LMFDB - Embedded newform 952.2.cw.b.369.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(73,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 0, 8, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.cw (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [288,0,0,0,0,0,0,0,0,0,0,0,0,0,32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			369.13
Character	$\chi$	$=$	952.369
Dual form			952.2.cw.b.129.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.487596 - 0.988748i) q^{3} +(-0.0798482 - 0.0700250i) q^{5} +(-2.19196 + 1.48165i) q^{7} +(1.08641 + 1.41584i) q^{9} +(-1.32947 - 0.0871378i) q^{11} +(4.43841 - 4.43841i) q^{13} +(-0.108171 + 0.0448058i) q^{15} +(1.86185 - 3.67879i) q^{17} +(-0.479438 + 3.64170i) q^{19} +(0.396185 + 2.88975i) q^{21} +(4.95786 - 2.44495i) q^{23} +(-0.651159 - 4.94604i) q^{25} +(5.17341 - 1.02905i) q^{27} +(-0.0401398 + 0.201796i) q^{29} +(8.79679 + 4.33810i) q^{31} +(-0.734400 + 1.27202i) q^{33} +(0.278777 + 0.0351851i) q^{35} +(-0.248002 - 3.78379i) q^{37} +(-2.22432 - 6.55263i) q^{39} +(1.35901 + 6.83218i) q^{41} +(2.37636 - 5.73704i) q^{43} +(0.0123961 - 0.189128i) q^{45} +(1.46587 + 5.47070i) q^{47} +(2.60942 - 6.49545i) q^{49} +(-2.72957 - 3.63466i) q^{51} +(4.61872 - 6.01924i) q^{53} +(0.100054 + 0.100054i) q^{55} +(3.36695 + 2.24972i) q^{57} +(-11.7775 + 1.55054i) q^{59} +(1.86127 - 5.48314i) q^{61} +(-4.47916 - 1.49379i) q^{63} +(-0.665199 + 0.0435995i) q^{65} +(-2.78463 + 1.60771i) q^{67} -6.09422i q^{69} +(-3.05696 + 2.04259i) q^{71} +(-10.8755 + 3.69175i) q^{73} +(-5.20789 - 1.76784i) q^{75} +(3.04325 - 1.77880i) q^{77} +(3.88723 + 7.88253i) q^{79} +(0.119373 - 0.445506i) q^{81} +(-6.53228 - 15.7703i) q^{83} +(-0.406272 + 0.163369i) q^{85} +(0.179954 + 0.138083i) q^{87} +(4.84791 - 1.29899i) q^{89} +(-3.15267 + 16.3050i) q^{91} +(8.57857 - 6.58257i) q^{93} +(0.293292 - 0.257210i) q^{95} +(7.45011 + 1.48192i) q^{97} +(-1.32097 - 1.97698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 32 q^{15} + 48 q^{21} - 32 q^{29} - 72 q^{31} - 16 q^{37} - 32 q^{39} + 32 q^{43} + 24 q^{47} - 48 q^{49} - 16 q^{53} - 128 q^{57} - 72 q^{61} - 40 q^{63} + 32 q^{65} + 80 q^{71} + 96 q^{73} - 216 q^{75}+ \cdots + 192 q^{99}+O(q^{100}) $ 288 * q + 32 * q^15 + 48 * q^21 - 32 * q^29 - 72 * q^31 - 16 * q^37 - 32 * q^39 + 32 * q^43 + 24 * q^47 - 48 * q^49 - 16 * q^53 - 128 * q^57 - 72 * q^61 - 40 * q^63 + 32 * q^65 + 80 * q^71 + 96 * q^73 - 216 * q^75 - 8 * q^77 + 32 * q^79 + 64 * q^81 - 96 * q^85 + 144 * q^87 - 144 * q^89 + 64 * q^91 - 32 * q^93 + 64 * q^95 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{13}{16}\right)$

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
$3$	0.487596	−	0.988748i	0.281514	−	0.570854i	−0.709485	−	0.704720i	$-0.751073\pi$
$3$	0.487596	−	0.988748i	0.281514	−	0.570854i	0.990999	+	0.133866i	$0.0427393\pi$
$4$		0			0
$5$	−0.0798482	−	0.0700250i	−0.0357092	−	0.0313161i	0.641305	−	0.767286i	$-0.278393\pi$
$5$	−0.0798482	−	0.0700250i	−0.0357092	−	0.0313161i	−0.677014	+	0.735970i	$0.736727\pi$
$6$		0			0
$7$	−2.19196	+	1.48165i	−0.828485	+	0.560011i
$7$	−2.19196	+	1.48165i	−0.828485	+	0.560011i
$8$		0			0
$9$	1.08641	+	1.41584i	0.362137	+	0.471947i
$10$		0			0
$11$	−1.32947	−	0.0871378i	−0.400849	−	0.0262730i	−0.136354	−	0.990660i	$-0.543539\pi$
$11$	−1.32947	−	0.0871378i	−0.400849	−	0.0262730i	−0.264495	+	0.964387i	$0.585205\pi$
$12$		0			0
$13$	4.43841	−	4.43841i	1.23099	−	1.23099i	0.267413	−	0.963582i	$-0.413831\pi$
$13$	4.43841	−	4.43841i	1.23099	−	1.23099i	0.963582	−	0.267413i	$-0.0861687\pi$
$14$		0			0
$15$	−0.108171	+	0.0448058i	−0.0279296	+	0.0115688i
$16$		0			0
$17$	1.86185	−	3.67879i	0.451564	−	0.892239i
$17$	1.86185	−	3.67879i	0.451564	−	0.892239i
$18$		0			0
$19$	−0.479438	+	3.64170i	−0.109991	+	0.835462i	0.844151	+	0.536106i	$0.180105\pi$
$19$	−0.479438	+	3.64170i	−0.109991	+	0.835462i	−0.954141	+	0.299356i	$0.903228\pi$
$20$		0			0
$21$	0.396185	+	2.88975i	0.0864546	+	0.630595i
$22$		0			0
$23$	4.95786	−	2.44495i	1.03379	−	0.509807i	0.155446	−	0.987844i	$-0.450318\pi$
$23$	4.95786	−	2.44495i	1.03379	−	0.509807i	0.878339	+	0.478038i	$0.158652\pi$
$24$		0			0
$25$	−0.651159	−	4.94604i	−0.130232	−	0.989208i
$26$		0			0
$27$	5.17341	−	1.02905i	0.995623	−	0.198042i
$28$		0			0
$29$	−0.0401398	+	0.201796i	−0.00745378	+	0.0374727i	−0.984333	−	0.176318i	$-0.943581\pi$
$29$	−0.0401398	+	0.201796i	−0.00745378	+	0.0374727i	0.976879	+	0.213791i	$0.0685812\pi$
$30$		0			0
$31$	8.79679	+	4.33810i	1.57995	+	0.779145i	0.999385	−	0.0350686i	$-0.0111650\pi$
$31$	8.79679	+	4.33810i	1.57995	+	0.779145i	0.580565	+	0.814214i	$0.302832\pi$
$32$		0			0
$33$	−0.734400	+	1.27202i	−0.127843	+	0.221430i
$34$		0			0
$35$	0.278777	+	0.0351851i	0.0471219	+	0.00594738i
$36$		0			0
$37$	−0.248002	−	3.78379i	−0.0407713	−	0.622050i	−0.968534	−	0.248880i	$-0.919937\pi$
$37$	−0.248002	−	3.78379i	−0.0407713	−	0.622050i	0.927763	−	0.373170i	$-0.121729\pi$
$38$		0			0
$39$	−2.22432	−	6.55263i	−0.356176	−	1.04926i
$40$		0			0
$41$	1.35901	+	6.83218i	0.212241	+	1.06701i	0.929111	+	0.369801i	$0.120574\pi$
$41$	1.35901	+	6.83218i	0.212241	+	1.06701i	−0.716870	+	0.697207i	$0.754426\pi$
$42$		0			0
$43$	2.37636	−	5.73704i	0.362391	−	0.874890i	−0.632558	−	0.774513i	$-0.717995\pi$
$43$	2.37636	−	5.73704i	0.362391	−	0.874890i	0.994949	−	0.100377i	$-0.0320049\pi$
$44$		0			0
$45$	0.0123961	−	0.189128i	0.00184790	−	0.0281936i
$46$		0			0
$47$	1.46587	+	5.47070i	0.213819	+	0.797983i	0.986579	+	0.163285i	$0.0522090\pi$
$47$	1.46587	+	5.47070i	0.213819	+	0.797983i	−0.772760	+	0.634698i	$0.781124\pi$
$48$		0			0
$49$	2.60942	−	6.49545i	0.372774	−	0.927922i
$50$		0			0
$51$	−2.72957	−	3.63466i	−0.382216	−	0.508955i
$52$		0			0
$53$	4.61872	−	6.01924i	0.634430	−	0.826806i	−0.359917	−	0.932984i	$-0.617195\pi$
$53$	4.61872	−	6.01924i	0.634430	−	0.826806i	0.994347	+	0.106179i	$0.0338616\pi$
$54$		0			0
$55$	0.100054	+	0.100054i	0.0134912	+	0.0134912i
$56$		0			0
$57$	3.36695	+	2.24972i	0.445963	+	0.297983i
$58$		0			0
$59$	−11.7775	+	1.55054i	−1.53330	+	0.201863i	−0.849414	−	0.527727i	$-0.823044\pi$
$59$	−11.7775	+	1.55054i	−1.53330	+	0.201863i	−0.683885	+	0.729590i	$0.739711\pi$
$60$		0			0
$61$	1.86127	−	5.48314i	0.238312	−	0.702044i	−0.760310	−	0.649560i	$-0.774953\pi$
$61$	1.86127	−	5.48314i	0.238312	−	0.702044i	0.998622	−	0.0524835i	$-0.0167137\pi$
$62$		0			0
$63$	−4.47916	−	1.49379i	−0.564321	−	0.188200i
$64$		0			0
$65$	−0.665199	+	0.0435995i	−0.0825078	+	0.00540785i
$66$		0			0
$67$	−2.78463	+	1.60771i	−0.340196	+	0.196413i	−0.660359	−	0.750950i	$-0.729596\pi$
$67$	−2.78463	+	1.60771i	−0.340196	+	0.196413i	0.320162	+	0.947363i	$0.396263\pi$
$68$		0			0
$69$		−	6.09422i		−	0.733658i
$70$		0			0
$71$	−3.05696	+	2.04259i	−0.362794	+	0.242411i	−0.723585	−	0.690236i	$-0.757507\pi$
$71$	−3.05696	+	2.04259i	−0.362794	+	0.242411i	0.360791	+	0.932647i	$0.382507\pi$
$72$		0			0
$73$	−10.8755	+	3.69175i	−1.27289	+	0.432086i	−0.874452	−	0.485111i	$-0.838779\pi$
