LMFDB - Embedded newform 1512.2.j.d.323.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.21
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.116049 - 1.40944i) q^{2} +(-1.97307 + 0.327128i) q^{4} +2.99711 q^{5} +1.00000i q^{7} +(0.690040 + 2.74296i) q^{8} +O(q^{10})$	\(q+(-0.116049 - 1.40944i) q^{2} +(-1.97307 + 0.327128i) q^{4} +2.99711 q^{5} +1.00000i q^{7} +(0.690040 + 2.74296i) q^{8} +(-0.347810 - 4.22425i) q^{10} -5.36291i q^{11} +4.55519i q^{13} +(1.40944 - 0.116049i) q^{14} +(3.78597 - 1.29089i) q^{16} -0.958700i q^{17} +0.532227 q^{19} +(-5.91349 + 0.980437i) q^{20} +(-7.55872 + 0.622358i) q^{22} +2.78680 q^{23} +3.98265 q^{25} +(6.42028 - 0.528623i) q^{26} +(-0.327128 - 1.97307i) q^{28} +5.15616 q^{29} -4.66569i q^{31} +(-2.25879 - 5.18631i) q^{32} +(-1.35123 + 0.111256i) q^{34} +2.99711i q^{35} -6.10293i q^{37} +(-0.0617642 - 0.750144i) q^{38} +(2.06812 + 8.22095i) q^{40} +12.3255i q^{41} +4.45583 q^{43} +(1.75436 + 10.5814i) q^{44} +(-0.323404 - 3.92784i) q^{46} +1.40285 q^{47} -1.00000 q^{49} +(-0.462180 - 5.61332i) q^{50} +(-1.49013 - 8.98768i) q^{52} +9.57019 q^{53} -16.0732i q^{55} +(-2.74296 + 0.690040i) q^{56} +(-0.598365 - 7.26732i) q^{58} -0.0356973i q^{59} -5.13661i q^{61} +(-6.57604 + 0.541447i) q^{62} +(-7.04769 + 3.78551i) q^{64} +13.6524i q^{65} +8.59546 q^{67} +(0.313617 + 1.89158i) q^{68} +(4.22425 - 0.347810i) q^{70} +13.3269 q^{71} +6.50808 q^{73} +(-8.60174 + 0.708237i) q^{74} +(-1.05012 + 0.174106i) q^{76} +5.36291 q^{77} +1.90581i q^{79} +(11.3470 - 3.86893i) q^{80} +(17.3721 - 1.43036i) q^{82} -3.13371i q^{83} -2.87332i q^{85} +(-0.517093 - 6.28024i) q^{86} +(14.7103 - 3.70062i) q^{88} -5.91323i q^{89} -4.55519 q^{91} +(-5.49854 + 0.911640i) q^{92} +(-0.162799 - 1.97724i) q^{94} +1.59514 q^{95} -16.0057 q^{97} +(0.116049 + 1.40944i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.116049	−	1.40944i	−0.0820587	−	0.996627i
$2$	−0.116049	−	1.40944i	−0.0820587	−	0.996627i
$3$		0			0
$3$		0			0
$4$	−1.97307	+	0.327128i	−0.986533	+	0.163564i
$5$	2.99711			1.34035			0.670173	−	0.742205i	$-0.266220\pi$
$5$	2.99711			1.34035			0.670173	+	0.742205i	$0.266220\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.690040	+	2.74296i	0.243966	+	0.969784i
$9$		0			0
$10$	−0.347810	−	4.22425i	−0.109987	−	1.33583i
$11$		−	5.36291i		−	1.61698i	−0.588512	−	0.808488i	$-0.700286\pi$
$11$		−	5.36291i		−	1.61698i	0.588512	−	0.808488i	$-0.299714\pi$
$12$		0			0
$13$			4.55519i			1.26338i	0.775221	+	0.631691i	$0.217639\pi$
$13$			4.55519i			1.26338i	−0.775221	+	0.631691i	$0.782361\pi$
$14$	1.40944	−	0.116049i	0.376690	−	0.0310153i
$15$		0			0
$16$	3.78597	−	1.29089i	0.946494	−	0.322722i
$17$		−	0.958700i		−	0.232519i	−0.993219	−	0.116259i	$-0.962910\pi$
$17$		−	0.958700i		−	0.232519i	0.993219	−	0.116259i	$-0.0370904\pi$
$18$		0			0
$19$	0.532227			0.122101			0.0610506	−	0.998135i	$-0.480555\pi$
$19$	0.532227			0.122101			0.0610506	+	0.998135i	$0.480555\pi$
$20$	−5.91349	+	0.980437i	−1.32230	+	0.219232i
$21$		0			0
$22$	−7.55872	+	0.622358i	−1.61152	+	0.132687i
$23$	2.78680			0.581088			0.290544	−	0.956862i	$-0.406164\pi$
$23$	2.78680			0.581088			0.290544	+	0.956862i	$0.406164\pi$
$24$		0			0
$25$	3.98265			0.796529
$26$	6.42028	−	0.528623i	1.25912	−	0.103671i
$27$		0			0
$28$	−0.327128	−	1.97307i	−0.0618214	−	0.372874i
$29$	5.15616			0.957475			0.478737	−	0.877958i	$-0.341095\pi$
$29$	5.15616			0.957475			0.478737	+	0.877958i	$0.341095\pi$
$30$		0			0
$31$		−	4.66569i		−	0.837983i	−0.907990	−	0.418992i	$-0.862384\pi$
$31$		−	4.66569i		−	0.837983i	0.907990	−	0.418992i	$-0.137616\pi$
$32$	−2.25879	−	5.18631i	−0.399302	−	0.916819i
$33$		0			0
$34$	−1.35123	+	0.111256i	−0.231735	+	0.0190802i
$35$			2.99711i			0.506603i
$36$		0			0
$37$		−	6.10293i		−	1.00332i	−0.865066	−	0.501658i	$-0.832724\pi$
$37$		−	6.10293i		−	1.00332i	0.865066	−	0.501658i	$-0.167276\pi$
$38$	−0.0617642	−	0.750144i	−0.0100195	−	0.121689i
$39$		0			0
$40$	2.06812	+	8.22095i	0.326999	+	1.29985i
$41$			12.3255i			1.92492i	0.271423	+	0.962460i	$0.412506\pi$
$41$			12.3255i			1.92492i	−0.271423	+	0.962460i	$0.587494\pi$
$42$		0			0
$43$	4.45583			0.679508			0.339754	−	0.940514i	$-0.389656\pi$
$43$	4.45583			0.679508			0.339754	+	0.940514i	$0.389656\pi$
$44$	1.75436	+	10.5814i	0.264479	+	1.59520i
$45$		0			0
$46$	−0.323404	−	3.92784i	−0.0476833	−	0.579128i
$47$	1.40285			0.204627			0.102314	−	0.994752i	$-0.467375\pi$
$47$	1.40285			0.204627			0.102314	+	0.994752i	$0.467375\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.462180	−	5.61332i	−0.0653622	−	0.793843i
$51$		0			0
$52$	−1.49013	−	8.98768i	−0.206644	−	1.24637i
$53$	9.57019			1.31457			0.657283	−	0.753644i	$-0.271705\pi$
$53$	9.57019			1.31457			0.657283	+	0.753644i	$0.271705\pi$
$54$		0			0
$55$		−	16.0732i		−	2.16731i
$56$	−2.74296	+	0.690040i	−0.366544	+	0.0922105i
$57$		0			0
$58$	−0.598365	−	7.26732i	−0.0785692	−	0.954246i
$59$		−	0.0356973i		−	0.00464739i	−0.999997	−	0.00232369i	$-0.999260\pi$
$59$		−	0.0356973i		−	0.00464739i	0.999997	−	0.00232369i	$-0.000739655\pi$
$60$		0			0
$61$		−	5.13661i		−	0.657675i	−0.944386	−	0.328838i	$-0.893343\pi$
$61$		−	5.13661i		−	0.657675i	0.944386	−	0.328838i	$-0.106657\pi$
$62$	−6.57604	+	0.541447i	−0.835157	+	0.0687639i
$63$		0			0
$64$	−7.04769	+	3.78551i	−0.880961	+	0.473189i
$65$			13.6524i			1.69337i
$66$		0			0
$67$	8.59546			1.05010			0.525051	−	0.851071i	$-0.324046\pi$
$67$	8.59546			1.05010			0.525051	+	0.851071i	$0.324046\pi$
$68$	0.313617	+	1.89158i	0.0380317	+	0.229387i
$69$		0			0
$70$	4.22425	−	0.347810i	0.504895	−	0.0415712i
$71$	13.3269			1.58161			0.790804	−	0.612070i	$-0.209663\pi$
$71$	13.3269			1.58161			0.790804	+	0.612070i	$0.209663\pi$
$72$		0			0
$73$	6.50808			0.761713			0.380857	−	0.924634i	$-0.375629\pi$
$73$	6.50808			0.761713			0.380857	+	0.924634i	$0.375629\pi$
$74$	−8.60174	+	0.708237i	−0.999932	+	0.0823309i
$75$		0			0
$76$	−1.05012	+	0.174106i	−0.120457	+	0.0199714i
$77$	5.36291			0.611160
$78$		0			0
$79$			1.90581i			0.214420i	0.994236	+	0.107210i	$0.0341917\pi$
$79$			1.90581i			0.214420i	−0.994236	+	0.107210i	$0.965808\pi$
$80$	11.3470	−	3.86893i	1.26863	−	0.432560i
$81$		0			0
$82$	17.3721	−	1.43036i	1.91843	−	0.157957i
$83$		−	3.13371i		−	0.343970i	−0.985100	−	0.171985i	$-0.944982\pi$
$83$		−	3.13371i		−	0.343970i	0.985100	−	0.171985i	$-0.0550180\pi$
$84$		0			0
$85$		−	2.87332i		−	0.311656i
