LMFDB - Embedded newform 546.2.bv.a.515.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.11
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.398691 - 1.68554i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.89818 - 0.508616i) q^{5} +(-0.821356 + 1.52492i) q^{6} +(1.71379 - 2.01567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68209 - 1.34402i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.398691 - 1.68554i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.89818 - 0.508616i) q^{5} +(-0.821356 + 1.52492i) q^{6} +(1.71379 - 2.01567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68209 - 1.34402i) q^{9} +(1.70186 + 0.982571i) q^{10} +(2.87835 - 0.771252i) q^{11} +(1.18805 - 1.26037i) q^{12} +(-3.35607 - 1.31786i) q^{13} +(-2.17709 + 1.50343i) q^{14} +(-1.61408 + 2.99668i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.01939 - 1.76563i) q^{17} +(2.24284 + 1.99240i) q^{18} +(-1.12940 + 4.21497i) q^{19} +(-1.38957 - 1.38957i) q^{20} +(-2.71422 - 3.69229i) q^{21} -2.97989 q^{22} +(-1.60906 - 2.78697i) q^{23} +(-1.47377 + 0.909940i) q^{24} +(-0.985722 - 0.569107i) q^{25} +(2.90063 + 2.14157i) q^{26} +(-3.33472 + 3.98492i) q^{27} +(2.49202 - 0.888729i) q^{28} -6.15008i q^{29} +(2.33468 - 2.47682i) q^{30} +(-2.95519 + 0.791840i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.152403 - 5.15907i) q^{33} +(-1.44163 + 1.44163i) q^{34} +(-4.27828 + 2.95445i) q^{35} +(-1.65075 - 2.50500i) q^{36} +(3.92765 + 1.05241i) q^{37} +(2.18183 - 3.77904i) q^{38} +(-3.55935 + 5.13138i) q^{39} +(0.982571 + 1.70186i) q^{40} +(-7.22551 + 7.22551i) q^{41} +(1.66610 + 4.26897i) q^{42} +1.92779i q^{43} +(2.87835 + 0.771252i) q^{44} +(4.40751 + 3.91535i) q^{45} +(0.832911 + 3.10846i) q^{46} +(0.203159 - 0.758199i) q^{47} +(1.65907 - 0.497493i) q^{48} +(-1.12586 - 6.90887i) q^{49} +(0.804839 + 0.804839i) q^{50} +(-2.56962 - 2.42216i) q^{51} +(-2.24751 - 2.81934i) q^{52} +(-3.77663 - 2.18044i) q^{53} +(4.25247 - 2.98605i) q^{54} -5.85591 q^{55} +(-2.63713 + 0.213464i) q^{56} +(6.65422 + 3.58412i) q^{57} +(-1.59176 + 5.94052i) q^{58} +(-2.58491 + 0.692626i) q^{59} +(-2.89618 + 1.78816i) q^{60} +(2.72566 + 4.72098i) q^{61} +3.05944 q^{62} +(-7.30564 + 3.10285i) q^{63} +1.00000i q^{64} +(5.70016 + 4.20850i) q^{65} +(-1.18806 + 5.02272i) q^{66} +(-0.655866 + 0.175739i) q^{67} +(1.76563 - 1.01939i) q^{68} +(-5.33907 + 1.60099i) q^{69} +(4.89717 - 1.74648i) q^{70} +(7.64671 - 7.64671i) q^{71} +(0.946159 + 2.84689i) q^{72} +(-3.05864 - 11.4150i) q^{73} +(-3.52144 - 2.03310i) q^{74} +(-1.35225 + 1.43458i) q^{75} +(-3.08557 + 3.08557i) q^{76} +(3.37829 - 7.12357i) q^{77} +(4.76616 - 4.03530i) q^{78} +(-4.89586 - 8.47987i) q^{79} +(-0.508616 - 1.89818i) q^{80} +(5.38722 + 7.20957i) q^{81} +(8.84941 - 5.10921i) q^{82} +(4.83395 - 4.83395i) q^{83} +(-0.504442 - 4.55473i) q^{84} +(-2.83301 + 2.83301i) q^{85} +(0.498949 - 1.86210i) q^{86} +(-10.3662 - 2.45198i) q^{87} +(-2.58066 - 1.48994i) q^{88} +(-3.24426 + 12.1077i) q^{89} +(-3.24396 - 4.92268i) q^{90} +(-8.40798 + 4.50621i) q^{91} -3.21812i q^{92} +(0.156471 + 5.29679i) q^{93} +(-0.392473 + 0.679782i) q^{94} +(4.28760 - 7.42635i) q^{95} +(-1.73130 + 0.0511439i) q^{96} +(7.26398 + 7.26398i) q^{97} +(-0.700646 + 6.96485i) q^{98} +(-8.75658 - 1.79999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.398691	−	1.68554i	0.230184	−	0.973147i