$73$	−10.8755	+	3.69175i	−1.27289	+	0.432086i	−0.398433	+	0.917198i	$0.630446\pi$
$74$		0			0
$75$	−5.20789	−	1.76784i	−0.601355	−	0.204133i
$76$		0			0
$77$	3.04325	−	1.77880i	0.346810	−	0.202713i
$78$		0			0
$79$	3.88723	+	7.88253i	0.437348	+	0.886854i	0.998259	+	0.0589780i	$0.0187842\pi$
$79$	3.88723	+	7.88253i	0.437348	+	0.886854i	−0.560911	+	0.827876i	$0.689549\pi$
$80$		0			0
$81$	0.119373	−	0.445506i	0.0132637	−	0.0495007i
$82$		0			0
$83$	−6.53228	−	15.7703i	−0.717010	−	1.73102i	−0.681691	−	0.731640i	$-0.738755\pi$
$83$	−6.53228	−	15.7703i	−0.717010	−	1.73102i	−0.0353194	−	0.999376i	$-0.511245\pi$
$84$		0			0
$85$	−0.406272	+	0.163369i	−0.0440664	+	0.0177199i
$86$		0			0
$87$	0.179954	+	0.138083i	0.0192931	+	0.0148041i
$88$		0			0
$89$	4.84791	−	1.29899i	0.513877	−	0.137693i	0.00744416	−	0.999972i	$-0.497630\pi$
$89$	4.84791	−	1.29899i	0.513877	−	0.137693i	0.506433	+	0.862279i	$0.330964\pi$
$90$		0			0
$91$	−3.15267	+	16.3050i	−0.330489	+	1.70923i
$92$		0			0
$93$	8.57857	−	6.58257i	0.889556	−	0.682580i
$94$		0			0
$95$	0.293292	−	0.257210i	0.0300911	−	0.0263892i
$96$		0			0
$97$	7.45011	+	1.48192i	0.756444	+	0.150466i	0.558223	−	0.829691i	$-0.311483\pi$
$97$	7.45011	+	1.48192i	0.756444	+	0.150466i	0.198221	+	0.980157i	$0.436483\pi$
$98$		0			0
$99$	−1.32097	−	1.97698i	−0.132763	−	0.198694i
$100$		0			0
$101$	0.587307	+	1.01725i	0.0584393	+	0.101220i	0.893765	−	0.448536i	$-0.148054\pi$
$101$	0.587307	+	1.01725i	0.0584393	+	0.101220i	−0.835326	+	0.549755i	$0.814721\pi$
$102$		0			0
$103$	3.07882	+	1.77756i	0.303365	+	0.175148i	0.643954	−	0.765065i	$-0.277293\pi$
$103$	3.07882	+	1.77756i	0.303365	+	0.175148i	−0.340589	+	0.940212i	$0.610626\pi$
$104$		0			0
$105$	0.170720	−	0.258484i	0.0166606	−	0.0252255i
$106$		0			0
$107$	4.57877	−	5.22109i	0.442647	−	0.504742i	−0.486894	−	0.873461i	$-0.661870\pi$
$107$	4.57877	−	5.22109i	0.442647	−	0.504742i	0.929541	+	0.368719i	$0.120204\pi$
$108$		0			0
$109$	10.1175	+	11.5368i	0.969084	+	1.10503i	0.994435	+	0.105349i	$0.0335961\pi$
$109$	10.1175	+	11.5368i	0.969084	+	1.10503i	−0.0253517	+	0.999679i	$0.508071\pi$
$110$		0			0
$111$	−3.86213	−	1.59975i	−0.366578	−	0.151841i
$112$		0			0
$113$	−4.14307	+	6.20054i	−0.389747	+	0.583298i	−0.973515	−	0.228623i	$-0.926578\pi$
$113$	−4.14307	+	6.20054i	−0.389747	+	0.583298i	0.583768	+	0.811921i	$0.301578\pi$
$114$		0			0
$115$	−0.567084	−	0.151950i	−0.0528808	−	0.0141694i
$116$		0			0
$117$	11.1060	+	1.46214i	1.02675	+	0.135175i
$118$		0			0
$119$	1.36959	+	10.8224i	0.125550	+	0.992087i
$120$		0			0
$121$	−9.14601	−	1.20409i	−0.831455	−	0.109463i
$122$		0			0
$123$	7.41795	+	1.98763i	0.668854	+	0.179219i
$124$		0			0
$125$	−0.589371	+	0.882056i	−0.0527149	+	0.0788935i
$126$		0			0
$127$	12.1043	+	5.01376i	1.07408	+	0.444900i	0.848430	−	0.529308i	$-0.177548\pi$
$127$	12.1043	+	5.01376i	1.07408	+	0.444900i	0.225653	+	0.974208i	$0.427548\pi$
$128$		0			0
$129$	−4.51378	−	5.14698i	−0.397416	−	0.453166i
$130$		0			0
$131$	−11.9871	+	13.6686i	−1.04732	+	1.19423i	−0.0668055	+	0.997766i	$0.521281\pi$
$131$	−11.9871	+	13.6686i	−1.04732	+	1.19423i	−0.980510	+	0.196469i	$0.937053\pi$
$132$		0			0
$133$	−4.34481	−	8.69283i	−0.376743	−	0.753764i
$134$		0			0
$135$	−0.485147	−	0.280100i	−0.0417548	−	0.0241071i
$136$		0			0
$137$	−5.03020	−	8.71257i	−0.429759	−	0.744365i	0.567092	−	0.823654i	$-0.308068\pi$
$137$	−5.03020	−	8.71257i	−0.429759	−	0.744365i	−0.996852	+	0.0792892i	$0.974735\pi$
$138$		0			0
$139$	−2.78571	−	4.16911i	−0.236281	−	0.353619i	0.694313	−	0.719674i	$-0.255709\pi$
$139$	−2.78571	−	4.16911i	−0.236281	−	0.353619i	−0.930594	+	0.366054i	$0.880709\pi$
$140$		0			0
$141$	6.12389	+	1.21812i	0.515725	+	0.102584i
$142$		0			0
$143$	−6.28747	+	5.51397i	−0.525785	+	0.461101i
$144$		0			0
$145$	0.0173359	−	0.0133023i	0.00143967	−	0.00110470i
$146$		0			0
$147$	−5.15002	−	5.74722i	−0.424767	−	0.474023i
$148$		0			0
$149$	8.90213	−	2.38532i	0.729291	−	0.195413i	0.124978	−	0.992160i	$-0.460114\pi$
$149$	8.90213	−	2.38532i	0.729291	−	0.195413i	0.604314	+	0.796747i	$0.293447\pi$
$150$		0			0
$151$	−19.3290	−	14.8317i	−1.57297	−	1.20699i	−0.866406	−	0.499340i	$-0.833576\pi$
$151$	−19.3290	−	14.8317i	−1.57297	−	1.20699i	−0.706568	−	0.707645i	$-0.749758\pi$
$152$		0			0
$153$	7.23132	−	1.36061i	0.584617	−	0.109999i
$154$		0			0
$155$	−0.398633	−	0.962384i	−0.0320189	−	0.0773006i
$156$		0			0
$157$	−4.57065	+	17.0579i	−0.364777	+	1.36137i	0.502945	+	0.864318i	$0.332250\pi$
$157$	−4.57065	+	17.0579i	−0.364777	+	1.36137i	−0.867723	+	0.497049i	$0.834417\pi$
$158$		0			0
$159$	−3.69943	−	7.50171i	−0.293384	−	0.594924i
$160$		0			0
$161$	−7.24490	+	12.7051i	−0.570978	+	1.00130i
$162$		0			0
$163$	7.37101	+	2.50212i	0.577342	+	0.195981i	0.594810	−	0.803866i	$-0.297227\pi$
$163$	7.37101	+	2.50212i	0.577342	+	0.195981i	−0.0174682	+	0.999847i	$0.505561\pi$
$164$		0			0
$165$	0.147714	−	0.0501420i	0.0114995	−	0.00390355i
$166$		0			0
$167$	−15.1382	+	10.1150i	−1.17143	+	0.782726i	−0.980042	−	0.198788i	$-0.936299\pi$
$167$	−15.1382	+	10.1150i	−1.17143	+	0.782726i	−0.191390	+	0.981514i	$0.561299\pi$
$168$		0			0
$169$		−	26.3990i		−	2.03070i
$170$		0			0
$171$	−5.67693	+	3.27758i	−0.434126	+	0.250643i
$172$		0			0
$173$	2.91856	−	0.191292i	0.221894	−	0.0145437i	0.0459494	−	0.998944i	$-0.485369\pi$
$173$	2.91856	−	0.191292i	0.221894	−	0.0145437i	0.175945	+	0.984400i	$0.443702\pi$
$174$		0			0
$175$	8.75562	+	9.87676i	0.661863	+	0.746613i
$176$		0			0
$177$	−4.20957	+	12.4010i	−0.316411	+	0.932116i
$178$		0			0
$179$	4.28394	−	0.563991i	0.320197	−	0.0421547i	0.0312851	−	0.999511i	$-0.490040\pi$
$179$	4.28394	−	0.563991i	0.320197	−	0.0421547i	0.288911	+	0.957356i	$0.406707\pi$
$180$		0			0
$181$	14.9715	+	10.0036i	1.11282	+	0.743562i	0.969250	−	0.246078i	$-0.0791419\pi$
$181$	14.9715	+	10.0036i	1.11282	+	0.743562i	0.143570	+	0.989640i	$0.454142\pi$
$182$		0			0
$183$	−4.51389	−	4.51389i	−0.333676	−	0.333676i
$184$		0			0
$185$	−0.245157	+	0.319495i	−0.0180243	+	0.0234897i
$186$		0			0
$187$	−2.79582	+	4.72859i	−0.204451	+	0.345789i
$188$		0			0
$189$	−9.81523	+	9.92084i	−0.713953	+	0.721635i
$190$		0			0
$191$	0.562910	+	2.10081i	0.0407307	+	0.152009i	0.983296	−	0.182012i	$-0.0582610\pi$
$191$	0.562910	+	2.10081i	0.0407307	+	0.152009i	−0.942566	+	0.334021i	$0.891594\pi$
$192$		0			0
$193$	−1.20917	+	18.4484i	−0.0870383	+	1.32795i	0.701371	+	0.712796i	$0.252572\pi$
$193$	−1.20917	+	18.4484i	−0.0870383	+	1.32795i	−0.788409	+	0.615151i	$0.789095\pi$
$194$		0			0
$195$	−0.281240	+	0.678973i	−0.0201400	+	0.0486223i
$196$		0			0
$197$	4.79192	+	24.0906i	0.341410	+	1.71638i	0.645518	+	0.763745i	$0.276642\pi$
$197$	4.79192	+	24.0906i	0.341410	+	1.71638i	−0.304108	+	0.952638i	$0.598358\pi$
$198$		0			0
$199$	−7.88740	−	23.2355i	−0.559123	−	1.64712i	−0.746919	−	0.664915i	$-0.768468\pi$
$199$	−7.88740	−	23.2355i	−0.559123	−	1.64712i	0.187796	−	0.982208i	$-0.439866\pi$
$200$		0			0
