LMFDB - Embedded newform 1152.2.p.f.959.1

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			959.1
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.f.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68783 - 0.388876i) q^{3} +(0.538609 - 0.932899i) q^{5} +(4.07105 - 2.35042i) q^{7} +(2.69755 + 1.31271i) q^{9} +O(q^{10})$	\(q+(-1.68783 - 0.388876i) q^{3} +(0.538609 - 0.932899i) q^{5} +(4.07105 - 2.35042i) q^{7} +(2.69755 + 1.31271i) q^{9} +(4.28563 - 2.47431i) q^{11} +(-1.05002 - 0.606232i) q^{13} +(-1.27186 + 1.36512i) q^{15} +3.12017i q^{17} -2.05903 q^{19} +(-7.78527 + 2.38398i) q^{21} +(1.71835 - 2.97627i) q^{23} +(1.91980 + 3.32519i) q^{25} +(-4.04253 - 3.26465i) q^{27} +(0.723042 + 1.25234i) q^{29} +(6.45450 + 3.72651i) q^{31} +(-8.19561 + 2.50964i) q^{33} -5.06384i q^{35} +9.04031i q^{37} +(1.53652 + 1.43155i) q^{39} +(-8.75630 - 5.05545i) q^{41} +(-0.0592540 - 0.102631i) q^{43} +(2.67756 - 1.80950i) q^{45} +(-1.98823 - 3.44372i) q^{47} +(7.54897 - 13.0752i) q^{49} +(1.21336 - 5.26632i) q^{51} +0.401027 q^{53} -5.33074i q^{55} +(3.47530 + 0.800709i) q^{57} +(-8.97357 - 5.18089i) q^{59} +(11.7417 - 6.77909i) q^{61} +(14.0673 - 0.996260i) q^{63} +(-1.13111 + 0.653045i) q^{65} +(4.94046 - 8.55712i) q^{67} +(-4.05769 + 4.35522i) q^{69} +12.8855 q^{71} +0.327300 q^{73} +(-1.94721 - 6.35893i) q^{75} +(11.6313 - 20.1461i) q^{77} +(-8.98705 + 5.18867i) q^{79} +(5.55357 + 7.08223i) q^{81} +(-8.21751 + 4.74438i) q^{83} +(2.91081 + 1.68055i) q^{85} +(-0.733366 - 2.39492i) q^{87} -9.80272i q^{89} -5.69961 q^{91} +(-9.44496 - 8.79972i) q^{93} +(-1.10902 + 1.92087i) q^{95} +(2.79591 + 4.84266i) q^{97} +(14.8088 - 1.04877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.68783	−	0.388876i	−0.974470	−	0.224518i
$3$	−1.68783	−	0.388876i	−0.974470	−	0.224518i
$4$		0			0
$5$	0.538609	−	0.932899i	0.240873	−	0.417205i	−0.720090	−	0.693881i	$-0.755899\pi$
$5$	0.538609	−	0.932899i	0.240873	−	0.417205i	0.960963	+	0.276676i	$0.0892328\pi$
$6$		0			0
$7$	4.07105	−	2.35042i	1.53871	−	0.888376i	0.539798	−	0.841795i	$-0.318501\pi$
$7$	4.07105	−	2.35042i	1.53871	−	0.888376i	0.998914	−	0.0465815i	$-0.0148327\pi$
$8$		0			0
$9$	2.69755	+	1.31271i	0.899184	+	0.437571i
$10$		0			0
$11$	4.28563	−	2.47431i	1.29216	−	0.746032i	0.313127	−	0.949711i	$-0.398623\pi$
$11$	4.28563	−	2.47431i	1.29216	−	0.746032i	0.979038	+	0.203679i	$0.0652900\pi$
$12$		0			0
$13$	−1.05002	−	0.606232i	−0.291225	−	0.168139i	0.347269	−	0.937765i	$-0.387109\pi$
$13$	−1.05002	−	0.606232i	−0.291225	−	0.168139i	−0.638494	+	0.769627i	$0.720442\pi$
$14$		0			0
$15$	−1.27186	+	1.36512i	−0.328394	+	0.352474i
$16$		0			0
$17$			3.12017i			0.756753i	0.925652	+	0.378376i	$0.123518\pi$
$17$			3.12017i			0.756753i	−0.925652	+	0.378376i	$0.876482\pi$
$18$		0			0
$19$	−2.05903			−0.472375			−0.236187	−	0.971708i	$-0.575898\pi$
$19$	−2.05903			−0.472375			−0.236187	+	0.971708i	$0.575898\pi$
$20$		0			0
$21$	−7.78527	+	2.38398i	−1.69889	+	0.520228i
$22$		0			0
$23$	1.71835	−	2.97627i	0.358301	−	0.620596i	−0.629376	−	0.777101i	$-0.716689\pi$
$23$	1.71835	−	2.97627i	0.358301	−	0.620596i	0.987677	+	0.156505i	$0.0500228\pi$
$24$		0			0
$25$	1.91980	+	3.32519i	0.383960	+	0.665038i
$26$		0			0
$27$	−4.04253	−	3.26465i	−0.777985	−	0.628283i
$28$		0			0
$29$	0.723042	+	1.25234i	0.134265	+	0.232555i	0.925317	−	0.379195i	$-0.123799\pi$
$29$	0.723042	+	1.25234i	0.134265	+	0.232555i	−0.791051	+	0.611750i	$0.790466\pi$
$30$		0			0
$31$	6.45450	+	3.72651i	1.15926	+	0.669301i	0.951127	−	0.308799i	$-0.0999271\pi$
$31$	6.45450	+	3.72651i	1.15926	+	0.669301i	0.208136	+	0.978100i	$0.433260\pi$
$32$		0			0
$33$	−8.19561	+	2.50964i	−1.42667	+	0.436872i
$34$		0			0
$35$		−	5.06384i		−	0.855945i
$36$		0			0
$37$			9.04031i			1.48622i	0.669171	+	0.743109i	$0.266649\pi$
$37$			9.04031i			1.48622i	−0.669171	+	0.743109i	$0.733351\pi$
$38$		0			0
$39$	1.53652	+	1.43155i	0.246040	+	0.229231i
$40$		0			0
$41$	−8.75630	−	5.05545i	−1.36750	−	0.789529i	−0.376896	−	0.926256i	$-0.623009\pi$
$41$	−8.75630	−	5.05545i	−1.36750	−	0.789529i	−0.990609	+	0.136726i	$0.956342\pi$
$42$		0			0
$43$	−0.0592540	−	0.102631i	−0.00903614	−	0.0156511i	0.861472	−	0.507805i	$-0.169543\pi$
$43$	−0.0592540	−	0.102631i	−0.00903614	−	0.0156511i	−0.870508	+	0.492154i	$0.836210\pi$
$44$		0			0
$45$	2.67756	−	1.80950i	0.399146	−	0.269745i
$46$		0			0
$47$	−1.98823	−	3.44372i	−0.290014	−	0.502319i	0.683799	−	0.729671i	$-0.260327\pi$
$47$	−1.98823	−	3.44372i	−0.290014	−	0.502319i	−0.973813	+	0.227352i	$0.926993\pi$
$48$		0			0
$49$	7.54897	−	13.0752i	1.07842	−	1.86789i
$50$		0			0
$51$	1.21336	−	5.26632i	0.169904	−	0.737433i
$52$		0			0
$53$	0.401027			0.0550853			0.0275426	−	0.999621i	$-0.491232\pi$
$53$	0.401027			0.0550853			0.0275426	+	0.999621i	$0.491232\pi$
$54$		0			0
$55$		−	5.33074i		−	0.718797i
$56$		0			0
$57$	3.47530	+	0.800709i	0.460315	+	0.106056i
$58$		0			0
$59$	−8.97357	−	5.18089i	−1.16826	−	0.674495i	−0.214990	−	0.976616i	$-0.568972\pi$
$59$	−8.97357	−	5.18089i	−1.16826	−	0.674495i	−0.953269	+	0.302121i	$0.902305\pi$
$60$		0			0
$61$	11.7417	−	6.77909i	1.50337	−	0.867973i	0.503381	−	0.864065i	$-0.332089\pi$
$61$	11.7417	−	6.77909i	1.50337	−	0.867973i	0.999992	−	0.00390851i	$-0.00124412\pi$
$62$		0			0
$63$	14.0673	−	0.996260i	1.77231	−	0.125517i
$64$		0			0
$65$	−1.13111	+	0.653045i	−0.140297	+	0.0810002i
$66$		0			0
$67$	4.94046	−	8.55712i	0.603573	−	1.04542i	−0.388702	−	0.921363i	$-0.627077\pi$
$67$	4.94046	−	8.55712i	0.603573	−	1.04542i	0.992275	−	0.124056i	$-0.0395901\pi$
$68$		0			0
$69$	−4.05769	+	4.35522i	−0.488488	+	0.524307i
$70$		0			0
$71$	12.8855			1.52922			0.764612	−	0.644491i	$-0.222931\pi$
$71$	12.8855			1.52922			0.764612	+	0.644491i	$0.222931\pi$
$72$		0			0
$73$	0.327300			0.0383076			0.0191538	−	0.999817i	$-0.493903\pi$
$73$	0.327300			0.0383076			0.0191538	+	0.999817i	$0.493903\pi$
$74$		0			0
$75$	−1.94721	−	6.35893i	−0.224845	−	0.734265i
$76$		0			0
$77$	11.6313	−	20.1461i	1.32551	−	2.29586i
$78$		0			0
$79$	−8.98705	+	5.18867i	−1.01112	+	0.583771i	−0.911520	−	0.411256i	$-0.865090\pi$
$79$	−8.98705	+	5.18867i	−1.01112	+	0.583771i	−0.0996017	+	0.995027i	$0.531757\pi$
$80$		0			0
$81$	5.55357	+	7.08223i	0.617063	+	0.786914i
$82$		0			0
$83$	−8.21751	+	4.74438i	−0.901989	+	0.520764i	−0.877845	−	0.478945i	$-0.841019\pi$
$83$	−8.21751	+	4.74438i	−0.901989	+	0.520764i	−0.0241442	+	0.999708i	$0.507686\pi$
$84$		0			0
$85$	2.91081	+	1.68055i	0.315721	+	0.182282i
$86$		0			0