$3$	0.398691	−	1.68554i	0.230184	−	0.973147i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.89818	−	0.508616i	−0.848893	−	0.227460i	−0.191954	−	0.981404i	$-0.561482\pi$
$5$	−1.89818	−	0.508616i	−0.848893	−	0.227460i	−0.656939	+	0.753944i	$0.728149\pi$
$6$	−0.821356	+	1.52492i	−0.335317	+	0.622545i
$7$	1.71379	−	2.01567i	0.647751	−	0.761852i
$7$	1.71379	−	2.01567i	0.647751	−	0.761852i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.68209	−	1.34402i	−0.894030	−	0.448007i
$10$	1.70186	+	0.982571i	0.538177	+	0.310716i
$11$	2.87835	−	0.771252i	0.867856	−	0.232541i	0.202695	−	0.979242i	$-0.435030\pi$
$11$	2.87835	−	0.771252i	0.867856	−	0.232541i	0.665160	+	0.746701i	$0.268363\pi$
$12$	1.18805	−	1.26037i	0.342960	−	0.363839i
$13$	−3.35607	−	1.31786i	−0.930808	−	0.365509i
$13$	−3.35607	−	1.31786i	−0.930808	−	0.365509i
$14$	−2.17709	+	1.50343i	−0.581851	+	0.401808i
$15$	−1.61408	+	2.99668i	−0.416754	+	0.773740i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.01939	−	1.76563i	0.247238	−	0.428229i	−0.715520	−	0.698592i	$-0.753810\pi$
$17$	1.01939	−	1.76563i	0.247238	−	0.428229i	0.962758	+	0.270363i	$0.0871437\pi$
$18$	2.24284	+	1.99240i	0.528643	+	0.469613i
$19$	−1.12940	+	4.21497i	−0.259102	+	0.966980i	0.706661	+	0.707552i	$0.250201\pi$
$19$	−1.12940	+	4.21497i	−0.259102	+	0.966980i	−0.965762	+	0.259428i	$0.916466\pi$
$20$	−1.38957	−	1.38957i	−0.310716	−	0.310716i
$21$	−2.71422	−	3.69229i	−0.592292	−	0.805723i
$22$	−2.97989			−0.635314
$23$	−1.60906	−	2.78697i	−0.335512	−	0.581124i	0.648071	−	0.761580i	$-0.275576\pi$
$23$	−1.60906	−	2.78697i	−0.335512	−	0.581124i	−0.983583	+	0.180456i	$0.942243\pi$
$24$	−1.47377	+	0.909940i	−0.300833	+	0.185741i
$25$	−0.985722	−	0.569107i	−0.197144	−	0.113821i
$26$	2.90063	+	2.14157i	0.568861	+	0.419997i
$27$	−3.33472	+	3.98492i	−0.641768	+	0.766899i
$28$	2.49202	−	0.888729i	0.470947	−	0.167954i
$29$		−	6.15008i		−	1.14204i	−0.820935	−	0.571021i	$-0.806548\pi$
$29$		−	6.15008i		−	1.14204i	0.820935	−	0.571021i	$-0.193452\pi$
$30$	2.33468	−	2.47682i	0.426253	−	0.452203i
$31$	−2.95519	+	0.791840i	−0.530767	+	0.142219i	−0.514243	−	0.857645i	$-0.671927\pi$
$31$	−2.95519	+	0.791840i	−0.530767	+	0.142219i	−0.0165248	+	0.999863i	$0.505260\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.152403	−	5.15907i	−0.0265300	−	0.898078i
$34$	−1.44163	+	1.44163i	−0.247238	+	0.247238i
$35$	−4.27828	+	2.95445i	−0.723162	+	0.499393i
$36$	−1.65075	−	2.50500i	−0.275125	−	0.417500i
$37$	3.92765	+	1.05241i	0.645702	+	0.173015i	0.566785	−	0.823866i	$-0.308187\pi$
$37$	3.92765	+	1.05241i	0.645702	+	0.173015i	0.0789171	+	0.996881i	$0.474854\pi$
$38$	2.18183	−	3.77904i	0.353939	−	0.613041i
$39$	−3.55935	+	5.13138i	−0.569952	+	0.821678i
$40$	0.982571	+	1.70186i	0.155358	+	0.269088i
$41$	−7.22551	+	7.22551i	−1.12844	+	1.12844i	−0.138004	+	0.990432i	$0.544069\pi$
$41$	−7.22551	+	7.22551i	−1.12844	+	1.12844i	−0.990432	+	0.138004i	$0.955931\pi$
$42$	1.66610	+	4.26897i	0.257085	+	0.658716i
$43$			1.92779i			0.293985i	0.989138	+	0.146993i	$0.0469594\pi$
$43$			1.92779i			0.293985i	−0.989138	+	0.146993i	$0.953041\pi$
$44$	2.87835	+	0.771252i	0.433928	+	0.116271i
$45$	4.40751	+	3.91535i	0.657032	+	0.583666i
$46$	0.832911	+	3.10846i	0.122806	+	0.458318i
$47$	0.203159	−	0.758199i	0.0296338	−	0.110595i	−0.949525	−	0.313692i	$-0.898434\pi$