$201$	0.231841	+	3.53721i	0.0163528	+	0.249495i
$202$		0			0
$203$	−0.211007	−	0.501804i	−0.0148098	−	0.0352197i
$204$		0			0
$205$	0.369909	−	0.640702i	0.0258356	−	0.0447485i
$206$		0			0
$207$	8.84794	+	4.36332i	0.614974	+	0.303272i
$208$		0			0
$209$	0.954726	−	4.79973i	0.0660398	−	0.332004i
$210$		0			0
$211$	16.1207	−	3.20661i	1.10979	−	0.220752i	0.394033	−	0.919096i	$-0.371080\pi$
$211$	16.1207	−	3.20661i	1.10979	−	0.220752i	0.715762	+	0.698344i	$0.246080\pi$
$212$		0			0
$213$	0.529048	+	4.01852i	0.0362498	+	0.275344i
$214$		0			0
$215$	−0.591484	+	0.291688i	−0.0403389	+	0.0198929i
$216$		0			0
$217$	−25.7098	+	3.52482i	−1.74529	+	0.239280i
$218$		0			0
$219$	−1.65267	+	12.5532i	−0.111677	+	0.848270i
$220$		0			0
$221$	−8.06437	−	24.5917i	−0.542468	−	1.65421i
$222$		0			0
$223$	−12.0495	+	4.99105i	−0.806892	+	0.334225i	−0.747713	−	0.664022i	$-0.768848\pi$
$223$	−12.0495	+	4.99105i	−0.806892	+	0.334225i	−0.0591785	+	0.998247i	$0.518848\pi$
$224$		0			0
$225$	6.29538	−	6.29538i	0.419692	−	0.419692i
$226$		0			0
$227$	−22.1555	−	1.45215i	−1.47051	−	0.0963826i	−0.691040	−	0.722817i	$-0.742847\pi$
$227$	−22.1555	−	1.45215i	−1.47051	−	0.0963826i	−0.779474	+	0.626434i	$0.784514\pi$
$228$		0			0
$229$	0.177365	+	0.231146i	0.0117206	+	0.0152746i	0.799177	−	0.601096i	$-0.205269\pi$
$229$	0.177365	+	0.231146i	0.0117206	+	0.0152746i	−0.787456	+	0.616371i	$0.788602\pi$
$230$		0			0
$231$	−0.274908	−	3.87634i	−0.0180876	−	0.255045i
$232$		0			0
$233$	−22.2968	−	19.5538i	−1.46071	−	1.28101i	−0.886850	−	0.462057i	$-0.847112\pi$
$233$	−22.2968	−	19.5538i	−1.46071	−	1.28101i	−0.573861	−	0.818953i	$-0.694555\pi$
$234$		0			0
$235$	0.266038	−	0.539473i	0.0173544	−	0.0351913i
$236$		0			0
$237$	9.68923			0.629383
$238$		0			0
$239$	−3.43951			−0.222483			−0.111242	−	0.993793i	$-0.535483\pi$
$239$	−3.43951			−0.222483			−0.111242	+	0.993793i	$0.535483\pi$
$240$		0			0
$241$	1.44512	−	2.93041i	0.0930884	−	0.188765i	−0.845349	−	0.534215i	$-0.820607\pi$
$241$	1.44512	−	2.93041i	0.0930884	−	0.188765i	0.938437	+	0.345451i	$0.112274\pi$
$242$		0			0
$243$	11.5150	+	10.0984i	0.738690	+	0.647814i
$244$		0			0
$245$	−0.663201	+	0.335926i	−0.0423704	+	0.0214615i
$246$		0			0
$247$	14.0354	+	18.2913i	0.893052	+	1.16385i
$248$		0			0
$249$	−18.7780	−	1.23077i	−1.19001	−	0.0779971i
$250$		0			0
$251$	−1.56568	+	1.56568i	−0.0988249	+	0.0988249i	−0.754791	−	0.655966i	$-0.772262\pi$
$251$	−1.56568	+	1.56568i	−0.0988249	+	0.0988249i	0.655966	+	0.754791i	$0.272262\pi$
$252$		0			0
$253$	−6.80435	+	2.81846i	−0.427786	+	0.177195i
$254$		0			0
$255$	−0.0365659	+	0.481359i	−0.00228985	+	0.0301439i
$256$		0			0
$257$	−3.38603	+	25.7195i	−0.211215	+	1.60434i	0.477049	+	0.878877i	$0.341707\pi$
$257$	−3.38603	+	25.7195i	−0.211215	+	1.60434i	−0.688264	+	0.725461i	$0.741627\pi$
$258$		0			0
$259$	6.14986	+	7.92647i	0.382134	+	0.492527i
$260$		0			0
$261$	−0.329320	+	0.162403i	−0.0203844	+	0.0100525i
$262$		0			0
$263$	−1.22490	−	9.30402i	−0.0755304	−	0.573710i	−0.986805	−	0.161912i	$-0.948234\pi$
$263$	−1.22490	−	9.30402i	−0.0755304	−	0.573710i	0.911275	−	0.411799i	$-0.135099\pi$
$264$		0			0
$265$	−0.790294	+	0.157199i	−0.0485473	+	0.00965667i
$266$		0			0
$267$	1.07945	−	5.42674i	0.0660610	−	0.332111i
$268$		0			0
$269$	−8.11275	−	4.00077i	−0.494643	−	0.243931i	0.177818	−	0.984063i	$-0.443096\pi$
$269$	−8.11275	−	4.00077i	−0.494643	−	0.243931i	−0.672461	+	0.740132i	$0.734763\pi$
$270$		0			0
$271$	2.02723	−	3.51127i	0.123146	−	0.213294i	−0.797861	−	0.602842i	$-0.794035\pi$
$271$	2.02723	−	3.51127i	0.123146	−	0.213294i	0.921007	+	0.389547i	$0.127368\pi$
$272$		0			0
$273$	14.5843	+	11.0675i	0.882684	+	0.669834i
$274$		0			0
$275$	0.434706	+	6.63233i	0.0262138	+	0.399945i
$276$		0			0
$277$	−5.80002	−	17.0863i	−0.348489	−	1.02662i	−0.969978	−	0.243193i	$-0.921805\pi$
$277$	−5.80002	−	17.0863i	−0.348489	−	1.02662i	0.621488	−	0.783423i	$-0.286528\pi$
$278$		0			0
$279$	3.41489	+	17.1678i	0.204444	+	1.02781i
$280$		0			0
$281$	−11.7785	+	28.4358i	−0.702647	+	1.69634i	0.0149557	+	0.999888i	$0.495239\pi$
$281$	−11.7785	+	28.4358i	−0.702647	+	1.69634i	−0.717603	+	0.696452i	$0.754761\pi$
$282$		0			0
$283$	−0.222751	+	3.39853i	−0.0132412	+	0.202021i	0.986113	+	0.166078i	$0.0531103\pi$
$283$	−0.222751	+	3.39853i	−0.0132412	+	0.202021i	−0.999354	+	0.0359436i	$0.988556\pi$
$284$		0			0
$285$	−0.111308	−	0.415407i	−0.00659331	−	0.0246066i
$286$		0			0
$287$	−13.1018	−	12.9623i	−0.773375	−	0.765142i
$288$		0			0
$289$	−10.0671	−	13.6987i	−0.592180	−	0.805806i
$290$		0			0
$291$	5.09789	−	6.64370i	0.298844	−	0.389461i
$292$		0			0
$293$	−5.30636	−	5.30636i	−0.310001	−	0.310001i	0.534909	−	0.844910i	$-0.320346\pi$
$293$	−5.30636	−	5.30636i	−0.310001	−	0.310001i	−0.844910	+	0.534909i	$0.820346\pi$
$294$		0			0
$295$	1.04899	+	0.700911i	0.0610744	+	0.0408086i
$296$		0			0
$297$	−6.96754	+	0.917294i	−0.404298	+	0.0532268i
$298$		0			0
$299$	11.1534	−	32.8567i	0.645015	−	1.90015i
$300$		0			0
$301$	3.29139	+	16.0963i	0.189713	+	0.927776i
$302$		0			0
$303$	1.29217	−	0.0846932i	0.0742332	−	0.00486550i
$304$		0			0
$305$	−0.532576	+	0.307483i	−0.0304952	+	0.0176064i
$306$		0			0
$307$			8.00859i			0.457074i	0.973535	+	0.228537i	$0.0733942\pi$
$307$			8.00859i			0.457074i	−0.973535	+	0.228537i	$0.926606\pi$
$308$		0			0
$309$	3.25878	−	2.17744i	0.185385	−	0.123870i
$310$		0			0
$311$	8.62267	−	2.92700i	0.488947	−	0.165975i	−0.0660689	−	0.997815i	$-0.521046\pi$
$311$	8.62267	−	2.92700i	0.488947	−	0.165975i	0.555015	+	0.831840i	$0.312712\pi$
$312$		0			0
$313$	20.8171	+	7.06647i	1.17665	+	0.399420i	0.840199	−	0.542279i	$-0.182438\pi$
$313$	20.8171	+	7.06647i	1.17665	+	0.399420i	0.336456	+	0.941699i	$0.390772\pi$
$314$		0			0
$315$	0.253050	+	0.432929i	0.0142578	+	0.0243928i
$316$		0			0
$317$	−11.6551	−	23.6342i	−0.654614	−	1.32743i	−0.930520	−	0.366242i	$-0.880644\pi$
$317$	−11.6551	−	23.6342i	−0.654614	−	1.32743i	0.275905	−	0.961185i	$-0.411022\pi$
$318$		0			0
$319$	0.0709486	−	0.264784i	0.00397236	−	0.0148250i
$320$		0			0
$321$	−2.92975	−	7.07303i	−0.163523	−	0.394778i
$322$		0			0
$323$	12.5044	+	8.54403i	0.695764	+	0.475403i
$324$		0			0
$325$	−24.8427	−	19.0625i	−1.37802	−	1.05740i
$326$		0			0
$327$	16.3403	−	4.37837i	0.903620	−	0.242124i
$328$		0			0
$329$	−11.3188	−	9.81967i	−0.624026	−	0.541376i
$330$		0			0
$331$	12.1335	−	9.31034i	0.666916	−	0.511743i	−0.218919	−	0.975743i	$-0.570253\pi$
$331$	12.1335	−	9.31034i	0.666916	−	0.511743i	0.885835	+	0.464000i	$0.153586\pi$
$332$		0			0
$333$	5.08780	−	4.46188i	0.278810	−	0.244510i
$334$		0			0
$335$	0.334927	+	0.0666211i	0.0182990	+	0.00363990i
$336$		0			0
$337$	13.0943	+	19.5970i	0.713290	+	1.06751i	0.994176	+	0.107773i	$0.0343719\pi$
$337$	13.0943	+	19.5970i	0.713290	+	1.06751i	−0.280885	+	0.959741i	$0.590628\pi$
$338$		0			0
$339$	4.11063	+	7.11982i	0.223259	+	0.386695i
$340$		0			0
$341$	−11.3170	−	6.53388i	−0.612851	−	0.353830i
$342$		0			0
$343$	3.90424	+	18.1041i	0.210809	+	0.977527i