$87$	−0.733366	−	2.39492i	−0.0786251	−	0.256762i
$88$		0			0
$89$		−	9.80272i		−	1.03909i	−0.854444	−	0.519543i	$-0.826102\pi$
$89$		−	9.80272i		−	1.03909i	0.854444	−	0.519543i	$-0.173898\pi$
$90$		0			0
$91$	−5.69961			−0.597481
$92$		0			0
$93$	−9.44496	−	8.79972i	−0.979397	−	0.912488i
$94$		0			0
$95$	−1.10902	+	1.92087i	−0.113783	+	0.197077i
$96$		0			0
$97$	2.79591	+	4.84266i	0.283882	+	0.491698i	0.972337	−	0.233581i	$-0.0750443\pi$
$97$	2.79591	+	4.84266i	0.283882	+	0.491698i	−0.688455	+	0.725279i	$0.741711\pi$
$98$		0			0
$99$	14.8088	−	1.04877i	1.48834	−	0.105405i
$100$		0			0
$101$	−3.29078	−	5.69980i	−0.327445	−	0.567152i	0.654559	−	0.756011i	$-0.272854\pi$
$101$	−3.29078	−	5.69980i	−0.327445	−	0.567152i	−0.982004	+	0.188859i	$0.939521\pi$
$102$		0			0
$103$	−5.27010	−	3.04270i	−0.519279	−	0.299806i	0.217361	−	0.976091i	$-0.430255\pi$
$103$	−5.27010	−	3.04270i	−0.519279	−	0.299806i	−0.736639	+	0.676286i	$0.763589\pi$
$104$		0			0
$105$	−1.96920	+	8.54691i	−0.192175	+	0.834093i
$106$		0			0
$107$			8.55222i			0.826774i	0.910555	+	0.413387i	$0.135654\pi$
$107$			8.55222i			0.826774i	−0.910555	+	0.413387i	$0.864346\pi$
$108$		0			0
$109$			14.0641i			1.34710i	0.739142	+	0.673550i	$0.235231\pi$
$109$			14.0641i			1.34710i	−0.739142	+	0.673550i	$0.764769\pi$
$110$		0			0
$111$	3.51556	−	15.2585i	0.333682	−	1.44827i
$112$		0			0
$113$	−11.4863	−	6.63162i	−1.08054	−	0.623850i	−0.149498	−	0.988762i	$-0.547766\pi$
$113$	−11.4863	−	6.63162i	−1.08054	−	0.623850i	−0.931042	+	0.364911i	$0.881099\pi$
$114$		0			0
$115$	−1.85104	−	3.20610i	−0.172610	−	0.298970i
$116$		0			0
$117$	−2.03669	−	3.01372i	−0.188292	−	0.278619i
$118$		0			0
$119$	7.33372	+	12.7024i	0.672281	+	1.16443i
$120$		0			0
$121$	6.74439	−	11.6816i	0.613127	−	1.06197i
$122$		0			0
$123$	12.8132	+	11.9379i	1.15533	+	1.07640i
$124$		0			0
$125$	9.52218			0.851690
$126$		0			0
$127$		−	1.69445i		−	0.150358i	−0.997170	−	0.0751791i	$-0.976047\pi$
$127$		−	1.69445i		−	0.150358i	0.997170	−	0.0751791i	$-0.0239529\pi$
$128$		0			0
$129$	0.0601000	+	0.196266i	0.00529151	+	0.0172803i
$130$		0			0
$131$	4.75341	+	2.74438i	0.415308	+	0.239778i	0.693068	−	0.720873i	$-0.256259\pi$
$131$	4.75341	+	2.74438i	0.415308	+	0.239778i	−0.277760	+	0.960650i	$0.589592\pi$
$132$		0			0
$133$	−8.38243	+	4.83960i	−0.726849	+	0.419646i
$134$		0			0
$135$	−5.22294	+	2.01290i	−0.449519	+	0.173243i
$136$		0			0
$137$	−11.6559	+	6.72954i	−0.995832	+	0.574944i	−0.907012	−	0.421104i	$-0.861643\pi$
$137$	−11.6559	+	6.72954i	−0.995832	+	0.574944i	−0.0888193	+	0.996048i	$0.528309\pi$
$138$		0			0
$139$	6.33263	−	10.9684i	0.537126	−	0.930330i	−0.461931	−	0.886916i	$-0.652843\pi$
$139$	6.33263	−	10.9684i	0.537126	−	0.930330i	0.999057	−	0.0434141i	$-0.0138235\pi$
$140$		0			0
$141$	2.01662	+	6.58560i	0.169830	+	0.554608i
$142$		0			0
$143$	−6.00002			−0.501747
$144$		0			0
$145$	1.55775			0.129364
$146$		0			0
$147$	−17.8260	+	19.1331i	−1.47026	+	1.57807i
$148$		0			0
$149$	−4.82503	+	8.35719i	−0.395282	+	0.684648i	−0.993137	−	0.116956i	$-0.962686\pi$
$149$	−4.82503	+	8.35719i	−0.395282	+	0.684648i	0.597855	+	0.801604i	$0.296020\pi$
$150$		0			0
$151$	−3.55145	+	2.05043i	−0.289013	+	0.166862i	−0.637497	−	0.770453i	$-0.720030\pi$
$151$	−3.55145	+	2.05043i	−0.289013	+	0.166862i	0.348484	+	0.937315i	$0.386697\pi$
$152$		0			0
$153$	−4.09589	+	8.41682i	−0.331133	+	0.680460i
$154$		0			0
$155$	6.95291	−	4.01427i	0.558471	−	0.322434i
$156$		0			0
$157$	19.0033	+	10.9716i	1.51663	+	0.875625i	0.999809	+	0.0195297i	$0.00621691\pi$
$157$	19.0033	+	10.9716i	1.51663	+	0.875625i	0.516818	+	0.856095i	$0.327116\pi$
$158$		0			0
$159$	−0.676866	−	0.155950i	−0.0536789	−	0.0123676i
$160$		0			0
$161$		−	16.1554i		−	1.27322i
$162$		0			0
$163$	−8.42867			−0.660185			−0.330092	−	0.943949i	$-0.607080\pi$
$163$	−8.42867			−0.660185			−0.330092	+	0.943949i	$0.607080\pi$
$164$		0			0
$165$	−2.07300	+	8.99739i	−0.161383	+	0.700446i
$166$		0			0
$167$	−8.04030	+	13.9262i	−0.622177	+	1.07764i	0.366903	+	0.930259i	$0.380418\pi$
$167$	−8.04030	+	13.9262i	−0.622177	+	1.07764i	−0.989080	+	0.147383i	$0.952915\pi$
$168$		0			0
$169$	−5.76497	−	9.98521i	−0.443459	−	0.768093i
$170$		0			0
$171$	−5.55435	−	2.70292i	−0.424752	−	0.206698i
$172$		0			0
$173$	−9.55535	−	16.5504i	−0.726480	−	1.25830i	−0.958362	−	0.285556i	$-0.907822\pi$
$173$	−9.55535	−	16.5504i	−0.726480	−	1.25830i	0.231882	−	0.972744i	$-0.425512\pi$
$174$		0			0
$175$	15.6312	+	9.02468i	1.18161	+	0.682202i
$176$		0			0
$177$	13.1312	+	12.2341i	0.986998	+	0.919570i
$178$		0			0
$179$		−	0.424929i		−	0.0317607i	−0.999874	−	0.0158803i	$-0.994945\pi$
$179$		−	0.424929i		−	0.0317607i	0.999874	−	0.0158803i	$-0.00505508\pi$
$180$		0			0
$181$			13.0403i			0.969278i	0.874714	+	0.484639i	$0.161049\pi$
$181$			13.0403i			0.969278i	−0.874714	+	0.484639i	$0.838951\pi$
$182$		0			0
$183$	−22.4543	+	6.87588i	−1.65987	+	0.508280i
$184$		0			0
$185$	8.43369	+	4.86920i	0.620057	+	0.357990i
$186$		0			0
$187$	7.72026	+	13.3719i	0.564562	+	0.977849i
$188$		0			0
$189$	−24.1307	−	3.78891i	−1.75525	−	0.275603i
$190$		0			0
$191$	−10.3515	−	17.9294i	−0.749010	−	1.29732i	−0.948298	−	0.317382i	$-0.897196\pi$
$191$	−10.3515	−	17.9294i	−0.749010	−	1.29732i	0.199288	−	0.979941i	$-0.436137\pi$
$192$		0			0
$193$	−3.46861	+	6.00782i	−0.249676	+	0.432452i	−0.963436	−	0.267939i	$-0.913658\pi$
$193$	−3.46861	+	6.00782i	−0.249676	+	0.432452i	0.713760	+	0.700391i	$0.246991\pi$
$194$		0			0
$195$	2.16307	−	0.662370i	0.154901	−	0.0474333i
$196$		0			0
$197$	6.30640			0.449312			0.224656	−	0.974438i	$-0.427874\pi$
$197$	6.30640			0.449312			0.224656	+	0.974438i	$0.427874\pi$
$198$		0			0
$199$		−	22.7691i		−	1.61406i	−0.590510	−	0.807031i	$-0.701073\pi$
$199$		−	22.7691i		−	1.61406i	0.590510	−	0.807031i	$-0.298927\pi$
$200$		0			0
$201$	−11.6663	+	12.5218i	−0.822879	+	0.883217i
$202$		0			0
$203$	5.88708	+	3.39891i	0.413192	+	0.238556i
$204$		0			0
$205$	−9.43246	+	5.44583i	−0.658791	+	0.380353i
$206$		0			0
$207$	8.54234	−	5.77294i	0.593733	−	0.401247i
$208$		0			0
$209$	−8.82425	+	5.09468i	−0.610386	+	0.352407i
$210$		0			0
$211$	−5.45859	+	9.45455i	−0.375785	+	0.650878i	−0.990444	−	0.137915i	$-0.955960\pi$
$211$	−5.45859	+	9.45455i	−0.375785	+	0.650878i	0.614660	+	0.788792i	$0.289293\pi$
$212$		0			0
$213$	−21.7485	−	5.01085i	−1.49018	−	0.343338i
$214$		0			0
$215$	−0.127659			−0.00870627
$216$		0			0
$217$	35.0355			2.37836
$218$		0			0
$219$	−0.552427	−	0.127279i	−0.0373296	−	0.00860072i
