LMFDB - Embedded newform 1152.2.p.f.191.2

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			191.2
Character	$\chi$	$=$	1152.191
Dual form			1152.2.p.f.959.2

$q$-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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

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

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	$-0.00765878\pi$
$5$	1.07112	+	1.85524i	0.479020	+	0.829687i	−0.520690	+	0.853746i	$0.674325\pi$
$6$		0			0
$7$	−1.13037	−	0.652621i	−0.427241	−	0.246668i	0.270930	−	0.962599i	$-0.412669\pi$
$7$	−1.13037	−	0.652621i	−0.427241	−	0.246668i	−0.698170	+	0.715932i	$0.746002\pi$
$8$		0			0
$9$	1.77234	+	2.42050i	0.590781	+	0.806832i
$10$		0			0
$11$	−2.36103	−	1.36314i	−0.711876	−	0.411002i	0.0998790	−	0.995000i	$-0.468154\pi$
$11$	−2.36103	−	1.36314i	−0.711876	−	0.411002i	−0.811755	+	0.583998i	$0.801488\pi$
$12$		0			0
$13$	−1.16603	+	0.673209i	−0.323399	+	0.186715i	−0.652907	−	0.757438i	$-0.726451\pi$
$13$	−1.16603	+	0.673209i	−0.323399	+	0.186715i	0.329507	+	0.944153i	$0.393117\pi$
$14$		0			0
$15$	−0.201060	−	3.70502i	−0.0519135	−	0.956633i
$16$		0			0
$17$		−	4.27575i		−	1.03702i	−0.855071	−	0.518511i	$-0.826487\pi$
$17$		−	4.27575i		−	1.03702i	0.855071	−	0.518511i	$-0.173513\pi$
$18$		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	$-0.0984822\pi$
$23$	1.01947	+	1.76577i	0.212573	+	0.368188i	−0.739946	+	0.672666i	$0.765149\pi$
$24$		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	0.493440	+	0.869780i	$0.335739\pi$
$29$	−2.72776	+	4.72461i	−0.506531	+	0.877338i	−0.999971	+	0.00755840i	$0.997594\pi$
$30$		0			0
$31$	6.09216	−	3.51731i	1.09418	−	0.631728i	0.159497	−	0.987198i	$-0.449013\pi$
$31$	6.09216	−	3.51731i	1.09418	−	0.631728i	0.934688	+	0.355470i	$0.115679\pi$
$32$		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	−0.452709	−	0.891658i	$-0.649542\pi$
$41$	0.596355	−	0.344306i	0.0931350	−	0.0537715i	0.545844	+	0.837887i	$0.316209\pi$
$42$		0			0
$43$	−1.22839	+	2.12763i	−0.187327	+	0.324460i	−0.944358	−	0.328919i	$-0.893316\pi$
$43$	−1.22839	+	2.12763i	−0.187327	+	0.324460i	0.757031	+	0.653379i	$0.226649\pi$
$44$		0			0
$45$	−2.59220	+	5.88076i	−0.386422	+	0.876652i
$46$		0			0
$47$	6.56713	−	11.3746i	0.957914	−	1.65916i	0.230359	−	0.973106i	$-0.426010\pi$
$47$	6.56713	−	11.3746i	0.957914	−	1.65916i	0.727555	−	0.686049i	$-0.240657\pi$
$48$		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	$-0.271951\pi$
$53$	9.56171			1.31340			0.656701	+	0.754151i	$0.271951\pi$
$54$		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	−0.953463	−	0.301512i	$-0.902509\pi$
$59$	−8.97985	+	5.18452i	−1.16908	+	0.674967i	−0.215615	+	0.976479i	$0.569175\pi$
$60$		0			0
$61$	−7.68757	−	4.43842i	−0.984292	−	0.568281i	−0.0807290	−	0.996736i	$-0.525725\pi$
$61$	−7.68757	−	4.43842i	−0.984292	−	0.568281i	−0.903563	+	0.428455i	$0.859058\pi$
$62$		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	−0.941940	−	0.335782i	$-0.890999\pi$
$67$	−6.23532	−	10.7999i	−0.761766	−	1.31942i	0.180174	−	0.983635i	$-0.442334\pi$
$68$		0			0
$69$	−0.191364	−	3.52635i	−0.0230375	−	0.424522i
$70$		0			0
$71$	−4.94992			−0.587448			−0.293724	−	0.955890i	$-0.594895\pi$
$71$	−4.94992			−0.587448			−0.293724	+	0.955890i	$0.594895\pi$
