LMFDB - Embedded newform 1530.2.j.c.1007.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1530,2,Mod(863,1530)] 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("1530.863"); 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, 3, 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.j (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			1007.9
Character	$\chi$	$=$	1530.1007
Dual form			1530.2.j.c.863.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.23484 - 0.0740013i) q^{5} -0.956061i q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.63260 - 1.52795i) q^{10} +(-1.88313 + 1.88313i) q^{11} +(-1.95234 + 1.95234i) q^{13} +(-0.676037 + 0.676037i) q^{14} -1.00000 q^{16} +(-0.844925 + 4.03560i) q^{17} +1.26720 q^{19} +(0.0740013 + 2.23484i) q^{20} +2.66314 q^{22} +6.61248i q^{23} +(4.98905 - 0.330763i) q^{25} +2.76103 q^{26} +0.956061 q^{28} +(-2.53934 + 2.53934i) q^{29} +(-2.95950 + 2.95950i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.45106 - 2.25615i) q^{34} +(-0.0707497 - 2.13665i) q^{35} +7.53711 q^{37} +(-0.896042 - 0.896042i) q^{38} +(1.52795 - 1.63260i) q^{40} +(1.63281 - 1.63281i) q^{41} +(-1.45685 - 1.45685i) q^{43} +(-1.88313 - 1.88313i) q^{44} +(4.67573 - 4.67573i) q^{46} +(-4.83539 + 4.83539i) q^{47} +6.08595 q^{49} +(-3.76167 - 3.29390i) q^{50} +(-1.95234 - 1.95234i) q^{52} +(-7.57312 + 7.57312i) q^{53} +(-4.06914 + 4.34785i) q^{55} +(-0.676037 - 0.676037i) q^{56} +3.59117 q^{58} -2.87844i q^{59} +(-5.15140 - 5.15140i) q^{61} +4.18537 q^{62} -1.00000i q^{64} +(-4.21870 + 4.50765i) q^{65} +(2.85608 + 2.85608i) q^{67} +(-4.03560 - 0.844925i) q^{68} +(-1.46081 + 1.56086i) q^{70} +(2.91575 + 2.91575i) q^{71} -4.43701i q^{73} +(-5.32954 - 5.32954i) q^{74} +1.26720i q^{76} +(1.80038 + 1.80038i) q^{77} +(5.16067 - 5.16067i) q^{79} +(-2.23484 + 0.0740013i) q^{80} -2.30914 q^{82} +(-2.66034 + 2.66034i) q^{83} +(-1.58964 + 9.08147i) q^{85} +2.06030i q^{86} +2.66314i q^{88} +2.91210 q^{89} +(1.86656 + 1.86656i) q^{91} -6.61248 q^{92} +6.83827 q^{94} +(2.83198 - 0.0937741i) q^{95} +14.9887 q^{97} +(-4.30342 - 4.30342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{13} - 40 q^{16} - 16 q^{19} - 16 q^{22} - 8 q^{31} + 16 q^{37} - 8 q^{40} - 32 q^{43} - 56 q^{49} + 8 q^{52} + 32 q^{55} - 32 q^{58} - 64 q^{61} + 32 q^{67} - 32 q^{70} - 88 q^{79} + 32 q^{85}+ \cdots - 64 q^{97}+O(q^{100}) $ 40 * q + 8 * q^13 - 40 * q^16 - 16 * q^19 - 16 * q^22 - 8 * q^31 + 16 * q^37 - 8 * q^40 - 32 * q^43 - 56 * q^49 + 8 * q^52 + 32 * q^55 - 32 * q^58 - 64 * q^61 + 32 * q^67 - 32 * q^70 - 88 * q^79 + 32 * q^85 + 56 * q^91 + 16 * q^94 - 64 * q^97

Character values

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

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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
$5$	2.23484	−	0.0740013i	0.999452	−	0.0330944i
$5$	2.23484	−	0.0740013i	0.999452	−	0.0330944i
$6$		0			0
$7$		−	0.956061i		−	0.361357i	−0.983542	−	0.180678i	$-0.942171\pi$
$7$		−	0.956061i		−	0.361357i	0.983542	−	0.180678i	$-0.0578293\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−1.63260	−	1.52795i	−0.516273	−	0.483179i
$11$	−1.88313	+	1.88313i	−0.567784	+	0.567784i	−0.931507	−	0.363723i	$-0.881505\pi$
$11$	−1.88313	+	1.88313i	−0.567784	+	0.567784i	0.363723	+	0.931507i	$0.381505\pi$
$12$		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
$17$	−0.844925	+	4.03560i	−0.204924	+	0.978778i
$17$	−0.844925	+	4.03560i	−0.204924	+	0.978778i
$18$		0			0
$19$	1.26720			0.290715			0.145357	−	0.989379i	$-0.453567\pi$
$19$	1.26720			0.290715			0.145357	+	0.989379i	$0.453567\pi$
$20$	0.0740013	+	2.23484i	0.0165472	+	0.499726i
$21$		0			0
$22$	2.66314			0.567784
$23$			6.61248i			1.37880i	0.724382	+	0.689399i	$0.242125\pi$
$23$			6.61248i			1.37880i	−0.724382	+	0.689399i	$0.757875\pi$
$24$		0			0
$25$	4.98905	−	0.330763i	0.997810	−	0.0661525i
$26$	2.76103			0.541482
$27$		0			0
$28$	0.956061			0.180678
$29$	−2.53934	+	2.53934i	−0.471543	+	0.471543i	−0.902414	−	0.430870i	$-0.858207\pi$
$29$	−2.53934	+	2.53934i	−0.471543	+	0.471543i	0.430870	+	0.902414i	$0.358207\pi$
$30$		0			0
$31$	−2.95950	+	2.95950i	−0.531542	+	0.531542i	−0.921031	−	0.389489i	$-0.872652\pi$
$31$	−2.95950	+	2.95950i	−0.531542	+	0.531542i	0.389489	+	0.921031i	$0.372652\pi$
$32$	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
$37$	7.53711			1.23909			0.619546	−	0.784960i	$-0.287317\pi$
$37$	7.53711			1.23909			0.619546	+	0.784960i	$0.287317\pi$
$38$	−0.896042	−	0.896042i	−0.145357	−	0.145357i
$39$		0			0
$40$	1.52795	−	1.63260i	0.241589	−	0.258137i
$41$	1.63281	−	1.63281i	0.255002	−	0.255002i	−0.568016	−	0.823018i	$-0.692289\pi$
$41$	1.63281	−	1.63281i	0.255002	−	0.255002i	0.823018	+	0.568016i	$0.192289\pi$
$42$		0			0
$43$	−1.45685	−	1.45685i	−0.222168	−	0.222168i	0.587243	−	0.809411i	$-0.300213\pi$
$43$	−1.45685	−	1.45685i	−0.222168	−	0.222168i	−0.809411	+	0.587243i	$0.800213\pi$
$44$	−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	−0.965546	−	0.260232i	$-0.916201\pi$
$47$	−4.83539	+	4.83539i	−0.705314	+	0.705314i	0.260232	+	0.965546i	$0.416201\pi$
$48$		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
$58$	3.59117			0.471543
