LMFDB - Embedded newform 880.2.bo.i.801.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(81,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,1,0,3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 $ x^12 - x^11 + 5x^10 + 4x^9 + 28x^8 - 81x^7 + 335x^6 - 235x^5 + 782x^4 - 302x^3 + 711x^2 - 43x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			801.1
Root			$-0.398885 - 1.22764i$ of defining polynomial
Character	$\chi$	$=$	880.801
Dual form			880.2.bo.i.401.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.85331 + 1.34651i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(3.77298 + 2.74123i) q^{7} +(0.694624 - 2.13783i) q^{9} +(-0.146113 - 3.31340i) q^{11} +(1.83639 - 5.65184i) q^{13} +(1.85331 + 1.34651i) q^{15} +(-1.02078 - 3.14164i) q^{17} +(-3.39136 + 2.46397i) q^{19} -10.6836 q^{21} +1.71184 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.532447 - 1.63870i) q^{27} +(6.28365 + 4.56534i) q^{29} +(0.918410 - 2.82658i) q^{31} +(4.73232 + 5.94403i) q^{33} +(1.44115 - 4.43540i) q^{35} +(4.59926 + 3.34156i) q^{37} +(4.20684 + 12.9473i) q^{39} +(4.97349 - 3.61345i) q^{41} +4.42353 q^{43} -2.24785 q^{45} +(3.34320 - 2.42898i) q^{47} +(4.55790 + 14.0278i) q^{49} +(6.12207 + 4.44795i) q^{51} +(2.50336 - 7.70454i) q^{53} +(-3.10608 + 1.16286i) q^{55} +(2.96749 - 9.13299i) q^{57} +(-5.02817 - 3.65318i) q^{59} +(-0.472049 - 1.45282i) q^{61} +(8.48109 - 6.16188i) q^{63} -5.94269 q^{65} +7.46447 q^{67} +(-3.17257 + 2.30500i) q^{69} +(0.691418 + 2.12796i) q^{71} +(6.06277 + 4.40486i) q^{73} +(0.707902 - 2.17870i) q^{75} +(8.53152 - 12.9019i) q^{77} +(-5.41757 + 16.6736i) q^{79} +(8.64897 + 6.28385i) q^{81} +(-3.42346 - 10.5363i) q^{83} +(-2.67244 + 1.94164i) q^{85} -17.7928 q^{87} +12.8171 q^{89} +(22.4216 - 16.2903i) q^{91} +(2.10391 + 6.47518i) q^{93} +(3.39136 + 2.46397i) q^{95} +(-2.94728 + 9.07079i) q^{97} +(-7.18500 - 1.98921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} + 18 q^{13} - q^{15} + 3 q^{17} - 4 q^{19} - 28 q^{21} + 18 q^{23} - 3 q^{25} - 23 q^{27} + 15 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{35} + 6 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) $ 12 * q + q^3 + 3 * q^5 + q^7 - 10 * q^9 - 4 * q^11 + 18 * q^13 - q^15 + 3 * q^17 - 4 * q^19 - 28 * q^21 + 18 * q^23 - 3 * q^25 - 23 * q^27 + 15 * q^29 + 8 * q^31 + 4 * q^33 - 6 * q^35 + 6 * q^37 + 33 * q^39 + 2 * q^41 + 36 * q^43 - 10 * q^45 + 16 * q^47 - 16 * q^49 + 10 * q^51 + 19 * q^53 - 6 * q^55 + 62 * q^57 - 46 * q^59 + 18 * q^61 + 7 * q^63 + 2 * q^65 + 44 * q^67 - q^69 + 6 * q^71 + 25 * q^73 - 4 * q^75 + 10 * q^77 - 19 * q^79 + 30 * q^81 - 3 * q^85 - 6 * q^87 - 50 * q^89 + 46 * q^91 - 37 * q^93 + 4 * q^95 - 31 * q^97 - 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	−1.85331	+	1.34651i	−1.07001	+	0.777408i	−0.975914	−	0.218155i	$-0.929996\pi$
$3$	−1.85331	+	1.34651i	−1.07001	+	0.777408i	−0.0940959	+	0.995563i	$0.529996\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	3.77298	+	2.74123i	1.42605	+	1.03609i	0.990735	+	0.135809i	$0.0433634\pi$
$7$	3.77298	+	2.74123i	1.42605	+	1.03609i	0.435316	+	0.900278i	$0.356637\pi$
$8$		0			0
$9$	0.694624	−	2.13783i	0.231541	−	0.712611i
$10$		0			0
$11$	−0.146113	−	3.31340i	−0.0440546	−	0.999029i
$11$	−0.146113	−	3.31340i	−0.0440546	−	0.999029i
$12$		0			0
$13$	1.83639	−	5.65184i	0.509324	−	1.56754i	−0.284055	−	0.958808i	$-0.591680\pi$
$13$	1.83639	−	5.65184i	0.509324	−	1.56754i	0.793378	−	0.608729i	$-0.208320\pi$
$14$		0			0
$15$	1.85331	+	1.34651i	0.478523	+	0.347667i
$16$		0			0
$17$	−1.02078	−	3.14164i	−0.247576	−	0.761959i	−0.995202	−	0.0978400i	$-0.968807\pi$
$17$	−1.02078	−	3.14164i	−0.247576	−	0.761959i	0.747627	−	0.664119i	$-0.231193\pi$
$18$		0			0
$19$	−3.39136	+	2.46397i	−0.778031	+	0.565273i	−0.904387	−	0.426712i	$-0.859672\pi$
$19$	−3.39136	+	2.46397i	−0.778031	+	0.565273i	0.126356	+	0.991985i	$0.459672\pi$
$20$		0			0
$21$	−10.6836			−2.33135
$22$		0			0
$23$	1.71184			0.356942			0.178471	−	0.983945i	$-0.442885\pi$
$23$	1.71184			0.356942			0.178471	+	0.983945i	$0.442885\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−0.532447	−	1.63870i	−0.102469	−	0.315369i
$28$		0			0
$29$	6.28365	+	4.56534i	1.16684	+	0.847762i	0.990628	−	0.136590i	$-0.0436141\pi$
$29$	6.28365	+	4.56534i	1.16684	+	0.847762i	0.176216	+	0.984351i	$0.443614\pi$
$30$		0			0
$31$	0.918410	−	2.82658i	0.164951	−	0.507668i	−0.834081	−	0.551642i	$-0.814002\pi$
$31$	0.918410	−	2.82658i	0.164951	−	0.507668i	0.999033	+	0.0439734i	$0.0140017\pi$
$32$		0			0
$33$	4.73232	+	5.94403i	0.823792	+	1.03472i
$34$		0			0
$35$	1.44115	−	4.43540i	0.243599	−	0.749720i
$36$		0			0
$37$	4.59926	+	3.34156i	0.756114	+	0.549349i	0.897716	−	0.440575i	$-0.145225\pi$
$37$	4.59926	+	3.34156i	0.756114	+	0.549349i	−0.141602	+	0.989924i	$0.545225\pi$
$38$		0			0
$39$	4.20684	+	12.9473i	0.673634	+	2.07323i
$40$		0			0
$41$	4.97349	−	3.61345i	0.776729	−	0.564327i	−0.127266	−	0.991869i	$-0.540620\pi$
$41$	4.97349	−	3.61345i	0.776729	−	0.564327i	0.903996	+	0.427542i	$0.140620\pi$
$42$		0			0
$43$	4.42353			0.674582			0.337291	−	0.941401i	$-0.390489\pi$
$43$	4.42353			0.674582			0.337291	+	0.941401i	$0.390489\pi$
$44$		0			0
$45$	−2.24785			−0.335090
$46$		0			0
$47$	3.34320	−	2.42898i	0.487656	−	0.354303i	−0.316626	−	0.948550i	$-0.602550\pi$
$47$	3.34320	−	2.42898i	0.487656	−	0.354303i	0.804282	+	0.594247i	$0.202550\pi$
$48$		0			0
$49$	4.55790	+	14.0278i	0.651129	+	2.00397i
$50$		0			0
$51$	6.12207	+	4.44795i	0.857261	+	0.622837i
$52$		0			0
$53$	2.50336	−	7.70454i	0.343863	−	1.05830i	−0.618327	−	0.785921i	$-0.712189\pi$
$53$	2.50336	−	7.70454i	0.343863	−	1.05830i	0.962190	−	0.272380i	$-0.0878107\pi$
$54$		0			0
$55$	−3.10608	+	1.16286i	−0.418824	+	0.156800i
$56$		0			0
$57$	2.96749	−	9.13299i	0.393054	−	1.20969i
$58$		0			0
$59$	−5.02817	−	3.65318i	−0.654611	−	0.475603i	0.210227	−	0.977653i	$-0.432580\pi$
$59$	−5.02817	−	3.65318i	−0.654611	−	0.475603i	−0.864839	+	0.502049i	$0.832580\pi$
$60$		0			0
$61$	−0.472049	−	1.45282i	−0.0604396	−	0.186014i	0.916278	−	0.400543i	$-0.131178\pi$
$61$	−0.472049	−	1.45282i	−0.0604396	−	0.186014i	−0.976718	+	0.214529i	$0.931178\pi$
$62$		0			0
$63$	8.48109	−	6.16188i	1.06852	−	0.776323i
$64$		0			0
$65$	−5.94269			−0.737100
$66$		0			0
$67$	7.46447			0.911931			0.455965	−	0.889998i	$-0.349294\pi$
$67$	7.46447			0.911931			0.455965	+	0.889998i	$0.349294\pi$
$68$		0			0
$69$	−3.17257	+	2.30500i	−0.381932	+	0.277490i
$70$		0			0
$71$	0.691418	+	2.12796i	0.0820562	+	0.252543i	0.983665	−	0.180010i	$-0.0576129\pi$
$71$	0.691418	+	2.12796i	0.0820562	+	0.252543i	−0.901609	+	0.432553i	$0.857613\pi$
$72$		0			0