$47$	0.203159	−	0.758199i	0.0296338	−	0.110595i	0.979159	+	0.203097i	$0.0651008\pi$
$48$	1.65907	−	0.497493i	0.239466	−	0.0718070i
$49$	−1.12586	−	6.90887i	−0.160838	−	0.986981i
$50$	0.804839	+	0.804839i	0.113821	+	0.113821i
$51$	−2.56962	−	2.42216i	−0.359819	−	0.339170i
$52$	−2.24751	−	2.81934i	−0.311674	−	0.390972i
$53$	−3.77663	−	2.18044i	−0.518759	−	0.299506i	0.217667	−	0.976023i	$-0.430155\pi$
$53$	−3.77663	−	2.18044i	−0.518759	−	0.299506i	−0.736427	+	0.676517i	$0.763488\pi$
$54$	4.25247	−	2.98605i	0.578688	−	0.406350i
$55$	−5.85591			−0.789610
$56$	−2.63713	+	0.213464i	−0.352401	+	0.0285253i
$57$	6.65422	+	3.58412i	0.881373	+	0.474728i
$58$	−1.59176	+	5.94052i	−0.209008	+	0.780029i
$59$	−2.58491	+	0.692626i	−0.336527	+	0.0901722i	−0.423125	−	0.906071i	$-0.639067\pi$
$59$	−2.58491	+	0.692626i	−0.336527	+	0.0901722i	0.0865982	+	0.996243i	$0.472400\pi$
$60$	−2.89618	+	1.78816i	−0.373895	+	0.230851i
$61$	2.72566	+	4.72098i	0.348985	+	0.604459i	0.986069	−	0.166335i	$-0.0531932\pi$
$61$	2.72566	+	4.72098i	0.348985	+	0.604459i	−0.637085	+	0.770794i	$0.719860\pi$
$62$	3.05944			0.388549
$63$	−7.30564	+	3.10285i	−0.920424	+	0.390922i
$64$			1.00000i			0.125000i
$65$	5.70016	+	4.20850i	0.707017	+	0.522000i
$66$	−1.18806	+	5.02272i	−0.146239	+	0.618254i
$67$	−0.655866	+	0.175739i	−0.0801268	+	0.0214699i	−0.298660	−	0.954360i	$-0.596540\pi$
$67$	−0.655866	+	0.175739i	−0.0801268	+	0.0214699i	0.218533	+	0.975830i	$0.429873\pi$
$68$	1.76563	−	1.01939i	0.214114	−	0.123619i
$69$	−5.33907	+	1.60099i	−0.642749	+	0.192737i
$70$	4.89717	−	1.74648i	0.585324	−	0.208744i
$71$	7.64671	−	7.64671i	0.907497	−	0.907497i	−0.0885725	−	0.996070i	$-0.528231\pi$
$71$	7.64671	−	7.64671i	0.907497	−	0.907497i	0.996070	+	0.0885725i	$0.0282305\pi$
$72$	0.946159	+	2.84689i	0.111506	+	0.335509i
$73$	−3.05864	−	11.4150i	−0.357986	−	1.33602i	−0.876685	−	0.481066i	$-0.840250\pi$
$73$	−3.05864	−	11.4150i	−0.357986	−	1.33602i	0.518698	−	0.854957i	$-0.326417\pi$
$74$	−3.52144	−	2.03310i	−0.409359	−	0.236343i
$75$	−1.35225	+	1.43458i	−0.156144	+	0.165651i
$76$	−3.08557	+	3.08557i	−0.353939	+	0.353939i
$77$	3.37829	−	7.12357i	0.384992	−	0.811806i
$78$	4.76616	−	4.03530i	0.539662	−	0.456908i
$79$	−4.89586	−	8.47987i	−0.550827	−	0.954060i	−0.998215	−	0.0597205i	$-0.980979\pi$
$79$	−4.89586	−	8.47987i	−0.550827	−	0.954060i	0.447388	−	0.894340i	$-0.352354\pi$
$80$	−0.508616	−	1.89818i	−0.0568650	−	0.212223i
$81$	5.38722	+	7.20957i	0.598580	+	0.801063i
$82$	8.84941	−	5.10921i	0.977254	−	0.564218i
$83$	4.83395	−	4.83395i	0.530595	−	0.530595i	−0.390154	−	0.920749i	$-0.627578\pi$
$83$	4.83395	−	4.83395i	0.530595	−	0.530595i	0.920749	+	0.390154i	$0.127578\pi$
$84$	−0.504442	−	4.55473i	−0.0550392	−	0.496961i
$85$	−2.83301	+	2.83301i	−0.307284	+	0.307284i
$86$	0.498949	−	1.86210i	0.0538030	−	0.200796i
$87$	−10.3662	−	2.45198i	−1.11137	−	0.262880i
$88$	−2.58066	−	1.48994i	−0.275099	−	0.158829i
$89$	−3.24426	+	12.1077i	−0.343890	+	1.28342i	0.550013	+	0.835156i	$0.314623\pi$
$89$	−3.24426	+	12.1077i	−0.343890	+	1.28342i	−0.893903	+	0.448260i	$0.852044\pi$
$90$	−3.24396	−	4.92268i	−0.341943	−	0.518896i
$91$	−8.40798	+	4.50621i	−0.881396	+	0.472379i
$92$		−	3.21812i		−	0.335512i
$93$	0.156471	+	5.29679i	0.0162253	+	0.549251i
$94$	−0.392473	+	0.679782i	−0.0404805	+	0.0701142i
$95$	4.28760	−	7.42635i	0.439899	−	0.761927i
$96$	−1.73130	+	0.0511439i	−0.176700	+	0.00521985i