$59$		−	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	0.295709	−	0.955278i	$-0.404444\pi$
$61$	−5.15140	−	5.15140i	−0.659569	−	0.659569i	−0.955278	+	0.295709i	$0.904444\pi$
$62$	4.18537			0.531542
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.21870	+	4.50765i	−0.523265	+	0.559105i
$66$		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	$0.670645\pi$
$68$	−4.03560	−	0.844925i	−0.489389	−	0.102462i
$69$		0			0
$70$	−1.46081	+	1.56086i	−0.174600	+	0.186559i
$71$	2.91575	+	2.91575i	0.346036	+	0.346036i	0.858631	−	0.512595i	$-0.171316\pi$
$71$	2.91575	+	2.91575i	0.346036	+	0.346036i	−0.512595	+	0.858631i	$0.671316\pi$
$72$		0			0
$73$		−	4.43701i		−	0.519312i	−0.965701	−	0.259656i	$-0.916391\pi$
$73$		−	4.43701i		−	0.519312i	0.965701	−	0.259656i	$-0.0836092\pi$
$74$	−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	$-0.615333\pi$
$79$	5.16067	−	5.16067i	0.580621	−	0.580621i	0.935074	+	0.354453i	$0.115333\pi$
$80$	−2.23484	+	0.0740013i	−0.249863	+	0.00827360i
$81$		0			0
$82$	−2.30914			−0.255002
$83$	−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
$85$	−1.58964	+	9.08147i	−0.172420	+	0.985024i
$86$			2.06030i			0.222168i
$87$		0			0
$88$			2.66314i			0.283892i
$89$	2.91210			0.308682			0.154341	−	0.988018i	$-0.450675\pi$
$89$	2.91210			0.308682			0.154341	+	0.988018i	$0.450675\pi$
$90$		0			0
$91$	1.86656	+	1.86656i	0.195668	+	0.195668i
$92$	−6.61248			−0.689399
$93$		0			0
$94$	6.83827			0.705314
$95$	2.83198	−	0.0937741i	0.290555	−	0.00962102i
$96$		0			0
$97$	14.9887			1.52188			0.760938	−	0.648824i	$-0.224739\pi$
$97$	14.9887			1.52188			0.760938	+	0.648824i	$0.224739\pi$
$98$	−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	$-0.941330\pi$
$101$		−	3.68376i		−	0.366548i	0.983062	−	0.183274i	$-0.0586695\pi$
$102$		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
$107$			4.49366i			0.434418i	0.976125	+	0.217209i	$0.0696954\pi$
$107$			4.49366i			0.434418i	−0.976125	+	0.217209i	$0.930305\pi$
$108$		0			0
$109$	1.54296	−	1.54296i	0.147789	−	0.147789i	−0.629341	−	0.777129i	$-0.716675\pi$
$109$	1.54296	−	1.54296i	0.147789	−	0.147789i	0.777129	+	0.629341i	$0.216675\pi$
$110$	5.95171	−	0.197076i	0.567473	−	0.0187905i
$111$		0			0
$112$			0.956061i			0.0903392i
$113$			16.3843i			1.54131i	0.637254	+	0.770654i	$0.280070\pi$
$113$			16.3843i			1.54131i	−0.637254	+	0.770654i	$0.719930\pi$
$114$		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
$122$			7.28518i			0.659569i
$123$		0			0
$124$	−2.95950	−	2.95950i	−0.265771	−	0.265771i
$125$	11.1253	−	1.10840i	0.995074	−	0.0991382i
$126$		0			0
$127$	1.97773	−	1.97773i	0.175495	−	0.175495i	−0.613893	−	0.789389i	$-0.710398\pi$
$127$	1.97773	−	1.97773i	0.175495	−	0.175495i	0.789389	+	0.613893i	$0.210398\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	6.17046	−	0.204320i	0.541185	−	0.0179200i
$131$	1.23324	+	1.23324i	0.107749	+	0.107749i	0.758926	−	0.651177i	$-0.225724\pi$
$131$	1.23324	+	1.23324i	0.107749	+	0.107749i	−0.651177	+	0.758926i	$0.725724\pi$
$132$		0			0
$133$		−	1.21152i		−	0.105052i
$134$		−	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	$-0.483519\pi$
$137$	12.2948	−	12.2948i	1.05041	−	1.05041i	0.998660	−	0.0517532i	$-0.0164809\pi$
$138$		0			0
$139$	−5.63321	−	5.63321i	−0.477803	−	0.477803i	0.426626	−	0.904428i	$-0.359702\pi$
$139$	−5.63321	−	5.63321i	−0.477803	−	0.477803i	−0.904428	+	0.426626i	$0.859702\pi$
$140$	2.13665	−	0.0707497i	0.180579	−	0.00597944i
$141$		0			0
$142$		−	4.12349i		−	0.346036i
$143$		−	7.35301i		−	0.614890i
$144$		0			0
$145$	−5.48711	+	5.86294i	−0.455680	+	0.486891i
$146$	−3.13744	+	3.13744i	−0.259656	+	0.259656i
$147$		0			0
$148$			7.53711i			0.619546i
$149$	14.6670			1.20156			0.600782	−	0.799413i	$-0.294856\pi$
$149$	14.6670			1.20156			0.600782	+	0.799413i	$0.294856\pi$
$150$		0			0
$151$		−	18.0770i		−	1.47109i	−0.677478	−	0.735543i	$-0.736927\pi$
$151$		−	18.0770i		−	1.47109i	0.677478	−	0.735543i	$-0.263073\pi$
$152$	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	$0.676975\pi$
$158$	−7.29829			−0.580621
$159$		0			0
$160$	1.63260	+	1.52795i	0.129068	+	0.120795i
$161$	6.32193			0.498238
$162$		0			0
$163$	−7.12731			−0.558254			−0.279127	−	0.960254i	$-0.590045\pi$
$163$	−7.12731			−0.558254			−0.279127	+	0.960254i	$0.590045\pi$
$164$	1.63281	+	1.63281i	0.127501	+	0.127501i
$165$		0			0
$166$	3.76229			0.292010
$167$			4.05445i			0.313743i	0.987619	+	0.156872i	$0.0501409\pi$
$167$			4.05445i			0.313743i	−0.987619	+	0.156872i	$0.949859\pi$
$168$		0			0
$169$			5.37673i			0.413595i
$170$	7.54561	−	5.29753i	0.578722	−	0.406302i
$171$		0			0
$172$	1.45685	−	1.45685i	0.111084	−	0.111084i
$173$	13.2079			1.00417			0.502087	−	0.864817i	$-0.332566\pi$
$173$	13.2079			1.00417			0.502087	+	0.864817i	$0.332566\pi$
$174$		0			0
$175$	−0.316229	−	4.76983i	−0.0239047	−	0.360565i
$176$	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	0.933079	−	0.359671i	$-0.117111\pi$
$181$	7.71442	+	7.71442i	0.573408	+	0.573408i	−0.359671	+	0.933079i	$0.617111\pi$
$182$		−	2.63971i		−	0.195668i
$183$		0			0
$184$	4.67573	+	4.67573i	0.344699	+	0.344699i
$185$	16.8442	−	0.557756i	1.23841	−	0.0410070i
$186$		0			0
$187$	−6.00845	−	9.19065i	−0.439382	−	0.672087i