$72$		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	$-0.347416\pi$
$79$	−0.680856	−	0.393093i	−0.0766023	−	0.0442264i	−0.537812	+	0.843065i	$0.680749\pi$
$80$		0			0
$81$	−2.71761	+	8.57990i	−0.301956	+	0.953322i
$82$		0			0
$83$	1.82152	+	1.05165i	0.199938	+	0.115434i	0.596626	−	0.802519i	$-0.296507\pi$
$83$	1.82152	+	1.05165i	0.199938	+	0.115434i	−0.396689	+	0.917953i	$0.629841\pi$
$84$		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	$-0.776805\pi$
$89$		−	12.1722i		−	1.29025i	0.764077	−	0.645125i	$-0.223195\pi$
$90$		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	0.0894986	+	0.995987i	$0.471474\pi$
$97$	−8.05440	+	13.9506i	−0.817801	+	1.41647i	−0.907299	+	0.420485i	$0.861860\pi$
$98$		0			0
$99$	−0.885074	−	8.13081i	−0.0889533	−	0.817177i
$100$		0			0
$101$	7.26875	−	12.5898i	0.723267	−	1.25274i	−0.236416	−	0.971652i	$-0.575973\pi$
$101$	7.26875	−	12.5898i	0.723267	−	1.25274i	0.959683	−	0.281084i	$-0.0906938\pi$
$102$		0			0
$103$	3.14001	−	1.81289i	0.309395	−	0.178629i	−0.337261	−	0.941411i	$-0.609500\pi$
$103$	3.14001	−	1.81289i	0.309395	−	0.178629i	0.646656	+	0.762782i	$0.276167\pi$
$104$		0			0
$105$	−2.19070	+	4.31927i	−0.213791	+	0.421518i
$106$		0			0
$107$		−	11.6508i		−	1.12632i	−0.826347	−	0.563161i	$-0.809585\pi$
$107$		−	11.6508i		−	1.12632i	0.826347	−	0.563161i	$-0.190415\pi$
$108$		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	0.168003	−	0.985786i	$-0.446268\pi$
$113$	11.7540	−	6.78616i	1.10572	−	0.638388i	0.937718	+	0.347398i	$0.112935\pi$
$114$		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	−0.426524	−	0.904476i	$-0.640262\pi$
$131$	1.64258	−	0.948346i	0.143513	−	0.0828573i	0.570037	+	0.821619i	$0.306929\pi$
$132$		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	0.608508	−	0.793548i	$-0.291768\pi$
$137$	2.63976	+	1.52407i	0.225530	+	0.130210i	−0.382978	+	0.923757i	$0.625102\pi$
$138$		0			0
$139$	−1.82552	−	3.16190i	−0.154839	−	0.268189i	0.778161	−	0.628064i	$-0.216152\pi$
$139$	−1.82552	−	3.16190i	−0.154839	−	0.268189i	−0.933000	+	0.359875i	$0.882819\pi$
$140$		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	0.996345	+	0.0854250i	$0.0272248\pi$
$149$	6.98401	+	12.0967i	0.572153	+	0.990997i	−0.424192	+	0.905572i	$0.639442\pi$
$150$		0			0
$151$	−19.4354	−	11.2211i	−1.58163	−	0.913156i	−0.994621	−	0.103578i	$-0.966971\pi$
$151$	−19.4354	−	11.2211i	−1.58163	−	0.913156i	−0.587012	−	0.809578i	$-0.699696\pi$
$152$		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	$-0.706039\pi$
$157$	−2.67761	+	1.54592i	−0.213697	+	0.123378i	0.389332	+	0.921098i	$0.372706\pi$
$158$		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	0.999993	+	0.00369641i	$0.00117661\pi$
$167$	6.50275	+	11.2631i	0.503198	+	0.871564i	−0.496795	+	0.867868i	$0.665490\pi$
$168$		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	$-0.899134\pi$
$173$	−2.69963	+	4.67590i	−0.205249	+	0.355502i	0.744963	+	0.667106i	$0.232467\pi$
$174$		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	$0.0561153\pi$
$179$			4.69284i			0.350759i	−0.984501	+	0.175380i	$0.943885\pi$
$180$		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	$-0.862459\pi$
$191$	−1.26279	+	2.18721i	−0.0913720	+	0.158261i	0.816717	+	0.577039i	$0.195792\pi$
$192$		0			0
$193$	−5.77236	−	9.99802i	−0.415504	−	0.719673i	0.579978	−	0.814632i	$-0.303061\pi$
