LMFDB - Embedded newform 900.2.bj.e.523.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$ , degree $8$ , 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.8
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.e.487.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04515 - 0.952711i) q^{2} +(0.184684 + 1.99145i) q^{4} +(-1.38078 + 1.75882i) q^{5} +(3.44825 + 3.44825i) q^{7} +(1.70426 - 2.25732i) q^{8} +(3.11877 - 0.522748i) q^{10} +(0.665578 + 0.916089i) q^{11} +(-0.0598699 - 0.378004i) q^{13} +(-0.318759 - 6.88912i) q^{14} +(-3.93178 + 0.735579i) q^{16} +(0.869332 + 0.442947i) q^{17} +(0.904594 + 2.78406i) q^{19} +(-3.75762 - 2.42494i) q^{20} +(0.177138 - 1.59155i) q^{22} +(-0.211827 + 1.33742i) q^{23} +(-1.18689 - 4.85709i) q^{25} +(-0.297555 + 0.452110i) q^{26} +(-6.23019 + 7.50386i) q^{28} +(-6.57862 - 2.13752i) q^{29} +(5.91690 - 1.92252i) q^{31} +(4.81010 + 2.97706i) q^{32} +(-0.486584 - 1.29117i) q^{34} +(-10.8261 + 1.30357i) q^{35} +(-8.95424 + 1.41821i) q^{37} +(1.70696 - 3.77158i) q^{38} +(1.61702 + 6.11435i) q^{40} +(5.06982 + 3.68344i) q^{41} +(-4.02869 + 4.02869i) q^{43} +(-1.70143 + 1.49465i) q^{44} +(1.49557 - 1.19600i) q^{46} +(-9.68440 + 4.93445i) q^{47} +16.7808i q^{49} +(-3.38692 + 6.20716i) q^{50} +(0.741720 - 0.189039i) q^{52} +(8.69751 - 4.43160i) q^{53} +(-2.53025 - 0.0942872i) q^{55} +(13.6605 - 1.90710i) q^{56} +(4.83921 + 8.50156i) q^{58} +(3.65195 + 2.65330i) q^{59} +(6.58194 - 4.78206i) q^{61} +(-8.01566 - 3.62777i) q^{62} +(-2.19101 - 7.69412i) q^{64} +(0.747507 + 0.416640i) q^{65} +(-5.19430 + 10.1944i) q^{67} +(-0.721557 + 1.81304i) q^{68} +(12.5569 + 8.95173i) q^{70} +(-2.75549 - 0.895311i) q^{71} +(3.17780 + 0.503314i) q^{73} +(10.7097 + 7.04856i) q^{74} +(-5.37726 + 2.31563i) q^{76} +(-0.863825 + 5.45398i) q^{77} +(3.19543 - 9.83453i) q^{79} +(4.13518 - 7.93097i) q^{80} +(-1.78948 - 8.67982i) q^{82} +(-9.67363 - 4.92896i) q^{83} +(-1.97942 + 0.917386i) q^{85} +(8.04876 - 0.372415i) q^{86} +(3.20222 + 0.0588286i) q^{88} +(8.22988 + 11.3275i) q^{89} +(1.09700 - 1.50990i) q^{91} +(-2.70254 - 0.174844i) q^{92} +(14.8228 + 4.06919i) q^{94} +(-6.14570 - 2.25315i) q^{95} +(-4.93021 - 9.67608i) q^{97} +(15.9873 - 17.5385i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$224 q - 4 q^{10} + 16 q^{13} - 16 q^{16} + 28 q^{22} - 32 q^{25} + 28 q^{28} - 100 q^{34} - 104 q^{37} + 60 q^{40} + 156 q^{52} + 144 q^{58} - 48 q^{61} + 60 q^{64} + 28 q^{70} + 40 q^{73} + 64 q^{82} + 136 q^{85}+ \cdots - 160 q^{97}+O(q^{100})$ 224 * q - 4 * q^10 + 16 * q^13 - 16 * q^16 + 28 * q^22 - 32 * q^25 + 28 * q^28 - 100 * q^34 - 104 * q^37 + 60 * q^40 + 156 * q^52 + 144 * q^58 - 48 * q^61 + 60 * q^64 + 28 * q^70 + 40 * q^73 + 64 * q^82 + 136 * q^85 + 148 * q^88 + 40 * q^94 - 160 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$ .

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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

)

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

$2$	−1.04515	−	0.952711i	−0.739034	−	0.673668i
$2$	−1.04515	−	0.952711i	−0.739034	−	0.673668i
$3$		0			0
$3$		0			0
$4$	0.184684	+	1.99145i	0.0923419	+	0.995727i
$5$	−1.38078	+	1.75882i	−0.617504	+	0.786568i
$5$	−1.38078	+	1.75882i	−0.617504	+	0.786568i
$6$		0			0
$7$	3.44825	+	3.44825i	1.30332	+	1.30332i	0.926143	+	0.377172i	$0.123103\pi$
$7$	3.44825	+	3.44825i	1.30332	+	1.30332i	0.377172	+	0.926143i	$0.376897\pi$
$8$	1.70426	−	2.25732i	0.602546	−	0.798084i
$9$		0			0
$10$	3.11877	−	0.522748i	0.986242	−	0.165307i
$11$	0.665578	+	0.916089i	0.200679	+	0.276211i	0.897482	−	0.441052i	$-0.145395\pi$
$11$	0.665578	+	0.916089i	0.200679	+	0.276211i	−0.696802	+	0.717263i	$0.745395\pi$
$12$		0			0
$13$	−0.0598699	−	0.378004i	−0.0166049	−	0.104839i	0.977994	−	0.208634i	$-0.0669016\pi$
$13$	−0.0598699	−	0.378004i	−0.0166049	−	0.104839i	−0.994599	+	0.103794i	$0.966902\pi$
$14$	−0.318759	−	6.88912i	−0.0851918	−	1.84120i
$15$		0			0
$16$	−3.93178	+	0.735579i	−0.982946	+	0.183895i
$17$	0.869332	+	0.442947i	0.210844	+	0.107430i	0.556224	−	0.831033i	$-0.312250\pi$
$17$	0.869332	+	0.442947i	0.210844	+	0.107430i	−0.345380	+	0.938463i	$0.612250\pi$
$18$		0			0
$19$	0.904594	+	2.78406i	0.207528	+	0.638706i	0.999600	+	0.0282783i	$0.00900246\pi$
$19$	0.904594	+	2.78406i	0.207528	+	0.638706i	−0.792072	+	0.610428i	$0.790998\pi$
$20$	−3.75762	−	2.42494i	−0.840229	−	0.542232i
$21$		0			0
$22$	0.177138	−	1.59155i	0.0377660	−	0.339321i
$23$	−0.211827	+	1.33742i	−0.0441690	+	0.278872i	−0.999881	−	0.0154316i	$-0.995088\pi$
$23$	−0.211827	+	1.33742i	−0.0441690	+	0.278872i	0.955712	+	0.294304i	$0.0950878\pi$
$24$		0			0
$25$	−1.18689	−	4.85709i	−0.237378	−	0.971417i
$26$	−0.297555	+	0.452110i	−0.0583554	+	0.0886660i
$27$		0			0
$28$	−6.23019	+	7.50386i	−1.17740	+	1.41810i
$29$	−6.57862	−	2.13752i	−1.22162	−	0.396928i	−0.373948	−	0.927450i	$-0.621996\pi$
$29$	−6.57862	−	2.13752i	−1.22162	−	0.396928i	−0.847671	+	0.530522i	$0.821996\pi$
$30$		0			0
$31$	5.91690	−	1.92252i	1.06271	−	0.345294i	0.275064	−	0.961426i	$-0.411301\pi$
$31$	5.91690	−	1.92252i	1.06271	−	0.345294i	0.787643	+	0.616132i	$0.211301\pi$
$32$	4.81010	+	2.97706i	0.850314	+	0.526275i
$33$		0			0
$34$	−0.486584	−	1.29117i	−0.0834484	−	0.221434i
$35$	−10.8261	+	1.30357i	−1.82995	+	0.220344i
$36$		0			0
$37$	−8.95424	+	1.41821i	−1.47207	+	0.233153i	−0.840350	−	0.542045i	$-0.817650\pi$
$37$	−8.95424	+	1.41821i	−1.47207	+	0.233153i	−0.631719	+	0.775198i	$0.717650\pi$
$38$	1.70696	−	3.77158i	0.276906	−	0.611831i
$39$		0			0
$40$	1.61702	+	6.11435i	0.255673	+	0.966763i
$41$	5.06982	+	3.68344i	0.791772	+	0.575256i	0.908489	−	0.417909i	$-0.137237\pi$
$41$	5.06982	+	3.68344i	0.791772	+	0.575256i	−0.116717	+	0.993165i	$0.537237\pi$
$42$		0			0
$43$	−4.02869	+	4.02869i	−0.614369	+	0.614369i	−0.944081	−	0.329713i	$-0.893048\pi$
$43$	−4.02869	+	4.02869i	−0.614369	+	0.614369i	0.329713	+	0.944081i	$0.393048\pi$
$44$	−1.70143	+	1.49465i	−0.256500	+	0.225328i
$45$		0			0
$46$	1.49557	−	1.19600i	0.220510	−	0.176341i
$47$	−9.68440	+	4.93445i	−1.41262	+	0.719763i	−0.983061	−	0.183278i	$-0.941329\pi$
$47$	−9.68440	+	4.93445i	−1.41262	+	0.719763i	−0.429554	+	0.903041i	$0.641329\pi$
$48$		0			0
$49$			16.7808i			2.39726i
$50$	−3.38692	+	6.20716i	−0.478983	+	0.877824i
$51$		0			0
$52$	0.741720	−	0.189039i	0.102858	−	0.0262150i
$53$	8.69751	−	4.43160i	1.19469	−	0.608727i	0.260494	−	0.965475i	$-0.416114\pi$
$53$	8.69751	−	4.43160i	1.19469	−	0.608727i	0.934201	+	0.356748i	$0.116114\pi$
$54$		0			0
$55$	−2.53025	−	0.0942872i	−0.341179	−	0.0127137i
$56$	13.6605	−	1.90710i	1.82546	−	0.254847i
$57$		0			0
$58$	4.83921	+	8.50156i	0.635420	+	1.11631i
$59$	3.65195	+	2.65330i	0.475443	+	0.345430i	0.799559	−	0.600588i	$-0.205067\pi$
$59$	3.65195	+	2.65330i	0.475443	+	0.345430i	−0.324116	+	0.946018i	$0.605067\pi$
$60$		0			0
$61$	6.58194	−	4.78206i	0.842732	−	0.612280i	−0.0804007	−	0.996763i	$-0.525620\pi$
$61$	6.58194	−	4.78206i	0.842732	−	0.612280i	0.923132	+	0.384482i	$0.125620\pi$
$62$	−8.01566	−	3.62777i	−1.01799	−	0.460728i
$63$		0			0
$64$	−2.19101	−	7.69412i	−0.273876	−	0.961765i
$65$	0.747507	+	0.416640i	0.0927169	+	0.0516778i
$66$		0			0
$67$	−5.19430	+	10.1944i	−0.634585	+	1.24544i	0.319976	+	0.947426i	$0.396325\pi$
$67$	−5.19430	+	10.1944i	−0.634585	+	1.24544i	−0.954561	+	0.298017i	$0.903675\pi$
$68$	−0.721557	+	1.81304i	−0.0875016	+	0.219863i
$69$		0			0