$188$	−4.83539	−	4.83539i	−0.352657	−	0.352657i
$189$		0			0
$190$	−2.06882	−	1.93621i	−0.150088	−	0.140467i
$191$			26.7181i			1.93325i	0.256187	+	0.966627i	$0.417534\pi$
$191$			26.7181i			1.93325i	−0.256187	+	0.966627i	$0.582466\pi$
$192$		0			0
$193$	−9.03047			−0.650027			−0.325014	−	0.945709i	$-0.605369\pi$
$193$	−9.03047			−0.650027			−0.325014	+	0.945709i	$0.605369\pi$
$194$	−10.5986	−	10.5986i	−0.760938	−	0.760938i
$195$		0			0
$196$			6.08595i			0.434711i
$197$	8.00413			0.570270			0.285135	−	0.958487i	$-0.407962\pi$
$197$	8.00413			0.570270			0.285135	+	0.958487i	$0.407962\pi$
$198$		0			0
$199$	−3.51012	−	3.51012i	−0.248826	−	0.248826i	0.571663	−	0.820489i	$-0.306298\pi$
$199$	−3.51012	−	3.51012i	−0.248826	−	0.248826i	−0.820489	+	0.571663i	$0.806298\pi$
$200$	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	0.979653	−	0.200699i	$-0.0643215\pi$
$211$	11.3150	+	11.3150i	0.778953	+	0.778953i	−0.200699	+	0.979653i	$0.564321\pi$
$212$	−7.57312	−	7.57312i	−0.520124	−	0.520124i
$213$		0			0
$214$	3.17750	−	3.17750i	0.217209	−	0.217209i
$215$	−3.36365	−	3.14803i	−0.229399	−	0.214694i
$216$		0			0
$217$	2.82946	+	2.82946i	0.192077	+	0.192077i
$218$	−2.18207			−0.147789
$219$		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	$-0.873659\pi$
$223$	−19.5450	−	19.5450i	−1.30883	−	1.30883i	−0.386573	−	0.922259i	$-0.626341\pi$
$224$	0.676037	−	0.676037i	0.0451696	−	0.0451696i
$225$		0			0
$226$	11.5855	−	11.5855i	0.770654	−	0.770654i
$227$	−25.5978			−1.69898			−0.849491	−	0.527603i	$-0.823091\pi$
$227$	−25.5978			−1.69898			−0.849491	+	0.527603i	$0.823091\pi$
$228$		0			0
$229$	10.2022			0.674182			0.337091	−	0.941472i	$-0.390557\pi$
$229$	10.2022			0.674182			0.337091	+	0.941472i	$0.390557\pi$
$230$	10.1035	−	10.7955i	0.666206	−	0.711836i
$231$		0			0
$232$			3.59117i			0.235772i
$233$	−19.5475			−1.28060			−0.640298	−	0.768126i	$-0.721189\pi$
$233$	−19.5475			−1.28060			−0.640298	+	0.768126i	$0.721189\pi$
$234$		0			0
$235$	−10.4485	+	11.1642i	−0.681585	+	0.728269i
$236$	2.87844			0.187370
$237$		0			0
$238$	−2.15702	−	3.29942i	−0.139819	−	0.213870i
$239$	25.0580			1.62087			0.810433	−	0.585831i	$-0.199232\pi$
$239$	25.0580			1.62087			0.810433	+	0.585831i	$0.199232\pi$
$240$		0			0
$241$	−9.79340	+	9.79340i	−0.630849	+	0.630849i	−0.948281	−	0.317432i	$-0.897179\pi$
$241$	−9.79340	+	9.79340i	−0.630849	+	0.630849i	0.317432	+	0.948281i	$0.397179\pi$
$242$	2.76314	−	2.76314i	0.177621	−	0.177621i
$243$		0			0
$244$	5.15140	−	5.15140i	0.329785	−	0.329785i
$245$	13.6011	−	0.450368i	0.868945	−	0.0287730i
$246$		0			0
$247$	−2.47400	+	2.47400i	−0.157417	+	0.157417i
$248$			4.18537i			0.265771i
$249$		0			0
$250$	−8.65050	−	7.08299i	−0.547106	−	0.447968i
$251$		−	19.2063i		−	1.21229i	−0.795353	−	0.606146i	$-0.792715\pi$
$251$		−	19.2063i		−	1.21229i	0.795353	−	0.606146i	$-0.207285\pi$
$252$		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
$260$	−4.50765	−	4.21870i	−0.279553	−	0.261633i
$261$		0			0
$262$		−	1.74407i		−	0.107749i
$263$	−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
$265$	−16.3643	+	17.4852i	−1.00525	+	1.07411i
$266$	−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	$-0.705174\pi$
$269$	3.25560	−	3.25560i	0.198498	−	0.198498i	0.799356	+	0.600858i	$0.205174\pi$
$270$		0			0
$271$	−3.46198			−0.210300			−0.105150	−	0.994456i	$-0.533532\pi$
$271$	−3.46198			−0.210300			−0.105150	+	0.994456i	$0.533532\pi$
$272$	0.844925	−	4.03560i	0.0512311	−	0.244694i
$273$		0			0
$274$	−17.3874			−1.05041
$275$	−8.77214	+	10.0179i	−0.528980	+	0.604101i
$276$		0			0
$277$	−10.6782			−0.641588			−0.320794	−	0.947149i	$-0.603950\pi$
$277$	−10.6782			−0.641588			−0.320794	+	0.947149i	$0.603950\pi$
$278$			7.96656i			0.477803i
$279$		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
$283$	27.6017			1.64075			0.820375	−	0.571826i	$-0.193765\pi$
$283$	27.6017			1.64075			0.820375	+	0.571826i	$0.193765\pi$
$284$	−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
$292$	4.43701			0.259656
$293$	15.7217	+	15.7217i	0.918469	+	0.918469i	0.996918	−	0.0784487i	$-0.0249967\pi$
$293$	15.7217	+	15.7217i	0.918469	+	0.918469i	−0.0784487	+	0.996918i	$0.524997\pi$
$294$		0			0
$295$	−0.213008	−	6.43285i	−0.0124018	−	0.374535i
$296$	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	0.518175	−	0.855275i	$-0.326612\pi$
$311$	−5.94482	−	5.94482i	−0.337100	−	0.337100i	−0.855275	+	0.518175i	$0.826612\pi$
$312$		0			0
$313$	12.2937			0.694880			0.347440	−	0.937702i	$-0.387051\pi$
$313$	12.2937			0.694880			0.347440	+	0.937702i	$0.387051\pi$
$314$		−	5.69886i		−	0.321605i
$315$		0			0
$316$	5.16067	+	5.16067i	0.290310	+	0.290310i
$317$	−5.79422			−0.325436			−0.162718	−	0.986673i	$-0.552026\pi$
$317$	−5.79422			−0.325436			−0.162718	+	0.986673i	$0.552026\pi$
$318$		0			0
$319$		−	9.56379i		−	0.535470i
$320$	−0.0740013	−	2.23484i	−0.00413680	−	0.124932i
$321$		0			0
$322$	−4.47028	−	4.47028i	−0.249119	−	0.249119i
$323$	−1.07069	+	5.11390i	−0.0595745	+	0.284545i
$324$		0			0
$325$	−9.09456	+	10.3861i	−0.504475	+	0.576116i
$326$	5.03977	+	5.03977i	0.279127	+	0.279127i
$327$		0			0
$328$		−	2.30914i		−	0.127501i
$329$	4.62292	+	4.62292i	0.254870	+	0.254870i
$330$		0			0