$86$	−0.517093	−	6.28024i	−0.0557595	−	0.677216i
$87$		0			0
$88$	14.7103	−	3.70062i	1.56812	−	0.394487i
$89$		−	5.91323i		−	0.626801i	−0.949621	−	0.313401i	$-0.898532\pi$
$89$		−	5.91323i		−	0.626801i	0.949621	−	0.313401i	$-0.101468\pi$
$90$		0			0
$91$	−4.55519			−0.477513
$92$	−5.49854	+	0.911640i	−0.573262	+	0.0950450i
$93$		0			0
$94$	−0.162799	−	1.97724i	−0.0167914	−	0.203937i
$95$	1.59514			0.163658
$96$		0			0
$97$	−16.0057			−1.62514			−0.812568	−	0.582867i	$-0.801931\pi$
$97$	−16.0057			−1.62514			−0.812568	+	0.582867i	$0.801931\pi$
$98$	0.116049	+	1.40944i	0.0117227	+	0.142375i
$99$		0			0
$100$	−7.85802	+	1.30283i	−0.785802	+	0.130283i
$101$	−16.1028			−1.60229			−0.801143	−	0.598473i	$-0.795774\pi$
$101$	−16.1028			−1.60229			−0.801143	+	0.598473i	$0.795774\pi$
$102$		0			0
$103$		−	18.0349i		−	1.77703i	−0.458850	−	0.888514i	$-0.651739\pi$
$103$		−	18.0349i		−	1.77703i	0.458850	−	0.888514i	$-0.348261\pi$
$104$	−12.4947	+	3.14326i	−1.22521	+	0.308222i
$105$		0			0
$106$	−1.11061	−	13.4886i	−0.107872	−	1.31013i
$107$		−	9.08345i		−	0.878131i	−0.898455	−	0.439065i	$-0.855310\pi$
$107$		−	9.08345i		−	0.878131i	0.898455	−	0.439065i	$-0.144690\pi$
$108$		0			0
$109$			17.2591i			1.65312i	0.562848	+	0.826560i	$0.309706\pi$
$109$			17.2591i			1.65312i	−0.562848	+	0.826560i	$0.690294\pi$
$110$	−22.6543	+	1.86527i	−2.16000	+	0.177847i
$111$		0			0
$112$	1.29089	+	3.78597i	0.121978	+	0.357741i
$113$			1.27590i			0.120026i	0.998198	+	0.0600131i	$0.0191142\pi$
$113$			1.27590i			0.120026i	−0.998198	+	0.0600131i	$0.980886\pi$
$114$		0			0
$115$	8.35233			0.778859
$116$	−10.1734	+	1.68672i	−0.944580	+	0.156608i
$117$		0			0
$118$	−0.0503133	+	0.00414262i	−0.00463171	+	0.000381359i
$119$	0.958700			0.0878838
$120$		0			0
$121$	−17.7608			−1.61461
$122$	−7.23976	+	0.596096i	−0.655457	+	0.0539680i
$123$		0			0
$124$	1.52628	+	9.20572i	0.137064	+	0.826698i
$125$	−3.04912			−0.272721
$126$		0			0
$127$		−	12.7265i		−	1.12929i	−0.825333	−	0.564646i	$-0.809013\pi$
$127$		−	12.7265i		−	1.12929i	0.825333	−	0.564646i	$-0.190987\pi$
$128$	6.15334	+	9.49402i	0.543883	+	0.839161i
$129$		0			0
$130$	19.2423	−	1.58434i	1.68766	−	0.138956i
$131$			13.3457i			1.16602i	0.812465	+	0.583011i	$0.198125\pi$
$131$			13.3457i			1.16602i	−0.812465	+	0.583011i	$0.801875\pi$
$132$		0			0
$133$			0.532227i			0.0461499i
$134$	−0.997491	−	12.1148i	−0.0861701	−	1.04656i
$135$		0			0
$136$	2.62968	−	0.661541i	0.225493	−	0.0567267i
$137$		−	17.0901i		−	1.46011i	−0.683390	−	0.730053i	$-0.739495\pi$
$137$		−	17.0901i		−	1.46011i	0.683390	−	0.730053i	$-0.260505\pi$
$138$		0			0
$139$	−16.0609			−1.36227			−0.681134	−	0.732158i	$-0.738513\pi$
$139$	−16.0609			−1.36227			−0.681134	+	0.732158i	$0.738513\pi$
$140$	−0.980437	−	5.91349i	−0.0828621	−	0.499781i
$141$		0			0
$142$	−1.54656	−	18.7835i	−0.129785	−	1.57627i
$143$	24.4290			2.04286
$144$		0			0
$145$	15.4536			1.28335
$146$	−0.755254	−	9.17278i	−0.0625052	−	0.759145i
$147$		0			0
$148$	1.99644	+	12.0415i	0.164106	+	0.989804i
$149$	1.37457			0.112609			0.0563047	−	0.998414i	$-0.482068\pi$
$149$	1.37457			0.112609			0.0563047	+	0.998414i	$0.482068\pi$
$150$		0			0
$151$			5.50504i			0.447994i	0.974590	+	0.223997i	$0.0719105\pi$
$151$			5.50504i			0.447994i	−0.974590	+	0.223997i	$0.928089\pi$
$152$	0.367258	+	1.45988i	0.0297885	+	0.118412i
$153$		0			0
$154$	−0.622358	−	7.55872i	−0.0501510	−	0.609099i
$155$		−	13.9836i		−	1.12319i
$156$		0			0
$157$			18.7801i			1.49881i	0.662110	+	0.749407i	$0.269661\pi$
$157$			18.7801i			1.49881i	−0.662110	+	0.749407i	$0.730339\pi$
$158$	2.68613	−	0.221166i	0.213697	−	0.0175951i
$159$		0			0
$160$	−6.76985	−	15.5439i	−0.535203	−	1.22886i
$161$			2.78680i			0.219630i
$162$		0			0
$163$	−17.7671			−1.39163			−0.695813	−	0.718223i	$-0.744956\pi$
$163$	−17.7671			−1.39163			−0.695813	+	0.718223i	$0.744956\pi$
$164$	−4.03202	−	24.3190i	−0.314848	−	1.89900i
$165$		0			0
$166$	−4.41679	+	0.363663i	−0.342810	+	0.0282257i
$167$	−18.1777			−1.40663			−0.703315	−	0.710878i	$-0.748298\pi$
$167$	−18.1777			−1.40663			−0.703315	+	0.710878i	$0.748298\pi$
$168$		0			0
$169$	−7.74971			−0.596132
$170$	−4.04979	+	0.333445i	−0.310605	+	0.0255741i
$171$		0			0
$172$	−8.79164	+	1.45763i	−0.670357	+	0.111143i
$173$	2.38643			0.181437			0.0907186	−	0.995877i	$-0.471084\pi$
$173$	2.38643			0.181437			0.0907186	+	0.995877i	$0.471084\pi$
$174$		0			0
$175$			3.98265i			0.301060i
$176$	−6.92292	−	20.3038i	−0.521835	−	1.53046i
$177$		0			0
$178$	−8.33437	+	0.686222i	−0.624687	+	0.0514345i
$179$			6.73152i			0.503137i	0.967839	+	0.251569i	$0.0809464\pi$
$179$			6.73152i			0.503137i	−0.967839	+	0.251569i	$0.919054\pi$
$180$		0			0
$181$		−	1.20606i		−	0.0896460i	−0.998995	−	0.0448230i	$-0.985728\pi$
$181$		−	1.20606i		−	0.0896460i	0.998995	−	0.0448230i	$-0.0142724\pi$
$182$	0.528623	+	6.42028i	0.0391841	+	0.475903i
$183$		0			0
$184$	1.92300	+	7.64408i	0.141766	+	0.563529i
$185$		−	18.2911i		−	1.34479i
$186$		0			0
$187$	−5.14142			−0.375978
$188$	−2.76792	+	0.458912i	−0.201871	+	0.0334696i
$189$		0			0
$190$	−0.185114	−	2.24826i	−0.0134296	−	0.163106i
$191$	15.5066			1.12202			0.561008	−	0.827810i	$-0.310414\pi$
$191$	15.5066			1.12202			0.561008	+	0.827810i	$0.310414\pi$
$192$		0			0
$193$	7.67734			0.552627			0.276314	−	0.961068i	$-0.410887\pi$
$193$	7.67734			0.552627			0.276314	+	0.961068i	$0.410887\pi$
$194$	1.85744	+	22.5592i	0.133357	+	1.61965i
$195$		0			0
$196$	1.97307	−	0.327128i	0.140933	−	0.0233663i
$197$	23.1208			1.64729			0.823644	−	0.567107i	$-0.191938\pi$
$197$	23.1208			1.64729			0.823644	+	0.567107i	$0.191938\pi$
$198$		0			0
$199$			1.14987i			0.0815122i	0.999169	+	0.0407561i	$0.0129767\pi$
$199$			1.14987i			0.0815122i	−0.999169	+	0.0407561i	$0.987023\pi$
$200$	2.74819	+	10.9242i	0.194326	+	0.772461i
$201$		0			0
$202$	1.86870	+	22.6960i	0.131482	+	1.59688i
$203$			5.15616i			0.361891i
$204$		0			0
$205$			36.9408i			2.58006i
$206$	−25.4191	+	2.09292i	−1.77103	+	0.145821i
$207$		0			0
$208$	5.88024	+	17.2458i	0.407721	+	1.19578i
$209$		−	2.85428i		−	0.197435i
$210$		0			0
$211$	15.6643			1.07837			0.539186	−	0.842187i	$-0.318732\pi$
$211$	15.6643			1.07837			0.539186	+	0.842187i	$0.318732\pi$
$212$	−18.8826	+	3.13068i	−1.29686	+	0.215016i
$213$		0			0
$214$	−12.8026	+	1.05412i	−0.875169	+	0.0720583i
$215$	13.3546			0.910776
$216$		0			0
$217$	4.66569			0.316728