$70$	12.5569	+	8.95173i	1.50083	+	1.06994i
$71$	−2.75549	−	0.895311i	−0.327016	−	0.106254i	0.140908	−	0.990023i	$-0.454998\pi$
$71$	−2.75549	−	0.895311i	−0.327016	−	0.106254i	−0.467924	+	0.883769i	$0.654998\pi$
$72$		0			0
$73$	3.17780	+	0.503314i	0.371933	+	0.0589084i	0.339603	−	0.940569i	$-0.389707\pi$
$73$	3.17780	+	0.503314i	0.371933	+	0.0589084i	0.0323299	+	0.999477i	$0.489707\pi$
$74$	10.7097	+	7.04856i	1.24498	+	0.819378i
$75$		0			0
$76$	−5.37726	+	2.31563i	−0.616814	+	0.265621i
$77$	−0.863825	+	5.45398i	−0.0984420	+	0.621539i
$78$		0			0
$79$	3.19543	−	9.83453i	0.359514	−	1.10647i	−0.593831	−	0.804590i	$-0.702385\pi$
$79$	3.19543	−	9.83453i	0.359514	−	1.10647i	0.953345	−	0.301881i	$-0.0976147\pi$
$80$	4.13518	−	7.93097i	0.462327	−	0.886709i
$81$		0			0
$82$	−1.78948	−	8.67982i	−0.197615	−	0.958525i
$83$	−9.67363	−	4.92896i	−1.06182	−	0.541023i	−0.166312	−	0.986073i	$-0.553186\pi$
$83$	−9.67363	−	4.92896i	−1.06182	−	0.541023i	−0.895506	+	0.445050i	$0.853186\pi$
$84$		0			0
$85$	−1.97942	+	0.917386i	−0.214698	+	0.0995044i
$86$	8.04876	−	0.372415i	0.867920	−	0.0401585i
$87$		0			0
$88$	3.20222	+	0.0588286i	0.341358	+	0.00627115i
$89$	8.22988	+	11.3275i	0.872366	+	1.20071i	0.978477	+	0.206354i	$0.0661599\pi$
$89$	8.22988	+	11.3275i	0.872366	+	1.20071i	−0.106112	+	0.994354i	$0.533840\pi$
$90$		0			0
$91$	1.09700	−	1.50990i	0.114997	−	0.158280i
$92$	−2.70254	−	0.174844i	−0.281759	−	0.0182287i
$93$		0			0
$94$	14.8228	+	4.06919i	1.52885	+	0.419705i
$95$	−6.14570	−	2.25315i	−0.630535	−	0.231168i
$96$		0			0
$97$	−4.93021	−	9.67608i	−0.500587	−	0.982457i	−0.993655	−	0.112467i	$-0.964125\pi$
$97$	−4.93021	−	9.67608i	−0.500587	−	0.982457i	0.493069	−	0.869990i	$-0.335875\pi$
$98$	15.9873	−	17.5385i	1.61496	−	1.77166i
$99$		0			0
$100$	9.45347	−	3.26066i	0.945347	−	0.326066i
$101$	0.642043			0.0638857			0.0319429	−	0.999490i	$-0.489831\pi$
$101$	0.642043			0.0638857			0.0319429	+	0.999490i	$0.489831\pi$
$102$		0			0
$103$	−0.889862	−	1.74645i	−0.0876807	−	0.172083i	0.843002	−	0.537910i	$-0.180786\pi$
$103$	−0.889862	−	1.74645i	−0.0876807	−	0.172083i	−0.930683	+	0.365827i	$0.880786\pi$
$104$	−0.955310	−	0.509070i	−0.0936758	−	0.0499184i
$105$		0			0
$106$	−13.3123	−	3.65452i	−1.29300	−	0.354958i
$107$	2.25202	+	2.25202i	0.217711	+	0.217711i	0.807533	−	0.589822i	$-0.200802\pi$
$107$	2.25202	+	2.25202i	0.217711	+	0.217711i	−0.589822	+	0.807533i	$0.700802\pi$
$108$		0			0
$109$	−5.68371	+	7.82296i	−0.544401	+	0.749303i	−0.989239	−	0.146307i	$-0.953261\pi$
$109$	−5.68371	+	7.82296i	−0.544401	+	0.749303i	0.444838	+	0.895611i	$0.353261\pi$
$110$	2.55467	+	2.50914i	0.243578	+	0.239237i
$111$		0			0
$112$	−16.0942	−	11.0213i	−1.52076	−	1.04142i
$113$	3.29273	+	20.7895i	0.309754	+	1.95571i	0.293912	+	0.955832i	$0.405043\pi$
$113$	3.29273	+	20.7895i	0.309754	+	1.95571i	0.0158414	+	0.999875i	$0.494957\pi$
$114$		0			0
$115$	−2.05980	−	2.21926i	−0.192077	−	0.206947i
$116$	3.04182	−	13.4958i	0.282425	−	1.25305i
$117$		0			0
$118$	−1.28902	−	6.25235i	−0.118664	−	0.575575i
$119$	1.47028	+	4.52506i	0.134781	+	0.414812i
$120$		0			0
$121$	3.00296	−	9.24217i	0.272996	−	0.840197i
$122$	−11.4351	−	1.27271i	−1.03528	−	0.115226i
$123$		0			0
$124$	4.92136	+	11.4282i	0.441952	+	1.02628i
$125$	10.1816	+	4.61905i	0.910668	+	0.413140i
$126$		0			0
$127$	6.98557	+	1.10641i	0.619869	+	0.0981777i	0.458468	−	0.888711i	$-0.348399\pi$
$127$	6.98557	+	1.10641i	0.619869	+	0.0981777i	0.161402	+	0.986889i	$0.448399\pi$
$128$	−5.04033	+	10.1289i	−0.445507	+	0.895279i
$129$		0			0
$130$	−0.384321	−	1.14761i	−0.0337072	−	0.100652i
$131$	17.4296	−	5.66323i	1.52283	−	0.494798i	0.576254	−	0.817271i	$-0.304514\pi$
$131$	17.4296	−	5.66323i	1.52283	−	0.494798i	0.946579	+	0.322473i	$0.104514\pi$
$132$		0			0
$133$	−6.48085	+	12.7194i	−0.561961	+	1.10291i
$134$	15.1411	−	5.70601i	1.30799	−	0.492924i
$135$		0			0
$136$	2.48144	−	1.20747i	0.212782	−	0.103539i
$137$	−12.3832	+	1.96131i	−1.05797	+	0.167566i	−0.661092	−	0.750305i	$-0.729907\pi$
$137$	−12.3832	+	1.96131i	−1.05797	+	0.167566i	−0.396879	+	0.917871i	$0.629907\pi$
$138$		0			0
$139$	−2.48077	+	1.80238i	−0.210416	+	0.152876i	−0.688002	−	0.725709i	$-0.741512\pi$
$139$	−2.48077	+	1.80238i	−0.210416	+	0.152876i	0.477586	+	0.878585i	$0.341512\pi$
$140$	−4.59541	−	21.3190i	−0.388383	−	1.80178i
$141$		0			0
$142$	2.02693	+	3.56092i	0.170096	+	0.298825i
$143$	0.306437	−	0.306437i	0.0256255	−	0.0256255i
$144$		0			0
$145$	12.8431	−	8.61915i	1.06657	−	0.715782i
$146$	−2.84177	−	3.55356i	−0.235186	−	0.294095i
$147$		0			0
$148$	−4.47801	−	17.5700i	−0.368090	−	1.44425i
$149$			4.15928i			0.340741i	0.985380	+	0.170371i	$0.0544965\pi$
$149$			4.15928i			0.340741i	−0.985380	+	0.170371i	$0.945504\pi$
$150$		0			0
$151$		−	6.04909i		−	0.492268i	−0.969236	−	0.246134i	$-0.920840\pi$
$151$		−	6.04909i		−	0.492268i	0.969236	−	0.246134i	$-0.0791603\pi$
$152$	7.82617	+	2.70279i	0.634786	+	0.219225i
$153$		0			0
$154$	6.09889	−	4.87726i	0.491463	−	0.393021i
$155$	−4.78858	+	13.0613i	−0.384628	+	1.04911i
$156$		0			0
$157$	7.27059	−	7.27059i	0.580256	−	0.580256i	−0.354717	−	0.934974i	$-0.615423\pi$
$157$	7.27059	−	7.27059i	0.580256	−	0.580256i	0.934974	+	0.354717i	$0.115423\pi$
$158$	−12.7092	+	7.23425i	−1.01109	+	0.575526i
$159$		0			0
$160$	−11.8778	+	4.34944i	−0.939023	+	0.343853i
$161$	−5.34221	+	3.88134i	−0.421025	+	0.305892i
$162$		0			0
$163$	−15.3694	+	2.43428i	−1.20383	+	0.190667i	−0.725942	−	0.687756i	$-0.758596\pi$
$163$	−15.3694	+	2.43428i	−1.20383	+	0.190667i	−0.477883	+	0.878423i	$0.658596\pi$
$164$	−6.39908	+	10.7766i	−0.499684	+	0.841509i
$165$		0			0
$166$	5.41453	+	14.3677i	0.420249	+	1.11515i
$167$	−6.72665	+	13.2018i	−0.520524	+	1.02159i	0.469795	+	0.882775i	$0.344328\pi$
$167$	−6.72665	+	13.2018i	−0.520524	+	1.02159i	−0.990319	+	0.138810i	$0.955672\pi$
$168$		0			0
$169$	12.2244	−	3.97196i	0.940341	−	0.305535i
$170$	2.94280	+	0.927008i	0.225702	+	0.0710983i
$171$		0			0
$172$	−8.76698	−	7.27891i	−0.668476	−	0.555012i
$173$	−13.1116	−	2.07667i	−0.996857	−	0.157887i	−0.363374	−	0.931643i	$-0.618375\pi$
$173$	−13.1116	−	2.07667i	−0.996857	−	0.157887i	−0.633483	+	0.773757i	$0.718375\pi$
$174$		0			0
$175$	12.6557	−	20.8411i	0.956685	−	1.57544i
$176$	−3.29076	−	3.11228i	−0.248051	−	0.234597i
$177$		0			0
$178$	2.19032	−	19.6796i	0.164171	−	1.47505i
$179$	−7.26523	+	22.3601i	−0.543029	+	1.67127i	0.182602	+	0.983187i	$0.441548\pi$
$179$	−7.26523	+	22.3601i	−0.543029	+	1.67127i	−0.725631	+	0.688084i	$0.758452\pi$
$180$		0			0
$181$	−5.35786	−	16.4898i	−0.398247	−	1.22568i	−0.926404	−	0.376531i	$-0.877117\pi$
$181$	−5.35786	−	16.4898i	−0.398247	−	1.22568i	0.528157	−	0.849147i	$-0.322883\pi$
$182$	−2.58503	+	0.532943i	−0.191615	+	0.0395044i
$183$		0			0
$184$	2.65799	+	2.75748i	0.195950	+	0.203284i
$185$	9.86946	−	17.7071i	0.725617	−	1.30185i
$186$		0			0
$187$	0.172829	+	1.09120i	0.0126385	+	0.0797965i
$188$	−11.6153	−	18.3747i	−0.847132	−	1.34012i
$189$		0			0
$190$	4.27658	+	8.20996i	0.310256	+	0.595613i
$191$	1.56971	−	2.16053i	0.113581	−	0.156330i	−0.748442	−	0.663200i	$-0.769198\pi$
$191$	1.56971	−	2.16053i	0.113581	−	0.156330i	0.862022	+	0.506870i	$0.169198\pi$
$192$		0			0
$193$	5.46235	+	5.46235i	0.393188	+	0.393188i	0.875822	−	0.482634i	$-0.160320\pi$
$193$	5.46235	+	5.46235i	0.393188	+	0.393188i	−0.482634	+	0.875822i	$0.660320\pi$
$194$	−4.06569	+	14.8100i	−0.291900	+	1.06330i
$195$		0			0
