LMFDB - Embedded newform 1152.2.p.g.959.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			959.2
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.g.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54472 + 0.783472i) q^{3} +(-1.07112 + 1.85524i) q^{5} +(1.13037 - 0.652621i) q^{7} +(1.77234 - 2.42050i) q^{9} +O(q^{10})$	\(q+(-1.54472 + 0.783472i) q^{3} +(-1.07112 + 1.85524i) q^{5} +(1.13037 - 0.652621i) q^{7} +(1.77234 - 2.42050i) q^{9} +(-2.36103 + 1.36314i) q^{11} +(1.16603 + 0.673209i) q^{13} +(0.201060 - 3.70502i) q^{15} +4.27575i q^{17} -2.16174 q^{19} +(-1.23480 + 1.89374i) q^{21} +(-1.01947 + 1.76577i) q^{23} +(0.205398 + 0.355759i) q^{25} +(-0.841387 + 5.12758i) q^{27} +(2.72776 + 4.72461i) q^{29} +(-6.09216 - 3.51731i) q^{31} +(2.57915 - 3.95547i) q^{33} +2.79615i q^{35} -10.3381i q^{37} +(-2.32864 - 0.126368i) q^{39} +(0.596355 + 0.344306i) q^{41} +(-1.22839 - 2.12763i) q^{43} +(2.59220 + 5.88076i) q^{45} +(-6.56713 - 11.3746i) q^{47} +(-2.64817 + 4.58677i) q^{49} +(-3.34993 - 6.60485i) q^{51} -9.56171 q^{53} -5.84035i q^{55} +(3.33929 - 1.69366i) q^{57} +(-8.97985 - 5.18452i) q^{59} +(7.68757 - 4.43842i) q^{61} +(0.423741 - 3.89273i) q^{63} +(-2.49793 + 1.44218i) q^{65} +(-6.23532 + 10.7999i) q^{67} +(0.191364 - 3.52635i) q^{69} +4.94992 q^{71} -12.8268 q^{73} +(-0.596010 - 0.388627i) q^{75} +(-1.77923 + 3.08171i) q^{77} +(0.680856 - 0.393093i) q^{79} +(-2.71761 - 8.57990i) q^{81} +(1.82152 - 1.05165i) q^{83} +(-7.93253 - 4.57985i) q^{85} +(-7.91523 - 5.16110i) q^{87} +12.1722i q^{89} +1.75740 q^{91} +(12.1664 + 0.660234i) q^{93} +(2.31548 - 4.01053i) q^{95} +(-8.05440 - 13.9506i) q^{97} +(-0.885074 + 8.13081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{7} - 4 q^{9}+O(q^{10}) $ 24 * q + 12 * q^7 - 4 * q^9	$ 24 q + 12 q^{7} - 4 q^{9} + 20 q^{15} - 12 q^{23} - 12 q^{25} - 36 q^{31} + 4 q^{33} + 20 q^{39} - 12 q^{41} + 12 q^{47} + 12 q^{49} + 4 q^{57} - 92 q^{63} - 48 q^{65} + 24 q^{73} + 84 q^{79} - 20 q^{81} + 68 q^{87} + 24 q^{95} - 12 q^{97}+O(q^{100}) $ 24 * q + 12 * q^7 - 4 * q^9 + 20 * q^15 - 12 * q^23 - 12 * q^25 - 36 * q^31 + 4 * q^33 + 20 * q^39 - 12 * q^41 + 12 * q^47 + 12 * q^49 + 4 * q^57 - 92 * q^63 - 48 * q^65 + 24 * q^73 + 84 * q^79 - 20 * q^81 + 68 * q^87 + 24 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.54472	+	0.783472i	−0.891847	+	0.452338i
$3$	−1.54472	+	0.783472i	−0.891847	+	0.452338i
$4$		0			0
$5$	−1.07112	+	1.85524i	−0.479020	+	0.829687i	−0.999711	−	0.0240584i	$-0.992341\pi$
$5$	−1.07112	+	1.85524i	−0.479020	+	0.829687i	0.520690	+	0.853746i	$0.325675\pi$
$6$		0			0
$7$	1.13037	−	0.652621i	0.427241	−	0.246668i	−0.270930	−	0.962599i	$-0.587331\pi$
$7$	1.13037	−	0.652621i	0.427241	−	0.246668i	0.698170	+	0.715932i	$0.253998\pi$
$8$		0			0
$9$	1.77234	−	2.42050i	0.590781	−	0.806832i
$10$		0			0
$11$	−2.36103	+	1.36314i	−0.711876	+	0.411002i	−0.811755	−	0.583998i	$-0.801488\pi$
$11$	−2.36103	+	1.36314i	−0.711876	+	0.411002i	0.0998790	+	0.995000i	$0.468154\pi$
$12$		0			0
$13$	1.16603	+	0.673209i	0.323399	+	0.186715i	0.652907	−	0.757438i	$-0.273549\pi$
$13$	1.16603	+	0.673209i	0.323399	+	0.186715i	−0.329507	+	0.944153i	$0.606883\pi$
$14$		0			0
$15$	0.201060	−	3.70502i	0.0519135	−	0.956633i
$16$		0			0
$17$			4.27575i			1.03702i	0.855071	+	0.518511i	$0.173513\pi$
$17$			4.27575i			1.03702i	−0.855071	+	0.518511i	$0.826487\pi$
$18$		0			0
$19$	−2.16174			−0.495937			−0.247968	−	0.968768i	$-0.579763\pi$
$19$	−2.16174			−0.495937			−0.247968	+	0.968768i	$0.579763\pi$
$20$		0			0
$21$	−1.23480	+	1.89374i	−0.269456	+	0.413247i
$22$		0			0
$23$	−1.01947	+	1.76577i	−0.212573	+	0.368188i	−0.952519	−	0.304479i	$-0.901518\pi$
$23$	−1.01947	+	1.76577i	−0.212573	+	0.368188i	0.739946	+	0.672666i	$0.234851\pi$
$24$		0			0
$25$	0.205398	+	0.355759i	0.0410796	+	0.0711519i
$26$		0			0
$27$	−0.841387	+	5.12758i	−0.161925	+	0.986803i
$28$		0			0
$29$	2.72776	+	4.72461i	0.506531	+	0.877338i	0.999971	+	0.00755840i	$0.00240594\pi$
$29$	2.72776	+	4.72461i	0.506531	+	0.877338i	−0.493440	+	0.869780i	$0.664261\pi$
$30$		0			0
$31$	−6.09216	−	3.51731i	−1.09418	−	0.631728i	−0.159497	−	0.987198i	$-0.550987\pi$
$31$	−6.09216	−	3.51731i	−1.09418	−	0.631728i	−0.934688	+	0.355470i	$0.884321\pi$
$32$		0			0
$33$	2.57915	−	3.95547i	0.448973	−	0.688559i
$34$		0			0
$35$			2.79615i			0.472635i
$36$		0			0
$37$		−	10.3381i		−	1.69957i	−0.527126	−	0.849787i	$-0.676731\pi$
$37$		−	10.3381i		−	1.69957i	0.527126	−	0.849787i	$-0.323269\pi$
$38$		0			0
$39$	−2.32864	−	0.126368i	−0.372881	−	0.0202351i
$40$		0			0
$41$	0.596355	+	0.344306i	0.0931350	+	0.0537715i	0.545844	−	0.837887i	$-0.316209\pi$
$41$	0.596355	+	0.344306i	0.0931350	+	0.0537715i	−0.452709	+	0.891658i	$0.649542\pi$
$42$		0			0
$43$	−1.22839	−	2.12763i	−0.187327	−	0.324460i	0.757031	−	0.653379i	$-0.226649\pi$
$43$	−1.22839	−	2.12763i	−0.187327	−	0.324460i	−0.944358	+	0.328919i	$0.893316\pi$
$44$		0			0
$45$	2.59220	+	5.88076i	0.386422	+	0.876652i
$46$		0			0
$47$	−6.56713	−	11.3746i	−0.957914	−	1.65916i	−0.727555	−	0.686049i	$-0.759343\pi$
$47$	−6.56713	−	11.3746i	−0.957914	−	1.65916i	−0.230359	−	0.973106i	$-0.573990\pi$
$48$		0			0
$49$	−2.64817	+	4.58677i	−0.378310	+	0.655252i
$50$		0			0
$51$	−3.34993	−	6.60485i	−0.469084	−	0.924864i
$52$		0			0
$53$	−9.56171			−1.31340			−0.656701	−	0.754151i	$-0.728049\pi$
$53$	−9.56171			−1.31340			−0.656701	+	0.754151i	$0.728049\pi$
$54$		0			0
$55$		−	5.84035i		−	0.787513i
$56$		0			0
$57$	3.33929	−	1.69366i	0.442299	−	0.224331i
$58$		0			0
$59$	−8.97985	−	5.18452i	−1.16908	−	0.674967i	−0.215615	−	0.976479i	$-0.569175\pi$
$59$	−8.97985	−	5.18452i	−1.16908	−	0.674967i	−0.953463	+	0.301512i	$0.902509\pi$
$60$		0			0
$61$	7.68757	−	4.43842i	0.984292	−	0.568281i	0.0807290	−	0.996736i	$-0.474275\pi$
$61$	7.68757	−	4.43842i	0.984292	−	0.568281i	0.903563	+	0.428455i	$0.140942\pi$
$62$		0			0
$63$	0.423741	−	3.89273i	0.0533863	−	0.490438i
$64$		0			0
$65$	−2.49793	+	1.44218i	−0.309829	+	0.178880i
$66$		0			0
$67$	−6.23532	+	10.7999i	−0.761766	+	1.31942i	0.180174	+	0.983635i	$0.442334\pi$
$67$	−6.23532	+	10.7999i	−0.761766	+	1.31942i	−0.941940	+	0.335782i	$0.890999\pi$
$68$		0			0
$69$	0.191364	−	3.52635i	0.0230375	−	0.424522i
$70$		0			0
$71$	4.94992			0.587448			0.293724	−	0.955890i	$-0.405105\pi$
$71$	4.94992			0.587448			0.293724	+	0.955890i	$0.405105\pi$
$72$		0			0
$73$	−12.8268			−1.50126			−0.750630	−	0.660723i	$-0.770250\pi$
$73$	−12.8268			−1.50126			−0.750630	+	0.660723i	$0.770250\pi$
$74$		0			0
$75$	−0.596010	−	0.388627i	−0.0688214	−	0.0448747i
$76$		0			0
$77$	−1.77923	+	3.08171i	−0.202762	+	0.351194i
$78$		0			0
