LMFDB - Embedded newform 1530.2.u.c.557.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1530,2,Mod(557,1530)] 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("1530.557"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1530, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.u (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.9
Character	$\chi$	$=$	1530.557
Dual form			1530.2.u.c.1313.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.0740013 - 2.23484i) q^{5} -0.956061 q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.52795 + 1.63260i) q^{10} +(-1.88313 - 1.88313i) q^{11} +(-1.95234 + 1.95234i) q^{13} +(0.676037 + 0.676037i) q^{14} -1.00000 q^{16} +(4.03560 - 0.844925i) q^{17} -1.26720 q^{19} +(2.23484 - 0.0740013i) q^{20} +2.66314i q^{22} -6.61248 q^{23} +(-4.98905 + 0.330763i) q^{25} +2.76103 q^{26} -0.956061i q^{28} +(2.53934 + 2.53934i) q^{29} +(-2.95950 - 2.95950i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.45106 - 2.25615i) q^{34} +(0.0707497 + 2.13665i) q^{35} +7.53711i q^{37} +(0.896042 + 0.896042i) q^{38} +(-1.63260 - 1.52795i) q^{40} +(1.63281 + 1.63281i) q^{41} +(1.45685 + 1.45685i) q^{43} +(1.88313 - 1.88313i) q^{44} +(4.67573 + 4.67573i) q^{46} +(4.83539 - 4.83539i) q^{47} -6.08595 q^{49} +(3.76167 + 3.29390i) q^{50} +(-1.95234 - 1.95234i) q^{52} +(-7.57312 + 7.57312i) q^{53} +(-4.06914 + 4.34785i) q^{55} +(-0.676037 + 0.676037i) q^{56} -3.59117i q^{58} -2.87844i q^{59} +(-5.15140 + 5.15140i) q^{61} +4.18537i q^{62} -1.00000i q^{64} +(4.50765 + 4.21870i) q^{65} +(2.85608 + 2.85608i) q^{67} +(0.844925 + 4.03560i) q^{68} +(1.46081 - 1.56086i) q^{70} +(2.91575 - 2.91575i) q^{71} +4.43701 q^{73} +(5.32954 - 5.32954i) q^{74} -1.26720i q^{76} +(1.80038 + 1.80038i) q^{77} +(-5.16067 - 5.16067i) q^{79} +(0.0740013 + 2.23484i) q^{80} -2.30914i q^{82} +(-2.66034 + 2.66034i) q^{83} +(-2.18692 - 8.95642i) q^{85} -2.06030i q^{86} -2.66314 q^{88} -2.91210 q^{89} +(1.86656 - 1.86656i) q^{91} -6.61248i q^{92} -6.83827 q^{94} +(0.0937741 + 2.83198i) q^{95} +14.9887i q^{97} +(4.30342 + 4.30342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{10} + 8 q^{13} - 40 q^{16} + 16 q^{19} - 8 q^{31} + 32 q^{43} + 56 q^{49} + 8 q^{52} + 32 q^{55} - 64 q^{61} + 32 q^{67} + 32 q^{70} + 88 q^{79} + 72 q^{85} + 16 q^{88} + 56 q^{91} - 16 q^{94}+O(q^{100}) $ 40 * q + 8 * q^10 + 8 * q^13 - 40 * q^16 + 16 * q^19 - 8 * q^31 + 32 * q^43 + 56 * q^49 + 8 * q^52 + 32 * q^55 - 64 * q^61 + 32 * q^67 + 32 * q^70 + 88 * q^79 + 72 * q^85 + 16 * q^88 + 56 * q^91 - 16 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.0740013	−	2.23484i	−0.0330944	−	0.999452i
$5$	−0.0740013	−	2.23484i	−0.0330944	−	0.999452i
$6$		0			0
$7$	−0.956061			−0.361357			−0.180678	−	0.983542i	$-0.557829\pi$
$7$	−0.956061			−0.361357			−0.180678	+	0.983542i	$0.557829\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−1.52795	+	1.63260i	−0.483179	+	0.516273i
$11$	−1.88313	−	1.88313i	−0.567784	−	0.567784i	0.363723	−	0.931507i	$-0.381505\pi$
$11$	−1.88313	−	1.88313i	−0.567784	−	0.567784i	−0.931507	+	0.363723i	$0.881505\pi$
$12$		0			0
$13$	−1.95234	+	1.95234i	−0.541482	+	0.541482i	−0.923963	−	0.382481i	$-0.875070\pi$
$13$	−1.95234	+	1.95234i	−0.541482	+	0.541482i	0.382481	+	0.923963i	$0.375070\pi$
$14$	0.676037	+	0.676037i	0.180678	+	0.180678i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.03560	−	0.844925i	0.978778	−	0.204924i
$17$	4.03560	−	0.844925i	0.978778	−	0.204924i
$18$		0			0
$19$	−1.26720			−0.290715			−0.145357	−	0.989379i	$-0.546433\pi$
$19$	−1.26720			−0.290715			−0.145357	+	0.989379i	$0.546433\pi$
$20$	2.23484	−	0.0740013i	0.499726	−	0.0165472i
$21$		0			0
$22$			2.66314i			0.567784i
$23$	−6.61248			−1.37880			−0.689399	−	0.724382i	$-0.742125\pi$
$23$	−6.61248			−1.37880			−0.689399	+	0.724382i	$0.742125\pi$
$24$		0			0
$25$	−4.98905	+	0.330763i	−0.997810	+	0.0661525i
$26$	2.76103			0.541482
$27$		0			0
$28$		−	0.956061i		−	0.180678i
$29$	2.53934	+	2.53934i	0.471543	+	0.471543i	0.902414	−	0.430870i	$-0.141793\pi$
$29$	2.53934	+	2.53934i	0.471543	+	0.471543i	−0.430870	+	0.902414i	$0.641793\pi$
$30$		0			0
$31$	−2.95950	−	2.95950i	−0.531542	−	0.531542i	0.389489	−	0.921031i	$-0.372652\pi$
$31$	−2.95950	−	2.95950i	−0.531542	−	0.531542i	−0.921031	+	0.389489i	$0.872652\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−3.45106	−	2.25615i	−0.591851	−	0.386927i
$35$	0.0707497	+	2.13665i	0.0119589	+	0.361159i
$36$		0			0
$37$			7.53711i			1.23909i	0.784960	+	0.619546i	$0.212683\pi$
$37$			7.53711i			1.23909i	−0.784960	+	0.619546i	$0.787317\pi$
$38$	0.896042	+	0.896042i	0.145357	+	0.145357i
$39$		0			0
$40$	−1.63260	−	1.52795i	−0.258137	−	0.241589i
$41$	1.63281	+	1.63281i	0.255002	+	0.255002i	0.823018	−	0.568016i	$-0.192289\pi$
$41$	1.63281	+	1.63281i	0.255002	+	0.255002i	−0.568016	+	0.823018i	$0.692289\pi$
$42$		0			0
$43$	1.45685	+	1.45685i	0.222168	+	0.222168i	0.809411	−	0.587243i	$-0.199787\pi$
$43$	1.45685	+	1.45685i	0.222168	+	0.222168i	−0.587243	+	0.809411i	$0.699787\pi$
$44$	1.88313	−	1.88313i	0.283892	−	0.283892i
$45$		0			0
$46$	4.67573	+	4.67573i	0.689399	+	0.689399i
$47$	4.83539	−	4.83539i	0.705314	−	0.705314i	−0.260232	−	0.965546i	$-0.583799\pi$
$47$	4.83539	−	4.83539i	0.705314	−	0.705314i	0.965546	+	0.260232i	$0.0837991\pi$
$48$		0			0
$49$	−6.08595			−0.869421
$50$	3.76167	+	3.29390i	0.531981	+	0.465828i
$51$		0			0
$52$	−1.95234	−	1.95234i	−0.270741	−	0.270741i
$53$	−7.57312	+	7.57312i	−1.04025	+	1.04025i	−0.0410932	+	0.999155i	$0.513084\pi$
$53$	−7.57312	+	7.57312i	−1.04025	+	1.04025i	−0.999155	+	0.0410932i	$0.986916\pi$
$54$		0			0
$55$	−4.06914	+	4.34785i	−0.548682	+	0.586263i
$56$	−0.676037	+	0.676037i	−0.0903392	+	0.0903392i
$57$		0			0
$58$		−	3.59117i		−	0.471543i
$59$		−	2.87844i		−	0.374741i	−0.982289	−	0.187370i	$-0.940004\pi$
$59$		−	2.87844i		−	0.374741i	0.982289	−	0.187370i	$-0.0599964\pi$
$60$		0			0
$61$	−5.15140	+	5.15140i	−0.659569	+	0.659569i	−0.955278	−	0.295709i	$-0.904444\pi$
$61$	−5.15140	+	5.15140i	−0.659569	+	0.659569i	0.295709	+	0.955278i	$0.404444\pi$
$62$			4.18537i			0.531542i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	4.50765	+	4.21870i	0.559105	+	0.523265i
$66$		0			0
$67$	2.85608	+	2.85608i	0.348925	+	0.348925i	0.859709	−	0.510784i	$-0.170645\pi$
$67$	2.85608	+	2.85608i	0.348925	+	0.348925i	−0.510784	+	0.859709i	$0.670645\pi$
$68$	0.844925	+	4.03560i	0.102462	+	0.489389i
$69$		0			0
$70$	1.46081	−	1.56086i	0.174600	−	0.186559i
$71$	2.91575	−	2.91575i	0.346036	−	0.346036i	−0.512595	−	0.858631i	$-0.671316\pi$
$71$	2.91575	−	2.91575i	0.346036	−	0.346036i	0.858631	+	0.512595i	$0.171316\pi$
$72$		0			0
$73$	4.43701			0.519312			0.259656	−	0.965701i	$-0.416391\pi$
$73$	4.43701			0.519312			0.259656	+	0.965701i	$0.416391\pi$
$74$	5.32954	−	5.32954i	0.619546	−	0.619546i
$75$		0			0
$76$		−	1.26720i		−	0.145357i
$77$	1.80038	+	1.80038i	0.205173	+	0.205173i