$73$	6.06277	+	4.40486i	0.709593	+	0.515550i	0.883043	−	0.469293i	$-0.155491\pi$
$73$	6.06277	+	4.40486i	0.709593	+	0.515550i	−0.173449	+	0.984843i	$0.555491\pi$
$74$		0			0
$75$	0.707902	−	2.17870i	0.0817415	−	0.251574i
$76$		0			0
$77$	8.53152	−	12.9019i	0.972257	−	1.47031i
$78$		0			0
$79$	−5.41757	+	16.6736i	−0.609524	+	1.87592i	−0.147478	+	0.989065i	$0.547116\pi$
$79$	−5.41757	+	16.6736i	−0.609524	+	1.87592i	−0.462046	+	0.886856i	$0.652884\pi$
$80$		0			0
$81$	8.64897	+	6.28385i	0.960997	+	0.698205i
$82$		0			0
$83$	−3.42346	−	10.5363i	−0.375773	−	1.15651i	−0.942955	−	0.332919i	$-0.891966\pi$
$83$	−3.42346	−	10.5363i	−0.375773	−	1.15651i	0.567182	−	0.823592i	$-0.308034\pi$
$84$		0			0
$85$	−2.67244	+	1.94164i	−0.289867	+	0.210600i
$86$		0			0
$87$	−17.7928			−1.90759
$88$		0			0
$89$	12.8171			1.35861			0.679305	−	0.733856i	$-0.262281\pi$
$89$	12.8171			1.35861			0.679305	+	0.733856i	$0.262281\pi$
$90$		0			0
$91$	22.4216	−	16.2903i	2.35043	−	1.70768i
$92$		0			0
$93$	2.10391	+	6.47518i	0.218166	+	0.671444i
$94$		0			0
$95$	3.39136	+	2.46397i	0.347946	+	0.252798i
$96$		0			0
$97$	−2.94728	+	9.07079i	−0.299251	+	0.921000i	0.682509	+	0.730877i	$0.260889\pi$
$97$	−2.94728	+	9.07079i	−0.299251	+	0.921000i	−0.981760	+	0.190123i	$0.939111\pi$
$98$		0			0
$99$	−7.18500	−	1.98921i	−0.722120	−	0.199923i
$100$		0			0
$101$	−3.31449	+	10.2010i	−0.329804	+	1.01503i	0.639421	+	0.768857i	$0.279174\pi$
$101$	−3.31449	+	10.2010i	−0.329804	+	1.01503i	−0.969225	+	0.246176i	$0.920826\pi$
$102$		0			0
$103$	2.08617	+	1.51569i	0.205557	+	0.149346i	0.685801	−	0.727789i	$-0.259452\pi$
$103$	2.08617	+	1.51569i	0.205557	+	0.149346i	−0.480244	+	0.877135i	$0.659452\pi$
$104$		0			0
$105$	3.30141	+	10.1607i	0.322185	+	0.991583i
$106$		0			0
$107$	−14.2627	+	10.3625i	−1.37883	+	1.00178i	−0.381842	+	0.924228i	$0.624710\pi$
$107$	−14.2627	+	10.3625i	−1.37883	+	1.00178i	−0.996988	+	0.0775516i	$0.975290\pi$
$108$		0			0
$109$	−15.3476			−1.47004			−0.735019	−	0.678047i	$-0.762827\pi$
$109$	−15.3476			−1.47004			−0.735019	+	0.678047i	$0.762827\pi$
$110$		0			0
$111$	−13.0233			−1.23612
$112$		0			0
$113$	−0.256405	+	0.186289i	−0.0241206	+	0.0175246i	−0.599780	−	0.800165i	$-0.704745\pi$
$113$	−0.256405	+	0.186289i	−0.0241206	+	0.0175246i	0.575660	+	0.817689i	$0.304745\pi$
$114$		0			0
$115$	−0.528986	−	1.62805i	−0.0493282	−	0.151817i
$116$		0			0
$117$	−10.8071	−	7.85181i	−0.999115	−	0.725900i
$118$		0			0
$119$	4.76057	−	14.6515i	0.436401	−	1.34310i
$120$		0			0
$121$	−10.9573	+	0.968261i	−0.996118	+	0.0880237i
$122$		0			0
$123$	−4.35188	+	13.3937i	−0.392396	+	1.20767i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	−5.58305	−	17.1829i	−0.495415	−	1.52473i	−0.816308	−	0.577616i	$-0.803983\pi$
$127$	−5.58305	−	17.1829i	−0.495415	−	1.52473i	0.320893	−	0.947115i	$-0.396017\pi$
$128$		0			0
$129$	−8.19817	+	5.95632i	−0.721809	+	0.524425i
$130$		0			0
$131$	7.95176			0.694749			0.347374	−	0.937727i	$-0.387073\pi$
$131$	7.95176			0.694749			0.347374	+	0.937727i	$0.387073\pi$
$132$		0			0
$133$	−19.5498			−1.69518
$134$		0			0
$135$	−1.39396	+	1.01277i	−0.119973	+	0.0871658i
$136$		0			0
$137$	−2.49608	−	7.68214i	−0.213254	−	0.656329i	−0.999273	−	0.0381266i	$-0.987861\pi$
$137$	−2.49608	−	7.68214i	−0.213254	−	0.656329i	0.786019	−	0.618203i	$-0.212139\pi$
$138$		0			0
$139$	9.16128	+	6.65606i	0.777049	+	0.564559i	0.904092	−	0.427338i	$-0.140548\pi$
$139$	9.16128	+	6.65606i	0.777049	+	0.564559i	−0.127043	+	0.991897i	$0.540548\pi$
$140$		0			0
$141$	−2.92535	+	9.00331i	−0.246359	+	0.758215i
$142$		0			0
$143$	−18.9951	−	5.25891i	−1.58845	−	0.439772i
$144$		0			0
$145$	2.40014	−	7.38687i	0.199321	−	0.613446i
$146$		0			0
$147$	−27.3358	−	19.8606i	−2.25462	−	1.63807i
$148$		0			0
$149$	0.726731	+	2.23665i	0.0595361	+	0.183233i	0.976401	−	0.215963i	$-0.0692891\pi$
$149$	0.726731	+	2.23665i	0.0595361	+	0.183233i	−0.916865	+	0.399196i	$0.869289\pi$
$150$		0			0
$151$	11.9143	−	8.65622i	0.969569	−	0.704433i	0.0142158	−	0.999899i	$-0.495475\pi$
$151$	11.9143	−	8.65622i	0.969569	−	0.704433i	0.955353	+	0.295466i	$0.0954748\pi$
$152$		0			0
$153$	−7.42536			−0.600305
$154$		0			0
$155$	−2.97204			−0.238720
$156$		0			0
$157$	13.3118	−	9.67162i	1.06240	−	0.771880i	0.0878701	−	0.996132i	$-0.471994\pi$
$157$	13.3118	−	9.67162i	1.06240	−	0.771880i	0.974531	+	0.224252i	$0.0719940\pi$
$158$		0			0
$159$	5.73474	+	17.6497i	0.454794	+	1.39971i
$160$		0			0
$161$	6.45872	+	4.69253i	0.509018	+	0.369823i
$162$		0			0
$163$	−1.62618	+	5.00486i	−0.127372	+	0.392011i	−0.994326	−	0.106378i	$-0.966075\pi$
$163$	−1.62618	+	5.00486i	−0.127372	+	0.392011i	0.866954	+	0.498389i	$0.166075\pi$
$164$		0			0
$165$	4.19074	−	6.33751i	0.326249	−	0.493375i
$166$		0			0
$167$	6.65917	−	20.4948i	0.515302	−	1.58594i	−0.267430	−	0.963577i	$-0.586174\pi$
$167$	6.65917	−	20.4948i	0.515302	−	1.58594i	0.782732	−	0.622359i	$-0.213826\pi$
$168$		0			0
$169$	−18.0537	−	13.1168i	−1.38874	−	1.00898i
$170$		0			0
$171$	2.91183	+	8.96169i	0.222673	+	0.685318i
$172$		0			0
$173$	5.73128	−	4.16402i	0.435741	−	0.316584i	−0.348199	−	0.937420i	$-0.613207\pi$
$173$	5.73128	−	4.16402i	0.435741	−	0.316584i	0.783940	+	0.620836i	$0.213207\pi$
$174$		0			0
$175$	−4.66366			−0.352539
$176$		0			0
$177$	14.2378			1.07018
$178$		0			0
$179$	7.10931	−	5.16521i	0.531375	−	0.386066i	−0.289497	−	0.957179i	$-0.593488\pi$
$179$	7.10931	−	5.16521i	0.531375	−	0.386066i	0.820872	+	0.571113i	$0.193488\pi$
$180$		0			0
$181$	−3.90756	−	12.0262i	−0.290446	−	0.893902i	−0.984713	−	0.174184i	$-0.944271\pi$
$181$	−3.90756	−	12.0262i	−0.290446	−	0.893902i	0.694267	−	0.719718i	$-0.255729\pi$
$182$		0			0
$183$	2.83108	+	2.05690i	0.209280	+	0.152051i
$184$		0			0
$185$	1.75676	−	5.40675i	0.129160	−	0.397513i
$186$		0			0
$187$	−10.2604	+	3.84129i	−0.750313	+	0.280903i
$188$		0			0
$189$	2.48315	−	7.64235i	0.180623	−	0.555899i
$190$		0			0
$191$	−14.3378	−	10.4170i	−1.03744	−	0.753747i	−0.0676586	−	0.997709i	$-0.521553\pi$
$191$	−14.3378	−	10.4170i	−1.03744	−	0.753747i	−0.969785	+	0.243962i	$0.921553\pi$
$192$		0			0
$193$	−1.55602	−	4.78895i	−0.112005	−	0.344716i	0.879306	−	0.476258i	$-0.158007\pi$
$193$	−1.55602	−	4.78895i	−0.112005	−	0.344716i	−0.991311	+	0.131542i	$0.958007\pi$
$194$		0			0
$195$	11.0137	−	8.00189i	0.788704	−	0.573027i
$196$		0			0
$197$	−15.0557			−1.07268			−0.536338	−	0.844003i	$-0.680193\pi$
$197$	−15.0557			−1.07268			−0.536338	+	0.844003i	$0.680193\pi$
$198$		0			0
$199$	−2.56534			−0.181852			−0.0909259	−	0.995858i	$-0.528983\pi$
$199$	−2.56534			−0.181852			−0.0909259	+	0.995858i	$0.528983\pi$
$200$		0			0
$201$	−13.8340	+	10.0510i	−0.975775	+	0.708942i