$79$	0.680856	−	0.393093i	0.0766023	−	0.0442264i	−0.461210	−	0.887291i	$-0.652584\pi$
$79$	0.680856	−	0.393093i	0.0766023	−	0.0442264i	0.537812	+	0.843065i	$0.319251\pi$
$80$		0			0
$81$	−2.71761	−	8.57990i	−0.301956	−	0.953322i
$82$		0			0
$83$	1.82152	−	1.05165i	0.199938	−	0.115434i	−0.396689	−	0.917953i	$-0.629841\pi$
$83$	1.82152	−	1.05165i	0.199938	−	0.115434i	0.596626	+	0.802519i	$0.296507\pi$
$84$		0			0
$85$	−7.93253	−	4.57985i	−0.860404	−	0.496754i
$86$		0			0
$87$	−7.91523	−	5.16110i	−0.848602	−	0.553328i
$88$		0			0
$89$			12.1722i			1.29025i	0.764077	+	0.645125i	$0.223195\pi$
$89$			12.1722i			1.29025i	−0.764077	+	0.645125i	$0.776805\pi$
$90$		0			0
$91$	1.75740			0.184226
$92$		0			0
$93$	12.1664	+	0.660234i	1.26160	+	0.0684631i
$94$		0			0
$95$	2.31548	−	4.01053i	0.237564	−	0.411472i
$96$		0			0
$97$	−8.05440	−	13.9506i	−0.817801	−	1.41647i	−0.907299	−	0.420485i	$-0.861860\pi$
$97$	−8.05440	−	13.9506i	−0.817801	−	1.41647i	0.0894986	−	0.995987i	$-0.471474\pi$
$98$		0			0
$99$	−0.885074	+	8.13081i	−0.0889533	+	0.817177i
$100$		0			0
$101$	−7.26875	−	12.5898i	−0.723267	−	1.25274i	−0.959683	−	0.281084i	$-0.909306\pi$
$101$	−7.26875	−	12.5898i	−0.723267	−	1.25274i	0.236416	−	0.971652i	$-0.424027\pi$
$102$		0			0
$103$	−3.14001	−	1.81289i	−0.309395	−	0.178629i	0.337261	−	0.941411i	$-0.390500\pi$
$103$	−3.14001	−	1.81289i	−0.309395	−	0.178629i	−0.646656	+	0.762782i	$0.723833\pi$
$104$		0			0
$105$	−2.19070	−	4.31927i	−0.213791	−	0.421518i
$106$		0			0
$107$			11.6508i			1.12632i	0.826347	+	0.563161i	$0.190415\pi$
$107$			11.6508i			1.12632i	−0.826347	+	0.563161i	$0.809585\pi$
$108$		0			0
$109$		−	6.96341i		−	0.666974i	−0.942755	−	0.333487i	$-0.891775\pi$
$109$		−	6.96341i		−	0.666974i	0.942755	−	0.333487i	$-0.108225\pi$
$110$		0			0
$111$	8.09962	+	15.9695i	0.768782	+	1.51576i
$112$		0			0
$113$	11.7540	+	6.78616i	1.10572	+	0.638388i	0.937718	−	0.347398i	$-0.112935\pi$
$113$	11.7540	+	6.78616i	1.10572	+	0.638388i	0.168003	+	0.985786i	$0.446268\pi$
$114$		0			0
$115$	−2.18394	−	3.78270i	−0.203654	−	0.352739i
$116$		0			0
$117$	3.69611	−	1.62922i	0.341705	−	0.150621i
$118$		0			0
$119$	2.79045	+	4.83319i	0.255800	+	0.443058i
$120$		0			0
$121$	−1.78370	+	3.08946i	−0.162155	+	0.280860i
$122$		0			0
$123$	−1.19096	−	0.0646296i	−0.107385	−	0.00582745i
$124$		0			0
$125$	−11.5912			−1.03675
$126$		0			0
$127$			22.0340i			1.95520i	0.210465	+	0.977601i	$0.432502\pi$
$127$			22.0340i			1.95520i	−0.210465	+	0.977601i	$0.567498\pi$
$128$		0			0
$129$	3.56446	+	2.32419i	0.313833	+	0.204634i
$130$		0			0
$131$	1.64258	+	0.948346i	0.143513	+	0.0828573i	0.570037	−	0.821619i	$-0.306929\pi$
$131$	1.64258	+	0.948346i	0.143513	+	0.0828573i	−0.426524	+	0.904476i	$0.640262\pi$
$132$		0			0
$133$	−2.44357	+	1.41080i	−0.211884	+	0.122331i
$134$		0			0
$135$	−8.61165	−	7.05323i	−0.741172	−	0.607046i
$136$		0			0
$137$	2.63976	−	1.52407i	0.225530	−	0.130210i	−0.382978	−	0.923757i	$-0.625102\pi$
$137$	2.63976	−	1.52407i	0.225530	−	0.130210i	0.608508	+	0.793548i	$0.291768\pi$
$138$		0			0
$139$	−1.82552	+	3.16190i	−0.154839	+	0.268189i	−0.933000	−	0.359875i	$-0.882819\pi$
$139$	−1.82552	+	3.16190i	−0.154839	+	0.268189i	0.778161	+	0.628064i	$0.216152\pi$
$140$		0			0
$141$	19.0561	+	12.4254i	1.60481	+	1.04641i
$142$		0			0
$143$	−3.67071			−0.306960
$144$		0			0
$145$	−11.6870			−0.970555
$146$		0			0
$147$	0.497088	−	9.16006i	0.0409991	−	0.755509i
$148$		0			0
$149$	−6.98401	+	12.0967i	−0.572153	+	0.990997i	0.424192	+	0.905572i	$0.360558\pi$
$149$	−6.98401	+	12.0967i	−0.572153	+	0.990997i	−0.996345	+	0.0854250i	$0.972775\pi$
$150$		0			0
$151$	19.4354	−	11.2211i	1.58163	−	0.913156i	0.587012	−	0.809578i	$-0.300304\pi$
$151$	19.4354	−	11.2211i	1.58163	−	0.913156i	0.994621	−	0.103578i	$-0.0330292\pi$
$152$		0			0
$153$	10.3494	+	7.57809i	0.836702	+	0.612653i
$154$		0			0
$155$	13.0509	−	7.53494i	1.04827	−	0.605221i
$156$		0			0
$157$	2.67761	+	1.54592i	0.213697	+	0.123378i	0.603028	−	0.797720i	$-0.293961\pi$
$157$	2.67761	+	1.54592i	0.213697	+	0.123378i	−0.389332	+	0.921098i	$0.627294\pi$
$158$		0			0
$159$	14.7702	−	7.49133i	1.17135	−	0.594101i
$160$		0			0
$161$			2.66130i			0.209740i
$162$		0			0
$163$	10.4313			0.817042			0.408521	−	0.912749i	$-0.366045\pi$
$163$	10.4313			0.817042			0.408521	+	0.912749i	$0.366045\pi$
$164$		0			0
$165$	4.57575	+	9.02173i	0.356222	+	0.702341i
$166$		0			0
$167$	−6.50275	+	11.2631i	−0.503198	+	0.871564i	0.496795	+	0.867868i	$0.334510\pi$
$167$	−6.50275	+	11.2631i	−0.503198	+	0.871564i	−0.999993	+	0.00369641i	$0.998823\pi$
$168$		0			0
$169$	−5.59358	−	9.68836i	−0.430275	−	0.745259i
$170$		0			0
$171$	−3.83134	+	5.23248i	−0.292990	+	0.400138i
$172$		0			0
$173$	2.69963	+	4.67590i	0.205249	+	0.355502i	0.950212	−	0.311604i	$-0.100866\pi$
$173$	2.69963	+	4.67590i	0.205249	+	0.355502i	−0.744963	+	0.667106i	$0.767533\pi$
$174$		0			0
$175$	0.464352	+	0.268094i	0.0351017	+	0.0202660i
$176$		0			0
$177$	17.9333	+	0.973185i	1.34795	+	0.0731491i
$178$		0			0
$179$		−	4.69284i		−	0.350759i	−0.984501	−	0.175380i	$-0.943885\pi$
$179$		−	4.69284i		−	0.350759i	0.984501	−	0.175380i	$-0.0561153\pi$
$180$		0			0
$181$		−	6.33810i		−	0.471108i	−0.971861	−	0.235554i	$-0.924310\pi$
$181$		−	6.33810i		−	0.471108i	0.971861	−	0.235554i	$-0.0756904\pi$
$182$		0			0
$183$	−8.39779	+	12.8791i	−0.620783	+	0.952053i
$184$		0			0
$185$	19.1796	+	11.0734i	1.41011	+	0.814130i
$186$		0			0
$187$	−5.82844	−	10.0952i	−0.426218	−	0.738231i
$188$		0			0
$189$	2.39529	+	6.34518i	0.174231	+	0.461544i
$190$		0			0
$191$	1.26279	+	2.18721i	0.0913720	+	0.158261i	0.908089	−	0.418778i	$-0.137541\pi$
$191$	1.26279	+	2.18721i	0.0913720	+	0.158261i	−0.816717	+	0.577039i	$0.804208\pi$
$192$		0			0
$193$	−5.77236	+	9.99802i	−0.415504	+	0.719673i	−0.995481	−	0.0949590i	$-0.969728\pi$
$193$	−5.77236	+	9.99802i	−0.415504	+	0.719673i	0.579978	+	0.814632i	$0.303061\pi$
$194$		0			0
$195$	2.72870	−	4.18482i	0.195406	−	0.299681i
$196$		0			0
$197$	−2.44368			−0.174105			−0.0870526	−	0.996204i	$-0.527745\pi$
$197$	−2.44368			−0.174105			−0.0870526	+	0.996204i	$0.527745\pi$
$198$		0			0
$199$		−	5.28327i		−	0.374521i	−0.982310	−	0.187261i	$-0.940039\pi$
$199$		−	5.28327i		−	0.374521i	0.982310	−	0.187261i	$-0.0599609\pi$
$200$		0			0
$201$	1.17043	−	21.5680i	0.0825558	−	1.52129i
$202$		0			0
$203$	6.16676	+	3.56038i	0.432822	+	0.249890i
$204$		0			0
$205$	−1.27754	+	0.737586i	−0.0892270	+	0.0515153i
$206$		0			0
$207$	2.46719	+	5.59716i	0.171482	+	0.389029i
$208$		0			0
$209$	5.10392	−	2.94675i	0.353046	−	0.203831i
$210$		0			0
$211$	7.23279	−	12.5276i	0.497926	−	0.862432i	−0.502072	−	0.864826i	$-0.667429\pi$