$193$	−5.77236	−	9.99802i	−0.415504	−	0.719673i	−0.995481	+	0.0949590i	$0.969728\pi$
$194$		0			0
$195$	2.72870	+	4.18482i	0.195406	+	0.299681i
$196$		0			0
$197$	2.44368			0.174105			0.0870526	−	0.996204i	$-0.472255\pi$
$197$	2.44368			0.174105			0.0870526	+	0.996204i	$0.472255\pi$
$198$		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	0.999997	−	0.00239362i	$-0.000761913\pi$
$211$	7.23279	+	12.5276i	0.497926	+	0.862432i	−0.502072	+	0.864826i	$0.667429\pi$
$212$		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	$-0.110601\pi$
$223$	16.6575	+	9.61719i	1.11547	+	0.644015i	0.175227	+	0.984528i	$0.443934\pi$
$224$		0			0
$225$	1.22515	−	0.133363i	0.0816766	−	0.00889086i
$226$		0			0
$227$	−0.503060	−	0.290442i	−0.0333893	−	0.0192773i	0.483212	−	0.875503i	$-0.339470\pi$
$227$	−0.503060	−	0.290442i	−0.0333893	−	0.0192773i	−0.516602	+	0.856226i	$0.672803\pi$
$228$		0			0
$229$	7.78703	−	4.49584i	0.514581	−	0.297094i	−0.220134	−	0.975470i	$-0.570649\pi$
$229$	7.78703	−	4.49584i	0.514581	−	0.297094i	0.734715	+	0.678376i	$0.237316\pi$
$230$		0			0
$231$	−0.333978	−	6.15437i	−0.0219742	−	0.404928i
$232$		0			0
$233$			1.68699i			0.110518i	0.998472	+	0.0552592i	$0.0175985\pi$
$233$			1.68699i			0.110518i	−0.998472	+	0.0552592i	$0.982401\pi$
$234$		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	$-0.202802\pi$
$239$	−1.75123	−	3.03323i	−0.113278	−	0.196203i	−0.917090	+	0.398680i	$0.869468\pi$
$240$		0			0
$241$	1.18735	−	2.05655i	0.0764837	−	0.132474i	−0.825247	−	0.564772i	$-0.808964\pi$
$241$	1.18735	−	2.05655i	0.0764837	−	0.132474i	0.901731	+	0.432299i	$0.142297\pi$
$242$		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	$0.174205\pi$
$251$			16.4883i			1.04073i	−0.853942	+	0.520367i	$0.825795\pi$
$252$		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	−0.436900	−	0.899510i	$-0.643924\pi$
$257$	1.98224	−	1.14444i	0.123649	−	0.0713885i	0.560549	+	0.828122i	$0.310590\pi$
$258$		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	−0.0638398	+	0.997960i	$0.520335\pi$
$263$	−14.5336	+	25.1729i	−0.896179	+	1.55223i	−0.832339	+	0.554267i	$0.812999\pi$
$264$		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	$-0.386993\pi$
$269$	11.4025			0.695223			0.347612	+	0.937639i	$0.386993\pi$
$270$		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	$-0.579004\pi$
$277$	−20.1047	−	11.6075i	−1.20798	−	0.697425i	−0.962317	+	0.271931i	$0.912338\pi$
$278$		0			0
$279$	19.3110	+	8.51218i	1.15612	+	0.509611i
$280$		0			0
$281$	−12.7582	−	7.36593i	−0.761088	−	0.439415i	0.0685980	−	0.997644i	$-0.478147\pi$
$281$	−12.7582	−	7.36593i	−0.761088	−	0.439415i	−0.829686	+	0.558230i	$0.811481\pi$
$282$		0			0
$283$	−12.4785	−	21.6134i	−0.741770	−	1.28478i	−0.951689	−	0.307065i	$-0.900653\pi$
$283$	−12.4785	−	21.6134i	−0.741770	−	1.28478i	0.209919	−	0.977719i	$-0.432680\pi$
$284$		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	0.984317	+	0.176410i	$0.0564486\pi$
$293$	11.0395	+	19.1210i	0.644934	+	1.11706i	−0.339382	+	0.940648i	$0.610218\pi$
$294$		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	$-0.0409080\pi$
$311$	6.78751	+	11.7563i	0.384884	+	0.666639i	−0.606869	+	0.794802i	$0.707575\pi$
$312$		0			0
$313$	13.9417	−	24.1478i	0.788034	−	1.36491i	−0.139136	−	0.990273i	$-0.544433\pi$