$196$	−33.4183	+	3.09915i	−2.38702	+	0.221368i
$197$	−7.08233	−	13.8998i	−0.504595	−	0.990323i	−0.993045	−	0.117732i	$-0.962438\pi$
$197$	−7.08233	−	13.8998i	−0.504595	−	0.990323i	0.488451	−	0.872592i	$-0.337562\pi$
$198$		0			0
$199$	−16.7739			−1.18907			−0.594534	−	0.804070i	$-0.702663\pi$
$199$	−16.7739			−1.18907			−0.594534	+	0.804070i	$0.702663\pi$
$200$	−12.9868	−	5.59854i	−0.918304	−	0.395876i
$201$		0			0
$202$	−0.671033	−	0.611682i	−0.0472137	−	0.0430378i
$203$	−15.3140	−	30.0554i	−1.07483	−	2.10948i
$204$		0			0
$205$	−13.4788	+	3.83087i	−0.941400	+	0.267560i
$206$	−0.733824	+	2.67309i	−0.0511279	+	0.186243i
$207$		0			0
$208$	0.513447	+	1.44219i	0.0356012	+	0.0999979i
$209$	−1.94836	+	2.68169i	−0.134771	+	0.185497i
$210$		0			0
$211$	8.21221	+	11.3031i	0.565352	+	0.778140i	0.991995	−	0.126280i	$-0.0403038\pi$
$211$	8.21221	+	11.3031i	0.565352	+	0.778140i	−0.426643	+	0.904420i	$0.640304\pi$
$212$	10.4316	+	16.5023i	0.716447	+	1.13338i
$213$		0			0
$214$	−0.208179	−	4.49923i	−0.0142308	−	0.307561i
$215$	−1.52300	−	12.6485i	−0.103868	−	0.862618i
$216$		0			0
$217$	27.0323	+	13.7736i	1.83507	+	0.935015i
$218$	13.3934	−	2.76124i	0.907113	−	0.187015i
$219$		0			0
$220$	−0.279528	−	5.05629i	−0.0188458	−	0.340895i
$221$	0.115389	−	0.355130i	0.00776188	−	0.0238886i
$222$		0			0
$223$	−1.10929	+	7.00378i	−0.0742836	+	0.469008i	0.922304	+	0.386465i	$0.126304\pi$
$223$	−1.10929	+	7.00378i	−0.0742836	+	0.469008i	−0.996588	+	0.0825427i	$0.973696\pi$
$224$	6.32079	+	26.8521i	0.422325	+	1.79413i
$225$		0			0
$226$	16.3649	−	24.8651i	1.08858	−	1.65400i
$227$	−2.15510	−	0.341335i	−0.143039	−	0.0226552i	0.0845042	−	0.996423i	$-0.473069\pi$
$227$	−2.15510	−	0.341335i	−0.143039	−	0.0226552i	−0.227543	+	0.973768i	$0.573069\pi$
$228$		0			0
$229$	−7.26018	−	2.35897i	−0.479766	−	0.155885i	0.0591428	−	0.998250i	$-0.481163\pi$
$229$	−7.26018	−	2.35897i	−0.479766	−	0.155885i	−0.538909	+	0.842364i	$0.681163\pi$
$230$	0.0384954	+	4.28185i	0.00253831	+	0.282337i
$231$		0			0
$232$	−16.0367	+	11.2072i	−1.05286	+	0.735787i
$233$	12.0468	−	23.6432i	0.789214	−	1.54892i	−0.0459655	−	0.998943i	$-0.514636\pi$
$233$	12.0468	−	23.6432i	0.789214	−	1.54892i	0.835180	−	0.549977i	$-0.185364\pi$
$234$		0			0
$235$	4.69323	−	23.8465i	0.306153	−	1.55557i
$236$	−4.60946	+	7.76271i	−0.300051	+	0.505310i
$237$		0			0
$238$	2.77441	−	6.13013i	0.179838	−	0.397357i
$239$	18.9812	−	13.7906i	1.22779	−	0.892042i	0.231068	−	0.972938i	$-0.425778\pi$
$239$	18.9812	−	13.7906i	1.22779	−	0.892042i	0.996723	+	0.0808951i	$0.0257779\pi$
$240$		0			0
$241$	−4.98282	−	3.62023i	−0.320972	−	0.233199i	0.415618	−	0.909539i	$-0.363565\pi$
$241$	−4.98282	−	3.62023i	−0.320972	−	0.233199i	−0.736590	+	0.676340i	$0.763565\pi$
$242$	−11.9437	+	6.79851i	−0.767768	+	0.437025i
$243$		0			0
$244$	10.7388	+	12.2245i	0.687484	+	0.782592i
$245$	−29.5144	−	23.1706i	−1.88561	−	1.48032i
$246$		0			0
$247$	0.998225	−	0.508621i	0.0635155	−	0.0323628i
$248$	5.74418	−	16.6328i	0.364756	−	1.05619i
$249$		0			0
$250$	−6.24067	−	14.5277i	−0.394695	−	0.918812i
$251$		−	2.57211i		−	0.162350i	−0.996700	−	0.0811750i	$-0.974133\pi$
$251$		−	2.57211i		−	0.162350i	0.996700	−	0.0811750i	$-0.0258673\pi$
$252$		0			0
$253$	−1.36619	+	0.696107i	−0.0858915	+	0.0437639i
$254$	−6.24690	−	7.81159i	−0.391965	−	0.490143i
$255$		0			0
$256$	14.9178	−	5.78428i	0.932365	−	0.361517i
$257$	11.1652	−	11.1652i	0.696464	−	0.696464i	−0.267182	−	0.963646i	$-0.586093\pi$
$257$	11.1652	−	11.1652i	0.696464	−	0.696464i	0.963646	+	0.267182i	$0.0860926\pi$
$258$		0			0
$259$	−35.7668	−	25.9861i	−2.22244	−	1.61470i
$260$	−0.691667	+	1.56557i	−0.0428953	+	0.0970928i
$261$		0			0
$262$	−23.6120	−	10.6865i	−1.45875	−	0.660211i
$263$	25.4425	−	4.02970i	1.56885	−	0.248482i	0.689368	−	0.724411i	$-0.257888\pi$
$263$	25.4425	−	4.02970i	1.56885	−	0.248482i	0.879484	+	0.475929i	$0.157888\pi$
$264$		0			0
$265$	−4.21496	+	21.4164i	−0.258923	+	1.31560i
$266$	18.8914	−	7.11931i	1.15830	−	0.436513i
$267$		0			0
$268$	−21.2610	−	8.46147i	−1.29872	−	0.516867i
$269$	16.5916	−	5.39093i	1.01161	−	0.328691i	0.244112	−	0.969747i	$-0.421504\pi$
$269$	16.5916	−	5.39093i	1.01161	−	0.328691i	0.767494	+	0.641057i	$0.221504\pi$
$270$		0			0
$271$	11.1341	+	3.61770i	0.676351	+	0.219760i	0.626997	−	0.779021i	$-0.284284\pi$
$271$	11.1341	+	3.61770i	0.676351	+	0.219760i	0.0493541	+	0.998781i	$0.484284\pi$
$272$	−3.74385	−	1.10211i	−0.227004	−	0.0668251i
$273$		0			0
$274$	14.8109	+	9.74777i	0.894760	+	0.588884i
$275$	3.65956	−	4.32007i	0.220680	−	0.260510i
$276$		0			0
$277$	3.29508	−	20.8043i	0.197982	−	1.25001i	−0.665795	−	0.746135i	$-0.731907\pi$
$277$	3.29508	−	20.8043i	0.197982	−	1.25001i	0.863777	−	0.503875i	$-0.168093\pi$
$278$	4.30992	+	0.479690i	0.258492	+	0.0287699i
$279$		0			0
$280$	−15.5079	+	26.6597i	−0.926775	+	1.59322i
$281$	4.13211	+	12.7173i	0.246501	+	0.758653i	0.995386	+	0.0959525i	$0.0305897\pi$
$281$	4.13211	+	12.7173i	0.246501	+	0.758653i	−0.748885	+	0.662700i	$0.769410\pi$
$282$		0			0
$283$	18.3418	+	9.34561i	1.09031	+	0.555539i	0.904251	−	0.427000i	$-0.140430\pi$
$283$	18.3418	+	9.34561i	1.09031	+	0.555539i	0.186055	+	0.982539i	$0.440430\pi$
$284$	1.27408	−	5.65277i	0.0756026	−	0.335430i
$285$		0			0
$286$	−0.612219	+	0.0283273i	−0.0362013	+	0.00167503i
$287$	4.78058	+	30.1834i	0.282189	+	1.78167i
$288$		0			0
$289$	−9.43281	−	12.9832i	−0.554871	−	0.763715i
$290$	−21.6346	−	3.22748i	−1.27043	−	0.189524i
$291$		0			0
$292$	−0.415438	+	6.42139i	−0.0243117	+	0.375784i
$293$	−11.5164	−	11.5164i	−0.672794	−	0.672794i	0.285565	−	0.958359i	$-0.407819\pi$
$293$	−11.5164	−	11.5164i	−0.672794	−	0.672794i	−0.958359	+	0.285565i	$0.907819\pi$
$294$		0			0
$295$	−9.70921	+	2.75950i	−0.565292	+	0.160664i
$296$	−12.0590	+	22.6296i	−0.700914	+	1.31532i
$297$		0			0
$298$	3.96259	−	4.34708i	0.229547	−	0.251819i
$299$	0.518234			0.0299702
$300$		0			0
$301$	−27.7838			−1.60143
$302$	−5.76303	+	6.32222i	−0.331625	+	0.363803i
$303$		0			0
$304$	−5.60456	−	10.2809i	−0.321444	−	0.589650i
$305$	−0.677437	+	18.1794i	−0.0387900	+	1.04095i
$306$		0			0
$307$	2.86400	+	2.86400i	0.163457	+	0.163457i	0.784096	−	0.620639i	$-0.213127\pi$
$307$	2.86400	+	2.86400i	0.163457	+	0.163457i	−0.620639	+	0.784096i	$0.713127\pi$
$308$	−11.0209	−	0.713007i	−0.627973	−	0.0406273i
$309$		0			0
$310$	17.4485	−	9.08894i	0.991007	−	0.516217i
$311$	−17.2238	−	23.7066i	−0.976674	−	1.34428i	−0.938602	−	0.345002i	$-0.887878\pi$
$311$	−17.2238	−	23.7066i	−0.976674	−	1.34428i	−0.0380720	−	0.999275i	$-0.512122\pi$
$312$		0			0
$313$	3.25048	+	20.5227i	0.183728	+	1.16001i	0.891314	+	0.453387i	$0.149784\pi$
$313$	3.25048	+	20.5227i	0.183728	+	1.16001i	−0.707586	+	0.706627i	$0.750216\pi$
$314$	−14.5256	+	0.672099i	−0.819729	+	0.0379287i
$315$		0			0
$316$	20.1752	+	4.54728i	1.13494	+	0.255804i
$317$	12.4309	+	6.33384i	0.698187	+	0.355744i	0.766788	−	0.641900i	$-0.221854\pi$
$317$	12.4309	+	6.33384i	0.698187	+	0.355744i	−0.0686013	+	0.997644i	$0.521854\pi$
$318$		0			0
$319$	−2.42042	−	7.44929i	−0.135518	−	0.417080i
$320$	16.5579	+	6.77030i	0.925613	+	0.378471i
$321$		0			0
$322$	9.28121	+	1.03299i	0.517222	+	0.0575662i
$323$	−0.446796	+	2.82096i	−0.0248604	+	0.156962i
$324$		0			0
$325$	−1.76494	+	0.739442i	−0.0979011	+	0.0410169i
$326$	18.3825	+	12.0984i	1.01811	+	0.670069i
$327$		0			0
$328$	16.9550	−	5.16668i	0.936182	−	0.285282i
$329$	−50.4094	−	16.3790i	−2.77916	−	0.903004i