$78$		0			0
$79$	−5.16067	−	5.16067i	−0.580621	−	0.580621i	0.354453	−	0.935074i	$-0.384667\pi$
$79$	−5.16067	−	5.16067i	−0.580621	−	0.580621i	−0.935074	+	0.354453i	$0.884667\pi$
$80$	0.0740013	+	2.23484i	0.00827360	+	0.249863i
$81$		0			0
$82$		−	2.30914i		−	0.255002i
$83$	−2.66034	+	2.66034i	−0.292010	+	0.292010i	−0.837874	−	0.545864i	$-0.816202\pi$
$83$	−2.66034	+	2.66034i	−0.292010	+	0.292010i	0.545864	+	0.837874i	$0.316202\pi$
$84$		0			0
$85$	−2.18692	−	8.95642i	−0.237204	−	0.971460i
$86$		−	2.06030i		−	0.222168i
$87$		0			0
$88$	−2.66314			−0.283892
$89$	−2.91210			−0.308682			−0.154341	−	0.988018i	$-0.549325\pi$
$89$	−2.91210			−0.308682			−0.154341	+	0.988018i	$0.549325\pi$
$90$		0			0
$91$	1.86656	−	1.86656i	0.195668	−	0.195668i
$92$		−	6.61248i		−	0.689399i
$93$		0			0
$94$	−6.83827			−0.705314
$95$	0.0937741	+	2.83198i	0.00962102	+	0.290555i
$96$		0			0
$97$			14.9887i			1.52188i	0.648824	+	0.760938i	$0.275261\pi$
$97$			14.9887i			1.52188i	−0.648824	+	0.760938i	$0.724739\pi$
$98$	4.30342	+	4.30342i	0.434711	+	0.434711i
$99$		0			0
$100$	−0.330763	−	4.98905i	−0.0330763	−	0.498905i
$101$			3.68376i			0.366548i	0.983062	+	0.183274i	$0.0586695\pi$
$101$			3.68376i			0.366548i	−0.983062	+	0.183274i	$0.941330\pi$
$102$		0			0
$103$	−12.0782	+	12.0782i	−1.19010	+	1.19010i	−0.213055	+	0.977040i	$0.568341\pi$
$103$	−12.0782	+	12.0782i	−1.19010	+	1.19010i	−0.977040	+	0.213055i	$0.931659\pi$
$104$			2.76103i			0.270741i
$105$		0			0
$106$	10.7100			1.04025
$107$	4.49366			0.434418			0.217209	−	0.976125i	$-0.430305\pi$
$107$	4.49366			0.434418			0.217209	+	0.976125i	$0.430305\pi$
$108$		0			0
$109$	−1.54296	−	1.54296i	−0.147789	−	0.147789i	0.629341	−	0.777129i	$-0.283325\pi$
$109$	−1.54296	−	1.54296i	−0.147789	−	0.147789i	−0.777129	+	0.629341i	$0.783325\pi$
$110$	5.95171	−	0.197076i	0.567473	−	0.0187905i
$111$		0			0
$112$	0.956061			0.0903392
$113$	−16.3843			−1.54131			−0.770654	−	0.637254i	$-0.780070\pi$
$113$	−16.3843			−1.54131			−0.770654	+	0.637254i	$0.780070\pi$
$114$		0			0
$115$	0.489332	+	14.7779i	0.0456305	+	1.37804i
$116$	−2.53934	+	2.53934i	−0.235772	+	0.235772i
$117$		0			0
$118$	−2.03536	+	2.03536i	−0.187370	+	0.187370i
$119$	−3.85828	+	0.807800i	−0.353688	+	0.0740509i
$120$		0			0
$121$		−	3.90767i		−	0.355243i
$122$	7.28518			0.659569
$123$		0			0
$124$	2.95950	−	2.95950i	0.265771	−	0.265771i
$125$	1.10840	+	11.1253i	0.0991382	+	0.995074i
$126$		0			0
$127$	−1.97773	+	1.97773i	−0.175495	+	0.175495i	−0.789389	−	0.613893i	$-0.789602\pi$
$127$	−1.97773	+	1.97773i	−0.175495	+	0.175495i	0.613893	+	0.789389i	$0.289602\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−0.204320	−	6.17046i	−0.0179200	−	0.541185i
$131$	1.23324	−	1.23324i	0.107749	−	0.107749i	−0.651177	−	0.758926i	$-0.725724\pi$
$131$	1.23324	−	1.23324i	0.107749	−	0.107749i	0.758926	+	0.651177i	$0.225724\pi$
$132$		0			0
$133$	1.21152			0.105052
$134$		−	4.03910i		−	0.348925i
$135$		0			0
$136$	2.25615	−	3.45106i	0.193463	−	0.295926i
$137$	−12.2948	+	12.2948i	−1.05041	+	1.05041i	−0.0517532	+	0.998660i	$0.516481\pi$
$137$	−12.2948	+	12.2948i	−1.05041	+	1.05041i	−0.998660	+	0.0517532i	$0.983519\pi$
$138$		0			0
$139$	5.63321	−	5.63321i	0.477803	−	0.477803i	−0.426626	−	0.904428i	$-0.640298\pi$
$139$	5.63321	−	5.63321i	0.477803	−	0.477803i	0.904428	+	0.426626i	$0.140298\pi$
$140$	−2.13665	+	0.0707497i	−0.180579	+	0.00597944i
$141$		0			0
$142$	−4.12349			−0.346036
$143$	7.35301			0.614890
$144$		0			0
$145$	5.48711	−	5.86294i	0.455680	−	0.486891i
$146$	−3.13744	−	3.13744i	−0.259656	−	0.259656i
$147$		0			0
$148$	−7.53711			−0.619546
$149$	−14.6670			−1.20156			−0.600782	−	0.799413i	$-0.705144\pi$
$149$	−14.6670			−1.20156			−0.600782	+	0.799413i	$0.705144\pi$
$150$		0			0
$151$			18.0770i			1.47109i	0.677478	+	0.735543i	$0.263073\pi$
$151$			18.0770i			1.47109i	−0.677478	+	0.735543i	$0.736927\pi$
$152$	−0.896042	+	0.896042i	−0.0726786	+	0.0726786i
$153$		0			0
$154$		−	2.54613i		−	0.205173i
$155$	−6.39502	+	6.83303i	−0.513660	+	0.548842i
$156$		0			0
$157$	4.02970	+	4.02970i	0.321605	+	0.321605i	0.849383	−	0.527778i	$-0.176975\pi$
$157$	4.02970	+	4.02970i	0.321605	+	0.321605i	−0.527778	+	0.849383i	$0.676975\pi$
$158$			7.29829i			0.580621i
$159$		0			0
$160$	1.52795	−	1.63260i	0.120795	−	0.129068i
$161$	6.32193			0.498238
$162$		0			0
$163$			7.12731i			0.558254i	0.960254	+	0.279127i	$0.0900450\pi$
$163$			7.12731i			0.558254i	−0.960254	+	0.279127i	$0.909955\pi$
$164$	−1.63281	+	1.63281i	−0.127501	+	0.127501i
$165$		0			0
$166$	3.76229			0.292010
$167$	4.05445			0.313743			0.156872	−	0.987619i	$-0.449859\pi$
$167$	4.05445			0.313743			0.156872	+	0.987619i	$0.449859\pi$
$168$		0			0
$169$			5.37673i			0.413595i
$170$	−4.78676	+	7.87953i	−0.367128	+	0.604332i
$171$		0			0
$172$	−1.45685	+	1.45685i	−0.111084	+	0.111084i
$173$		−	13.2079i		−	1.00417i	−0.864817	−	0.502087i	$-0.832566\pi$
$173$		−	13.2079i		−	1.00417i	0.864817	−	0.502087i	$-0.167434\pi$
$174$		0			0
$175$	4.76983	−	0.316229i	0.360565	−	0.0239047i
$176$	1.88313	+	1.88313i	0.141946	+	0.141946i
$177$		0			0
$178$	2.05917	+	2.05917i	0.154341	+	0.154341i
$179$		−	17.4142i		−	1.30160i	−0.759248	−	0.650801i	$-0.774433\pi$
$179$		−	17.4142i		−	1.30160i	0.759248	−	0.650801i	$-0.225567\pi$
$180$		0			0
$181$	7.71442	−	7.71442i	0.573408	−	0.573408i	−0.359671	−	0.933079i	$-0.617111\pi$
$181$	7.71442	−	7.71442i	0.573408	−	0.573408i	0.933079	+	0.359671i	$0.117111\pi$
$182$	−2.63971			−0.195668
$183$		0			0
$184$	−4.67573	+	4.67573i	−0.344699	+	0.344699i
$185$	16.8442	−	0.557756i	1.23841	−	0.0410070i
$186$		0			0
$187$	−9.19065	−	6.00845i	−0.672087	−	0.439382i
$188$	4.83539	+	4.83539i	0.352657	+	0.352657i
$189$		0			0
$190$	1.93621	−	2.06882i	0.140467	−	0.150088i
$191$		−	26.7181i		−	1.93325i	−0.256187	−	0.966627i	$-0.582466\pi$
$191$		−	26.7181i		−	1.93325i	0.256187	−	0.966627i	$-0.417534\pi$
$192$		0			0
$193$			9.03047i			0.650027i	0.945709	+	0.325014i	$0.105369\pi$
$193$			9.03047i			0.650027i	−0.945709	+	0.325014i	$0.894631\pi$
$194$	10.5986	−	10.5986i	0.760938	−	0.760938i
$195$		0			0
$196$		−	6.08595i		−	0.434711i
$197$			8.00413i			0.570270i	0.958487	+	0.285135i	$0.0920385\pi$
$197$			8.00413i			0.570270i	−0.958487	+	0.285135i	$0.907962\pi$
$198$		0			0
$199$	3.51012	−	3.51012i	0.248826	−	0.248826i	−0.571663	−	0.820489i	$-0.693702\pi$
$199$	3.51012	−	3.51012i	0.248826	−	0.248826i	0.820489	+	0.571663i	$0.193702\pi$
$200$	−3.29390	+	3.76167i	−0.232914	+	0.265991i
$201$		0			0
$202$	2.60481	−	2.60481i	0.183274	−	0.183274i
$203$	−2.42776	−	2.42776i	−0.170395	−	0.170395i
$204$		0			0
$205$	3.52824	−	3.76990i	0.246423	−	0.263301i
$206$	17.0811			1.19010
$207$		0			0
$208$	1.95234	−	1.95234i	0.135370	−	0.135370i
$209$	2.38629	+	2.38629i	0.165063	+	0.165063i
$210$		0			0
$211$	11.3150	−	11.3150i	0.778953	−	0.778953i	−0.200699	−	0.979653i	$-0.564321\pi$