$313$	13.9417	−	24.1478i	0.788034	−	1.36491i	0.927170	−	0.374641i	$-0.122234\pi$
$314$		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	$-0.889978\pi$
$317$	−3.15169	+	5.45888i	−0.177016	+	0.306601i	0.763841	+	0.645405i	$0.223311\pi$
$318$		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	−0.885485	−	0.464667i	$-0.846174\pi$
$331$	−0.733725	+	1.27085i	−0.0403292	+	0.0698522i	0.845156	+	0.534519i	$0.179507\pi$
$332$		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	0.829750	−	0.558136i	$-0.188483\pi$
$337$	−1.25721	−	2.17756i	−0.0684848	−	0.118619i	−0.898235	+	0.439516i	$0.855150\pi$
$338$		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	0.0491051	−	0.998794i	$-0.484363\pi$
$347$	17.4849	−	10.0949i	0.938638	−	0.541923i	0.889533	+	0.456871i	$0.151030\pi$
$348$		0			0
$349$	−6.58266	−	3.80050i	−0.352362	−	0.203436i	0.313363	−	0.949633i	$-0.398544\pi$
$349$	−6.58266	−	3.80050i	−0.352362	−	0.203436i	−0.665725	+	0.746197i	$0.731878\pi$
$350$		0			0
$351$	4.43302	+	5.41250i	0.236617	+	0.288898i
$352$		0			0
$353$	−8.78534	−	5.07222i	−0.467596	−	0.269967i	0.247637	−	0.968853i	$-0.420346\pi$
$353$	−8.78534	−	5.07222i	−0.467596	−	0.269967i	−0.715233	+	0.698886i	$0.753679\pi$
$354$		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	$-0.682928\pi$
$359$	−20.5983			−1.08714			−0.543570	+	0.839364i	$0.682928\pi$
$360$		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	$-0.442375\pi$
$367$	−11.1457	−	6.43498i	−0.581802	−	0.335903i	−0.761849	+	0.647755i	$0.775708\pi$
$368$		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	$-0.725285\pi$
$373$	−6.12551	+	3.53656i	−0.317167	+	0.183116i	0.332962	+	0.942940i	$0.391952\pi$
$374$		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	−0.999993	−	0.00375959i	$-0.998803\pi$
$383$	−9.84884	−	17.0587i	−0.503252	−	0.871659i	0.496741	−	0.867899i	$-0.334530\pi$
$384$		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	$-0.949798\pi$
$389$	−7.05645	+	12.2221i	−0.357776	+	0.619687i	0.629813	+	0.776747i	$0.283132\pi$
$390$		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	−0.930162	−	0.367149i	$-0.880334\pi$
$401$	−21.5726	+	12.4549i	−1.07728	+	0.621969i	−0.147120	+	0.989119i	$0.547000\pi$
$402$		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	0.612737	−	0.790287i	$-0.290069\pi$
$409$	−7.64539	−	13.2422i	−0.378040	−	0.654785i	−0.990777	+	0.135502i	$0.956735\pi$
$410$		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	−0.625799	−	0.779985i	$-0.715227\pi$
$419$	−5.38781	+	3.11065i	−0.263212	+	0.151965i	0.362587	+	0.931950i	$0.381894\pi$
$420$		0			0
$421$	−3.60960	−	2.08400i	−0.175921	−	0.101568i	0.409454	−	0.912331i	$-0.365719\pi$
$421$	−3.60960	−	2.08400i	−0.175921	−	0.101568i	−0.585375	+	0.810763i	$0.699053\pi$
$422$		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	$-0.189235\pi$
$431$	34.3973			1.65686			0.828429	+	0.560094i	$0.189235\pi$
$432$		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	$-0.621361\pi$
$439$	−28.5367	−	16.4757i	−1.36198	−	0.786342i	−0.989888	+	0.141852i	$0.954694\pi$
$440$		0			0
$441$	6.40879	−	14.5392i	0.305180	−	0.692343i
$442$		0			0
$443$	−3.04392	−	1.75741i	−0.144621	−	0.0834969i	0.425944	−	0.904750i	$-0.359942\pi$
$443$	−3.04392	−	1.75741i	−0.144621	−	0.0834969i	−0.570564	+	0.821253i	$0.693276\pi$
$444$		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	$0.225475\pi$