$211$	7.23279	−	12.5276i	0.497926	−	0.862432i	0.999997	+	0.00239362i	$0.000761913\pi$
$212$		0			0
$213$	−7.64626	+	3.87813i	−0.523913	+	0.265725i
$214$		0			0
$215$	5.26300			0.358934
$216$		0			0
$217$	−9.18189			−0.623307
$218$		0			0
$219$	19.8138	−	10.0494i	1.33889	−	0.679076i
$220$		0			0
$221$	−2.87847	+	4.98566i	−0.193627	+	0.335372i
$222$		0			0
$223$	−16.6575	+	9.61719i	−1.11547	+	0.644015i	−0.940240	−	0.340513i	$-0.889399\pi$
$223$	−16.6575	+	9.61719i	−1.11547	+	0.644015i	−0.175227	+	0.984528i	$0.556066\pi$
$224$		0			0
$225$	1.22515	+	0.133363i	0.0816766	+	0.00889086i
$226$		0			0
$227$	−0.503060	+	0.290442i	−0.0333893	+	0.0192773i	−0.516602	−	0.856226i	$-0.672803\pi$
$227$	−0.503060	+	0.290442i	−0.0333893	+	0.0192773i	0.483212	+	0.875503i	$0.339470\pi$
$228$		0			0
$229$	−7.78703	−	4.49584i	−0.514581	−	0.297094i	0.220134	−	0.975470i	$-0.429351\pi$
$229$	−7.78703	−	4.49584i	−0.514581	−	0.297094i	−0.734715	+	0.678376i	$0.762684\pi$
$230$		0			0
$231$	0.333978	−	6.15437i	0.0219742	−	0.404928i
$232$		0			0
$233$		−	1.68699i		−	0.110518i	−0.998472	−	0.0552592i	$-0.982401\pi$
$233$		−	1.68699i		−	0.110518i	0.998472	−	0.0552592i	$-0.0175985\pi$
$234$		0			0
$235$	28.1368			1.83544
$236$		0			0
$237$	−0.743758	+	1.14065i	−0.0483122	+	0.0740933i
$238$		0			0
$239$	1.75123	−	3.03323i	0.113278	−	0.196203i	−0.803812	−	0.594883i	$-0.797198\pi$
$239$	1.75123	−	3.03323i	0.113278	−	0.196203i	0.917090	+	0.398680i	$0.130532\pi$
$240$		0			0
$241$	1.18735	+	2.05655i	0.0764837	+	0.132474i	0.901731	−	0.432299i	$-0.142297\pi$
$241$	1.18735	+	2.05655i	0.0764837	+	0.132474i	−0.825247	+	0.564772i	$0.808964\pi$
$242$		0			0
$243$	10.9201	+	11.1244i	0.700522	+	0.713631i
$244$		0			0
$245$	−5.67303	−	9.82597i	−0.362436	−	0.627758i
$246$		0			0
$247$	−2.52066	−	1.45530i	−0.160386	−	0.0925986i
$248$		0			0
$249$	−1.98980	+	3.05163i	−0.126099	+	0.193389i
$250$		0			0
$251$		−	16.4883i		−	1.04073i	−0.853942	−	0.520367i	$-0.825795\pi$
$251$		−	16.4883i		−	1.04073i	0.853942	−	0.520367i	$-0.174205\pi$
$252$		0			0
$253$		−	5.55870i		−	0.349472i
$254$		0			0
$255$	15.8417	+	0.859683i	0.992049	+	0.0538354i
$256$		0			0
$257$	1.98224	+	1.14444i	0.123649	+	0.0713885i	0.560549	−	0.828122i	$-0.310590\pi$
$257$	1.98224	+	1.14444i	0.123649	+	0.0713885i	−0.436900	+	0.899510i	$0.643924\pi$
$258$		0			0
$259$	−6.74687	−	11.6859i	−0.419230	−	0.726127i
$260$		0			0
$261$	16.2704	+	1.77111i	1.00711	+	0.109629i
$262$		0			0
$263$	14.5336	+	25.1729i	0.896179	+	1.55223i	0.832339	+	0.554267i	$0.187001\pi$
$263$	14.5336	+	25.1729i	0.896179	+	1.55223i	0.0638398	+	0.997960i	$0.479665\pi$
$264$		0			0
$265$	10.2417	−	17.7392i	0.629146	−	1.08971i
$266$		0			0
$267$	−9.53658	−	18.8027i	−0.583629	−	1.15070i
$268$		0			0
$269$	−11.4025			−0.695223			−0.347612	−	0.937639i	$-0.613007\pi$
$269$	−11.4025			−0.695223			−0.347612	+	0.937639i	$0.613007\pi$
$270$		0			0
$271$			28.9854i			1.76074i	0.474287	+	0.880370i	$0.342706\pi$
$271$			28.9854i			1.76074i	−0.474287	+	0.880370i	$0.657294\pi$
$272$		0			0
$273$	−2.71470	+	1.37688i	−0.164301	+	0.0833323i
$274$		0			0
$275$	−0.969899	−	0.559972i	−0.0584871	−	0.0337676i
$276$		0			0
$277$	20.1047	−	11.6075i	1.20798	−	0.697425i	0.245659	−	0.969356i	$-0.420996\pi$
$277$	20.1047	−	11.6075i	1.20798	−	0.697425i	0.962317	+	0.271931i	$0.0876622\pi$
$278$		0			0
$279$	−19.3110	+	8.51218i	−1.15612	+	0.509611i
$280$		0			0
$281$	−12.7582	+	7.36593i	−0.761088	+	0.439415i	−0.829686	−	0.558230i	$-0.811481\pi$
$281$	−12.7582	+	7.36593i	−0.761088	+	0.439415i	0.0685980	+	0.997644i	$0.478147\pi$
$282$		0			0
$283$	−12.4785	+	21.6134i	−0.741770	+	1.28478i	0.209919	+	0.977719i	$0.432680\pi$
$283$	−12.4785	+	21.6134i	−0.741770	+	1.28478i	−0.951689	+	0.307065i	$0.900653\pi$
$284$		0			0
$285$	−0.434639	+	8.00928i	−0.0257458	+	0.474429i
$286$		0			0
$287$	0.898805			0.0530548
$288$		0			0
$289$	−1.28204			−0.0754142
$290$		0			0
$291$	23.3718	+	15.2395i	1.37008	+	0.893354i
$292$		0			0
$293$	−11.0395	+	19.1210i	−0.644934	+	1.11706i	0.339382	+	0.940648i	$0.389782\pi$
$293$	−11.0395	+	19.1210i	−0.644934	+	1.11706i	−0.984317	+	0.176410i	$0.943551\pi$
$294$		0			0
$295$	19.2370	−	11.1065i	1.12002	−	0.646645i
$296$		0			0
$297$	−5.00307	−	13.2533i	−0.290307	−	0.769033i
$298$		0			0
$299$	−2.37746	+	1.37263i	−0.137492	+	0.0793811i
$300$		0			0
$301$	−2.77707	−	1.60334i	−0.160068	−	0.0924151i
$302$		0			0
$303$	21.0920	+	13.7530i	1.21170	+	0.790087i
$304$		0			0
$305$			19.0163i			1.08887i
$306$		0			0
$307$	28.0180			1.59907			0.799535	−	0.600619i	$-0.205079\pi$
$307$	28.0180			1.59907			0.799535	+	0.600619i	$0.205079\pi$
$308$		0			0
$309$	6.27080	+	0.340297i	0.356733	+	0.0193588i
$310$		0			0
$311$	−6.78751	+	11.7563i	−0.384884	+	0.666639i	−0.991753	−	0.128163i	$-0.959092\pi$
$311$	−6.78751	+	11.7563i	−0.384884	+	0.666639i	0.606869	+	0.794802i	$0.292425\pi$
$312$		0			0
$313$	13.9417	+	24.1478i	0.788034	+	1.36491i	0.927170	+	0.374641i	$0.122234\pi$
$313$	13.9417	+	24.1478i	0.788034	+	1.36491i	−0.139136	+	0.990273i	$0.544433\pi$
$314$		0			0
$315$	6.76806	+	4.95573i	0.381337	+	0.279224i
$316$		0			0
$317$	3.15169	+	5.45888i	0.177016	+	0.306601i	0.940857	−	0.338803i	$-0.110022\pi$
$317$	3.15169	+	5.45888i	0.177016	+	0.306601i	−0.763841	+	0.645405i	$0.776689\pi$
$318$		0			0
$319$	−12.8806	−	7.43662i	−0.721176	−	0.416371i
$320$		0			0
$321$	−9.12805	−	17.9972i	−0.509478	−	1.00451i
$322$		0			0
$323$		−	9.24305i		−	0.514297i
$324$		0			0
$325$			0.553103i			0.0306806i
$326$		0			0
$327$	5.45564	+	10.7565i	0.301698	+	0.594838i
$328$		0			0
$329$	−14.8466	−	8.57169i	−0.818520	−	0.472573i
$330$		0			0
$331$	−0.733725	−	1.27085i	−0.0403292	−	0.0698522i	0.845156	−	0.534519i	$-0.179507\pi$
$331$	−0.733725	−	1.27085i	−0.0403292	−	0.0698522i	−0.885485	+	0.464667i	$0.846174\pi$
$332$		0			0
$333$	−25.0233	−	18.3227i	−1.37127	−	1.00408i
$334$		0			0
$335$	−13.3576	−	23.1360i	−0.729802	−	1.26405i
$336$		0			0
$337$	−1.25721	+	2.17756i	−0.0684848	+	0.118619i	−0.898235	−	0.439516i	$-0.855150\pi$
$337$	−1.25721	+	2.17756i	−0.0684848	+	0.118619i	0.829750	+	0.558136i	$0.188483\pi$
$338$		0			0
$339$	−23.4734	−	1.27383i	−1.27490	−	0.0691849i
$340$		0			0
$341$	19.1783			1.03857
$342$		0			0
$343$			16.0497i			0.866603i
$344$		0			0
$345$	6.33723	+	4.13217i	0.341185	+	0.222468i
$346$		0			0
$347$	17.4849	+	10.0949i	0.938638	+	0.541923i	0.889533	−	0.456871i	$-0.151030\pi$
$347$	17.4849	+	10.0949i	0.938638	+	0.541923i	0.0491051	+	0.998794i	$0.484363\pi$
$348$		0			0
$349$	6.58266	−	3.80050i	0.352362	−	0.203436i	−0.313363	−	0.949633i	$-0.601456\pi$