$211$	11.3150	−	11.3150i	0.778953	−	0.778953i	0.979653	+	0.200699i	$0.0643215\pi$
$212$	−7.57312	−	7.57312i	−0.520124	−	0.520124i
$213$		0			0
$214$	−3.17750	−	3.17750i	−0.217209	−	0.217209i
$215$	3.14803	−	3.36365i	0.214694	−	0.229399i
$216$		0			0
$217$	2.82946	+	2.82946i	0.192077	+	0.192077i
$218$			2.18207i			0.147789i
$219$		0			0
$220$	−4.34785	−	4.06914i	−0.293132	−	0.274341i
$221$	−6.22929	+	9.52846i	−0.419028	+	0.640953i
$222$		0			0
$223$	19.5450	+	19.5450i	1.30883	+	1.30883i	0.922259	+	0.386573i	$0.126341\pi$
$223$	19.5450	+	19.5450i	1.30883	+	1.30883i	0.386573	+	0.922259i	$0.373659\pi$
$224$	−0.676037	−	0.676037i	−0.0451696	−	0.0451696i
$225$		0			0
$226$	11.5855	+	11.5855i	0.770654	+	0.770654i
$227$		−	25.5978i		−	1.69898i	−0.527603	−	0.849491i	$-0.676909\pi$
$227$		−	25.5978i		−	1.69898i	0.527603	−	0.849491i	$-0.323091\pi$
$228$		0			0
$229$	−10.2022			−0.674182			−0.337091	−	0.941472i	$-0.609443\pi$
$229$	−10.2022			−0.674182			−0.337091	+	0.941472i	$0.609443\pi$
$230$	10.1035	−	10.7955i	0.666206	−	0.711836i
$231$		0			0
$232$	3.59117			0.235772
$233$			19.5475i			1.28060i	0.768126	+	0.640298i	$0.221189\pi$
$233$			19.5475i			1.28060i	−0.768126	+	0.640298i	$0.778811\pi$
$234$		0			0
$235$	−11.1642	−	10.4485i	−0.728269	−	0.681585i
$236$	2.87844			0.187370
$237$		0			0
$238$	3.29942	+	2.15702i	0.213870	+	0.139819i
$239$	−25.0580			−1.62087			−0.810433	−	0.585831i	$-0.800768\pi$
$239$	−25.0580			−1.62087			−0.810433	+	0.585831i	$0.800768\pi$
$240$		0			0
$241$	−9.79340	−	9.79340i	−0.630849	−	0.630849i	0.317432	−	0.948281i	$-0.397179\pi$
$241$	−9.79340	−	9.79340i	−0.630849	−	0.630849i	−0.948281	+	0.317432i	$0.897179\pi$
$242$	−2.76314	+	2.76314i	−0.177621	+	0.177621i
$243$		0			0
$244$	−5.15140	−	5.15140i	−0.329785	−	0.329785i
$245$	0.450368	+	13.6011i	0.0287730	+	0.868945i
$246$		0			0
$247$	2.47400	−	2.47400i	0.157417	−	0.157417i
$248$	−4.18537			−0.265771
$249$		0			0
$250$	7.08299	−	8.65050i	0.447968	−	0.547106i
$251$			19.2063i			1.21229i	0.795353	+	0.606146i	$0.207285\pi$
$251$			19.2063i			1.21229i	−0.795353	+	0.606146i	$0.792715\pi$
$252$		0			0
$253$	12.4521	+	12.4521i	0.782859	+	0.782859i
$254$	2.79694			0.175495
$255$		0			0
$256$	1.00000			0.0625000
$257$	−16.5016	−	16.5016i	−1.02934	−	1.02934i	−0.999556	−	0.0297879i	$-0.990517\pi$
$257$	−16.5016	−	16.5016i	−1.02934	−	1.02934i	−0.0297879	−	0.999556i	$-0.509483\pi$
$258$		0			0
$259$		−	7.20593i		−	0.447755i
$260$	−4.21870	+	4.50765i	−0.261633	+	0.279553i
$261$		0			0
$262$	−1.74407			−0.107749
$263$	−10.0571	+	10.0571i	−0.620148	+	0.620148i	−0.945569	−	0.325421i	$-0.894494\pi$
$263$	−10.0571	+	10.0571i	−0.620148	+	0.620148i	0.325421	+	0.945569i	$0.394494\pi$
$264$		0			0
$265$	17.4852	+	16.3643i	1.07411	+	1.00525i
$266$	−0.856671	−	0.856671i	−0.0525259	−	0.0525259i
$267$		0			0
$268$	−2.85608	+	2.85608i	−0.174463	+	0.174463i
$269$	−3.25560	−	3.25560i	−0.198498	−	0.198498i	0.600858	−	0.799356i	$-0.294826\pi$
$269$	−3.25560	−	3.25560i	−0.198498	−	0.198498i	−0.799356	+	0.600858i	$0.794826\pi$
$270$		0			0
$271$	−3.46198			−0.210300			−0.105150	−	0.994456i	$-0.533532\pi$
$271$	−3.46198			−0.210300			−0.105150	+	0.994456i	$0.533532\pi$
$272$	−4.03560	+	0.844925i	−0.244694	+	0.0512311i
$273$		0			0
$274$	17.3874			1.05041
$275$	10.0179	+	8.77214i	0.604101	+	0.528980i
$276$		0			0
$277$		−	10.6782i		−	0.641588i	−0.947149	−	0.320794i	$-0.896050\pi$
$277$		−	10.6782i		−	0.641588i	0.947149	−	0.320794i	$-0.103950\pi$
$278$	−7.96656			−0.477803
$279$		0			0
$280$	1.56086	+	1.46081i	0.0932795	+	0.0873000i
$281$	4.95486			0.295582			0.147791	−	0.989019i	$-0.452784\pi$
$281$	4.95486			0.295582			0.147791	+	0.989019i	$0.452784\pi$
$282$		0			0
$283$		−	27.6017i		−	1.64075i	−0.571826	−	0.820375i	$-0.693765\pi$
$283$		−	27.6017i		−	1.64075i	0.571826	−	0.820375i	$-0.306235\pi$
$284$	2.91575	+	2.91575i	0.173018	+	0.173018i
$285$		0			0
$286$	−5.19936	−	5.19936i	−0.307445	−	0.307445i
$287$	−1.56106	−	1.56106i	−0.0921466	−	0.0921466i
$288$		0			0
$289$	15.5722	−	6.81957i	0.916012	−	0.401151i
$290$	−8.02570	+	0.265751i	−0.471285	+	0.0156054i
$291$		0			0
$292$			4.43701i			0.259656i
$293$	−15.7217	−	15.7217i	−0.918469	−	0.918469i	0.0784487	−	0.996918i	$-0.475003\pi$
$293$	−15.7217	−	15.7217i	−0.918469	−	0.918469i	−0.996918	+	0.0784487i	$0.975003\pi$
$294$		0			0
$295$	−6.43285	+	0.213008i	−0.374535	+	0.0124018i
$296$	5.32954	+	5.32954i	0.309773	+	0.309773i
$297$		0			0
$298$	10.3711	+	10.3711i	0.600782	+	0.600782i
$299$	12.9098	−	12.9098i	0.746594	−	0.746594i
$300$		0			0
$301$	−1.39284	−	1.39284i	−0.0802819	−	0.0802819i
$302$	12.7824	−	12.7824i	0.735543	−	0.735543i
$303$		0			0
$304$	1.26720			0.0726786
$305$	11.8938	+	11.1314i	0.681036	+	0.637380i
$306$		0			0
$307$	−5.01961	−	5.01961i	−0.286484	−	0.286484i	0.549204	−	0.835688i	$-0.314931\pi$
$307$	−5.01961	−	5.01961i	−0.286484	−	0.286484i	−0.835688	+	0.549204i	$0.814931\pi$
$308$	−1.80038	+	1.80038i	−0.102586	+	0.102586i
$309$		0			0
$310$	9.35364	−	0.309723i	0.531251	−	0.0175911i
$311$	−5.94482	+	5.94482i	−0.337100	+	0.337100i	−0.855275	−	0.518175i	$-0.826612\pi$
$311$	−5.94482	+	5.94482i	−0.337100	+	0.337100i	0.518175	+	0.855275i	$0.326612\pi$
$312$		0			0
$313$		−	12.2937i		−	0.694880i	−0.937702	−	0.347440i	$-0.887051\pi$
$313$		−	12.2937i		−	0.694880i	0.937702	−	0.347440i	$-0.112949\pi$
$314$		−	5.69886i		−	0.321605i
$315$		0			0
$316$	5.16067	−	5.16067i	0.290310	−	0.290310i
$317$		−	5.79422i		−	0.325436i	−0.986673	−	0.162718i	$-0.947974\pi$
$317$		−	5.79422i		−	0.325436i	0.986673	−	0.162718i	$-0.0520261\pi$
$318$		0			0
$319$		−	9.56379i		−	0.535470i
$320$	−2.23484	+	0.0740013i	−0.124932	+	0.00413680i
$321$		0			0
$322$	−4.47028	−	4.47028i	−0.249119	−	0.249119i
$323$	−5.11390	+	1.07069i	−0.284545	+	0.0595745i
$324$		0			0
$325$	9.09456	−	10.3861i	0.504475	−	0.576116i
$326$	5.03977	−	5.03977i	0.279127	−	0.279127i
$327$		0			0
$328$	2.30914			0.127501
$329$	−4.62292	+	4.62292i	−0.254870	+	0.254870i
$330$		0			0
$331$		−	13.6433i		−	0.749902i	−0.927045	−	0.374951i	$-0.877659\pi$
$331$		−	13.6433i		−	0.749902i	0.927045	−	0.374951i	$-0.122341\pi$
$332$	−2.66034	−	2.66034i	−0.146005	−	0.146005i
$333$		0			0
$334$	−2.86693	−	2.86693i	−0.156872	−	0.156872i
$335$	6.17153	−	6.59424i	0.337187	−	0.360282i
$336$		0			0
$337$		−	0.786275i		−	0.0428311i	−0.999771	−	0.0214156i	$-0.993183\pi$
$337$		−	0.786275i		−	0.0428311i	0.999771	−	0.0214156i	$-0.00681731\pi$
$338$	3.80192	−	3.80192i	0.206797	−	0.206797i
$339$		0			0
$340$	8.95642	−	2.18692i	0.485730	−	0.118602i
$341$			11.1462i			0.603602i
$342$		0			0
$343$	12.5110			0.675528
$344$	2.06030			0.111084
$345$		0			0
$346$	−9.33937	+	9.33937i	−0.502087	+	0.502087i
$347$		−	30.6100i		−	1.64323i	−0.570041	−	0.821616i	$-0.693073\pi$
$347$		−	30.6100i		−	1.64323i	0.570041	−	0.821616i	$-0.306927\pi$
$348$		0			0
$349$	12.0908			0.647205			0.323602	−	0.946193i	$-0.395106\pi$