$344$		0			0
$345$	−0.426748	+	0.486612i	−0.0229753	+	0.0261983i
$346$		0			0
$347$	−17.2258	−	19.6423i	−0.924732	−	1.05445i	−0.998365	−	0.0571688i	$-0.981793\pi$
$347$	−17.2258	−	19.6423i	−0.924732	−	1.05445i	0.0736330	−	0.997285i	$-0.476541\pi$
$348$		0			0
$349$	1.56167	+	0.646865i	0.0835943	+	0.0346259i	0.424089	−	0.905621i	$-0.360594\pi$
$349$	1.56167	+	0.646865i	0.0835943	+	0.0346259i	−0.340494	+	0.940247i	$0.610594\pi$
$350$		0			0
$351$	18.3944	−	27.5291i	0.981818	−	1.46939i
$352$		0			0
$353$	−19.5886	−	5.24875i	−1.04260	−	0.279363i	−0.303407	−	0.952861i	$-0.598124\pi$
$353$	−19.5886	−	5.24875i	−1.04260	−	0.279363i	−0.739189	+	0.673498i	$0.764791\pi$
$354$		0			0
$355$	0.387125	+	0.0509660i	0.0205465	+	0.00270499i
$356$		0			0
$357$	11.3684	+	3.92278i	0.601681	+	0.207616i
$358$		0			0
$359$	−26.1478	−	3.44242i	−1.38003	−	0.181684i	−0.596286	−	0.802772i	$-0.703358\pi$
$359$	−26.1478	−	3.44242i	−1.38003	−	0.181684i	−0.783741	+	0.621088i	$0.786691\pi$
$360$		0			0
$361$	5.32050	+	1.42562i	0.280026	+	0.0750328i
$362$		0			0
$363$	−5.65011	+	8.45598i	−0.296554	+	0.443824i
$364$		0			0
$365$	1.12691	+	0.466780i	0.0589850	+	0.0244324i
$366$		0			0
$367$	7.25447	+	8.27214i	0.378680	+	0.431802i	0.909514	−	0.415674i	$-0.136454\pi$
$367$	7.25447	+	8.27214i	0.378680	+	0.431802i	−0.530833	+	0.847476i	$0.678121\pi$
$368$		0			0
$369$	−8.19684	+	9.34670i	−0.426710	+	0.486570i
$370$		0			0
$371$	−1.20567	+	20.0373i	−0.0625953	+	1.04028i
$372$		0			0
$373$	16.8343	+	9.71932i	0.871650	+	0.503247i	0.867896	−	0.496746i	$-0.165472\pi$
$373$	16.8343	+	9.71932i	0.871650	+	0.503247i	0.00375349	+	0.999993i	$0.498805\pi$
$374$		0			0
$375$	0.584755	+	1.01283i	0.0301966	+	0.0523021i
$376$		0			0
$377$	0.717499	+	1.07381i	0.0369531	+	0.0553042i
$378$		0			0
$379$	0.401823	+	0.0799275i	0.0206402	+	0.00410560i	0.205400	−	0.978678i	$-0.434151\pi$
$379$	0.401823	+	0.0799275i	0.0206402	+	0.00410560i	−0.184759	+	0.982784i	$0.559151\pi$
$380$		0			0
$381$	10.8594	−	9.52340i	0.556342	−	0.487899i
$382$		0			0
$383$	5.67784	−	4.35676i	0.290124	−	0.222620i	−0.453436	−	0.891289i	$-0.649802\pi$
$383$	5.67784	−	4.35676i	0.290124	−	0.222620i	0.743561	+	0.668668i	$0.233135\pi$
$384$		0			0
$385$	−0.367558	−	0.0710695i	−0.0187325	−	0.00362203i
$386$		0			0
$387$	10.7044	−	2.86824i	0.544137	−	0.145801i
$388$		0			0
$389$	−15.2120	−	11.6726i	−0.771279	−	0.591823i	0.146363	−	0.989231i	$-0.453243\pi$
$389$	−15.2120	−	11.6726i	−0.771279	−	0.591823i	−0.917642	+	0.397408i	$0.869910\pi$
$390$		0			0
$391$	0.236315	−	22.7911i	0.0119510	−	1.15259i
$392$		0			0
$393$	7.66998	+	18.5170i	0.386899	+	0.934058i
$394$		0			0
$395$	0.241585	−	0.901609i	0.0121555	−	0.0453649i
$396$		0			0
$397$	2.10167	+	4.26177i	0.105480	+	0.213892i	0.943214	−	0.332187i	$-0.107787\pi$
$397$	2.10167	+	4.26177i	0.105480	+	0.213892i	−0.837734	+	0.546079i	$0.816120\pi$
$398$		0			0
$399$	−10.7135	+	0.0573286i	−0.536347	+	0.00287002i
$400$		0			0
$401$	6.52043	+	2.21339i	0.325615	+	0.110531i	0.479460	−	0.877564i	$-0.340833\pi$
$401$	6.52043	+	2.21339i	0.325615	+	0.110531i	−0.153846	+	0.988095i	$0.549166\pi$
$402$		0			0
$403$	58.2981	−	19.7895i	2.90403	−	0.985787i
$404$		0			0
$405$	−0.0407283	+	0.0272138i	−0.00202380	+	0.00135226i
$406$		0			0
$407$			5.05202i			0.250419i
$408$		0			0
$409$	−23.0746	+	13.3221i	−1.14097	+	0.658737i	−0.946669	−	0.322206i	$-0.895576\pi$
$409$	−23.0746	+	13.3221i	−1.14097	+	0.658737i	−0.194296	+	0.980943i	$0.562242\pi$
$410$		0			0
$411$	−11.0672	+	0.725385i	−0.545907	+	0.0357806i
$412$		0			0
$413$	23.5185	−	20.8488i	1.15727	−	1.02590i
$414$		0			0
$415$	−0.582725	+	1.71665i	−0.0286049	+	0.0842672i
$416$		0			0
$417$	−5.48050	+	0.721522i	−0.268381	+	0.0353331i
$418$		0			0
$419$	−14.1928	−	9.48332i	−0.693363	−	0.463290i	0.158293	−	0.987392i	$-0.449401\pi$
$419$	−14.1928	−	9.48332i	−0.693363	−	0.463290i	−0.851656	+	0.524102i	$0.824401\pi$
$420$		0			0
$421$	19.8696	+	19.8696i	0.968386	+	0.968386i	0.999515	−	0.0311292i	$-0.00991033\pi$
$421$	19.8696	+	19.8696i	0.968386	+	0.968386i	−0.0311292	+	0.999515i	$0.509910\pi$
$422$		0			0
$423$	−6.15310	+	8.01887i	−0.299174	+	0.389891i
$424$		0			0
$425$	−19.4078	−	6.81329i	−0.941418	−	0.330493i
$426$		0			0
$427$	4.04425	+	14.7766i	0.195715	+	0.715090i
$428$		0			0
$429$	2.38617	+	8.90532i	0.115205	+	0.429953i
$430$		0			0
$431$	−0.309093	+	4.71585i	−0.0148885	+	0.227155i	0.983930	+	0.178555i	$0.0571424\pi$
$431$	−0.309093	+	4.71585i	−0.0148885	+	0.227155i	−0.998818	+	0.0485992i	$0.984524\pi$
$432$		0			0
$433$	−0.788886	+	1.90454i	−0.0379115	+	0.0915264i	−0.941701	−	0.336450i	$-0.890774\pi$
$433$	−0.788886	+	1.90454i	−0.0379115	+	0.0915264i	0.903790	+	0.427977i	$0.140774\pi$
$434$		0			0
$435$	−0.00469970	−	0.0236270i	−0.000225333	−	0.00113283i
$436$		0			0
$437$	6.52676	+	19.2272i	0.312217	+	0.919763i
$438$		0			0
$439$	0.467074	+	7.12617i	0.0222922	+	0.340114i	0.994408	+	0.105610i	$0.0336796\pi$
$439$	0.467074	+	7.12617i	0.0222922	+	0.340114i	−0.972115	+	0.234503i	$0.924654\pi$
$440$		0			0
$441$	12.0314	−	3.36222i	0.572925	−	0.160106i
$442$		0			0
$443$	7.45460	−	12.9117i	0.354179	−	0.613456i	−0.632798	−	0.774317i	$-0.718094\pi$
$443$	7.45460	−	12.9117i	0.354179	−	0.613456i	0.986977	+	0.160861i	$0.0514271\pi$
$444$		0			0
$445$	−0.478059	−	0.235752i	−0.0226621	−	0.0111757i
$446$		0			0
$447$	1.98217	−	9.96504i	0.0937534	−	0.471330i
$448$		0			0
$449$	2.87539	−	0.571951i	0.135698	−	0.0269921i	−0.126774	−	0.991932i	$-0.540462\pi$
$449$	2.87539	−	0.571951i	0.135698	−	0.0269921i	0.262472	+	0.964940i	$0.415462\pi$
$450$		0			0
$451$	−1.21141	−	9.20157i	−0.0570431	−	0.433285i
$452$		0			0
$453$	−24.0896	+	11.8797i	−1.13183	+	0.558155i
$454$		0			0
$455$	1.39349	−	1.08116i	0.0653280	−	0.0506856i
$456$		0			0
$457$	4.73133	−	35.9380i	0.221322	−	1.68111i	−0.415107	−	0.909773i	$-0.636256\pi$
$457$	4.73133	−	35.9380i	0.221322	−	1.68111i	0.636429	−	0.771335i	$-0.280411\pi$
$458$		0			0
$459$	5.84641	−	20.9478i	0.272887	−	0.977762i
$460$		0			0
$461$	11.0626	−	4.58229i	0.515238	−	0.213418i	−0.109886	−	0.993944i	$-0.535049\pi$
$461$	11.0626	−	4.58229i	0.515238	−	0.213418i	0.625124	+	0.780526i	$0.285049\pi$
$462$		0			0
$463$	3.48279	−	3.48279i	0.161859	−	0.161859i	−0.621531	−	0.783390i	$-0.713489\pi$
$463$	3.48279	−	3.48279i	0.161859	−	0.161859i	0.783390	+	0.621531i	$0.213489\pi$
$464$		0			0
$465$	−1.14593	−	0.0751080i	−0.0531411	−	0.00348305i
$466$		0			0
$467$	−16.2660	−	21.1982i	−0.752700	−	0.980938i	−0.999928	−	0.0119805i	$-0.996186\pi$
$467$	−16.2660	−	21.1982i	−0.752700	−	0.980938i	0.247228	−	0.968957i	$-0.420480\pi$
$468$		0			0
$469$	3.72175	−	7.64988i	0.171854	−	0.353239i
$470$		0			0
$471$	14.6373	+	12.8366i	0.674452	+	0.591478i
$472$		0			0
$473$	−3.65920	+	7.42012i	−0.168250	+	0.341178i
$474$		0			0
$475$	18.3242			0.840771
$476$		0			0
$477$	13.5401			0.619959
$478$		0			0
$479$	−1.78535	+	3.62034i	−0.0815748	+	0.165417i	−0.933838	−	0.357695i	$-0.883563\pi$
