889i	0.0863200	+	0.996267i	$0.472489\pi$
$762$		0			0
$763$	1.94744	−	7.26795i	0.0705021	−	0.263117i
$764$		0			0
$765$	6.80385	−	25.3923i	0.245994	−	0.918061i
$766$		0			0
$767$	16.2224	+	28.0981i	0.585758	+	1.01456i
$768$		0			0
$769$	10.1244	−	17.5359i	0.365094	−	0.632361i	−0.623698	−	0.781666i	$-0.714370\pi$
$769$	10.1244	−	17.5359i	0.365094	−	0.632361i	0.988791	+	0.149305i	$0.0477036\pi$
$770$		0			0
$771$			15.3397i			0.552447i
$772$		0			0
$773$	4.41154	+	4.41154i	0.158672	+	0.158672i	0.781978	−	0.623306i	$-0.214211\pi$
$773$	4.41154	+	4.41154i	0.158672	+	0.158672i	−0.623306	+	0.781978i	$0.714211\pi$
$774$		0			0
$775$		−	74.1051i		−	2.66193i
$776$		0			0
$777$	2.19615	−	0.588457i	0.0787865	−	0.0211108i
$778$		0			0
$779$	−2.59808	+	0.696152i	−0.0930857	+	0.0249422i
$780$		0			0
$781$	−31.3205	−	8.39230i	−1.12074	−	0.300300i
$782$		0			0
$783$	−3.29423	+	12.2942i	−0.117726	+	0.439360i
$784$		0			0
$785$	9.46410	+	16.3923i	0.337788	+	0.585066i
$786$		0			0
$787$	13.3468	+	49.8109i	0.475762	+	1.77557i	0.618477	+	0.785803i	$0.287750\pi$
$787$	13.3468	+	49.8109i	0.475762	+	1.77557i	−0.142716	+	0.989764i	$0.545583\pi$
$788$		0			0
$789$	23.4904	−	40.6865i	0.836280	−	1.44848i
$790$		0			0
$791$		−	10.1436i		−	0.360665i
$792$		0			0
$793$			19.6077i			0.696290i
$794$		0			0
$795$	5.07180			0.179878
$796$		0			0
$797$	14.5167	+	54.1769i	0.514206	+	1.91904i	0.368142	+	0.929770i	$0.379994\pi$
$797$	14.5167	+	54.1769i	0.514206	+	1.91904i	0.146065	+	0.989275i	$0.453339\pi$
$798$		0			0
$799$	−10.9545	−	18.9737i	−0.387542	−	0.671242i
$800$		0			0
$801$	5.19615	+	3.00000i	0.183597	+	0.106000i
$802$		0			0
$803$	27.8923	+	7.47372i	0.984298	+	0.263742i
$804$		0			0
$805$	−3.46410	+	0.928203i	−0.122094	+	0.0327149i
$806$		0			0
$807$	3.00000	−	11.1962i	0.105605	−	0.394123i
$808$		0			0
$809$		−	28.3205i		−	0.995696i	−0.867264	−	0.497848i	$-0.834124\pi$
$809$		−	28.3205i		−	0.995696i	0.867264	−	0.497848i	$-0.165876\pi$
$810$		0			0
$811$	−5.02628	−	5.02628i	−0.176497	−	0.176497i	0.613330	−	0.789827i	$-0.289830\pi$
$811$	−5.02628	−	5.02628i	−0.176497	−	0.176497i	−0.789827	+	0.613330i	$0.789830\pi$
$812$		0			0
$813$	−30.5885	+	17.6603i	−1.07278	+	0.619372i
$814$		0			0
$815$	−19.1244	+	33.1244i	−0.669897	+	1.16030i
$816$		0			0
$817$	0.571797	+	0.990381i	0.0200046	+	0.0346490i
$818$		0			0
$819$	−13.3923	+	3.58846i	−0.467965	+	0.125391i
$820$		0			0
$821$	−8.63397	+	32.2224i	−0.301328	+	1.12457i	0.634733	+	0.772732i	$0.281110\pi$
$821$	−8.63397	+	32.2224i	−0.301328	+	1.12457i	−0.936061	+	0.351839i	$0.885556\pi$
$822$		0			0
$823$	10.7321	+	6.19615i	0.374096	+	0.215984i	0.675246	−	0.737592i	$-0.264037\pi$
$823$	10.7321	+	6.19615i	0.374096	+	0.215984i	−0.301151	+	0.953577i	$0.597371\pi$
$824$		0			0
$825$	−36.0788	−	36.0788i	−1.25610	−	1.25610i
$826$		0			0
$827$	−24.4641	−	24.4641i	−0.850700	−	0.850700i	0.139519	−	0.990219i	$-0.455444\pi$