$202$		0			0
$203$	11.1934	+	34.4498i	0.785625	+	2.41790i
$204$		0			0
$205$	−4.97349	−	3.61345i	−0.347364	−	0.252375i
$206$		0			0
$207$	1.18908	−	3.65962i	0.0826470	−	0.254361i
$208$		0			0
$209$	8.65964	+	10.8769i	0.599000	+	0.752373i
$210$		0			0
$211$	−3.00333	+	9.24329i	−0.206758	+	0.636335i	0.792879	+	0.609379i	$0.208581\pi$
$211$	−3.00333	+	9.24329i	−0.206758	+	0.636335i	−0.999637	+	0.0269555i	$0.991419\pi$
$212$		0			0
$213$	−4.14674	−	3.01278i	−0.284130	−	0.206432i
$214$		0			0
$215$	−1.36694	−	4.20702i	−0.0932249	−	0.286917i
$216$		0			0
$217$	11.2134	−	8.14704i	0.761217	−	0.553057i
$218$		0			0
$219$	−17.1674			−1.16006
$220$		0			0
$221$	−19.6306			−1.32050
$222$		0			0
$223$	0.439704	−	0.319464i	0.0294448	−	0.0213929i	−0.572966	−	0.819579i	$-0.694207\pi$
$223$	0.439704	−	0.319464i	0.0294448	−	0.0213929i	0.602410	+	0.798187i	$0.294207\pi$
$224$		0			0
$225$	0.694624	+	2.13783i	0.0463083	+	0.142522i
$226$		0			0
$227$	4.20468	+	3.05488i	0.279075	+	0.202759i	0.718514	−	0.695513i	$-0.244823\pi$
$227$	4.20468	+	3.05488i	0.279075	+	0.202759i	−0.439439	+	0.898272i	$0.644823\pi$
$228$		0			0
$229$	−1.26424	+	3.89093i	−0.0835433	+	0.257120i	−0.984099	−	0.177621i	$-0.943160\pi$
$229$	−1.26424	+	3.89093i	−0.0835433	+	0.257120i	0.900556	+	0.434741i	$0.143160\pi$
$230$		0			0
$231$	1.56101	+	35.3991i	0.102707	+	2.32909i
$232$		0			0
$233$	4.30912	−	13.2621i	0.282300	−	0.868829i	−0.704895	−	0.709311i	$-0.749006\pi$
$233$	4.30912	−	13.2621i	0.282300	−	0.868829i	0.987195	−	0.159518i	$-0.0509940\pi$
$234$		0			0
$235$	−3.34320	−	2.42898i	−0.218086	−	0.158449i
$236$		0			0
$237$	−12.4107	−	38.1961i	−0.806159	−	2.48110i
$238$		0			0
$239$	0.423576	−	0.307746i	0.0273988	−	0.0199064i	−0.574002	−	0.818854i	$-0.694610\pi$
$239$	0.423576	−	0.307746i	0.0273988	−	0.0199064i	0.601400	+	0.798948i	$0.294610\pi$
$240$		0			0
$241$	−6.38011			−0.410979			−0.205489	−	0.978659i	$-0.565879\pi$
$241$	−6.38011			−0.410979			−0.205489	+	0.978659i	$0.565879\pi$
$242$		0			0
$243$	−19.3214			−1.23947
$244$		0			0
$245$	11.9327	−	8.66965i	0.762355	−	0.553884i
$246$		0			0
$247$	7.69806	+	23.6922i	0.489816	+	1.50750i
$248$		0			0
$249$	20.5320	+	14.9174i	1.30116	+	0.945350i
$250$		0			0
$251$	−4.21539	+	12.9736i	−0.266073	+	0.818888i	0.725371	+	0.688358i	$0.241668\pi$
$251$	−4.21539	+	12.9736i	−0.266073	+	0.818888i	−0.991444	+	0.130530i	$0.958332\pi$
$252$		0			0
$253$	−0.250121	−	5.67201i	−0.0157250	−	0.356596i
$254$		0			0
$255$	2.33842	−	7.19693i	0.146438	−	0.450689i
$256$		0			0
$257$	1.94734	+	1.41483i	0.121472	+	0.0882546i	0.646863	−	0.762607i	$-0.276081\pi$
$257$	1.94734	+	1.41483i	0.121472	+	0.0882546i	−0.525391	+	0.850861i	$0.676081\pi$
$258$		0			0
$259$	8.19293	+	25.2152i	0.509084	+	1.56680i
$260$		0			0
$261$	14.1247	−	10.2622i	0.874298	−	0.635214i
$262$		0			0
$263$	11.7841			0.726641			0.363321	−	0.931664i	$-0.381643\pi$
$263$	11.7841			0.726641			0.363321	+	0.931664i	$0.381643\pi$
$264$		0			0
$265$	−8.10104			−0.497643
$266$		0			0
$267$	−23.7541	+	17.2584i	−1.45373	+	1.05619i
$268$		0			0
$269$	−4.67964	−	14.4024i	−0.285323	−	0.878133i	−0.986302	−	0.164951i	$-0.947253\pi$
$269$	−4.67964	−	14.4024i	−0.285323	−	0.878133i	0.700979	−	0.713182i	$-0.252747\pi$
$270$		0			0
$271$	−8.55443	−	6.21516i	−0.519645	−	0.377544i	0.296825	−	0.954932i	$-0.404072\pi$
$271$	−8.55443	−	6.21516i	−0.519645	−	0.377544i	−0.816470	+	0.577388i	$0.804072\pi$
$272$		0			0
$273$	−19.6193	+	60.3819i	−1.18741	+	3.65448i
$274$		0			0
$275$	2.06578	+	2.59472i	0.124571	+	0.156467i
$276$		0			0
$277$	−7.77227	+	23.9206i	−0.466990	+	1.43725i	0.389472	+	0.921038i	$0.372658\pi$
$277$	−7.77227	+	23.9206i	−0.466990	+	1.43725i	−0.856462	+	0.516210i	$0.827342\pi$
$278$		0			0
$279$	−5.40480	−	3.92682i	−0.323577	−	0.235092i
$280$		0			0
$281$	−0.0998021	−	0.307159i	−0.00595369	−	0.0183236i	0.948036	−	0.318164i	$-0.103066\pi$
$281$	−0.0998021	−	0.307159i	−0.00595369	−	0.0183236i	−0.953989	+	0.299841i	$0.903066\pi$
$282$		0			0
$283$	17.2906	−	12.5624i	1.02782	−	0.746754i	0.0599481	−	0.998201i	$-0.480906\pi$
$283$	17.2906	−	12.5624i	1.02782	−	0.746754i	0.967871	+	0.251447i	$0.0809065\pi$
$284$		0			0
$285$	−9.60300			−0.568832
$286$		0			0
$287$	28.6702			1.69235
$288$		0			0
$289$	4.92539	−	3.57850i	0.289729	−	0.210500i
$290$		0			0
$291$	−6.75168	−	20.7795i	−0.395791	−	1.21812i
$292$		0			0
$293$	8.49478	+	6.17182i	0.496271	+	0.360562i	0.807591	−	0.589743i	$-0.200771\pi$
$293$	8.49478	+	6.17182i	0.496271	+	0.360562i	−0.311320	+	0.950305i	$0.600771\pi$
$294$		0			0
$295$	−1.92059	+	5.91096i	−0.111821	+	0.344150i
$296$		0			0
$297$	−5.35189	+	2.00365i	−0.310548	+	0.116263i
$298$		0			0
$299$	3.14360	−	9.67501i	0.181799	−	0.559521i
$300$		0			0
$301$	16.6899	+	12.1259i	0.961988	+	0.698925i
$302$		0			0
$303$	−7.59290	−	23.3686i	−0.436201	−	1.34249i
$304$		0			0
$305$	−1.23584	+	0.897890i	−0.0707640	+	0.0514130i
$306$		0			0
$307$	29.0598			1.65853			0.829266	−	0.558854i	$-0.188759\pi$
$307$	29.0598			1.65853			0.829266	+	0.558854i	$0.188759\pi$
$308$		0			0
$309$	−5.90722			−0.336050
$310$		0			0
$311$	−16.1385	+	11.7253i	−0.915131	+	0.664882i	−0.942307	−	0.334749i	$-0.891348\pi$
$311$	−16.1385	+	11.7253i	−0.915131	+	0.664882i	0.0271763	+	0.999631i	$0.491348\pi$
$312$		0			0
$313$	5.40163	+	16.6245i	0.305318	+	0.939672i	0.979558	+	0.201160i	$0.0644712\pi$
$313$	5.40163	+	16.6245i	0.305318	+	0.939672i	−0.674240	+	0.738512i	$0.735529\pi$
$314$		0			0
$315$	−8.48109	−	6.16188i	−0.477855	−	0.347182i
$316$		0			0
$317$	−9.21783	+	28.3696i	−0.517725	+	1.59339i	0.260544	+	0.965462i	$0.416098\pi$
$317$	−9.21783	+	28.3696i	−0.517725	+	1.59339i	−0.778269	+	0.627931i	$0.783902\pi$
$318$		0			0
$319$	14.2087	−	21.4873i	0.795534	−	1.20306i
$320$		0			0
$321$	12.4801	−	38.4098i	0.696572	−	2.14383i
$322$		0			0
$323$	11.2027	+	8.13926i	0.623336	+	0.452880i
$324$		0			0
$325$	1.83639	+	5.65184i	0.101865	+	0.313507i
$326$		0			0
$327$	28.4440	−	20.6657i	1.57295	−	1.14282i
$328$		0			0
$329$	19.2722			1.06251
$330$		0			0
$331$	−29.4740			−1.62004			−0.810018	−	0.586405i	$-0.800543\pi$
$331$	−29.4740			−1.62004			−0.810018	+	0.586405i	$0.800543\pi$
$332$		0			0
$333$	10.3385	−	7.51133i	0.566544	−	0.411618i
$334$		0			0
$335$	−2.30665	−	7.09914i	−0.126026	−	0.387867i
$336$		0			0
$337$	−16.9636	−	12.3248i	−0.924068	−	0.671375i	0.0204651	−	0.999791i	$-0.493485\pi$
$337$	−16.9636	−	12.3248i	−0.924068	−	0.671375i	−0.944533	+	0.328416i	$0.893485\pi$
$338$		0			0
$339$	0.224358	−	0.690504i	0.0121855	−	0.0375030i
$340$		0			0
$341$	−9.49978	−	2.63007i	−0.514442	−	0.142426i
$342$		0			0