$330$		0			0
$331$	26.4957	−	8.60896i	1.45633	−	0.473191i	0.529386	−	0.848381i	$-0.322423\pi$
$331$	26.4957	−	8.60896i	1.45633	−	0.473191i	0.926948	+	0.375190i	$0.122423\pi$
$332$	8.02923	−	20.1749i	0.440661	−	1.10724i
$333$		0			0
$334$	19.6079	−	7.38932i	1.07289	−	0.404326i
$335$	−10.7579	−	23.2120i	−0.587766	−	1.26821i
$336$		0			0
$337$	23.7132	−	3.75580i	1.29174	−	0.204591i	0.527517	−	0.849545i	$-0.323123\pi$
$337$	23.7132	−	3.75580i	1.29174	−	0.204591i	0.764222	+	0.644953i	$0.223123\pi$
$338$	−16.5605	−	7.49505i	−0.900773	−	0.407677i
$339$		0			0
$340$	−2.19250	−	3.77250i	−0.118905	−	0.204593i
$341$	5.69936	+	4.14082i	0.308637	+	0.224238i
$342$		0			0
$343$	−33.7267	+	33.7267i	−1.82107	+	1.82107i
$344$	2.22812	+	15.9600i	0.120132	+	0.860504i
$345$		0			0
$346$	11.7251	+	14.6620i	0.630348	+	0.788234i
$347$	17.5573	−	8.94587i	0.942523	−	0.480239i	0.0859695	−	0.996298i	$-0.472601\pi$
$347$	17.5573	−	8.94587i	0.942523	−	0.480239i	0.856553	+	0.516058i	$0.172601\pi$
$348$		0			0
$349$		−	5.15255i		−	0.275810i	−0.990445	−	0.137905i	$-0.955963\pi$
$349$		−	5.15255i		−	0.275810i	0.990445	−	0.137905i	$-0.0440368\pi$
$350$	−33.0827	+	9.72487i	−1.76835	+	0.519816i
$351$		0			0
$352$	0.474245	+	6.38795i	0.0252773	+	0.340479i
$353$	12.0507	−	6.14012i	0.641392	−	0.326806i	−0.102869	−	0.994695i	$-0.532802\pi$
$353$	12.0507	−	6.14012i	0.641392	−	0.326806i	0.744261	+	0.667889i	$0.232802\pi$
$354$		0			0
$355$	5.37941	−	3.61017i	0.285509	−	0.191608i
$356$	−21.0382	+	18.4814i	−1.11502	+	0.979514i
$357$		0			0
$358$	28.8960	−	16.4480i	1.52720	−	0.869304i
$359$	26.0169	+	18.9024i	1.37312	+	0.997632i	0.997486	+	0.0708643i	$0.0225757\pi$
$359$	26.0169	+	18.9024i	1.37312	+	0.997632i	0.375636	+	0.926767i	$0.377424\pi$
$360$		0			0
$361$	8.43865	−	6.13104i	0.444139	−	0.322686i
$362$	−10.1102	+	22.3388i	−0.531382	+	1.17410i
$363$		0			0
$364$	3.20949	+	1.90578i	0.168223	+	0.0998900i
$365$	−5.27308	+	4.89420i	−0.276005	+	0.256174i
$366$		0			0
$367$	−9.01595	+	17.6948i	−0.470629	+	0.923661i	0.526660	+	0.850076i	$0.323444\pi$
$367$	−9.01595	+	17.6948i	−0.470629	+	0.923661i	−0.997289	+	0.0735850i	$0.976556\pi$
$368$	−0.150923	−	5.41428i	−0.00786739	−	0.282239i
$369$		0			0
$370$	−27.1849	+	9.10389i	−1.41327	+	0.473289i
$371$	45.2724	+	14.7099i	2.35043	+	0.763700i
$372$		0			0
$373$	12.5823	+	1.99284i	0.651487	+	0.103185i	0.473425	−	0.880834i	$-0.343017\pi$
$373$	12.5823	+	1.99284i	0.651487	+	0.103185i	0.178061	+	0.984019i	$0.443017\pi$
$374$	0.858966	−	1.30513i	0.0444161	−	0.0674865i
$375$		0			0
$376$	−5.36608	+	30.2704i	−0.276734	+	1.56108i
$377$	−0.414130	+	2.61472i	−0.0213288	+	0.134665i
$378$		0			0
$379$	−1.14962	+	3.53817i	−0.0590521	+	0.181744i	−0.976231	−	0.216731i	$-0.930460\pi$
$379$	−1.14962	+	3.53817i	−0.0590521	+	0.181744i	0.917179	+	0.398475i	$0.130460\pi$
$380$	3.35204	−	12.6550i	0.171956	−	0.649188i
$381$		0			0
$382$	−3.69895	+	0.762594i	−0.189255	+	0.0390177i
$383$	9.64571	+	4.91473i	0.492873	+	0.251131i	0.682717	−	0.730683i	$-0.260798\pi$
$383$	9.64571	+	4.91473i	0.492873	+	0.251131i	−0.189844	+	0.981814i	$0.560798\pi$
$384$		0			0
$385$	−8.39981	−	9.05006i	−0.428094	−	0.461234i
$386$	−0.504943	−	10.9130i	−0.0257009	−	0.555458i
$387$		0			0
$388$	18.3589	−	11.6053i	0.932034	−	0.589170i
$389$	10.4403	+	14.3698i	0.529342	+	0.728577i	0.987030	−	0.160536i	$-0.0513223\pi$
$389$	10.4403	+	14.3698i	0.529342	+	0.728577i	−0.457688	+	0.889113i	$0.651322\pi$
$390$		0			0
$391$	−0.776556	+	1.06884i	−0.0392721	+	0.0540535i
$392$	37.8797	+	28.5989i	1.91322	+	1.44446i
$393$		0			0
$394$	−5.84043	+	21.2749i	−0.294237	+	1.07181i
$395$	12.8850	+	19.1995i	0.648313	+	0.966033i
$396$		0			0
$397$	13.9286	+	27.3364i	0.699057	+	1.37198i	0.918134	+	0.396269i	$0.129695\pi$
$397$	13.9286	+	27.3364i	0.699057	+	1.37198i	−0.219077	+	0.975708i	$0.570305\pi$
$398$	17.5312	+	15.9806i	0.878762	+	0.801038i
$399$		0			0
$400$	8.23937	+	18.2240i	0.411968	+	0.911198i
$401$	−5.94140			−0.296699			−0.148350	−	0.988935i	$-0.547396\pi$
$401$	−5.94140			−0.296699			−0.148350	+	0.988935i	$0.547396\pi$
$402$		0			0
$403$	−1.08096	−	2.12151i	−0.0538466	−	0.105680i
$404$	0.118575	+	1.27860i	0.00589933	+	0.0636128i
$405$		0			0
$406$	−12.6287	+	46.0023i	−0.626750	+	2.28305i
$407$	−7.25895	−	7.25895i	−0.359813	−	0.359813i
$408$		0			0
$409$	1.52169	−	2.09443i	0.0752427	−	0.103563i	−0.769737	−	0.638361i	$-0.779613\pi$
$409$	1.52169	−	2.09443i	0.0752427	−	0.103563i	0.844979	+	0.534799i	$0.179613\pi$
$410$	17.7371	+	8.83756i	0.875973	+	0.436456i
$411$		0			0
$412$	3.31364	−	2.09466i	0.163251	−	0.103197i
$413$	3.44360	+	21.7421i	0.169449	+	1.06986i
$414$		0			0
$415$	22.0263	−	10.2083i	1.08123	−	0.501108i
$416$	0.837360	−	1.99647i	0.0410549	−	0.0978852i
$417$		0			0
$418$	4.59122	−	0.946549i	0.224564	−	0.0462972i
$419$	−4.92657	−	15.1624i	−0.240679	−	0.740733i	−0.996317	−	0.0857438i	$-0.972673\pi$
$419$	−4.92657	−	15.1624i	−0.240679	−	0.740733i	0.755639	−	0.654989i	$-0.227327\pi$
$420$		0			0
$421$	−3.87186	+	11.9164i	−0.188703	+	0.580768i	−0.999992	−	0.00387660i	$-0.998766\pi$
$421$	−3.87186	+	11.9164i	−0.188703	+	0.580768i	0.811290	+	0.584645i	$0.198766\pi$
$422$	2.18562	−	19.6374i	0.106394	−	0.955932i
$423$		0			0
$424$	4.81924	−	27.1857i	0.234043	−	1.32025i
$425$	1.11963	−	4.74815i	0.0543100	−	0.230319i
$426$		0			0
$427$	39.1859	+	6.20644i	1.89634	+	0.300351i
$428$	−4.06889	+	4.90071i	−0.196677	+	0.236885i
$429$		0			0
$430$	−10.4586	+	14.6705i	−0.504357	+	0.707476i
$431$	−0.172476	+	0.0560408i	−0.00830786	+	0.00269939i	−0.313168	−	0.949698i	$-0.601390\pi$
$431$	−0.172476	+	0.0560408i	−0.00830786	+	0.00269939i	0.304860	+	0.952397i	$0.401390\pi$
$432$		0			0
$433$	−0.946710	+	1.85802i	−0.0454960	+	0.0892909i	−0.912635	−	0.408775i	$-0.865956\pi$
$433$	−0.946710	+	1.85802i	−0.0454960	+	0.0892909i	0.867139	+	0.498066i	$0.165956\pi$
$434$	−15.1305	−	40.1495i	−0.726289	−	1.92724i
$435$		0			0
$436$	−16.6288	−	9.87408i	−0.796373	−	0.472883i
$437$	−3.91508	+	0.620088i	−0.187284	+	0.0296628i
$438$		0			0
$439$	−25.8490	+	18.7804i	−1.23371	+	0.896340i	−0.997162	−	0.0752806i	$-0.976015\pi$
$439$	−25.8490	+	18.7804i	−1.23371	+	0.896340i	−0.236544	+	0.971621i	$0.576015\pi$
$440$	−4.52504	+	5.55090i	−0.215723	+	0.264629i
$441$		0			0
$442$	−0.458935	+	0.261233i	−0.0218293	+	0.0124256i
$443$	15.5829	−	15.5829i	0.740368	−	0.740368i	−0.232281	−	0.972649i	$-0.574619\pi$
$443$	15.5829	−	15.5829i	0.740368	−	0.740368i	0.972649	+	0.232281i	$0.0746188\pi$
$444$		0			0
$445$	−31.2866	−	1.16586i	−1.48313	−	0.0552672i
$446$	7.83196	−	6.26318i	0.370854	−	0.296570i
$447$		0			0
$448$	18.9761	−	34.0864i	0.896536	−	1.61043i
$449$			4.93653i			0.232969i	0.993192	+	0.116485i	$0.0371626\pi$
$449$			4.93653i			0.232969i	−0.993192	+	0.116485i	$0.962837\pi$
$450$		0			0
$451$			7.09601i			0.334138i
$452$	−40.7931	+	10.3968i	−1.91875	+	0.489024i
$453$		0			0
$454$	1.92722	+	2.40994i	0.0904487	+	0.113104i
$455$	1.14091	+	4.01427i	0.0534868	+	0.188192i
$456$		0			0
$457$	6.22919	−	6.22919i	0.291389	−	0.291389i	−0.546240	−	0.837629i	$-0.683941\pi$
$457$	6.22919	−	6.22919i	0.291389	−	0.291389i	0.837629	+	0.546240i	$0.183941\pi$
$458$	5.34057	+	9.38234i	0.249548	+	0.438408i
$459$		0			0
$460$	4.03914	−	4.51186i	0.188326	−	0.210367i
$461$	0.269250	−	0.195622i	0.0125402	−	0.00911102i	−0.581497	−	0.813548i	$-0.697533\pi$
$461$	0.269250	−	0.195622i	0.0125402	−	0.00911102i	0.594038	+	0.804437i	$0.297533\pi$