$827$	−24.4641	−	24.4641i	−0.850700	−	0.850700i	−0.990219	+	0.139519i	$0.955444\pi$
$828$		0			0
$829$	24.5167	−	24.5167i	0.851499	−	0.851499i	−0.138819	−	0.990318i	$-0.544331\pi$
$829$	24.5167	−	24.5167i	0.851499	−	0.851499i	0.990318	+	0.138819i	$0.0443306\pi$
$830$		0			0
$831$	7.31347	+	27.2942i	0.253701	+	0.946826i
$832$		0			0
$833$	7.33013	−	12.6962i	0.253974	−	0.439896i
$834$		0			0
$835$	2.00000	+	0.535898i	0.0692129	+	0.0185455i
$836$		0			0
$837$	−33.5885	−	19.3923i	−1.16099	−	0.670296i
$838$		0			0
$839$	−35.4449	+	20.4641i	−1.22369	+	0.706499i	−0.965703	−	0.259649i	$-0.916393\pi$
$839$	−35.4449	+	20.4641i	−1.22369	+	0.706499i	−0.257989	+	0.966148i	$0.583060\pi$
$840$		0			0
$841$	−19.9186	−	11.5000i	−0.686848	−	0.396552i
$842$		0			0
$843$	−8.66025	+	15.0000i	−0.298275	+	0.516627i
$844$		0			0
$845$	73.3731	−	73.3731i	2.52411	−	2.52411i
$846$		0			0
$847$	1.60770			0.0552411
$848$		0			0
$849$	−35.1962	+	35.1962i	−1.20793	+	1.20793i
$850$		0			0
$851$	0.588457	+	2.19615i	0.0201721	+	0.0752831i
$852$		0			0
$853$	3.36603	−	12.5622i	0.115251	−	0.430121i	−0.884055	−	0.467383i	$-0.845197\pi$
$853$	3.36603	−	12.5622i	0.115251	−	0.430121i	0.999306	+	0.0372621i	$0.0118636\pi$
$854$		0			0
$855$	5.19615	+	9.00000i	0.177705	+	0.307794i
$856$		0			0
$857$	−20.9090	+	12.0718i	−0.714237	+	0.412365i	−0.812628	−	0.582783i	$-0.801964\pi$
$857$	−20.9090	+	12.0718i	−0.714237	+	0.412365i	0.0983911	+	0.995148i	$0.468630\pi$
$858$		0			0
$859$	−30.8205	+	8.25833i	−1.05158	+	0.281771i	−0.742905	−	0.669396i	$-0.766553\pi$
$859$	−30.8205	+	8.25833i	−1.05158	+	0.281771i	−0.308677	+	0.951167i	$0.599886\pi$
$860$		0			0
$861$	−3.29423	+	1.90192i	−0.112267	+	0.0648174i
$862$		0			0
$863$	8.53590			0.290565			0.145283	−	0.989390i	$-0.453591\pi$
$863$	8.53590			0.290565			0.145283	+	0.989390i	$0.453591\pi$
$864$		0			0
$865$	50.2487			1.70851
$866$		0			0
$867$	−17.7846	+	10.2679i	−0.603997	+	0.348718i
$868$		0			0
$869$	34.3923	−	9.21539i	1.16668	−	0.312611i
$870$		0			0
$871$	−29.6147	+	17.0981i	−1.00346	+	0.579346i
$872$		0			0
$873$	−24.8038			−0.839483
$874$		0			0
$875$	−3.60770	+	13.4641i	−0.121962	+	0.455170i
$876$		0			0
$877$	0.411543	+	1.53590i	0.0138968	+	0.0518636i	0.972526	−	0.232794i	$-0.0747868\pi$
$877$	0.411543	+	1.53590i	0.0138968	+	0.0518636i	−0.958629	+	0.284658i	$0.908120\pi$
$878$		0			0
$879$	17.1962	−	17.1962i	0.580012	−	0.580012i
$880$		0			0
$881$	−7.32051			−0.246634			−0.123317	−	0.992367i	$-0.539353\pi$
$881$	−7.32051			−0.246634			−0.123317	+	0.992367i	$0.539353\pi$
$882$		0			0
$883$	14.3660	−	14.3660i	0.483455	−	0.483455i	−0.422778	−	0.906233i	$-0.638945\pi$
$883$	14.3660	−	14.3660i	0.483455	−	0.483455i	0.906233	+	0.422778i	$0.138945\pi$
$884$		0			0
$885$	17.1962	−	29.7846i	0.578042	−	1.00120i
$886$		0			0
$887$	33.1244	+	19.1244i	1.11221	+	0.642133i	0.939400	−	0.342823i	$-0.111383\pi$
$887$	33.1244	+	19.1244i	1.11221	+	0.642133i	0.172807	+	0.984956i	$0.444716\pi$