$343$	−11.1685	+	34.3730i	−0.603040	+	1.85597i
$344$		0			0
$345$	3.17257	+	2.30500i	0.170805	+	0.124097i
$346$		0			0
$347$	2.24674	+	6.91474i	0.120611	+	0.371203i	0.993076	−	0.117474i	$-0.0374797\pi$
$347$	2.24674	+	6.91474i	0.120611	+	0.371203i	−0.872465	+	0.488677i	$0.837480\pi$
$348$		0			0
$349$	−15.5681	+	11.3109i	−0.833339	+	0.605456i	−0.920502	−	0.390738i	$-0.872220\pi$
$349$	−15.5681	+	11.3109i	−0.833339	+	0.605456i	0.0871630	+	0.996194i	$0.472220\pi$
$350$		0			0
$351$	−10.2395			−0.546542
$352$		0			0
$353$	14.5882			0.776454			0.388227	−	0.921564i	$-0.373088\pi$
$353$	14.5882			0.776454			0.388227	+	0.921564i	$0.373088\pi$
$354$		0			0
$355$	1.81015	−	1.31515i	0.0960730	−	0.0698011i
$356$		0			0
$357$	10.9056	+	33.5640i	0.577186	+	1.77639i
$358$		0			0
$359$	2.07608	+	1.50836i	0.109571	+	0.0796081i	0.641222	−	0.767356i	$-0.278428\pi$
$359$	2.07608	+	1.50836i	0.109571	+	0.0796081i	−0.531650	+	0.846964i	$0.678428\pi$
$360$		0			0
$361$	−0.441140	+	1.35769i	−0.0232179	+	0.0714574i
$362$		0			0
$363$	19.0035	−	16.5486i	0.997426	−	0.868576i
$364$		0			0
$365$	2.31577	−	7.12721i	0.121213	−	0.373055i
$366$		0			0
$367$	−17.6293	−	12.8085i	−0.920244	−	0.668596i	0.0233410	−	0.999728i	$-0.492570\pi$
$367$	−17.6293	−	12.8085i	−0.920244	−	0.668596i	−0.943585	+	0.331131i	$0.892570\pi$
$368$		0			0
$369$	−4.27026	−	13.1425i	−0.222301	−	0.684171i
$370$		0			0
$371$	30.5650	−	22.2068i	1.58686	−	1.15292i
$372$		0			0
$373$	19.7684			1.02357			0.511783	−	0.859115i	$-0.328985\pi$
$373$	19.7684			1.02357			0.511783	+	0.859115i	$0.328985\pi$
$374$		0			0
$375$	−2.29082			−0.118297
$376$		0			0
$377$	37.3418	−	27.1304i	1.92320	−	1.39729i
$378$		0			0
$379$	4.18387	+	12.8766i	0.214911	+	0.661428i	0.999160	+	0.0409817i	$0.0130485\pi$
$379$	4.18387	+	12.8766i	0.214911	+	0.661428i	−0.784249	+	0.620446i	$0.786951\pi$
$380$		0			0
$381$	33.4840	+	24.3276i	1.71544	+	1.24634i
$382$		0			0
$383$	−4.44790	+	13.6892i	−0.227277	+	0.699486i	0.770776	+	0.637107i	$0.219869\pi$
$383$	−4.44790	+	13.6892i	−0.227277	+	0.699486i	−0.998053	+	0.0623795i	$0.980131\pi$
$384$		0			0
$385$	−14.9068	−	4.12704i	−0.759723	−	0.210334i
$386$		0			0
$387$	3.07269	−	9.45677i	0.156194	−	0.480714i
$388$		0			0
$389$	12.3136	+	8.94633i	0.624323	+	0.453597i	0.854429	−	0.519569i	$-0.173907\pi$
$389$	12.3136	+	8.94633i	0.624323	+	0.453597i	−0.230106	+	0.973166i	$0.573907\pi$
$390$		0			0
$391$	−1.74741	−	5.37797i	−0.0883702	−	0.271976i
$392$		0			0
$393$	−14.7371	+	10.7071i	−0.743388	+	0.540103i
$394$		0			0
$395$	17.5316			0.882111
$396$		0			0
$397$	−37.0013			−1.85704			−0.928520	−	0.371282i	$-0.878918\pi$
$397$	−37.0013			−1.85704			−0.928520	+	0.371282i	$0.878918\pi$
$398$		0			0
$399$	36.2319	−	26.3240i	1.81386	−	1.31785i
$400$		0			0
$401$	−7.60503	−	23.4059i	−0.379777	−	1.16883i	−0.940199	−	0.340626i	$-0.889361\pi$
$401$	−7.60503	−	23.4059i	−0.379777	−	1.16883i	0.560422	−	0.828207i	$-0.310639\pi$
$402$		0			0
$403$	−14.2888	−	10.3814i	−0.711775	−	0.517135i
$404$		0			0
$405$	3.30361	−	10.1675i	0.164158	−	0.505226i
$406$		0			0
$407$	10.3999	−	15.7275i	0.515505	−	0.779581i
$408$		0			0
$409$	5.66569	−	17.4372i	0.280150	−	0.862215i	−0.707660	−	0.706553i	$-0.750249\pi$
$409$	5.66569	−	17.4372i	0.280150	−	0.862215i	0.987810	−	0.155661i	$-0.0497509\pi$
$410$		0			0
$411$	14.9701	+	10.8764i	0.738420	+	0.536493i
$412$		0			0
$413$	−8.95696	−	27.5667i	−0.440743	−	1.35647i
$414$		0			0
$415$	−8.96273	+	6.51180i	−0.439963	+	0.319652i
$416$		0			0
$417$	−25.9411			−1.27034
$418$		0			0
$419$	−23.6524			−1.15550			−0.577748	−	0.816215i	$-0.696068\pi$
$419$	−23.6524			−1.15550			−0.577748	+	0.816215i	$0.696068\pi$
$420$		0			0
$421$	−9.45914	+	6.87247i	−0.461010	+	0.334944i	−0.793928	−	0.608012i	$-0.791967\pi$
$421$	−9.45914	+	6.87247i	−0.461010	+	0.334944i	0.332917	+	0.942956i	$0.391967\pi$
$422$		0			0
$423$	−2.87048	−	8.83444i	−0.139568	−	0.429545i
$424$		0			0
$425$	2.67244	+	1.94164i	0.129632	+	0.0941834i
$426$		0			0
$427$	2.20147	−	6.77544i	0.106537	−	0.327886i
$428$		0			0
$429$	42.2851	−	15.8307i	2.04154	−	0.764315i
$430$		0			0
$431$	1.67524	−	5.15585i	0.0806933	−	0.248349i	−0.902569	−	0.430546i	$-0.858321\pi$
$431$	1.67524	−	5.15585i	0.0806933	−	0.248349i	0.983262	+	0.182197i	$0.0583210\pi$
$432$		0			0
$433$	11.3653	+	8.25735i	0.546180	+	0.396823i	0.826375	−	0.563120i	$-0.190399\pi$
$433$	11.3653	+	8.25735i	0.546180	+	0.396823i	−0.280195	+	0.959943i	$0.590399\pi$
$434$		0			0
$435$	5.49829	+	16.9220i	0.263623	+	0.811347i
$436$		0			0
$437$	−5.80545	+	4.21791i	−0.277712	+	0.201770i
$438$		0			0
$439$	−13.4133			−0.640184			−0.320092	−	0.947386i	$-0.603714\pi$
$439$	−13.4133			−0.640184			−0.320092	+	0.947386i	$0.603714\pi$
$440$		0			0
$441$	33.1551			1.57881
$442$		0			0
$443$	−22.7987	+	16.5642i	−1.08320	+	0.786989i	−0.978238	−	0.207488i	$-0.933471\pi$
$443$	−22.7987	+	16.5642i	−1.08320	+	0.786989i	−0.104959	+	0.994477i	$0.533471\pi$
$444$		0			0
$445$	−3.96070	−	12.1898i	−0.187755	−	0.577852i
$446$		0			0
$447$	−4.35852	−	3.16665i	−0.206151	−	0.149778i
$448$		0			0
$449$	−11.5888	+	35.6668i	−0.546911	+	1.68322i	0.169490	+	0.985532i	$0.445788\pi$
$449$	−11.5888	+	35.6668i	−0.546911	+	1.68322i	−0.716402	+	0.697688i	$0.754212\pi$
$450$		0			0
$451$	−12.6995	−	15.9512i	−0.597997	−	0.751114i
$452$		0			0
$453$	−10.4252	+	32.0853i	−0.489817	+	1.50750i
$454$		0			0
$455$	−22.4216	−	16.2903i	−1.05114	−	0.763700i
$456$		0			0
$457$	4.80038	+	14.7740i	0.224552	+	0.691101i	0.998337	+	0.0576517i	$0.0183613\pi$
$457$	4.80038	+	14.7740i	0.224552	+	0.691101i	−0.773785	+	0.633449i	$0.781639\pi$
$458$		0			0
$459$	−4.60470	+	3.34551i	−0.214929	+	0.156155i
$460$		0			0
$461$	−20.4407			−0.952018			−0.476009	−	0.879440i	$-0.657917\pi$
$461$	−20.4407			−0.952018			−0.476009	+	0.879440i	$0.657917\pi$
$462$		0			0
$463$	9.64734			0.448350			0.224175	−	0.974549i	$-0.428031\pi$
$463$	9.64734			0.448350			0.224175	+	0.974549i	$0.428031\pi$
$464$		0			0
$465$	5.50811	−	4.00188i	0.255433	−	0.185583i
$466$		0			0
$467$	−4.31921	−	13.2932i	−0.199869	−	0.615134i	−0.999885	−	0.0151554i	$-0.995176\pi$
$467$	−4.31921	−	13.2932i	−0.199869	−	0.615134i	0.800016	−	0.599979i	$-0.204824\pi$
$468$		0			0
$469$	28.1633	+	20.4618i	1.30046	+	0.944839i
$470$		0			0
$471$	−11.6481	+	35.8491i	−0.536715	+	1.65184i
$472$		0			0
$473$	−0.646333	−	14.6569i	−0.0297184	−	0.673927i
$474$		0			0
$475$	1.29538	−	3.98678i	0.0594363	−	0.182926i
$476$		0			0
$477$	−14.7321	−	10.7035i	−0.674539	−	0.490081i
$478$		0			0
$479$	−8.88347	−	27.3405i	−0.405896	−	1.24922i	−0.920145	−	0.391578i	$-0.871929\pi$
$479$	−8.88347	−	27.3405i	−0.405896	−	1.24922i	0.514249	−	0.857641i	$-0.328071\pi$