$479$	−1.78535	+	3.62034i	−0.0815748	+	0.165417i	0.852264	+	0.523113i	$0.175229\pi$
$480$		0			0
$481$	−17.8947	−	15.6933i	−0.815930	−	0.715552i
$482$		0			0
$483$	9.02951	+	13.3583i	0.410857	+	0.607825i
$484$		0			0
$485$	−0.491106	−	0.640022i	−0.0223000	−	0.0290619i
$486$		0			0
$487$	9.94879	+	0.652078i	0.450823	+	0.0295485i	0.289124	−	0.957292i	$-0.406636\pi$
$487$	9.94879	+	0.652078i	0.450823	+	0.0295485i	0.161699	+	0.986840i	$0.448303\pi$
$488$		0			0
$489$	6.06804	−	6.06804i	0.274406	−	0.274406i
$490$		0			0
$491$	−16.7169	+	6.92437i	−0.754424	+	0.312492i	−0.726545	−	0.687119i	$-0.758875\pi$
$491$	−16.7169	+	6.92437i	−0.754424	+	0.312492i	−0.0278785	+	0.999611i	$0.508875\pi$
$492$		0			0
$493$	0.667634	+	0.523380i	0.0300687	+	0.0235718i
$494$		0			0
$495$	−0.0329604	+	0.250359i	−0.00148146	+	0.0112528i
$496$		0			0
$497$	3.67433	−	9.00663i	0.164816	−	0.404003i
$498$		0			0
$499$	10.6461	−	5.25007i	0.476585	−	0.235025i	−0.188100	−	0.982150i	$-0.560233\pi$
$499$	10.6461	−	5.25007i	0.476585	−	0.235025i	0.664684	+	0.747124i	$0.268566\pi$
$500$		0			0
$501$	2.61988	+	19.9000i	0.117048	+	0.889065i
$502$		0			0
$503$	14.9914	−	2.98198i	0.668434	−	0.132960i	0.150803	−	0.988564i	$-0.451814\pi$
$503$	14.9914	−	2.98198i	0.668434	−	0.132960i	0.517631	+	0.855604i	$0.326814\pi$
$504$		0			0
$505$	0.0243372	−	0.122351i	0.00108299	−	0.00544457i
$506$		0			0
$507$	−26.1020	−	12.8721i	−1.15923	−	0.571669i
$508$		0			0
$509$	12.2938	−	21.2934i	0.544911	−	0.943814i	−0.453701	−	0.891154i	$-0.649897\pi$
$509$	12.2938	−	21.2934i	0.544911	−	0.943814i	0.998613	−	0.0526599i	$-0.0167699\pi$
$510$		0			0
$511$	18.3689	−	24.2059i	0.812593	−	1.07081i
$512$		0			0
$513$	1.26717	+	19.3334i	0.0559471	+	0.853588i
$514$		0			0
$515$	−0.121365	−	0.357529i	−0.00534797	−	0.0157546i
$516$		0			0
$517$	−1.47212	−	7.40084i	−0.0647437	−	0.325488i
$518$		0			0
$519$	1.23394	−	2.97899i	0.0541639	−	0.130763i
$520$		0			0
$521$	−1.14939	+	17.5363i	−0.0503558	+	0.768281i	0.895777	+	0.444503i	$0.146620\pi$
$521$	−1.14939	+	17.5363i	−0.0503558	+	0.768281i	−0.946133	+	0.323778i	$0.895047\pi$
$522$		0			0
$523$	8.69895	+	32.4649i	0.380379	+	1.41959i	0.845324	+	0.534253i	$0.179407\pi$
$523$	8.69895	+	32.4649i	0.380379	+	1.41959i	−0.464946	+	0.885339i	$0.653926\pi$
$524$		0			0
$525$	14.0348	−	3.84123i	0.612530	−	0.167645i
$526$		0			0
$527$	32.3372	−	24.2847i	1.40863	−	1.05786i
$528$		0			0
$529$	4.60111	−	5.99628i	0.200048	−	0.260708i
$530$		0			0
$531$	−14.9905	−	14.9905i	−0.650533	−	0.650533i
$532$		0			0
$533$	36.3559	+	24.2922i	1.57475	+	1.05221i
$534$		0			0
$535$	−0.731213	+	0.0962660i	−0.0316131	+	0.00416194i
$536$		0			0
$537$	1.53119	−	4.51073i	0.0660756	−	0.194653i
$538$		0			0
$539$	−4.03513	+	8.40810i	−0.173806	+	0.362163i
$540$		0			0
$541$	7.53839	−	0.494092i	0.324101	−	0.0212427i	0.0975155	−	0.995234i	$-0.468910\pi$
$541$	7.53839	−	0.494092i	0.324101	−	0.0212427i	0.226585	+	0.973991i	$0.427244\pi$
$542$		0			0
$543$	17.1911	−	9.92527i	0.737740	−	0.425934i
$544$		0			0
$545$		−	1.62967i		−	0.0698076i
$546$		0			0
$547$	21.8915	−	14.6275i	0.936015	−	0.625425i	0.00880229	−	0.999961i	$-0.497198\pi$
$547$	21.8915	−	14.6275i	0.936015	−	0.625425i	0.927212	+	0.374536i	$0.122198\pi$
$548$		0			0
$549$	9.78536	−	3.32168i	0.417629	−	0.141766i
$550$		0			0
$551$	−0.715637	−	0.242926i	−0.0304872	−	0.0103490i
$552$		0			0
$553$	−20.1998	−	11.5187i	−0.858984	−	0.489825i
$554$		0			0
$555$	0.196362	+	0.398183i	0.00833511	+	0.0169019i
$556$		0			0
$557$	5.02982	−	18.7716i	0.213120	−	0.795376i	−0.773699	−	0.633553i	$-0.781596\pi$
$557$	5.02982	−	18.7716i	0.213120	−	0.795376i	0.986820	−	0.161823i	$-0.0517375\pi$
$558$		0			0
$559$	−14.9161	−	36.0106i	−0.630883	−	1.52309i
$560$		0			0
$561$	3.31215	+	5.07001i	0.139839	+	0.214056i
$562$		0			0
$563$	19.6376	+	15.0685i	0.827628	+	0.635061i	0.933203	−	0.359350i	$-0.117002\pi$
$563$	19.6376	+	15.0685i	0.827628	+	0.635061i	−0.105575	+	0.994411i	$0.533668\pi$
$564$		0			0
$565$	0.765010	−	0.204984i	0.0321842	−	0.00862373i
$566$		0			0
$567$	0.398423	+	1.15340i	0.0167322	+	0.0484384i
$568$		0			0
$569$	21.5840	−	16.5620i	0.904847	−	0.694313i	−0.0476495	−	0.998864i	$-0.515173\pi$
$569$	21.5840	−	16.5620i	0.904847	−	0.694313i	0.952496	+	0.304551i	$0.0985064\pi$
$570$		0			0
$571$	−6.42183	+	5.63180i	−0.268745	+	0.235683i	−0.783102	−	0.621893i	$-0.786364\pi$
$571$	−6.42183	+	5.63180i	−0.268745	+	0.235683i	0.514357	+	0.857576i	$0.328031\pi$
$572$		0			0
$573$	2.35164	+	0.467771i	0.0982412	+	0.0195414i
$574$		0			0
$575$	−15.3212	−	22.9297i	−0.638937	−	0.956236i
$576$		0			0
$577$	7.30896	+	12.6595i	0.304276	+	0.527022i	0.977100	−	0.212781i	$-0.0682521\pi$
$577$	7.30896	+	12.6595i	0.304276	+	0.527022i	−0.672824	+	0.739803i	$0.734919\pi$
$578$		0			0
$579$	17.6513	+	10.1910i	0.733561	+	0.423522i
$580$		0			0
$581$	37.6846	+	24.8894i	1.56342	+	1.03259i
$582$		0			0
$583$	−6.66494	+	7.59990i	−0.276033	+	0.314756i
$584$		0			0
$585$	−0.784411	−	0.894449i	−0.0324314	−	0.0369809i
$586$		0			0
$587$	18.8298	+	7.79956i	0.777189	+	0.321922i	0.735781	−	0.677220i	$-0.236815\pi$
$587$	18.8298	+	7.79956i	0.777189	+	0.321922i	0.0414086	+	0.999142i	$0.486815\pi$
$588$		0			0
$589$	−20.0156	+	29.9554i	−0.824726	+	1.23429i
$590$		0			0
$591$	26.1560	+	7.00849i	1.07592	+	0.288291i
$592$		0			0
$593$	−3.27743	−	0.431482i	−0.134588	−	0.0177188i	0.0629312	−	0.998018i	$-0.479955\pi$
$593$	−3.27743	−	0.431482i	−0.134588	−	0.0177188i	−0.197519	+	0.980299i	$0.563288\pi$
$594$		0			0
$595$	0.648479	−	0.960054i	0.0265850	−	0.0393584i
$596$		0			0
$597$	−26.8199	−	3.53091i	−1.09767	−	0.144511i
$598$		0			0
$599$	11.3776	+	3.04861i	0.464875	+	0.124563i	0.483651	−	0.875261i	$-0.339310\pi$
$599$	11.3776	+	3.04861i	0.464875	+	0.124563i	−0.0187761	+	0.999824i	$0.505977\pi$
$600$		0			0
$601$	−23.8253	+	35.6571i	−0.971855	+	1.45448i	−0.0828626	+	0.996561i	$0.526406\pi$
$601$	−23.8253	+	35.6571i	−0.971855	+	1.45448i	−0.888992	+	0.457922i	$0.848594\pi$
$602$		0			0
$603$	−5.30151	−	2.19596i	−0.215894	−	0.0894263i
$604$		0			0
$605$	0.645975	+	0.736594i	0.0262626	+	0.0299468i
$606$		0			0
$607$	5.17096	−	5.89635i	0.209883	−	0.239326i	−0.637314	−	0.770604i	$-0.719955\pi$
$607$	5.17096	−	5.89635i	0.209883	−	0.239326i	0.847197	+	0.531278i	$0.178288\pi$
$608$		0			0
$609$	−0.599044	−	0.0360452i	−0.0242745	−	0.00146063i
$610$		0			0
$611$	30.7874	+	17.7751i	1.24552	+	0.719103i
$612$		0			0
$613$	−23.1545	−	40.1048i	−0.935202	−	1.61982i	−0.774273	−	0.632851i	$-0.781884\pi$
$613$	−23.1545	−	40.1048i	−0.935202	−	1.61982i	−0.160928	−	0.986966i	$-0.551449\pi$
$614$		0			0
$615$	−0.453126	−	0.678151i	−0.0182718	−	0.0273457i
$616$		0			0
$617$	−38.2011	−	7.59868i	−1.53792	−	0.305911i	−0.647862	−	0.761758i	$-0.724337\pi$
$617$	−38.2011	−	7.59868i	−1.53792	−	0.305911i	−0.890058	+	0.455846i	$0.849337\pi$
$618$		0			0
$619$	−17.0575	+	14.9591i	−0.685600	+	0.601255i	−0.929622	−	0.368515i	$-0.879866\pi$