$349$	6.58266	−	3.80050i	0.352362	−	0.203436i	0.665725	+	0.746197i	$0.268122\pi$
$350$		0			0
$351$	−4.43302	+	5.41250i	−0.236617	+	0.288898i
$352$		0			0
$353$	−8.78534	+	5.07222i	−0.467596	+	0.269967i	−0.715233	−	0.698886i	$-0.753679\pi$
$353$	−8.78534	+	5.07222i	−0.467596	+	0.269967i	0.247637	+	0.968853i	$0.420346\pi$
$354$		0			0
$355$	−5.30197	+	9.18328i	−0.281399	+	0.487398i
$356$		0			0
$357$	−8.09714	−	5.27971i	−0.428546	−	0.279432i
$358$		0			0
$359$	20.5983			1.08714			0.543570	−	0.839364i	$-0.317072\pi$
$359$	20.5983			1.08714			0.543570	+	0.839364i	$0.317072\pi$
$360$		0			0
$361$	−14.3269			−0.754047
$362$		0			0
$363$	0.334818	−	6.16985i	0.0175734	−	0.323833i
$364$		0			0
$365$	13.7390	−	23.7967i	0.719133	−	1.24558i
$366$		0			0
$367$	11.1457	−	6.43498i	0.581802	−	0.335903i	−0.180047	−	0.983658i	$-0.557625\pi$
$367$	11.1457	−	6.43498i	0.581802	−	0.335903i	0.761849	+	0.647755i	$0.224292\pi$
$368$		0			0
$369$	1.89034	−	0.833247i	0.0984069	−	0.0433771i
$370$		0			0
$371$	−10.8083	+	6.24017i	−0.561139	+	0.323974i
$372$		0			0
$373$	6.12551	+	3.53656i	0.317167	+	0.183116i	0.650129	−	0.759824i	$-0.274715\pi$
$373$	6.12551	+	3.53656i	0.317167	+	0.183116i	−0.332962	+	0.942940i	$0.608048\pi$
$374$		0			0
$375$	17.9053	−	9.08141i	0.924624	−	0.468962i
$376$		0			0
$377$			7.34540i			0.378307i
$378$		0			0
$379$	−26.0887			−1.34009			−0.670043	−	0.742322i	$-0.733724\pi$
$379$	−26.0887			−1.34009			−0.670043	+	0.742322i	$0.733724\pi$
$380$		0			0
$381$	−17.2630	−	34.0365i	−0.884412	−	1.74374i
$382$		0			0
$383$	9.84884	−	17.0587i	0.503252	−	0.871659i	−0.496741	−	0.867899i	$-0.665470\pi$
$383$	9.84884	−	17.0587i	0.503252	−	0.871659i	0.999993	−	0.00375959i	$-0.00119672\pi$
$384$		0			0
$385$	−3.81154	−	6.60178i	−0.194254	−	0.336458i
$386$		0			0
$387$	−7.32704	−	0.797580i	−0.372454	−	0.0405433i
$388$		0			0
$389$	7.05645	+	12.2221i	0.357776	+	0.619687i	0.987589	−	0.157060i	$-0.0502017\pi$
$389$	7.05645	+	12.2221i	0.357776	+	0.619687i	−0.629813	+	0.776747i	$0.716868\pi$
$390$		0			0
$391$	−7.54998	−	4.35898i	−0.381819	−	0.220443i
$392$		0			0
$393$	−3.28034	−	0.178014i	−0.165471	−	0.00897961i
$394$		0			0
$395$			1.68420i			0.0847413i
$396$		0			0
$397$		−	17.1597i		−	0.861220i	−0.902538	−	0.430610i	$-0.858298\pi$
$397$		−	17.1597i		−	0.861220i	0.902538	−	0.430610i	$-0.141702\pi$
$398$		0			0
$399$	2.66932	−	4.09376i	0.133633	−	0.204944i
$400$		0			0
$401$	−21.5726	−	12.4549i	−1.07728	−	0.621969i	−0.147120	−	0.989119i	$-0.547000\pi$
$401$	−21.5726	−	12.4549i	−1.07728	−	0.621969i	−0.930162	+	0.367149i	$0.880334\pi$
$402$		0			0
$403$	−4.73577	−	8.20260i	−0.235906	−	0.408601i
$404$		0			0
$405$	18.8286	+	4.14831i	0.935602	+	0.206131i
$406$		0			0
$407$	14.0923	+	24.4085i	0.698528	+	1.20989i
$408$		0			0
$409$	−7.64539	+	13.2422i	−0.378040	+	0.654785i	−0.990777	−	0.135502i	$-0.956735\pi$
$409$	−7.64539	+	13.2422i	−0.378040	+	0.654785i	0.612737	+	0.790287i	$0.290069\pi$
$410$		0			0
$411$	−2.88364	+	4.42244i	−0.142239	+	0.218143i
$412$		0			0
$413$	−13.5341			−0.665970
$414$		0			0
$415$			4.50580i			0.221181i
$416$		0			0
$417$	0.342669	−	6.31451i	0.0167806	−	0.309223i
$418$		0			0
$419$	−5.38781	−	3.11065i	−0.263212	−	0.151965i	0.362587	−	0.931950i	$-0.381894\pi$
$419$	−5.38781	−	3.11065i	−0.263212	−	0.151965i	−0.625799	+	0.779985i	$0.715227\pi$
$420$		0			0
$421$	3.60960	−	2.08400i	0.175921	−	0.101568i	−0.409454	−	0.912331i	$-0.634281\pi$
$421$	3.60960	−	2.08400i	0.175921	−	0.101568i	0.585375	+	0.810763i	$0.300947\pi$
$422$		0			0
$423$	−39.1714	−	4.26397i	−1.90458	−	0.207321i
$424$		0			0
$425$	−1.52114	+	0.878230i	−0.0737861	+	0.0426004i
$426$		0			0
$427$	5.79321	−	10.0341i	0.280353	−	0.485586i
$428$		0			0
$429$	5.67024	−	2.87590i	0.273762	−	0.138850i
$430$		0			0
$431$	−34.3973			−1.65686			−0.828429	−	0.560094i	$-0.810765\pi$
$431$	−34.3973			−1.65686			−0.828429	+	0.560094i	$0.810765\pi$
$432$		0			0
$433$	23.7319			1.14048			0.570241	−	0.821478i	$-0.306850\pi$
$433$	23.7319			1.14048			0.570241	+	0.821478i	$0.306850\pi$
$434$		0			0
$435$	18.0532	−	9.15646i	0.865586	−	0.439019i
$436$		0			0
$437$	2.20382	−	3.81712i	0.105423	−	0.182598i
$438$		0			0
$439$	28.5367	−	16.4757i	1.36198	−	0.786342i	0.372096	−	0.928194i	$-0.378639\pi$
$439$	28.5367	−	16.4757i	1.36198	−	0.786342i	0.989888	+	0.141852i	$0.0453059\pi$
$440$		0			0
$441$	6.40879	+	14.5392i	0.305180	+	0.692343i
$442$		0			0
$443$	−3.04392	+	1.75741i	−0.144621	+	0.0834969i	−0.570564	−	0.821253i	$-0.693276\pi$
$443$	−3.04392	+	1.75741i	−0.144621	+	0.0834969i	0.425944	+	0.904750i	$0.359942\pi$
$444$		0			0
$445$	−22.5823	−	13.0379i	−1.07050	−	0.618056i
$446$		0			0
$447$	1.31097	−	24.1578i	0.0620066	−	1.14262i
$448$		0			0
$449$		−	27.5711i		−	1.30116i	−0.759437	−	0.650581i	$-0.774525\pi$
$449$		−	27.5711i		−	1.30116i	0.759437	−	0.650581i	$-0.225475\pi$
$450$		0			0
$451$	−1.87735			−0.0884008
$452$		0			0
$453$	−21.2310	+	32.5606i	−0.997519	+	1.52983i
$454$		0			0
$455$	−1.88239	+	3.26040i	−0.0882479	+	0.152850i
$456$		0			0
$457$	−3.69999	−	6.40857i	−0.173078	−	0.299780i	0.766416	−	0.642344i	$-0.222038\pi$
$457$	−3.69999	−	6.40857i	−0.173078	−	0.299780i	−0.939494	+	0.342564i	$0.888705\pi$
$458$		0			0
$459$	−21.9242	−	3.59756i	−1.02334	−	0.167920i
$460$		0			0
$461$	6.03604	+	10.4547i	0.281126	+	0.486925i	0.971662	−	0.236373i	$-0.0759586\pi$
$461$	6.03604	+	10.4547i	0.281126	+	0.486925i	−0.690536	+	0.723298i	$0.742625\pi$
$462$		0			0
$463$	−11.6479	−	6.72493i	−0.541325	−	0.312534i	0.204291	−	0.978910i	$-0.434511\pi$
$463$	−11.6479	−	6.72493i	−0.541325	−	0.312534i	−0.745616	+	0.666376i	$0.767845\pi$
$464$		0			0
$465$	−14.2566	+	21.8644i	−0.661134	+	1.01394i
$466$		0			0
$467$			12.9746i			0.600391i	0.953878	+	0.300196i	$0.0970519\pi$
$467$			12.9746i			0.600391i	−0.953878	+	0.300196i	$0.902948\pi$
$468$		0			0
$469$			16.2772i			0.751612i
$470$		0			0
$471$	−5.34735	−	0.290184i	−0.246393	−	0.0133710i
$472$		0			0
$473$	5.80051	+	3.34892i	0.266708	+	0.153984i
$474$		0			0
$475$	−0.444016	−	0.769058i	−0.0203729	−	0.0352868i
$476$		0			0
$477$	−16.9466	+	23.1441i	−0.775932	+	1.05969i
$478$		0			0
$479$	−7.54472	−	13.0678i	−0.344727	−	0.597085i	0.640577	−	0.767894i	$-0.278695\pi$
$479$	−7.54472	−	13.0678i	−0.344727	−	0.597085i	−0.985304	+	0.170809i	$0.945362\pi$
$480$		0			0
$481$	6.95971	−	12.0546i	0.317335	−	0.549641i
$482$		0			0
$483$	−2.08505	−	4.11097i	−0.0948733	−	0.187056i
$484$		0			0
$485$	34.5090			1.56697
$486$		0			0
$487$			8.93710i			0.404979i	0.979284	+	0.202489i	$0.0649032\pi$
$487$			8.93710i			0.404979i	−0.979284	+	0.202489i	$0.935097\pi$
$488$		0			0
$489$	−16.1135	+	8.17263i	−0.728676	+	0.369579i