$480$		0			0
$481$	27.3320	−	19.8578i	1.24623	−	0.905440i
$482$		0			0
$483$	−18.2886			−0.832158
$484$		0			0
$485$	9.53760			0.433080
$486$		0			0
$487$	8.33237	−	6.05382i	0.377576	−	0.274325i	−0.382770	−	0.923844i	$-0.625030\pi$
$487$	8.33237	−	6.05382i	0.377576	−	0.274325i	0.760345	+	0.649519i	$0.225030\pi$
$488$		0			0
$489$	−3.72528	−	11.4652i	−0.168463	−	0.518475i
$490$		0			0
$491$	−5.95322	−	4.32527i	−0.268665	−	0.195197i	0.445293	−	0.895385i	$-0.353099\pi$
$491$	−5.95322	−	4.32527i	−0.268665	−	0.195197i	−0.713958	+	0.700188i	$0.753099\pi$
$492$		0			0
$493$	7.92842	−	24.4012i	0.357078	−	1.09897i
$494$		0			0
$495$	0.328440	+	7.44804i	0.0147623	+	0.334765i
$496$		0			0
$497$	−3.22453	+	9.92409i	−0.144640	+	0.445156i
$498$		0			0
$499$	2.29474	+	1.66722i	0.102727	+	0.0746352i	0.637963	−	0.770067i	$-0.279777\pi$
$499$	2.29474	+	1.66722i	0.102727	+	0.0746352i	−0.535236	+	0.844702i	$0.679777\pi$
$500$		0			0
$501$	15.2550	+	46.9499i	0.681541	+	2.09757i
$502$		0			0
$503$	−11.1930	+	8.13221i	−0.499072	+	0.362597i	−0.808663	−	0.588273i	$-0.799808\pi$
$503$	−11.1930	+	8.13221i	−0.499072	+	0.362597i	0.309590	+	0.950870i	$0.399808\pi$
$504$		0			0
$505$	10.7259			0.477297
$506$		0			0
$507$	51.1209			2.27036
$508$		0			0
$509$	−20.1862	+	14.6661i	−0.894737	+	0.650064i	−0.937109	−	0.349038i	$-0.886509\pi$
$509$	−20.1862	+	14.6661i	−0.894737	+	0.650064i	0.0423720	+	0.999102i	$0.486509\pi$
$510$		0			0
$511$	10.8000	+	33.2389i	0.477762	+	1.47040i
$512$		0			0
$513$	5.84343	+	4.24550i	0.257994	+	0.187443i
$514$		0			0
$515$	0.796847	−	2.45244i	0.0351133	−	0.108068i
$516$		0			0
$517$	−8.53667	−	10.7225i	−0.375442	−	0.471574i
$518$		0			0
$519$	−5.01495	+	15.4344i	−0.220132	+	0.677496i
$520$		0			0
$521$	−1.39596	−	1.01422i	−0.0611581	−	0.0444339i	0.556786	−	0.830656i	$-0.312034\pi$
$521$	−1.39596	−	1.01422i	−0.0611581	−	0.0444339i	−0.617944	+	0.786222i	$0.712034\pi$
$522$		0			0
$523$	4.61819	+	14.2133i	0.201939	+	0.621505i	0.999825	+	0.0186967i	$0.00595170\pi$
$523$	4.61819	+	14.2133i	0.201939	+	0.621505i	−0.797886	+	0.602808i	$0.794048\pi$
$524$		0			0
$525$	8.64321	−	6.27966i	0.377221	−	0.274067i
$526$		0			0
$527$	−9.81758			−0.427660
$528$		0			0
$529$	−20.0696			−0.872592
$530$		0			0
$531$	−11.3026	+	8.21180i	−0.490490	+	0.356362i
$532$		0			0
$533$	−11.2894	−	34.7451i	−0.488997	−	1.50498i
$534$		0			0
$535$	14.2627	+	10.3625i	0.616632	+	0.448009i
$536$		0			0
$537$	−6.22075	+	19.1455i	−0.268445	+	0.826189i
$538$		0			0
$539$	45.8138	−	17.1518i	1.97334	−	0.738781i
$540$		0			0
$541$	−12.3669	+	38.0613i	−0.531693	+	1.63638i	0.218995	+	0.975726i	$0.429722\pi$
$541$	−12.3669	+	38.0613i	−0.531693	+	1.63638i	−0.750688	+	0.660657i	$0.770278\pi$
$542$		0			0
$543$	23.4353	+	17.0268i	1.00571	+	0.730689i
$544$		0			0
$545$	4.74268	+	14.5965i	0.203154	+	0.625244i
$546$		0			0
$547$	18.6066	−	13.5185i	0.795561	−	0.578009i	−0.114047	−	0.993475i	$-0.536382\pi$
$547$	18.6066	−	13.5185i	0.795561	−	0.578009i	0.909609	+	0.415466i	$0.136382\pi$
$548$		0			0
$549$	−3.43378			−0.146550
$550$		0			0
$551$	−32.5589			−1.38706
$552$		0			0
$553$	−66.1464	+	48.0581i	−2.81283	+	2.04364i
$554$		0			0
$555$	4.02442	+	12.3859i	0.170827	+	0.525752i
$556$		0			0
$557$	−9.64838	−	7.00996i	−0.408815	−	0.297022i	0.364307	−	0.931279i	$-0.381306\pi$
$557$	−9.64838	−	7.00996i	−0.408815	−	0.297022i	−0.773122	+	0.634257i	$0.781306\pi$
$558$		0			0
$559$	8.12333	−	25.0010i	0.343580	−	1.05743i
$560$		0			0
$561$	13.8433	−	20.9348i	0.584466	−	0.883868i
$562$		0			0
$563$	12.1429	−	37.3719i	0.511761	−	1.57504i	−0.277339	−	0.960772i	$-0.589453\pi$
$563$	12.1429	−	37.3719i	0.511761	−	1.57504i	0.789100	−	0.614265i	$-0.210547\pi$
$564$		0			0
$565$	0.256405	+	0.186289i	0.0107871	+	0.00783725i
$566$		0			0
$567$	15.4069	+	47.4176i	0.647030	+	1.99135i
$568$		0			0
$569$	13.9066	−	10.1037i	0.582995	−	0.423570i	−0.256808	−	0.966462i	$-0.582671\pi$
$569$	13.9066	−	10.1037i	0.582995	−	0.423570i	0.839802	+	0.542892i	$0.182671\pi$
$570$		0			0
$571$	26.4297			1.10605			0.553025	−	0.833165i	$-0.313473\pi$
$571$	26.4297			1.10605			0.553025	+	0.833165i	$0.313473\pi$
$572$		0			0
$573$	40.5989			1.69604
$574$		0			0
$575$	−1.38490	+	1.00619i	−0.0577545	+	0.0419611i
$576$		0			0
$577$	3.20877	+	9.87559i	0.133583	+	0.411126i	0.995367	−	0.0961494i	$-0.0306527\pi$
$577$	3.20877	+	9.87559i	0.133583	+	0.411126i	−0.861784	+	0.507275i	$0.830653\pi$
$578$		0			0
$579$	9.33217	+	6.78022i	0.387832	+	0.281776i
$580$		0			0
$581$	15.9658	−	49.1378i	0.662374	−	2.03858i
$582$		0			0
$583$	−25.8940	−	7.16891i	−1.07242	−	0.296906i
$584$		0			0
$585$	−4.12794	+	12.7045i	−0.170669	+	0.525266i
$586$		0			0
$587$	−17.2197	−	12.5109i	−0.710735	−	0.516379i	0.172676	−	0.984979i	$-0.444759\pi$
$587$	−17.2197	−	12.5109i	−0.710735	−	0.516379i	−0.883411	+	0.468600i	$0.844759\pi$
$588$		0			0
$589$	3.84993	+	11.8489i	0.158634	+	0.488224i
$590$		0			0
$591$	27.9030	−	20.2727i	1.14777	−	0.833907i
$592$		0			0
$593$	−6.74652			−0.277046			−0.138523	−	0.990359i	$-0.544236\pi$
$593$	−6.74652			−0.277046			−0.138523	+	0.990359i	$0.544236\pi$
$594$		0			0
$595$	−15.4055			−0.631565
$596$		0			0
$597$	4.75437	−	3.45425i	0.194583	−	0.141373i
$598$		0			0
$599$	1.26509	+	3.89353i	0.0516900	+	0.159085i	0.973569	−	0.228392i	$-0.0733467\pi$
$599$	1.26509	+	3.89353i	0.0516900	+	0.159085i	−0.921879	+	0.387477i	$0.873347\pi$
$600$		0			0
$601$	−1.99582	−	1.45005i	−0.0814112	−	0.0591487i	0.546335	−	0.837567i	$-0.316022\pi$
$601$	−1.99582	−	1.45005i	−0.0814112	−	0.0591487i	−0.627746	+	0.778418i	$0.716022\pi$
$602$		0			0
$603$	5.18501	−	15.9578i	0.211150	−	0.649852i
$604$		0			0
$605$	4.30686	+	10.1218i	0.175099	+	0.411510i
$606$		0			0
$607$	−8.63465	+	26.5747i	−0.350470	+	1.07863i	0.608120	+	0.793845i	$0.291924\pi$
$607$	−8.63465	+	26.5747i	−0.350470	+	1.07863i	−0.958590	+	0.284790i	$0.908076\pi$
$608$		0			0
$609$	−67.1319	−	48.7742i	−2.72032	−	1.97643i
$610$		0			0
$611$	−7.58876	−	23.3558i	−0.307008	−	0.944874i
$612$		0			0
$613$	31.4825	−	22.8734i	1.27157	−	0.923848i	0.272304	−	0.962211i	$-0.412214\pi$
$613$	31.4825	−	22.8734i	1.27157	−	0.923848i	0.999264	+	0.0383629i	$0.0122143\pi$
$614$		0			0
$615$	14.0830			0.567881
$616$		0			0
$617$	−0.639294			−0.0257370			−0.0128685	−	0.999917i	$-0.504096\pi$
$617$	−0.639294			−0.0257370			−0.0128685	+	0.999917i	$0.504096\pi$
$618$		0			0
$619$	−15.6081	+	11.3400i	−0.627344	+	0.455792i	−0.855479	−	0.517837i	$-0.826737\pi$
$619$	−15.6081	+	11.3400i	−0.627344	+	0.455792i	0.228135	+	0.973630i	$0.426737\pi$
$620$		0			0
$621$	−0.911462	−	2.80519i	−0.0365757	−	0.112568i