$218$	24.3257	−	2.00289i	1.64755	−	0.135653i
$219$		0			0
$220$	5.25799	+	31.7135i	0.354494	+	2.13812i
$221$	4.36705			0.293760
$222$		0			0
$223$		−	13.9655i		−	0.935198i	−0.883941	−	0.467599i	$-0.845119\pi$
$223$		−	13.9655i		−	0.935198i	0.883941	−	0.467599i	$-0.154881\pi$
$224$	5.18631	−	2.25879i	0.346525	−	0.150922i
$225$		0			0
$226$	1.79830	−	0.148066i	0.119621	−	0.00984919i
$227$			26.1607i			1.73635i	0.496262	+	0.868173i	$0.334705\pi$
$227$			26.1607i			1.73635i	−0.496262	+	0.868173i	$0.665295\pi$
$228$		0			0
$229$		−	6.01986i		−	0.397803i	−0.980019	−	0.198902i	$-0.936263\pi$
$229$		−	6.01986i		−	0.397803i	0.980019	−	0.198902i	$-0.0637374\pi$
$230$	−0.969276	−	11.7721i	−0.0639122	−	0.776232i
$231$		0			0
$232$	3.55796	+	14.1432i	0.233591	+	0.928544i
$233$			13.4333i			0.880046i	0.897986	+	0.440023i	$0.145030\pi$
$233$			13.4333i			0.880046i	−0.897986	+	0.440023i	$0.854970\pi$
$234$		0			0
$235$	4.20450			0.274271
$236$	0.0116776	+	0.0704330i	0.000760145	+	0.00458480i
$237$		0			0
$238$	−0.111256	−	1.35123i	−0.00721164	−	0.0875875i
$239$	−26.3499			−1.70443			−0.852215	−	0.523191i	$-0.824741\pi$
$239$	−26.3499			−1.70443			−0.852215	+	0.523191i	$0.824741\pi$
$240$		0			0
$241$	−12.9481			−0.834063			−0.417031	−	0.908892i	$-0.636929\pi$
$241$	−12.9481			−0.834063			−0.417031	+	0.908892i	$0.636929\pi$
$242$	2.06111	+	25.0328i	0.132493	+	1.60917i
$243$		0			0
$244$	1.68033	+	10.1349i	0.107572	+	0.648818i
$245$	−2.99711			−0.191478
$246$		0			0
$247$			2.42439i			0.154260i
$248$	12.7978	−	3.21952i	0.812663	−	0.204439i
$249$		0			0
$250$	0.353846	+	4.29756i	0.0223792	+	0.271802i
$251$			20.5607i			1.29778i	0.760881	+	0.648891i	$0.224767\pi$
$251$			20.5607i			1.29778i	−0.760881	+	0.648891i	$0.775233\pi$
$252$		0			0
$253$		−	14.9453i		−	0.939605i
$254$	−17.9373	+	1.47689i	−1.12548	+	0.0926683i
$255$		0			0
$256$	12.6672	−	9.77455i	0.791700	−	0.610910i
$257$		−	1.25071i		−	0.0780174i	−0.999239	−	0.0390087i	$-0.987580\pi$
$257$		−	1.25071i		−	0.0780174i	0.999239	−	0.0390087i	$-0.0124200\pi$
$258$		0			0
$259$	6.10293			0.379218
$260$	−4.46607	−	26.9370i	−0.276974	−	1.67056i
$261$		0			0
$262$	18.8101	−	1.54875i	1.16209	−	0.0956822i
$263$	−25.0372			−1.54386			−0.771931	−	0.635706i	$-0.780709\pi$
$263$	−25.0372			−1.54386			−0.771931	+	0.635706i	$0.780709\pi$
$264$		0			0
$265$	28.6829			1.76197
$266$	0.750144	−	0.0617642i	0.0459943	−	0.00378700i
$267$		0			0
$268$	−16.9594	+	2.81181i	−1.03596	+	0.171759i
$269$	0.520900			0.0317598			0.0158799	−	0.999874i	$-0.494945\pi$
$269$	0.520900			0.0317598			0.0158799	+	0.999874i	$0.494945\pi$
$270$		0			0
$271$		−	7.99100i		−	0.485419i	−0.970099	−	0.242709i	$-0.921964\pi$
$271$		−	7.99100i		−	0.485419i	0.970099	−	0.242709i	$-0.0780361\pi$
$272$	−1.23758	−	3.62961i	−0.0750390	−	0.220078i
$273$		0			0
$274$	−24.0876	+	1.98328i	−1.45518	+	0.119815i
$275$		−	21.3586i		−	1.28797i
$276$		0			0
$277$			32.8049i			1.97106i	0.169509	+	0.985529i	$0.445782\pi$
$277$			32.8049i			1.97106i	−0.169509	+	0.985529i	$0.554218\pi$
$278$	1.86385	+	22.6370i	0.111786	+	1.35767i
$279$		0			0
$280$	−8.22095	+	2.06812i	−0.491296	+	0.123594i
$281$		−	7.13786i		−	0.425809i	−0.977073	−	0.212905i	$-0.931708\pi$
$281$		−	7.13786i		−	0.425809i	0.977073	−	0.212905i	$-0.0682924\pi$
$282$		0			0
$283$	−4.47861			−0.266226			−0.133113	−	0.991101i	$-0.542497\pi$
$283$	−4.47861			−0.266226			−0.133113	+	0.991101i	$0.542497\pi$
$284$	−26.2948	+	4.35959i	−1.56031	+	0.258694i
$285$		0			0
$286$	−2.83495	−	34.4314i	−0.167634	−	2.03597i
$287$	−12.3255			−0.727551
$288$		0			0
$289$	16.0809			0.945935
$290$	−1.79336	−	21.7809i	−0.105310	−	1.27902i
$291$		0			0
$292$	−12.8409	+	2.12898i	−0.751455	+	0.124589i
$293$	23.4454			1.36969			0.684846	−	0.728688i	$-0.259869\pi$
$293$	23.4454			1.36969			0.684846	+	0.728688i	$0.259869\pi$
$294$		0			0
$295$		−	0.106988i		−	0.00622911i
$296$	16.7401	−	4.21127i	0.973000	−	0.244775i
$297$		0			0
$298$	−0.159517	−	1.93738i	−0.00924058	−	0.112230i
$299$			12.6944i			0.734135i
$300$		0			0
$301$			4.45583i			0.256830i
$302$	7.75905	−	0.638852i	0.446483	−	0.0367618i
$303$		0			0
$304$	2.01500	−	0.687046i	0.115568	−	0.0394048i
$305$		−	15.3950i		−	0.881513i
$306$		0			0
$307$	−5.07164			−0.289454			−0.144727	−	0.989472i	$-0.546230\pi$
$307$	−5.07164			−0.289454			−0.144727	+	0.989472i	$0.546230\pi$
$308$	−10.5814	+	1.75436i	−0.602929	+	0.0999637i
$309$		0			0
$310$	−19.7091	+	1.62278i	−1.11940	+	0.0921674i
$311$	5.43039			0.307929			0.153964	−	0.988076i	$-0.450796\pi$
$311$	5.43039			0.307929			0.153964	+	0.988076i	$0.450796\pi$
$312$		0			0
$313$	12.5124			0.707245			0.353622	−	0.935388i	$-0.384950\pi$
$313$	12.5124			0.707245			0.353622	+	0.935388i	$0.384950\pi$
$314$	26.4695	−	2.17940i	1.49376	−	0.122991i
$315$		0			0
$316$	−0.623443	−	3.76028i	−0.0350714	−	0.211533i
$317$	−9.29939			−0.522306			−0.261153	−	0.965297i	$-0.584103\pi$
$317$	−9.29939			−0.522306			−0.261153	+	0.965297i	$0.584103\pi$
$318$		0			0
$319$		−	27.6520i		−	1.54821i
$320$	−21.1227	+	11.3456i	−1.18079	+	0.634237i
$321$		0			0
$322$	3.92784	−	0.323404i	0.218890	−	0.0180226i
$323$		−	0.510246i		−	0.0283908i
$324$		0			0
$325$			18.1417i			1.00632i
$326$	2.06185	+	25.0417i	0.114195	+	1.38693i
$327$		0			0
$328$	−33.8084	+	8.50509i	−1.86676	+	0.469615i
$329$			1.40285i			0.0773418i
$330$		0			0
$331$	−21.4879			−1.18108			−0.590541	−	0.807008i	$-0.701086\pi$
$331$	−21.4879			−1.18108			−0.590541	+	0.807008i	$0.701086\pi$
$332$	1.02513	+	6.18302i	0.0562610	+	0.339337i
$333$		0			0
$334$	2.10949	+	25.6204i	0.115426	+	1.40189i
$335$	25.7615			1.40750
$336$		0			0
$337$	−28.1982			−1.53605			−0.768026	−	0.640419i	$-0.778761\pi$
$337$	−28.1982			−1.53605			−0.768026	+	0.640419i	$0.778761\pi$
$338$	0.899343	+	10.9228i	0.0489178	+	0.594121i
$339$		0			0
$340$	0.939945	+	5.66926i	0.0509757	+	0.307459i
$341$	−25.0217			−1.35500
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	3.07470	+	12.2222i	0.165777	+	0.658975i
$345$		0			0
$346$	−0.276942	−	3.36354i	−0.0148885	−	0.180825i
$347$		−	21.2134i		−	1.13880i	−0.822062	−	0.569398i	$-0.807176\pi$
$347$		−	21.2134i		−	1.13880i	0.822062	−	0.569398i	$-0.192824\pi$
$348$		0			0
$349$			31.7541i			1.69976i	0.526979	+	0.849878i	$0.323325\pi$
$349$			31.7541i			1.69976i	−0.526979	+	0.849878i	$0.676675\pi$
$350$	5.61332	−	0.462180i	0.300044	−	0.0247046i
$351$		0			0