$97$	7.26398	+	7.26398i	0.737546	+	0.737546i	0.972102	−	0.234557i	$-0.0753639\pi$
$97$	7.26398	+	7.26398i	0.737546	+	0.737546i	−0.234557	+	0.972102i	$0.575364\pi$
$98$	−0.700646	+	6.96485i	−0.0707759	+	0.703556i
$99$	−8.75658	−	1.79999i	−0.880069	−	0.180906i
$100$	−0.569107	−	0.985722i	−0.0569107	−	0.0985722i
$101$	2.37895	−	4.12046i	0.236714	−	0.410001i	−0.723055	−	0.690790i	$-0.757263\pi$
$101$	2.37895	−	4.12046i	0.236714	−	0.410001i	0.959769	+	0.280789i	$0.0905962\pi$
$102$	1.85516	+	3.00470i	0.183689	+	0.297509i
$103$	9.00320	−	5.19800i	0.887112	−	0.512174i	0.0141153	−	0.999900i	$-0.495507\pi$
$103$	9.00320	−	5.19800i	0.887112	−	0.512174i	0.872997	+	0.487726i	$0.162173\pi$
$104$	1.44123	+	3.30497i	0.141325	+	0.324079i
$105$	3.27413	+	8.38913i	0.319523	+	0.818696i
$106$	3.08360	+	3.08360i	0.299506	+	0.299506i
$107$	12.8840	−	7.43856i	1.24554	−	0.719113i	0.275324	−	0.961352i	$-0.411215\pi$
$107$	12.8840	−	7.43856i	1.24554	−	0.719113i	0.970217	+	0.242238i	$0.0778816\pi$
$108$	−4.88042	+	1.78368i	−0.469618	+	0.171635i
$109$	10.5021	−	2.81402i	1.00592	−	0.269535i	0.281995	−	0.959416i	$-0.409004\pi$
$109$	10.5021	−	2.81402i	1.00592	−	0.269535i	0.723922	+	0.689881i	$0.242337\pi$
$110$	5.65637	+	1.51562i	0.539314	+	0.144509i
$111$	3.33980	−	6.20063i	0.317000	−	0.588538i
$112$	2.60252	+	0.476348i	0.245915	+	0.0450106i
$113$		−	16.1384i		−	1.51817i	−0.650991	−	0.759085i	$-0.725647\pi$
$113$		−	16.1384i		−	1.51817i	0.650991	−	0.759085i	$-0.274353\pi$
$114$	−5.49984	−	5.18423i	−0.515108	−	0.485547i
$115$	1.63679	+	6.10858i	0.152631	+	0.569628i
$116$	3.07504	−	5.32613i	0.285510	−	0.494519i
$117$	7.23006	+	8.04526i	0.668420	+	0.743784i
$118$	2.67610			0.246355
$119$	−1.81192	−	5.08067i	−0.166098	−	0.465744i
$120$	3.26030	−	0.977646i	0.297623	−	0.0892464i
$121$	−1.83620	+	1.06013i	−0.166928	+	0.0963756i
$122$	−1.41090	−	5.26556i	−0.127737	−	0.476722i
$123$	9.29815	+	15.0596i	0.838386	+	1.35788i
$124$	−2.95519	−	0.791840i	−0.265384	−	0.0711094i
$125$	8.52945	+	8.52945i	0.762897	+	0.762897i
$126$	7.85978	−	1.10628i	0.700205	−	0.0985557i
$127$		−	7.54690i		−	0.669679i	−0.942275	−	0.334840i	$-0.891318\pi$
$127$		−	7.54690i		−	0.669679i	0.942275	−	0.334840i	$-0.108682\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	3.24937	+	0.768593i	0.286091	+	0.0676708i
$130$	−4.41669	−	5.54041i	−0.387369	−	0.485926i
$131$	0.524403	−	0.302764i	0.0458173	−	0.0264526i	−0.476916	−	0.878949i	$-0.658246\pi$
$131$	0.524403	−	0.302764i	0.0458173	−	0.0264526i	0.522734	+	0.852496i	$0.324912\pi$
$132$	2.44755	−	4.54409i	0.213032	−	0.395512i
$133$	6.56045	+	9.50006i	0.568863	+	0.823759i
$134$	0.679003			0.0586569
$135$	8.35671	−	5.86801i	0.719231	−	0.505038i
$136$	−1.96931	+	0.527674i	−0.168867	+	0.0452477i
$137$	4.50842	−	1.20803i	0.385181	−	0.103209i	−0.0610320	−	0.998136i	$-0.519439\pi$
$137$	4.50842	−	1.20803i	0.385181	−	0.103209i	0.446213	+	0.894927i	$0.352772\pi$
$138$	5.57152	−	0.164587i	0.474279	−	0.0140106i
$139$	1.20568			0.102265			0.0511323	−	0.998692i	$-0.483717\pi$
$139$	1.20568			0.102265			0.0511323	+	0.998692i	$0.483717\pi$
$140$	−5.18233	+	0.419487i	−0.437987	+	0.0354532i
$141$	−1.19698	−	0.644719i	−0.100804	−	0.0542952i
$142$	−9.36527	+	5.40704i	−0.785916	+	0.453749i
$143$	−10.6764	−	1.20489i	−0.892803	−	0.100758i
$144$	−0.177090	−	2.99477i	−0.0147575	−	0.249564i