$449$			27.5711i			1.30116i	−0.759437	+	0.650581i	$0.774525\pi$
$450$		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	−0.939494	−	0.342564i	$-0.888705\pi$
$457$	−3.69999	+	6.40857i	−0.173078	+	0.299780i	0.766416	+	0.642344i	$0.222038\pi$
$458$		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	$-0.924041\pi$
$461$	−6.03604	+	10.4547i	−0.281126	+	0.486925i	0.690536	+	0.723298i	$0.257375\pi$
$462$		0			0
$463$	11.6479	−	6.72493i	0.541325	−	0.312534i	−0.204291	−	0.978910i	$-0.565489\pi$
$463$	11.6479	−	6.72493i	0.541325	−	0.312534i	0.745616	+	0.666376i	$0.232155\pi$
$464$		0			0
$465$	−14.2566	−	21.8644i	−0.661134	−	1.01394i
$466$		0			0
$467$		−	12.9746i		−	0.600391i	−0.953878	−	0.300196i	$-0.902948\pi$
$467$		−	12.9746i		−	0.600391i	0.953878	−	0.300196i	$-0.0970519\pi$
$468$		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	$-0.721305\pi$
$479$	7.54472	−	13.0678i	0.344727	−	0.597085i	0.985304	+	0.170809i	$0.0546381\pi$
$480$		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	−0.254666	−	0.967029i	$-0.581966\pi$
$491$	10.0926	−	5.82696i	0.455472	−	0.262967i	0.710138	+	0.704062i	$0.248632\pi$
$492$		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	−0.996899	−	0.0786941i	$-0.974925\pi$
$499$	−12.6569	−	21.9224i	−0.566601	−	0.981381i	0.430298	−	0.902687i	$-0.358408\pi$
$500$		0			0
$501$	−1.22063	−	22.4931i	−0.0545337	−	1.00492i
$502$		0			0
$503$	27.4640			1.22456			0.612279	−	0.790642i	$-0.290253\pi$
$503$	27.4640			1.22456			0.612279	+	0.790642i	$0.290253\pi$
$504$		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	$-0.302149\pi$
$509$	−9.31530	−	16.1346i	−0.412894	−	0.715153i	−0.995205	+	0.0978134i	$0.968815\pi$
$510$		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	$0.177044\pi$
$521$			24.1019i			1.05593i	−0.849268	+	0.527963i	$0.822956\pi$
$522$		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	0.484474	+	0.874806i	$0.339011\pi$
$547$	−12.0534	+	20.8771i	−0.515367	+	0.892642i	−0.999841	+	0.0178365i	$0.994322\pi$
$548$		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	$-0.213537\pi$
$557$	36.9729			1.56659			0.783295	+	0.621650i	$0.213537\pi$
$558$		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	−0.185602	−	0.982625i	$-0.559423\pi$
$563$	13.5859	−	7.84380i	0.572576	−	0.330577i	0.758177	+	0.652048i	$0.226090\pi$
$564$		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	0.963612	−	0.267304i	$-0.0861327\pi$
$569$	28.9567	+	16.7181i	1.21393	+	0.700861i	0.250314	+	0.968165i	$0.419466\pi$
$570$		0			0
$571$	−18.1141	−	31.3746i	−0.758053	−	1.31299i	−0.943842	−	0.330397i	$-0.892817\pi$
$571$	−18.1141	−	31.3746i	−0.758053	−	1.31299i	0.185788	−	0.982590i	$-0.440516\pi$
$572$		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	−0.447538	−	0.894265i	$-0.647699\pi$
$587$	−35.0281	−	20.2235i	−1.44576	−	0.834711i	−0.998225	+	0.0595537i	$0.981032\pi$
$588$		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	$-0.936201\pi$
$593$		−	9.69635i		−	0.398181i	0.979981	−	0.199091i	$-0.0637988\pi$
$594$		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	−0.878878	−	0.477047i	$-0.841707\pi$
$599$	−20.8663	−	36.1415i	−0.852574	−	1.47670i	0.0263039	−	0.999654i	$-0.491626\pi$
$600$		0			0
$601$	−1.58836	+	2.75112i	−0.0647905	+	0.112220i	−0.896601	−	0.442839i	$-0.853971\pi$