$888$		0			0
$889$	3.92820	−	2.26795i	0.131748	−	0.0760646i
$890$		0			0
$891$	−25.7942	+	6.91154i	−0.864139	+	0.231545i
$892$		0			0
$893$	8.36603	+	2.24167i	0.279958	+	0.0750146i
$894$		0			0
$895$	32.5885	−	56.4449i	1.08931	−	1.88674i
$896$		0			0
$897$	−3.58846	−	13.3923i	−0.119815	−	0.447156i
$898$		0			0
$899$	−12.9282	+	12.9282i	−0.431180	+	0.431180i
$900$		0			0
$901$	1.21539	+	1.21539i	0.0404905	+	0.0404905i
$902$		0			0
$903$	1.14359	+	1.14359i	0.0380564	+	0.0380564i
$904$		0			0
$905$	−63.3731	−	36.5885i	−2.10659	−	1.21624i
$906$		0			0
$907$	−4.50000	+	16.7942i	−0.149420	+	0.557643i	0.850099	+	0.526623i	$0.176542\pi$
$907$	−4.50000	+	16.7942i	−0.149420	+	0.557643i	−0.999519	+	0.0310198i	$0.990124\pi$
$908$		0			0
$909$	16.3923	+	16.3923i	0.543698	+	0.543698i
$910$		0			0
$911$	4.46410	+	7.73205i	0.147902	+	0.256174i	0.930452	−	0.366414i	$-0.119415\pi$
$911$	4.46410	+	7.73205i	0.147902	+	0.256174i	−0.782550	+	0.622588i	$0.786081\pi$
$912$		0			0
$913$	2.09808	−	3.63397i	0.0694362	−	0.120267i
$914$		0			0
$915$	18.0000	−	10.3923i	0.595062	−	0.343559i
$916$		0			0
$917$	−1.66025	−	1.66025i	−0.0548264	−	0.0548264i
$918$		0			0
$919$		−	32.9808i		−	1.08793i	−0.839106	−	0.543967i	$-0.816921\pi$
$919$		−	32.9808i		−	1.08793i	0.839106	−	0.543967i	$-0.183079\pi$
$920$		0			0
$921$	10.1603	−	37.9186i	0.334792	−	1.24946i
$922$		0			0
$923$	−66.6410	+	17.8564i	−2.19352	+	0.587751i
$924$		0			0
$925$	17.1962	+	4.60770i	0.565406	+	0.151500i
$926$		0			0
$927$	23.7058	−	13.6865i	0.778600	−	0.449525i
$928$		0			0
$929$	−18.4641	−	31.9808i	−0.605788	−	1.04925i	−0.991926	−	0.126814i	$-0.959525\pi$
$929$	−18.4641	−	31.9808i	−0.605788	−	1.04925i	0.386139	−	0.922441i	$-0.373809\pi$
$930$		0			0
$931$	1.50000	+	5.59808i	0.0491605	+	0.183470i
$932$		0			0
$933$	−27.8038			−0.910257
$934$		0			0
$935$		−	26.0000i		−	0.850291i
$936$		0			0
$937$		−	51.1769i		−	1.67188i	−0.548823	−	0.835938i	$-0.684924\pi$
$937$		−	51.1769i		−	1.67188i	0.548823	−	0.835938i	$-0.315076\pi$
$938$		0			0
$939$	24.6506	−	42.6962i	0.804443	−	1.39334i
$940$		0			0
$941$	3.26795	+	12.1962i	0.106532	+	0.397583i	0.998514	−	0.0544870i	$-0.0173523\pi$
$941$	3.26795	+	12.1962i	0.106532	+	0.397583i	−0.891982	+	0.452070i	$0.850686\pi$
$942$		0			0
$943$	−1.90192	−	3.29423i	−0.0619352	−	0.107275i
$944$		0			0
$945$	10.3923	+	10.3923i	0.338062	+	0.338062i
$946$		0			0
$947$	−14.9904	−	4.01666i	−0.487122	−	0.130524i	0.00689497	−	0.999976i	$-0.497805\pi$
$947$	−14.9904	−	4.01666i	−0.487122	−	0.130524i	−0.494017	+	0.869452i	$0.664472\pi$
$948$		0			0
$949$	59.3468	−	15.9019i	1.92648	−	0.516198i
$950$		0			0
$951$	54.5429	−	14.6147i	1.76868	−	0.473915i
$952$		0			0
$953$			59.1051i			1.91460i	0.289092	+	0.957301i	$0.406647\pi$
$953$			59.1051i			1.91460i	−0.289092	+	0.957301i	$0.593353\pi$
$954$		0			0
$955$	38.3923	+	38.3923i	1.24235	+	1.24235i