$462$		0			0
$463$	−10.3280	+	1.63579i	−0.479982	+	0.0760217i	−0.391737	−	0.920077i	$-0.628126\pi$
$463$	−10.3280	+	1.63579i	−0.479982	+	0.0760217i	−0.0882447	+	0.996099i	$0.528126\pi$
$464$	27.4380	+	3.56518i	1.27378	+	0.165509i
$465$		0			0
$466$	−35.1159	+	13.2336i	−1.62671	+	0.613036i
$467$	9.29525	−	18.2429i	0.430133	−	0.844183i	−0.569619	−	0.821909i	$-0.692909\pi$
$467$	9.29525	−	18.2429i	0.430133	−	0.844183i	0.999752	−	0.0222742i	$-0.00709069\pi$
$468$		0			0
$469$	−53.0640	+	17.2415i	−2.45027	+	0.796140i
$470$	−27.6240	+	20.4519i	−1.27420	+	0.943377i
$471$		0			0
$472$	12.2132	−	3.72173i	0.562159	−	0.171306i
$473$	−6.37204	−	1.00923i	−0.292987	−	0.0464045i
$474$		0			0
$475$	12.4487	−	7.69806i	0.571188	−	0.353211i
$476$	−8.73992	+	3.76371i	−0.400594	+	0.172509i
$477$		0			0
$478$	−32.9767	−	3.67027i	−1.50832	−	0.167874i
$479$	6.48175	−	19.9488i	0.296159	−	0.911482i	−0.686671	−	0.726968i	$-0.740929\pi$
$479$	6.48175	−	19.9488i	0.296159	−	0.911482i	0.982830	−	0.184514i	$-0.0590712\pi$
$480$		0			0
$481$	1.07218	+	3.29983i	0.0488872	+	0.150459i
$482$	1.75877	+	8.53087i	0.0801097	+	0.388571i
$483$		0			0
$484$	18.9600	+	4.27338i	0.861816	+	0.194245i
$485$	23.8260	+	4.68920i	1.08188	+	0.212925i
$486$		0			0
$487$	3.28173	+	20.7200i	0.148709	+	0.938914i	0.943342	+	0.331823i	$0.107664\pi$
$487$	3.28173	+	20.7200i	0.148709	+	0.938914i	−0.794632	+	0.607091i	$0.792336\pi$
$488$	0.422674	−	23.0074i	0.0191335	−	1.04150i
$489$		0			0
$490$	8.77214	+	52.3356i	0.396285	+	2.36428i
$491$	−7.62203	+	10.4908i	−0.343977	+	0.473444i	−0.945598	−	0.325338i	$-0.894522\pi$
$491$	−7.62203	+	10.4908i	−0.343977	+	0.473444i	0.601620	+	0.798782i	$0.294522\pi$
$492$		0			0
$493$	−4.77220	−	4.77220i	−0.214929	−	0.214929i
$494$	−1.52787	−	0.419434i	−0.0687419	−	0.0188712i
$495$		0			0
$496$	−21.8498	+	11.9113i	−0.981086	+	0.534832i
$497$	−6.41434	−	12.5889i	−0.287722	−	0.564687i
$498$		0			0
$499$	30.5022			1.36547			0.682733	−	0.730668i	$-0.260791\pi$
$499$	30.5022			1.36547			0.682733	+	0.730668i	$0.260791\pi$
$500$	−7.31825	+	21.1292i	−0.327282	+	0.944927i
$501$		0			0
$502$	−2.45047	+	2.68824i	−0.109370	+	0.119982i
$503$	−4.26886	−	8.37810i	−0.190339	−	0.373561i	0.776040	−	0.630684i	$-0.217226\pi$
$503$	−4.26886	−	8.37810i	−0.190339	−	0.373561i	−0.966379	+	0.257123i	$0.917226\pi$
$504$		0			0
$505$	−0.886521	+	1.12924i	−0.0394497	+	0.0502504i
$506$	2.09106	+	0.574044i	0.0929591	+	0.0255194i
$507$		0			0
$508$	−0.913235	+	14.1158i	−0.0405182	+	0.626287i
$509$	12.1536	−	16.7281i	0.538701	−	0.741458i	−0.449724	−	0.893167i	$-0.648478\pi$
$509$	12.1536	−	16.7281i	0.538701	−	0.741458i	0.988425	+	0.151709i	$0.0484778\pi$
$510$		0			0
$511$	9.22228	+	12.6934i	0.407970	+	0.561522i
$512$	−21.1022	−	8.16695i	−0.932592	−	0.360932i
$513$		0			0
$514$	−22.3065	+	1.03212i	−0.983896	+	0.0455247i
$515$	4.30040	+	0.846361i	0.189498	+	0.0372951i
$516$		0			0
$517$	−10.9661	−	5.58752i	−0.482289	−	0.245739i
$518$	12.6245	+	61.2348i	0.554688	+	2.69050i
$519$		0			0
$520$	2.21444	−	0.977303i	0.0971094	−	0.0428576i
$521$	7.34822	−	22.6155i	0.321931	−	0.990803i	−0.650875	−	0.759185i	$-0.725598\pi$
$521$	7.34822	−	22.6155i	0.321931	−	0.990803i	0.972807	−	0.231618i	$-0.0744020\pi$
$522$		0			0
$523$	3.90499	−	24.6551i	0.170753	−	1.07809i	−0.742245	−	0.670129i	$-0.766239\pi$
$523$	3.90499	−	24.6551i	0.170753	−	1.07809i	0.912998	−	0.407964i	$-0.133761\pi$
$524$	14.4970	+	33.6644i	0.633305	+	1.47064i
$525$		0			0
$526$	−30.4304	−	20.0277i	−1.32683	−	0.873249i
$527$	5.99533	+	0.949566i	0.261161	+	0.0413638i
$528$		0			0
$529$	20.1305	+	6.54078i	0.875238	+	0.284382i
$530$	24.8089	−	18.3678i	1.07763	−	0.797845i
$531$		0			0
$532$	−26.5270	−	10.5572i	−1.15009	−	0.457715i
$533$	1.08882	−	2.13694i	0.0471622	−	0.0925610i
$534$		0			0
$535$	−7.07045	+	0.851352i	−0.305682	+	0.0368071i
$536$	14.1596	+	29.0991i	0.611601	+	1.25689i
$537$		0			0
$538$	−22.4767	−	10.1726i	−0.969039	−	0.438573i
$539$	−15.3727	+	11.1689i	−0.662150	+	0.481080i
$540$		0			0
$541$	1.77850	+	1.29215i	0.0764635	+	0.0555540i	0.625360	−	0.780336i	$-0.284952\pi$
$541$	1.77850	+	1.29215i	0.0764635	+	0.0555540i	−0.548897	+	0.835890i	$0.684952\pi$
$542$	−8.19025	−	14.3887i	−0.351801	−	0.618047i
$543$		0			0
$544$	2.86290	+	4.71868i	0.122746	+	0.202312i
$545$	−5.91121	−	20.7984i	−0.253208	−	0.890906i
$546$		0			0
$547$	−21.9911	+	11.2050i	−0.940272	+	0.479092i	−0.855785	−	0.517332i	$-0.826925\pi$
$547$	−21.9911	+	11.2050i	−0.940272	+	0.479092i	−0.0844870	+	0.996425i	$0.526925\pi$
$548$	−6.19284	−	24.2984i	−0.264545	−	1.03798i
$549$		0			0
$550$	−7.94056	+	1.02862i	−0.338587	+	0.0438607i
$551$		−	20.2488i		−	0.862629i
$552$		0			0
$553$	44.9305	−	22.8933i	1.91064	−	0.973520i
$554$	−23.2644	+	18.6044i	−0.988408	+	0.790425i
$555$		0			0
$556$	−4.04752	−	4.60746i	−0.171653	−	0.195400i
$557$	−9.15739	+	9.15739i	−0.388011	+	0.388011i	−0.873978	−	0.485966i	$-0.838468\pi$
$557$	−9.15739	+	9.15739i	−0.388011	+	0.388011i	0.485966	+	0.873978i	$0.338468\pi$
$558$		0			0
$559$	1.76406	+	1.28166i	0.0746116	+	0.0542085i
$560$	41.6071	−	13.0888i	1.75822	−	0.553104i
$561$		0			0
$562$	7.79726	−	17.2283i	0.328908	−	0.726730i
$563$	−28.6678	+	4.54054i	−1.20820	+	0.191361i	−0.727864	−	0.685721i	$-0.759487\pi$
$563$	−28.6678	+	4.54054i	−1.20820	+	0.191361i	−0.480340	+	0.877082i	$0.659487\pi$
$564$		0			0
$565$	−41.1114	−	22.9144i	−1.72957	−	0.964014i
$566$	−10.2663	−	27.2420i	−0.431524	−	1.14507i
$567$		0			0
$568$	−6.71706	+	4.69418i	−0.281842	+	0.196963i
$569$	14.1150	−	4.58626i	0.591734	−	0.192266i	0.00218334	−	0.999998i	$-0.499305\pi$
$569$	14.1150	−	4.58626i	0.591734	−	0.192266i	0.589550	+	0.807732i	$0.299305\pi$
$570$		0			0
$571$	15.9952	+	5.19714i	0.669376	+	0.217494i	0.623938	−	0.781474i	$-0.285532\pi$
$571$	15.9952	+	5.19714i	0.669376	+	0.217494i	0.0454380	+	0.998967i	$0.485532\pi$
$572$	0.666849	+	0.553661i	0.0278824	+	0.0231497i
$573$		0			0
$574$	23.7596	−	36.1007i	0.991707	−	1.50681i
$575$	6.74740	−	0.558513i	0.281386	−	0.0232916i
$576$		0			0
$577$	−0.474490	+	2.99581i	−0.0197533	+	0.124717i	−0.995594	−	0.0937637i	$-0.970110\pi$
$577$	−0.474490	+	2.99581i	−0.0197533	+	0.124717i	0.975841	+	0.218481i	$0.0701102\pi$
$578$	−2.51047	+	22.5561i	−0.104422	+	0.938210i
$579$		0			0
$580$	19.5366	+	23.9847i	0.811212	+	0.995911i
$581$	−16.3608	−	50.3533i	−0.678760	−	2.08901i
$582$		0			0
$583$	9.84861	+	5.01812i	0.407888	+	0.207829i
$584$	6.55193	−	6.31554i	0.271121	−	0.261339i
$585$		0			0
$586$	1.06458	+	23.0081i	0.0439775	+	0.950458i
$587$	−5.91133	−	37.3227i	−0.243987	−	1.54047i	−0.740269	−	0.672311i	$-0.765302\pi$
$587$	−5.91133	−	37.3227i	−0.243987	−	1.54047i	0.496282	−	0.868161i	$-0.334698\pi$
$588$		0			0
$589$	10.7048	+	14.7339i	0.441083	+	0.607099i
$590$	12.7766	+	6.36598i	0.526004	+	0.262083i
$591$		0			0
$592$	34.1629	−	12.1627i	1.40409	−	0.499882i
$593$	3.22677	+	3.22677i	0.132507	+	0.132507i	0.770250	−	0.637742i	$-0.220132\pi$
$593$	3.22677	+	3.22677i	0.132507	+	0.132507i	−0.637742	+	0.770250i	$0.720132\pi$
$594$		0			0
$595$	−9.98890	−	3.66216i	−0.409505	−	0.150134i
$596$	−8.28301	+	0.768151i	−0.339285	+	0.0314647i
$597$		0			0
$598$	−0.541633	−	0.493727i	−0.0221490	−	0.0201900i
$599$	17.2089			0.703136			0.351568	−	0.936162i	$-0.385649\pi$
$599$	17.2089			0.703136			0.351568	+	0.936162i	$0.385649\pi$
$600$		0			0
$601$	38.1195			1.55493			0.777463	−	0.628929i	$-0.216506\pi$