$352$	−27.8137	+	12.1137i	−1.48248	+	0.645662i
$353$			7.37308i			0.392429i	0.980561	+	0.196215i	$0.0628650\pi$
$353$			7.37308i			0.392429i	−0.980561	+	0.196215i	$0.937135\pi$
$354$		0			0
$355$	39.9420			2.11990
$356$	1.93438	+	11.6672i	0.102522	+	0.618360i
$357$		0			0
$358$	9.48770	−	0.781183i	0.501441	−	0.0412868i
$359$	14.8384			0.783142			0.391571	−	0.920148i	$-0.371932\pi$
$359$	14.8384			0.783142			0.391571	+	0.920148i	$0.371932\pi$
$360$		0			0
$361$	−18.7167			−0.985091
$362$	−1.69988	+	0.139962i	−0.0893436	+	0.00735624i
$363$		0			0
$364$	8.98768	−	1.49013i	0.471082	−	0.0781040i
$365$	19.5054			1.02096
$366$		0			0
$367$			13.3215i			0.695379i	0.937610	+	0.347690i	$0.113034\pi$
$367$			13.3215i			0.695379i	−0.937610	+	0.347690i	$0.886966\pi$
$368$	10.5507	−	3.59745i	0.549996	−	0.187530i
$369$		0			0
$370$	−25.7803	+	2.12266i	−1.34026	+	0.110352i
$371$			9.57019i			0.496859i
$372$		0			0
$373$		−	24.7297i		−	1.28046i	−0.768185	−	0.640228i	$-0.778840\pi$
$373$		−	24.7297i		−	1.28046i	0.768185	−	0.640228i	$-0.221160\pi$
$374$	0.596654	+	7.24654i	0.0308522	+	0.374710i
$375$		0			0
$376$	0.968025	+	3.84797i	0.0499221	+	0.198444i
$377$			23.4873i			1.20966i
$378$		0			0
$379$	−20.7764			−1.06721			−0.533606	−	0.845733i	$-0.679163\pi$
$379$	−20.7764			−1.06721			−0.533606	+	0.845733i	$0.679163\pi$
$380$	−3.14732	+	0.521815i	−0.161454	+	0.0267685i
$381$		0			0
$382$	−1.79952	−	21.8556i	−0.0920712	−	1.11823i
$383$	−4.92022			−0.251411			−0.125706	−	0.992068i	$-0.540119\pi$
$383$	−4.92022			−0.251411			−0.125706	+	0.992068i	$0.540119\pi$
$384$		0			0
$385$	16.0732			0.819166
$386$	−0.890945	−	10.8208i	−0.0453479	−	0.550763i
$387$		0			0
$388$	31.5803	−	5.23592i	1.60325	−	0.265814i
$389$	34.4298			1.74566			0.872830	−	0.488025i	$-0.162283\pi$
$389$	34.4298			1.74566			0.872830	+	0.488025i	$0.162283\pi$
$390$		0			0
$391$		−	2.67170i		−	0.135114i
$392$	−0.690040	−	2.74296i	−0.0348523	−	0.138541i
$393$		0			0
$394$	−2.68313	−	32.5875i	−0.135174	−	1.64173i
$395$			5.71191i			0.287397i
$396$		0			0
$397$			21.8751i			1.09788i	0.835861	+	0.548941i	$0.184969\pi$
$397$			21.8751i			1.09788i	−0.835861	+	0.548941i	$0.815031\pi$
$398$	1.62068	−	0.133441i	0.0812373	−	0.00668879i
$399$		0			0
$400$	15.0782	−	5.14116i	0.753910	−	0.257058i
$401$		−	29.0637i		−	1.45137i	−0.688027	−	0.725685i	$-0.741523\pi$
$401$		−	29.0637i		−	1.45137i	0.688027	−	0.725685i	$-0.258477\pi$
$402$		0			0
$403$	21.2531			1.05869
$404$	31.7718	−	5.26767i	1.58071	−	0.262076i
$405$		0			0
$406$	7.26732	−	0.598365i	0.360671	−	0.0296964i
$407$	−32.7295			−1.62234
$408$		0			0
$409$	−4.15951			−0.205674			−0.102837	−	0.994698i	$-0.532792\pi$
$409$	−4.15951			−0.205674			−0.102837	+	0.994698i	$0.532792\pi$
$410$	52.0661	−	4.28693i	2.57136	−	0.211717i
$411$		0			0
$412$	5.89971	+	35.5839i	0.290658	+	1.75310i
$413$	0.0356973			0.00175655
$414$		0			0
$415$		−	9.39207i		−	0.461039i
$416$	23.6246	−	10.2892i	1.15829	−	0.504471i
$417$		0			0
$418$	−4.02295	+	0.331235i	−0.196769	+	0.0162013i
$419$			22.5241i			1.10038i	0.835041	+	0.550188i	$0.185444\pi$
$419$			22.5241i			1.10038i	−0.835041	+	0.550188i	$0.814556\pi$
$420$		0			0
$421$			32.7375i			1.59553i	0.602970	+	0.797764i	$0.293984\pi$
$421$			32.7375i			1.59553i	−0.602970	+	0.797764i	$0.706016\pi$
$422$	−1.81782	−	22.0779i	−0.0884899	−	1.07474i
$423$		0			0
$424$	6.60381	+	26.2507i	0.320710	+	1.27485i
$425$		−	3.81816i		−	0.185208i
$426$		0			0
$427$	5.13661			0.248578
$428$	2.97145	+	17.9222i	0.143631	+	0.866305i
$429$		0			0
$430$	−1.54978	−	18.8226i	−0.0747371	−	0.907704i
$431$	28.1991			1.35830			0.679152	−	0.733998i	$-0.262348\pi$
$431$	28.1991			1.35830			0.679152	+	0.733998i	$0.262348\pi$
$432$		0			0
$433$	−22.1414			−1.06405			−0.532024	−	0.846729i	$-0.678569\pi$
$433$	−22.1414			−1.06405			−0.532024	+	0.846729i	$0.678569\pi$
$434$	−0.541447	−	6.57604i	−0.0259903	−	0.315660i
$435$		0			0
$436$	−5.64593	−	34.0533i	−0.270391	−	1.63086i
$437$	1.48321			0.0709515
$438$		0			0
$439$			24.6966i			1.17870i	0.807876	+	0.589352i	$0.200617\pi$
$439$			24.6966i			1.17870i	−0.807876	+	0.589352i	$0.799383\pi$
$440$	44.0882	−	11.0912i	2.10182	−	0.528750i
$441$		0			0
$442$	−0.506790	−	6.15512i	−0.0241056	−	0.292769i
$443$			24.6550i			1.17139i	0.810531	+	0.585696i	$0.199179\pi$
$443$			24.6550i			1.17139i	−0.810531	+	0.585696i	$0.800821\pi$
$444$		0			0
$445$		−	17.7226i		−	0.840131i
$446$	−19.6836	+	1.62068i	−0.932044	+	0.0767412i
$447$		0			0
$448$	−3.78551	−	7.04769i	−0.178848	−	0.332972i
$449$		−	4.80960i		−	0.226979i	−0.993539	−	0.113489i	$-0.963797\pi$
$449$		−	4.80960i		−	0.226979i	0.993539	−	0.113489i	$-0.0362028\pi$
$450$		0			0
$451$	66.1005			3.11255
$452$	−0.417381	−	2.51743i	−0.0196320	−	0.118410i
$453$		0			0
$454$	36.8720	−	3.03591i	1.73049	−	0.142482i
$455$	−13.6524			−0.640033
$456$		0			0
$457$	−20.5555			−0.961548			−0.480774	−	0.876845i	$-0.659644\pi$
$457$	−20.5555			−0.961548			−0.480774	+	0.876845i	$0.659644\pi$
$458$	−8.48465	+	0.698596i	−0.396462	+	0.0326432i
$459$		0			0
$460$	−16.4797	+	2.73228i	−0.768370	+	0.127393i
$461$	−6.96146			−0.324228			−0.162114	−	0.986772i	$-0.551831\pi$
$461$	−6.96146			−0.324228			−0.162114	+	0.986772i	$0.551831\pi$
$462$		0			0
$463$			0.214819i			0.00998347i	0.999988	+	0.00499174i	$0.00158893\pi$
$463$			0.214819i			0.00998347i	−0.999988	+	0.00499174i	$0.998411\pi$
$464$	19.5211	−	6.65604i	0.906244	−	0.308999i
$465$		0			0
$466$	18.9335	−	1.55892i	0.877078	−	0.0722155i
$467$		−	30.4215i		−	1.40774i	−0.710328	−	0.703870i	$-0.751454\pi$
$467$		−	30.4215i		−	1.40774i	0.710328	−	0.703870i	$-0.248546\pi$
$468$		0			0
$469$			8.59546i			0.396901i
$470$	−0.487926	−	5.92601i	−0.0225064	−	0.273346i
$471$		0			0
$472$	0.0979162	−	0.0246325i	0.00450696	−	0.00113380i
$473$		−	23.8962i		−	1.09875i
$474$		0			0
$475$	2.11967			0.0972572
$476$	−1.89158	+	0.313617i	−0.0867003	+	0.0143746i
$477$		0			0
$478$	3.05786	+	37.1387i	0.139863	+	1.69868i
$479$	36.9888			1.69006			0.845030	−	0.534719i	$-0.179582\pi$
$479$	36.9888			1.69006			0.845030	+	0.534719i	$0.179582\pi$
$480$		0			0
$481$	27.8000			1.26757
$482$	1.50261	+	18.2497i	0.0684421	+	0.831250i
$483$		0			0
$484$	35.0431	−	5.81004i	1.59287	−	0.264093i
$485$	−47.9709			−2.17824
$486$		0			0
$487$			10.2932i			0.466431i	0.972425	+	0.233215i	$0.0749248\pi$
$487$			10.2932i			0.466431i	−0.972425	+	0.233215i	$0.925075\pi$