$601$	−1.58836	+	2.75112i	−0.0647905	+	0.112220i	0.831811	+	0.555060i	$0.187305\pi$
$602$		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	$-0.635707\pi$
$607$	4.14402	−	2.39255i	0.168201	−	0.0971107i	0.581737	+	0.813377i	$0.302373\pi$
$608$		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	−0.992773	−	0.120011i	$-0.961707\pi$
$617$	−34.4083	+	19.8657i	−1.38523	+	0.799761i	−0.392454	+	0.919772i	$0.628374\pi$
$618$		0			0
$619$	−18.1582	+	31.4510i	−0.729840	+	1.26412i	0.227110	+	0.973869i	$0.427072\pi$
$619$	−18.1582	+	31.4510i	−0.729840	+	1.26412i	−0.956950	+	0.290252i	$0.906261\pi$
$620$		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	0.731885	−	0.681429i	$-0.238641\pi$
$641$	12.8537	+	7.42111i	0.507692	+	0.293116i	−0.224192	+	0.974545i	$0.571974\pi$
$642$		0			0
$643$	−16.9226	−	29.3107i	−0.667361	−	1.15590i	−0.978639	−	0.205584i	$-0.934091\pi$
$643$	−16.9226	−	29.3107i	−0.667361	−	1.15590i	0.311279	−	0.950319i	$-0.399243\pi$
$644$		0			0
$645$	8.12989	+	4.12342i	0.320114	+	0.162359i
$646$		0			0
$647$	17.5923			0.691624			0.345812	−	0.938304i	$-0.387603\pi$
$647$	17.5923			0.691624			0.345812	+	0.938304i	$0.387603\pi$
$648$		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	−0.999982	−	0.00592671i	$-0.998113\pi$
$653$	−12.9079	−	22.3571i	−0.505124	−	0.874900i	0.494859	−	0.868974i	$-0.335220\pi$
$654$		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	0.0775113	−	0.996991i	$-0.475303\pi$
$659$	−19.1802	−	11.0737i	−0.747153	−	0.431369i	−0.824664	+	0.565622i	$0.808636\pi$
$660$		0			0
$661$	−16.8395	+	9.72232i	−0.654983	+	0.378154i	−0.790363	−	0.612639i	$-0.790108\pi$
$661$	−16.8395	+	9.72232i	−0.654983	+	0.378154i	0.135380	+	0.990794i	$0.456774\pi$
$662$		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	−0.550540	−	0.834808i	$-0.685578\pi$
$673$	11.6142	−	20.1164i	0.447695	−	0.775431i	0.998236	+	0.0593778i	$0.0189117\pi$
$674$		0			0
$675$	−1.99700	−	0.753862i	−0.0768647	−	0.0290162i
$676$		0			0
$677$	14.3138	−	24.7922i	0.550123	−	0.952841i	−0.448142	−	0.893962i	$-0.647914\pi$
$677$	14.3138	−	24.7922i	0.550123	−	0.952841i	0.998265	−	0.0588787i	$-0.0187525\pi$
$678$		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	$-0.751692\pi$
$683$		−	36.7625i		−	1.40668i	0.710855	−	0.703339i	$-0.248308\pi$
$684$		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	−0.251545	−	0.967846i	$-0.580939\pi$
$691$	18.7269	−	32.4360i	0.712407	−	1.23392i	0.963951	−	0.266079i	$-0.0857281\pi$
$692$		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	$-0.584978\pi$
$701$	−13.9693			−0.527615			−0.263807	+	0.964575i	$0.584978\pi$
$702$		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	$-0.182479\pi$
$709$	21.0480	+	12.1521i	0.790476	+	0.456381i	−0.0496543	+	0.998766i	$0.515812\pi$
$710$		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	$-0.725341\pi$
$719$	−34.8725			−1.30052			−0.650262	+	0.759710i	$0.725341\pi$
$720$		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	$-0.160321\pi$
$727$	24.1521	+	13.9443i	0.895754	+	0.517164i	0.0199335	+	0.999801i	$0.493655\pi$
$728$		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	$-0.467407\pi$
$733$	27.4750	−	15.8627i	1.01481	−	0.585902i	0.912597	+	0.408860i	$0.134074\pi$
$734$		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	$-0.0858842\pi$