$622$		0			0
$623$	48.3587	+	35.1346i	1.93745	+	1.40764i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	−30.6949	−	8.49805i	−1.22584	−	0.339379i
$628$		0			0
$629$	5.80313	−	17.8602i	0.231386	−	0.712133i
$630$		0			0
$631$	13.2570	+	9.63174i	0.527751	+	0.383434i	0.819516	−	0.573057i	$-0.194242\pi$
$631$	13.2570	+	9.63174i	0.527751	+	0.383434i	−0.291765	+	0.956490i	$0.594242\pi$
$632$		0			0
$633$	−6.88008	−	21.1747i	−0.273459	−	0.841619i
$634$		0			0
$635$	−14.6166	+	10.6196i	−0.580042	+	0.421425i
$636$		0			0
$637$	87.6528			3.47293
$638$		0			0
$639$	5.02951			0.198964
$640$		0			0
$641$	7.38771	−	5.36749i	0.291797	−	0.212003i	−0.432250	−	0.901754i	$-0.642280\pi$
$641$	7.38771	−	5.36749i	0.291797	−	0.212003i	0.724047	+	0.689751i	$0.242280\pi$
$642$		0			0
$643$	−12.2080	−	37.5724i	−0.481437	−	1.48171i	−0.837076	−	0.547087i	$-0.815737\pi$
$643$	−12.2080	−	37.5724i	−0.481437	−	1.48171i	0.355639	−	0.934623i	$-0.384263\pi$
$644$		0			0
$645$	8.19817	+	5.95632i	0.322803	+	0.234530i
$646$		0			0
$647$	−1.31884	+	4.05896i	−0.0518488	+	0.159574i	−0.973628	−	0.228140i	$-0.926735\pi$
$647$	−1.31884	+	4.05896i	−0.0518488	+	0.159574i	0.921779	+	0.387715i	$0.126735\pi$
$648$		0			0
$649$	−11.3698	+	17.1941i	−0.446303	+	0.674928i
$650$		0			0
$651$	−9.81192	+	30.1980i	−0.384560	+	1.18355i
$652$		0			0
$653$	3.53416	+	2.56772i	0.138302	+	0.100482i	0.654785	−	0.755815i	$-0.272759\pi$
$653$	3.53416	+	2.56772i	0.138302	+	0.100482i	−0.516483	+	0.856297i	$0.672759\pi$
$654$		0			0
$655$	−2.45723	−	7.56257i	−0.0960119	−	0.295494i
$656$		0			0
$657$	13.6282	−	9.90147i	0.531687	−	0.386293i
$658$		0			0
$659$	0.146275			0.00569808			0.00284904	−	0.999996i	$-0.499093\pi$
$659$	0.146275			0.00569808			0.00284904	+	0.999996i	$0.499093\pi$
$660$		0			0
$661$	41.7505			1.62391			0.811953	−	0.583723i	$-0.198405\pi$
$661$	41.7505			1.62391			0.811953	+	0.583723i	$0.198405\pi$
$662$		0			0
$663$	36.3816	−	26.4328i	1.41294	−	1.02656i
$664$		0			0
$665$	6.04122	+	18.5930i	0.234269	+	0.721005i
$666$		0			0
$667$	10.7566	+	7.81511i	0.416496	+	0.302602i
$668$		0			0
$669$	−0.384748	+	1.18413i	−0.0148752	+	0.0457812i
$670$		0			0
$671$	−4.74480	+	1.77636i	−0.183171	+	0.0685757i
$672$		0			0
$673$	0.799949	−	2.46199i	0.0308358	−	0.0949027i	−0.934454	−	0.356083i	$-0.884112\pi$
$673$	0.799949	−	2.46199i	0.0308358	−	0.0949027i	0.965290	+	0.261181i	$0.0841119\pi$
$674$		0			0
$675$	1.39396	+	1.01277i	0.0536537	+	0.0389817i
$676$		0			0
$677$	13.9186	+	42.8370i	0.534934	+	1.64636i	0.743791	+	0.668413i	$0.233026\pi$
$677$	13.9186	+	42.8370i	0.534934	+	1.64636i	−0.208856	+	0.977946i	$0.566974\pi$
$678$		0			0
$679$	−35.9851	+	26.1447i	−1.38098	+	1.00334i
$680$		0			0
$681$	−11.9060			−0.456239
$682$		0			0
$683$	34.4943			1.31989			0.659944	−	0.751314i	$-0.270580\pi$
$683$	34.4943			1.31989			0.659944	+	0.751314i	$0.270580\pi$
$684$		0			0
$685$	−6.53482	+	4.74782i	−0.249683	+	0.181405i
$686$		0			0
$687$	−2.89614	−	8.91341i	−0.110495	−	0.340068i
$688$		0			0
$689$	−38.9477	−	28.2971i	−1.48379	−	1.07803i
$690$		0			0
$691$	−6.86210	+	21.1194i	−0.261046	+	0.803418i	0.731531	+	0.681808i	$0.238806\pi$
$691$	−6.86210	+	21.1194i	−0.261046	+	0.803418i	−0.992578	+	0.121611i	$0.961194\pi$
$692$		0			0
$693$	−21.6560	−	27.2010i	−0.822643	−	1.03328i
$694$		0			0
$695$	3.49930	−	10.7697i	0.132736	−	0.408519i
$696$		0			0
$697$	−16.4290	−	11.9364i	−0.622293	−	0.452123i
$698$		0			0
$699$	9.87141	+	30.3811i	0.373371	+	1.14912i
$700$		0			0
$701$	−6.48043	+	4.70831i	−0.244763	+	0.177830i	−0.703402	−	0.710792i	$-0.748337\pi$
$701$	−6.48043	+	4.70831i	−0.244763	+	0.177830i	0.458640	+	0.888622i	$0.348337\pi$
$702$		0			0
$703$	−23.8312			−0.898812
$704$		0			0
$705$	9.46664			0.356534
$706$		0			0
$707$	−40.4687	+	29.4022i	−1.52198	+	1.10578i
$708$		0			0
$709$	3.93756	+	12.1186i	0.147878	+	0.455122i	0.997370	−	0.0724796i	$-0.0230912\pi$
$709$	3.93756	+	12.1186i	0.147878	+	0.455122i	−0.849492	+	0.527602i	$0.823091\pi$
$710$		0			0
$711$	31.8821	+	23.1637i	1.19567	+	0.868707i
$712$		0			0
$713$	1.57217	−	4.83864i	0.0588781	−	0.181208i
$714$		0			0
$715$	0.868303	+	19.6905i	0.0324727	+	0.736384i
$716$		0			0
$717$	−0.370635	+	1.14070i	−0.0138416	+	0.0426001i
$718$		0			0
$719$	−4.97964	−	3.61792i	−0.185709	−	0.134926i	0.491046	−	0.871133i	$-0.336615\pi$
$719$	−4.97964	−	3.61792i	−0.185709	−	0.134926i	−0.676755	+	0.736208i	$0.736615\pi$
$720$		0			0
$721$	3.71622	+	11.4373i	0.138399	+	0.425949i
$722$		0			0
$723$	11.8243	−	8.59088i	0.439751	−	0.319498i
$724$		0			0
$725$	−7.76702			−0.288460
$726$		0			0
$727$	9.77647			0.362589			0.181295	−	0.983429i	$-0.441971\pi$
$727$	9.77647			0.362589			0.181295	+	0.983429i	$0.441971\pi$
$728$		0			0
$729$	9.86165	−	7.16491i	0.365246	−	0.265367i
$730$		0			0
$731$	−4.51545	−	13.8971i	−0.167010	−	0.514004i
$732$		0			0
$733$	17.9574	+	13.0468i	0.663272	+	0.481895i	0.867766	−	0.496972i	$-0.165555\pi$
$733$	17.9574	+	13.0468i	0.663272	+	0.481895i	−0.204494	+	0.978868i	$0.565555\pi$
$734$		0			0
$735$	−10.4413	+	32.1351i	−0.385134	+	1.18532i
$736$		0			0
$737$	−1.09065	−	24.7328i	−0.0401748	−	0.911045i
$738$		0			0
$739$	−6.41509	+	19.7436i	−0.235983	+	0.726281i	0.761007	+	0.648744i	$0.224705\pi$
$739$	−6.41509	+	19.7436i	−0.235983	+	0.726281i	−0.996990	+	0.0775365i	$0.975295\pi$
$740$		0			0
$741$	−46.1687	−	33.5435i	−1.69605	−	1.23225i
$742$		0			0
$743$	10.7212	+	32.9965i	0.393323	+	1.21052i	0.930260	+	0.366901i	$0.119581\pi$
$743$	10.7212	+	32.9965i	0.393323	+	1.21052i	−0.536937	+	0.843622i	$0.680419\pi$
$744$		0			0
$745$	1.90261	−	1.38232i	0.0697061	−	0.0506444i
$746$		0			0
$747$	−24.9029			−0.911150
$748$		0			0
$749$	−82.2189			−3.00421
$750$		0			0
$751$	−16.6954	+	12.1299i	−0.609224	+	0.442627i	−0.849141	−	0.528166i	$-0.822880\pi$
$751$	−16.6954	+	12.1299i	−0.609224	+	0.442627i	0.239917	+	0.970793i	$0.422880\pi$
$752$		0			0
$753$	−9.65669	−	29.7202i	−0.351909	−	1.08307i
$754$		0			0
$755$	−11.9143	−	8.65622i	−0.433605	−	0.315032i
$756$		0			0
$757$	−7.31734	+	22.5204i	−0.265953	+	0.818520i	0.725519	+	0.688202i	$0.241600\pi$
$757$	−7.31734	+	22.5204i	−0.265953	+	0.818520i	−0.991472	+	0.130318i	$0.958400\pi$
$758$		0			0
$759$	8.10096	+	10.1752i	0.294046	+	0.369336i
$760$		0			0
$761$	14.3705	−	44.2278i	0.520930	−	1.60326i	−0.251297	−	0.967910i	$-0.580857\pi$
$761$	14.3705	−	44.2278i	0.520930	−	1.60326i	0.772227	−	0.635347i	$-0.219143\pi$
$762$		0			0
$763$	−57.9063	−	42.0714i	−2.09635	−	1.52309i
$764$		0			0
$765$	2.29456	+	7.06194i	0.0829601	+	0.255325i
$766$		0			0
$767$	−29.8808	+	21.7097i	−1.07893	+	0.783892i
$768$		0			0