$331$			13.6433i			0.749902i	0.927045	+	0.374951i	$0.122341\pi$
$331$			13.6433i			0.749902i	−0.927045	+	0.374951i	$0.877659\pi$
$332$	−2.66034	−	2.66034i	−0.146005	−	0.146005i
$333$		0			0
$334$	2.86693	−	2.86693i	0.156872	−	0.156872i
$335$	6.59424	+	6.17153i	0.360282	+	0.337187i
$336$		0			0
$337$	−0.786275			−0.0428311			−0.0214156	−	0.999771i	$-0.506817\pi$
$337$	−0.786275			−0.0428311			−0.0214156	+	0.999771i	$0.506817\pi$
$338$	3.80192	−	3.80192i	0.206797	−	0.206797i
$339$		0			0
$340$	−9.08147	−	1.58964i	−0.492512	−	0.0862101i
$341$		−	11.1462i		−	0.603602i
$342$		0			0
$343$		−	12.5110i		−	0.675528i
$344$	−2.06030			−0.111084
$345$		0			0
$346$	−9.33937	−	9.33937i	−0.502087	−	0.502087i
$347$	−30.6100			−1.64323			−0.821616	−	0.570041i	$-0.806927\pi$
$347$	−30.6100			−1.64323			−0.821616	+	0.570041i	$0.806927\pi$
$348$		0			0
$349$	−12.0908			−0.647205			−0.323602	−	0.946193i	$-0.604894\pi$
$349$	−12.0908			−0.647205			−0.323602	+	0.946193i	$0.604894\pi$
$350$	−3.14917	+	3.59639i	−0.168330	+	0.192235i
$351$		0			0
$352$	−2.66314			−0.141946
$353$	6.14878	+	6.14878i	0.327267	+	0.327267i	0.851546	−	0.524280i	$-0.175665\pi$
$353$	6.14878	+	6.14878i	0.327267	+	0.327267i	−0.524280	+	0.851546i	$0.675665\pi$
$354$		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
$362$		−	10.9098i		−	0.573408i
$363$		0			0
$364$	−1.86656	+	1.86656i	−0.0978341	+	0.0978341i
$365$	−0.328344	−	9.91601i	−0.0171863	−	0.519028i
$366$		0			0
$367$		−	4.69865i		−	0.245267i	−0.992452	−	0.122634i	$-0.960866\pi$
$367$		−	4.69865i		−	0.245267i	0.992452	−	0.122634i	$-0.0391340\pi$
$368$		−	6.61248i		−	0.344699i
$369$		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
$377$		−	9.91531i		−	0.510665i
$378$		0			0
$379$	−15.4980	−	15.4980i	−0.796077	−	0.796077i	0.186398	−	0.982474i	$-0.440319\pi$
$379$	−15.4980	−	15.4980i	−0.796077	−	0.796077i	−0.982474	+	0.186398i	$0.940319\pi$
$380$	0.0937741	+	2.83198i	0.00481051	+	0.145278i
$381$		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
$385$	4.15680	+	3.89034i	0.211850	+	0.198270i
$386$	6.38551	+	6.38551i	0.325014	+	0.325014i
$387$		0			0
$388$			14.9887i			0.760938i
$389$		−	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
$397$			14.1213i			0.708726i	0.935108	+	0.354363i	$0.115302\pi$
$397$			14.1213i			0.708726i	−0.935108	+	0.354363i	$0.884698\pi$
$398$			4.96405i			0.248826i
$399$		0			0
$400$	−4.98905	+	0.330763i	−0.249452	+	0.0165381i
$401$	9.27440	−	9.27440i	0.463142	−	0.463142i	−0.436542	−	0.899684i	$-0.643797\pi$
$401$	9.27440	−	9.27440i	0.463142	−	0.463142i	0.899684	+	0.436542i	$0.143797\pi$
$402$		0			0
$403$		−	11.5559i		−	0.575641i
$404$	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
$413$	−2.75196			−0.135415
$414$		0			0
$415$	−5.74857	+	6.14231i	−0.282186	+	0.301514i
$416$	−2.76103			−0.135370
$417$		0			0
$418$	3.37472			0.165063
$419$	−12.0537	−	12.0537i	−0.588863	−	0.588863i	0.348461	−	0.937323i	$-0.386704\pi$
$419$	−12.0537	−	12.0537i	−0.588863	−	0.588863i	−0.937323	+	0.348461i	$0.886704\pi$
$420$		0			0
$421$	26.9876			1.31530			0.657648	−	0.753326i	$-0.271552\pi$
$421$	26.9876			1.31530			0.657648	+	0.753326i	$0.271552\pi$
$422$		−	16.0018i		−	0.778953i
$423$		0			0
$424$			10.7100i			0.520124i
$425$	−2.88054	+	20.4133i	−0.139727	+	0.990190i
$426$		0			0
$427$	−4.92505	+	4.92505i	−0.238340	+	0.238340i
$428$	−4.49366			−0.217209
$429$		0			0
$430$	0.152465	+	4.60445i	0.00735251	+	0.222046i
$431$	2.88276	−	2.88276i	0.138858	−	0.138858i	−0.634261	−	0.773119i	$-0.718696\pi$
$431$	2.88276	−	2.88276i	0.138858	−	0.138858i	0.773119	+	0.634261i	$0.218696\pi$
$432$		0			0
$433$	−0.359052	−	0.359052i	−0.0172549	−	0.0172549i	0.698427	−	0.715682i	$-0.253884\pi$
$433$	−0.359052	−	0.359052i	−0.0172549	−	0.0172549i	−0.715682	+	0.698427i	$0.753884\pi$
$434$		−	4.00147i		−	0.192077i
$435$		0			0
$436$	1.54296	+	1.54296i	0.0738944	+	0.0738944i
$437$			8.37930i			0.400836i
$438$		0			0
$439$	9.91117	+	9.91117i	0.473034	+	0.473034i	0.902895	−	0.429861i	$-0.141437\pi$
$439$	9.91117	+	9.91117i	0.473034	+	0.473034i	−0.429861	+	0.902895i	$0.641437\pi$
$440$	0.197076	+	5.95171i	0.00939523	+	0.283736i
$441$		0			0
$442$	−2.33286	+	11.1424i	−0.110963	+	0.529991i
$443$	25.7078	+	25.7078i	1.22141	+	1.22141i	0.967130	+	0.254283i	$0.0818393\pi$
$443$	25.7078	+	25.7078i	1.22141	+	1.22141i	0.254283	+	0.967130i	$0.418161\pi$
$444$		0			0
$445$	6.50810	−	0.215500i	0.308513	−	0.0102157i
$446$			27.6408i			1.30883i
$447$		0			0
$448$	−0.956061			−0.0451696
$449$	−17.6634	−	17.6634i	−0.833587	−	0.833587i	0.154419	−	0.988005i	$-0.450649\pi$
$449$	−17.6634	−	17.6634i	−0.833587	−	0.833587i	−0.988005	+	0.154419i	$0.950649\pi$
$450$		0			0
$451$			6.14957i			0.289572i
$452$	−16.3843			−0.770654
$453$		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	−0.559107	−	0.829095i	$-0.688856\pi$
$457$	5.77169	−	5.77169i	0.269988	−	0.269988i	0.829095	+	0.559107i	$0.188856\pi$
$458$	−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
$470$	15.2825	−	0.506041i	0.704927	−	0.0233419i
$471$		0			0
$472$	−2.03536	−	2.03536i	−0.0936851	−	0.0936851i
$473$	5.48688			0.252287
$474$		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	0.268452	−	0.963293i	$-0.413488\pi$