$488$	14.0895	−	3.54447i	0.637803	−	0.160450i
$489$		0			0
$490$	0.347810	+	4.22425i	0.0157125	+	0.190832i
$491$		−	1.77521i		−	0.0801142i	−0.999197	−	0.0400571i	$-0.987246\pi$
$491$		−	1.77521i		−	0.0801142i	0.999197	−	0.0400571i	$-0.0127540\pi$
$492$		0			0
$493$		−	4.94321i		−	0.222631i
$494$	3.41704	−	0.281347i	0.153740	−	0.0126584i
$495$		0			0
$496$	−6.02290	−	17.6642i	−0.270436	−	0.793146i
$497$			13.3269i			0.597791i
$498$		0			0
$499$	−27.4254			−1.22773			−0.613864	−	0.789412i	$-0.710386\pi$
$499$	−27.4254			−1.22773			−0.613864	+	0.789412i	$0.710386\pi$
$500$	6.01611	−	0.997452i	0.269049	−	0.0446074i
$501$		0			0
$502$	28.9792	−	2.38604i	1.29340	−	0.106494i
$503$	−31.1546			−1.38911			−0.694557	−	0.719437i	$-0.744400\pi$
$503$	−31.1546			−1.38911			−0.694557	+	0.719437i	$0.744400\pi$
$504$		0			0
$505$	−48.2617			−2.14762
$506$	−21.0646	+	1.73439i	−0.936436	+	0.0771028i
$507$		0			0
$508$	4.16319	+	25.1102i	0.184712	+	1.11408i
$509$	−3.20979			−0.142271			−0.0711356	−	0.997467i	$-0.522662\pi$
$509$	−3.20979			−0.142271			−0.0711356	+	0.997467i	$0.522662\pi$
$510$		0			0
$511$			6.50808i			0.287901i
$512$	−15.2467	−	16.7194i	−0.673815	−	0.738900i
$513$		0			0
$514$	−1.76281	+	0.145144i	−0.0777543	+	0.00640201i
$515$		−	54.0524i		−	2.38183i
$516$		0			0
$517$		−	7.52337i		−	0.330877i
$518$	−0.708237	−	8.60174i	−0.0311181	−	0.377939i
$519$		0			0
$520$	−37.4480	+	9.42069i	−1.64220	+	0.413124i
$521$			34.3057i			1.50296i	0.659756	+	0.751480i	$0.270660\pi$
$521$			34.3057i			1.50296i	−0.659756	+	0.751480i	$0.729340\pi$
$522$		0			0
$523$	−37.4283			−1.63662			−0.818312	−	0.574774i	$-0.805090\pi$
$523$	−37.4283			−1.63662			−0.818312	+	0.574774i	$0.805090\pi$
$524$	−4.36576	−	26.3320i	−0.190719	−	1.15032i
$525$		0			0
$526$	2.90554	+	35.2886i	0.126687	+	1.53866i
$527$	−4.47300			−0.194847
$528$		0			0
$529$	−15.2338			−0.662337
$530$	−3.32861	−	40.4269i	−0.144585	−	1.75603i
$531$		0			0
$532$	−0.174106	−	1.05012i	−0.00754846	−	0.0455284i
$533$	−56.1449			−2.43191
$534$		0			0
$535$		−	27.2241i		−	1.17700i
$536$	5.93121	+	23.5770i	0.256189	+	1.01837i
$537$		0			0
$538$	−0.0604497	−	0.734180i	−0.00260617	−	0.0316527i
$539$			5.36291i			0.230997i
$540$		0			0
$541$			1.04111i			0.0447610i	0.999750	+	0.0223805i	$0.00712453\pi$
$541$			1.04111i			0.0447610i	−0.999750	+	0.0223805i	$0.992875\pi$
$542$	−11.2629	+	0.927344i	−0.483782	+	0.0398328i
$543$		0			0
$544$	−4.97212	+	2.16550i	−0.213178	+	0.0928453i
$545$			51.7273i			2.21576i
$546$		0			0
$547$	3.89746			0.166643			0.0833216	−	0.996523i	$-0.473447\pi$
$547$	3.89746			0.166643			0.0833216	+	0.996523i	$0.473447\pi$
$548$	5.59065	+	33.7199i	0.238821	+	1.44044i
$549$		0			0
$550$	−30.1037	+	2.47863i	−1.28363	+	0.105689i
$551$	2.74425			0.116909
$552$		0			0
$553$	−1.90581			−0.0810432
$554$	46.2367	−	3.80697i	1.96441	−	0.161742i
$555$		0			0
$556$	31.6892	−	5.25397i	1.34392	−	0.222818i
$557$	−32.1046			−1.36031			−0.680157	−	0.733067i	$-0.738088\pi$
$557$	−32.1046			−1.36031			−0.680157	+	0.733067i	$0.738088\pi$
$558$		0			0
$559$			20.2971i			0.858477i
$560$	3.86893	+	11.3470i	0.163492	+	0.479497i
$561$		0			0
$562$	−10.0604	+	0.828339i	−0.424373	+	0.0349414i
$563$		−	9.40478i		−	0.396364i	−0.980165	−	0.198182i	$-0.936496\pi$
$563$		−	9.40478i		−	0.396364i	0.980165	−	0.198182i	$-0.0635037\pi$
$564$		0			0
$565$			3.82399i			0.160877i
$566$	0.519736	+	6.31235i	0.0218461	+	0.265328i
$567$		0			0
$568$	9.19607	+	36.5551i	0.385858	+	1.53382i
$569$		−	5.32036i		−	0.223041i	−0.993762	−	0.111521i	$-0.964428\pi$
$569$		−	5.32036i		−	0.223041i	0.993762	−	0.111521i	$-0.0355721\pi$
$570$		0			0
$571$	−47.3101			−1.97986			−0.989932	−	0.141542i	$-0.954794\pi$
$571$	−47.3101			−1.97986			−0.989932	+	0.141542i	$0.954794\pi$
$572$	−48.2001	+	7.99142i	−2.01535	+	0.334138i
$573$		0			0
$574$	1.43036	+	17.3721i	0.0597020	+	0.725098i
$575$	11.0988			0.462853
$576$		0			0
$577$	21.0280			0.875407			0.437704	−	0.899119i	$-0.355792\pi$
$577$	21.0280			0.875407			0.437704	+	0.899119i	$0.355792\pi$
$578$	−1.86617	−	22.6651i	−0.0776222	−	0.942745i
$579$		0			0
$580$	−30.4909	+	5.05529i	−1.26607	+	0.209910i
$581$	3.13371			0.130008
$582$		0			0
$583$		−	51.3240i		−	2.12562i
$584$	4.49084	+	17.8514i	0.185832	+	0.738697i
$585$		0			0
$586$	−2.72080	−	33.0449i	−0.112395	−	1.36507i
$587$		−	18.8579i		−	0.778348i	−0.921164	−	0.389174i	$-0.872761\pi$
$587$		−	18.8579i		−	0.778348i	0.921164	−	0.389174i	$-0.127239\pi$
$588$		0			0
$589$		−	2.48321i		−	0.102319i
$590$	−0.150794	+	0.0124159i	−0.00620810	+	0.000511153i
$591$		0			0
$592$	−7.87822	−	23.1056i	−0.323793	−	0.949632i
$593$		−	15.7984i		−	0.648764i	−0.945926	−	0.324382i	$-0.894844\pi$
$593$		−	15.7984i		−	0.648764i	0.945926	−	0.324382i	$-0.105156\pi$
$594$		0			0
$595$	2.87332			0.117795
$596$	−2.71212	+	0.449661i	−0.111093	+	0.0184188i
$597$		0			0
$598$	17.8920	−	1.47317i	0.731659	−	0.0602422i
$599$	−24.1841			−0.988136			−0.494068	−	0.869423i	$-0.664491\pi$
$599$	−24.1841			−0.988136			−0.494068	+	0.869423i	$0.664491\pi$
$600$		0			0
$601$	31.5679			1.28768			0.643842	−	0.765159i	$-0.277340\pi$
$601$	31.5679			1.28768			0.643842	+	0.765159i	$0.277340\pi$
$602$	6.28024	−	0.517093i	0.255964	−	0.0210751i
$603$		0			0
$604$	−1.80085	−	10.8618i	−0.0732757	−	0.441961i
$605$	−53.2309			−2.16414
$606$		0			0
$607$		−	23.4349i		−	0.951194i	−0.879663	−	0.475597i	$-0.842232\pi$
$607$		−	23.4349i		−	0.951194i	0.879663	−	0.475597i	$-0.157768\pi$
$608$	−1.20219	−	2.76029i	−0.0487553	−	0.111945i
$609$		0			0
$610$	−21.6983	+	1.78656i	−0.878540	+	0.0723359i
$611$			6.39025i			0.258522i
$612$		0			0
$613$		−	21.4865i		−	0.867832i	−0.900953	−	0.433916i	$-0.857132\pi$
$613$		−	21.4865i		−	0.867832i	0.900953	−	0.433916i	$-0.142868\pi$
$614$	0.588556	+	7.14819i	0.0237522	+	0.288477i
$615$		0			0
$616$	3.70062	+	14.7103i	0.149102	+	0.592693i
$617$			12.4334i			0.500549i	0.968175	+	0.250275i	$0.0805209\pi$
$617$			12.4334i			0.500549i	−0.968175	+	0.250275i	$0.919479\pi$
$618$		0			0
$619$	−20.4500			−0.821956			−0.410978	−	0.911645i	$-0.634813\pi$
$619$	−20.4500			−0.821956			−0.410978	+	0.911645i	$0.634813\pi$
$620$	4.57442	+	27.5905i	0.183713	+	1.10806i
$621$		0			0
$622$	−0.630189	−	7.65383i	−0.0252683	−	0.306890i
$623$	5.91323			0.236909
$624$		0			0
$625$	−29.0518			−1.16207
$626$	−1.45205	−	17.6356i	−0.0580356	−	0.704859i
$627$		0			0