$601$	38.1195			1.55493			0.777463	+	0.628929i	$0.216506\pi$
$602$	29.0383	+	26.4699i	1.18351	+	1.07883i
$603$		0			0
$604$	12.0465	−	1.11717i	0.490165	−	0.0454570i
$605$	12.1089	+	18.0431i	0.492295	+	0.733555i
$606$		0			0
$607$	20.3631	+	20.3631i	0.826511	+	0.826511i	0.987032	−	0.160521i	$-0.0513174\pi$
$607$	20.3631	+	20.3631i	0.826511	+	0.826511i	−0.160521	+	0.987032i	$0.551317\pi$
$608$	−3.93711	+	16.0846i	−0.159671	+	0.652318i
$609$		0			0
$610$	18.0278	−	18.3549i	0.729923	−	0.743167i
$611$	2.44504	+	3.36531i	0.0989159	+	0.136146i
$612$		0			0
$613$	−3.33954	−	21.0850i	−0.134883	−	0.851616i	−0.958629	−	0.284658i	$-0.908120\pi$
$613$	−3.33954	−	21.0850i	−0.134883	−	0.851616i	0.823746	−	0.566958i	$-0.191880\pi$
$614$	−0.264750	−	5.72188i	−0.0106844	−	0.230916i
$615$		0			0
$616$	10.8392	+	11.2449i	0.436724	+	0.453071i
$617$	−20.9180	−	10.6583i	−0.842127	−	0.429085i	−0.0209650	−	0.999780i	$-0.506674\pi$
$617$	−20.9180	−	10.6583i	−0.842127	−	0.429085i	−0.821162	+	0.570695i	$0.806674\pi$
$618$		0			0
$619$	−0.134035	−	0.412516i	−0.00538731	−	0.0165804i	0.948327	−	0.317295i	$-0.102775\pi$
$619$	−0.134035	−	0.412516i	−0.00538731	−	0.0165804i	−0.953714	+	0.300715i	$0.902775\pi$
$620$	−26.8954	−	7.12403i	−1.08015	−	0.286108i
$621$		0			0
$622$	−4.58399	+	41.1863i	−0.183801	+	1.65142i
$623$	−10.6812	+	67.4386i	−0.427934	+	2.70187i
$624$		0			0
$625$	−22.1826	+	11.5297i	−0.887303	+	0.461186i
$626$	16.1550	−	24.5461i	0.645683	−	0.981061i
$627$		0			0
$628$	15.8218	+	13.1363i	0.631359	+	0.524195i
$629$	−8.41240	−	2.73336i	−0.335424	−	0.108986i
$630$		0			0
$631$	16.2307	−	5.27366i	0.646132	−	0.209941i	0.0324242	−	0.999474i	$-0.489677\pi$
$631$	16.2307	−	5.27366i	0.646132	−	0.209941i	0.613708	+	0.789533i	$0.289677\pi$
$632$	−16.7539	−	23.9737i	−0.666433	−	0.953623i
$633$		0			0
$634$	−6.95782	−	18.4628i	−0.276330	−	0.733253i
$635$	−11.5915	+	10.7587i	−0.459995	+	0.426944i
$636$		0			0
$637$	6.34321	−	1.00467i	0.251327	−	0.0398063i
$638$	−4.56731	+	10.0916i	−0.180822	+	0.399530i
$639$		0			0
$640$	−10.8553	−	22.8509i	−0.429095	−	0.903259i
$641$	12.5185	+	9.09522i	0.494451	+	0.359240i	0.806893	−	0.590697i	$-0.201147\pi$
$641$	12.5185	+	9.09522i	0.494451	+	0.359240i	−0.312442	+	0.949937i	$0.601147\pi$
$642$		0			0
$643$	−28.3880	+	28.3880i	−1.11951	+	1.11951i	−0.127702	+	0.991813i	$0.540760\pi$
$643$	−28.3880	+	28.3880i	−1.11951	+	1.11951i	−0.991813	+	0.127702i	$0.959240\pi$
$644$	−8.71613	−	9.92194i	−0.343464	−	0.390979i
$645$		0			0
$646$	3.15452	−	2.52266i	0.124113	−	0.0992527i
$647$	−18.4230	+	9.38699i	−0.724283	+	0.369041i	−0.776942	−	0.629572i	$-0.783230\pi$
$647$	−18.4230	+	9.38699i	−0.724283	+	0.369041i	0.0526593	+	0.998613i	$0.483230\pi$
$648$		0			0
$649$			5.11149i			0.200643i
$650$	2.54910	+	0.908646i	0.0999840	+	0.0356400i
$651$		0			0
$652$	−7.68623	−	30.1579i	−0.301016	−	1.18108i
$653$	−8.91662	+	4.54324i	−0.348934	+	0.177791i	−0.619669	−	0.784863i	$-0.712733\pi$
$653$	−8.91662	+	4.54324i	−0.348934	+	0.177791i	0.270735	+	0.962654i	$0.412733\pi$
$654$		0			0
$655$	−14.1059	+	38.4752i	−0.551163	+	1.50335i
$656$	−22.6429	−	10.7532i	−0.884056	−	0.419843i
$657$		0			0
$658$	37.0810	+	65.1442i	1.44557	+	2.53958i
$659$	−33.4079	−	24.2722i	−1.30139	−	0.945512i	−0.301418	−	0.953492i	$-0.597460\pi$
$659$	−33.4079	−	24.2722i	−1.30139	−	0.945512i	−0.999968	+	0.00798023i	$0.997460\pi$
$660$		0			0
$661$	−14.7870	+	10.7434i	−0.575150	+	0.417871i	−0.836972	−	0.547245i	$-0.815676\pi$
$661$	−14.7870	+	10.7434i	−0.575150	+	0.417871i	0.261823	+	0.965116i	$0.415676\pi$
$662$	−35.8938	−	16.2450i	−1.39505	−	0.631381i
$663$		0			0
$664$	−27.6126	+	13.4363i	−1.07158	+	0.521429i
$665$	−13.4225	−	28.9613i	−0.520501	−	1.12307i
$666$		0			0
$667$	4.25231	−	8.34562i	0.164650	−	0.323144i
$668$	−27.5331	−	10.9577i	−1.06529	−	0.423964i
$669$		0			0
$670$	−10.8707	+	34.5093i	−0.419973	+	1.33321i
$671$	8.76159	+	2.84681i	0.338237	+	0.109900i
$672$		0			0
$673$	48.1900	+	7.63255i	1.85759	+	0.294213i	0.982005	−	0.188853i	$-0.0604769\pi$
$673$	48.1900	+	7.63255i	1.85759	+	0.294213i	0.875584	+	0.483066i	$0.160477\pi$
$674$	−28.3621	−	18.6664i	−1.09247	−	0.719004i
$675$		0			0
$676$	10.1676	+	23.6108i	0.391063	+	0.908109i
$677$	−3.79889	+	23.9853i	−0.146003	+	0.921829i	0.800546	+	0.599271i	$0.204543\pi$
$677$	−3.79889	+	23.9853i	−0.146003	+	0.921829i	−0.946550	+	0.322558i	$0.895457\pi$
$678$		0			0
$679$	16.3649	−	50.3661i	0.628029	−	1.93287i
$680$	−1.30261	+	6.03165i	−0.0499527	+	0.231303i
$681$		0			0
$682$	−2.01168	−	9.75763i	−0.0770313	−	0.373639i
$683$	22.8040	+	11.6192i	0.872573	+	0.444598i	0.832128	−	0.554584i	$-0.187123\pi$
$683$	22.8040	+	11.6192i	0.872573	+	0.444598i	0.0404447	+	0.999182i	$0.487123\pi$
$684$		0			0
$685$	13.6489	−	24.4880i	0.521499	−	0.935638i
$686$	67.3813	−	3.11772i	2.57263	−	0.119035i
$687$		0			0
$688$	12.8765	−	18.8033i	0.490912	−	0.716871i
$689$	−2.19588	−	3.02237i	−0.0836564	−	0.115143i
$690$		0			0
$691$	25.8483	−	35.5771i	0.983315	−	1.35342i	0.0482902	−	0.998833i	$-0.484623\pi$
$691$	25.8483	−	35.5771i	0.983315	−	1.35342i	0.935024	−	0.354583i	$-0.115377\pi$
$692$	1.71410	−	26.4947i	0.0651603	−	1.00718i
$693$		0			0
$694$	−26.8728	−	7.37720i	−1.02008	−	0.280035i
$695$	0.255329	−	6.85191i	0.00968519	−	0.259908i
$696$		0			0
$697$	2.77579	+	5.44779i	0.105140	+	0.206350i
$698$	−4.90889	+	5.38520i	−0.185804	+	0.203833i
$699$		0			0
$700$	43.8415	+	21.3543i	1.65705	+	0.807118i
$701$	3.03450			0.114612			0.0573058	−	0.998357i	$-0.481749\pi$
$701$	3.03450			0.114612			0.0573058	+	0.998357i	$0.481749\pi$
$702$		0			0
$703$	−12.0483	−	23.6462i	−0.454412	−	0.891833i
$704$	5.59021	−	7.12819i	0.210689	−	0.268654i
$705$		0			0
$706$	−18.4445	−	5.06344i	−0.694169	−	0.190565i
$707$	2.21392	+	2.21392i	0.0832632	+	0.0832632i
$708$		0			0
$709$	2.95107	−	4.06180i	0.110830	−	0.152544i	−0.749999	−	0.661439i	$-0.769946\pi$
$709$	2.95107	−	4.06180i	0.110830	−	0.152544i	0.860829	+	0.508895i	$0.169946\pi$
$710$	−9.06175	−	1.35185i	−0.340081	−	0.0507339i
$711$		0			0
$712$	39.5956	+	0.727418i	1.48391	+	0.0272611i
$713$	1.31786	+	8.32065i	0.0493543	+	0.311611i
$714$		0			0
$715$	0.115845	+	0.962089i	0.00433236	+	0.0359801i
$716$	−45.8709	−	10.3388i	−1.71427	−	0.386380i
$717$		0			0
$718$	−9.18312	−	44.5425i	−0.342711	−	1.66231i
$719$	−2.16330	−	6.65796i	−0.0806776	−	0.248300i	0.902580	−	0.430523i	$-0.141671\pi$
$719$	−2.16330	−	6.65796i	−0.0806776	−	0.248300i	−0.983257	+	0.182223i	$0.941671\pi$
$720$		0			0
$721$	2.95374	−	9.09067i	0.110003	−	0.338554i
$722$	−14.6608	−	1.63173i	−0.545618	−	0.0607267i
$723$		0			0
$724$	31.8492	−	13.7153i	1.18367	−	0.509727i
$725$	−2.57404	+	34.4899i	−0.0955973	+	1.28092i
$726$		0			0
$727$	−32.4515	−	5.13982i	−1.20356	−	0.190625i	−0.477735	−	0.878504i	$-0.658542\pi$
$727$	−32.4515	−	5.13982i	−1.20356	−	0.190625i	−0.725826	+	0.687878i	$0.758542\pi$
$728$	−1.53875	−	5.04955i	−0.0570297	−	0.187149i
$729$		0			0
$730$	10.1739	−	0.0914673i	0.376554	−	0.00338536i
$731$	−5.28676	+	1.71777i	−0.195538	+	0.0635341i
$732$		0			0
$733$	−1.41894	+	2.78484i	−0.0524099	+	0.102860i	−0.915726	−	0.401803i	$-0.868384\pi$
$733$	−1.41894	+	2.78484i	−0.0524099	+	0.102860i	0.863316	+	0.504664i	$0.168384\pi$
$734$	26.2811	−	9.90415i	0.970052	−	0.365569i
$735$		0			0
$736$	−5.00051	+	5.80253i	−0.184321	+	0.213884i
$737$	−12.7962	+	2.02671i	−0.471353	+	0.0746550i
$738$		0			0