$220$		0			0
$221$	1.89155	−	3.27626i	0.127239	−	0.220385i
$222$		0			0
$223$	−15.8367	+	9.14333i	−1.06050	+	0.612283i	−0.925572	−	0.378572i	$-0.876415\pi$
$223$	−15.8367	+	9.14333i	−1.06050	+	0.612283i	−0.134933	+	0.990855i	$0.543082\pi$
$224$		0			0
$225$	0.813735	+	11.4900i	0.0542490	+	0.766001i
$226$		0			0
$227$	3.01058	−	1.73816i	0.199819	−	0.115366i	−0.396752	−	0.917926i	$-0.629863\pi$
$227$	3.01058	−	1.73816i	0.199819	−	0.115366i	0.596571	+	0.802560i	$0.296529\pi$
$228$		0			0
$229$	6.77911	+	3.91392i	0.447976	+	0.258639i	0.706975	−	0.707238i	$-0.250059\pi$
$229$	6.77911	+	3.91392i	0.447976	+	0.258639i	−0.258999	+	0.965878i	$0.583393\pi$
$230$		0			0
$231$	−27.4660	+	29.4800i	−1.80713	+	1.93964i
$232$		0			0
$233$			11.9622i			0.783669i	0.920036	+	0.391835i	$0.128159\pi$
$233$			11.9622i			0.783669i	−0.920036	+	0.391835i	$0.871841\pi$
$234$		0			0
$235$	−4.28353			−0.279426
$236$		0			0
$237$	17.1864	−	5.26276i	1.11637	−	0.341853i
$238$		0			0
$239$	1.26987	−	2.19948i	0.0821412	−	0.142273i	−0.822028	−	0.569447i	$-0.807157\pi$
$239$	1.26987	−	2.19948i	0.0821412	−	0.142273i	0.904169	+	0.427174i	$0.140491\pi$
$240$		0			0
$241$	2.01191	+	3.48473i	0.129599	+	0.224471i	0.923521	−	0.383548i	$-0.125298\pi$
$241$	2.01191	+	3.48473i	0.129599	+	0.224471i	−0.793923	+	0.608019i	$0.791964\pi$
$242$		0			0
$243$	−6.61938	−	14.1133i	−0.424633	−	0.905365i
$244$		0			0
$245$	−8.13189	−	14.0849i	−0.519528	−	0.899848i
$246$		0			0
$247$	2.16204	+	1.24825i	0.137567	+	0.0794244i
$248$		0			0
$249$	15.7148	−	4.81213i	0.995882	−	0.304956i
$250$		0			0
$251$			8.64335i			0.545563i	0.962076	+	0.272782i	$0.0879437\pi$
$251$			8.64335i			0.545563i	−0.962076	+	0.272782i	$0.912056\pi$
$252$		0			0
$253$		−	17.0069i		−	1.06922i
$254$		0			0
$255$	−4.25942	−	3.96843i	−0.266735	−	0.248513i
$256$		0			0
$257$	−11.1468	−	6.43561i	−0.695319	−	0.401443i	0.110283	−	0.993900i	$-0.464824\pi$
$257$	−11.1468	−	6.43561i	−0.695319	−	0.401443i	−0.805602	+	0.592458i	$0.798158\pi$
$258$		0			0
$259$	21.2485	+	36.8035i	1.32032	+	2.28686i
$260$		0			0
$261$	0.306472	+	4.32741i	0.0189701	+	0.267860i
$262$		0			0
$263$	−2.90296	−	5.02808i	−0.179004	−	0.310045i	0.762535	−	0.646946i	$-0.223954\pi$
$263$	−2.90296	−	5.02808i	−0.179004	−	0.310045i	−0.941540	+	0.336902i	$0.890621\pi$
$264$		0			0
$265$	0.215997	−	0.374117i	0.0132686	−	0.0229819i
$266$		0			0
$267$	−3.81204	+	16.5453i	−0.233293	+	1.01256i
$268$		0			0
$269$	−3.75093			−0.228699			−0.114349	−	0.993441i	$-0.536478\pi$
$269$	−3.75093			−0.228699			−0.114349	+	0.993441i	$0.536478\pi$
$270$		0			0
$271$			22.3745i			1.35916i	0.733603	+	0.679578i	$0.237837\pi$
$271$			22.3745i			1.35916i	−0.733603	+	0.679578i	$0.762163\pi$
$272$		0			0
$273$	9.61998	+	2.21644i	0.582227	+	0.134145i
$274$		0			0
$275$	16.4551	+	9.50035i	0.992279	+	0.572893i
$276$		0			0
$277$	7.37669	−	4.25893i	0.443222	−	0.255894i	−0.261741	−	0.965138i	$-0.584297\pi$
$277$	7.37669	−	4.25893i	0.443222	−	0.255894i	0.704963	+	0.709244i	$0.250963\pi$
$278$		0			0
$279$	12.5195	+	18.5254i	0.749524	+	1.10908i
$280$		0			0
$281$	10.7826	−	6.22534i	0.643236	−	0.371373i	−0.142624	−	0.989777i	$-0.545554\pi$
$281$	10.7826	−	6.22534i	0.643236	−	0.371373i	0.785860	+	0.618404i	$0.212221\pi$
$282$		0			0
$283$	−8.15797	+	14.1300i	−0.484941	+	0.839942i	−0.999850	−	0.0173026i	$-0.994492\pi$
$283$	−8.15797	+	14.1300i	−0.484941	+	0.839942i	0.514910	+	0.857244i	$0.327825\pi$
$284$		0			0
$285$	2.61881	−	2.81084i	0.155125	−	0.166500i
$286$		0			0
$287$	−47.5298			−2.80560
$288$		0			0
$289$	7.26453			0.427325
$290$		0			0
$291$	−2.83584	−	9.26087i	−0.166240	−	0.542882i
$292$		0			0
$293$	6.80318	−	11.7835i	0.397446	−	0.688397i	−0.595964	−	0.803011i	$-0.703230\pi$
$293$	6.80318	−	11.7835i	0.397446	−	0.688397i	0.993410	+	0.114614i	$0.0365633\pi$
$294$		0			0
$295$	−9.66650	+	5.58096i	−0.562805	+	0.324936i
$296$		0			0
$297$	−25.4025	−	3.98862i	−1.47400	−	0.231443i
$298$		0			0
$299$	−3.60862	+	2.08344i	−0.208692	+	0.120488i
$300$		0			0
$301$	−0.482452	−	0.278544i	−0.0278081	−	0.0160550i
$302$		0			0
$303$	3.33777	+	10.9000i	0.191750	+	0.626189i
$304$		0			0
$305$		−	14.6051i		−	0.836287i
$306$		0			0
$307$	7.53173			0.429859			0.214929	−	0.976630i	$-0.431048\pi$
$307$	7.53173			0.429859			0.214929	+	0.976630i	$0.431048\pi$
$308$		0			0
$309$	7.71182	+	7.18497i	0.438710	+	0.408739i
$310$		0			0
$311$	10.7246	−	18.5755i	0.608136	−	1.05332i	−0.383411	−	0.923578i	$-0.625251\pi$
$311$	10.7246	−	18.5755i	0.608136	−	1.05332i	0.991547	−	0.129745i	$-0.0414158\pi$
$312$		0			0
$313$	−7.12564	−	12.3420i	−0.402765	−	0.697609i	0.591294	−	0.806456i	$-0.298617\pi$
$313$	−7.12564	−	12.3420i	−0.402765	−	0.697609i	−0.994058	+	0.108847i	$0.965284\pi$
$314$		0			0
$315$	6.64737	−	13.6600i	0.374537	−	0.769652i
$316$		0			0
$317$	17.3799	+	30.1029i	0.976153	+	1.69075i	0.676075	+	0.736833i	$0.263679\pi$
$317$	17.3799	+	30.1029i	0.976153	+	1.69075i	0.300078	+	0.953915i	$0.402987\pi$
$318$		0			0
$319$	6.19737	+	3.57805i	0.346986	+	0.200333i
$320$		0			0
$321$	3.32575	−	14.4347i	0.185625	−	0.805667i
$322$		0			0
$323$		−	6.42454i		−	0.357471i
$324$		0			0
$325$		−	4.65538i		−	0.258234i
$326$		0			0
$327$	5.46920	−	23.7379i	0.302447	−	1.31271i
$328$		0			0
$329$	−16.1884	−	9.34638i	−0.892496	−	0.515283i
$330$		0			0
$331$	6.85837	+	11.8791i	0.376970	+	0.652932i	0.990620	−	0.136647i	$-0.0436325\pi$
$331$	6.85837	+	11.8791i	0.376970	+	0.652932i	−0.613650	+	0.789579i	$0.710299\pi$
$332$		0			0
$333$	−11.8673	+	24.3867i	−0.650326	+	1.33638i
$334$		0			0
$335$	−5.32195	−	9.21790i	−0.290769	−	0.503627i
$336$		0			0
$337$	−2.12713	+	3.68431i	−0.115872	+	0.200697i	−0.918128	−	0.396284i	$-0.870300\pi$
$337$	−2.12713	+	3.68431i	−0.115872	+	0.200697i	0.802256	+	0.596981i	$0.203633\pi$
$338$		0			0
$339$	16.8081	+	15.6598i	0.912889	+	0.850524i
$340$		0			0
$341$	36.8821			1.99728
$342$		0			0
$343$		−	38.0671i		−	2.05543i
$344$		0			0
$345$	1.87747	+	6.13118i	0.101080	+	0.330092i
$346$		0			0
$347$	−12.9663	−	7.48608i	−0.696066	−	0.401874i	0.109814	−	0.993952i	$-0.464974\pi$
$347$	−12.9663	−	7.48608i	−0.696066	−	0.401874i	−0.805881	+	0.592078i	$0.798308\pi$
$348$		0			0
$349$	−14.1751	+	8.18402i	−0.758777	+	0.438080i	−0.828857	−	0.559461i	$-0.811008\pi$
$349$	−14.1751	+	8.18402i	−0.758777	+	0.438080i	0.0700793	+	0.997541i	$0.477675\pi$
$350$		0			0
$351$	2.26562	+	5.87868i	0.120930	+	0.313781i
$352$		0			0
$353$	−14.6621	+	8.46517i	−0.780385	+	0.450555i	−0.836567	−	0.547865i	$-0.815441\pi$