$349$	12.0908			0.647205			0.323602	+	0.946193i	$0.395106\pi$
$350$	−3.59639	−	3.14917i	−0.192235	−	0.168330i
$351$		0			0
$352$		−	2.66314i		−	0.141946i
$353$	−6.14878	−	6.14878i	−0.327267	−	0.327267i	0.524280	−	0.851546i	$-0.324335\pi$
$353$	−6.14878	−	6.14878i	−0.327267	−	0.327267i	−0.851546	+	0.524280i	$0.824335\pi$
$354$		0			0
$355$	−6.73201	−	6.30047i	−0.357298	−	0.334394i
$356$		−	2.91210i		−	0.154341i
$357$		0			0
$358$	−12.3137	+	12.3137i	−0.650801	+	0.650801i
$359$		−	8.52400i		−	0.449880i	−0.974373	−	0.224940i	$-0.927781\pi$
$359$		−	8.52400i		−	0.449880i	0.974373	−	0.224940i	$-0.0722185\pi$
$360$		0			0
$361$	−17.3942			−0.915485
$362$	−10.9098			−0.573408
$363$		0			0
$364$	1.86656	+	1.86656i	0.0978341	+	0.0978341i
$365$	−0.328344	−	9.91601i	−0.0171863	−	0.519028i
$366$		0			0
$367$	−4.69865			−0.245267			−0.122634	−	0.992452i	$-0.539134\pi$
$367$	−4.69865			−0.245267			−0.122634	+	0.992452i	$0.539134\pi$
$368$	6.61248			0.344699
$369$		0			0
$370$	−12.3051	−	11.5163i	−0.639710	−	0.598703i
$371$	7.24036	−	7.24036i	0.375901	−	0.375901i
$372$		0			0
$373$	6.79992	−	6.79992i	0.352086	−	0.352086i	−0.508799	−	0.860885i	$-0.669910\pi$
$373$	6.79992	−	6.79992i	0.352086	−	0.352086i	0.860885	+	0.508799i	$0.169910\pi$
$374$	2.25016	+	10.7474i	0.116353	+	0.555734i
$375$		0			0
$376$		−	6.83827i		−	0.352657i
$377$	−9.91531			−0.510665
$378$		0			0
$379$	15.4980	−	15.4980i	0.796077	−	0.796077i	−0.186398	−	0.982474i	$-0.559681\pi$
$379$	15.4980	−	15.4980i	0.796077	−	0.796077i	0.982474	+	0.186398i	$0.0596813\pi$
$380$	−2.83198	+	0.0937741i	−0.145278	+	0.00481051i
$381$		0			0
$382$	−18.8926	+	18.8926i	−0.966627	+	0.966627i
$383$	−13.0376	+	13.0376i	−0.666188	+	0.666188i	−0.956831	−	0.290643i	$-0.906131\pi$
$383$	−13.0376	+	13.0376i	−0.666188	+	0.666188i	0.290643	+	0.956831i	$0.406131\pi$
$384$		0			0
$385$	3.89034	−	4.15680i	0.198270	−	0.211850i
$386$	6.38551	−	6.38551i	0.325014	−	0.325014i
$387$		0			0
$388$	−14.9887			−0.760938
$389$		−	38.6711i		−	1.96070i	−0.197255	−	0.980352i	$-0.563203\pi$
$389$		−	38.6711i		−	1.96070i	0.197255	−	0.980352i	$-0.436797\pi$
$390$		0			0
$391$	−26.6853	+	5.58705i	−1.34954	+	0.282549i
$392$	−4.30342	+	4.30342i	−0.217355	+	0.217355i
$393$		0			0
$394$	5.65977	−	5.65977i	0.285135	−	0.285135i
$395$	−11.1514	+	11.9152i	−0.561087	+	0.599518i
$396$		0			0
$397$	14.1213			0.708726			0.354363	−	0.935108i	$-0.384698\pi$
$397$	14.1213			0.708726			0.354363	+	0.935108i	$0.384698\pi$
$398$	−4.96405			−0.248826
$399$		0			0
$400$	4.98905	−	0.330763i	0.249452	−	0.0165381i
$401$	9.27440	+	9.27440i	0.463142	+	0.463142i	0.899684	−	0.436542i	$-0.143797\pi$
$401$	9.27440	+	9.27440i	0.463142	+	0.463142i	−0.436542	+	0.899684i	$0.643797\pi$
$402$		0			0
$403$	11.5559			0.575641
$404$	−3.68376			−0.183274
$405$		0			0
$406$			3.43337i			0.170395i
$407$	14.1933	−	14.1933i	0.703537	−	0.703537i
$408$		0			0
$409$		−	11.4600i		−	0.566662i	−0.959022	−	0.283331i	$-0.908560\pi$
$409$		−	11.4600i		−	0.566662i	0.959022	−	0.283331i	$-0.0914395\pi$
$410$	−5.16056	+	0.170879i	−0.254862	+	0.00843913i
$411$		0			0
$412$	−12.0782	−	12.0782i	−0.595048	−	0.595048i
$413$			2.75196i			0.135415i
$414$		0			0
$415$	6.14231	+	5.74857i	0.301514	+	0.282186i
$416$	−2.76103			−0.135370
$417$		0			0
$418$		−	3.37472i		−	0.165063i
$419$	12.0537	−	12.0537i	0.588863	−	0.588863i	−0.348461	−	0.937323i	$-0.613296\pi$
$419$	12.0537	−	12.0537i	0.588863	−	0.588863i	0.937323	+	0.348461i	$0.113296\pi$
$420$		0			0
$421$	26.9876			1.31530			0.657648	−	0.753326i	$-0.271552\pi$
$421$	26.9876			1.31530			0.657648	+	0.753326i	$0.271552\pi$
$422$	−16.0018			−0.778953
$423$		0			0
$424$			10.7100i			0.520124i
$425$	−19.8544	+	5.55020i	−0.963078	+	0.269224i
$426$		0			0
$427$	4.92505	−	4.92505i	0.238340	−	0.238340i
$428$			4.49366i			0.217209i
$429$		0			0
$430$	−4.60445	+	0.152465i	−0.222046	+	0.00735251i
$431$	2.88276	+	2.88276i	0.138858	+	0.138858i	0.773119	−	0.634261i	$-0.218696\pi$
$431$	2.88276	+	2.88276i	0.138858	+	0.138858i	−0.634261	+	0.773119i	$0.718696\pi$
$432$		0			0
$433$	0.359052	+	0.359052i	0.0172549	+	0.0172549i	0.715682	−	0.698427i	$-0.246116\pi$
$433$	0.359052	+	0.359052i	0.0172549	+	0.0172549i	−0.698427	+	0.715682i	$0.746116\pi$
$434$		−	4.00147i		−	0.192077i
$435$		0			0
$436$	1.54296	−	1.54296i	0.0738944	−	0.0738944i
$437$	8.37930			0.400836
$438$		0			0
$439$	−9.91117	+	9.91117i	−0.473034	+	0.473034i	−0.902895	−	0.429861i	$-0.858563\pi$
$439$	−9.91117	+	9.91117i	−0.473034	+	0.473034i	0.429861	+	0.902895i	$0.358563\pi$
$440$	0.197076	+	5.95171i	0.00939523	+	0.283736i
$441$		0			0
$442$	11.1424	−	2.33286i	0.529991	−	0.110963i
$443$	−25.7078	−	25.7078i	−1.22141	−	1.22141i	−0.967130	−	0.254283i	$-0.918161\pi$
$443$	−25.7078	−	25.7078i	−1.22141	−	1.22141i	−0.254283	−	0.967130i	$-0.581839\pi$
$444$		0			0
$445$	0.215500	+	6.50810i	0.0102157	+	0.308513i
$446$		−	27.6408i		−	1.30883i
$447$		0			0
$448$			0.956061i			0.0451696i
$449$	17.6634	−	17.6634i	0.833587	−	0.833587i	−0.154419	−	0.988005i	$-0.549351\pi$
$449$	17.6634	−	17.6634i	0.833587	−	0.833587i	0.988005	+	0.154419i	$0.0493505\pi$
$450$		0			0
$451$		−	6.14957i		−	0.289572i
$452$		−	16.3843i		−	0.770654i
$453$		0			0
$454$	−18.1003	+	18.1003i	−0.849491	+	0.849491i
$455$	−4.30959	−	4.03333i	−0.202037	−	0.189086i
$456$		0			0
$457$	−5.77169	+	5.77169i	−0.269988	+	0.269988i	−0.829095	−	0.559107i	$-0.811144\pi$
$457$	−5.77169	+	5.77169i	−0.269988	+	0.269988i	0.559107	+	0.829095i	$0.311144\pi$
$458$	7.21406	+	7.21406i	0.337091	+	0.337091i
$459$		0			0
$460$	−14.7779	+	0.489332i	−0.689021	+	0.0228152i
$461$	−20.4301			−0.951525			−0.475763	−	0.879574i	$-0.657828\pi$
$461$	−20.4301			−0.951525			−0.475763	+	0.879574i	$0.657828\pi$
$462$		0			0
$463$	−29.1278	+	29.1278i	−1.35369	+	1.35369i	−0.472187	+	0.881498i	$0.656535\pi$
$463$	−29.1278	+	29.1278i	−1.35369	+	1.35369i	−0.881498	+	0.472187i	$0.843465\pi$
$464$	−2.53934	−	2.53934i	−0.117886	−	0.117886i
$465$		0			0
$466$	13.8221	−	13.8221i	0.640298	−	0.640298i
$467$	−5.32865	−	5.32865i	−0.246580	−	0.246580i	0.572985	−	0.819566i	$-0.305785\pi$
$467$	−5.32865	−	5.32865i	−0.246580	−	0.246580i	−0.819566	+	0.572985i	$0.805785\pi$
$468$		0			0
$469$	−2.73058	−	2.73058i	−0.126087	−	0.126087i
$470$	0.506041	+	15.2825i	0.0233419	+	0.704927i
$471$		0			0
$472$	−2.03536	−	2.03536i	−0.0936851	−	0.0936851i
$473$		−	5.48688i		−	0.252287i
$474$		0			0
$475$	6.32210	−	0.419141i	0.290078	−	0.0192315i
$476$	−0.807800	−	3.85828i	−0.0370254	−	0.176844i
$477$		0			0
$478$	17.7187	+	17.7187i	0.810433	+	0.810433i
$479$	−26.9581	−	26.9581i	−1.23174	−	1.23174i	−0.963293	−	0.268452i	$-0.913488\pi$
$479$	−26.9581	−	26.9581i	−1.23174	−	1.23174i	−0.268452	−	0.963293i	$-0.586512\pi$
$480$		0			0
$481$	−14.7150	−	14.7150i	−0.670946	−	0.670946i
$482$			13.8500i			0.630849i
$483$		0			0
$484$	3.90767			0.177621
$485$	33.4975	−	1.10919i	1.52104	−	0.0503656i