$628$	−6.14349	−	37.0543i	−0.245152	−	1.47863i
$629$	−5.85088			−0.233290
$630$		0			0
$631$		−	14.3682i		−	0.571990i	−0.958231	−	0.285995i	$-0.907676\pi$
$631$		−	14.3682i		−	0.571990i	0.958231	−	0.285995i	$-0.0923240\pi$
$632$	−5.22756	+	1.31508i	−0.207941	+	0.0523112i
$633$		0			0
$634$	1.07918	+	13.1070i	0.0428597	+	0.520544i
$635$		−	38.1426i		−	1.51364i
$636$		0			0
$637$		−	4.55519i		−	0.180483i
$638$	−38.9739	+	3.20898i	−1.54299	+	0.127045i
$639$		0			0
$640$	18.4422	+	28.4546i	0.728992	+	1.12477i
$641$		−	13.7983i		−	0.544998i	−0.962156	−	0.272499i	$-0.912150\pi$
$641$		−	13.7983i		−	0.544998i	0.962156	−	0.272499i	$-0.0878502\pi$
$642$		0			0
$643$	−36.7203			−1.44811			−0.724053	−	0.689745i	$-0.757723\pi$
$643$	−36.7203			−1.44811			−0.724053	+	0.689745i	$0.757723\pi$
$644$	−0.911640	−	5.49854i	−0.0359236	−	0.216673i
$645$		0			0
$646$	−0.719163	+	0.0592133i	−0.0282951	+	0.00232972i
$647$	−1.59099			−0.0625483			−0.0312742	−	0.999511i	$-0.509956\pi$
$647$	−1.59099			−0.0625483			−0.0312742	+	0.999511i	$0.509956\pi$
$648$		0			0
$649$	−0.191441			−0.00751472
$650$	25.5697	−	2.10532i	1.00293	−	0.0825773i
$651$		0			0
$652$	35.0556	−	5.81211i	1.37288	−	0.227620i
$653$	22.5953			0.884223			0.442111	−	0.896960i	$-0.354230\pi$
$653$	22.5953			0.884223			0.442111	+	0.896960i	$0.354230\pi$
$654$		0			0
$655$			39.9986i			1.56287i
$656$	15.9109	+	46.6640i	0.621215	+	1.82192i
$657$		0			0
$658$	1.97724	−	0.162799i	0.0770809	−	0.00634657i
$659$			24.8372i			0.967520i	0.875201	+	0.483760i	$0.160729\pi$
$659$			24.8372i			0.967520i	−0.875201	+	0.483760i	$0.839271\pi$
$660$		0			0
$661$		−	28.3986i		−	1.10458i	−0.833653	−	0.552288i	$-0.813755\pi$
$661$		−	28.3986i		−	1.10458i	0.833653	−	0.552288i	$-0.186245\pi$
$662$	2.49364	+	30.2860i	0.0969181	+	1.17710i
$663$		0			0
$664$	8.59566	−	2.16239i	0.333576	−	0.0839169i
$665$			1.59514i			0.0618569i
$666$		0			0
$667$	14.3692			0.556377
$668$	35.8657	−	5.94642i	1.38769	−	0.230074i
$669$		0			0
$670$	−2.98959	−	36.3094i	−0.115498	−	1.40275i
$671$	−27.5471			−1.06345
$672$		0			0
$673$	3.94402			0.152031			0.0760153	−	0.997107i	$-0.475780\pi$
$673$	3.94402			0.152031			0.0760153	+	0.997107i	$0.475780\pi$
$674$	3.27236	+	39.7437i	0.126046	+	1.53087i
$675$		0			0
$676$	15.2907	−	2.53515i	0.588103	−	0.0975057i
$677$	8.72694			0.335403			0.167702	−	0.985838i	$-0.446365\pi$
$677$	8.72694			0.335403			0.167702	+	0.985838i	$0.446365\pi$
$678$		0			0
$679$		−	16.0057i		−	0.614243i
$680$	7.88142	−	1.98271i	0.302239	−	0.0760334i
$681$		0			0
$682$	2.90373	+	35.2667i	0.111190	+	1.35043i
$683$		−	23.0246i		−	0.881014i	−0.897749	−	0.440507i	$-0.854799\pi$
$683$		−	23.0246i		−	0.881014i	0.897749	−	0.440507i	$-0.145201\pi$
$684$		0			0
$685$		−	51.2209i		−	1.95705i
$686$	−1.40944	+	0.116049i	−0.0538128	+	0.00443076i
$687$		0			0
$688$	16.8697	−	5.75199i	0.643150	−	0.219292i
$689$			43.5940i			1.66080i
$690$		0			0
$691$	−19.5528			−0.743823			−0.371912	−	0.928268i	$-0.621298\pi$
$691$	−19.5528			−0.743823			−0.371912	+	0.928268i	$0.621298\pi$
$692$	−4.70859	+	0.780669i	−0.178994	+	0.0296766i
$693$		0			0
$694$	−29.8992	+	2.46179i	−1.13496	+	0.0934482i
$695$	−48.1363			−1.82591
$696$		0			0
$697$	11.8165			0.447580
$698$	44.7556	−	3.68502i	1.69402	−	0.139480i
$699$		0			0
$700$	−1.30283	−	7.85802i	−0.0492425	−	0.297005i
$701$	22.1070			0.834971			0.417486	−	0.908684i	$-0.362911\pi$
$701$	22.1070			0.834971			0.417486	+	0.908684i	$0.362911\pi$
$702$		0			0
$703$		−	3.24814i		−	0.122506i
$704$	20.3013	+	37.7961i	0.765135	+	1.42449i
$705$		0			0
$706$	10.3919	−	0.855636i	0.391106	−	0.0322023i
$707$		−	16.1028i		−	0.605607i
$708$		0			0
$709$			15.3427i			0.576207i	0.957599	+	0.288104i	$0.0930247\pi$
$709$			15.3427i			0.576207i	−0.957599	+	0.288104i	$0.906975\pi$
$710$	−4.63521	−	56.2960i	−0.173956	−	2.11275i
$711$		0			0
$712$	16.2198	−	4.08037i	0.607862	−	0.152918i
$713$		−	13.0024i		−	0.486942i
$714$		0			0
$715$	73.2164			2.73814
$716$	−2.20207	−	13.2817i	−0.0822952	−	0.496361i
$717$		0			0
$718$	−1.72198	−	20.9139i	−0.0642637	−	0.780501i
$719$	−15.1069			−0.563392			−0.281696	−	0.959504i	$-0.590897\pi$
$719$	−15.1069			−0.563392			−0.281696	+	0.959504i	$0.590897\pi$
$720$		0			0
$721$	18.0349			0.671653
$722$	2.17205	+	26.3802i	0.0808354	+	0.981769i
$723$		0			0
$724$	0.394537	+	2.37964i	0.0146629	+	0.0884387i
$725$	20.5352			0.762657
$726$		0			0
$727$			20.4051i			0.756784i	0.925645	+	0.378392i	$0.123523\pi$
$727$			20.4051i			0.756784i	−0.925645	+	0.378392i	$0.876477\pi$
$728$	−3.14326	−	12.4947i	−0.116497	−	0.463085i
$729$		0			0
$730$	−2.26358	−	27.4918i	−0.0837787	−	1.01752i
$731$		−	4.27180i		−	0.157998i
$732$		0			0
$733$			39.8824i			1.47309i	0.676389	+	0.736544i	$0.263544\pi$
$733$			39.8824i			1.47309i	−0.676389	+	0.736544i	$0.736456\pi$
$734$	18.7760	−	1.54595i	0.693034	−	0.0570619i
$735$		0			0
$736$	−6.29480	−	14.4532i	−0.232030	−	0.532752i
$737$		−	46.0966i		−	1.69799i
$738$		0			0
$739$	31.8675			1.17226			0.586132	−	0.810216i	$-0.300650\pi$
$739$	31.8675			1.17226			0.586132	+	0.810216i	$0.300650\pi$
$740$	5.98354	+	36.0896i	0.219959	+	1.32668i
$741$		0			0
$742$	13.4886	−	1.11061i	0.495184	−	0.0407717i
$743$	−36.1243			−1.32527			−0.662636	−	0.748942i	$-0.730562\pi$
$743$	−36.1243			−1.32527			−0.662636	+	0.748942i	$0.730562\pi$
$744$		0			0
$745$	4.11974			0.150936
$746$	−34.8552	+	2.86985i	−1.27614	+	0.105073i
$747$		0			0
$748$	10.1443	−	1.68190i	0.370914	−	0.0614964i
$749$	9.08345			0.331902
$750$		0			0
$751$		−	7.07701i		−	0.258244i	−0.991629	−	0.129122i	$-0.958784\pi$
$751$		−	7.07701i		−	0.258244i	0.991629	−	0.129122i	$-0.0412159\pi$
$752$	5.31117	−	1.81093i	0.193678	−	0.0660378i
$753$		0			0
$754$	33.1040	−	2.72566i	1.20558	−	0.0992628i
$755$			16.4992i			0.600467i
$756$		0			0
$757$			25.8712i			0.940304i	0.882585	+	0.470152i	$0.155801\pi$
$757$			25.8712i			0.940304i	−0.882585	+	0.470152i	$0.844199\pi$
$758$	2.41107	+	29.2832i	0.0875741	+	1.06361i
$759$		0			0
$760$	1.10071	+	4.37541i	0.0399270	+	0.158713i
$761$		−	3.07176i		−	0.111351i	−0.998449	−	0.0556757i	$-0.982269\pi$
$761$		−	3.07176i		−	0.111351i	0.998449	−	0.0556757i	$-0.0177313\pi$
$762$		0			0
$763$	−17.2591			−0.624821
$764$	−30.5955	+	5.07263i	−1.10691	+	0.183521i
$765$		0			0
$766$	0.570984	+	6.93477i	0.0206305	+	0.250563i
$767$	0.162608			0.00587142
$768$		0			0