$490$		0			0
$491$	10.0926	+	5.82696i	0.455472	+	0.262967i	0.710138	−	0.704062i	$-0.248632\pi$
$491$	10.0926	+	5.82696i	0.455472	+	0.262967i	−0.254666	+	0.967029i	$0.581966\pi$
$492$		0			0
$493$	−20.2013	+	11.6632i	−0.909819	+	0.525284i
$494$		0			0
$495$	−14.1365	−	10.3511i	−0.635391	−	0.465247i
$496$		0			0
$497$	5.59526	−	3.23043i	0.250982	−	0.144904i
$498$		0			0
$499$	−12.6569	+	21.9224i	−0.566601	+	0.981381i	0.430298	+	0.902687i	$0.358408\pi$
$499$	−12.6569	+	21.9224i	−0.566601	+	0.981381i	−0.996899	+	0.0786941i	$0.974925\pi$
$500$		0			0
$501$	1.22063	−	22.4931i	0.0545337	−	1.00492i
$502$		0			0
$503$	−27.4640			−1.22456			−0.612279	−	0.790642i	$-0.709747\pi$
$503$	−27.4640			−1.22456			−0.612279	+	0.790642i	$0.709747\pi$
$504$		0			0
$505$	31.1428			1.38584
$506$		0			0
$507$	16.2311	+	10.5834i	0.720848	+	0.470027i
$508$		0			0
$509$	9.31530	−	16.1346i	0.412894	−	0.715153i	−0.582311	−	0.812966i	$-0.697851\pi$
$509$	9.31530	−	16.1346i	0.412894	−	0.715153i	0.995205	+	0.0978134i	$0.0311848\pi$
$510$		0			0
$511$	−14.4990	+	8.37102i	−0.641399	+	0.370312i
$512$		0			0
$513$	1.81886	−	11.0845i	0.0803046	−	0.489392i
$514$		0			0
$515$	6.72667	−	3.88364i	0.296412	−	0.171134i
$516$		0			0
$517$	31.0103	+	17.9038i	1.36383	+	0.787409i
$518$		0			0
$519$	−7.83362	−	5.10788i	−0.343858	−	0.224211i
$520$		0			0
$521$		−	24.1019i		−	1.05593i	−0.849268	−	0.527963i	$-0.822956\pi$
$521$		−	24.1019i		−	1.05593i	0.849268	−	0.527963i	$-0.177044\pi$
$522$		0			0
$523$	33.9903			1.48629			0.743146	−	0.669129i	$-0.233333\pi$
$523$	33.9903			1.48629			0.743146	+	0.669129i	$0.233333\pi$
$524$		0			0
$525$	−0.927340	−	0.0503239i	−0.0404724	−	0.00219631i
$526$		0			0
$527$	15.0391	−	26.0486i	0.655116	−	1.13469i
$528$		0			0
$529$	9.42138	+	16.3183i	0.409625	+	0.709492i
$530$		0			0
$531$	−28.4645	+	12.5470i	−1.23525	+	0.544491i
$532$		0			0
$533$	0.463580	+	0.802943i	0.0200799	+	0.0347793i
$534$		0			0
$535$	−21.6149	−	12.4794i	−0.934494	−	0.539530i
$536$		0			0
$537$	3.67671	+	7.24914i	0.158662	+	0.312823i
$538$		0			0
$539$		−	14.4393i		−	0.621945i
$540$		0			0
$541$			38.0055i			1.63399i	0.576648	+	0.816993i	$0.304361\pi$
$541$			38.0055i			1.63399i	−0.576648	+	0.816993i	$0.695639\pi$
$542$		0			0
$543$	4.96573	+	9.79062i	0.213100	+	0.420156i
$544$		0			0
$545$	12.9188	+	7.45866i	0.553380	+	0.319494i
$546$		0			0
$547$	−12.0534	−	20.8771i	−0.515367	−	0.892642i	−0.999841	−	0.0178365i	$-0.994322\pi$
$547$	−12.0534	−	20.8771i	−0.515367	−	0.892642i	0.484474	−	0.874806i	$-0.339011\pi$
$548$		0			0
$549$	2.88182	−	26.4741i	0.122993	−	1.12989i
$550$		0			0
$551$	−5.89669	−	10.2134i	−0.251207	−	0.435104i
$552$		0			0
$553$	0.513081	−	0.888682i	0.0218184	−	0.0377906i
$554$		0			0
$555$	−38.3029	−	2.07858i	−1.62587	−	0.0882308i
$556$		0			0
$557$	−36.9729			−1.56659			−0.783295	−	0.621650i	$-0.786463\pi$
$557$	−36.9729			−1.56659			−0.783295	+	0.621650i	$0.786463\pi$
$558$		0			0
$559$		−	3.30784i		−	0.139907i
$560$		0			0
$561$	16.9126	+	11.0278i	0.714051	+	0.465594i
$562$		0			0
$563$	13.5859	+	7.84380i	0.572576	+	0.330577i	0.758177	−	0.652048i	$-0.226090\pi$
$563$	13.5859	+	7.84380i	0.572576	+	0.330577i	−0.185602	+	0.982625i	$0.559423\pi$
$564$		0			0
$565$	−25.1799	+	14.5376i	−1.05933	+	0.611602i
$566$		0			0
$567$	−8.67133	−	7.92492i	−0.364162	−	0.332815i
$568$		0			0
$569$	28.9567	−	16.7181i	1.21393	−	0.700861i	0.250314	−	0.968165i	$-0.419466\pi$
$569$	28.9567	−	16.7181i	1.21393	−	0.700861i	0.963612	+	0.267304i	$0.0861327\pi$
$570$		0			0
$571$	−18.1141	+	31.3746i	−0.758053	+	1.31299i	0.185788	+	0.982590i	$0.440516\pi$
$571$	−18.1141	+	31.3746i	−0.758053	+	1.31299i	−0.943842	+	0.330397i	$0.892817\pi$
$572$		0			0
$573$	−3.66427	−	2.38928i	−0.153077	−	0.0998135i
$574$		0			0
$575$	−0.837584			−0.0349297
$576$		0			0
$577$	4.34600			0.180926			0.0904631	−	0.995900i	$-0.471165\pi$
$577$	4.34600			0.180926			0.0904631	+	0.995900i	$0.471165\pi$
$578$		0			0
$579$	1.08353	−	19.9667i	0.0450299	−	0.829786i
$580$		0			0
$581$	1.37266	−	2.37752i	0.0569477	−	0.0986363i
$582$		0			0
$583$	22.5754	−	13.0339i	0.934979	−	0.539811i
$584$		0			0
$585$	−0.936393	+	8.60225i	−0.0387151	+	0.355659i
$586$		0			0
$587$	−35.0281	+	20.2235i	−1.44576	+	0.834711i	−0.998225	−	0.0595537i	$-0.981032\pi$
$587$	−35.0281	+	20.2235i	−1.44576	+	0.834711i	−0.447538	+	0.894265i	$0.647699\pi$
$588$		0			0
$589$	13.1697	+	7.60351i	0.542646	+	0.313297i
$590$		0			0
$591$	3.77481	−	1.91456i	0.155275	−	0.0787543i
$592$		0			0
$593$			9.69635i			0.398181i	0.979981	+	0.199091i	$0.0637988\pi$
$593$			9.69635i			0.398181i	−0.979981	+	0.199091i	$0.936201\pi$
$594$		0			0
$595$	−11.9556			−0.490133
$596$		0			0
$597$	4.13930	+	8.16119i	0.169410	+	0.334015i
$598$		0			0
$599$	20.8663	−	36.1415i	0.852574	−	1.47670i	−0.0263039	−	0.999654i	$-0.508374\pi$
$599$	20.8663	−	36.1415i	0.852574	−	1.47670i	0.878878	−	0.477047i	$-0.158293\pi$
$600$		0			0
$601$	−1.58836	−	2.75112i	−0.0647905	−	0.112220i	0.831811	−	0.555060i	$-0.187305\pi$
$601$	−1.58836	−	2.75112i	−0.0647905	−	0.112220i	−0.896601	+	0.442839i	$0.853971\pi$
$602$		0			0
$603$	15.0900	+	34.2337i	0.614511	+	1.39410i
$604$		0			0
$605$	−3.82112	−	6.61838i	−0.155351	−	0.269075i
$606$		0			0
$607$	−4.14402	−	2.39255i	−0.168201	−	0.0971107i	0.413536	−	0.910488i	$-0.364293\pi$
$607$	−4.14402	−	2.39255i	−0.168201	−	0.0971107i	−0.581737	+	0.813377i	$0.697627\pi$
$608$		0			0
$609$	−12.3154	−	0.668319i	−0.499045	−	0.0270816i
$610$		0			0
$611$		−	17.6842i		−	0.715426i
$612$		0			0
$613$			37.8359i			1.52818i	0.645111	+	0.764089i	$0.276811\pi$
$613$			37.8359i			1.52818i	−0.645111	+	0.764089i	$0.723189\pi$
$614$		0			0
$615$	1.39556	−	2.14028i	0.0562745	−	0.0863045i
$616$		0			0
$617$	−34.4083	−	19.8657i	−1.38523	−	0.799761i	−0.392454	−	0.919772i	$-0.628374\pi$
$617$	−34.4083	−	19.8657i	−1.38523	−	0.799761i	−0.992773	+	0.120011i	$0.961707\pi$
$618$		0			0
$619$	−18.1582	−	31.4510i	−0.729840	−	1.26412i	−0.956950	−	0.290252i	$-0.906261\pi$
$619$	−18.1582	−	31.4510i	−0.729840	−	1.26412i	0.227110	−	0.973869i	$-0.427072\pi$
$620$		0			0
$621$	−8.19634	−	6.71309i	−0.328908	−	0.269387i
$622$		0			0
$623$	7.94383	+	13.7591i	0.318263	+	0.551247i
$624$		0			0
$625$	11.3886	−	19.7257i	0.455545	−	0.789028i
$626$		0			0
$627$	−5.57545	+	8.55069i	−0.222662	+	0.341482i
$628$		0			0
$629$	44.2032			1.76250
$630$		0			0
$631$		−	30.0129i		−	1.19480i	−0.801945	−	0.597398i	$-0.796201\pi$
$631$		−	30.0129i		−	1.19480i	0.801945	−	0.597398i	$-0.203799\pi$
$632$		0			0
$633$	−1.35767	+	25.0183i	−0.0539624	+	0.994388i
$634$		0			0
$635$	−40.8783	−	23.6011i	−1.62221	−	0.936581i