$353$	−14.6621	+	8.46517i	−0.780385	+	0.450555i	0.0561818	+	0.998421i	$0.482107\pi$
$354$		0			0
$355$	6.94024	−	12.0208i	0.368350	−	0.638000i
$356$		0			0
$357$	−7.43844	−	24.2914i	−0.393684	−	1.28564i
$358$		0			0
$359$	20.9540			1.10591			0.552955	−	0.833211i	$-0.313500\pi$
$359$	20.9540			1.10591			0.552955	+	0.833211i	$0.313500\pi$
$360$		0			0
$361$	−14.7604			−0.776862
$362$		0			0
$363$	−15.9261	+	17.0939i	−0.835904	+	0.897197i
$364$		0			0
$365$	0.176287	−	0.305338i	0.00922728	−	0.0159821i
$366$		0			0
$367$	−15.1275	+	8.73384i	−0.789647	+	0.455903i	−0.839838	−	0.542837i	$-0.817350\pi$
$367$	−15.1275	+	8.73384i	−0.789647	+	0.455903i	0.0501914	+	0.998740i	$0.484017\pi$
$368$		0			0
$369$	−16.9842	−	25.1319i	−0.884163	−	1.30831i
$370$		0			0
$371$	1.63260	−	0.942582i	0.0847604	−	0.0489364i
$372$		0			0
$373$	17.5467	+	10.1306i	0.908534	+	0.524542i	0.879959	−	0.475049i	$-0.157570\pi$
$373$	17.5467	+	10.1306i	0.908534	+	0.524542i	0.0285749	+	0.999592i	$0.490903\pi$
$374$		0			0
$375$	−16.0718	−	3.70295i	−0.829946	−	0.191219i
$376$		0			0
$377$		−	1.75332i		−	0.0903008i
$378$		0			0
$379$	−20.0937			−1.03214			−0.516072	−	0.856545i	$-0.672606\pi$
$379$	−20.0937			−1.03214			−0.516072	+	0.856545i	$0.672606\pi$
$380$		0			0
$381$	−0.658931	+	2.85995i	−0.0337581	+	0.146520i
$382$		0			0
$383$	−1.82133	+	3.15464i	−0.0930659	+	0.161195i	−0.908800	−	0.417233i	$-0.863000\pi$
$383$	−1.82133	+	3.15464i	−0.0930659	+	0.161195i	0.815734	+	0.578427i	$0.196333\pi$
$384$		0			0
$385$	−12.5295	−	21.7017i	−0.638562	−	1.10602i
$386$		0			0
$387$	−0.0251156	−	0.354636i	−0.00127670	−	0.0180271i
$388$		0			0
$389$	−9.87792	−	17.1091i	−0.500831	−	0.867464i	−1.00000		0.000959266i	$-0.999695\pi$
$389$	−9.87792	−	17.1091i	−0.500831	−	0.867464i	0.499169	−	0.866505i	$-0.333639\pi$
$390$		0			0
$391$	9.28648	+	5.36155i	0.469638	+	0.271145i
$392$		0			0
$393$	−6.95573	−	6.48054i	−0.350870	−	0.326900i
$394$		0			0
$395$			11.1787i			0.562460i
$396$		0			0
$397$		−	4.63889i		−	0.232819i	−0.993201	−	0.116410i	$-0.962861\pi$
$397$		−	4.63889i		−	0.232819i	0.993201	−	0.116410i	$-0.0371385\pi$
$398$		0			0
$399$	16.0301	−	4.90870i	0.802511	−	0.245743i
$400$		0			0
$401$	21.4727	+	12.3972i	1.07229	+	0.619089i	0.928807	−	0.370564i	$-0.120835\pi$
$401$	21.4727	+	12.3972i	1.07229	+	0.619089i	0.143486	+	0.989652i	$0.454169\pi$
$402$		0			0
$403$	−4.51826	−	7.82585i	−0.225070	−	0.389834i
$404$		0			0
$405$	9.59820	−	1.36636i	0.476939	−	0.0678951i
$406$		0			0
$407$	22.3685	+	38.7434i	1.10877	+	1.92044i
$408$		0			0
$409$	−6.97230	+	12.0764i	−0.344758	+	0.597138i	−0.985310	−	0.170777i	$-0.945372\pi$
$409$	−6.97230	+	12.0764i	−0.344758	+	0.597138i	0.640552	+	0.767915i	$0.278706\pi$
$410$		0			0
$411$	22.2902	−	6.82563i	1.09949	−	0.336684i
$412$		0			0
$413$	−48.7091			−2.39682
$414$		0			0
$415$			10.2215i			0.501753i
$416$		0			0
$417$	−14.9538	+	16.0503i	−0.732289	+	0.785984i
$418$		0			0
$419$	−15.0259	−	8.67521i	−0.734063	−	0.423812i	0.0858435	−	0.996309i	$-0.472642\pi$
$419$	−15.0259	−	8.67521i	−0.734063	−	0.423812i	−0.819907	+	0.572497i	$0.805975\pi$
$420$		0			0
$421$	7.33241	−	4.23337i	0.357360	−	0.206322i	−0.310562	−	0.950553i	$-0.600517\pi$
$421$	7.33241	−	4.23337i	0.357360	−	0.206322i	0.667922	+	0.744231i	$0.267184\pi$
$422$		0			0
$423$	−0.842741	−	11.8996i	−0.0409755	−	0.578578i
$424$		0			0
$425$	−10.3752	+	5.99010i	−0.503269	+	0.290563i
$426$		0			0
$427$	31.8674	−	55.1960i	1.54217	−	2.67112i
$428$		0			0
$429$	10.1270	+	2.33326i	0.488937	+	0.112651i
$430$		0			0
$431$	12.1512			0.585302			0.292651	−	0.956219i	$-0.405463\pi$
$431$	12.1512			0.585302			0.292651	+	0.956219i	$0.405463\pi$
$432$		0			0
$433$	19.4672			0.935532			0.467766	−	0.883852i	$-0.345059\pi$
$433$	19.4672			0.935532			0.467766	+	0.883852i	$0.345059\pi$
$434$		0			0
$435$	−2.62922	−	0.605771i	−0.126061	−	0.0290445i
$436$		0			0
$437$	−3.53815	+	6.12825i	−0.169252	+	0.293154i
$438$		0			0
$439$	−7.44979	+	4.30114i	−0.355559	+	0.205282i	−0.667131	−	0.744940i	$-0.732478\pi$
$439$	−7.44979	+	4.30114i	−0.355559	+	0.205282i	0.311572	+	0.950223i	$0.399145\pi$
$440$		0			0
$441$	37.5277	−	25.3614i	1.78703	−	1.20768i
$442$		0			0
$443$	−14.6579	+	8.46276i	−0.696419	+	0.402078i	−0.806012	−	0.591899i	$-0.798379\pi$
$443$	−14.6579	+	8.46276i	−0.696419	+	0.402078i	0.109593	+	0.993977i	$0.465045\pi$
$444$		0			0
$445$	−9.14494	−	5.27984i	−0.433512	−	0.250288i
$446$		0			0
$447$	11.3937	−	12.2292i	0.538906	−	0.578421i
$448$		0			0
$449$			40.9499i			1.93255i	0.257522	+	0.966273i	$0.417094\pi$
$449$			40.9499i			1.93255i	−0.257522	+	0.966273i	$0.582906\pi$
$450$		0			0
$451$	−50.0350			−2.35606
$452$		0			0
$453$	6.79162	−	2.07971i	0.319098	−	0.0977133i
$454$		0			0
$455$	−3.06986	+	5.31716i	−0.143917	+	0.249272i
$456$		0			0
$457$	7.34163	+	12.7161i	0.343427	+	0.594833i	0.985067	−	0.172173i	$-0.0550788\pi$
$457$	7.34163	+	12.7161i	0.343427	+	0.594833i	−0.641640	+	0.767006i	$0.721745\pi$
$458$		0			0
$459$	10.1863	−	12.6134i	0.475455	−	0.588742i
$460$		0			0
$461$	18.6860	+	32.3651i	0.870294	+	1.50739i	0.861693	+	0.507431i	$0.169405\pi$
$461$	18.6860	+	32.3651i	0.870294	+	1.50739i	0.00860141	+	0.999963i	$0.497262\pi$
$462$		0			0
$463$	1.24136	+	0.716699i	0.0576909	+	0.0333078i	0.528568	−	0.848891i	$-0.322729\pi$
$463$	1.24136	+	0.716699i	0.0576909	+	0.0333078i	−0.470877	+	0.882199i	$0.656062\pi$
$464$		0			0
$465$	−13.2964	+	4.07159i	−0.616606	+	0.188815i
$466$		0			0
$467$			14.7591i			0.682970i	0.939887	+	0.341485i	$0.110930\pi$
$467$			14.7591i			0.682970i	−0.939887	+	0.341485i	$0.889070\pi$
$468$		0			0
$469$		−	46.4486i		−	2.14480i
$470$		0			0
$471$	−27.8078	−	25.9080i	−1.28131	−	1.19378i
$472$		0			0
$473$	−0.507881	−	0.293225i	−0.0233524	−	0.0134825i
$474$		0			0
$475$	−3.95293	−	6.84668i	−0.181373	−	0.314147i
$476$		0			0
$477$	1.08179	+	0.526433i	0.0495318	+	0.0241037i
$478$		0			0
$479$	12.3517	+	21.3938i	0.564365	+	0.977509i	0.997108	+	0.0759917i	$0.0242123\pi$
$479$	12.3517	+	21.3938i	0.564365	+	0.977509i	−0.432743	+	0.901517i	$0.642454\pi$
$480$		0			0
$481$	5.48052	−	9.49255i	0.249890	−	0.432823i
$482$		0			0
$483$	−6.28245	+	27.2676i	−0.285861	+	1.24072i
$484$		0			0
$485$	6.02362			0.273519
$486$		0			0
$487$		−	34.5414i		−	1.56522i	−0.622513	−	0.782610i	$-0.713888\pi$
$487$		−	34.5414i		−	1.56522i	0.622513	−	0.782610i	$-0.286112\pi$
$488$		0			0
$489$	14.2262	+	3.27771i	0.643330	+	0.148223i
$490$		0			0