$739$	−20.2292	+	14.6973i	−0.744142	+	0.540651i	−0.894005	−	0.448056i	$-0.852116\pi$
$739$	−20.2292	+	14.6973i	−0.744142	+	0.540651i	0.149864	+	0.988707i	$0.452116\pi$
$740$	37.0857	+	16.3844i	1.36330	+	0.602301i
$741$		0			0
$742$	−33.3023	−	58.5056i	−1.22256	−	2.14781i
$743$	14.2547	−	14.2547i	0.522956	−	0.522956i	−0.395507	−	0.918463i	$-0.629431\pi$
$743$	14.2547	−	14.2547i	0.522956	−	0.522956i	0.918463	+	0.395507i	$0.129431\pi$
$744$		0			0
$745$	−7.31542	−	5.74305i	−0.268016	−	0.210409i
$746$	−11.2518	−	14.0701i	−0.411958	−	0.515143i
$747$		0			0
$748$	−2.14116	+	0.545709i	−0.0782885	+	0.0199531i
$749$			15.5311i			0.567493i
$750$		0			0
$751$		−	19.9242i		−	0.727043i	−0.931586	−	0.363522i	$-0.881574\pi$
$751$		−	19.9242i		−	0.727043i	0.931586	−	0.363522i	$-0.118426\pi$
$752$	34.4473	−	26.5248i	1.25616	−	0.967261i
$753$		0			0
$754$	2.92390	−	2.33823i	0.106482	−	0.0851532i
$755$	10.6393	+	8.35247i	0.387202	+	0.303977i
$756$		0			0
$757$	−22.1849	+	22.1849i	−0.806324	+	0.806324i	−0.984075	−	0.177752i	$-0.943118\pi$
$757$	−22.1849	+	22.1849i	−0.806324	+	0.806324i	0.177752	+	0.984075i	$0.443118\pi$
$758$	4.57239	−	2.60267i	0.166077	−	0.0945332i
$759$		0			0
$760$	−15.5599	+	10.0329i	−0.564418	+	0.363930i
$761$	−41.1545	+	29.9005i	−1.49185	+	1.08389i	−0.518361	+	0.855162i	$0.673458\pi$
$761$	−41.1545	+	29.9005i	−1.49185	+	1.08389i	−0.973490	+	0.228732i	$0.926542\pi$
$762$		0			0
$763$	−46.5743	+	7.37665i	−1.68610	+	0.267053i
$764$	4.59249	+	2.72700i	0.166151	+	0.0986594i
$765$		0			0
$766$	−5.39891	−	14.3262i	−0.195070	−	0.517627i
$767$	0.784314	−	1.53930i	0.0283199	−	0.0555810i
$768$		0			0
$769$	−32.6790	+	10.6180i	−1.17843	+	0.382896i	−0.831785	−	0.555099i	$-0.812681\pi$
$769$	−32.6790	+	10.6180i	−1.17843	+	0.382896i	−0.346649	+	0.937995i	$0.612681\pi$
$770$	0.156983	+	17.4613i	0.00565728	+	0.629261i
$771$		0			0
$772$	−9.86921	+	11.8868i	−0.355201	+	0.427816i
$773$	11.0837	+	1.75548i	0.398652	+	0.0631403i	0.352542	−	0.935796i	$-0.385317\pi$
$773$	11.0837	+	1.75548i	0.398652	+	0.0631403i	0.0461104	+	0.998936i	$0.485317\pi$
$774$		0			0
$775$	−16.3606	−	26.4571i	−0.587688	−	0.950367i
$776$	−30.2444	−	5.36147i	−1.08571	−	0.192465i
$777$		0			0
$778$	2.77860	−	24.9651i	0.0996175	−	0.895044i
$779$	−5.66876	+	17.4467i	−0.203105	+	0.625092i
$780$		0			0
$781$	−1.01380	−	3.12017i	−0.0362768	−	0.111648i
$782$	1.82991	−	0.377264i	0.0654376	−	0.0134909i
$783$		0			0
$784$	−12.3436	−	65.9786i	−0.440844	−	2.35638i
$785$	2.74856	+	22.8267i	0.0981004	+	0.814721i
$786$		0			0
$787$	4.95187	+	31.2648i	0.176515	+	1.11447i	0.903743	+	0.428076i	$0.140808\pi$
$787$	4.95187	+	31.2648i	0.176515	+	1.11447i	−0.727228	+	0.686396i	$0.759192\pi$
$788$	26.3729	−	16.6712i	0.939497	−	0.593887i
$789$		0			0
$790$	4.82484	−	32.3421i	0.171660	−	1.15068i
$791$	−60.3330	+	83.0413i	−2.14520	+	2.95261i
$792$		0			0
$793$	−2.20170	−	2.20170i	−0.0781846	−	0.0781846i
$794$	11.4862	−	41.8407i	0.407631	−	1.48487i
$795$		0			0
$796$	−3.09786	−	33.4044i	−0.109801	−	1.18399i
$797$	8.73067	+	17.1349i	0.309256	+	0.606949i	0.992361	−	0.123371i	$-0.0393707\pi$
$797$	8.73067	+	17.1349i	0.309256	+	0.606949i	−0.683104	+	0.730321i	$0.739371\pi$
$798$		0			0
$799$	−10.6047			−0.375166
$800$	8.75078	−	26.8965i	0.309387	−	0.950936i
$801$		0			0
$802$	6.20966	+	5.66043i	0.219271	+	0.199877i
$803$	1.65399	+	3.24614i	0.0583681	+	0.114554i
$804$		0			0
$805$	0.549839	−	14.7553i	0.0193793	−	0.520054i
$806$	−0.891415	+	3.24715i	−0.0313988	+	0.114376i
$807$		0			0
$808$	1.09421	−	1.44930i	0.0384941	−	0.0509862i
$809$	7.61410	−	10.4799i	0.267698	−	0.368454i	−0.653913	−	0.756570i	$-0.726874\pi$
$809$	7.61410	−	10.4799i	0.267698	−	0.368454i	0.921611	+	0.388116i	$0.126874\pi$
$810$		0			0
$811$	−12.7466	−	17.5442i	−0.447595	−	0.616061i	0.524284	−	0.851544i	$-0.324333\pi$
$811$	−12.7466	−	17.5442i	−0.447595	−	0.616061i	−0.971879	+	0.235482i	$0.924333\pi$
$812$	57.0257	−	36.0479i	2.00121	−	1.26503i
$813$		0			0
$814$	0.671023	+	14.5024i	0.0235193	+	0.508308i
$815$	16.9403	−	30.3932i	0.593394	−	1.06463i
$816$		0			0
$817$	−14.8604	−	7.57176i	−0.519900	−	0.264902i
$818$	−3.58578	+	0.739262i	−0.125374	+	0.0258477i
$819$		0			0
$820$	−10.1183	−	26.1349i	−0.353347	−	0.912671i
$821$	4.44219	−	13.6717i	0.155033	−	0.477144i	−0.843131	−	0.537709i	$-0.819290\pi$
$821$	4.44219	−	13.6717i	0.155033	−	0.477144i	0.998164	+	0.0605645i	$0.0192901\pi$
$822$		0			0
$823$	4.81502	−	30.4008i	0.167841	−	1.05971i	−0.749616	−	0.661873i	$-0.769762\pi$
$823$	4.81502	−	30.4008i	0.167841	−	1.05971i	0.917457	−	0.397834i	$-0.130238\pi$
$824$	−5.45886	−	0.967700i	−0.190168	−	0.0337114i
$825$		0			0
$826$	17.1148	−	26.0045i	0.595500	−	0.904812i
$827$	9.24250	+	1.46387i	0.321393	+	0.0509037i	0.315047	−	0.949076i	$-0.397980\pi$
$827$	9.24250	+	1.46387i	0.321393	+	0.0509037i	0.00634652	+	0.999980i	$0.497980\pi$
$828$		0			0
$829$	3.27588	+	1.06440i	0.113776	+	0.0369681i	0.365352	−	0.930870i	$-0.380949\pi$
$829$	3.27588	+	1.06440i	0.113776	+	0.0369681i	−0.251576	+	0.967838i	$0.580949\pi$
$830$	−32.7464	−	10.3154i	−1.13665	−	0.358054i
$831$		0			0
$832$	−2.77723	+	1.28886i	−0.0962831	+	0.0446830i
$833$	−7.43301	+	14.5881i	−0.257539	+	0.505448i
$834$		0			0
$835$	−13.9315	−	30.0597i	−0.482121	−	1.04026i
$836$	−5.70030	−	3.38481i	−0.197149	−	0.117066i
$837$		0			0
$838$	−9.29639	+	20.5406i	−0.321138	+	0.709564i
$839$	1.69383	−	1.23064i	0.0584776	−	0.0424864i	−0.558162	−	0.829732i	$-0.688493\pi$
$839$	1.69383	−	1.23064i	0.0584776	−	0.0424864i	0.616640	+	0.787245i	$0.288493\pi$
$840$		0			0
$841$	15.2477	+	11.0781i	0.525784	+	0.382004i
$842$	15.3995	−	8.76564i	0.530703	−	0.302084i
$843$		0			0
$844$	−20.9930	+	18.4418i	−0.722610	+	0.634792i
$845$	−9.89330	+	26.9850i	−0.340340	+	0.928311i
$846$		0			0
$847$	42.2242	−	21.5143i	1.45084	−	0.739241i
$848$	−30.9369	+	23.8218i	−1.06238	+	0.818044i
$849$		0			0
$850$	−5.69380	+	3.89585i	−0.195296	+	0.133627i
$851$		−	12.2760i		−	0.420817i
$852$		0			0
$853$	−33.8979	+	17.2718i	−1.16064	+	0.591376i	−0.924814	−	0.380419i	$-0.875780\pi$
$853$	−33.8979	+	17.2718i	−1.16064	+	0.591376i	−0.235827	+	0.971795i	$0.575780\pi$
$854$	−35.0423	−	43.8195i	−1.19912	−	1.49947i
$855$		0			0
$856$	8.92157	−	1.24551i	0.304933	−	0.0425708i
$857$	32.6730	−	32.6730i	1.11609	−	1.11609i	0.123779	−	0.992310i	$-0.460499\pi$
$857$	32.6730	−	32.6730i	1.11609	−	1.11609i	0.992310	−	0.123779i	$-0.0395013\pi$
$858$		0			0
$859$	−30.2637	−	21.9879i	−1.03258	−	0.750217i	−0.0637605	−	0.997965i	$-0.520309\pi$
$859$	−30.2637	−	21.9879i	−1.03258	−	0.750217i	−0.968824	+	0.247748i	$0.920309\pi$
$860$	24.9076	−	5.36895i	0.849341	−	0.183080i
$861$		0			0
$862$	0.233654	+	0.105748i	0.00795829	+	0.00360181i
$863$	−52.4831	+	8.31251i	−1.78655	+	0.282961i	−0.960019	−	0.279936i	$-0.909687\pi$
$863$	−52.4831	+	8.31251i	−1.78655	+	0.282961i	−0.826527	+	0.562897i	$0.809687\pi$
$864$		0			0
$865$	21.7567	−	20.1935i	0.739752	−	0.686600i
$866$	2.75961	−	1.03998i	0.0937755	−	0.0353398i
$867$		0			0
$868$	−22.4371	+	56.3773i	−0.761566	+	1.91357i
$869$	11.1361	−	3.61834i	0.377767	−	0.122744i
$870$		0			0
$871$	4.16450	+	1.35313i	0.141109	+	0.0458490i
$872$	7.97243	+	26.1623i	0.269980	+	0.885968i
$873$		0			0
$874$	4.68262	+	3.08186i	0.158392	+	0.104245i
$875$	19.1810	+	51.0362i	0.648435	+	1.72534i
$876$		0			0
$877$	0.559164	−	3.53042i	0.0188816	−	0.119214i	−0.976447	−	0.215756i	$-0.930778\pi$