$486$		0			0
$487$	−31.1558			−1.41180			−0.705902	−	0.708310i	$-0.749458\pi$
$487$	−31.1558			−1.41180			−0.705902	+	0.708310i	$0.749458\pi$
$488$			7.28518i			0.329785i
$489$		0			0
$490$	9.29900	−	9.93592i	0.420086	−	0.448859i
$491$	7.28365			0.328707			0.164353	−	0.986402i	$-0.447446\pi$
$491$	7.28365			0.328707			0.164353	+	0.986402i	$0.447446\pi$
$492$		0			0
$493$	12.3933	+	8.10222i	0.558167	+	0.364905i
$494$	−3.49876			−0.157417
$495$		0			0
$496$	2.95950	+	2.95950i	0.132886	+	0.132886i
$497$	−2.78763	+	2.78763i	−0.125042	+	0.125042i
$498$		0			0
$499$	−28.8990	−	28.8990i	−1.29370	−	1.29370i	−0.932482	−	0.361215i	$-0.882362\pi$
$499$	−28.8990	−	28.8990i	−1.29370	−	1.29370i	−0.361215	−	0.932482i	$-0.617638\pi$
$500$	−11.1253	+	1.10840i	−0.497537	+	0.0495691i
$501$		0			0
$502$	13.5809	−	13.5809i	0.606146	−	0.606146i
$503$	22.7436			1.01409			0.507045	−	0.861920i	$-0.330738\pi$
$503$	22.7436			1.01409			0.507045	+	0.861920i	$0.330738\pi$
$504$		0			0
$505$	8.23263	−	0.272603i	0.366347	−	0.0121307i
$506$		−	17.6100i		−	0.782859i
$507$		0			0
$508$	−1.97773	−	1.97773i	−0.0877477	−	0.0877477i
$509$	16.9804			0.752644			0.376322	−	0.926489i	$-0.377189\pi$
$509$	16.9804			0.752644			0.376322	+	0.926489i	$0.377189\pi$
$510$		0			0
$511$	−4.24205			−0.187657
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			23.3368i			1.02934i
$515$	27.8866	+	26.0990i	1.22883	+	1.15006i
$516$		0			0
$517$	−18.2113			−0.800932
$518$	−5.09536	+	5.09536i	−0.223877	+	0.223877i
$519$		0			0
$520$	6.17046	−	0.204320i	0.270593	−	0.00896001i
$521$	30.8160	+	30.8160i	1.35007	+	1.35007i	0.885574	+	0.464498i	$0.153765\pi$
$521$	30.8160	+	30.8160i	1.35007	+	1.35007i	0.464498	+	0.885574i	$0.346235\pi$
$522$		0			0
$523$	6.05956	−	6.05956i	0.264966	−	0.264966i	−0.562102	−	0.827068i	$-0.690007\pi$
$523$	6.05956	−	6.05956i	0.264966	−	0.264966i	0.827068	+	0.562102i	$0.190007\pi$
$524$	1.23324	+	1.23324i	0.0538745	+	0.0538745i
$525$		0			0
$526$	14.2229			0.620148
$527$	−14.4439	−	9.44282i	−0.629188	−	0.411336i
$528$		0			0
$529$	20.7249			0.901082
$530$	−0.792555	−	23.9352i	−0.0344264	−	1.03968i
$531$		0			0
$532$			1.21152i			0.0525259i
$533$	−6.37559			−0.276158
$534$		0			0
$535$	−0.332537	−	10.0426i	−0.0143768	−	0.434180i
$536$	4.03910			0.174463
$537$		0			0
$538$			4.60412i			0.198498i
$539$	11.4606	+	11.4606i	0.493643	+	0.493643i
$540$		0			0
$541$	1.72774	+	1.72774i	0.0742812	+	0.0742812i	0.743271	−	0.668990i	$-0.233273\pi$
$541$	1.72774	+	1.72774i	0.0742812	+	0.0742812i	−0.668990	+	0.743271i	$0.733273\pi$
$542$	2.44799	+	2.44799i	0.105150	+	0.105150i
$543$		0			0
$544$	3.45106	+	2.25615i	0.147963	+	0.0967317i
$545$	−3.33409	+	3.56245i	−0.142817	+	0.152599i
$546$		0			0
$547$			21.7136i			0.928408i	0.885728	+	0.464204i	$0.153659\pi$
$547$			21.7136i			0.928408i	−0.885728	+	0.464204i	$0.846341\pi$
$548$	−12.2948	−	12.2948i	−0.525207	−	0.525207i
$549$		0			0
$550$	−0.880868	−	13.2865i	−0.0375603	−	0.566540i
$551$	−3.21784	−	3.21784i	−0.137085	−	0.137085i
$552$		0			0
$553$	4.93391	+	4.93391i	0.209811	+	0.209811i
$554$	−7.55059	+	7.55059i	−0.320794	+	0.320794i
$555$		0			0
$556$	5.63321	+	5.63321i	0.238901	+	0.238901i
$557$	−12.4890	+	12.4890i	−0.529177	+	0.529177i	−0.920327	−	0.391150i	$-0.872077\pi$
$557$	−12.4890	+	12.4890i	−0.529177	+	0.529177i	0.391150	+	0.920327i	$0.372077\pi$
$558$		0			0
$559$	−5.68855			−0.240600
$560$	−0.0707497	−	2.13665i	−0.00298972	−	0.0902897i
$561$		0			0
$562$	−3.50362	−	3.50362i	−0.147791	−	0.147791i
$563$	−20.4018	+	20.4018i	−0.859832	+	0.859832i	−0.991318	−	0.131486i	$-0.958025\pi$
$563$	−20.4018	+	20.4018i	−0.859832	+	0.859832i	0.131486	+	0.991318i	$0.458025\pi$
$564$		0			0
$565$	1.21246	+	36.6164i	0.0510087	+	1.54046i
$566$	−19.5173	+	19.5173i	−0.820375	+	0.820375i
$567$		0			0
$568$		−	4.12349i		−	0.173018i
$569$			33.6842i			1.41212i	0.708154	+	0.706058i	$0.249528\pi$
$569$			33.6842i			1.41212i	−0.708154	+	0.706058i	$0.750472\pi$
$570$		0			0
$571$	−18.3652	+	18.3652i	−0.768559	+	0.768559i	−0.977853	−	0.209294i	$-0.932884\pi$
$571$	−18.3652	+	18.3652i	−0.768559	+	0.768559i	0.209294	+	0.977853i	$0.432884\pi$
$572$			7.35301i			0.307445i
$573$		0			0
$574$			2.20768i			0.0921466i
$575$	32.9900	−	2.18716i	1.37578	−	0.0912109i
$576$		0			0
$577$	4.04107	+	4.04107i	0.168232	+	0.168232i	0.786202	−	0.617970i	$-0.212045\pi$
$577$	4.04107	+	4.04107i	0.168232	+	0.168232i	−0.617970	+	0.786202i	$0.712045\pi$
$578$	−15.8334	−	6.18905i	−0.658581	−	0.257430i
$579$		0			0
$580$	5.86294	+	5.48711i	0.243445	+	0.227840i
$581$	2.54344	−	2.54344i	0.105520	−	0.105520i
$582$		0			0
$583$	28.5223			1.18127
$584$	3.13744	−	3.13744i	0.129828	−	0.129828i
$585$		0			0
$586$			22.2338i			0.918469i
$587$	3.66396	+	3.66396i	0.151228	+	0.151228i	0.778666	−	0.627438i	$-0.215897\pi$
$587$	3.66396	+	3.66396i	0.151228	+	0.151228i	−0.627438	+	0.778666i	$0.715897\pi$
$588$		0			0
$589$	3.75027	+	3.75027i	0.154527	+	0.154527i
$590$	4.69933	+	4.39810i	0.193469	+	0.181067i
$591$		0			0
$592$		−	7.53711i		−	0.309773i
$593$	22.3770	−	22.3770i	0.918915	−	0.918915i	−0.0780360	−	0.996951i	$-0.524865\pi$
$593$	22.3770	−	22.3770i	0.918915	−	0.918915i	0.996951	+	0.0780360i	$0.0248649\pi$
$594$		0			0
$595$	2.09082	+	8.56288i	0.0857154	+	0.351044i
$596$		−	14.6670i		−	0.600782i
$597$		0			0
$598$	−18.2572			−0.746594
$599$	9.17056			0.374699			0.187350	−	0.982293i	$-0.440010\pi$
$599$	9.17056			0.374699			0.187350	+	0.982293i	$0.440010\pi$
$600$		0			0
$601$	5.82720	−	5.82720i	0.237697	−	0.237697i	−0.578199	−	0.815896i	$-0.696244\pi$
$601$	5.82720	−	5.82720i	0.237697	−	0.237697i	0.815896	+	0.578199i	$0.196244\pi$
$602$			1.96977i			0.0802819i
$603$		0			0
$604$	−18.0770			−0.735543
$605$	−8.73303	+	0.289173i	−0.355048	+	0.0117565i
$606$		0			0
$607$			33.8794i			1.37512i	0.726127	+	0.687561i	$0.241319\pi$
$607$			33.8794i			1.37512i	−0.726127	+	0.687561i	$0.758681\pi$
$608$	−0.896042	−	0.896042i	−0.0363393	−	0.0363393i
$609$		0			0
$610$	−0.539113	−	16.2812i	−0.0218280	−	0.659208i
$611$			18.8807i			0.763829i
$612$		0			0
$613$	14.9677	−	14.9677i	0.604540	−	0.604540i	−0.336974	−	0.941514i	$-0.609404\pi$
$613$	14.9677	−	14.9677i	0.604540	−	0.604540i	0.941514	+	0.336974i	$0.109404\pi$
$614$			7.09880i			0.286484i
$615$		0			0
$616$	2.54613			0.102586
$617$	13.8559			0.557818			0.278909	−	0.960317i	$-0.410027\pi$
$617$	13.8559			0.557818			0.278909	+	0.960317i	$0.410027\pi$
$618$		0			0
$619$	−16.1152	−	16.1152i	−0.647726	−	0.647726i	0.304717	−	0.952443i	$-0.401438\pi$
$619$	−16.1152	−	16.1152i	−0.647726	−	0.647726i	−0.952443	+	0.304717i	$0.901438\pi$
$620$	−6.83303	−	6.39502i	−0.274421	−	0.256830i
$621$		0			0
$622$	8.40724			0.337100
$623$	2.78415			0.111545
$624$		0			0
$625$	24.7812	−	3.30038i	0.991248	−	0.132015i
$626$	−8.69295	+	8.69295i	−0.347440	+	0.347440i
$627$		0			0
$628$	−4.02970	+	4.02970i	−0.160803	+	0.160803i