$491$	31.8995	+	18.4172i	1.43961	+	0.831156i	0.997822	−	0.0659653i	$-0.0210127\pi$
$491$	31.8995	+	18.4172i	1.43961	+	0.831156i	0.441783	+	0.897122i	$0.354346\pi$
$492$		0			0
$493$	−3.90753	+	2.25601i	−0.175986	+	0.101606i
$494$		0			0
$495$	6.99774	−	14.3799i	0.314525	−	0.646331i
$496$		0			0
$497$	52.4574	−	30.2863i	2.35304	−	1.35853i
$498$		0			0
$499$	20.9375	−	36.2648i	0.937291	−	1.62344i	0.166793	−	0.985992i	$-0.446659\pi$
$499$	20.9375	−	36.2648i	0.937291	−	1.62344i	0.770497	−	0.637443i	$-0.220008\pi$
$500$		0			0
$501$	18.9862	−	20.3784i	0.848242	−	0.910440i
$502$		0			0
$503$	10.4048			0.463929			0.231964	−	0.972724i	$-0.425485\pi$
$503$	10.4048			0.463929			0.231964	+	0.972724i	$0.425485\pi$
$504$		0			0
$505$	−7.08979			−0.315491
$506$		0			0
$507$	5.84728	+	19.0952i	0.259687	+	0.848048i
$508$		0			0
$509$	7.73328	−	13.3944i	0.342771	−	0.593698i	−0.642175	−	0.766558i	$-0.721968\pi$
$509$	7.73328	−	13.3944i	0.342771	−	0.593698i	0.984946	+	0.172861i	$0.0553010\pi$
$510$		0			0
$511$	1.33245	−	0.769293i	0.0589443	−	0.0340315i
$512$		0			0
$513$	8.32371	+	6.72203i	0.367501	+	0.296785i
$514$		0			0
$515$	−5.67706	+	3.27765i	−0.250161	+	0.144430i
$516$		0			0
$517$	−17.0417	−	9.83900i	−0.749491	−	0.432719i
$518$		0			0
$519$	9.69179	+	31.6501i	0.425423	+	1.38928i
$520$		0			0
$521$		−	14.2431i		−	0.624002i	−0.950082	−	0.312001i	$-0.899001\pi$
$521$		−	14.2431i		−	0.624002i	0.950082	−	0.312001i	$-0.100999\pi$
$522$		0			0
$523$	−2.33839			−0.102251			−0.0511254	−	0.998692i	$-0.516281\pi$
$523$	−2.33839			−0.102251			−0.0511254	+	0.998692i	$0.516281\pi$
$524$		0			0
$525$	−22.8734	−	21.3107i	−0.998275	−	0.930077i
$526$		0			0
$527$	−11.6273	+	20.1392i	−0.506495	+	0.877275i
$528$		0			0
$529$	5.59453	+	9.69002i	0.243241	+	0.421305i
$530$		0			0
$531$	−17.4056	−	25.7555i	−0.755340	−	1.11769i
$532$		0			0
$533$	6.12956	+	10.6167i	0.265501	+	0.459861i
$534$		0			0
$535$	7.97836	+	4.60631i	0.344934	+	0.199148i
$536$		0			0
$537$	−0.165244	+	0.717208i	−0.00713082	+	0.0309498i
$538$		0			0
$539$		−	74.7139i		−	3.21815i
$540$		0			0
$541$			25.7952i			1.10902i	0.832176	+	0.554512i	$0.187095\pi$
$541$			25.7952i			1.10902i	−0.832176	+	0.554512i	$0.812905\pi$
$542$		0			0
$543$	5.07106	−	22.0098i	0.217620	−	0.944533i
$544$		0			0
$545$	13.1204	+	7.57507i	0.562017	+	0.324480i
$546$		0			0
$547$	−7.47104	−	12.9402i	−0.319439	−	0.553284i	0.660932	−	0.750445i	$-0.270161\pi$
$547$	−7.47104	−	12.9402i	−0.319439	−	0.553284i	−0.980371	+	0.197162i	$0.936828\pi$
$548$		0			0
$549$	40.5729	−	2.87341i	1.73161	−	0.122634i
$550$		0			0
$551$	−1.48877	−	2.57862i	−0.0634236	−	0.109853i
$552$		0			0
$553$	−24.3911	+	42.2467i	−1.03722	+	1.79651i
$554$		0			0
$555$	−12.3411	−	11.4980i	−0.523852	−	0.488065i
$556$		0			0
$557$	−25.4302			−1.07751			−0.538756	−	0.842462i	$-0.681105\pi$
$557$	−25.4302			−1.07751			−0.538756	+	0.842462i	$0.681105\pi$
$558$		0			0
$559$			0.143687i			0.00607730i
$560$		0			0
$561$	−7.83050	−	25.5717i	−0.330604	−	1.07964i
$562$		0			0
$563$	−21.5279	−	12.4291i	−0.907292	−	0.523825i	−0.0277333	−	0.999615i	$-0.508829\pi$
$563$	−21.5279	−	12.4291i	−0.907292	−	0.523825i	−0.879559	+	0.475790i	$0.842162\pi$
$564$		0			0
$565$	−12.3733	+	7.14371i	−0.520547	+	0.300538i
$566$		0			0
$567$	39.2551	+	15.7789i	1.64856	+	0.662650i
$568$		0			0
$569$	18.6202	−	10.7504i	0.780600	−	0.450680i	−0.0560427	−	0.998428i	$-0.517848\pi$
$569$	18.6202	−	10.7504i	0.780600	−	0.450680i	0.836643	+	0.547749i	$0.184515\pi$
$570$		0			0
$571$	−14.5882	+	25.2675i	−0.610498	+	1.05741i	0.380658	+	0.924716i	$0.375697\pi$
$571$	−14.5882	+	25.2675i	−0.610498	+	1.05741i	−0.991157	+	0.132698i	$0.957636\pi$
$572$		0			0
$573$	10.4993	+	34.2872i	0.438616	+	1.43237i
$574$		0			0
$575$	13.1956			0.550293
$576$		0			0
$577$	−34.8813			−1.45213			−0.726063	−	0.687628i	$-0.758652\pi$
$577$	−34.8813			−1.45213			−0.726063	+	0.687628i	$0.758652\pi$
$578$		0			0
$579$	8.19073	−	8.79132i	0.340395	−	0.365355i
$580$		0			0
$581$	−22.3026	+	38.6293i	−0.925268	+	1.60261i
$582$		0			0
$583$	1.71865	−	0.992263i	0.0711792	−	0.0410954i
$584$		0			0
$585$	−3.90848	+	0.276802i	−0.161596	+	0.0114444i
$586$		0			0
$587$	−20.5905	+	11.8879i	−0.849862	+	0.490668i	−0.860604	−	0.509274i	$-0.829914\pi$
$587$	−20.5905	+	11.8879i	−0.849862	+	0.490668i	0.0107423	+	0.999942i	$0.496581\pi$
$588$		0			0
$589$	−13.2900	−	7.67301i	−0.547607	−	0.316161i
$590$		0			0
$591$	−10.6441	−	2.45241i	−0.437841	−	0.100879i
$592$		0			0
$593$			33.9535i			1.39430i	0.716923	+	0.697152i	$0.245550\pi$
$593$			33.9535i			1.39430i	−0.716923	+	0.697152i	$0.754450\pi$
$594$		0			0
$595$	15.8000			0.647739
$596$		0			0
$597$	−8.85437	+	38.4305i	−0.362385	+	1.57285i
$598$		0			0
$599$	8.46524	−	14.6622i	0.345881	−	0.599083i	−0.639633	−	0.768681i	$-0.720914\pi$
$599$	8.46524	−	14.6622i	0.345881	−	0.599083i	0.985513	+	0.169598i	$0.0542469\pi$
$600$		0			0
$601$	10.5145	+	18.2116i	0.428895	+	0.742868i	0.996775	−	0.0802433i	$-0.0255697\pi$
$601$	10.5145	+	18.2116i	0.428895	+	0.742868i	−0.567880	+	0.823111i	$0.692236\pi$
$602$		0			0
$603$	24.5602	−	16.5979i	1.00017	−	0.675918i
$604$		0			0
$605$	−7.26519	−	12.5837i	−0.295372	−	0.511599i
$606$		0			0
$607$	24.0727	+	13.8984i	0.977082	+	0.564119i	0.901388	−	0.433012i	$-0.142549\pi$
$607$	24.0727	+	13.8984i	0.977082	+	0.564119i	0.0756944	+	0.997131i	$0.475883\pi$
$608$		0			0
$609$	−8.61464	−	8.02612i	−0.349083	−	0.325235i
$610$		0			0
$611$			4.82133i			0.195050i
$612$		0			0
$613$		−	13.4417i		−	0.542906i	−0.962452	−	0.271453i	$-0.912496\pi$
$613$		−	13.4417i		−	0.542906i	0.962452	−	0.271453i	$-0.0875042\pi$
$614$		0			0
$615$	18.0382	−	5.52359i	0.727368	−	0.222733i
$616$		0			0
$617$	11.1656	+	6.44644i	0.449509	+	0.259524i	0.707623	−	0.706591i	$-0.249768\pi$
$617$	11.1656	+	6.44644i	0.449509	+	0.259524i	−0.258114	+	0.966114i	$0.583101\pi$
$618$		0			0
$619$	−6.59418	−	11.4215i	−0.265043	−	0.459067i	0.702532	−	0.711652i	$-0.252053\pi$
$619$	−6.59418	−	11.4215i	−0.265043	−	0.459067i	−0.967575	+	0.252585i	$0.918719\pi$
$620$		0			0
$621$	−16.6630	+	6.42185i	−0.668663	+	0.257700i
$622$		0			0
$623$	−23.0405	−	39.9073i	−0.923099	−	1.59885i
$624$		0			0
$625$	−4.47026	+	7.74272i	−0.178810	+	0.309709i
$626$		0			0
$627$	16.8750	−	5.16743i	0.673924	−	0.206367i
$628$		0			0
$629$	−28.2073			−1.12470
$630$		0			0
$631$		−	6.49548i		−	0.258581i	−0.991607	−	0.129290i	$-0.958730\pi$
$631$		−	6.49548i		−	0.258581i	0.991607	−	0.129290i	$-0.0412699\pi$
$632$		0			0