$619$	−17.0575	+	14.9591i	−0.685600	+	0.601255i	0.244022	+	0.969770i	$0.421533\pi$
$620$		0			0
$621$	23.1331	−	17.7506i	0.928298	−	0.712308i
$622$		0			0
$623$	−8.70179	+	10.0303i	−0.348630	+	0.401854i
$624$		0			0
$625$	−23.9848	+	6.42672i	−0.959394	+	0.257069i
$626$		0			0
$627$	−4.28020	−	3.28432i	−0.170935	−	0.131163i
$628$		0			0
$629$	−14.3815	−	6.13247i	−0.573428	−	0.244518i
$630$		0			0
$631$	−9.93277	−	23.9798i	−0.395417	−	0.954622i	−0.988738	−	0.149656i	$-0.952183\pi$
$631$	−9.93277	−	23.9798i	−0.395417	−	0.954622i	0.593321	−	0.804966i	$-0.297817\pi$
$632$		0			0
$633$	4.68987	−	17.5028i	0.186406	−	0.695675i
$634$		0			0
$635$	−0.615417	−	1.24794i	−0.0244221	−	0.0495231i
$636$		0			0
$637$	−17.2478	−	40.4112i	−0.683384	−	1.60115i
$638$		0			0
$639$	−6.21310	−	2.10906i	−0.245786	−	0.0834332i
$640$		0			0
$641$	−35.3623	+	12.0039i	−1.39673	+	0.474125i	−0.915446	−	0.402441i	$-0.868162\pi$
$641$	−35.3623	+	12.0039i	−1.39673	+	0.474125i	−0.481281	+	0.876566i	$0.659828\pi$
$642$		0			0
$643$	−14.5483	+	9.72087i	−0.573729	+	0.383354i	−0.808322	−	0.588740i	$-0.799624\pi$
$643$	−14.5483	+	9.72087i	−0.573729	+	0.383354i	0.234593	+	0.972094i	$0.424624\pi$
$644$		0			0
$645$			0.727054i			0.0286277i
$646$		0			0
$647$	−23.8966	+	13.7967i	−0.939473	+	0.542405i	−0.889795	−	0.456361i	$-0.849153\pi$
$647$	−23.8966	+	13.7967i	−0.939473	+	0.542405i	−0.0496776	+	0.998765i	$0.515819\pi$
$648$		0			0
$649$	15.7929	−	1.03512i	0.619925	−	0.0406320i
$650$		0			0
$651$	−9.05085	+	27.1392i	−0.354731	+	1.06367i
$652$		0			0
$653$	−5.11048	+	15.0550i	−0.199988	+	0.589147i	−0.999940	−	0.0109172i	$-0.996525\pi$
$653$	−5.11048	+	15.0550i	−0.199988	+	0.589147i	0.799952	+	0.600064i	$0.204858\pi$
$654$		0			0
$655$	1.91429	−	0.252021i	0.0747976	−	0.00984729i
$656$		0			0
$657$	−17.0422	−	11.3873i	−0.664881	−	0.444259i
$658$		0			0
$659$	−0.291923	−	0.291923i	−0.0113717	−	0.0113717i	0.701398	−	0.712770i	$-0.252560\pi$
$659$	−0.291923	−	0.291923i	−0.0113717	−	0.0113717i	−0.712770	+	0.701398i	$0.752560\pi$
$660$		0			0
$661$	13.6701	−	17.8152i	0.531704	−	0.692930i	−0.447851	−	0.894108i	$-0.647811\pi$
$661$	13.6701	−	17.8152i	0.531704	−	0.692930i	0.979555	+	0.201179i	$0.0644772\pi$
$662$		0			0
$663$	−28.2471	−	4.01717i	−1.09703	−	0.156014i
$664$		0			0
$665$	−0.261790	+	0.998352i	−0.0101518	+	0.0387144i
$666$		0			0
$667$	0.294374	+	1.09862i	0.0113982	+	0.0425387i
$668$		0			0
$669$	−0.940385	+	14.3475i	−0.0363574	+	0.554706i
$670$		0			0
$671$	−2.95229	+	7.12746i	−0.113972	+	0.275152i
$672$		0			0
$673$	−1.97794	−	9.94379i	−0.0762441	−	0.383305i	−1.00000		0.000323056i	$-0.999897\pi$
$673$	−1.97794	−	9.94379i	−0.0762441	−	0.383305i	0.923756	−	0.382982i	$-0.125103\pi$
$674$		0			0
$675$	−8.45846	−	24.9178i	−0.325566	−	0.959087i
$676$		0			0
$677$	2.11852	+	32.3224i	0.0814213	+	1.24225i	0.821688	+	0.569937i	$0.193032\pi$
$677$	2.11852	+	32.3224i	0.0814213	+	1.24225i	−0.740267	+	0.672313i	$0.765301\pi$
$678$		0			0
$679$	−18.5261	+	7.79015i	−0.710965	+	0.298958i
$680$		0			0
$681$	−12.2388	+	21.1982i	−0.468991	+	0.812316i
$682$		0			0
$683$	−31.5572	−	15.5623i	−1.20750	−	0.595475i	−0.276687	−	0.960960i	$-0.589236\pi$
$683$	−31.5572	−	15.5623i	−1.20750	−	0.595475i	−0.930817	+	0.365485i	$0.880903\pi$
$684$		0			0
$685$	−0.208445	+	1.04792i	−0.00796427	+	0.0400391i
$686$		0			0
$687$	0.315027	−	0.0626629i	0.0120190	−	0.00239074i
$688$		0			0
$689$	−6.21606	−	47.2157i	−0.236813	−	1.79877i
$690$		0			0
$691$	12.2396	−	6.03588i	0.465614	−	0.229616i	−0.194321	−	0.980938i	$-0.562250\pi$
$691$	12.2396	−	6.03588i	0.465614	−	0.229616i	0.659935	+	0.751322i	$0.270584\pi$
$692$		0			0
$693$	5.82472	+	2.37624i	0.221263	+	0.0902660i
$694$		0			0
$695$	−0.0695080	+	0.527965i	−0.00263659	+	0.0200269i
$696$		0			0
$697$	27.6645	+	7.72097i	1.04787	+	0.292452i
$698$		0			0
$699$	−30.2056	+	12.5116i	−1.14248	+	0.473231i
$700$		0			0
$701$	−32.2128	+	32.2128i	−1.21666	+	1.21666i	−0.247868	+	0.968794i	$0.579730\pi$
$701$	−32.2128	+	32.2128i	−1.21666	+	1.21666i	−0.968794	+	0.247868i	$0.920270\pi$
$702$		0			0
$703$	13.8983	+	0.910943i	0.524184	+	0.0343569i
$704$		0			0
$705$	−0.403683	−	0.526090i	−0.0152036	−	0.0198137i
$706$		0			0
$707$	−2.79456	−	1.35958i	−0.105100	−	0.0511324i
$708$		0			0
$709$	1.72766	+	1.51512i	0.0648838	+	0.0569015i	0.691174	−	0.722689i	$-0.257094\pi$
$709$	1.72766	+	1.51512i	0.0648838	+	0.0569015i	−0.626290	+	0.779590i	$0.715427\pi$
$710$		0			0
$711$	−6.93726	+	14.0674i	−0.260168	+	0.527568i
$712$		0			0
$713$	54.2197			2.03054
$714$		0			0
$715$	0.888159			0.0332152
$716$		0			0
$717$	−1.67709	+	3.40081i	−0.0626321	+	0.127005i
$718$		0			0
$719$	16.9166	+	14.8354i	0.630881	+	0.553268i	0.913948	−	0.405832i	$-0.133018\pi$
$719$	16.9166	+	14.8354i	0.630881	+	0.553268i	−0.283066	+	0.959100i	$0.591352\pi$
$720$		0			0
$721$	−9.38238	+	0.665393i	−0.349418	+	0.0247805i
$722$		0			0
$723$	−2.19280	−	2.85772i	−0.0815513	−	0.106280i
$724$		0			0
$725$	1.02423	+	0.0671316i	0.0380390	+	0.00249321i
$726$		0			0
$727$	−24.1821	+	24.1821i	−0.896864	+	0.896864i	−0.995157	−	0.0982935i	$-0.968662\pi$
$727$	−24.1821	+	24.1821i	−0.896864	+	0.896864i	0.0982935	+	0.995157i	$0.468662\pi$
$728$		0			0
$729$	16.8778	−	6.99102i	0.625105	−	0.258927i
$730$		0			0
$731$	−16.6810	−	19.4236i	−0.616968	−	0.718408i
$732$		0			0
$733$	1.25547	−	9.53627i	0.0463720	−	0.352230i	−0.952491	−	0.304565i	$-0.901489\pi$
$733$	1.25547	−	9.53627i	0.0463720	−	0.352230i	0.998863	−	0.0476648i	$-0.0151779\pi$
$734$		0			0
$735$	0.00877100	+	0.819535i	0.000323523	+	0.0302290i
$736$		0			0
$737$	3.84216	−	1.89474i	0.141528	−	0.0697938i
$738$		0			0
$739$	−3.30360	−	25.0933i	−0.121525	−	0.923073i	−0.938229	−	0.346016i	$-0.887534\pi$
$739$	−3.30360	−	25.0933i	−0.121525	−	0.923073i	0.816704	−	0.577057i	$-0.195799\pi$
$740$		0			0
$741$	24.9291	−	4.95871i	0.915794	−	0.182163i
$742$		0			0
$743$	0.878210	−	4.41506i	0.0322184	−	0.161973i	−0.961327	−	0.275410i	$-0.911186\pi$
$743$	0.878210	−	4.41506i	0.0322184	−	0.161973i	0.993545	+	0.113438i	$0.0361862\pi$
$744$		0			0
$745$	−0.877851	−	0.432908i	−0.0321620	−	0.0158605i
$746$		0			0
$747$	15.2315	−	26.3817i	0.557291	−	0.965257i
$748$		0			0
$749$	−2.30068	+	18.2286i	−0.0840649	+	0.666058i
$750$		0			0
$751$	−0.0651670	−	0.994256i	−0.00237798	−	0.0362809i	0.996505	−	0.0835328i	$-0.0266203\pi$
$751$	−0.0651670	−	0.994256i	−0.00237798	−	0.0362809i	−0.998883	+	0.0472519i	$0.984954\pi$
$752$		0			0
$753$	0.784643	+	2.31148i	0.0285940	+	0.0842352i
$754$		0			0
$755$	0.504799	+	2.53780i	0.0183715	+	0.0923599i
$756$		0			0
$757$	8.69911	−	21.0015i	0.316175	−	0.763313i	−0.683276	−	0.730161i	$-0.739445\pi$
$757$	8.69911	−	21.0015i	0.316175	−	0.763313i	0.999450	−	0.0331526i	$-0.0105547\pi$
$758$		0			0
$759$	−0.531037	+	8.10206i	−0.0192754	+	0.294086i
$760$		0			0
$761$	4.00113	+	14.9324i	0.145041	+	0.541300i	0.999754	+	0.0221984i	$0.00706656\pi$
$761$	4.00113	+	14.9324i	0.145041	+	0.541300i	−0.854713	+	0.519101i	$0.826267\pi$
$762$		0			0