$769$	39.3610			1.41940			0.709698	−	0.704506i	$-0.248831\pi$
$769$	39.3610			1.41940			0.709698	+	0.704506i	$0.248831\pi$
$770$	−1.86527	−	22.6543i	−0.0672197	−	0.816403i
$771$		0			0
$772$	−15.1479	+	2.51147i	−0.545185	+	0.0903899i
$773$	−48.9129			−1.75928			−0.879638	−	0.475644i	$-0.842215\pi$
$773$	−48.9129			−1.75928			−0.879638	+	0.475644i	$0.842215\pi$
$774$		0			0
$775$		−	18.5818i		−	0.667478i
$776$	−11.0446	−	43.9031i	−0.396478	−	1.57603i
$777$		0			0
$778$	−3.99553	−	48.5269i	−0.143247	−	1.73977i
$779$			6.55996i			0.235035i
$780$		0			0
$781$		−	71.4707i		−	2.55742i
$782$	−3.76562	+	0.310047i	−0.134658	+	0.0110873i
$783$		0			0
$784$	−3.78597	+	1.29089i	−0.135213	+	0.0461032i
$785$			56.2859i			2.00893i
$786$		0			0
$787$	16.5486			0.589893			0.294946	−	0.955514i	$-0.404698\pi$
$787$	16.5486			0.589893			0.294946	+	0.955514i	$0.404698\pi$
$788$	−45.6188	+	7.56346i	−1.62510	+	0.269437i
$789$		0			0
$790$	8.05062	−	0.662859i	0.286428	−	0.0235835i
$791$	−1.27590			−0.0453656
$792$		0			0
$793$	23.3982			0.830895
$794$	30.8318	−	2.53858i	1.09418	−	0.0900908i
$795$		0			0
$796$	−0.376155	−	2.26877i	−0.0133325	−	0.0804145i
$797$	6.15737			0.218105			0.109053	−	0.994036i	$-0.465218\pi$
$797$	6.15737			0.218105			0.109053	+	0.994036i	$0.465218\pi$
$798$		0			0
$799$		−	1.34491i		−	0.0475797i
$800$	−8.99598	−	20.6552i	−0.318056	−	0.730273i
$801$		0			0
$802$	−40.9636	+	3.37280i	−1.44648	+	0.119098i
$803$		−	34.9022i		−	1.23167i
$804$		0			0
$805$			8.35233i			0.294381i
$806$	−2.46639	−	29.9551i	−0.0868750	−	1.05512i
$807$		0			0
$808$	−11.1116	−	44.1693i	−0.390903	−	1.55387i
$809$		−	10.7152i		−	0.376728i	−0.982099	−	0.188364i	$-0.939682\pi$
$809$		−	10.7152i		−	0.376728i	0.982099	−	0.188364i	$-0.0603185\pi$
$810$		0			0
$811$	1.60272			0.0562791			0.0281395	−	0.999604i	$-0.491042\pi$
$811$	1.60272			0.0562791			0.0281395	+	0.999604i	$0.491042\pi$
$812$	−1.68672	−	10.1734i	−0.0591924	−	0.357018i
$813$		0			0
$814$	3.79821	+	46.1303i	0.133127	+	1.61687i
$815$	−53.2498			−1.86526
$816$		0			0
$817$	2.37151			0.0829687
$818$	0.482705	+	5.86260i	0.0168774	+	0.204981i
$819$		0			0
$820$	−12.0844	−	72.8867i	−0.422005	−	2.54531i
$821$	−5.62139			−0.196188			−0.0980940	−	0.995177i	$-0.531275\pi$
$821$	−5.62139			−0.196188			−0.0980940	+	0.995177i	$0.531275\pi$
$822$		0			0
$823$		−	10.5605i		−	0.368114i	−0.982916	−	0.184057i	$-0.941077\pi$
$823$		−	10.5605i		−	0.368114i	0.982916	−	0.184057i	$-0.0589232\pi$
$824$	49.4689	−	12.4448i	1.72333	−	0.433534i
$825$		0			0
$826$	−0.00414262	−	0.0503133i	−0.000144140	−	0.00175062i
$827$			37.6285i			1.30847i	0.756290	+	0.654236i	$0.227010\pi$
$827$			37.6285i			1.30847i	−0.756290	+	0.654236i	$0.772990\pi$
$828$		0			0
$829$		−	2.85388i		−	0.0991193i	−0.998771	−	0.0495596i	$-0.984218\pi$
$829$		−	2.85388i		−	0.0991193i	0.998771	−	0.0495596i	$-0.0157818\pi$
$830$	−13.2376	+	1.08994i	−0.459484	+	0.0378322i
$831$		0			0
$832$	−17.2437	−	32.1035i	−0.597817	−	1.11299i
$833$			0.958700i			0.0332170i
$834$		0			0
$835$	−54.4804			−1.88537
$836$	0.933716	+	5.63169i	0.0322932	+	0.194776i
$837$		0			0
$838$	31.7465	−	2.61389i	1.09666	−	0.0902954i
$839$	9.63628			0.332681			0.166341	−	0.986068i	$-0.446805\pi$
$839$	9.63628			0.332681			0.166341	+	0.986068i	$0.446805\pi$
$840$		0			0
$841$	−2.41401			−0.0832418
$842$	46.1417	−	3.79914i	1.59015	−	0.130927i
$843$		0			0
$844$	−30.9066	+	5.12422i	−1.06385	+	0.176383i
$845$	−23.2267			−0.799023
$846$		0			0
$847$		−	17.7608i		−	0.610267i
$848$	36.2325	−	12.3541i	1.24423	−	0.424240i
$849$		0			0
$850$	−5.38148	+	0.443092i	−0.184583	+	0.0151979i
$851$		−	17.0076i		−	0.583015i
$852$		0			0
$853$		−	4.13385i		−	0.141540i	−0.997493	−	0.0707701i	$-0.977454\pi$
$853$		−	4.13385i		−	0.141540i	0.997493	−	0.0707701i	$-0.0225457\pi$
$854$	−0.596096	−	7.23976i	−0.0203980	−	0.247740i
$855$		0			0
$856$	24.9156	−	6.26795i	0.851597	−	0.214234i
$857$		−	32.0416i		−	1.09452i	−0.836963	−	0.547260i	$-0.815671\pi$
$857$		−	32.0416i		−	1.09452i	0.836963	−	0.547260i	$-0.184329\pi$
$858$		0			0
$859$	−17.8213			−0.608055			−0.304027	−	0.952663i	$-0.598331\pi$
$859$	−17.8213			−0.608055			−0.304027	+	0.952663i	$0.598331\pi$
$860$	−26.3495	+	4.36866i	−0.898510	+	0.148970i
$861$		0			0
$862$	−3.27247	−	39.7451i	−0.111461	−	1.35372i
$863$	2.53777			0.0863868			0.0431934	−	0.999067i	$-0.486247\pi$
$863$	2.53777			0.0863868			0.0431934	+	0.999067i	$0.486247\pi$
$864$		0			0
$865$	7.15239			0.243189
$866$	2.56948	+	31.2071i	0.0873145	+	1.06046i
$867$		0			0
$868$	−9.20572	+	1.52628i	−0.312463	+	0.0518053i
$869$	10.2207			0.346713
$870$		0			0
$871$			39.1539i			1.32668i
$872$	−47.3410	+	11.9095i	−1.60317	+	0.403305i
$873$		0			0
$874$	−0.172124	−	2.09050i	−0.00582219	−	0.0707122i
$875$		−	3.04912i		−	0.103079i
$876$		0			0
$877$		−	46.9723i		−	1.58614i	−0.609129	−	0.793072i	$-0.708481\pi$
$877$		−	46.9723i		−	1.58614i	0.609129	−	0.793072i	$-0.291519\pi$
$878$	34.8085	−	2.86601i	1.17473	−	0.0967230i
$879$		0			0
$880$	−20.7487	−	60.8527i	−0.699440	−	2.05134i
$881$		−	45.8003i		−	1.54305i	−0.636198	−	0.771525i	$-0.719494\pi$
$881$		−	45.8003i		−	1.54305i	0.636198	−	0.771525i	$-0.280506\pi$
$882$		0			0
$883$	35.1176			1.18180			0.590901	−	0.806744i	$-0.298772\pi$
$883$	35.1176			1.18180			0.590901	+	0.806744i	$0.298772\pi$
$884$	−8.61648	+	1.42859i	−0.289804	+	0.0480485i
$885$		0			0
$886$	34.7498	−	2.86117i	1.16744	−	0.0961230i
$887$	−10.1586			−0.341091			−0.170546	−	0.985350i	$-0.554553\pi$
$887$	−10.1586			−0.341091			−0.170546	+	0.985350i	$0.554553\pi$
$888$		0			0
$889$	12.7265			0.426833
$890$	−24.9790	+	2.05668i	−0.837298	+	0.0689401i
$891$		0			0
$892$	4.56850	+	27.5548i	0.152965	+	0.922604i
$893$	0.746636			0.0249852
$894$		0			0
$895$			20.1751i			0.674378i
$896$	−9.49402	+	6.15334i	−0.317173	+	0.205569i
$897$		0			0
$898$	−6.77886	+	0.558147i	−0.226213	+	0.0186256i
$899$		−	24.0571i		−	0.802348i
$900$		0			0
$901$		−	9.17494i		−	0.305661i
$902$	−7.67087	−	93.1650i	−0.255412	−	3.10205i
$903$		0			0
$904$	−3.49973	+	0.880419i	−0.116399	+	0.0292823i
$905$		−	3.61470i		−	0.120157i
$906$		0			0
$907$	35.4243			1.17625			0.588123	−	0.808772i	$-0.299867\pi$
$907$	35.4243			1.17625			0.588123	+	0.808772i	$0.299867\pi$
$908$	−8.55789	−	51.6167i	−0.284004	−	1.71296i
$909$		0			0
$910$	1.58434	+	19.2423i	0.0525203	+	0.637875i
$911$	37.6389			1.24703			0.623517	−	0.781810i	$-0.285703\pi$