$145$	−3.12803	+	11.6740i	−0.259769	+	0.969471i
$146$			11.8177i			0.978037i
$147$	−12.0940	−	0.856815i	−0.997500	−	0.0706689i
$148$	2.87524	+	2.87524i	0.236343	+	0.236343i
$149$	19.1684	+	5.13616i	1.57034	+	0.420771i	0.935918	−	0.352218i	$-0.114572\pi$
$149$	19.1684	+	5.13616i	1.57034	+	0.420771i	0.634420	+	0.772988i	$0.281239\pi$
$150$	1.67747	−	1.03571i	0.136965	−	0.0845650i
$151$	−1.85076	−	6.90714i	−0.150613	−	0.562095i	−0.999441	−	0.0334265i	$-0.989358\pi$
$151$	−1.85076	−	6.90714i	−0.150613	−	0.562095i	0.848828	−	0.528669i	$-0.177309\pi$
$152$	3.77904	−	2.18183i	0.306520	−	0.176970i
$153$	−5.10714	+	3.36551i	−0.412888	+	0.272085i
$154$	−5.10690	+	6.00648i	−0.411525	+	0.484016i
$155$	6.01223			0.482914
$156$	−5.64817	+	2.66423i	−0.452216	+	0.213309i
$157$	9.36594	−	16.2223i	0.747484	−	1.29468i	−0.201542	−	0.979480i	$-0.564595\pi$
$157$	9.36594	−	16.2223i	0.747484	−	1.29468i	0.949025	−	0.315200i	$-0.102072\pi$
$158$	2.53428	+	9.45807i	0.201617	+	0.752444i
$159$	−5.18092	+	5.49633i	−0.410874	+	0.435888i
$160$			1.96514i			0.155358i
$161$	−8.37521	−	1.53294i	−0.660059	−	0.120813i
$162$	−3.33768	−	8.35822i	−0.262233	−	0.656684i
$163$	4.61017	+	1.23529i	0.361096	+	0.0967554i	0.434806	−	0.900524i	$-0.356817\pi$
$163$	4.61017	+	1.23529i	0.361096	+	0.0967554i	−0.0737095	+	0.997280i	$0.523484\pi$
$164$	−9.87024	+	2.64472i	−0.770736	+	0.206518i
$165$	−2.33470	+	9.87037i	−0.181756	+	0.768407i
$166$	−5.92036	+	3.41812i	−0.459509	+	0.265298i
$167$	15.2569	+	15.2569i	1.18061	+	1.18061i	0.979586	+	0.201026i	$0.0644277\pi$
$167$	15.2569	+	15.2569i	1.18061	+	1.18061i	0.201026	+	0.979586i	$0.435572\pi$
$168$	−0.691596	+	4.53009i	−0.0533578	+	0.349504i
$169$	9.52648	+	8.84569i	0.732806	+	0.680438i
$170$	3.46972	−	2.00324i	0.266115	−	0.153642i
$171$	8.69415	−	9.78700i	0.664858	−	0.748430i
$172$	−0.963895	+	1.66952i	−0.0734963	+	0.127299i
$173$	3.41329	+	5.91199i	0.259508	+	0.449481i	0.966110	−	0.258130i	$-0.0831064\pi$
$173$	3.41329	+	5.91199i	0.259508	+	0.449481i	−0.706602	+	0.707611i	$0.749773\pi$
$174$	9.37837	+	5.05141i	0.710973	+	0.382946i
$175$	−2.83645	+	1.01156i	−0.214415	+	0.0764670i
$176$	2.10710	+	2.10710i	0.158829	+	0.158829i
$177$	0.136866	+	4.63312i	0.0102875	+	0.348247i
$178$	6.26742	−	10.8555i	0.469763	−	0.813654i
$179$	−5.31136	+	9.19954i	−0.396990	+	0.687606i	−0.993353	−	0.115108i	$-0.963278\pi$
$179$	−5.31136	+	9.19954i	−0.396990	+	0.687606i	0.596363	+	0.802715i	$0.296612\pi$
$180$	1.85934	+	5.59455i	0.138587	+	0.416993i
$181$		−	19.6947i		−	1.46390i	−0.681359	−	0.731950i	$-0.738611\pi$
$181$		−	19.6947i		−	1.46390i	0.681359	−	0.731950i	$-0.261389\pi$
$182$	9.28778	−	2.17652i	0.688456	−	0.161334i
$183$	9.04409	−	2.71199i	0.668558	−	0.200476i
$184$	−0.832911	+	3.10846i	−0.0614030	+	0.229159i
$185$	−6.92013	−	3.99534i	−0.508778	−	0.293743i
$186$	1.21977	−	5.15680i	0.0894379	−	0.378115i
$187$	1.57241	−	5.86832i	0.114986	−	0.429134i
$188$	0.555040	−	0.555040i	0.0404805	−	0.0404805i
$189$	2.31729	+	13.5510i	0.168558	+	0.985692i
$190$	−6.06359	+	6.06359i	−0.439899	+	0.439899i
$191$	20.9344	−	12.0865i	1.51476	−	0.874546i	0.514908	−	0.857245i	$-0.327826\pi$
$191$	20.9344	−	12.0865i	1.51476	−	0.874546i	0.999850	−	0.0173008i	$-0.00550729\pi$
$192$	1.68554	+	0.398691i	0.121643	+	0.0287731i
$193$	1.85200	+	6.91174i	0.133310	+	0.497518i	0.999999	−	0.00132974i	$-0.000423269\pi$