$636$		0			0
$637$	−6.17571	+	3.56555i	−0.244690	+	0.141272i
$638$		0			0
$639$	8.77296	−	11.9813i	0.347053	−	0.473972i
$640$		0			0
$641$	12.8537	−	7.42111i	0.507692	−	0.293116i	−0.224192	−	0.974545i	$-0.571974\pi$
$641$	12.8537	−	7.42111i	0.507692	−	0.293116i	0.731885	+	0.681429i	$0.238641\pi$
$642$		0			0
$643$	−16.9226	+	29.3107i	−0.667361	+	1.15590i	0.311279	+	0.950319i	$0.399243\pi$
$643$	−16.9226	+	29.3107i	−0.667361	+	1.15590i	−0.978639	+	0.205584i	$0.934091\pi$
$644$		0			0
$645$	−8.12989	+	4.12342i	−0.320114	+	0.162359i
$646$		0			0
$647$	−17.5923			−0.691624			−0.345812	−	0.938304i	$-0.612397\pi$
$647$	−17.5923			−0.691624			−0.345812	+	0.938304i	$0.612397\pi$
$648$		0			0
$649$	28.2689			1.10965
$650$		0			0
$651$	14.1835	−	7.19376i	0.555894	−	0.281946i
$652$		0			0
$653$	12.9079	−	22.3571i	0.505124	−	0.874900i	−0.494859	−	0.868974i	$-0.664780\pi$
$653$	12.9079	−	22.3571i	0.505124	−	0.874900i	0.999982	−	0.00592671i	$-0.00188654\pi$
$654$		0			0
$655$	−3.51881	+	2.03159i	−0.137491	+	0.0793807i
$656$		0			0
$657$	−22.7334	+	31.0471i	−0.886915	+	1.21126i
$658$		0			0
$659$	−19.1802	+	11.0737i	−0.747153	+	0.431369i	−0.824664	−	0.565622i	$-0.808636\pi$
$659$	−19.1802	+	11.0737i	−0.747153	+	0.431369i	0.0775113	+	0.996991i	$0.475303\pi$
$660$		0			0
$661$	16.8395	+	9.72232i	0.654983	+	0.378154i	0.790363	−	0.612639i	$-0.209892\pi$
$661$	16.8395	+	9.72232i	0.654983	+	0.378154i	−0.135380	+	0.990794i	$0.543226\pi$
$662$		0			0
$663$	0.540318	−	9.95668i	0.0209842	−	0.386685i
$664$		0			0
$665$		−	6.04453i		−	0.234397i
$666$		0			0
$667$	−11.1234			−0.430700
$668$		0			0
$669$	18.1964	−	27.9066i	0.703513	−	1.07893i
$670$		0			0
$671$	−12.1004	+	20.9585i	−0.467130	+	0.809092i
$672$		0			0
$673$	11.6142	+	20.1164i	0.447695	+	0.775431i	0.998236	−	0.0593778i	$-0.0189117\pi$
$673$	11.6142	+	20.1164i	0.447695	+	0.775431i	−0.550540	+	0.834808i	$0.685578\pi$
$674$		0			0
$675$	−1.99700	+	0.753862i	−0.0768647	+	0.0290162i
$676$		0			0
$677$	−14.3138	−	24.7922i	−0.550123	−	0.952841i	−0.998265	−	0.0588787i	$-0.981247\pi$
$677$	−14.3138	−	24.7922i	−0.550123	−	0.952841i	0.448142	−	0.893962i	$-0.352086\pi$
$678$		0			0
$679$	−18.2090	−	10.5129i	−0.698796	−	0.403450i
$680$		0			0
$681$	0.549536	−	0.842786i	0.0210583	−	0.0322956i
$682$		0			0
$683$			36.7625i			1.40668i	0.710855	+	0.703339i	$0.248308\pi$
$683$			36.7625i			1.40668i	−0.710855	+	0.703339i	$0.751692\pi$
$684$		0			0
$685$			6.52984i			0.249492i
$686$		0			0
$687$	15.5512	+	0.843914i	0.593314	+	0.0321973i
$688$		0			0
$689$	−11.1493	−	6.43703i	−0.424753	−	0.245231i
$690$		0			0
$691$	18.7269	+	32.4360i	0.712407	+	1.23392i	0.963951	+	0.266079i	$0.0857281\pi$
$691$	18.7269	+	32.4360i	0.712407	+	1.23392i	−0.251545	+	0.967846i	$0.580939\pi$
$692$		0			0
$693$	4.30587	+	9.76846i	0.163567	+	0.371073i
$694$		0			0
$695$	−3.91071	−	6.77355i	−0.148342	−	0.256936i
$696$		0			0
$697$	−1.47216	+	2.54986i	−0.0557622	+	0.0965830i
$698$		0			0
$699$	1.32171	+	2.60594i	0.0499917	+	0.0985655i
$700$		0			0
$701$	13.9693			0.527615			0.263807	−	0.964575i	$-0.415022\pi$
$701$	13.9693			0.527615			0.263807	+	0.964575i	$0.415022\pi$
$702$		0			0
$703$			22.3483i			0.842881i
$704$		0			0
$705$	−43.4635	+	22.0444i	−1.63693	+	0.830239i
$706$		0			0
$707$	−16.4328	−	9.48747i	−0.618019	−	0.356813i
$708$		0			0
$709$	−21.0480	+	12.1521i	−0.790476	+	0.456381i	−0.840130	−	0.542385i	$-0.817521\pi$
$709$	−21.0480	+	12.1521i	−0.790476	+	0.456381i	0.0496543	+	0.998766i	$0.484188\pi$
$710$		0			0
$711$	0.255231	−	2.34470i	0.00957192	−	0.0879333i
$712$		0			0
$713$	12.4215	−	7.17156i	0.465189	−	0.268577i
$714$		0			0
$715$	3.93178	−	6.81004i	0.147040	−	0.254681i
$716$		0			0
$717$	−0.328724	+	6.05754i	−0.0122764	+	0.226223i
$718$		0			0
$719$	34.8725			1.30052			0.650262	−	0.759710i	$-0.274659\pi$
$719$	34.8725			1.30052			0.650262	+	0.759710i	$0.274659\pi$
$720$		0			0
$721$	−4.73251			−0.176248
$722$		0			0
$723$	−3.44537	−	2.24654i	−0.128135	−	0.0835497i
$724$		0			0
$725$	−1.12055	+	1.94085i	−0.0416162	+	0.0720813i
$726$		0			0
$727$	−24.1521	+	13.9443i	−0.895754	+	0.517164i	−0.875820	−	0.482638i	$-0.839679\pi$
$727$	−24.1521	+	13.9443i	−0.895754	+	0.517164i	−0.0199335	+	0.999801i	$0.506345\pi$
$728$		0			0
$729$	−25.5841	−	8.62856i	−0.947561	−	0.319576i
$730$		0			0
$731$	9.09721	−	5.25227i	0.336472	−	0.194262i
$732$		0			0
$733$	−27.4750	−	15.8627i	−1.01481	−	0.585902i	−0.102215	−	0.994762i	$-0.532593\pi$
$733$	−27.4750	−	15.8627i	−1.01481	−	0.585902i	−0.912597	+	0.408860i	$0.865926\pi$
$734$		0			0
$735$	16.4616	+	10.7337i	0.607196	+	0.395920i
$736$		0			0
$737$		−	33.9984i		−	1.25235i
$738$		0			0
$739$	−1.80482			−0.0663913			−0.0331957	−	0.999449i	$-0.510568\pi$
$739$	−1.80482			−0.0663913			−0.0331957	+	0.999449i	$0.510568\pi$
$740$		0			0
$741$	5.03391	+	0.273174i	0.184925	+	0.0100353i
$742$		0			0
$743$	−6.84368	+	11.8536i	−0.251070	+	0.434866i	−0.963821	−	0.266551i	$-0.914116\pi$
$743$	−6.84368	+	11.8536i	−0.251070	+	0.434866i	0.712751	+	0.701418i	$0.247449\pi$
$744$		0			0
$745$	−14.9614	−	25.9140i	−0.548145	−	0.949415i
$746$		0			0
$747$	0.682829	−	6.27287i	0.0249834	−	0.229512i
$748$		0			0
$749$	7.60353	+	13.1697i	0.277827	+	0.481210i
$750$		0			0
$751$	−20.8511	−	12.0384i	−0.760868	−	0.439287i	0.0687396	−	0.997635i	$-0.478102\pi$
$751$	−20.8511	−	12.0384i	−0.760868	−	0.439287i	−0.829607	+	0.558348i	$0.811436\pi$
$752$		0			0
$753$	12.9182	+	25.4699i	0.470764	+	0.928176i
$754$		0			0
$755$			48.0764i			1.74968i
$756$		0			0
$757$			11.0608i			0.402013i	0.979590	+	0.201007i	$0.0644213\pi$
$757$			11.0608i			0.402013i	−0.979590	+	0.201007i	$0.935579\pi$
$758$		0			0
$759$	4.35508	+	8.58665i	0.158080	+	0.311676i
$760$		0			0
$761$	−0.392113	−	0.226386i	−0.0142141	−	0.00820650i	0.492876	−	0.870099i	$-0.335946\pi$
$761$	−0.392113	−	0.226386i	−0.0142141	−	0.00820650i	−0.507090	+	0.861893i	$0.669279\pi$
$762$		0			0
$763$	−4.54447	−	7.87125i	−0.164521	−	0.284958i
$764$		0			0
$765$	−25.1447	+	11.0836i	−0.909107	+	0.400728i
$766$		0			0
$767$	−6.98053	−	12.0906i	−0.252052	−	0.436568i
$768$		0			0
$769$	1.71970	−	2.97861i	0.0620139	−	0.107411i	−0.833352	−	0.552743i	$-0.813581\pi$
$769$	1.71970	−	2.97861i	0.0620139	−	0.107411i	0.895366	+	0.445332i	$0.146914\pi$
$770$		0			0
$771$	−3.95865	−	0.214824i	−0.142567	−	0.00773668i
$772$		0			0
$773$	27.5126			0.989558			0.494779	−	0.869019i	$-0.335249\pi$
$773$	27.5126			0.989558			0.494779	+	0.869019i	$0.335249\pi$
$774$		0			0
$775$		−	2.88979i		−	0.103804i
$776$		0			0
$777$	19.5776	+	12.7655i	0.702344	+	0.457961i
$778$		0			0
$779$	−1.28916	−	0.744298i	−0.0461890	−	0.0266673i