$956$		0			0
$957$			12.5885i			0.406927i
$958$		0			0
$959$	6.02628	−	10.4378i	0.194599	−	0.337055i
$960$		0			0
$961$	−12.3564	−	21.4019i	−0.398594	−	0.690385i
$962$		0			0
$963$	55.2846	−	14.8135i	1.78152	−	0.477357i
$964$		0			0
$965$	18.2679	−	68.1769i	0.588066	−	2.19469i
$966$		0			0
$967$	9.16987	+	5.29423i	0.294883	+	0.170251i	0.640142	−	0.768257i	$-0.278876\pi$
$967$	9.16987	+	5.29423i	0.294883	+	0.170251i	−0.345259	+	0.938508i	$0.612209\pi$
$968$		0			0
$969$	−0.911543	+	3.40192i	−0.0292830	+	0.109286i
$970$		0			0
$971$	−22.4641	−	22.4641i	−0.720907	−	0.720907i	0.247883	−	0.968790i	$-0.420265\pi$
$971$	−22.4641	−	22.4641i	−0.720907	−	0.720907i	−0.968790	+	0.247883i	$0.920265\pi$
$972$		0			0
$973$	4.85641	−	4.85641i	0.155689	−	0.155689i
$974$		0			0
$975$	−104.863	−	28.0981i	−3.35832	−	0.899859i
$976$		0			0
$977$	−9.93782	+	17.2128i	−0.317939	+	0.550687i	−0.980058	−	0.198712i	$-0.936324\pi$
$977$	−9.93782	+	17.2128i	−0.317939	+	0.550687i	0.662119	+	0.749399i	$0.269657\pi$
$978$		0			0
$979$	5.73205	+	1.53590i	0.183197	+	0.0490875i
$980$		0			0
$981$	−7.98076	−	29.7846i	−0.254806	−	0.950949i
$982$		0			0
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	−0.704425	−	0.709779i	$-0.748795\pi$
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	0.262474	+	0.964939i	$0.415462\pi$
$984$		0			0
$985$	17.3205	+	10.0000i	0.551877	+	0.318626i
$986$		0			0
$987$	12.2487			0.389881
$988$		0			0
$989$	−1.14359	+	1.14359i	−0.0363642	+	0.0363642i
$990$		0			0
$991$	32.6410			1.03688			0.518438	−	0.855115i	$-0.326514\pi$
$991$	32.6410			1.03688			0.518438	+	0.855115i	$0.326514\pi$
$992$		0			0
$993$	8.83013	+	32.9545i	0.280216	+	1.04578i
$994$		0			0
$995$	−0.875644	−	3.26795i	−0.0277598	−	0.103601i
$996$		0			0
$997$	−8.60770	+	32.1244i	−0.272608	+	1.01739i	0.684819	+	0.728713i	$0.259881\pi$
$997$	−8.60770	+	32.1244i	−0.272608	+	1.01739i	−0.957427	+	0.288675i	$0.906785\pi$
$998$		0			0
$999$	6.58846	−	6.58846i	0.208450	−	0.208450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.d.49.1		4
3.2	odd	2		1728.2.bc.d.1009.1		4
4.3	odd	2		144.2.x.b.85.1	yes	4
9.2	odd	6		1728.2.bc.a.1585.1		4
9.7	even	3		576.2.bb.c.241.1		4
12.11	even	2		432.2.y.c.37.1		4
16.3	odd	4		144.2.x.c.13.1	yes	4
16.13	even	4		576.2.bb.c.337.1		4
36.7	odd	6		144.2.x.c.133.1	yes	4
36.11	even	6		432.2.y.b.181.1		4
48.29	odd	4		1728.2.bc.a.145.1		4
48.35	even	4		432.2.y.b.253.1		4
144.29	odd	12		1728.2.bc.d.721.1		4
144.61	even	12	inner	576.2.bb.d.529.1		4
144.83	even	12		432.2.y.c.397.1		4
144.115	odd	12		144.2.x.b.61.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.b.61.1	✓	4	144.115	odd	12
144.2.x.b.85.1	yes	4	4.3	odd	2
144.2.x.c.13.1	yes	4	16.3	odd	4
144.2.x.c.133.1	yes	4	36.7	odd	6
432.2.y.b.181.1		4	36.11	even	6
432.2.y.b.253.1		4	48.35	even	4
432.2.y.c.37.1		4	12.11	even	2
432.2.y.c.397.1		4	144.83	even	12
576.2.bb.c.241.1		4	9.7	even	3
576.2.bb.c.337.1		4	16.13	even	4