$911$	37.6389			1.24703			0.623517	+	0.781810i	$0.285703\pi$
$912$		0			0
$913$	−16.8058			−0.556191
$914$	2.38544	+	28.9719i	0.0789034	+	0.958305i
$915$		0			0
$916$	1.96926	+	11.8776i	0.0650663	+	0.392446i
$917$	−13.3457			−0.440715
$918$		0			0
$919$			39.1964i			1.29297i	0.762927	+	0.646485i	$0.223762\pi$
$919$			39.1964i			1.29297i	−0.762927	+	0.646485i	$0.776238\pi$
$920$	5.76344	+	22.9101i	0.190015	+	0.755325i
$921$		0			0
$922$	0.807868	+	9.81179i	0.0266057	+	0.323134i
$923$			60.7063i			1.99817i
$924$		0			0
$925$		−	24.3058i		−	0.799171i
$926$	0.302775	−	0.0249294i	0.00994981	−	0.000819231i
$927$		0			0
$928$	−11.6467	−	26.7415i	−0.382322	−	0.877832i
$929$			9.19387i			0.301641i	0.988561	+	0.150821i	$0.0481916\pi$
$929$			9.19387i			0.301641i	−0.988561	+	0.150821i	$0.951808\pi$
$930$		0			0
$931$	−0.532227			−0.0174430
$932$	−4.39442	−	26.5048i	−0.143944	−	0.868195i
$933$		0			0
$934$	−42.8775	+	3.53038i	−1.40299	+	0.115517i
$935$	−15.4094			−0.503940
$936$		0			0
$937$	−48.7873			−1.59381			−0.796905	−	0.604104i	$-0.793531\pi$
$937$	−48.7873			−1.59381			−0.796905	+	0.604104i	$0.793531\pi$
$938$	12.1148	−	0.997491i	0.395563	−	0.0325692i
$939$		0			0
$940$	−8.29575	+	1.37541i	−0.270578	+	0.0448609i
$941$	0.0818594			0.00266854			0.00133427	−	0.999999i	$-0.499575\pi$
$941$	0.0818594			0.00266854			0.00133427	+	0.999999i	$0.499575\pi$
$942$		0			0
$943$			34.3487i			1.11855i
$944$	−0.0460812	−	0.135149i	−0.00149982	−	0.00439872i
$945$		0			0
$946$	−33.6803	+	2.77312i	−1.09504	+	0.0901619i
$947$			21.5632i			0.700711i	0.936617	+	0.350356i	$0.113939\pi$
$947$			21.5632i			0.700711i	−0.936617	+	0.350356i	$0.886061\pi$
$948$		0			0
$949$			29.6455i			0.962334i
$950$	−0.245985	−	2.98756i	−0.00798080	−	0.0969292i
$951$		0			0
$952$	0.661541	+	2.62968i	0.0214407	+	0.0852283i
$953$		−	13.2536i		−	0.429325i	−0.976688	−	0.214662i	$-0.931135\pi$
$953$		−	13.2536i		−	0.429325i	0.976688	−	0.214662i	$-0.0688651\pi$
$954$		0			0
$955$	46.4748			1.50389
$956$	51.9900	−	8.61978i	1.68148	−	0.278784i
$957$		0			0
$958$	−4.29250	−	52.1336i	−0.138684	−	1.68436i
$959$	17.0901			0.551868
$960$		0			0
$961$	9.23129			0.297784
$962$	−3.22615	−	39.1825i	−0.104015	−	1.26330i
$963$		0			0
$964$	25.5475	−	4.23570i	0.822830	−	0.136423i
$965$	23.0098			0.740712
$966$		0			0
$967$			6.74105i			0.216778i	0.994109	+	0.108389i	$0.0345691\pi$
$967$			6.74105i			0.216778i	−0.994109	+	0.108389i	$0.965431\pi$
$968$	−12.2556	−	48.7171i	−0.393911	−	1.56583i
$969$		0			0
$970$	5.56695	+	67.6123i	0.178744	+	2.17090i
$971$		−	23.5075i		−	0.754391i	−0.926134	−	0.377196i	$-0.876888\pi$
$971$		−	23.5075i		−	0.754391i	0.926134	−	0.377196i	$-0.123112\pi$
$972$		0			0
$973$		−	16.0609i		−	0.514889i
$974$	14.5077	−	1.19452i	0.464858	−	0.0382747i
$975$		0			0
$976$	−6.63080	−	19.4471i	−0.212247	−	0.622486i
$977$			13.3757i			0.427927i	0.976842	+	0.213964i	$0.0686374\pi$
$977$			13.3757i			0.427927i	−0.976842	+	0.213964i	$0.931363\pi$
$978$		0			0
$979$	−31.7121			−1.01352
$980$	5.91349	−	0.980437i	0.188899	−	0.0313189i
$981$		0			0
$982$	−2.50206	+	0.206011i	−0.0798440	+	0.00657407i
$983$	−18.3093			−0.583975			−0.291987	−	0.956422i	$-0.594317\pi$
$983$	−18.3093			−0.583975			−0.291987	+	0.956422i	$0.594317\pi$
$984$		0			0
$985$	69.2955			2.20794
$986$	−6.96718	+	0.573652i	−0.221880	+	0.0182688i
$987$		0			0
$988$	−0.793086	−	4.78348i	−0.0252314	−	0.152183i
$989$	12.4175			0.394853
$990$		0			0
$991$		−	58.0580i		−	1.84427i	−0.386865	−	0.922136i	$-0.626442\pi$
$991$		−	58.0580i		−	1.84427i	0.386865	−	0.922136i	$-0.373558\pi$
$992$	−24.1978	+	10.5388i	−0.768279	+	0.334609i
$993$		0			0
$994$	18.7835	−	1.54656i	0.595775	−	0.0490540i
$995$			3.44629i			0.109255i
$996$		0			0
$997$		−	53.3202i		−	1.68867i	−0.535818	−	0.844334i	$-0.679997\pi$
$997$		−	53.3202i		−	1.68867i	0.535818	−	0.844334i	$-0.320003\pi$
$998$	3.18267	+	38.6545i	0.100746	+	1.22359i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.21	✓	48
3.2	odd	2	inner	1512.2.j.d.323.28	yes	48
4.3	odd	2		6048.2.j.d.5615.44		48
8.3	odd	2	inner	1512.2.j.d.323.27	yes	48
8.5	even	2		6048.2.j.d.5615.6		48
12.11	even	2		6048.2.j.d.5615.5		48
24.5	odd	2		6048.2.j.d.5615.43		48
24.11	even	2	inner	1512.2.j.d.323.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.21	✓	48	1.1	even	1	trivial
1512.2.j.d.323.22	yes	48	24.11	even	2	inner
1512.2.j.d.323.27	yes	48	8.3	odd	2	inner
1512.2.j.d.323.28	yes	48	3.2	odd	2	inner
6048.2.j.d.5615.5		48	12.11	even	2
6048.2.j.d.5615.6		48	8.5	even	2
6048.2.j.d.5615.43		48	24.5	odd	2
6048.2.j.d.5615.44		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.116049 - 1.40944i) q^{2} +(-1.97307 + 0.327128i) q^{4} +2.99711 q^{5} +1.00000i q^{7} +(0.690040 + 2.74296i) q^{8} +O(q^{10})\)	\(q+(-0.116049 - 1.40944i) q^{2} +(-1.97307 + 0.327128i) q^{4} +2.99711 q^{5} +1.00000i q^{7} +(0.690040 + 2.74296i) q^{8} +(-0.347810 - 4.22425i) q^{10} -5.36291i q^{11} +4.55519i q^{13} +(1.40944 - 0.116049i) q^{14} +(3.78597 - 1.29089i) q^{16} -0.958700i q^{17} +0.532227 q^{19} +(-5.91349 + 0.980437i) q^{20} +(-7.55872 + 0.622358i) q^{22} +2.78680 q^{23} +3.98265 q^{25} +(6.42028 - 0.528623i) q^{26} +(-0.327128 - 1.97307i) q^{28} +5.15616 q^{29} -4.66569i q^{31} +(-2.25879 - 5.18631i) q^{32} +(-1.35123 + 0.111256i) q^{34} +2.99711i q^{35} -6.10293i q^{37} +(-0.0617642 - 0.750144i) q^{38} +(2.06812 + 8.22095i) q^{40} +12.3255i q^{41} +4.45583 q^{43} +(1.75436 + 10.5814i) q^{44} +(-0.323404 - 3.92784i) q^{46} +1.40285 q^{47} -1.00000 q^{49} +(-0.462180 - 5.61332i) q^{50} +(-1.49013 - 8.98768i) q^{52} +9.57019 q^{53} -16.0732i q^{55} +(-2.74296 + 0.690040i) q^{56} +(-0.598365 - 7.26732i) q^{58} -0.0356973i q^{59} -5.13661i q^{61} +(-6.57604 + 0.541447i) q^{62} +(-7.04769 + 3.78551i) q^{64} +13.6524i q^{65} +8.59546 q^{67} +(0.313617 + 1.89158i) q^{68} +(4.22425 - 0.347810i) q^{70} +13.3269 q^{71} +6.50808 q^{73} +(-8.60174 + 0.708237i) q^{74} +(-1.05012 + 0.174106i) q^{76} +5.36291 q^{77} +1.90581i q^{79} +(11.3470 - 3.86893i) q^{80} +(17.3721 - 1.43036i) q^{82} -3.13371i q^{83} -2.87332i q^{85} +(-0.517093 - 6.28024i) q^{86} +(14.7103 - 3.70062i) q^{88} -5.91323i q^{89} -4.55519 q^{91} +(-5.49854 + 0.911640i) q^{92} +(-0.162799 - 1.97724i) q^{94} +1.59514 q^{95} -16.0057 q^{97} +(0.116049 + 1.40944i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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