$193$	1.85200	+	6.91174i	0.133310	+	0.497518i	−0.866690	+	0.498848i	$0.833757\pi$
$194$	−5.13641	−	8.89652i	−0.368773	−	0.638733i
$195$	9.36619	−	7.92995i	0.670727	−	0.567875i
$196$	2.47941	−	6.54619i	0.177100	−	0.467585i
$197$	−14.7417	+	14.7417i	−1.05030	+	1.05030i	−0.0516350	+	0.998666i	$0.516443\pi$
$197$	−14.7417	+	14.7417i	−1.05030	+	1.05030i	−0.998666	+	0.0516350i	$0.983557\pi$
$198$	7.99233	+	4.00503i	0.567990	+	0.284625i
$199$	3.88217	+	2.24137i	0.275200	+	0.158887i	0.631248	−	0.775581i	$-0.282543\pi$
$199$	3.88217	+	2.24137i	0.275200	+	0.158887i	−0.356049	+	0.934467i	$0.615876\pi$
$200$	0.294591	+	1.09943i	0.0208308	+	0.0777414i
$201$	0.0347268	+	1.17555i	0.00244944	+	0.0829172i
$202$	−3.36434	+	3.36434i	−0.236714	+	0.236714i
$203$	−12.3965	−	10.5399i	−0.870067	−	0.739759i
$204$	−1.01428	−	3.38247i	−0.0710137	−	0.236820i
$205$	17.3904	−	10.0403i	1.21460	−	0.701247i
$206$	−10.0418	+	2.69068i	−0.699643	+	0.187469i
$207$	0.569898	+	9.63752i	0.0396106	+	0.669854i
$208$	−0.536735	−	3.56538i	−0.0372159	−	0.247214i
$209$			13.0032i			0.899451i
$210$	−0.991301	−	8.95069i	−0.0684063	−	0.617656i
$211$	−21.2853			−1.46534			−0.732670	−	0.680584i	$-0.761726\pi$
$211$	−21.2853			−1.46534			−0.732670	+	0.680584i	$0.761726\pi$
$212$	−2.18044	−	3.77663i	−0.149753	−	0.259380i
$213$	−9.84016	−	15.9375i	−0.674237	−	1.09202i
$214$	−14.3702	+	3.85048i	−0.982327	+	0.263214i
$215$	0.980506	−	3.65930i	0.0668699	−	0.249562i
$216$	5.17577	−	0.459760i	0.352167	−	0.0312827i
$217$	−3.46848	+	7.31373i	−0.235455	+	0.496489i
$218$	−10.8726			−0.736382
$219$	−20.4599	+	0.604401i	−1.38255	+	0.0408416i
$220$	−5.07136	−	2.92795i	−0.341911	−	0.197403i
$221$	−5.74800	+	4.58218i	−0.386653	+	0.308231i
$222$	−4.83084	+	5.12494i	−0.324225	+	0.343964i
$223$	−16.4129	−	16.4129i	−1.09909	−	1.09909i	−0.994517	−	0.104574i	$-0.966652\pi$
$223$	−16.4129	−	16.4129i	−1.09909	−	1.09909i	−0.104574	−	0.994517i	$-0.533348\pi$
$224$	−2.39055	−	1.13370i	−0.159725	−	0.0757484i
$225$	1.87890	+	2.85123i	0.125260	+	0.190082i
$226$	−4.17692	+	15.5885i	−0.277844	+	1.03693i
$227$	−1.11711	−	4.16910i	−0.0741449	−	0.276713i	0.918893	−	0.394507i	$-0.129084\pi$
$227$	−1.11711	−	4.16910i	−0.0741449	−	0.276713i	−0.993038	+	0.117794i	$0.962418\pi$
$228$	3.97066	+	6.43104i	0.262964	+	0.425906i
$229$	18.4670	+	4.94822i	1.22033	+	0.326988i	0.810809	−	0.585311i	$-0.199027\pi$
$229$	18.4670	+	4.94822i	1.22033	+	0.326988i	0.409526	+	0.912298i	$0.365694\pi$
$230$		−	6.32406i		−	0.416996i
$231$	−10.6602	−	8.53435i	−0.701388	−	0.561519i
$232$	−4.34877	+	4.34877i	−0.285510	+	0.285510i
$233$	−7.85397	−	13.6035i	−0.514530	−	0.891193i	−0.999858	−	0.0168603i	$-0.994633\pi$
$233$	−7.85397	−	13.6035i	−0.514530	−	0.891193i	0.485327	−	0.874332i	$-0.338700\pi$
$234$	−4.90144	−	9.64240i	−0.320417	−	0.630343i
$235$	−0.771265	+	1.33587i	−0.0503118	+	0.0871425i
$236$	−2.58491	−	0.692626i	−0.168264	−	0.0450861i
$237$	−16.2451	+	4.87131i	−1.05523	+	0.316426i
$238$	0.435206	+	5.37651i	0.0282102	+	0.348507i
$239$	−18.2934	+	18.2934i	−1.18330	+	1.18330i	−0.204417	+	0.978884i	$0.565530\pi$
$239$	−18.2934	+	18.2934i	−1.18330	+	1.18330i	−0.978884	+	0.204417i	$0.934470\pi$
$240$	−3.40224	+	0.100505i	−0.219614	+	0.00648757i
$241$	−7.52585	−	28.0869i	−0.484783	−	1.80923i	−0.581037	−	0.813877i	$-0.697353\pi$
$241$	−7.52585	−	28.0869i	−0.484783	−	1.80923i	0.0962542	−	0.995357i	$-0.469314\pi$