$479$	26.9581	−	26.9581i	1.23174	−	1.23174i	0.963293	−	0.268452i	$-0.0865119\pi$
$480$		0			0
$481$	−14.7150	+	14.7150i	−0.670946	+	0.670946i
$482$	13.8500			0.630849
$483$		0			0
$484$	−3.90767			−0.177621
$485$	33.4975	−	1.10919i	1.52104	−	0.0503656i
$486$		0			0
$487$		−	31.1558i		−	1.41180i	−0.708310	−	0.705902i	$-0.750542\pi$
$487$		−	31.1558i		−	1.41180i	0.708310	−	0.705902i	$-0.249458\pi$
$488$	−7.28518			−0.329785
$489$		0			0
$490$	−9.93592	−	9.29900i	−0.448859	−	0.420086i
$491$	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
$493$	−8.10222	−	12.3933i	−0.364905	−	0.558167i
$494$	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	0.361215	−	0.932482i	$-0.382362\pi$
$499$	28.8990	−	28.8990i	1.29370	−	1.29370i	0.932482	−	0.361215i	$-0.117638\pi$
$500$	1.10840	+	11.1253i	0.0495691	+	0.497537i
$501$		0			0
$502$	−13.5809	+	13.5809i	−0.606146	+	0.606146i
$503$		−	22.7436i		−	1.01409i	−0.861920	−	0.507045i	$-0.830738\pi$
$503$		−	22.7436i		−	1.01409i	0.861920	−	0.507045i	$-0.169262\pi$
$504$		0			0
$505$	−0.272603	−	8.23263i	−0.0121307	−	0.366347i
$506$			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	$-0.622811\pi$
$509$	−16.9804			−0.752644			−0.376322	+	0.926489i	$0.622811\pi$
$510$		0			0
$511$	−4.24205			−0.187657
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			23.3368i			1.02934i
$515$	−26.0990	+	27.8866i	−1.15006	+	1.22883i
$516$		0			0
$517$		−	18.2113i		−	0.800932i
$518$	−5.09536	+	5.09536i	−0.223877	+	0.223877i
$519$		0			0
$520$	0.204320	+	6.17046i	0.00896001	+	0.270593i
$521$	30.8160	−	30.8160i	1.35007	−	1.35007i	0.464498	−	0.885574i	$-0.346235\pi$
$521$	30.8160	−	30.8160i	1.35007	−	1.35007i	0.885574	−	0.464498i	$-0.153765\pi$
$522$		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
$527$	−9.44282	−	14.4439i	−0.411336	−	0.629188i
$528$		0			0
$529$	−20.7249			−0.901082
$530$	23.9352	−	0.792555i	1.03968	−	0.0344264i
$531$		0			0
$532$	1.21152			0.0525259
$533$			6.37559i			0.276158i
$534$		0			0
$535$	0.332537	+	10.0426i	0.0143768	+	0.434180i
$536$	4.03910			0.174463
$537$		0			0
$538$	−4.60412			−0.198498
$539$	−11.4606	+	11.4606i	−0.493643	+	0.493643i
$540$		0			0
$541$	1.72774	−	1.72774i	0.0742812	−	0.0742812i	−0.668990	−	0.743271i	$-0.733273\pi$
$541$	1.72774	−	1.72774i	0.0742812	−	0.0742812i	0.743271	+	0.668990i	$0.233273\pi$
$542$	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
$547$	21.7136			0.928408			0.464204	−	0.885728i	$-0.346341\pi$
$547$	21.7136			0.928408			0.464204	+	0.885728i	$0.346341\pi$
$548$	12.2948	+	12.2948i	0.525207	+	0.525207i
$549$		0			0
$550$	13.2865	−	0.880868i	0.566540	−	0.0375603i
$551$	−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	−0.391150	−	0.920327i	$-0.627923\pi$
$557$	12.4890	−	12.4890i	0.529177	−	0.529177i	0.920327	+	0.391150i	$0.127923\pi$
$558$		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
$568$	4.12349			0.173018
$569$			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	0.209294	−	0.977853i	$-0.432884\pi$
$571$	−18.3652	−	18.3652i	−0.768559	−	0.768559i	−0.977853	+	0.209294i	$0.932884\pi$
$572$	7.35301			0.307445
$573$		0			0
$574$			2.20768i			0.0921466i
$575$	2.18716	+	32.9900i	0.0912109	+	1.37578i
$576$		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	$0.712045\pi$
$578$	6.18905	+	15.8334i	0.257430	+	0.658581i
$579$		0			0
$580$	−5.86294	−	5.48711i	−0.243445	−	0.227840i
$581$	2.54344	+	2.54344i	0.105520	+	0.105520i
$582$		0			0
$583$		−	28.5223i		−	1.18127i
$584$	−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
$590$	−4.39810	+	4.69933i	−0.181067	+	0.193469i
$591$		0			0
$592$	−7.53711			−0.309773
$593$	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
$595$	8.68243	+	1.51979i	0.355945	+	0.0623052i
$596$			14.6670i			0.600782i
$597$		0			0
$598$			18.2572i			0.746594i
$599$	−9.17056			−0.374699			−0.187350	−	0.982293i	$-0.559990\pi$
$599$	−9.17056			−0.374699			−0.187350	+	0.982293i	$0.559990\pi$
$600$		0			0
$601$	5.82720	+	5.82720i	0.237697	+	0.237697i	0.815896	−	0.578199i	$-0.196244\pi$
$601$	5.82720	+	5.82720i	0.237697	+	0.237697i	−0.578199	+	0.815896i	$0.696244\pi$
$602$	1.96977			0.0802819
$603$		0			0
$604$	18.0770			0.735543
$605$	0.289173	+	8.73303i	0.0117565	+	0.355048i
$606$		0			0
$607$	33.8794			1.37512			0.687561	−	0.726127i	$-0.258681\pi$
$607$	33.8794			1.37512			0.687561	+	0.726127i	$0.258681\pi$
$608$	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
$617$			13.8559i			0.557818i	0.960317	+	0.278909i	$0.0899729\pi$
$617$			13.8559i			0.557818i	−0.960317	+	0.278909i	$0.910027\pi$
$618$		0			0
$619$	16.1152	−	16.1152i	0.647726	−	0.647726i	−0.304717	−	0.952443i	$-0.598562\pi$
$619$	16.1152	−	16.1152i	0.647726	−	0.647726i	0.952443	+	0.304717i	$0.0985618\pi$
$620$	−6.83303	−	6.39502i	−0.274421	−	0.256830i
$621$		0			0
$622$			8.40724i			0.337100i
$623$		−	2.78415i		−	0.111545i
$624$		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	$-0.993503\pi$
$631$		−	1.02543i		−	0.0408219i	0.999792	−	0.0204110i	$-0.00649746\pi$
$632$		−	7.29829i		−	0.290310i
$633$		0			0
$634$	4.09713	+	4.09713i	0.162718	+	0.162718i
$635$	4.27357	−	4.56628i	0.169591	−	0.181207i
$636$		0			0
$637$	−11.8818	+	11.8818i	−0.470776	+	0.470776i