$763$	−39.2708	−	10.2977i	−1.42170	−	0.372801i
$764$		0			0
$765$	−0.672684	−	0.397730i	−0.0243210	−	0.0143800i
$766$		0			0
$767$	−45.3915	+	59.1553i	−1.63899	+	2.13597i
$768$		0			0
$769$	28.7142	+	28.7142i	1.03546	+	1.03546i	0.999348	+	0.0361130i	$0.0114976\pi$
$769$	28.7142	+	28.7142i	1.03546	+	1.03546i	0.0361130	+	0.999348i	$0.488502\pi$
$770$		0			0
$771$	23.7791	+	15.8887i	0.856382	+	0.572216i
$772$		0			0
$773$	27.2977	−	3.59381i	0.981830	−	0.129260i	0.377513	−	0.926004i	$-0.376779\pi$
$773$	27.2977	−	3.59381i	0.981830	−	0.129260i	0.604317	+	0.796744i	$0.293446\pi$
$774$		0			0
$775$	15.7283	−	46.3341i	0.564977	−	1.66437i
$776$		0			0
$777$	10.8359	−	2.21574i	0.388737	−	0.0794893i
$778$		0			0
$779$	−25.5323	+	1.67347i	−0.914789	+	0.0599585i
$780$		0			0
$781$	4.24210	−	2.44918i	0.151794	−	0.0876386i
$782$		0			0
$783$			1.08528i			0.0387848i
$784$		0			0
$785$	1.55944	−	1.04198i	0.0556586	−	0.0371899i
$786$		0			0
$787$	11.5557	−	3.92265i	0.411918	−	0.139827i	−0.107785	−	0.994174i	$-0.534376\pi$
$787$	11.5557	−	3.92265i	0.411918	−	0.139827i	0.519703	+	0.854347i	$0.326043\pi$
$788$		0			0
$789$	−9.79658	−	3.32549i	−0.348768	−	0.118391i
$790$		0			0
$791$	−0.105576	−	19.7300i	−0.00375385	−	0.701517i
$792$		0			0
$793$	−16.0753	−	32.5975i	−0.570852	−	1.15757i
$794$		0			0
$795$	−0.229914	+	0.858051i	−0.00815421	+	0.0304319i
$796$		0			0
$797$	8.13758	+	19.6459i	0.288248	+	0.695892i	0.999978	−	0.00656064i	$-0.00208833\pi$
$797$	8.13758	+	19.6459i	0.288248	+	0.695892i	−0.711731	+	0.702452i	$0.752088\pi$
$798$		0			0
$799$	22.8548	+	4.79296i	0.808545	+	0.169563i
$800$		0			0
$801$	7.10599	+	5.45262i	0.251078	+	0.192659i
$802$		0			0
$803$	14.7803	−	3.96038i	0.521587	−	0.139759i
$804$		0			0
$805$	1.46816	−	0.507152i	0.0517460	−	0.0178748i
$806$		0			0
$807$	−7.91150	+	6.07071i	−0.278498	+	0.213699i
$808$		0			0
$809$	3.57202	−	3.13258i	0.125586	−	0.110136i	−0.594249	−	0.804281i	$-0.702551\pi$
$809$	3.57202	−	3.13258i	0.125586	−	0.110136i	0.719835	+	0.694145i	$0.244217\pi$
$810$		0			0
$811$	5.88089	+	1.16978i	0.206506	+	0.0410766i	0.297259	−	0.954797i	$-0.403927\pi$
$811$	5.88089	+	1.16978i	0.206506	+	0.0410766i	−0.0907532	+	0.995873i	$0.528927\pi$
$812$		0			0
$813$	−2.48329	−	3.71650i	−0.0870927	−	0.130343i
$814$		0			0
$815$	−0.413351	−	0.715944i	−0.0144790	−	0.0250784i
$816$		0			0
$817$	19.7532	+	11.4045i	0.691078	+	0.398994i
$818$		0			0
$819$	−26.5104	+	13.2503i	−0.926349	+	0.463003i
$820$		0			0
$821$	−27.2519	+	31.0748i	−0.951098	+	1.08452i	0.0452368	+	0.998976i	$0.485596\pi$
$821$	−27.2519	+	31.0748i	−0.951098	+	1.08452i	−0.996335	+	0.0855427i	$0.972738\pi$
$822$		0			0
$823$	9.48280	+	10.8131i	0.330550	+	0.376920i	0.893111	−	0.449836i	$-0.148517\pi$
$823$	9.48280	+	10.8131i	0.330550	+	0.376920i	−0.562562	+	0.826755i	$0.690184\pi$
$824$		0			0
$825$	6.76967	+	2.80409i	0.235689	+	0.0976258i
$826$		0			0
$827$	−2.91213	+	4.35831i	−0.101265	+	0.151553i	−0.878642	−	0.477482i	$-0.841550\pi$
$827$	−2.91213	+	4.35831i	−0.101265	+	0.151553i	0.777377	+	0.629035i	$0.216550\pi$
$828$		0			0
$829$	−52.6236	−	14.1004i	−1.82769	−	0.489729i	−0.830009	−	0.557750i	$-0.811665\pi$
$829$	−52.6236	−	14.1004i	−1.82769	−	0.489729i	−0.997684	+	0.0680214i	$0.978331\pi$
$830$		0			0
$831$	−19.7221	−	2.59647i	−0.684153	−	0.0900704i
$832$		0			0
$833$	−19.0371	−	21.6931i	−0.659597	−	0.751620i
$834$		0			0
$835$	1.91707	+	0.252387i	0.0663428	+	0.00873420i
$836$		0			0
$837$	49.9735	+	13.3904i	1.72734	+	0.462839i
$838$		0			0
$839$	−11.1168	+	16.6375i	−0.383796	+	0.574391i	−0.972193	−	0.234181i	$-0.924759\pi$
$839$	−11.1168	+	16.6375i	−0.383796	+	0.574391i	0.588397	+	0.808572i	$0.299759\pi$
$840$		0			0
$841$	26.7534	+	11.0816i	0.922531	+	0.382125i
$842$		0			0
$843$	22.3727	+	25.5112i	0.770557	+	0.878652i
$844$		0			0
$845$	−1.84859	+	2.10792i	−0.0635935	+	0.0725145i
$846$		0			0
$847$	21.8318	−	10.9119i	0.750149	−	0.374936i
$848$		0			0
$849$	3.25167	+	1.87735i	0.111597	+	0.0644306i
$850$		0			0
$851$	−10.4807	−	18.1531i	−0.359274	−	0.622281i
$852$		0			0
$853$	−6.92031	−	10.3570i	−0.236947	−	0.354616i	0.693871	−	0.720099i	$-0.255904\pi$
$853$	−6.92031	−	10.3570i	−0.236947	−	0.354616i	−0.930818	+	0.365483i	$0.880904\pi$
$854$		0			0
$855$	0.682805	+	0.135818i	0.0233514	+	0.00464489i
$856$		0			0
$857$	−0.601860	+	0.527817i	−0.0205591	+	0.0180299i	−0.669564	−	0.742755i	$-0.733519\pi$
$857$	−0.601860	+	0.527817i	−0.0205591	+	0.0180299i	0.649005	+	0.760784i	$0.275186\pi$
$858$		0			0
$859$	−42.5997	+	32.6879i	−1.45348	+	1.11530i	−0.482570	+	0.875857i	$0.660297\pi$
$859$	−42.5997	+	32.6879i	−1.45348	+	1.11530i	−0.970912	+	0.239438i	$0.923037\pi$
$860$		0			0
$861$	−19.2049	+	6.63399i	−0.654500	+	0.226086i
$862$		0			0
$863$	11.7249	−	3.14168i	0.399120	−	0.106944i	−0.0536751	−	0.998558i	$-0.517094\pi$
$863$	11.7249	−	3.14168i	0.399120	−	0.106944i	0.452795	+	0.891615i	$0.350427\pi$
$864$		0			0
$865$	−0.246437	−	0.189098i	−0.00837911	−	0.00642951i
$866$		0			0
$867$	−18.4532	+	3.27435i	−0.626704	+	0.111203i
$868$		0			0
$869$	−4.48108	−	10.8183i	−0.152010	−	0.366985i
$870$		0			0
$871$	−5.22367	+	19.4950i	−0.176997	+	0.660563i
$872$		0			0
$873$	5.99573	+	12.1581i	0.202925	+	0.411491i
$874$		0			0
$875$	−0.0150187	−	2.80668i	−0.000507724	−	0.0948830i
$876$		0			0
$877$	−6.97049	−	2.36616i	−0.235377	−	0.0798996i	0.201259	−	0.979538i	$-0.435497\pi$
$877$	−6.97049	−	2.36616i	−0.235377	−	0.0798996i	−0.436636	+	0.899638i	$0.643830\pi$
$878$		0			0
$879$	−7.83402	+	2.65929i	−0.264235	+	0.0896957i
$880$		0			0
$881$	−6.61380	+	4.41920i	−0.222825	+	0.148887i	−0.661973	−	0.749528i	$-0.730280\pi$
$881$	−6.61380	+	4.41920i	−0.222825	+	0.148887i	0.439148	+	0.898415i	$0.355280\pi$
$882$		0			0
$883$			39.6083i			1.33293i	0.745538	+	0.666463i	$0.232192\pi$
$883$			39.6083i			1.33293i	−0.745538	+	0.666463i	$0.767808\pi$
$884$		0			0
$885$	1.20451	−	0.695422i	0.0404890	−	0.0233764i
$886$		0			0
$887$	−43.9138	+	2.87826i	−1.47448	+	0.0966426i	−0.781316	−	0.624136i	$-0.785451\pi$
$887$	−43.9138	+	2.87826i	−1.47448	+	0.0966426i	−0.693165	+	0.720779i	$0.743784\pi$
$888$		0			0
$889$	−33.9608	+	6.94435i	−1.13901	+	0.232906i
$890$		0			0
$891$	−0.197523	+	0.581883i	−0.00661726	+	0.0194938i
$892$		0			0
$893$	−20.6254	+	2.71539i	−0.690203	+	0.0908670i
$894$		0			0
$895$	−0.381558	−	0.254949i	−0.0127541	−	0.00852200i
$896$		0			0
$897$	−27.0487	−	27.0487i	−0.903129	−	0.903129i
$898$		0			0
$899$	−1.22851	+	1.60103i	−0.0409732	+	0.0533974i
$900$		0			0
$901$	−13.5442	−	28.1982i	−0.451222	−	0.939419i
$902$		0			0
$903$	17.5201	+	4.59415i	0.583031	+	0.152884i
$904$		0			0
$905$	−0.494941	−	1.84715i	−0.0164524	−	0.0614012i
$906$		0			0
$907$	−1.81378	+	27.6730i	−0.0602256	+	0.918865i	0.855689	+	0.517491i	$0.173134\pi$
$907$	−1.81378	+	27.6730i	−0.0602256	+	0.918865i	−0.915914	+	0.401374i	$0.868533\pi$
$908$		0			0
$909$	−0.802200	+	1.93668i	−0.0266073	+	0.0642357i
$910$		0			0