$743$	6.84368	+	11.8536i	0.251070	+	0.434866i	−0.712751	+	0.701418i	$0.752551\pi$
$744$		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	$-0.521898\pi$
$751$	20.8511	−	12.0384i	0.760868	−	0.439287i	0.829607	+	0.558348i	$0.188564\pi$
$752$		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	−0.507090	−	0.861893i	$-0.669279\pi$
$761$	−0.392113	+	0.226386i	−0.0142141	+	0.00820650i	0.492876	+	0.870099i	$0.335946\pi$
$762$		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	0.895366	−	0.445332i	$-0.146914\pi$
$769$	1.71970	+	2.97861i	0.0620139	+	0.107411i	−0.833352	+	0.552743i	$0.813581\pi$
$770$		0			0
$771$	−3.95865	+	0.214824i	−0.142567	+	0.00773668i
$772$		0			0
$773$	−27.5126			−0.989558			−0.494779	−	0.869019i	$-0.664751\pi$
$773$	−27.5126			−0.989558			−0.494779	+	0.869019i	$0.664751\pi$
$774$		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	0.915107	−	0.403211i	$-0.132106\pi$
$787$	3.03995	+	5.26534i	0.108362	+	0.187689i	−0.806745	+	0.590900i	$0.798773\pi$
$788$		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	−0.878105	−	0.478468i	$-0.841192\pi$
$797$	−24.0930	−	41.7303i	−0.853418	−	1.47816i	0.0246874	−	0.999695i	$-0.492141\pi$
$798$		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	$0.219450\pi$
$809$			36.1846i			1.27218i	−0.771614	+	0.636092i	$0.780550\pi$
$810$		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	$-0.718901\pi$
$821$	10.0803	−	17.4596i	0.351806	−	0.609345i	0.986566	+	0.163364i	$0.0522344\pi$
$822$		0			0
$823$	−9.63955	+	5.56539i	−0.336013	+	0.193997i	−0.658508	−	0.752574i	$-0.728812\pi$
$823$	−9.63955	+	5.56539i	−0.336013	+	0.193997i	0.322494	+	0.946571i	$0.395479\pi$
$824$		0			0
$825$	1.93695	−	0.105112i	0.0674359	−	0.00365954i
$826$		0			0
$827$			54.2010i			1.88475i	0.334554	+	0.942376i	$0.391414\pi$
$827$			54.2010i			1.88475i	−0.334554	+	0.942376i	$0.608586\pi$
$828$		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	$-0.671738\pi$
$839$	14.0812	−	24.3894i	0.486138	−	0.842016i	0.999873	+	0.0159329i	$0.00507181\pi$
$840$		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	$-0.310848\pi$
$853$	3.57043	+	2.06139i	0.122249	+	0.0705806i	−0.437628	+	0.899156i	$0.644181\pi$
$854$		0			0
$855$	5.60366	−	12.7127i	0.191641	−	0.434764i
$856$		0			0
$857$	−47.2719	−	27.2924i	−1.61478	−	0.932292i	−0.988242	−	0.152899i	$-0.951139\pi$
$857$	−47.2719	−	27.2924i	−1.61478	−	0.932292i	−0.626535	−	0.779393i	$-0.715528\pi$
$858$		0			0
$859$	3.19815	+	5.53937i	0.109120	+	0.189001i	0.915414	−	0.402514i	$-0.131864\pi$
$859$	3.19815	+	5.53937i	0.109120	+	0.189001i	−0.806294	+	0.591515i	$0.798530\pi$
$860$		0			0
$861$	1.38840	+	0.704188i	0.0473167	+	0.0239987i
$862$		0			0
$863$	20.4752			0.696985			0.348493	−	0.937312i	$-0.386694\pi$
$863$	20.4752			0.696985			0.348493	+	0.937312i	$0.386694\pi$
$864$		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	−0.601426	+	0.798928i	$0.705401\pi$
$877$	−47.2059	+	27.2544i	−1.59403	+	0.920314i	−0.992605	+	0.121386i	$0.961266\pi$
$878$		0			0
$879$	−2.07222	−	38.1858i	−0.0698943	−	1.28797i
$880$		0			0
$881$			28.0171i			0.943919i	0.881620	+	0.471960i	$0.156453\pi$
$881$			28.0171i			0.943919i	−0.881620	+	0.471960i	$0.843547\pi$
$882$		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	$-0.00250700\pi$