$638$	−6.76262	+	6.76262i	−0.267735	+	0.267735i
$639$		0			0
$640$	−1.52795	+	1.63260i	−0.0603974	+	0.0645342i
$641$	−14.6244	−	14.6244i	−0.577629	−	0.577629i	0.356620	−	0.934250i	$-0.383929\pi$
$641$	−14.6244	−	14.6244i	−0.577629	−	0.577629i	−0.934250	+	0.356620i	$0.883929\pi$
$642$		0			0
$643$			14.0281i			0.553214i	0.960983	+	0.276607i	$0.0892101\pi$
$643$			14.0281i			0.553214i	−0.960983	+	0.276607i	$0.910790\pi$
$644$			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	−0.529887	−	0.848068i	$-0.677766\pi$
$647$	8.09332	−	8.09332i	0.318181	−	0.318181i	0.848068	+	0.529887i	$0.177766\pi$
$648$		0			0
$649$	5.42046	+	5.42046i	0.212772	+	0.212772i
$650$	13.7749	−	0.913245i	0.540296	−	0.0358204i
$651$		0			0
$652$		−	7.12731i		−	0.279127i
$653$		−	48.9384i		−	1.91511i	−0.288257	−	0.957553i	$-0.593076\pi$
$653$		−	48.9384i		−	1.91511i	0.288257	−	0.957553i	$-0.406924\pi$
$654$		0			0
$655$	2.84737	+	2.66484i	0.111256	+	0.104124i
$656$	−1.63281	+	1.63281i	−0.0637504	+	0.0637504i
$657$		0			0
$658$		−	6.53780i		−	0.254870i
$659$	−22.5542			−0.878586			−0.439293	−	0.898344i	$-0.644771\pi$
$659$	−22.5542			−0.878586			−0.439293	+	0.898344i	$0.644771\pi$
$660$		0			0
$661$			32.2676i			1.25506i	0.778591	+	0.627531i	$0.215934\pi$
$661$			32.2676i			1.25506i	−0.778591	+	0.627531i	$0.784066\pi$
$662$	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
$668$	−4.05445			−0.156872
$669$		0			0
$670$	−0.298899	−	9.02676i	−0.0115475	−	0.348734i
$671$	19.4015			0.748986
$672$		0			0
$673$	22.2768			0.858709			0.429355	−	0.903136i	$-0.358741\pi$
$673$	22.2768			0.858709			0.429355	+	0.903136i	$0.358741\pi$
$674$	0.555980	+	0.555980i	0.0214156	+	0.0214156i
$675$		0			0
$676$	−5.37673			−0.206797
$677$			7.24062i			0.278280i	0.990273	+	0.139140i	$0.0444337\pi$
$677$			7.24062i			0.278280i	−0.990273	+	0.139140i	$0.955566\pi$
$678$		0			0
$679$		−	14.3301i		−	0.549941i
$680$	5.29753	+	7.54561i	0.203151	+	0.289361i
$681$		0			0
$682$	−7.88158	+	7.88158i	−0.301801	+	0.301801i
$683$	−13.1612			−0.503600			−0.251800	−	0.967779i	$-0.581023\pi$
$683$	−13.1612			−0.503600			−0.251800	+	0.967779i	$0.581023\pi$
$684$		0			0
$685$	26.5671	−	28.3867i	1.01507	−	1.08460i
$686$	−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	0.664266	−	0.747497i	$-0.268744\pi$
$691$	−2.18788	−	2.18788i	−0.0832310	−	0.0832310i	−0.747497	+	0.664266i	$0.768744\pi$
$692$			13.2079i			0.502087i
$693$		0			0
$694$	21.6446	+	21.6446i	0.821616	+	0.821616i
$695$	−13.0062	−	12.1725i	−0.493354	−	0.461728i
$696$		0			0
$697$	5.20976	+	7.96897i	0.197334	+	0.301846i
$698$	8.54947	+	8.54947i	0.323602	+	0.323602i
$699$		0			0
$700$	4.76983	−	0.316229i	0.180283	−	0.0119523i
$701$		−	32.8456i		−	1.24056i	−0.784380	−	0.620280i	$-0.787019\pi$
$701$		−	32.8456i		−	1.24056i	0.784380	−	0.620280i	$-0.212981\pi$
$702$		0			0
$703$	9.55098			0.360222
$704$	1.88313	+	1.88313i	0.0709730	+	0.0709730i
$705$		0			0
$706$		−	8.69569i		−	0.327267i
$707$	−3.52190			−0.132455
$708$		0			0
$709$	35.6948	+	35.6948i	1.34055	+	1.34055i	0.895516	+	0.445030i	$0.146807\pi$
$709$	35.6948	+	35.6948i	1.34055	+	1.34055i	0.445030	+	0.895516i	$0.353193\pi$
$710$	−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	$-0.969335\pi$
$719$	−24.1106	+	24.1106i	−0.899174	+	0.899174i	0.0961892	+	0.995363i	$0.469335\pi$
$720$		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
$725$	−11.8290	+	13.5088i	−0.439317	+	0.501704i
$726$		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	$0.653031\pi$
$728$	2.63971			0.0978341
$729$		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	0.687832	−	0.725870i	$-0.258562\pi$
$733$	−1.02983	−	1.02983i	−0.0380376	−	0.0380376i	−0.725870	+	0.687832i	$0.758562\pi$
$734$	−3.32245	+	3.32245i	−0.122634	+	0.122634i
$735$		0			0
$736$	−4.67573	+	4.67573i	−0.172350	+	0.172350i
$737$	−10.7567			−0.396228
$738$		0			0
$739$	44.1533			1.62421			0.812103	−	0.583514i	$-0.198323\pi$
$739$	44.1533			1.62421			0.812103	+	0.583514i	$0.198323\pi$
$740$	0.557756	+	16.8442i	0.0205035	+	0.619207i
$741$		0			0
$742$		−	10.2394i		−	0.375901i
$743$	−26.6995			−0.979509			−0.489755	−	0.871860i	$-0.662914\pi$
$743$	−26.6995			−0.979509			−0.489755	+	0.871860i	$0.662914\pi$
$744$		0			0
$745$	32.7784	−	1.08537i	1.20091	−	0.0397650i
$746$	−9.61653			−0.352086
$747$		0			0
$748$	9.19065	−	6.00845i	0.336044	−	0.219691i
$749$	4.29621			0.156980
$750$		0			0
$751$	−6.90274	+	6.90274i	−0.251885	+	0.251885i	−0.821743	−	0.569858i	$-0.806998\pi$
$751$	−6.90274	+	6.90274i	−0.251885	+	0.251885i	0.569858	+	0.821743i	$0.306998\pi$
$752$	4.83539	−	4.83539i	0.176328	−	0.176328i
$753$		0			0
$754$	−7.01118	+	7.01118i	−0.255332	+	0.255332i
$755$	−1.33772	−	40.3993i	−0.0486847	−	1.47028i
$756$		0			0
$757$	−1.62241	+	1.62241i	−0.0589675	+	0.0589675i	−0.735976	−	0.677008i	$-0.763276\pi$
$757$	−1.62241	+	1.62241i	−0.0589675	+	0.0589675i	0.677008	+	0.735976i	$0.263276\pi$
$758$			21.9174i			0.796077i
$759$		0			0
$760$	1.93621	−	2.06882i	0.0702336	−	0.0750441i
$761$		−	9.42144i		−	0.341527i	−0.985312	−	0.170764i	$-0.945377\pi$
$761$		−	9.42144i		−	0.341527i	0.985312	−	0.170764i	$-0.0546234\pi$
$762$		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	$0.911706\pi$