$629$	6.36829	+	30.4168i	0.253920	+	1.21280i
$630$		0			0
$631$			1.02543i			0.0408219i	0.999792	+	0.0204110i	$0.00649746\pi$
$631$			1.02543i			0.0408219i	−0.999792	+	0.0204110i	$0.993503\pi$
$632$	−7.29829			−0.290310
$633$		0			0
$634$	−4.09713	+	4.09713i	−0.162718	+	0.162718i
$635$	4.56628	+	4.27357i	0.181207	+	0.169591i
$636$		0			0
$637$	11.8818	−	11.8818i	0.470776	−	0.470776i
$638$	−6.76262	+	6.76262i	−0.267735	+	0.267735i
$639$		0			0
$640$	1.63260	+	1.52795i	0.0645342	+	0.0603974i
$641$	−14.6244	+	14.6244i	−0.577629	+	0.577629i	−0.934250	−	0.356620i	$-0.883929\pi$
$641$	−14.6244	+	14.6244i	−0.577629	+	0.577629i	0.356620	+	0.934250i	$0.383929\pi$
$642$		0			0
$643$	−14.0281			−0.553214			−0.276607	−	0.960983i	$-0.589210\pi$
$643$	−14.0281			−0.553214			−0.276607	+	0.960983i	$0.589210\pi$
$644$			6.32193i			0.249119i
$645$		0			0
$646$	4.37316	+	2.85898i	0.172060	+	0.112485i
$647$	−8.09332	+	8.09332i	−0.318181	+	0.318181i	−0.848068	−	0.529887i	$-0.822234\pi$
$647$	−8.09332	+	8.09332i	−0.318181	+	0.318181i	0.529887	+	0.848068i	$0.322234\pi$
$648$		0			0
$649$	−5.42046	+	5.42046i	−0.212772	+	0.212772i
$650$	−13.7749	+	0.913245i	−0.540296	+	0.0358204i
$651$		0			0
$652$	−7.12731			−0.279127
$653$	48.9384			1.91511			0.957553	−	0.288257i	$-0.0930757\pi$
$653$	48.9384			1.91511			0.957553	+	0.288257i	$0.0930757\pi$
$654$		0			0
$655$	−2.84737	−	2.66484i	−0.111256	−	0.104124i
$656$	−1.63281	−	1.63281i	−0.0637504	−	0.0637504i
$657$		0			0
$658$	6.53780			0.254870
$659$	22.5542			0.878586			0.439293	−	0.898344i	$-0.355229\pi$
$659$	22.5542			0.878586			0.439293	+	0.898344i	$0.355229\pi$
$660$		0			0
$661$		−	32.2676i		−	1.25506i	−0.778591	−	0.627531i	$-0.784066\pi$
$661$		−	32.2676i		−	1.25506i	0.778591	−	0.627531i	$-0.215934\pi$
$662$	−9.64725	+	9.64725i	−0.374951	+	0.374951i
$663$		0			0
$664$			3.76229i			0.146005i
$665$	−0.0896537	−	2.70755i	−0.00347662	−	0.104994i
$666$		0			0
$667$	−16.7913	−	16.7913i	−0.650163	−	0.650163i
$668$			4.05445i			0.156872i
$669$		0			0
$670$	−9.02676	+	0.298899i	−0.348734	+	0.0115475i
$671$	19.4015			0.748986
$672$		0			0
$673$		−	22.2768i		−	0.858709i	−0.903136	−	0.429355i	$-0.858741\pi$
$673$		−	22.2768i		−	0.858709i	0.903136	−	0.429355i	$-0.141259\pi$
$674$	−0.555980	+	0.555980i	−0.0214156	+	0.0214156i
$675$		0			0
$676$	−5.37673			−0.206797
$677$	7.24062			0.278280			0.139140	−	0.990273i	$-0.455566\pi$
$677$	7.24062			0.278280			0.139140	+	0.990273i	$0.455566\pi$
$678$		0			0
$679$		−	14.3301i		−	0.549941i
$680$	−7.87953	−	4.78676i	−0.302166	−	0.183564i
$681$		0			0
$682$	7.88158	−	7.88158i	0.301801	−	0.301801i
$683$			13.1612i			0.503600i	0.967779	+	0.251800i	$0.0810225\pi$
$683$			13.1612i			0.503600i	−0.967779	+	0.251800i	$0.918977\pi$
$684$		0			0
$685$	28.3867	+	26.5671i	1.08460	+	1.01507i
$686$	−8.84658	−	8.84658i	−0.337764	−	0.337764i
$687$		0			0
$688$	−1.45685	−	1.45685i	−0.0555420	−	0.0555420i
$689$		−	29.5706i		−	1.12655i
$690$		0			0
$691$	−2.18788	+	2.18788i	−0.0832310	+	0.0832310i	−0.747497	−	0.664266i	$-0.768744\pi$
$691$	−2.18788	+	2.18788i	−0.0832310	+	0.0832310i	0.664266	+	0.747497i	$0.268744\pi$
$692$	13.2079			0.502087
$693$		0			0
$694$	−21.6446	+	21.6446i	−0.821616	+	0.821616i
$695$	−13.0062	−	12.1725i	−0.493354	−	0.461728i
$696$		0			0
$697$	7.96897	+	5.20976i	0.301846	+	0.197334i
$698$	−8.54947	−	8.54947i	−0.323602	−	0.323602i
$699$		0			0
$700$	0.316229	+	4.76983i	0.0119523	+	0.180283i
$701$			32.8456i			1.24056i	0.784380	+	0.620280i	$0.212981\pi$
$701$			32.8456i			1.24056i	−0.784380	+	0.620280i	$0.787019\pi$
$702$		0			0
$703$		−	9.55098i		−	0.360222i
$704$	−1.88313	+	1.88313i	−0.0709730	+	0.0709730i
$705$		0			0
$706$			8.69569i			0.327267i
$707$		−	3.52190i		−	0.132455i
$708$		0			0
$709$	−35.6948	+	35.6948i	−1.34055	+	1.34055i	−0.445030	+	0.895516i	$0.646807\pi$
$709$	−35.6948	+	35.6948i	−1.34055	+	1.34055i	−0.895516	+	0.445030i	$0.853193\pi$
$710$	0.305144	+	9.21536i	0.0114518	+	0.345846i
$711$		0			0
$712$	−2.05917	+	2.05917i	−0.0771706	+	0.0771706i
$713$	19.5696	+	19.5696i	0.732889	+	0.732889i
$714$		0			0
$715$	−0.544132	−	16.4328i	−0.0203494	−	0.614553i
$716$	17.4142			0.650801
$717$		0			0
$718$	−6.02738	+	6.02738i	−0.224940	+	0.224940i
$719$	24.1106	+	24.1106i	0.899174	+	0.899174i	0.995363	−	0.0961892i	$-0.0306654\pi$
$719$	24.1106	+	24.1106i	0.899174	+	0.899174i	−0.0961892	+	0.995363i	$0.530665\pi$
$720$		0			0
$721$	11.5474	−	11.5474i	0.430049	−	0.430049i
$722$	12.2996	+	12.2996i	0.457743	+	0.457743i
$723$		0			0
$724$	7.71442	+	7.71442i	0.286704	+	0.286704i
$725$	−13.5088	−	11.8290i	−0.501704	−	0.439317i
$726$		0			0
$727$	11.4374	+	11.4374i	0.424189	+	0.424189i	0.886643	−	0.462454i	$-0.153031\pi$
$727$	11.4374	+	11.4374i	0.424189	+	0.424189i	−0.462454	+	0.886643i	$0.653031\pi$
$728$		−	2.63971i		−	0.0978341i
$729$		0			0
$730$	−6.77950	+	7.24385i	−0.250921	+	0.268107i
$731$	7.11021	+	4.64835i	0.262981	+	0.171925i
$732$		0			0
$733$	1.02983	+	1.02983i	0.0380376	+	0.0380376i	0.725870	−	0.687832i	$-0.241438\pi$
$733$	1.02983	+	1.02983i	0.0380376	+	0.0380376i	−0.687832	+	0.725870i	$0.741438\pi$
$734$	3.32245	+	3.32245i	0.122634	+	0.122634i
$735$		0			0
$736$	−4.67573	−	4.67573i	−0.172350	−	0.172350i
$737$		−	10.7567i		−	0.396228i
$738$		0			0
$739$	−44.1533			−1.62421			−0.812103	−	0.583514i	$-0.801677\pi$
$739$	−44.1533			−1.62421			−0.812103	+	0.583514i	$0.801677\pi$
$740$	0.557756	+	16.8442i	0.0205035	+	0.619207i
$741$		0			0
$742$	−10.2394			−0.375901
$743$			26.6995i			0.979509i	0.871860	+	0.489755i	$0.162914\pi$
$743$			26.6995i			0.979509i	−0.871860	+	0.489755i	$0.837086\pi$
$744$		0			0
$745$	1.08537	+	32.7784i	0.0397650	+	1.20091i
$746$	−9.61653			−0.352086
$747$		0			0
$748$	6.00845	−	9.19065i	0.219691	−	0.336044i
$749$	−4.29621			−0.156980
$750$		0			0
$751$	−6.90274	−	6.90274i	−0.251885	−	0.251885i	0.569858	−	0.821743i	$-0.306998\pi$
$751$	−6.90274	−	6.90274i	−0.251885	−	0.251885i	−0.821743	+	0.569858i	$0.806998\pi$
$752$	−4.83539	+	4.83539i	−0.176328	+	0.176328i
$753$		0			0
$754$	7.01118	+	7.01118i	0.255332	+	0.255332i
$755$	40.3993	−	1.33772i	1.47028	−	0.0486847i
$756$		0			0
$757$	1.62241	−	1.62241i	0.0589675	−	0.0589675i	−0.677008	−	0.735976i	$-0.736724\pi$
$757$	1.62241	−	1.62241i	0.0589675	−	0.0589675i	0.735976	+	0.677008i	$0.236724\pi$
$758$	−21.9174			−0.796077
$759$		0			0
$760$	2.06882	+	1.93621i	0.0750441	+	0.0702336i
$761$			9.42144i			0.341527i	0.985312	+	0.170764i	$0.0546234\pi$
$761$			9.42144i			0.341527i	−0.985312	+	0.170764i	$0.945377\pi$
$762$		0			0
$763$	1.47516	+	1.47516i	0.0534045	+	0.0534045i
$764$	26.7181			0.966627
$765$		0			0
$766$	18.4379			0.666188
$767$	5.61969	+	5.61969i	0.202915	+	0.202915i
$768$		0			0
$769$			15.1876i			0.547679i	0.961775	+	0.273840i	$0.0882937\pi$
$769$			15.1876i			0.547679i	−0.961775	+	0.273840i	$0.911706\pi$
$770$	−5.69019	+	0.188417i	−0.205060	+	0.00679007i