$780$		0			0
$781$	−11.6869	+	6.74744i	−0.418190	+	0.241442i
$782$		0			0
$783$	−26.5209	+	10.0116i	−0.947780	+	0.357784i
$784$		0			0
$785$	−5.73609	+	3.31173i	−0.204730	+	0.118201i
$786$		0			0
$787$	3.03995	−	5.26534i	0.108362	−	0.187689i	−0.806745	−	0.590900i	$-0.798773\pi$
$787$	3.03995	−	5.26534i	0.108362	−	0.187689i	0.915107	+	0.403211i	$0.132106\pi$
$788$		0			0
$789$	−42.1726	−	27.4985i	−1.50139	−	0.978973i
$790$		0			0
$791$	17.7152			0.629879
$792$		0			0
$793$	11.9519			0.424426
$794$		0			0
$795$	−1.92248	+	35.4263i	−0.0681832	+	1.25644i
$796$		0			0
$797$	24.0930	−	41.7303i	0.853418	−	1.47816i	−0.0246874	−	0.999695i	$-0.507859\pi$
$797$	24.0930	−	41.7303i	0.853418	−	1.47816i	0.878105	−	0.478468i	$-0.158808\pi$
$798$		0			0
$799$	48.6349	−	28.0794i	1.72058	−	0.993377i
$800$		0			0
$801$	29.4627	+	21.5733i	1.04101	+	0.762255i
$802$		0			0
$803$	30.2843	−	17.4847i	1.06871	−	0.617021i
$804$		0			0
$805$	−4.93734	−	2.85058i	−0.174018	−	0.100470i
$806$		0			0
$807$	17.6137	−	8.93355i	0.620033	−	0.314476i
$808$		0			0
$809$		−	36.1846i		−	1.27218i	−0.771614	−	0.636092i	$-0.780550\pi$
$809$		−	36.1846i		−	1.27218i	0.771614	−	0.636092i	$-0.219450\pi$
$810$		0			0
$811$	34.6514			1.21678			0.608388	−	0.793640i	$-0.291817\pi$
$811$	34.6514			1.21678			0.608388	+	0.793640i	$0.291817\pi$
$812$		0			0
$813$	−22.7093	−	44.7745i	−0.796450	−	1.57031i
$814$		0			0
$815$	−11.1732	+	19.3525i	−0.391380	+	0.677889i
$816$		0			0
$817$	2.65545	+	4.59937i	0.0929024	+	0.160912i
$818$		0			0
$819$	3.11472	−	4.25379i	0.108837	−	0.148639i
$820$		0			0
$821$	−10.0803	−	17.4596i	−0.351806	−	0.609345i	0.634760	−	0.772709i	$-0.281099\pi$
$821$	−10.0803	−	17.4596i	−0.351806	−	0.609345i	−0.986566	+	0.163364i	$0.947766\pi$
$822$		0			0
$823$	9.63955	+	5.56539i	0.336013	+	0.193997i	0.658508	−	0.752574i	$-0.271188\pi$
$823$	9.63955	+	5.56539i	0.336013	+	0.193997i	−0.322494	+	0.946571i	$0.604521\pi$
$824$		0			0
$825$	1.93695	+	0.105112i	0.0674359	+	0.00365954i
$826$		0			0
$827$		−	54.2010i		−	1.88475i	−0.334554	−	0.942376i	$-0.608586\pi$
$827$		−	54.2010i		−	1.88475i	0.334554	−	0.942376i	$-0.391414\pi$
$828$		0			0
$829$			13.2828i			0.461331i	0.973033	+	0.230665i	$0.0740903\pi$
$829$			13.2828i			0.461331i	−0.973033	+	0.230665i	$0.925910\pi$
$830$		0			0
$831$	−21.9621	+	33.6818i	−0.761858	+	1.16841i
$832$		0			0
$833$	−19.6119	−	11.3229i	−0.679511	−	0.392316i
$834$		0			0
$835$	−13.9305	−	24.1283i	−0.482084	−	0.834993i
$836$		0			0
$837$	23.1612	−	28.2786i	0.800567	−	0.977452i
$838$		0			0
$839$	−14.0812	−	24.3894i	−0.486138	−	0.842016i	0.513735	−	0.857949i	$-0.328262\pi$
$839$	−14.0812	−	24.3894i	−0.486138	−	0.842016i	−0.999873	+	0.0159329i	$0.994928\pi$
$840$		0			0
$841$	−0.381300	+	0.660432i	−0.0131483	+	0.0227735i
$842$		0			0
$843$	13.9368	−	21.3740i	0.480010	−	0.736160i
$844$		0			0
$845$	23.9656			0.824442
$846$		0			0
$847$			4.65633i			0.159993i
$848$		0			0
$849$	2.34234	−	43.1633i	0.0803888	−	1.48136i
$850$		0			0
$851$	18.2547	+	10.5393i	0.625762	+	0.361284i
$852$		0			0
$853$	−3.57043	+	2.06139i	−0.122249	+	0.0705806i	−0.559878	−	0.828575i	$-0.689152\pi$
$853$	−3.57043	+	2.06139i	−0.122249	+	0.0705806i	0.437628	+	0.899156i	$0.355819\pi$
$854$		0			0
$855$	−5.60366	−	12.7127i	−0.191641	−	0.434764i
$856$		0			0
$857$	−47.2719	+	27.2924i	−1.61478	+	0.932292i	−0.626535	+	0.779393i	$0.715528\pi$
$857$	−47.2719	+	27.2924i	−1.61478	+	0.932292i	−0.988242	+	0.152899i	$0.951139\pi$
$858$		0			0
$859$	3.19815	−	5.53937i	0.109120	−	0.189001i	−0.806294	−	0.591515i	$-0.798530\pi$
$859$	3.19815	−	5.53937i	0.109120	−	0.189001i	0.915414	+	0.402514i	$0.131864\pi$
$860$		0			0
$861$	−1.38840	+	0.704188i	−0.0473167	+	0.0239987i
$862$		0			0
$863$	−20.4752			−0.696985			−0.348493	−	0.937312i	$-0.613306\pi$
$863$	−20.4752			−0.696985			−0.348493	+	0.937312i	$0.613306\pi$
$864$		0			0
$865$	−11.5665			−0.393274
$866$		0			0
$867$	1.98040	−	1.00444i	0.0672579	−	0.0341127i
$868$		0			0
$869$	−1.07168	+	1.85620i	−0.0363542	+	0.0629674i
$870$		0			0
$871$	−14.5412	+	8.39535i	−0.492709	+	0.284466i
$872$		0			0
$873$	−48.0426	−	5.22965i	−1.62600	−	0.176997i
$874$		0			0
$875$	−13.1024	+	7.56469i	−0.442943	+	0.255733i
$876$		0			0
$877$	47.2059	+	27.2544i	1.59403	+	0.920314i	0.992605	+	0.121386i	$0.0387339\pi$
$877$	47.2059	+	27.2544i	1.59403	+	0.920314i	0.601426	+	0.798928i	$0.294599\pi$
$878$		0			0
$879$	2.07222	−	38.1858i	0.0698943	−	1.28797i
$880$		0			0
$881$		−	28.0171i		−	0.943919i	−0.881620	−	0.471960i	$-0.843547\pi$
$881$		−	28.0171i		−	0.943919i	0.881620	−	0.471960i	$-0.156453\pi$
$882$		0			0
$883$	16.4423			0.553327			0.276663	−	0.960967i	$-0.410771\pi$
$883$	16.4423			0.553327			0.276663	+	0.960967i	$0.410771\pi$
$884$		0			0
$885$	−21.0143	+	32.2281i	−0.706386	+	1.08334i
$886$		0			0
$887$	−14.6877	+	25.4398i	−0.493164	+	0.854185i	−0.999969	−	0.00787590i	$-0.997493\pi$
$887$	−14.6877	+	25.4398i	−0.493164	+	0.854185i	0.506805	+	0.862061i	$0.330826\pi$
$888$		0			0
$889$	14.3799	+	24.9067i	0.482285	+	0.835343i
$890$		0			0
$891$	18.1119	+	16.5529i	0.606773	+	0.554543i
$892$		0			0
$893$	14.1964	+	24.5889i	0.475064	+	0.822836i
$894$		0			0
$895$	8.70632	+	5.02660i	0.291020	+	0.168021i
$896$		0			0
$897$	2.59710	−	3.98301i	0.0867148	−	0.132989i
$898$		0			0
$899$		−	38.3775i		−	1.27996i
$900$		0			0
$901$		−	40.8835i		−	1.36203i
$902$		0			0
$903$	5.54598	+	0.300963i	0.184559	+	0.0100154i
$904$		0			0
$905$	11.7587	+	6.78888i	0.390872	+	0.225670i
$906$		0			0
$907$	9.99859	+	17.3181i	0.331998	+	0.575037i	0.982903	−	0.184122i	$-0.0589441\pi$
$907$	9.99859	+	17.3181i	0.331998	+	0.575037i	−0.650906	+	0.759158i	$0.725611\pi$
$908$		0			0
$909$	−43.3564	−	4.71953i	−1.43804	−	0.156537i
$910$		0			0
$911$	10.4921	+	18.1729i	0.347620	+	0.602096i	0.985826	−	0.167770i	$-0.0536566\pi$
$911$	10.4921	+	18.1729i	0.347620	+	0.602096i	−0.638206	+	0.769866i	$0.720323\pi$
$912$		0			0
$913$	−2.86710	+	4.96597i	−0.0948873	+	0.164350i
$914$		0			0
$915$	−14.8988	−	29.3750i	−0.492538	−	0.971108i
$916$		0			0
$917$	2.47564			0.0817529
$918$		0			0
$919$			36.9502i			1.21888i	0.792834	+	0.609438i	$0.208605\pi$
$919$			36.9502i			1.21888i	−0.792834	+	0.609438i	$0.791395\pi$
$920$		0			0
$921$	−43.2800	+	21.9513i	−1.42613	+	0.723320i
$922$		0			0
$923$	5.77177	+	3.33233i	0.189980	+	0.109685i
$924$		0			0
$925$	3.67788	−	2.12342i	0.120928	−	0.0698177i
$926$		0			0
$927$	−9.95326	+	4.38733i	−0.326908	+	0.144099i
$928$		0			0
$929$	−28.2952	+	16.3362i	−0.928336	+	0.535975i	−0.886285	−	0.463141i	$-0.846722\pi$
$929$	−28.2952	+	16.3362i	−0.928336	+	0.535975i	−0.0420509	+	0.999115i	$0.513389\pi$