$769$	8.48780			0.306078			0.153039	−	0.988220i	$-0.451094\pi$
$769$	8.48780			0.306078			0.153039	+	0.988220i	$0.451094\pi$
$770$		0			0
$771$	−5.51412			−0.198586
$772$		0			0
$773$	−36.2516	+	26.3384i	−1.30388	+	0.947325i	−0.999986	−	0.00538094i	$-0.998287\pi$
$773$	−36.2516	+	26.3384i	−1.30388	+	0.947325i	−0.303895	+	0.952706i	$0.598287\pi$
$774$		0			0
$775$	0.918410	+	2.82658i	0.0329903	+	0.101534i
$776$		0			0
$777$	−49.1366	−	35.6998i	−1.76277	−	1.28072i
$778$		0			0
$779$	−7.96347	+	24.5090i	−0.285321	+	0.878127i
$780$		0			0
$781$	6.94978	−	2.60187i	0.248683	−	0.0931022i
$782$		0			0
$783$	4.13553	−	12.7278i	0.147792	−	0.454856i
$784$		0			0
$785$	−13.3118	−	9.67162i	−0.475120	−	0.345195i
$786$		0			0
$787$	−1.39122	−	4.28172i	−0.0495915	−	0.152627i	0.923194	−	0.384334i	$-0.125569\pi$
$787$	−1.39122	−	4.28172i	−0.0495915	−	0.152627i	−0.972786	+	0.231707i	$0.925569\pi$
$788$		0			0
$789$	−21.8397	+	15.8675i	−0.777513	+	0.564896i
$790$		0			0
$791$	−1.47807			−0.0525542
$792$		0			0
$793$	−9.07795			−0.322367
$794$		0			0
$795$	15.0137	−	10.9081i	0.532483	−	0.386871i
$796$		0			0
$797$	10.7449	+	33.0695i	0.380605	+	1.17138i	0.939619	+	0.342223i	$0.111180\pi$
$797$	10.7449	+	33.0695i	0.380605	+	1.17138i	−0.559014	+	0.829158i	$0.688820\pi$
$798$		0			0
$799$	−11.0436	−	8.02368i	−0.390696	−	0.283857i
$800$		0			0
$801$	8.90308	−	27.4009i	0.314575	−	0.968162i
$802$		0			0
$803$	13.7092	−	20.7320i	0.483788	−	0.731617i
$804$		0			0
$805$	2.46701	−	7.59268i	0.0869507	−	0.267607i
$806$		0			0
$807$	28.0659	+	20.3910i	0.987965	+	0.717799i
$808$		0			0
$809$	16.5478	+	50.9290i	0.581790	+	1.79057i	0.611794	+	0.791017i	$0.290448\pi$
$809$	16.5478	+	50.9290i	0.581790	+	1.79057i	−0.0300036	+	0.999550i	$0.509552\pi$
$810$		0			0
$811$	−14.2011	+	10.3177i	−0.498667	+	0.362303i	−0.808508	−	0.588485i	$-0.799724\pi$
$811$	−14.2011	+	10.3177i	−0.498667	+	0.362303i	0.309840	+	0.950789i	$0.399724\pi$
$812$		0			0
$813$	24.2228			0.849530
$814$		0			0
$815$	5.26242			0.184334
$816$		0			0
$817$	−15.0018	+	10.8994i	−0.524845	+	0.381322i
$818$		0			0
$819$	−19.2513	−	59.2494i	−0.672694	−	2.07034i
$820$		0			0
$821$	−10.0045	−	7.26871i	−0.349160	−	0.253680i	0.399356	−	0.916796i	$-0.369234\pi$
$821$	−10.0045	−	7.26871i	−0.349160	−	0.253680i	−0.748517	+	0.663116i	$0.769234\pi$
$822$		0			0
$823$	4.33731	−	13.3489i	0.151189	−	0.465312i	−0.846566	−	0.532284i	$-0.821334\pi$
$823$	4.33731	−	13.3489i	0.151189	−	0.465312i	0.997755	+	0.0669720i	$0.0213338\pi$
$824$		0			0
$825$	−7.32234	−	2.02723i	−0.254931	−	0.0705791i
$826$		0			0
$827$	7.97527	−	24.5454i	0.277327	−	0.853526i	−0.711267	−	0.702922i	$-0.751878\pi$
$827$	7.97527	−	24.5454i	0.277327	−	0.853526i	0.988594	−	0.150604i	$-0.0481217\pi$
$828$		0			0
$829$	−11.3328	−	8.23376i	−0.393604	−	0.285970i	0.373327	−	0.927700i	$-0.378217\pi$
$829$	−11.3328	−	8.23376i	−0.393604	−	0.285970i	−0.766931	+	0.641730i	$0.778217\pi$
$830$		0			0
$831$	−17.8049	−	54.7977i	−0.617644	−	1.90091i
$832$		0			0
$833$	39.4176	−	28.6386i	1.36574	−	0.992268i
$834$		0			0
$835$	−21.5495			−0.745752
$836$		0			0
$837$	−5.12093			−0.177005
$838$		0			0
$839$	5.50277	−	3.99799i	0.189977	−	0.138026i	−0.488731	−	0.872434i	$-0.662540\pi$
$839$	5.50277	−	3.99799i	0.189977	−	0.138026i	0.678708	+	0.734408i	$0.262540\pi$
$840$		0			0
$841$	9.68043	+	29.7933i	0.333808	+	1.02736i
$842$		0			0
$843$	0.598557	+	0.434877i	0.0206154	+	0.0149780i
$844$		0			0
$845$	−6.89589	+	21.2234i	−0.237226	+	0.730106i
$846$		0			0
$847$	−43.9959	−	26.3832i	−1.51172	−	0.906539i
$848$		0			0
$849$	−15.1295	+	46.5639i	−0.519244	+	1.59807i
$850$		0			0
$851$	7.87318	+	5.72020i	0.269889	+	0.196086i
$852$		0			0
$853$	−14.4917	−	44.6010i	−0.496188	−	1.52711i	−0.815097	−	0.579324i	$-0.803317\pi$
$853$	−14.4917	−	44.6010i	−0.496188	−	1.52711i	0.318909	−	0.947785i	$-0.396683\pi$
$854$		0			0
$855$	7.62327	−	5.53863i	0.260710	−	0.189417i
$856$		0			0
$857$	−2.79309			−0.0954100			−0.0477050	−	0.998861i	$-0.515191\pi$
$857$	−2.79309			−0.0954100			−0.0477050	+	0.998861i	$0.515191\pi$
$858$		0			0
$859$	−5.83184			−0.198980			−0.0994898	−	0.995039i	$-0.531721\pi$
$859$	−5.83184			−0.198980			−0.0994898	+	0.995039i	$0.531721\pi$
$860$		0			0
$861$	−53.1348	+	38.6047i	−1.81083	+	1.31564i
$862$		0			0
$863$	−13.8593	−	42.6544i	−0.471775	−	1.45197i	−0.850258	−	0.526366i	$-0.823554\pi$
$863$	−13.8593	−	42.6544i	−0.471775	−	1.45197i	0.378483	−	0.925608i	$-0.376446\pi$
$864$		0			0
$865$	−5.73128	−	4.16402i	−0.194869	−	0.141581i
$866$		0			0
$867$	−4.30979	+	13.2642i	−0.146368	+	0.450474i
$868$		0			0
$869$	56.0378	+	15.5144i	1.90095	+	0.526289i
$870$		0			0
$871$	13.7077	−	42.1880i	0.464468	−	1.42948i
$872$		0			0
$873$	17.3446	+	12.6016i	0.587026	+	0.426499i
$874$		0			0
$875$	1.44115	+	4.43540i	0.0487197	+	0.149944i
$876$		0			0
$877$	12.8380	−	9.32736i	0.433509	−	0.314962i	−0.349542	−	0.936921i	$-0.613663\pi$
$877$	12.8380	−	9.32736i	0.433509	−	0.314962i	0.783050	+	0.621958i	$0.213663\pi$
$878$		0			0
$879$	−24.0539			−0.811318
$880$		0			0
$881$	−30.1411			−1.01548			−0.507740	−	0.861510i	$-0.669519\pi$
$881$	−30.1411			−1.01548			−0.507740	+	0.861510i	$0.669519\pi$
$882$		0			0
$883$	−34.6023	+	25.1400i	−1.16446	+	0.846030i	−0.990335	−	0.138694i	$-0.955710\pi$
$883$	−34.6023	+	25.1400i	−1.16446	+	0.846030i	−0.174124	+	0.984724i	$0.555710\pi$
$884$		0			0
$885$	−4.39972	−	13.5409i	−0.147895	−	0.455174i
$886$		0			0
$887$	5.38867	+	3.91510i	0.180934	+	0.131456i	0.674566	−	0.738215i	$-0.264331\pi$
$887$	5.38867	+	3.91510i	0.180934	+	0.131456i	−0.493632	+	0.869671i	$0.664331\pi$
$888$		0			0
$889$	26.0374	−	80.1349i	0.873267	−	2.68764i
$890$		0			0
$891$	19.5572	−	29.5757i	0.655191	−	0.990823i
$892$		0			0
$893$	−5.35308	+	16.4751i	−0.179134	+	0.551317i
$894$		0			0
$895$	−7.10931	−	5.16521i	−0.237638	−	0.172654i
$896$		0			0
$897$	7.20142	+	22.1637i	0.240449	+	0.740025i
$898$		0			0
$899$	18.6752	−	13.5684i	0.622854	−	0.452530i
$900$		0			0
$901$	−26.7603			−0.891514
$902$		0			0
$903$	−47.2592			−1.57269
$904$		0			0
$905$	−10.2301	+	7.43261i	−0.340060	+	0.247068i
$906$		0			0
$907$	11.5359	+	35.5039i	0.383043	+	1.17889i	0.937890	+	0.346934i	$0.112777\pi$
$907$	11.5359	+	35.5039i	0.383043	+	1.17889i	−0.554846	+	0.831953i	$0.687223\pi$
$908$		0			0
$909$	19.5056	+	14.1717i	0.646961	+	0.470045i
$910$		0			0
$911$	4.55019	−	14.0040i	0.150755	−	0.463975i	−0.846952	−	0.531670i	$-0.821565\pi$
$911$	4.55019	−	14.0040i	0.150755	−	0.463975i	0.997706	+	0.0676955i	$0.0215646\pi$
$912$		0			0
$913$	−34.4109	+	12.8828i	−1.13883	+	0.426358i
$914$		0			0
$915$	1.08138	−	3.32814i	0.0357493	−	0.110025i
$916$		0			0