$633$	12.8898	−	13.8350i	0.512324	−	0.549891i
$634$		0			0
$635$	−1.58075	−	0.912648i	−0.0627302	−	0.0362173i
$636$		0			0
$637$	−15.8532	+	9.15285i	−0.628127	+	0.362649i
$638$		0			0
$639$	34.7592	+	16.9149i	1.37505	+	0.669145i
$640$		0			0
$641$	−27.0483	+	15.6164i	−1.06835	+	0.616809i	−0.927729	−	0.373255i	$-0.878242\pi$
$641$	−27.0483	+	15.6164i	−1.06835	+	0.616809i	−0.140616	+	0.990064i	$0.544908\pi$
$642$		0			0
$643$	−8.12404	+	14.0713i	−0.320381	+	0.554916i	−0.980567	−	0.196186i	$-0.937144\pi$
$643$	−8.12404	+	14.0713i	−0.320381	+	0.554916i	0.660186	+	0.751102i	$0.270478\pi$
$644$		0			0
$645$	0.215467	+	0.0496435i	0.00848400	+	0.00195471i
$646$		0			0
$647$	22.1277			0.869929			0.434964	−	0.900448i	$-0.356761\pi$
$647$	22.1277			0.869929			0.434964	+	0.900448i	$0.356761\pi$
$648$		0			0
$649$	−51.2765			−2.01278
$650$		0			0
$651$	−59.1340	−	13.6244i	−2.31764	−	0.533984i
$652$		0			0
$653$	−18.5882	+	32.1957i	−0.727412	+	1.25991i	0.230562	+	0.973058i	$0.425944\pi$
$653$	−18.5882	+	32.1957i	−0.727412	+	1.25991i	−0.957974	+	0.286856i	$0.907390\pi$
$654$		0			0
$655$	5.12047	−	2.95630i	0.200073	−	0.115512i
$656$		0			0
$657$	0.882908	+	0.429651i	0.0344455	+	0.0167623i
$658$		0			0
$659$	40.8491	−	23.5842i	1.59125	−	0.918711i	0.598161	−	0.801376i	$-0.295898\pi$
$659$	40.8491	−	23.5842i	1.59125	−	0.918711i	0.993092	−	0.117334i	$-0.0374349\pi$
$660$		0			0
$661$	−33.1291	−	19.1271i	−1.28857	−	0.743957i	−0.310172	−	0.950680i	$-0.600387\pi$
$661$	−33.1291	−	19.1271i	−1.28857	−	0.743957i	−0.978399	+	0.206723i	$0.933720\pi$
$662$		0			0
$663$	−4.46667	+	4.79419i	−0.173471	+	0.186191i
$664$		0			0
$665$			10.4266i			0.404327i
$666$		0			0
$667$	4.96976			0.192430
$668$		0			0
$669$	30.2853	−	9.27389i	1.17090	−	0.358549i
$670$		0			0
$671$	33.5471	−	58.1053i	1.29507	−	2.24313i
$672$		0			0
$673$	2.66960	+	4.62389i	0.102906	+	0.178238i	0.912881	−	0.408227i	$-0.133853\pi$
$673$	2.66960	+	4.62389i	0.102906	+	0.178238i	−0.809975	+	0.586465i	$0.800519\pi$
$674$		0			0
$675$	3.09474	−	19.7097i	0.119117	−	0.758625i
$676$		0			0
$677$	2.31625	+	4.01186i	0.0890206	+	0.154188i	0.907097	−	0.420921i	$-0.138293\pi$
$677$	2.31625	+	4.01186i	0.0890206	+	0.154188i	−0.818077	+	0.575109i	$0.804960\pi$
$678$		0			0
$679$	22.7646	+	13.1432i	0.873626	+	0.504388i
$680$		0			0
$681$	−5.75727	+	1.76298i	−0.220619	+	0.0675574i
$682$		0			0
$683$			6.06774i			0.232175i	0.993239	+	0.116088i	$0.0370354\pi$
$683$			6.06774i			0.232175i	−0.993239	+	0.116088i	$0.962965\pi$
$684$		0			0
$685$			14.4984i			0.553955i
$686$		0			0
$687$	−9.91997	−	9.24227i	−0.378470	−	0.352615i
$688$		0			0
$689$	−0.421088	−	0.243115i	−0.0160422	−	0.00926196i
$690$		0			0
$691$	11.0823	+	19.1951i	0.421590	+	0.730216i	0.996095	−	0.0882853i	$-0.0281387\pi$
$691$	11.0823	+	19.1951i	0.421590	+	0.730216i	−0.574505	+	0.818501i	$0.694805\pi$
$692$		0			0
$693$	57.8221	−	39.0764i	2.19648	−	1.48439i
$694$		0			0
$695$	−6.82162	−	11.8154i	−0.258759	−	0.448184i
$696$		0			0
$697$	15.7739	−	27.3212i	0.597479	−	1.03486i
$698$		0			0
$699$	4.65181	−	20.1902i	0.175947	−	0.763662i
$700$		0			0
$701$	−7.47732			−0.282414			−0.141207	−	0.989980i	$-0.545098\pi$
$701$	−7.47732			−0.282414			−0.141207	+	0.989980i	$0.545098\pi$
$702$		0			0
$703$		−	18.6143i		−	0.702052i
$704$		0			0
$705$	7.22987	+	1.66576i	0.272293	+	0.0627362i
$706$		0			0
$707$	−26.7939	−	15.4695i	−1.00769	−	0.581789i
$708$		0			0
$709$	38.8031	−	22.4030i	1.45728	−	0.841362i	0.458404	−	0.888744i	$-0.348421\pi$
$709$	38.8031	−	22.4030i	1.45728	−	0.841362i	0.998877	+	0.0473824i	$0.0150879\pi$
$710$		0			0
$711$	−31.0543	+	2.19929i	−1.16463	+	0.0824799i
$712$		0			0
$713$	22.1822	−	12.8069i	0.830730	−	0.479622i
$714$		0			0
$715$	−3.23167	+	5.59741i	−0.120857	+	0.209331i
$716$		0			0
$717$	−2.99866	+	3.21854i	−0.111987	+	0.120198i
$718$		0			0
$719$	−4.62241			−0.172387			−0.0861933	−	0.996278i	$-0.527470\pi$
$719$	−4.62241			−0.172387			−0.0861933	+	0.996278i	$0.527470\pi$
$720$		0			0
$721$	−28.6065			−1.06536
$722$		0			0
$723$	−2.04064	−	6.66402i	−0.0758922	−	0.247838i
$724$		0			0
$725$	−2.77619	+	4.80850i	−0.103105	+	0.178583i
$726$		0			0
$727$	1.19976	−	0.692682i	0.0444967	−	0.0256902i	−0.477587	−	0.878585i	$-0.658488\pi$
$727$	1.19976	−	0.692682i	0.0444967	−	0.0256902i	0.522083	+	0.852894i	$0.325155\pi$
$728$		0			0
$729$	5.68409	+	26.3949i	0.210522	+	0.977589i
$730$		0			0
$731$	0.320226	−	0.184883i	0.0118440	−	0.00683813i
$732$		0			0
$733$	−31.9391	−	18.4400i	−1.17970	−	0.681098i	−0.223752	−	0.974646i	$-0.571831\pi$
$733$	−31.9391	−	18.4400i	−1.17970	−	0.681098i	−0.955944	+	0.293548i	$0.905164\pi$
$734$		0			0
$735$	8.24801	+	26.9352i	0.304232	+	0.993518i
$736$		0			0
$737$		−	48.8968i		−	1.80114i
$738$		0			0
$739$	6.13367			0.225631			0.112815	−	0.993616i	$-0.464013\pi$
$739$	6.13367			0.225631			0.112815	+	0.993616i	$0.464013\pi$
$740$		0			0
$741$	−3.16374	−	2.94760i	−0.116223	−	0.108283i
$742$		0			0
$743$	−4.31592	+	7.47540i	−0.158336	+	0.274246i	−0.934269	−	0.356570i	$-0.883946\pi$
$743$	−4.31592	+	7.47540i	−0.158336	+	0.274246i	0.775933	+	0.630816i	$0.217280\pi$
$744$		0			0
$745$	5.19761	+	9.00253i	0.190426	+	0.329827i
$746$		0			0
$747$	−28.3952	+	2.01097i	−1.03893	+	0.0735777i
$748$		0			0
$749$	20.1013	+	34.8165i	0.734486	+	1.27217i
$750$		0			0
$751$	18.0911	+	10.4449i	0.660153	+	0.381140i	0.792335	−	0.610086i	$-0.208865\pi$
$751$	18.0911	+	10.4449i	0.660153	+	0.381140i	−0.132182	+	0.991225i	$0.542198\pi$
$752$		0			0
$753$	3.36119	−	14.5885i	0.122489	−	0.531635i
$754$		0			0
$755$			4.41753i			0.160770i
$756$		0			0
$757$			25.5413i			0.928313i	0.885753	+	0.464157i	$0.153643\pi$
$757$			25.5413i			0.928313i	−0.885753	+	0.464157i	$0.846357\pi$
$758$		0			0
$759$	−6.61358	+	28.7048i	−0.240058	+	1.04192i
$760$		0			0
$761$	35.8817	+	20.7163i	1.30071	+	0.750965i	0.980526	−	0.196390i	$-0.0629218\pi$
$761$	35.8817	+	20.7163i	1.30071	+	0.750965i	0.320184	+	0.947355i	$0.396255\pi$
$762$		0			0
$763$	33.0566	+	57.2558i	1.19673	+	2.07280i
$764$		0			0
$765$	5.64596	+	8.35444i	0.204130	+	0.302055i
$766$		0			0
$767$	6.28165	+	10.8801i	0.226817	+	0.392859i
$768$		0			0
$769$	−8.41361	+	14.5728i	−0.303403	+	0.525509i	−0.976904	−	0.213677i	$-0.931456\pi$
$769$	−8.41361	+	14.5728i	−0.303403	+	0.525509i	0.673502	+	0.739186i	$0.264789\pi$
$770$		0			0
$771$	16.3113	+	15.1970i	0.587437	+	0.547305i
$772$		0			0
$773$	45.3934			1.63269			0.816344	−	0.577566i	$-0.195998\pi$