576.2.bb.d.49.1		4	1.1	even	1	trivial
576.2.bb.d.529.1		4	144.61	even	12	inner
1728.2.bc.a.145.1		4	48.29	odd	4
1728.2.bc.a.1585.1		4	9.2	odd	6
1728.2.bc.d.721.1		4	144.29	odd	12
1728.2.bc.d.1009.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.73205 + 1.00000i) q^{5} +(0.633975 - 0.366025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.73205 + 1.00000i) q^{5} +(0.633975 - 0.366025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(0.767949 - 2.86603i) q^{11} +(-1.63397 - 6.09808i) q^{13} +(-4.73205 + 4.73205i) q^{15} -2.26795 q^{17} +(0.633975 - 0.633975i) q^{19} +(0.633975 - 1.09808i) q^{21} +(1.09808 + 0.633975i) q^{23} +(8.59808 - 4.96410i) q^{25} -5.19615i q^{27} +(-2.36603 - 0.633975i) q^{29} +(3.73205 - 6.46410i) q^{31} +(-1.33013 - 4.96410i) q^{33} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-7.73205 - 7.73205i) q^{39} +(-2.59808 - 1.50000i) q^{41} +(-0.330127 + 1.23205i) q^{43} +(-3.00000 + 11.1962i) q^{45} +(4.83013 + 8.36603i) q^{47} +(-3.23205 + 5.59808i) q^{49} +(-3.40192 + 1.96410i) q^{51} +(-0.535898 - 0.535898i) q^{53} +11.4641i q^{55} +(0.401924 - 1.50000i) q^{57} +(-4.96410 + 1.33013i) q^{59} +(-3.00000 - 0.803848i) q^{61} -2.19615i q^{63} +(12.1962 + 21.1244i) q^{65} +(-1.40192 - 5.23205i) q^{67} +2.19615 q^{69} -10.9282i q^{71} +9.73205i q^{73} +(8.59808 - 14.8923i) q^{75} +(-0.562178 - 2.09808i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(1.36603 + 0.366025i) q^{83} +(8.46410 - 2.26795i) q^{85} +(-4.09808 + 1.09808i) q^{87} +2.00000i q^{89} +(-3.26795 - 3.26795i) q^{91} -12.9282i q^{93} +(-1.73205 + 3.00000i) q^{95} +(-4.13397 - 7.16025i) q^{97} +(-6.29423 - 6.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 8 q^{5} + 6 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 8 * q^5 + 6 * q^7 + 6 * q^9	\( 4 q + 6 q^{3} - 8 q^{5} + 6 q^{7} + 6 q^{9} + 10 q^{11} - 10 q^{13} - 12 q^{15} - 16 q^{17} + 6 q^{19} + 6 q^{21} - 6 q^{23} + 24 q^{25} - 6 q^{29} + 8 q^{31} + 12 q^{33} - 8 q^{35} + 12 q^{37} - 24 q^{39} + 16 q^{43} - 12 q^{45} + 2 q^{47} - 6 q^{49} - 24 q^{51} - 16 q^{53} + 12 q^{57} - 6 q^{59} - 12 q^{61} + 28 q^{65} - 16 q^{67} - 12 q^{69} + 24 q^{75} + 22 q^{77} + 24 q^{79} - 18 q^{81} + 2 q^{83} + 20 q^{85} - 6 q^{87} - 20 q^{91} - 20 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 8 * q^5 + 6 * q^7 + 6 * q^9 + 10 * q^11 - 10 * q^13 - 12 * q^15 - 16 * q^17 + 6 * q^19 + 6 * q^21 - 6 * q^23 + 24 * q^25 - 6 * q^29 + 8 * q^31 + 12 * q^33 - 8 * q^35 + 12 * q^37 - 24 * q^39 + 16 * q^43 - 12 * q^45 + 2 * q^47 - 6 * q^49 - 24 * q^51 - 16 * q^53 + 12 * q^57 - 6 * q^59 - 12 * q^61 + 28 * q^65 - 16 * q^67 - 12 * q^69 + 24 * q^75 + 22 * q^77 + 24 * q^79 - 18 * q^81 + 2 * q^83 + 20 * q^85 - 6 * q^87 - 20 * q^91 - 20 * q^97 + 6 * q^99

Introduction

L-functions

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Database

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