$917$	30.0018	+	21.7976i	0.990747	+	0.719820i
$918$		0			0
$919$	10.5128	+	32.3552i	0.346787	+	1.06730i	0.960620	+	0.277864i	$0.0896265\pi$
$919$	10.5128	+	32.3552i	0.346787	+	1.06730i	−0.613834	+	0.789435i	$0.710374\pi$
$920$		0			0
$921$	−53.8569	+	39.1293i	−1.77465	+	1.28936i
$922$		0			0
$923$	13.2966			0.437664
$924$		0			0
$925$	−5.68500			−0.186922
$926$		0			0
$927$	4.68941	−	3.40705i	0.154020	−	0.111902i
$928$		0			0
$929$	5.77838	+	17.7840i	0.189582	+	0.583475i	0.999997	−	0.00238187i	$-0.000758173\pi$
$929$	5.77838	+	17.7840i	0.189582	+	0.583475i	−0.810415	+	0.585857i	$0.800758\pi$
$930$		0			0
$931$	−50.0215	−	36.3427i	−1.63939	−	1.19108i
$932$		0			0
$933$	14.1214	−	43.4613i	0.462315	−	1.42286i
$934$		0			0
$935$	6.82392	+	8.57117i	0.223166	+	0.280307i
$936$		0			0
$937$	0.0378104	−	0.116369i	0.00123521	−	0.00380160i	−0.950437	−	0.310917i	$-0.899364\pi$
$937$	0.0378104	−	0.116369i	0.00123521	−	0.00380160i	0.951672	+	0.307116i	$0.0993638\pi$
$938$		0			0
$939$	−32.3959	−	23.5370i	−1.05720	−	0.768102i
$940$		0			0
$941$	9.21831	+	28.3710i	0.300508	+	0.924869i	0.981315	+	0.192407i	$0.0616292\pi$
$941$	9.21831	+	28.3710i	0.300508	+	0.924869i	−0.680807	+	0.732463i	$0.738371\pi$
$942$		0			0
$943$	8.51380	−	6.18564i	0.277248	−	0.201432i
$944$		0			0
$945$	−8.03564			−0.261399
$946$		0			0
$947$	49.0368			1.59348			0.796741	−	0.604320i	$-0.206555\pi$
$947$	49.0368			1.59348			0.796741	+	0.604320i	$0.206555\pi$
$948$		0			0
$949$	36.0292	−	26.1767i	1.16956	−	0.849732i
$950$		0			0
$951$	−21.1164	−	64.9895i	−0.684745	−	2.10743i
$952$		0			0
$953$	−27.1125	−	19.6984i	−0.878260	−	0.638093i	0.0545306	−	0.998512i	$-0.482634\pi$
$953$	−27.1125	−	19.6984i	−0.878260	−	0.638093i	−0.932791	+	0.360419i	$0.882634\pi$
$954$		0			0
$955$	−5.47653	+	16.8550i	−0.177216	+	0.545416i
$956$		0			0
$957$	2.59976	+	58.9548i	0.0840382	+	1.90574i
$958$		0			0
$959$	11.6409	−	35.8269i	0.375903	−	1.15691i
$960$		0			0
$961$	17.9335	+	13.0294i	0.578499	+	0.420304i
$962$		0			0
$963$	12.2460	+	37.6894i	0.394623	+	1.21452i
$964$		0			0
$965$	−4.07373	+	2.95973i	−0.131138	+	0.0952772i
$966$		0			0
$967$	−52.5565			−1.69010			−0.845052	−	0.534685i	$-0.820430\pi$
$967$	−52.5565			−1.69010			−0.845052	+	0.534685i	$0.820430\pi$
$968$		0			0
$969$	−31.7217			−1.01905
$970$		0			0
$971$	3.46962	−	2.52083i	0.111345	−	0.0808971i	−0.530719	−	0.847548i	$-0.678078\pi$
$971$	3.46962	−	2.52083i	0.111345	−	0.0808971i	0.642065	+	0.766651i	$0.278078\pi$
$972$		0			0
$973$	16.3195	+	50.2263i	0.523180	+	1.61018i
$974$		0			0
$975$	−11.0137	−	8.00189i	−0.352719	−	0.256266i
$976$		0			0
$977$	−6.66156	+	20.5022i	−0.213122	+	0.655923i	0.786159	+	0.618024i	$0.212066\pi$
$977$	−6.66156	+	20.5022i	−0.213122	+	0.655923i	−0.999282	+	0.0378988i	$0.987934\pi$
$978$		0			0
$979$	−1.87274	−	42.4683i	−0.0598531	−	1.35729i
$980$		0			0
$981$	−10.6608	+	32.8107i	−0.340375	+	1.04757i
$982$		0			0
$983$	21.3311	+	15.4979i	0.680356	+	0.494307i	0.873476	−	0.486868i	$-0.161861\pi$
$983$	21.3311	+	15.4979i	0.680356	+	0.494307i	−0.193120	+	0.981175i	$0.561861\pi$
$984$		0			0
$985$	4.65248	+	14.3189i	0.148240	+	0.456237i
$986$		0			0
$987$	−35.7174	+	25.9502i	−1.13690	+	0.826005i
$988$		0			0
$989$	7.57235			0.240787
$990$		0			0
$991$	49.3520			1.56772			0.783858	−	0.620940i	$-0.213249\pi$
$991$	49.3520			1.56772			0.783858	+	0.620940i	$0.213249\pi$
$992$		0			0
$993$	54.6244	−	39.6870i	1.73345	−	1.25943i
$994$		0			0
$995$	0.792732	+	2.43978i	0.0251313	+	0.0773462i
$996$		0			0
$997$	2.28959	+	1.66349i	0.0725122	+	0.0526832i	0.623451	−	0.781863i	$-0.285730\pi$
$997$	2.28959	+	1.66349i	0.0725122	+	0.0526832i	−0.550939	+	0.834546i	$0.685730\pi$
$998$		0			0
$999$	3.02696	−	9.31603i	0.0957688	−	0.294746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.i.801.1		12
4.3	odd	2		440.2.y.c.361.3	✓	12
11.4	even	5		9680.2.a.dc.1.5		6
11.5	even	5	inner	880.2.bo.i.401.1		12
11.7	odd	10		9680.2.a.dd.1.5		6
44.7	even	10		4840.2.a.ba.1.2		6
44.15	odd	10		4840.2.a.bb.1.2		6
44.27	odd	10		440.2.y.c.401.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.c.361.3	✓	12	4.3	odd	2
440.2.y.c.401.3	yes	12	44.27	odd	10
880.2.bo.i.401.1		12	11.5	even	5	inner
880.2.bo.i.801.1		12	1.1	even	1	trivial
4840.2.a.ba.1.2		6	44.7	even	10
4840.2.a.bb.1.2		6	44.15	odd	10
9680.2.a.dc.1.5		6	11.4	even	5
9680.2.a.dd.1.5		6	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.85331 + 1.34651i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(3.77298 + 2.74123i) q^{7} +(0.694624 - 2.13783i) q^{9} +(-0.146113 - 3.31340i) q^{11} +(1.83639 - 5.65184i) q^{13} +(1.85331 + 1.34651i) q^{15} +(-1.02078 - 3.14164i) q^{17} +(-3.39136 + 2.46397i) q^{19} -10.6836 q^{21} +1.71184 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.532447 - 1.63870i) q^{27} +(6.28365 + 4.56534i) q^{29} +(0.918410 - 2.82658i) q^{31} +(4.73232 + 5.94403i) q^{33} +(1.44115 - 4.43540i) q^{35} +(4.59926 + 3.34156i) q^{37} +(4.20684 + 12.9473i) q^{39} +(4.97349 - 3.61345i) q^{41} +4.42353 q^{43} -2.24785 q^{45} +(3.34320 - 2.42898i) q^{47} +(4.55790 + 14.0278i) q^{49} +(6.12207 + 4.44795i) q^{51} +(2.50336 - 7.70454i) q^{53} +(-3.10608 + 1.16286i) q^{55} +(2.96749 - 9.13299i) q^{57} +(-5.02817 - 3.65318i) q^{59} +(-0.472049 - 1.45282i) q^{61} +(8.48109 - 6.16188i) q^{63} -5.94269 q^{65} +7.46447 q^{67} +(-3.17257 + 2.30500i) q^{69} +(0.691418 + 2.12796i) q^{71} +(6.06277 + 4.40486i) q^{73} +(0.707902 - 2.17870i) q^{75} +(8.53152 - 12.9019i) q^{77} +(-5.41757 + 16.6736i) q^{79} +(8.64897 + 6.28385i) q^{81} +(-3.42346 - 10.5363i) q^{83} +(-2.67244 + 1.94164i) q^{85} -17.7928 q^{87} +12.8171 q^{89} +(22.4216 - 16.2903i) q^{91} +(2.10391 + 6.47518i) q^{93} +(3.39136 + 2.46397i) q^{95} +(-2.94728 + 9.07079i) q^{97} +(-7.18500 - 1.98921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} + 18 q^{13} - q^{15} + 3 q^{17} - 4 q^{19} - 28 q^{21} + 18 q^{23} - 3 q^{25} - 23 q^{27} + 15 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{35} + 6 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) \) 12 * q + q^3 + 3 * q^5 + q^7 - 10 * q^9 - 4 * q^11 + 18 * q^13 - q^15 + 3 * q^17 - 4 * q^19 - 28 * q^21 + 18 * q^23 - 3 * q^25 - 23 * q^27 + 15 * q^29 + 8 * q^31 + 4 * q^33 - 6 * q^35 + 6 * q^37 + 33 * q^39 + 2 * q^41 + 36 * q^43 - 10 * q^45 + 16 * q^47 - 16 * q^49 + 10 * q^51 + 19 * q^53 - 6 * q^55 + 62 * q^57 - 46 * q^59 + 18 * q^61 + 7 * q^63 + 2 * q^65 + 44 * q^67 - q^69 + 6 * q^71 + 25 * q^73 - 4 * q^75 + 10 * q^77 - 19 * q^79 + 30 * q^81 - 3 * q^85 - 6 * q^87 - 50 * q^89 + 46 * q^91 - 37 * q^93 + 4 * q^95 - 31 * q^97 - 79 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more