$773$	45.3934			1.63269			0.816344	+	0.577566i	$0.195998\pi$
$774$		0			0
$775$			28.6166i			1.02794i
$776$		0			0
$777$	−21.5519	−	70.3812i	−0.773172	−	2.52491i
$778$		0			0
$779$	18.0295	+	10.4094i	0.645975	+	0.372954i
$780$		0			0
$781$	55.2223	−	31.8826i	1.97601	−	1.14085i
$782$		0			0
$783$	1.16555	−	7.42312i	0.0416535	−	0.265281i
$784$		0			0
$785$	20.4707	−	11.8188i	0.730631	−	0.421830i
$786$		0			0
$787$	12.6788	−	21.9603i	0.451950	−	0.782800i	−0.546557	−	0.837422i	$-0.684062\pi$
$787$	12.6788	−	21.9603i	0.451950	−	0.782800i	0.998507	+	0.0546214i	$0.0173952\pi$
$788$		0			0
$789$	2.94441	+	9.61544i	0.104824	+	0.342319i
$790$		0			0
$791$	−62.3484			−2.21686
$792$		0			0
$793$	−16.4388			−0.583759
$794$		0			0
$795$	−0.510052	+	0.547451i	−0.0180897	+	0.0194161i
$796$		0			0
$797$	3.96853	−	6.87370i	0.140573	−	0.243479i	−0.787140	−	0.616775i	$-0.788439\pi$
$797$	3.96853	−	6.87370i	0.140573	−	0.243479i	0.927712	+	0.373296i	$0.121772\pi$
$798$		0			0
$799$	10.7450	−	6.20363i	0.380131	−	0.219469i
$800$		0			0
$801$	12.8682	−	26.4433i	0.454674	−	0.934329i
$802$		0			0
$803$	1.40269	−	0.809841i	0.0494997	−	0.0285787i
$804$		0			0
$805$	−15.0714	−	8.70146i	−0.531196	−	0.306686i
$806$		0			0
$807$	6.33095	+	1.45865i	0.222860	+	0.0513468i
$808$		0			0
$809$			31.0973i			1.09332i	0.837354	+	0.546661i	$0.184101\pi$
$809$			31.0973i			1.09332i	−0.837354	+	0.546661i	$0.815899\pi$
$810$		0			0
$811$	−33.1896			−1.16544			−0.582722	−	0.812671i	$-0.698012\pi$
$811$	−33.1896			−1.16544			−0.582722	+	0.812671i	$0.698012\pi$
$812$		0			0
$813$	8.70091	−	37.7644i	0.305154	−	1.32446i
$814$		0			0
$815$	−4.53976	+	7.86310i	−0.159021	+	0.275432i
$816$		0			0
$817$	0.122006	+	0.211320i	0.00426845	+	0.00739317i
$818$		0			0
$819$	−15.3750	−	7.48195i	−0.537245	−	0.261441i
$820$		0			0
$821$	−26.8779	−	46.5538i	−0.938044	−	1.62474i	−0.769113	−	0.639112i	$-0.779302\pi$
$821$	−26.8779	−	46.5538i	−0.938044	−	1.62474i	−0.168931	−	0.985628i	$-0.554032\pi$
$822$		0			0
$823$	0.166035	+	0.0958606i	0.00578763	+	0.00334149i	0.502891	−	0.864350i	$-0.332270\pi$
$823$	0.166035	+	0.0958606i	0.00578763	+	0.00334149i	−0.497103	+	0.867691i	$0.665603\pi$
$824$		0			0
$825$	−24.0790	−	22.4340i	−0.838322	−	0.781051i
$826$		0			0
$827$		−	22.8393i		−	0.794202i	−0.917775	−	0.397101i	$-0.870016\pi$
$827$		−	22.8393i		−	0.794202i	0.917775	−	0.397101i	$-0.129984\pi$
$828$		0			0
$829$		−	32.7863i		−	1.13872i	−0.822089	−	0.569358i	$-0.807192\pi$
$829$		−	32.7863i		−	1.13872i	0.822089	−	0.569358i	$-0.192808\pi$
$830$		0			0
$831$	−14.1068	+	4.31975i	−0.489360	+	0.149850i
$832$		0			0
$833$	40.7969	+	23.5541i	1.41353	+	0.816100i
$834$		0			0
$835$	8.66116	+	15.0016i	0.299732	+	0.519151i
$836$		0			0
$837$	−13.9268	−	36.1362i	−0.481379	−	1.24905i
$838$		0			0
$839$	−6.80362	−	11.7842i	−0.234887	−	0.406836i	0.724353	−	0.689430i	$-0.242139\pi$
$839$	−6.80362	−	11.7842i	−0.234887	−	0.406836i	−0.959240	+	0.282593i	$0.908805\pi$
$840$		0			0
$841$	13.4544	−	23.3037i	0.463946	−	0.803577i
$842$		0			0
$843$	−20.6201	+	6.31423i	−0.710194	+	0.217474i
$844$		0			0
$845$	−12.4203			−0.427270
$846$		0			0
$847$		−	63.4087i		−	2.17875i
$848$		0			0
$849$	19.2641	−	20.6766i	0.661142	−	0.709621i
$850$		0			0
$851$	26.9064	+	15.5344i	0.922340	+	0.532513i
$852$		0			0
$853$	1.31821	−	0.761067i	0.0451345	−	0.0260584i	−0.477263	−	0.878761i	$-0.658371\pi$
$853$	1.31821	−	0.761067i	0.0451345	−	0.0260584i	0.522397	+	0.852702i	$0.325038\pi$
$854$		0			0
$855$	−5.51318	+	3.72583i	−0.188547	+	0.127421i
$856$		0			0
$857$	−14.7528	+	8.51753i	−0.503946	+	0.290953i	−0.730342	−	0.683082i	$-0.760639\pi$
$857$	−14.7528	+	8.51753i	−0.503946	+	0.290953i	0.226396	+	0.974035i	$0.427306\pi$
$858$		0			0
$859$	10.3773	−	17.9740i	0.354069	−	0.613265i	−0.632889	−	0.774242i	$-0.718131\pi$
$859$	10.3773	−	17.9740i	0.354069	−	0.613265i	0.986958	+	0.160977i	$0.0514645\pi$
$860$		0			0
$861$	80.2223	+	18.4832i	2.73397	+	0.629905i
$862$		0			0
$863$	12.4712			0.424525			0.212263	−	0.977213i	$-0.431917\pi$
$863$	12.4712			0.424525			0.212263	+	0.977213i	$0.431917\pi$
$864$		0			0
$865$	−20.5864			−0.699959
$866$		0			0
$867$	−12.2613	−	2.82500i	−0.416416	−	0.0959420i
$868$		0			0
$869$	−25.6767	+	44.4734i	−0.871024	+	1.50866i
$870$		0			0
$871$	−10.3752	+	5.99013i	−0.351550	+	0.202968i
$872$		0			0
$873$	1.18509	+	16.7336i	0.0401092	+	0.566346i
$874$		0			0
$875$	38.7653	−	22.3812i	1.31051	−	0.756621i
$876$		0			0
$877$	−15.7116	−	9.07108i	−0.530542	−	0.306309i	0.210695	−	0.977552i	$-0.432427\pi$
$877$	−15.7116	−	9.07108i	−0.530542	−	0.306309i	−0.741237	+	0.671243i	$0.765761\pi$
$878$		0			0
$879$	−16.0649	+	17.2429i	−0.541856	+	0.581588i
$880$		0			0
$881$			1.15687i			0.0389760i	0.999810	+	0.0194880i	$0.00620362\pi$
$881$			1.15687i			0.0389760i	−0.999810	+	0.0194880i	$0.993796\pi$
$882$		0			0
$883$	−23.9132			−0.804744			−0.402372	−	0.915476i	$-0.631814\pi$
$883$	−23.9132			−0.804744			−0.402372	+	0.915476i	$0.631814\pi$
$884$		0			0
$885$	18.4857	−	5.66065i	0.621391	−	0.190281i
$886$		0			0
$887$	−2.97669	+	5.15578i	−0.0999474	+	0.173114i	−0.911663	−	0.410939i	$-0.865201\pi$
$887$	−2.97669	+	5.15578i	−0.0999474	+	0.173114i	0.811715	+	0.584053i	$0.198534\pi$
$888$		0			0
$889$	−3.98268	−	6.89820i	−0.133575	−	0.231358i
$890$		0			0
$891$	41.3241	+	16.6105i	1.38441	+	0.556474i
$892$		0			0
$893$	4.09384	+	7.09074i	0.136995	+	0.237283i
$894$		0			0
$895$	−0.396415	−	0.228871i	−0.0132507	−	0.00765030i
$896$		0			0
$897$	6.90095	−	2.11319i	0.230416	−	0.0705574i
$898$		0			0
$899$			10.7777i			0.359456i
$900$		0			0
$901$			1.25127i			0.0416859i
$902$		0			0
$903$	0.705978	+	0.657749i	0.0234935	+	0.0218885i
$904$		0			0
$905$	12.1653	+	7.02363i	0.404388	+	0.233473i
$906$		0			0
$907$	−12.1801	−	21.0965i	−0.404433	−	0.700499i	0.589822	−	0.807533i	$-0.299198\pi$
$907$	−12.1801	−	21.0965i	−0.404433	−	0.700499i	−0.994255	+	0.107034i	$0.965865\pi$
$908$		0			0
$909$	−1.39485	−	19.6954i	−0.0462641	−	0.653254i
$910$		0			0
$911$	11.2288	+	19.4488i	0.372026	+	0.644367i	0.989877	−	0.141928i	$-0.0453300\pi$
$911$	11.2288	+	19.4488i	0.372026	+	0.644367i	−0.617851	+	0.786295i	$0.711997\pi$
$912$		0			0
$913$	−23.4781	+	40.6653i	−0.777013	+	1.34583i
$914$		0			0
$915$	−5.67958	+	24.6510i	−0.187761	+	0.814936i
$916$		0			0
$917$	25.8018			0.852052
$918$		0			0
$919$			35.5861i			1.17388i	0.809631	+	0.586939i	$0.199667\pi$
$919$			35.5861i			1.17388i	−0.809631	+	0.586939i	$0.800333\pi$
$920$		0			0