$242$	2.04802	−	0.548765i	0.131652	−	0.0352759i
$243$	14.2998	−	6.20599i	0.917336	−	0.398114i
$244$			5.45131i			0.348985i
$245$	−1.37687	+	13.6869i	−0.0879649	+	0.874425i
$246$	−5.08360	−	16.9530i	−0.324118	−	1.08089i
$247$	9.34509	−	12.6574i	0.594614	−	0.805369i
$248$	2.64955	+	1.52972i	0.168247	+	0.0971372i
$249$	−6.22057	−	10.0751i	−0.394212	−	0.638482i
$250$	−6.03123	−	10.4464i	−0.381449	−	0.660689i
$251$	−29.6402			−1.87087			−0.935436	−	0.353497i	$-0.884993\pi$
$251$	−29.6402			−1.87087			−0.935436	+	0.353497i	$0.884993\pi$
$252$	−7.87829	−	0.965671i	−0.496286	−	0.0608316i
$253$	−6.78090	−	6.78090i	−0.426311	−	0.426311i
$254$	−1.95328	+	7.28975i	−0.122560	+	0.457399i
$255$	3.64566	+	5.90466i	0.228300	+	0.369764i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.7359	−	25.5233i	−0.919199	−	1.59210i	−0.800635	−	0.599153i	$-0.795504\pi$
$257$	−14.7359	−	25.5233i	−0.919199	−	1.59210i	−0.118564	−	0.992946i	$-0.537829\pi$
$258$	−2.93972	−	1.58340i	−0.183019	−	0.0985783i
$259$	8.85248	−	6.11325i	0.550066	−	0.379859i
$260$	2.83223	+	6.49474i	0.175647	+	0.402787i
$261$	−8.26583	+	16.4951i	−0.511642	+	1.02102i
$262$	−0.584896	+	0.156722i	−0.0361350	+	0.00968234i
$263$	−14.8496	−	8.57339i	−0.915663	−	0.528658i	−0.0334138	−	0.999442i	$-0.510638\pi$
$263$	−14.8496	−	8.57339i	−0.915663	−	0.528658i	−0.882249	+	0.470784i	$0.843971\pi$
$264$	−3.54025	+	3.75578i	−0.217887	+	0.231152i
$265$	6.05972	+	6.05972i	0.372246	+	0.372246i
$266$	−3.87811	−	10.8743i	−0.237782	−	0.666747i
$267$	19.1146	+	10.2956i	1.16979	+	0.630078i
$268$	−0.655866	−	0.175739i	−0.0400634	−	0.0107350i
$269$	−10.0976	−	5.82987i	−0.615663	−	0.355453i	0.159515	−	0.987195i	$-0.449007\pi$
$269$	−10.0976	−	5.82987i	−0.615663	−	0.355453i	−0.775179	+	0.631742i	$0.782340\pi$
$270$	−9.59072	+	3.50519i	−0.583673	+	0.213319i
$271$	−24.4953	−	6.56350i	−1.48798	−	0.398704i	−0.578928	−	0.815378i	$-0.696529\pi$
$271$	−24.4953	−	6.56350i	−1.48798	−	0.398704i	−0.909056	+	0.416674i	$0.863196\pi$
$272$	2.03878			0.123619
$273$	4.24321	+	15.9686i	0.256811	+	0.966462i
$274$	−4.66746			−0.281972
$275$	−3.27618	−	0.877849i	−0.197561	−	0.0529363i
$276$	−5.42427	−	1.28304i	−0.326503	−	0.0772297i
$277$	24.7727	+	14.3025i	1.48845	+	0.859356i	0.999913	−	0.0131886i	$-0.00419819\pi$
$277$	24.7727	+	14.3025i	1.48845	+	0.859356i	0.488535	+	0.872544i	$0.337532\pi$
$278$	−1.16460	−	0.312054i	−0.0698481	−	0.0187157i
$279$	8.99033	+	1.84804i	0.538237	+	0.110639i
$280$	5.11432	+	0.936092i	0.305639	+	0.0559422i
$281$	−0.448744	−	0.448744i	−0.0267698	−	0.0267698i	0.693595	−	0.720365i	$-0.256026\pi$
$281$	−0.448744	−	0.448744i	−0.0267698	−	0.0267698i	−0.720365	+	0.693595i	$0.756026\pi$
$282$	0.989325	+	0.932551i	0.0589135	+	0.0555326i
$283$	24.9591	+	14.4101i	1.48366	+	0.856594i	0.999828	−	0.0185645i	$-0.00590961\pi$
$283$	24.9591	+	14.4101i	1.48366	+	0.856594i	0.483836	+	0.875158i	$0.339243\pi$
$284$	10.4456	−	2.79889i	0.619832	−	0.166084i
$285$	−10.8080	−	10.1877i	−0.640209	−	0.603470i
$286$	10.0007	+	3.92708i	0.591356	+	0.232213i
$287$	2.18127	+	26.9473i	0.128756	+	1.59065i
$288$	−0.604047	+	2.93856i	−0.0355938	+	0.173156i
$289$	6.42170	+	11.1227i	0.377747	+	0.654277i
$290$	6.04290	−	10.4666i	0.354851	−	0.614620i
$291$	15.1398	−	9.34765i	0.887512	−	0.547969i
$292$	3.05864	−	11.4150i	0.178993	−	0.668012i