$770$	−0.188417	−	5.69019i	−0.00679007	−	0.205060i
$771$		0			0
$772$		−	9.03047i		−	0.325014i
$773$	−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
$775$	−13.7862	+	15.7440i	−0.495215	+	0.565541i
$776$	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
$782$	14.9188	+	22.8200i	0.533493	+	0.816043i
$783$		0			0
$784$	−6.08595			−0.217355
$785$	9.30395	+	8.70754i	0.332072	+	0.310786i
$786$		0			0
$787$	11.5134			0.410408			0.205204	−	0.978719i	$-0.434214\pi$
$787$	11.5134			0.410408			0.205204	+	0.978719i	$0.434214\pi$
$788$			8.00413i			0.285135i
$789$		0			0
$790$	−16.3105	+	0.540083i	−0.580303	+	0.0192153i
$791$	15.6644			0.556962
$792$		0			0
$793$	20.1146			0.714290
$794$	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
$802$	−13.1160			−0.463142
$803$	8.35544	+	8.35544i	0.294857	+	0.294857i
$804$		0			0
$805$	14.1285	−	0.467831i	0.497965	−	0.0164889i
$806$	−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	$-0.0308699\pi$
$809$	25.5552	+	25.5552i	0.898472	+	0.898472i	−0.0968287	+	0.995301i	$0.530870\pi$
$810$		0			0
$811$	−22.9303	+	22.9303i	−0.805190	+	0.805190i	−0.983902	−	0.178711i	$-0.942807\pi$
$811$	−22.9303	+	22.9303i	−0.805190	+	0.805190i	0.178711	+	0.983902i	$0.442807\pi$
$812$	−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	−0.999306	−	0.0372565i	$-0.988138\pi$
$821$	−29.7007	−	29.7007i	−1.03656	−	1.03656i	−0.0372565	−	0.999306i	$-0.511862\pi$
$822$		0			0
$823$	−18.0398			−0.628828			−0.314414	−	0.949286i	$-0.601808\pi$
$823$	−18.0398			−0.628828			−0.314414	+	0.949286i	$0.601808\pi$
$824$			17.0811i			0.595048i
$825$		0			0
$826$	1.94593	+	1.94593i	0.0677075	+	0.0677075i
$827$	17.0469			0.592778			0.296389	−	0.955067i	$-0.404218\pi$
$827$	17.0469			0.592778			0.296389	+	0.955067i	$0.404218\pi$
$828$		0			0
$829$			23.5645i			0.818428i	0.912439	+	0.409214i	$0.134197\pi$
$829$			23.5645i			0.818428i	−0.912439	+	0.409214i	$0.865803\pi$
$830$	8.40812	−	0.278414i	0.291850	−	0.00966390i
$831$		0			0
$832$	1.95234	+	1.95234i	0.0676852	+	0.0676852i
$833$	−5.14217	+	24.5605i	−0.178166	+	0.850970i
$834$		0			0
$835$	0.300035	+	9.06107i	0.0103831	+	0.313571i
$836$	−2.38629	−	2.38629i	−0.0825315	−	0.0825315i
$837$		0			0
$838$			17.0465i			0.588863i
$839$	22.0944	+	22.0944i	0.762782	+	0.762782i	0.976824	−	0.214043i	$-0.0686631\pi$
$839$	22.0944	+	22.0944i	0.762782	+	0.762782i	−0.214043	+	0.976824i	$0.568663\pi$
$840$		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
$845$	0.397885	+	12.0161i	0.0136877	+	0.413368i
$846$		0			0
$847$	3.73597			0.128369
$848$	7.57312	−	7.57312i	0.260062	−	0.260062i
$849$		0			0
$850$	16.4712	−	12.3975i	0.564959	−	0.425232i
$851$			49.8390i			1.70846i
$852$		0			0
$853$			30.9121i			1.05841i	0.848494	+	0.529205i	$0.177510\pi$
$853$			30.9121i			1.05841i	−0.848494	+	0.529205i	$0.822490\pi$
$854$	6.96507			0.238340
$855$		0			0
$856$	3.17750	+	3.17750i	0.108605	+	0.108605i
$857$	40.8719			1.39616			0.698079	−	0.716021i	$-0.254039\pi$
$857$	40.8719			1.39616			0.698079	+	0.716021i	$0.254039\pi$
$858$		0			0
$859$	6.70638			0.228819			0.114409	−	0.993434i	$-0.463502\pi$
$859$	6.70638			0.228819			0.114409	+	0.993434i	$0.463502\pi$
$860$	3.14803	−	3.36365i	0.107347	−	0.114699i
$861$		0			0
$862$	−4.07684			−0.138858
$863$	15.6237	+	15.6237i	0.531838	+	0.531838i	0.921119	−	0.389281i	$-0.127276\pi$
$863$	15.6237	+	15.6237i	0.531838	+	0.531838i	−0.389281	+	0.921119i	$0.627276\pi$
$864$		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
$872$		−	2.18207i		−	0.0738944i
$873$		0			0
$874$	5.92506	−	5.92506i	0.200418	−	0.200418i
$875$	−1.05970	−	10.6364i	−0.0358243	−	0.359577i
$876$		0			0
$877$			41.5253i			1.40221i	0.713058	+	0.701105i	$0.247309\pi$
$877$			41.5253i			1.40221i	−0.713058	+	0.701105i	$0.752691\pi$
$878$		−	14.0165i		−	0.473034i
$879$		0			0
$880$	4.06914	−	4.34785i	0.137171	−	0.146566i
$881$	15.5873	+	15.5873i	0.525149	+	0.525149i	0.919122	−	0.393973i	$-0.128900\pi$
$881$	15.5873	+	15.5873i	0.525149	+	0.525149i	−0.393973	+	0.919122i	$0.628900\pi$
$882$		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
$887$		−	2.15059i		−	0.0722097i	−0.999348	−	0.0361049i	$-0.988505\pi$
$887$		−	2.15059i		−	0.0722097i	0.999348	−	0.0361049i	$-0.0114950\pi$
$888$		0			0
$889$	−1.89083	−	1.89083i	−0.0634165	−	0.0634165i
$890$	−4.75430	−	4.44954i	−0.159364	−	0.149149i
$891$		0			0
$892$	19.5450	−	19.5450i	0.654416	−	0.654416i
$893$	−6.12738	+	6.12738i	−0.205045	+	0.205045i
$894$		0			0
$895$	−1.28868	−	38.9181i	−0.0430757	−	1.30089i
$896$	0.676037	+	0.676037i	0.0225848	+	0.0225848i
$897$		0			0
$898$			24.9798i			0.833587i
$899$		−	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
$907$		−	19.0637i		−	0.632999i	−0.948593	−	0.316500i	$-0.897492\pi$
$907$		−	19.0637i		−	0.632999i	0.948593	−	0.316500i	$-0.102508\pi$
$908$		−	25.5978i		−	0.849491i
$909$		0			0
$910$	−0.195342	−	5.89934i	−0.00647552	−	0.195561i
$911$	−22.4893	+	22.4893i	−0.745104	+	0.745104i	−0.973555	−	0.228451i	$-0.926634\pi$
$911$	−22.4893	+	22.4893i	−0.745104	+	0.745104i	0.228451	+	0.973555i	$0.426634\pi$
$912$		0			0
$913$		−	10.0195i		−	0.331597i
$914$	−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
$923$	−11.3851			−0.374744
$924$		0			0