$930$		0			0
$931$	5.72465	−	9.91539i	0.187618	−	0.324964i
$932$		0			0
$933$	1.27408	−	23.4781i	0.0417116	−	0.768637i
$934$		0			0
$935$	24.9719			0.816668
$936$		0			0
$937$	31.8176			1.03944			0.519718	−	0.854338i	$-0.326037\pi$
$937$	31.8176			1.03944			0.519718	+	0.854338i	$0.326037\pi$
$938$		0			0
$939$	−40.4553	−	26.3787i	−1.32021	−	0.860837i
$940$		0			0
$941$	−3.26311	+	5.65188i	−0.106374	+	0.184246i	−0.914299	−	0.405040i	$-0.867258\pi$
$941$	−3.26311	+	5.65188i	−0.106374	+	0.184246i	0.807924	+	0.589286i	$0.200591\pi$
$942$		0			0
$943$	−1.21593	+	0.702016i	−0.0395960	+	0.0228608i
$944$		0			0
$945$	−14.3375	−	2.35264i	−0.466398	−	0.0765314i
$946$		0			0
$947$	25.6572	−	14.8132i	0.833747	−	0.481364i	−0.0213869	−	0.999771i	$-0.506808\pi$
$947$	25.6572	−	14.8132i	0.833747	−	0.481364i	0.855134	+	0.518407i	$0.173475\pi$
$948$		0			0
$949$	−14.9564	−	8.63510i	−0.485506	−	0.280307i
$950$		0			0
$951$	−9.14536	−	5.96320i	−0.296559	−	0.193370i
$952$		0			0
$953$		−	1.03621i		−	0.0335660i	−0.999859	−	0.0167830i	$-0.994658\pi$
$953$		−	1.03621i		−	0.0335660i	0.999859	−	0.0167830i	$-0.00534244\pi$
$954$		0			0
$955$	−5.41039			−0.175076
$956$		0			0
$957$	25.7234	+	1.39593i	0.831518	+	0.0451239i
$958$		0			0
$959$	1.98928	−	3.44553i	0.0642371	−	0.111262i
$960$		0			0
$961$	9.24297	+	16.0093i	0.298160	+	0.516429i
$962$		0			0
$963$	28.2006	+	20.6491i	0.908752	+	0.665409i
$964$		0			0
$965$	−12.3658	−	21.4182i	−0.398069	−	0.689476i
$966$		0			0
$967$	7.37695	+	4.25908i	0.237227	+	0.136963i	0.613901	−	0.789383i	$-0.289599\pi$
$967$	7.37695	+	4.25908i	0.237227	+	0.136963i	−0.376675	+	0.926346i	$0.622933\pi$
$968$		0			0
$969$	7.24167	+	14.2780i	0.232636	+	0.458674i
$970$		0			0
$971$			44.7663i			1.43662i	0.695724	+	0.718309i	$0.255084\pi$
$971$			44.7663i			1.43662i	−0.695724	+	0.718309i	$0.744916\pi$
$972$		0			0
$973$			4.76550i			0.152775i
$974$		0			0
$975$	−0.433341	−	0.854391i	−0.0138780	−	0.0273624i
$976$		0			0
$977$	−18.0647	−	10.4296i	−0.577940	−	0.333674i	0.182374	−	0.983229i	$-0.441622\pi$
$977$	−18.0647	−	10.4296i	−0.577940	−	0.333674i	−0.760314	+	0.649555i	$0.774955\pi$
$978$		0			0
$979$	−16.5924	−	28.7389i	−0.530295	−	0.918498i
$980$		0			0
$981$	−16.8549	−	12.3415i	−0.538136	−	0.394035i
$982$		0			0
$983$	−3.56941	−	6.18241i	−0.113847	−	0.197188i	0.803471	−	0.595343i	$-0.202984\pi$
$983$	−3.56941	−	6.18241i	−0.113847	−	0.197188i	−0.917318	+	0.398155i	$0.869651\pi$
$984$		0			0
$985$	2.61748	−	4.53361i	0.0833998	−	0.144453i
$986$		0			0
$987$	29.6496	+	1.60899i	0.943757	+	0.0512147i
$988$		0			0
$989$	5.00919			0.159283
$990$		0			0
$991$		−	12.1928i		−	0.387317i	−0.981069	−	0.193658i	$-0.937965\pi$
$991$		−	12.1928i		−	0.387317i	0.981069	−	0.193658i	$-0.0620354\pi$
$992$		0			0
$993$	2.12908	+	1.38826i	0.0675642	+	0.0440550i
$994$		0			0
$995$	9.80172	+	5.65902i	0.310735	+	0.179403i
$996$		0			0
$997$	11.9482	−	6.89832i	0.378405	−	0.218472i	−0.298719	−	0.954341i	$-0.596559\pi$
$997$	11.9482	−	6.89832i	0.378405	−	0.218472i	0.677124	+	0.735869i	$0.263226\pi$
$998$		0			0
$999$	53.0094	+	8.69835i	1.67714	+	0.275204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.g.959.2	yes	24
3.2	odd	2		3456.2.p.g.2879.10		24
4.3	odd	2		1152.2.p.f.959.11	yes	24
8.3	odd	2		1152.2.p.f.959.2	yes	24
8.5	even	2	inner	1152.2.p.g.959.11	yes	24
9.2	odd	6		1152.2.p.f.191.2	✓	24
9.7	even	3		3456.2.p.f.575.3		24
12.11	even	2		3456.2.p.f.2879.10		24
24.5	odd	2		3456.2.p.g.2879.3		24
24.11	even	2		3456.2.p.f.2879.3		24
36.7	odd	6		3456.2.p.g.575.3		24
36.11	even	6	inner	1152.2.p.g.191.11	yes	24
72.11	even	6	inner	1152.2.p.g.191.2	yes	24
72.29	odd	6		1152.2.p.f.191.11	yes	24
72.43	odd	6		3456.2.p.g.575.10		24
72.61	even	6		3456.2.p.f.575.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.f.191.2	✓	24	9.2	odd	6
1152.2.p.f.191.11	yes	24	72.29	odd	6
1152.2.p.f.959.2	yes	24	8.3	odd	2
1152.2.p.f.959.11	yes	24	4.3	odd	2
1152.2.p.g.191.2	yes	24	72.11	even	6	inner
1152.2.p.g.191.11	yes	24	36.11	even	6	inner
1152.2.p.g.959.2	yes	24	1.1	even	1	trivial
1152.2.p.g.959.11	yes	24	8.5	even	2	inner
3456.2.p.f.575.3		24	9.7	even	3
3456.2.p.f.575.10		24	72.61	even	6
3456.2.p.f.2879.3		24	24.11	even	2
3456.2.p.f.2879.10		24	12.11	even	2
3456.2.p.g.575.3		24	36.7	odd	6
3456.2.p.g.575.10		24	72.43	odd	6
3456.2.p.g.2879.3		24	24.5	odd	2
3456.2.p.g.2879.10		24	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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54472 + 0.783472i) q^{3} +(-1.07112 + 1.85524i) q^{5} +(1.13037 - 0.652621i) q^{7} +(1.77234 - 2.42050i) q^{9} +O(q^{10})\)	\(q+(-1.54472 + 0.783472i) q^{3} +(-1.07112 + 1.85524i) q^{5} +(1.13037 - 0.652621i) q^{7} +(1.77234 - 2.42050i) q^{9} +(-2.36103 + 1.36314i) q^{11} +(1.16603 + 0.673209i) q^{13} +(0.201060 - 3.70502i) q^{15} +4.27575i q^{17} -2.16174 q^{19} +(-1.23480 + 1.89374i) q^{21} +(-1.01947 + 1.76577i) q^{23} +(0.205398 + 0.355759i) q^{25} +(-0.841387 + 5.12758i) q^{27} +(2.72776 + 4.72461i) q^{29} +(-6.09216 - 3.51731i) q^{31} +(2.57915 - 3.95547i) q^{33} +2.79615i q^{35} -10.3381i q^{37} +(-2.32864 - 0.126368i) q^{39} +(0.596355 + 0.344306i) q^{41} +(-1.22839 - 2.12763i) q^{43} +(2.59220 + 5.88076i) q^{45} +(-6.56713 - 11.3746i) q^{47} +(-2.64817 + 4.58677i) q^{49} +(-3.34993 - 6.60485i) q^{51} -9.56171 q^{53} -5.84035i q^{55} +(3.33929 - 1.69366i) q^{57} +(-8.97985 - 5.18452i) q^{59} +(7.68757 - 4.43842i) q^{61} +(0.423741 - 3.89273i) q^{63} +(-2.49793 + 1.44218i) q^{65} +(-6.23532 + 10.7999i) q^{67} +(0.191364 - 3.52635i) q^{69} +4.94992 q^{71} -12.8268 q^{73} +(-0.596010 - 0.388627i) q^{75} +(-1.77923 + 3.08171i) q^{77} +(0.680856 - 0.393093i) q^{79} +(-2.71761 - 8.57990i) q^{81} +(1.82152 - 1.05165i) q^{83} +(-7.93253 - 4.57985i) q^{85} +(-7.91523 - 5.16110i) q^{87} +12.1722i q^{89} +1.75740 q^{91} +(12.1664 + 0.660234i) q^{93} +(2.31548 - 4.01053i) q^{95} +(-8.05440 - 13.9506i) q^{97} +(-0.885074 + 8.13081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{7} - 4 q^{9}+O(q^{10}) \) 24 * q + 12 * q^7 - 4 * q^9	\( 24 q + 12 q^{7} - 4 q^{9} + 20 q^{15} - 12 q^{23} - 12 q^{25} - 36 q^{31} + 4 q^{33} + 20 q^{39} - 12 q^{41} + 12 q^{47} + 12 q^{49} + 4 q^{57} - 92 q^{63} - 48 q^{65} + 24 q^{73} + 84 q^{79} - 20 q^{81} + 68 q^{87} + 24 q^{95} - 12 q^{97}+O(q^{100}) \) 24 * q + 12 * q^7 - 4 * q^9 + 20 * q^15 - 12 * q^23 - 12 * q^25 - 36 * q^31 + 4 * q^33 + 20 * q^39 - 12 * q^41 + 12 * q^47 + 12 * q^49 + 4 * q^57 - 92 * q^63 - 48 * q^65 + 24 * q^73 + 84 * q^79 - 20 * q^81 + 68 * q^87 + 24 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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