$771$		0			0
$772$	−9.03047			−0.325014
$773$	−12.3050	+	12.3050i	−0.442581	+	0.442581i	−0.892879	−	0.450297i	$-0.851318\pi$
$773$	−12.3050	+	12.3050i	−0.442581	+	0.442581i	0.450297	+	0.892879i	$0.351318\pi$
$774$		0			0
$775$	15.7440	+	13.7862i	0.565541	+	0.495215i
$776$	10.5986	+	10.5986i	0.380469	+	0.380469i
$777$		0			0
$778$	−27.3446	+	27.3446i	−0.980352	+	0.980352i
$779$	−2.06909	−	2.06909i	−0.0741327	−	0.0741327i
$780$		0			0
$781$	−10.9814			−0.392947
$782$	22.8200	+	14.9188i	0.816043	+	0.533493i
$783$		0			0
$784$	6.08595			0.217355
$785$	8.70754	−	9.30395i	0.310786	−	0.332072i
$786$		0			0
$787$			11.5134i			0.410408i	0.978719	+	0.205204i	$0.0657858\pi$
$787$			11.5134i			0.410408i	−0.978719	+	0.205204i	$0.934214\pi$
$788$	−8.00413			−0.285135
$789$		0			0
$790$	16.3105	−	0.540083i	0.580303	−	0.0192153i
$791$	15.6644			0.556962
$792$		0			0
$793$		−	20.1146i		−	0.714290i
$794$	−9.98524	−	9.98524i	−0.354363	−	0.354363i
$795$		0			0
$796$	3.51012	+	3.51012i	0.124413	+	0.124413i
$797$	13.6618	+	13.6618i	0.483926	+	0.483926i	0.906383	−	0.422457i	$-0.138832\pi$
$797$	13.6618	+	13.6618i	0.483926	+	0.483926i	−0.422457	+	0.906383i	$0.638832\pi$
$798$		0			0
$799$	15.4282	−	23.5993i	0.545809	−	0.834881i
$800$	−3.76167	−	3.29390i	−0.132995	−	0.116457i
$801$		0			0
$802$		−	13.1160i		−	0.463142i
$803$	−8.35544	−	8.35544i	−0.294857	−	0.294857i
$804$		0			0
$805$	−0.467831	−	14.1285i	−0.0164889	−	0.497965i
$806$	−8.17127	−	8.17127i	−0.287821	−	0.287821i
$807$		0			0
$808$	2.60481	+	2.60481i	0.0916370	+	0.0916370i
$809$	−25.5552	+	25.5552i	−0.898472	+	0.898472i	−0.995301	−	0.0968287i	$-0.969130\pi$
$809$	−25.5552	+	25.5552i	−0.898472	+	0.898472i	0.0968287	+	0.995301i	$0.469130\pi$
$810$		0			0
$811$	−22.9303	−	22.9303i	−0.805190	−	0.805190i	0.178711	−	0.983902i	$-0.442807\pi$
$811$	−22.9303	−	22.9303i	−0.805190	−	0.805190i	−0.983902	+	0.178711i	$0.942807\pi$
$812$	2.42776	−	2.42776i	0.0851977	−	0.0851977i
$813$		0			0
$814$	−20.0724			−0.703537
$815$	15.9284	−	0.527430i	0.557948	−	0.0184751i
$816$		0			0
$817$	−1.84612	−	1.84612i	−0.0645875	−	0.0645875i
$818$	−8.10346	+	8.10346i	−0.283331	+	0.283331i
$819$		0			0
$820$	3.76990	+	3.52824i	0.131651	+	0.123211i
$821$	−29.7007	+	29.7007i	−1.03656	+	1.03656i	−0.0372565	+	0.999306i	$0.511862\pi$
$821$	−29.7007	+	29.7007i	−1.03656	+	1.03656i	−0.999306	+	0.0372565i	$0.988138\pi$
$822$		0			0
$823$			18.0398i			0.628828i	0.949286	+	0.314414i	$0.101808\pi$
$823$			18.0398i			0.628828i	−0.949286	+	0.314414i	$0.898192\pi$
$824$			17.0811i			0.595048i
$825$		0			0
$826$	1.94593	−	1.94593i	0.0677075	−	0.0677075i
$827$			17.0469i			0.592778i	0.955067	+	0.296389i	$0.0957825\pi$
$827$			17.0469i			0.592778i	−0.955067	+	0.296389i	$0.904218\pi$
$828$		0			0
$829$			23.5645i			0.818428i	0.912439	+	0.409214i	$0.134197\pi$
$829$			23.5645i			0.818428i	−0.912439	+	0.409214i	$0.865803\pi$
$830$	−0.278414	−	8.40812i	−0.00966390	−	0.291850i
$831$		0			0
$832$	1.95234	+	1.95234i	0.0676852	+	0.0676852i
$833$	−24.5605	+	5.14217i	−0.850970	+	0.178166i
$834$		0			0
$835$	−0.300035	−	9.06107i	−0.0103831	−	0.313571i
$836$	−2.38629	+	2.38629i	−0.0825315	+	0.0825315i
$837$		0			0
$838$	−17.0465			−0.588863
$839$	−22.0944	+	22.0944i	−0.762782	+	0.762782i	−0.976824	−	0.214043i	$-0.931337\pi$
$839$	−22.0944	+	22.0944i	−0.762782	+	0.762782i	0.214043	+	0.976824i	$0.431337\pi$
$840$		0			0
$841$		−	16.1035i		−	0.555294i
$842$	−19.0831	−	19.0831i	−0.657648	−	0.657648i
$843$		0			0
$844$	11.3150	+	11.3150i	0.389477	+	0.389477i
$845$	12.0161	−	0.397885i	0.413368	−	0.0136877i
$846$		0			0
$847$			3.73597i			0.128369i
$848$	7.57312	−	7.57312i	0.260062	−	0.260062i
$849$		0			0
$850$	17.9637	+	10.1146i	0.616151	+	0.346927i
$851$		−	49.8390i		−	1.70846i
$852$		0			0
$853$	−30.9121			−1.05841			−0.529205	−	0.848494i	$-0.677510\pi$
$853$	−30.9121			−1.05841			−0.529205	+	0.848494i	$0.677510\pi$
$854$	−6.96507			−0.238340
$855$		0			0
$856$	3.17750	−	3.17750i	0.108605	−	0.108605i
$857$			40.8719i			1.39616i	0.716021	+	0.698079i	$0.245961\pi$
$857$			40.8719i			1.39616i	−0.716021	+	0.698079i	$0.754039\pi$
$858$		0			0
$859$	−6.70638			−0.228819			−0.114409	−	0.993434i	$-0.536498\pi$
$859$	−6.70638			−0.228819			−0.114409	+	0.993434i	$0.536498\pi$
$860$	3.36365	+	3.14803i	0.114699	+	0.107347i
$861$		0			0
$862$		−	4.07684i		−	0.138858i
$863$	−15.6237	−	15.6237i	−0.531838	−	0.531838i	0.389281	−	0.921119i	$-0.372724\pi$
$863$	−15.6237	−	15.6237i	−0.531838	−	0.531838i	−0.921119	+	0.389281i	$0.872724\pi$
$864$		0			0
$865$	−29.5175	+	0.977399i	−1.00362	+	0.0332326i
$866$		−	0.507776i		−	0.0172549i
$867$		0			0
$868$	−2.82946	+	2.82946i	−0.0960383	+	0.0960383i
$869$			19.4364i			0.659334i
$870$		0			0
$871$	−11.1521			−0.377874
$872$	−2.18207			−0.0738944
$873$		0			0
$874$	−5.92506	−	5.92506i	−0.200418	−	0.200418i
$875$	−1.05970	−	10.6364i	−0.0358243	−	0.359577i
$876$		0			0
$877$	41.5253			1.40221			0.701105	−	0.713058i	$-0.252691\pi$
$877$	41.5253			1.40221			0.701105	+	0.713058i	$0.252691\pi$
$878$	14.0165			0.473034
$879$		0			0
$880$	4.06914	−	4.34785i	0.137171	−	0.146566i
$881$	15.5873	−	15.5873i	0.525149	−	0.525149i	−0.393973	−	0.919122i	$-0.628900\pi$
$881$	15.5873	−	15.5873i	0.525149	−	0.525149i	0.919122	+	0.393973i	$0.128900\pi$
$882$		0			0
$883$	37.5067	−	37.5067i	1.26220	−	1.26220i	0.312175	−	0.950024i	$-0.398942\pi$
$883$	37.5067	−	37.5067i	1.26220	−	1.26220i	0.950024	−	0.312175i	$-0.101058\pi$
$884$	−9.52846	−	6.22929i	−0.320477	−	0.209514i
$885$		0			0
$886$			36.3563i			1.22141i
$887$	−2.15059			−0.0722097			−0.0361049	−	0.999348i	$-0.511495\pi$
$887$	−2.15059			−0.0722097			−0.0361049	+	0.999348i	$0.511495\pi$
$888$		0			0
$889$	1.89083	−	1.89083i	0.0634165	−	0.0634165i
$890$	4.44954	−	4.75430i	0.149149	−	0.159364i
$891$		0			0
$892$	−19.5450	+	19.5450i	−0.654416	+	0.654416i
$893$	−6.12738	+	6.12738i	−0.205045	+	0.205045i
$894$		0			0
$895$	−38.9181	+	1.28868i	−1.30089	+	0.0430757i
$896$	0.676037	−	0.676037i	0.0225848	−	0.0225848i
$897$		0			0
$898$	−24.9798			−0.833587
$899$		−	15.0304i		−	0.501291i
$900$		0			0
$901$	−24.1634	+	36.9609i	−0.805000	+	1.23134i
$902$	−4.34840	+	4.34840i	−0.144786	+	0.144786i
$903$		0			0
$904$	−11.5855	+	11.5855i	−0.385327	+	0.385327i
$905$	−17.8114	−	16.6696i	−0.592071	−	0.554118i
$906$		0			0
$907$	−19.0637			−0.632999			−0.316500	−	0.948593i	$-0.602508\pi$
$907$	−19.0637			−0.632999			−0.316500	+	0.948593i	$0.602508\pi$
$908$	25.5978			0.849491
$909$		0			0
$910$	0.195342	+	5.89934i	0.00647552	+	0.195561i
$911$	−22.4893	−	22.4893i	−0.745104	−	0.745104i	0.228451	−	0.973555i	$-0.426634\pi$
$911$	−22.4893	−	22.4893i	−0.745104	−	0.745104i	−0.973555	+	0.228451i	$0.926634\pi$
$912$		0			0
$913$	10.0195			0.331597
$914$	8.16241			0.269988
$915$		0			0
$916$		−	10.2022i		−	0.337091i
$917$	−1.17906	+	1.17906i	−0.0389358	+	0.0389358i
$918$		0			0