$911$	−7.52096	−	37.8104i	−0.249180	−	1.25271i	−0.879320	−	0.476232i	$-0.842002\pi$
$911$	−7.52096	−	37.8104i	−0.249180	−	1.25271i	0.630139	−	0.776482i	$-0.282998\pi$
$912$		0			0
$913$	7.31025	+	21.5353i	0.241934	+	0.712714i
$914$		0			0
$915$	0.0443409	+	0.676511i	0.00146586	+	0.0223648i
$916$		0			0
$917$	6.02309	−	47.7218i	0.198900	−	1.57591i
$918$		0			0
$919$	−0.273051	+	0.472938i	−0.00900712	+	0.0156008i	−0.870494	−	0.492179i	$-0.836200\pi$
$919$	−0.273051	+	0.472938i	−0.00900712	+	0.0156008i	0.861487	+	0.507780i	$0.169534\pi$
$920$		0			0
$921$	7.91847	+	3.90496i	0.260923	+	0.128673i
$922$		0			0
$923$	−4.50216	+	22.6339i	−0.148191	+	0.745004i
$924$		0			0
$925$	−18.5533	+	3.69047i	−0.610028	+	0.121342i
$926$		0			0
$927$	0.828130	+	6.29027i	0.0271994	+	0.206600i
$928$		0			0
$929$	−8.10760	+	3.99822i	−0.266002	+	0.131177i	−0.570399	−	0.821368i	$-0.693212\pi$
$929$	−8.10760	+	3.99822i	−0.266002	+	0.131177i	0.304398	+	0.952545i	$0.401545\pi$
$930$		0			0
$931$	22.4034	+	12.6169i	0.734242	+	0.413502i
$932$		0			0
$933$	1.31032	−	9.95284i	0.0428978	−	0.325841i
$934$		0			0
$935$	0.554361	−	0.181792i	0.0181295	−	0.00594524i
$936$		0			0
$937$	14.9994	−	6.21294i	0.490008	−	0.202968i	−0.123978	−	0.992285i	$-0.539565\pi$
$937$	14.9994	−	6.21294i	0.490008	−	0.202968i	0.613986	+	0.789317i	$0.289565\pi$
$938$		0			0
$939$	17.1373	−	17.1373i	0.559255	−	0.559255i
$940$		0			0
$941$	−22.3416	−	1.46434i	−0.728315	−	0.0477363i	−0.303265	−	0.952906i	$-0.598077\pi$
$941$	−22.3416	−	1.46434i	−0.728315	−	0.0477363i	−0.425050	+	0.905170i	$0.639743\pi$
$942$		0			0
$943$	23.4421	+	30.5503i	0.763379	+	0.994855i
$944$		0			0
$945$	1.47843	−	0.104850i	0.0480935	−	0.00341076i
$946$		0			0
$947$	−1.38321	−	1.21304i	−0.0449483	−	0.0394186i	0.636577	−	0.771213i	$-0.280350\pi$
$947$	−1.38321	−	1.21304i	−0.0449483	−	0.0394186i	−0.681525	+	0.731795i	$0.738683\pi$
$948$		0			0
$949$	−31.8846	+	64.6556i	−1.03502	+	2.09881i
$950$		0			0
$951$	−29.0512			−0.942050
$952$		0			0
$953$	36.8614			1.19406			0.597029	−	0.802220i	$-0.296348\pi$
$953$	36.8614			1.19406			0.597029	+	0.802220i	$0.296348\pi$
$954$		0			0
$955$	0.102162	−	0.207163i	0.00330587	−	0.00670365i
$956$		0			0
$957$	−0.227210	−	0.199258i	−0.00734466	−	0.00644109i
$958$		0			0
$959$	23.9350	+	11.6446i	0.772902	+	0.376025i
$960$		0			0
$961$	39.6928	+	51.7287i	1.28041	+	1.66867i
$962$		0			0
$963$	12.3667	+	0.810554i	0.398510	+	0.0261197i
$964$		0			0
$965$	1.38840	−	1.38840i	0.0446942	−	0.0446942i
$966$		0			0
$967$	−37.7950	+	15.6552i	−1.21540	+	0.503437i	−0.895946	−	0.444163i	$-0.853501\pi$
$967$	−37.7950	+	15.6552i	−1.21540	+	0.503437i	−0.319458	+	0.947600i	$0.603501\pi$
$968$		0			0
$969$	14.5450	−	8.19767i	0.467253	−	0.263347i
$970$		0			0
$971$	1.60457	−	12.1879i	0.0514932	−	0.391130i	−0.946219	−	0.323527i	$-0.895131\pi$
$971$	1.60457	−	12.1879i	0.0514932	−	0.391130i	0.997712	−	0.0676032i	$-0.0215352\pi$
$972$		0			0
$973$	12.2834	+	5.01110i	0.393786	+	0.160648i
$974$		0			0
$975$	−30.9612	+	15.2684i	−0.991551	+	0.488979i
$976$		0			0
$977$	−0.0392278	−	0.297965i	−0.00125501	−	0.00953274i	0.990806	−	0.135291i	$-0.0431969\pi$
$977$	−0.0392278	−	0.297965i	−0.00125501	−	0.00953274i	−0.992061	+	0.125758i	$0.959864\pi$
$978$		0			0
$979$	−6.55832	+	1.30453i	−0.209605	+	0.0416930i
$980$		0			0
$981$	−5.34250	+	26.8586i	−0.170573	+	0.857528i
$982$		0			0
$983$	18.7251	+	9.23420i	0.597238	+	0.294525i	0.715672	−	0.698437i	$-0.246121\pi$
$983$	18.7251	+	9.23420i	0.597238	+	0.294525i	−0.118434	+	0.992962i	$0.537787\pi$
$984$		0			0
$985$	1.30432	−	2.25914i	0.0415590	−	0.0719823i
$986$		0			0
$987$	−15.2282	+	6.40340i	−0.484718	+	0.203822i
$988$		0			0
$989$	−2.24509	−	34.2535i	−0.0713898	−	1.08920i
$990$		0			0
$991$	16.2514	+	47.8751i	0.516243	+	1.52080i	0.822450	+	0.568838i	$0.192607\pi$
$991$	16.2514	+	47.8751i	0.516243	+	1.52080i	−0.306206	+	0.951965i	$0.599060\pi$
$992$		0			0
$993$	−3.28934	−	16.5366i	−0.104384	−	0.524774i
$994$		0			0
$995$	−0.997273	+	2.40763i	−0.0316157	+	0.0763270i
$996$		0			0
$997$	2.04888	−	31.2598i	0.0648886	−	0.990009i	−0.833981	−	0.551793i	$-0.813944\pi$
$997$	2.04888	−	31.2598i	0.0648886	−	0.990009i	0.898870	−	0.438216i	$-0.144390\pi$
$998$		0			0
$999$	−5.17674	−	19.3199i	−0.163785	−	0.611253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.cw.b.369.13	yes	288
7.3	odd	6	inner	952.2.cw.b.913.13	yes	288
17.10	odd	16	inner	952.2.cw.b.537.13	yes	288
119.10	even	48	inner	952.2.cw.b.129.13	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.cw.b.129.13	✓	288	119.10	even	48	inner
952.2.cw.b.369.13	yes	288	1.1	even	1	trivial
952.2.cw.b.537.13	yes	288	17.10	odd	16	inner
952.2.cw.b.913.13	yes	288	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.cw (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.487596 - 0.988748i) q^{3} +(-0.0798482 - 0.0700250i) q^{5} +(-2.19196 + 1.48165i) q^{7} +(1.08641 + 1.41584i) q^{9} +(-1.32947 - 0.0871378i) q^{11} +(4.43841 - 4.43841i) q^{13} +(-0.108171 + 0.0448058i) q^{15} +(1.86185 - 3.67879i) q^{17} +(-0.479438 + 3.64170i) q^{19} +(0.396185 + 2.88975i) q^{21} +(4.95786 - 2.44495i) q^{23} +(-0.651159 - 4.94604i) q^{25} +(5.17341 - 1.02905i) q^{27} +(-0.0401398 + 0.201796i) q^{29} +(8.79679 + 4.33810i) q^{31} +(-0.734400 + 1.27202i) q^{33} +(0.278777 + 0.0351851i) q^{35} +(-0.248002 - 3.78379i) q^{37} +(-2.22432 - 6.55263i) q^{39} +(1.35901 + 6.83218i) q^{41} +(2.37636 - 5.73704i) q^{43} +(0.0123961 - 0.189128i) q^{45} +(1.46587 + 5.47070i) q^{47} +(2.60942 - 6.49545i) q^{49} +(-2.72957 - 3.63466i) q^{51} +(4.61872 - 6.01924i) q^{53} +(0.100054 + 0.100054i) q^{55} +(3.36695 + 2.24972i) q^{57} +(-11.7775 + 1.55054i) q^{59} +(1.86127 - 5.48314i) q^{61} +(-4.47916 - 1.49379i) q^{63} +(-0.665199 + 0.0435995i) q^{65} +(-2.78463 + 1.60771i) q^{67} -6.09422i q^{69} +(-3.05696 + 2.04259i) q^{71} +(-10.8755 + 3.69175i) q^{73} +(-5.20789 - 1.76784i) q^{75} +(3.04325 - 1.77880i) q^{77} +(3.88723 + 7.88253i) q^{79} +(0.119373 - 0.445506i) q^{81} +(-6.53228 - 15.7703i) q^{83} +(-0.406272 + 0.163369i) q^{85} +(0.179954 + 0.138083i) q^{87} +(4.84791 - 1.29899i) q^{89} +(-3.15267 + 16.3050i) q^{91} +(8.57857 - 6.58257i) q^{93} +(0.293292 - 0.257210i) q^{95} +(7.45011 + 1.48192i) q^{97} +(-1.32097 - 1.97698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 32 q^{15} + 48 q^{21} - 32 q^{29} - 72 q^{31} - 16 q^{37} - 32 q^{39} + 32 q^{43} + 24 q^{47} - 48 q^{49} - 16 q^{53} - 128 q^{57} - 72 q^{61} - 40 q^{63} + 32 q^{65} + 80 q^{71} + 96 q^{73} - 216 q^{75}+ \cdots + 192 q^{99}+O(q^{100}) \) 288 * q + 32 * q^15 + 48 * q^21 - 32 * q^29 - 72 * q^31 - 16 * q^37 - 32 * q^39 + 32 * q^43 + 24 * q^47 - 48 * q^49 - 16 * q^53 - 128 * q^57 - 72 * q^61 - 40 * q^63 + 32 * q^65 + 80 * q^71 + 96 * q^73 - 216 * q^75 - 8 * q^77 + 32 * q^79 + 64 * q^81 - 96 * q^85 + 144 * q^87 - 144 * q^89 + 64 * q^91 - 32 * q^93 + 64 * q^95 + 192 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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