$921$	−12.7123	−	2.92891i	−0.418884	−	0.0965108i
$922$		0			0
$923$	−13.5301	−	7.81159i	−0.445348	−	0.257122i
$924$		0			0
$925$	−30.0607	+	17.3556i	−0.988391	+	0.570648i
$926$		0			0
$927$	−10.2222	−	15.1260i	−0.335741	−	0.496802i
$928$		0			0
$929$	−11.4661	+	6.61995i	−0.376190	+	0.217194i	−0.676159	−	0.736755i	$-0.736357\pi$
$929$	−11.4661	+	6.61995i	−0.376190	+	0.217194i	0.299969	+	0.953949i	$0.403024\pi$
$930$		0			0
$931$	−15.5436	+	26.9223i	−0.509420	+	0.882342i
$932$		0			0
$933$	−25.3249	+	27.1819i	−0.829100	+	0.889894i
$934$		0			0
$935$	16.6328			0.543952
$936$		0			0
$937$	10.4996			0.343007			0.171504	−	0.985183i	$-0.445137\pi$
$937$	10.4996			0.343007			0.171504	+	0.985183i	$0.445137\pi$
$938$		0			0
$939$	7.22738	+	23.6021i	0.235857	+	0.770227i
$940$		0			0
$941$	−0.713336	+	1.23553i	−0.0232541	+	0.0402773i	−0.877418	−	0.479726i	$-0.840736\pi$
$941$	−0.713336	+	1.23553i	−0.0232541	+	0.0402773i	0.854164	+	0.520003i	$0.174069\pi$
$942$		0			0
$943$	−30.0928	+	17.3741i	−0.979957	+	0.565779i
$944$		0			0
$945$	−16.5317	+	20.4707i	−0.537775	+	0.665913i
$946$		0			0
$947$	−20.2243	+	11.6765i	−0.657202	+	0.379436i	−0.791210	−	0.611545i	$-0.790549\pi$
$947$	−20.2243	+	11.6765i	−0.657202	+	0.379436i	0.134008	+	0.990980i	$0.457215\pi$
$948$		0			0
$949$	−0.343673	−	0.198420i	−0.0111561	−	0.00644098i
$950$		0			0
$951$	−17.6281	−	57.5673i	−0.571630	−	1.86675i
$952$		0			0
$953$		−	10.6044i		−	0.343511i	−0.985140	−	0.171756i	$-0.945056\pi$
$953$		−	10.6044i		−	0.343511i	0.985140	−	0.171756i	$-0.0549440\pi$
$954$		0			0
$955$	−22.3017			−0.721666
$956$		0			0
$957$	−9.06870	−	8.44916i	−0.293149	−	0.273123i
$958$		0			0
$959$	−31.6345	+	54.7926i	−1.02153	+	1.76935i
$960$		0			0
$961$	12.2737	+	21.2587i	0.395927	+	0.685765i
$962$		0			0
$963$	−11.2266	+	23.0700i	−0.361773	+	0.743422i
$964$		0			0
$965$	3.73646	+	6.47173i	0.120281	+	0.208332i
$966$		0			0
$967$	−23.7081	−	13.6879i	−0.762401	−	0.440172i	0.0677564	−	0.997702i	$-0.478416\pi$
$967$	−23.7081	−	13.6879i	−0.762401	−	0.440172i	−0.830157	+	0.557530i	$0.811749\pi$
$968$		0			0
$969$	−2.49835	+	10.8435i	−0.0802585	+	0.348345i
$970$		0			0
$971$			57.0592i			1.83112i	0.402185	+	0.915558i	$0.368251\pi$
$971$			57.0592i			1.83112i	−0.402185	+	0.915558i	$0.631749\pi$
$972$		0			0
$973$		−	59.5374i		−	1.90868i
$974$		0			0
$975$	−1.81036	+	7.85749i	−0.0579780	+	0.251641i
$976$		0			0
$977$	−42.8184	−	24.7212i	−1.36988	−	0.790902i	−0.378970	−	0.925409i	$-0.623722\pi$
$977$	−42.8184	−	24.7212i	−1.36988	−	0.790902i	−0.990913	+	0.134506i	$0.957055\pi$
$978$		0			0
$979$	−24.2549	−	42.0108i	−0.775191	−	1.34267i
$980$		0			0
$981$	−18.4622	+	37.9387i	−0.589452	+	1.21129i
$982$		0			0
$983$	8.51615	+	14.7504i	0.271623	+	0.470465i	0.969278	−	0.245970i	$-0.0791063\pi$
$983$	8.51615	+	14.7504i	0.271623	+	0.470465i	−0.697655	+	0.716434i	$0.745773\pi$
$984$		0			0
$985$	3.39669	−	5.88323i	0.108227	−	0.187455i
$986$		0			0
$987$	23.6887	+	22.0704i	0.754020	+	0.702508i
$988$		0			0
$989$	−0.407277			−0.0129506
$990$		0			0
$991$		−	2.85317i		−	0.0906340i	−0.998973	−	0.0453170i	$-0.985570\pi$
$991$		−	2.85317i		−	0.0906340i	0.998973	−	0.0453170i	$-0.0144298\pi$
$992$		0			0
$993$	−6.95630	−	22.7169i	−0.220752	−	0.720899i
$994$		0			0
$995$	−21.2413	−	12.2637i	−0.673395	−	0.388785i
$996$		0			0
$997$	−25.8113	+	14.9022i	−0.817452	+	0.471956i	−0.849537	−	0.527529i	$-0.823119\pi$
$997$	−25.8113	+	14.9022i	−0.817452	+	0.471956i	0.0320848	+	0.999485i	$0.489785\pi$
$998$		0			0
$999$	29.5135	−	36.5457i	0.933764	−	1.15626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.f.959.1	yes	24
3.2	odd	2		3456.2.p.f.2879.6		24
4.3	odd	2		1152.2.p.g.959.12	yes	24
8.3	odd	2		1152.2.p.g.959.1	yes	24
8.5	even	2	inner	1152.2.p.f.959.12	yes	24
9.2	odd	6		1152.2.p.g.191.1	yes	24
9.7	even	3		3456.2.p.g.575.7		24
12.11	even	2		3456.2.p.g.2879.6		24
24.5	odd	2		3456.2.p.f.2879.7		24
24.11	even	2		3456.2.p.g.2879.7		24
36.7	odd	6		3456.2.p.f.575.7		24
36.11	even	6	inner	1152.2.p.f.191.12	yes	24
72.11	even	6	inner	1152.2.p.f.191.1	✓	24
72.29	odd	6		1152.2.p.g.191.12	yes	24
72.43	odd	6		3456.2.p.f.575.6		24
72.61	even	6		3456.2.p.g.575.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.f.191.1	✓	24	72.11	even	6	inner
1152.2.p.f.191.12	yes	24	36.11	even	6	inner
1152.2.p.f.959.1	yes	24	1.1	even	1	trivial
1152.2.p.f.959.12	yes	24	8.5	even	2	inner
1152.2.p.g.191.1	yes	24	9.2	odd	6
1152.2.p.g.191.12	yes	24	72.29	odd	6
1152.2.p.g.959.1	yes	24	8.3	odd	2
1152.2.p.g.959.12	yes	24	4.3	odd	2
3456.2.p.f.575.6		24	72.43	odd	6
3456.2.p.f.575.7		24	36.7	odd	6
3456.2.p.f.2879.6		24	3.2	odd	2
3456.2.p.f.2879.7		24	24.5	odd	2
3456.2.p.g.575.6		24	72.61	even	6
3456.2.p.g.575.7		24	9.7	even	3
3456.2.p.g.2879.6		24	12.11	even	2
3456.2.p.g.2879.7		24	24.11	even	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)

\(f(q)\)	\(=\)	\(q+(-1.68783 - 0.388876i) q^{3} +(0.538609 - 0.932899i) q^{5} +(4.07105 - 2.35042i) q^{7} +(2.69755 + 1.31271i) q^{9} +O(q^{10})\)	\(q+(-1.68783 - 0.388876i) q^{3} +(0.538609 - 0.932899i) q^{5} +(4.07105 - 2.35042i) q^{7} +(2.69755 + 1.31271i) q^{9} +(4.28563 - 2.47431i) q^{11} +(-1.05002 - 0.606232i) q^{13} +(-1.27186 + 1.36512i) q^{15} +3.12017i q^{17} -2.05903 q^{19} +(-7.78527 + 2.38398i) q^{21} +(1.71835 - 2.97627i) q^{23} +(1.91980 + 3.32519i) q^{25} +(-4.04253 - 3.26465i) q^{27} +(0.723042 + 1.25234i) q^{29} +(6.45450 + 3.72651i) q^{31} +(-8.19561 + 2.50964i) q^{33} -5.06384i q^{35} +9.04031i q^{37} +(1.53652 + 1.43155i) q^{39} +(-8.75630 - 5.05545i) q^{41} +(-0.0592540 - 0.102631i) q^{43} +(2.67756 - 1.80950i) q^{45} +(-1.98823 - 3.44372i) q^{47} +(7.54897 - 13.0752i) q^{49} +(1.21336 - 5.26632i) q^{51} +0.401027 q^{53} -5.33074i q^{55} +(3.47530 + 0.800709i) q^{57} +(-8.97357 - 5.18089i) q^{59} +(11.7417 - 6.77909i) q^{61} +(14.0673 - 0.996260i) q^{63} +(-1.13111 + 0.653045i) q^{65} +(4.94046 - 8.55712i) q^{67} +(-4.05769 + 4.35522i) q^{69} +12.8855 q^{71} +0.327300 q^{73} +(-1.94721 - 6.35893i) q^{75} +(11.6313 - 20.1461i) q^{77} +(-8.98705 + 5.18867i) q^{79} +(5.55357 + 7.08223i) q^{81} +(-8.21751 + 4.74438i) q^{83} +(2.91081 + 1.68055i) q^{85} +(-0.733366 - 2.39492i) q^{87} -9.80272i q^{89} -5.69961 q^{91} +(-9.44496 - 8.79972i) q^{93} +(-1.10902 + 1.92087i) q^{95} +(2.79591 + 4.84266i) q^{97} +(14.8088 - 1.04877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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Database

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