$919$			49.0603i			1.61835i	0.587568	+	0.809175i	$0.300085\pi$
$919$			49.0603i			1.61835i	−0.587568	+	0.809175i	$0.699915\pi$
$920$	10.7955	+	10.1035i	0.355918	+	0.333103i
$921$		0			0
$922$	14.4463	+	14.4463i	0.475763	+	0.475763i
$923$			11.3851i			0.374744i
$924$		0			0
$925$	−2.49299	−	37.6030i	−0.0819691	−	1.23638i
$926$	41.1930			1.35369
$927$		0			0
$928$			3.59117i			0.117886i
$929$	20.9340	−	20.9340i	0.686821	−	0.686821i	−0.274707	−	0.961528i	$-0.588581\pi$
$929$	20.9340	−	20.9340i	0.686821	−	0.686821i	0.961528	+	0.274707i	$0.0885809\pi$
$930$		0			0
$931$	7.71208			0.252753
$932$	−19.5475			−0.640298
$933$		0			0
$934$			7.53584i			0.246580i
$935$	−12.7478	+	20.9843i	−0.416899	+	0.686260i
$936$		0			0
$937$	−11.9941	+	11.9941i	−0.391830	+	0.391830i	−0.875339	−	0.483509i	$-0.839362\pi$
$937$	−11.9941	+	11.9941i	−0.391830	+	0.391830i	0.483509	+	0.875339i	$0.339362\pi$
$938$			3.86163i			0.126087i
$939$		0			0
$940$	10.4485	−	11.1642i	0.340793	−	0.364135i
$941$	25.9135	+	25.9135i	0.844755	+	0.844755i	0.989473	−	0.144718i	$-0.0462274\pi$
$941$	25.9135	+	25.9135i	0.844755	+	0.844755i	−0.144718	+	0.989473i	$0.546227\pi$
$942$		0			0
$943$	−10.7969	−	10.7969i	−0.351596	−	0.351596i
$944$			2.87844i			0.0936851i
$945$		0			0
$946$	−3.87981	+	3.87981i	−0.126143	+	0.126143i
$947$	22.2402			0.722709			0.361355	−	0.932428i	$-0.382314\pi$
$947$	22.2402			0.722709			0.361355	+	0.932428i	$0.382314\pi$
$948$		0			0
$949$	−8.66255	+	8.66255i	−0.281198	+	0.281198i
$950$	−4.76677	−	4.17402i	−0.154655	−	0.135423i
$951$		0			0
$952$	−2.15702	+	3.29942i	−0.0699093	+	0.106935i
$953$	−5.72875	−	5.72875i	−0.185572	−	0.185572i	0.608207	−	0.793779i	$-0.291889\pi$
$953$	−5.72875	−	5.72875i	−0.185572	−	0.185572i	−0.793779	+	0.608207i	$0.791889\pi$
$954$		0			0
$955$	−59.7108	+	1.97718i	−1.93220	+	0.0639799i
$956$		−	25.0580i		−	0.810433i
$957$		0			0
$958$			38.1244i			1.23174i
$959$	11.7545	−	11.7545i	0.379574	−	0.379574i
$960$		0			0
$961$		−	13.4827i		−	0.434926i
$962$			20.8102i			0.670946i
$963$		0			0
$964$	9.79340	−	9.79340i	0.315424	−	0.315424i
$965$	20.1817	−	0.668267i	0.649671	−	0.0215123i
$966$		0			0
$967$	−0.228906	+	0.228906i	−0.00736112	+	0.00736112i	−0.710778	−	0.703417i	$-0.751657\pi$
$967$	−0.228906	+	0.228906i	−0.00736112	+	0.00736112i	0.703417	+	0.710778i	$0.251657\pi$
$968$	−2.76314	−	2.76314i	−0.0888107	−	0.0888107i
$969$		0			0
$970$	−24.4706	−	22.9020i	−0.785704	−	0.735339i
$971$	−41.6687			−1.33721			−0.668606	−	0.743617i	$-0.733109\pi$
$971$	−41.6687			−1.33721			−0.668606	+	0.743617i	$0.733109\pi$
$972$		0			0
$973$	−5.38569	+	5.38569i	−0.172657	+	0.172657i
$974$	22.0305	+	22.0305i	0.705902	+	0.705902i
$975$		0			0
$976$	5.15140	−	5.15140i	0.164892	−	0.164892i
$977$	−0.780819	−	0.780819i	−0.0249806	−	0.0249806i	0.694506	−	0.719487i	$-0.255623\pi$
$977$	−0.780819	−	0.780819i	−0.0249806	−	0.0249806i	−0.719487	+	0.694506i	$0.755623\pi$
$978$		0			0
$979$	5.48386	+	5.48386i	0.175265	+	0.175265i
$980$	−13.6011	+	0.450368i	−0.434472	+	0.0143865i
$981$		0			0
$982$	−5.15032	−	5.15032i	−0.164353	−	0.164353i
$983$		−	58.2275i		−	1.85717i	−0.371123	−	0.928584i	$-0.621027\pi$
$983$		−	58.2275i		−	1.85717i	0.371123	−	0.928584i	$-0.378973\pi$
$984$		0			0
$985$	17.8880	−	0.592316i	0.569958	−	0.0188728i
$986$	−3.03427	−	14.4925i	−0.0966308	−	0.461536i
$987$		0			0
$988$	2.47400	+	2.47400i	0.0787083	+	0.0787083i
$989$	−9.63341	−	9.63341i	−0.306325	−	0.306325i
$990$		0			0
$991$	11.5623	+	11.5623i	0.367288	+	0.367288i	0.866487	−	0.499199i	$-0.166372\pi$
$991$	11.5623	+	11.5623i	0.367288	+	0.367288i	−0.499199	+	0.866487i	$0.666372\pi$
$992$		−	4.18537i		−	0.132886i
$993$		0			0
$994$	3.94231			0.125042
$995$	−8.10431	−	7.58481i	−0.256924	−	0.240455i
$996$		0			0
$997$	−55.7008			−1.76406			−0.882032	−	0.471190i	$-0.843825\pi$
$997$	−55.7008			−1.76406			−0.882032	+	0.471190i	$0.843825\pi$
$998$			40.8694i			1.29370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.u.c.557.9	yes	40
3.2	odd	2	inner	1530.2.u.c.557.14	yes	40
5.3	odd	4		1530.2.j.c.863.9	✓	40
15.8	even	4		1530.2.j.c.863.14	yes	40
17.4	even	4		1530.2.j.c.1007.14	yes	40
51.38	odd	4		1530.2.j.c.1007.9	yes	40
85.38	odd	4	inner	1530.2.u.c.1313.14	yes	40
255.38	even	4	inner	1530.2.u.c.1313.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.j.c.863.9	✓	40	5.3	odd	4
1530.2.j.c.863.14	yes	40	15.8	even	4
1530.2.j.c.1007.9	yes	40	51.38	odd	4
1530.2.j.c.1007.14	yes	40	17.4	even	4
1530.2.u.c.557.9	yes	40	1.1	even	1	trivial
1530.2.u.c.557.14	yes	40	3.2	odd	2	inner
1530.2.u.c.1313.9	yes	40	255.38	even	4	inner
1530.2.u.c.1313.14	yes	40	85.38	odd	4	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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.0740013 - 2.23484i) q^{5} -0.956061 q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.52795 + 1.63260i) q^{10} +(-1.88313 - 1.88313i) q^{11} +(-1.95234 + 1.95234i) q^{13} +(0.676037 + 0.676037i) q^{14} -1.00000 q^{16} +(4.03560 - 0.844925i) q^{17} -1.26720 q^{19} +(2.23484 - 0.0740013i) q^{20} +2.66314i q^{22} -6.61248 q^{23} +(-4.98905 + 0.330763i) q^{25} +2.76103 q^{26} -0.956061i q^{28} +(2.53934 + 2.53934i) q^{29} +(-2.95950 - 2.95950i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.45106 - 2.25615i) q^{34} +(0.0707497 + 2.13665i) q^{35} +7.53711i q^{37} +(0.896042 + 0.896042i) q^{38} +(-1.63260 - 1.52795i) q^{40} +(1.63281 + 1.63281i) q^{41} +(1.45685 + 1.45685i) q^{43} +(1.88313 - 1.88313i) q^{44} +(4.67573 + 4.67573i) q^{46} +(4.83539 - 4.83539i) q^{47} -6.08595 q^{49} +(3.76167 + 3.29390i) q^{50} +(-1.95234 - 1.95234i) q^{52} +(-7.57312 + 7.57312i) q^{53} +(-4.06914 + 4.34785i) q^{55} +(-0.676037 + 0.676037i) q^{56} -3.59117i q^{58} -2.87844i q^{59} +(-5.15140 + 5.15140i) q^{61} +4.18537i q^{62} -1.00000i q^{64} +(4.50765 + 4.21870i) q^{65} +(2.85608 + 2.85608i) q^{67} +(0.844925 + 4.03560i) q^{68} +(1.46081 - 1.56086i) q^{70} +(2.91575 - 2.91575i) q^{71} +4.43701 q^{73} +(5.32954 - 5.32954i) q^{74} -1.26720i q^{76} +(1.80038 + 1.80038i) q^{77} +(-5.16067 - 5.16067i) q^{79} +(0.0740013 + 2.23484i) q^{80} -2.30914i q^{82} +(-2.66034 + 2.66034i) q^{83} +(-2.18692 - 8.95642i) q^{85} -2.06030i q^{86} -2.66314 q^{88} -2.91210 q^{89} +(1.86656 - 1.86656i) q^{91} -6.61248i q^{92} -6.83827 q^{94} +(0.0937741 + 2.83198i) q^{95} +14.9887i q^{97} +(4.30342 + 4.30342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{10} + 8 q^{13} - 40 q^{16} + 16 q^{19} - 8 q^{31} + 32 q^{43} + 56 q^{49} + 8 q^{52} + 32 q^{55} - 64 q^{61} + 32 q^{67} + 32 q^{70} + 88 q^{79} + 72 q^{85} + 16 q^{88} + 56 q^{91} - 16 q^{94}+O(q^{100}) \) 40 * q + 8 * q^10 + 8 * q^13 - 40 * q^16 + 16 * q^19 - 8 * q^31 + 32 * q^43 + 56 * q^49 + 8 * q^52 + 32 * q^55 - 64 * q^61 + 32 * q^67 + 32 * q^70 + 88 * q^79 + 72 * q^85 + 16 * q^88 + 56 * q^91 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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