$877$	0.559164	−	3.53042i	0.0188816	−	0.119214i	0.995329	+	0.0965424i	$0.0307783\pi$
$878$	44.9084	+	4.99826i	1.51559	+	0.168683i
$879$		0			0
$880$	10.0178	−	1.49048i	0.337699	−	0.0502442i
$881$	7.33129	+	22.5634i	0.246997	+	0.760180i	0.995302	+	0.0968241i	$0.0308684\pi$
$881$	7.33129	+	22.5634i	0.246997	+	0.760180i	−0.748304	+	0.663356i	$0.769132\pi$
$882$		0			0
$883$	34.4658	+	17.5612i	1.15987	+	0.590982i	0.924596	−	0.380948i	$-0.124402\pi$
$883$	34.4658	+	17.5612i	1.15987	+	0.590982i	0.235271	+	0.971930i	$0.424402\pi$
$884$	0.728536	+	0.164205i	0.0245033	+	0.00552280i
$885$		0			0
$886$	−31.1326	+	1.44050i	−1.04592	+	0.0483945i
$887$	−5.52267	−	34.8688i	−0.185433	−	1.17078i	−0.888233	−	0.459392i	$-0.848067\pi$
$887$	−5.52267	−	34.8688i	−0.185433	−	1.17078i	0.702800	−	0.711387i	$-0.251933\pi$
$888$		0			0
$889$	20.2728	+	27.9031i	0.679929	+	0.935842i
$890$	31.5885	+	31.0256i	1.05885	+	1.03998i
$891$		0			0
$892$	−14.1526	−	0.915615i	−0.473863	−	0.0306571i
$893$	−22.4982	−	22.4982i	−0.752875	−	0.752875i
$894$		0			0
$895$	−29.2957	−	43.6526i	−0.979246	−	1.45915i
$896$	−52.3073	+	17.5467i	−1.74747	+	0.586194i
$897$		0			0
$898$	4.70309	−	5.15942i	0.156944	−	0.172172i
$899$	−43.0345			−1.43528
$900$		0			0
$901$	9.52399			0.317290
$902$	6.76045	−	7.41641i	0.225098	−	0.246939i
$903$		0			0
$904$	52.5401	+	27.9978i	1.74746	+	0.931194i
$905$	36.4006	+	13.3453i	1.21000	+	0.443612i
$906$		0			0
$907$	−12.7734	−	12.7734i	−0.424135	−	0.424135i	0.462489	−	0.886625i	$-0.346956\pi$
$907$	−12.7734	−	12.7734i	−0.424135	−	0.424135i	−0.886625	+	0.462489i	$0.846956\pi$
$908$	0.281740	−	4.35483i	0.00934987	−	0.144520i
$909$		0			0
$910$	2.63201	−	5.28248i	0.0872503	−	0.175112i
$911$	−21.0752	−	29.0075i	−0.698253	−	0.961062i	−0.999971	−	0.00766504i	$-0.997560\pi$
$911$	−21.0752	−	29.0075i	−0.698253	−	0.961062i	0.301718	−	0.953397i	$-0.402440\pi$
$912$		0			0
$913$	−1.92318	−	12.1425i	−0.0636481	−	0.401858i
$914$	−12.4451	+	0.575831i	−0.411646	+	0.0190468i
$915$		0			0
$916$	3.35695	−	14.8940i	0.110917	−	0.492111i
$917$	79.6298	+	40.5734i	2.62961	+	1.33985i
$918$		0			0
$919$	4.91425	+	15.1245i	0.162106	+	0.498912i	0.998811	−	0.0487419i	$-0.0155212\pi$
$919$	4.91425	+	15.1245i	0.162106	+	0.498912i	−0.836705	+	0.547654i	$0.815521\pi$
$920$	−8.52001	+	0.867451i	−0.280896	+	0.0285990i
$921$		0			0
$922$	−0.467779	−	0.0520633i	−0.0154055	−	0.00171461i
$923$	−0.173460	+	1.09519i	−0.00570952	+	0.0360485i
$924$		0			0
$925$	17.5161	+	41.8083i	0.575925	+	1.37465i
$926$	12.3527	+	8.12993i	0.405936	+	0.267166i
$927$		0			0
$928$	−25.2803	−	29.8667i	−0.829867	−	0.980421i
$929$	13.9497	+	4.53255i	0.457676	+	0.148708i	0.528776	−	0.848761i	$-0.322651\pi$
$929$	13.9497	+	4.53255i	0.457676	+	0.148708i	−0.0711001	+	0.997469i	$0.522651\pi$
$930$		0			0
$931$	−46.7187	+	15.1798i	−1.53115	+	0.497499i
$932$	49.3093	+	19.6242i	1.61518	+	0.642812i
$933$		0			0
$934$	−27.0952	+	10.2110i	−0.886582	+	0.334113i
$935$	−2.15786	−	1.20273i	−0.0705697	−	0.0393336i
$936$		0			0
$937$	17.6258	−	2.79165i	0.575809	−	0.0911992i	0.138264	−	0.990395i	$-0.455848\pi$
$937$	17.6258	−	2.79165i	0.575809	−	0.0911992i	0.437545	+	0.899196i	$0.355848\pi$
$938$	71.8861	+	32.5346i	2.34716	+	1.06229i
$939$		0			0
$940$	48.3560	+	4.94229i	1.57720	+	0.161200i
$941$	32.8555	+	23.8709i	1.07106	+	0.778169i	0.976102	−	0.217312i	$-0.0697290\pi$
$941$	32.8555	+	23.8709i	1.07106	+	0.778169i	0.0949560	+	0.995481i	$0.469729\pi$
$942$		0			0
$943$	−6.00024	+	6.00024i	−0.195395	+	0.195395i
$944$	−16.3104	−	7.74589i	−0.530858	−	0.252107i
$945$		0			0
$946$	5.69824	+	7.12551i	0.185266	+	0.231670i
$947$	−6.28337	+	3.20154i	−0.204182	+	0.104036i	−0.553092	−	0.833120i	$-0.686552\pi$
$947$	−6.28337	+	3.20154i	−0.204182	+	0.104036i	0.348909	+	0.937156i	$0.386552\pi$
$948$		0			0
$949$		−	1.23135i		−	0.0399714i
$950$	−20.3449	−	3.81441i	−0.660074	−	0.123756i
$951$		0			0
$952$	12.7203	+	4.39297i	0.412266	+	0.142377i
$953$	−32.3125	+	16.4640i	−1.04671	+	0.533323i	−0.890775	−	0.454445i	$-0.849838\pi$
$953$	−32.3125	+	16.4640i	−1.04671	+	0.533323i	−0.155930	+	0.987768i	$0.549838\pi$
$954$		0			0
$955$	1.63254	+	5.74406i	0.0528279	+	0.185873i
$956$	30.9690	+	35.2533i	1.00161	+	1.14017i
$957$		0			0
$958$	−25.7798	+	14.6743i	−0.832908	+	0.474104i
$959$	−49.4635	−	35.9373i	−1.59726	−	1.16048i
$960$		0			0
$961$	6.23413	−	4.52936i	0.201101	−	0.146108i
$962$	2.02319	−	4.47030i	0.0652303	−	0.144128i
$963$		0			0
$964$	6.28928	−	10.5917i	0.202564	−	0.341134i
$965$	−17.1496	+	2.06498i	−0.552065	+	0.0664740i
$966$		0			0
$967$	−1.56312	+	3.06780i	−0.0502667	+	0.0986539i	−0.914773	−	0.403967i	$-0.867631\pi$
$967$	−1.56312	+	3.06780i	−0.0502667	+	0.0986539i	0.864507	+	0.502621i	$0.167631\pi$
$968$	−15.7447	−	22.5297i	−0.506055	−	0.724132i
$969$		0			0
$970$	−20.4343	−	27.6002i	−0.656107	−	0.886190i
$971$	−27.4780	−	8.92814i	−0.881810	−	0.286517i	−0.167101	−	0.985940i	$-0.553441\pi$
$971$	−27.4780	−	8.92814i	−0.881810	−	0.286517i	−0.714709	+	0.699422i	$0.753441\pi$
$972$		0			0
$973$	−14.7693	−	2.33924i	−0.473484	−	0.0749924i
$974$	16.3103	−	24.7821i	0.522615	−	0.794070i
$975$		0			0
$976$	−22.3612	+	23.6436i	−0.715764	+	0.756812i
$977$	−0.124456	+	0.785785i	−0.00398170	+	0.0251395i	−0.989599	−	0.143852i	$-0.954051\pi$
$977$	−0.124456	+	0.785785i	−0.00398170	+	0.0251395i	0.985618	+	0.168992i	$0.0540511\pi$
$978$		0			0
$979$	−4.89934	+	15.0786i	−0.156583	+	0.481914i
$980$	40.6924	−	63.0559i	1.29987	−	2.01425i
$981$		0			0
$982$	17.9609	−	3.70291i	0.573155	−	0.118165i
$983$	42.2667	+	21.5360i	1.34810	+	0.686891i	0.970955	−	0.239263i	$-0.0769059\pi$
$983$	42.2667	+	21.5360i	1.34810	+	0.686891i	0.377145	+	0.926154i	$0.376906\pi$
$984$		0			0
$985$	34.2265	+	6.73611i	1.09055	+	0.214630i
$986$	0.441145	+	9.53419i	0.0140489	+	0.303630i
$987$		0			0
$988$	1.19725	+	1.89399i	0.0380897	+	0.0602557i
$989$	−4.53468	−	6.24145i	−0.144194	−	0.198467i
$990$		0			0
$991$	−9.79781	+	13.4855i	−0.311238	+	0.428382i	−0.935767	−	0.352620i	$-0.885291\pi$
$991$	−9.79781	+	13.4855i	−0.311238	+	0.428382i	0.624529	+	0.781002i	$0.285291\pi$
$992$	34.1844	+	8.36747i	1.08535	+	0.265667i
$993$		0			0
$994$	−5.28958	+	19.2683i	−0.167775	+	0.611152i
$995$	23.1610	−	29.5022i	0.734254	−	0.935283i
$996$		0			0
$997$	−16.4461	−	32.2773i	−0.520853	−	1.02223i	−0.990257	−	0.139249i	$-0.955531\pi$
$997$	−16.4461	−	32.2773i	−0.520853	−	1.02223i	0.469404	−	0.882983i	$-0.344469\pi$
$998$	−31.8794	−	29.0598i	−1.00913	−	0.919871i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.e.523.8	yes	224
3.2	odd	2	inner	900.2.bj.e.523.21	yes	224
4.3	odd	2	inner	900.2.bj.e.523.24	yes	224
12.11	even	2	inner	900.2.bj.e.523.5	yes	224
25.12	odd	20	inner	900.2.bj.e.487.24	yes	224
75.62	even	20	inner	900.2.bj.e.487.5	✓	224
100.87	even	20	inner	900.2.bj.e.487.8	yes	224
300.287	odd	20	inner	900.2.bj.e.487.21	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.bj.e.487.5	✓	224	75.62	even	20	inner
900.2.bj.e.487.8	yes	224	100.87	even	20	inner
900.2.bj.e.487.21	yes	224	300.287	odd	20	inner
900.2.bj.e.487.24	yes	224	25.12	odd	20	inner
900.2.bj.e.523.5	yes	224	12.11	even	2	inner
900.2.bj.e.523.8	yes	224	1.1	even	1	trivial
900.2.bj.e.523.21	yes	224	3.2	odd	2	inner
900.2.bj.e.523.24	yes	224	4.3	odd	2	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	900.2.bj.e.523.8

Level	$900$
Weight	$2$
Character	900.523
Analytic conductor	$7.187$
Analytic rank	$0$
Dimension	$224$
Inner twists	$8$