$887$	14.6877	+	25.4398i	0.493164	+	0.854185i	−0.506805	+	0.862061i	$0.669174\pi$
$888$		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	−0.650906	−	0.759158i	$-0.725611\pi$
$907$	9.99859	−	17.3181i	0.331998	−	0.575037i	0.982903	+	0.184122i	$0.0589441\pi$
$908$		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	$-0.946343\pi$
$911$	−10.4921	+	18.1729i	−0.347620	+	0.602096i	0.638206	+	0.769866i	$0.279677\pi$
$912$		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	−0.0420509	−	0.999115i	$-0.513389\pi$
$929$	−28.2952	−	16.3362i	−0.928336	−	0.535975i	−0.886285	+	0.463141i	$0.846722\pi$
$930$		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	$-0.132742\pi$
$941$	3.26311	+	5.65188i	0.106374	+	0.184246i	−0.807924	+	0.589286i	$0.799409\pi$
$942$		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	0.855134	−	0.518407i	$-0.173475\pi$
$947$	25.6572	+	14.8132i	0.833747	+	0.481364i	−0.0213869	+	0.999771i	$0.506808\pi$
$948$		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	$0.00534244\pi$
$953$			1.03621i			0.0335660i	−0.999859	+	0.0167830i	$0.994658\pi$
$954$		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	$-0.710401\pi$
$967$	−7.37695	+	4.25908i	−0.237227	+	0.136963i	0.376675	+	0.926346i	$0.377067\pi$
$968$		0			0
$969$	7.24167	−	14.2780i	0.232636	−	0.458674i
$970$		0			0
$971$		−	44.7663i		−	1.43662i	−0.695724	−	0.718309i	$-0.744916\pi$
$971$		−	44.7663i		−	1.43662i	0.695724	−	0.718309i	$-0.255084\pi$
$972$		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	−0.760314	−	0.649555i	$-0.774955\pi$
$977$	−18.0647	+	10.4296i	−0.577940	+	0.333674i	0.182374	+	0.983229i	$0.441622\pi$
$978$		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	$-0.797016\pi$
$983$	3.56941	−	6.18241i	0.113847	−	0.197188i	0.917318	+	0.398155i	$0.130349\pi$
$984$		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	$-0.403441\pi$
$997$	−11.9482	−	6.89832i	−0.378405	−	0.218472i	−0.677124	+	0.735869i	$0.736774\pi$
$998$		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.f.191.2	✓	24
3.2	odd	2		3456.2.p.f.575.3		24
4.3	odd	2		1152.2.p.g.191.11	yes	24
8.3	odd	2		1152.2.p.g.191.2	yes	24
8.5	even	2	inner	1152.2.p.f.191.11	yes	24
9.4	even	3		3456.2.p.g.2879.10		24
9.5	odd	6		1152.2.p.g.959.2	yes	24
12.11	even	2		3456.2.p.g.575.3		24
24.5	odd	2		3456.2.p.f.575.10		24
24.11	even	2		3456.2.p.g.575.10		24
36.23	even	6	inner	1152.2.p.f.959.11	yes	24
36.31	odd	6		3456.2.p.f.2879.10		24
72.5	odd	6		1152.2.p.g.959.11	yes	24
72.13	even	6		3456.2.p.g.2879.3		24
72.59	even	6	inner	1152.2.p.f.959.2	yes	24
72.67	odd	6		3456.2.p.f.2879.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.f.191.2	✓	24	1.1	even	1	trivial
1152.2.p.f.191.11	yes	24	8.5	even	2	inner
1152.2.p.f.959.2	yes	24	72.59	even	6	inner
1152.2.p.f.959.11	yes	24	36.23	even	6	inner
1152.2.p.g.191.2	yes	24	8.3	odd	2
1152.2.p.g.191.11	yes	24	4.3	odd	2
1152.2.p.g.959.2	yes	24	9.5	odd	6
1152.2.p.g.959.11	yes	24	72.5	odd	6
3456.2.p.f.575.3		24	3.2	odd	2
3456.2.p.f.575.10		24	24.5	odd	2
3456.2.p.f.2879.3		24	72.67	odd	6
3456.2.p.f.2879.10		24	36.31	odd	6
3456.2.p.g.575.3		24	12.11	even	2
3456.2.p.g.575.10		24	24.11	even	2
3456.2.p.g.2879.3		24	72.13	even	6
3456.2.p.g.2879.10		24	9.4	even	3

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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