$925$	37.6030	−	2.49299i	1.23638	−	0.0819691i
$926$	41.1930			1.35369
$927$		0			0
$928$	−3.59117			−0.117886
$929$	−20.9340	−	20.9340i	−0.686821	−	0.686821i	0.274707	−	0.961528i	$-0.411419\pi$
$929$	−20.9340	−	20.9340i	−0.686821	−	0.686821i	−0.961528	+	0.274707i	$0.911419\pi$
$930$		0			0
$931$	7.71208			0.252753
$932$		−	19.5475i		−	0.640298i
$933$		0			0
$934$			7.53584i			0.246580i
$935$	−14.1081	−	20.0950i	−0.461383	−	0.657178i
$936$		0			0
$937$	11.9941	−	11.9941i	0.391830	−	0.391830i	−0.483509	−	0.875339i	$-0.660638\pi$
$937$	11.9941	−	11.9941i	0.391830	−	0.391830i	0.875339	+	0.483509i	$0.160638\pi$
$938$	−3.86163			−0.126087
$939$		0			0
$940$	−11.1642	−	10.4485i	−0.364135	−	0.340793i
$941$	25.9135	−	25.9135i	0.844755	−	0.844755i	−0.144718	−	0.989473i	$-0.546227\pi$
$941$	25.9135	−	25.9135i	0.844755	−	0.844755i	0.989473	+	0.144718i	$0.0462274\pi$
$942$		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
$947$			22.2402i			0.722709i	0.932428	+	0.361355i	$0.117686\pi$
$947$			22.2402i			0.722709i	−0.932428	+	0.361355i	$0.882314\pi$
$948$		0			0
$949$	8.66255	+	8.66255i	0.281198	+	0.281198i
$950$	−4.76677	−	4.17402i	−0.154655	−	0.135423i
$951$		0			0
$952$	3.29942	−	2.15702i	0.106935	−	0.0699093i
$953$	5.72875	+	5.72875i	0.185572	+	0.185572i	0.793779	−	0.608207i	$-0.208111\pi$
$953$	5.72875	+	5.72875i	0.185572	+	0.185572i	−0.608207	+	0.793779i	$0.708111\pi$
$954$		0			0
$955$	1.97718	+	59.7108i	0.0639799	+	1.93220i
$956$			25.0580i			0.810433i
$957$		0			0
$958$	−38.1244			−1.23174
$959$	−11.7545	−	11.7545i	−0.379574	−	0.379574i
$960$		0			0
$961$			13.4827i			0.434926i
$962$	20.8102			0.670946
$963$		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	−0.703417	−	0.710778i	$-0.748343\pi$
$967$	0.228906	−	0.228906i	0.00736112	−	0.00736112i	0.710778	+	0.703417i	$0.248343\pi$
$968$	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
$980$	0.450368	+	13.6011i	0.0143865	+	0.434472i
$981$		0			0
$982$	−5.15032	−	5.15032i	−0.164353	−	0.164353i
$983$	58.2275			1.85717			0.928584	−	0.371123i	$-0.121027\pi$
$983$	58.2275			1.85717			0.928584	+	0.371123i	$0.121027\pi$
$984$		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	−0.499199	−	0.866487i	$-0.666372\pi$
$991$	11.5623	−	11.5623i	0.367288	−	0.367288i	0.866487	+	0.499199i	$0.166372\pi$
$992$	−4.18537			−0.132886
$993$		0			0
$994$	−3.94231			−0.125042
$995$	−8.10431	−	7.58481i	−0.256924	−	0.240455i
$996$		0			0
$997$		−	55.7008i		−	1.76406i	−0.471190	−	0.882032i	$-0.656175\pi$
$997$		−	55.7008i		−	1.76406i	0.471190	−	0.882032i	$-0.343825\pi$
$998$	−40.8694			−1.29370
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.j.c.863.9	✓	40	255.98	even	4	inner
1530.2.j.c.863.14	yes	40	85.13	odd	4	inner
1530.2.j.c.1007.9	yes	40	1.1	even	1	trivial
1530.2.j.c.1007.14	yes	40	3.2	odd	2	inner
1530.2.u.c.557.9	yes	40	51.47	odd	4
1530.2.u.c.557.14	yes	40	17.13	even	4
1530.2.u.c.1313.9	yes	40	5.3	odd	4
1530.2.u.c.1313.14	yes	40	15.8	even	4

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.23484 - 0.0740013i) q^{5} -0.956061i q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.63260 - 1.52795i) q^{10} +(-1.88313 + 1.88313i) q^{11} +(-1.95234 + 1.95234i) q^{13} +(-0.676037 + 0.676037i) q^{14} -1.00000 q^{16} +(-0.844925 + 4.03560i) q^{17} +1.26720 q^{19} +(0.0740013 + 2.23484i) q^{20} +2.66314 q^{22} +6.61248i q^{23} +(4.98905 - 0.330763i) q^{25} +2.76103 q^{26} +0.956061 q^{28} +(-2.53934 + 2.53934i) q^{29} +(-2.95950 + 2.95950i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.45106 - 2.25615i) q^{34} +(-0.0707497 - 2.13665i) q^{35} +7.53711 q^{37} +(-0.896042 - 0.896042i) q^{38} +(1.52795 - 1.63260i) q^{40} +(1.63281 - 1.63281i) q^{41} +(-1.45685 - 1.45685i) q^{43} +(-1.88313 - 1.88313i) q^{44} +(4.67573 - 4.67573i) q^{46} +(-4.83539 + 4.83539i) q^{47} +6.08595 q^{49} +(-3.76167 - 3.29390i) q^{50} +(-1.95234 - 1.95234i) q^{52} +(-7.57312 + 7.57312i) q^{53} +(-4.06914 + 4.34785i) q^{55} +(-0.676037 - 0.676037i) q^{56} +3.59117 q^{58} -2.87844i q^{59} +(-5.15140 - 5.15140i) q^{61} +4.18537 q^{62} -1.00000i q^{64} +(-4.21870 + 4.50765i) q^{65} +(2.85608 + 2.85608i) q^{67} +(-4.03560 - 0.844925i) q^{68} +(-1.46081 + 1.56086i) q^{70} +(2.91575 + 2.91575i) q^{71} -4.43701i q^{73} +(-5.32954 - 5.32954i) q^{74} +1.26720i q^{76} +(1.80038 + 1.80038i) q^{77} +(5.16067 - 5.16067i) q^{79} +(-2.23484 + 0.0740013i) q^{80} -2.30914 q^{82} +(-2.66034 + 2.66034i) q^{83} +(-1.58964 + 9.08147i) q^{85} +2.06030i q^{86} +2.66314i q^{88} +2.91210 q^{89} +(1.86656 + 1.86656i) q^{91} -6.61248 q^{92} +6.83827 q^{94} +(2.83198 - 0.0937741i) q^{95} +14.9887 q^{97} +(-4.30342 - 4.30342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{13} - 40 q^{16} - 16 q^{19} - 16 q^{22} - 8 q^{31} + 16 q^{37} - 8 q^{40} - 32 q^{43} - 56 q^{49} + 8 q^{52} + 32 q^{55} - 32 q^{58} - 64 q^{61} + 32 q^{67} - 32 q^{70} - 88 q^{79} + 32 q^{85}+ \cdots - 64 q^{97}+O(q^{100}) \) 40 * q + 8 * q^13 - 40 * q^16 - 16 * q^19 - 16 * q^22 - 8 * q^31 + 16 * q^37 - 8 * q^40 - 32 * q^43 - 56 * q^49 + 8 * q^52 + 32 * q^55 - 32 * q^58 - 64 * q^61 + 32 * q^67 - 32 * q^70 - 88 * q^79 + 32 * q^85 + 56 * q^91 + 16 * q^94 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more