$293$	−2.61973	−	2.61973i	−0.153046	−	0.153046i	0.626431	−	0.779477i	$-0.284515\pi$
$293$	−2.61973	−	2.61973i	−0.153046	−	0.153046i	−0.779477	+	0.626431i	$0.784515\pi$
$294$	11.4602	+	3.95779i	0.668372	+	0.230823i
$295$	5.25892			0.306186
$296$	−2.03310	−	3.52144i	−0.118172	−	0.204679i
$297$	−6.52513	+	14.0419i	−0.378626	+	0.814795i
$298$	−17.1859	−	9.92231i	−0.995555	−	0.574784i
$299$	1.72728	+	11.4738i	0.0998911	+	0.663548i
$300$	−1.88837	+	0.566254i	−0.109025	+	0.0326927i
$301$	3.88579	+	3.30382i	0.223973	+	0.190429i
$302$			7.15080i			0.411482i
$303$	−5.99673	−	5.65260i	−0.344503	−	0.324733i
$304$	−4.21497	+	1.12940i	−0.241745	+	0.0647754i
$305$	−2.77263	−	10.3476i	−0.158760	−	0.592501i
$306$	5.80417	−	1.92901i	0.331802	−	0.110274i
$307$	−10.6314	+	10.6314i	−0.606768	+	0.606768i	−0.942100	−	0.335332i	$-0.891151\pi$
$307$	−10.6314	+	10.6314i	−0.606768	+	0.606768i	0.335332	+	0.942100i	$0.391151\pi$
$308$	6.48747	−	4.48005i	0.369658	−	0.255274i
$309$	−5.17194	−	17.2477i	−0.294222	−	0.981185i
$310$	−5.80737	−	1.55608i	−0.329836	−	0.0883794i
$311$	−7.17794	+	12.4326i	−0.407024	+	0.704986i	−0.994555	−	0.104216i	$-0.966767\pi$
$311$	−7.17794	+	12.4326i	−0.407024	+	0.704986i	0.587531	+	0.809202i	$0.300100\pi$
$312$	6.14527	−	1.11159i	0.347907	−	0.0629316i
$313$	6.41060	+	11.1035i	0.362349	+	0.627607i	0.988347	−	0.152218i	$-0.0486416\pi$
$313$	6.41060	+	11.1035i	0.362349	+	0.627607i	−0.625998	+	0.779825i	$0.715308\pi$
$314$	−13.2454	+	13.2454i	−0.747484	+	0.747484i
$315$	15.4456	−	2.17401i	0.870260	−	0.122491i
$316$		−	9.79172i		−	0.550827i
$317$	31.6985	+	8.49358i	1.78036	+	0.477047i	0.990650	−	0.136428i	$-0.0435622\pi$
$317$	31.6985	+	8.49358i	1.78036	+	0.477047i	0.789714	+	0.613475i	$0.210229\pi$
$318$	6.42694	−	3.96813i	0.360405	−	0.222522i
$319$	−4.74326	−	17.7021i	−0.265572	−	0.991127i
$320$	0.508616	−	1.89818i	0.0284325	−	0.106112i
$321$	−7.40127	−	24.6821i	−0.413099	−	1.37762i
$322$	7.69308	+	3.64837i	0.428718	+	0.203316i
$323$	6.29079	+	6.29079i	0.350029	+	0.350029i
$324$	1.06069	+	8.93728i	0.0589271	+	0.496515i
$325$	2.55815	+	3.20901i	0.141901	+	0.178004i
$326$	−4.13336	−	2.38640i	−0.228926	−	0.132170i
$327$	−0.556064	−	18.8236i	−0.0307504	−	1.04095i
$328$	10.2184			0.564218
$329$	−1.18011	−	1.70889i	−0.0650615	−	0.0942143i
$330$	4.80978	−	8.92978i	0.264770	−	0.491568i
$331$	1.70346	−	6.35741i	0.0936308	−	0.349435i	−0.903177	−	0.429267i	$-0.858772\pi$
$331$	1.70346	−	6.35741i	0.0936308	−	0.349435i	0.996808	+	0.0798323i	$0.0254385\pi$
$332$	6.60330	−	1.76935i	0.362403	−	0.0971057i
$333$	−9.11986	−	8.10150i	−0.499765	−	0.443960i
$334$	−10.7882	−	18.6858i	−0.590306	−	1.02244i
$335$	1.33434			0.0729026
$336$	1.84050	−	4.19673i	0.100408	−	0.228950i
$337$			10.8486i			0.590959i	0.955349	+	0.295479i	$0.0954793\pi$
$337$			10.8486i			0.590959i	−0.955349	+	0.295479i	$0.904521\pi$
$338$	−6.91244	−	11.0099i	−0.375987	−	0.598860i
$339$	−27.2019	−	6.43423i	−1.47740	−	0.349459i
$340$	−3.86997	+	1.03696i	−0.209879	+	0.0562368i
$341$	−7.89536	+	4.55839i	−0.427558	+	0.246851i
$342$	−10.9310	+	7.20330i	−0.591079	+	0.389510i
$343$	−15.8555	−	9.57096i	−0.856116	−	0.516783i
$344$	1.36315	−	1.36315i	0.0734963	−	0.0734963i
$345$	10.9488	−	0.323437i	0.589465	−	0.0174133i
$346$	−1.76685	−	6.59397i	−0.0949864	−	0.354494i
$347$	22.0582	+	12.7353i	1.18415	+	0.683666i	0.956970	−	0.290187i	$-0.0937177\pi$
$347$	22.0582	+	12.7353i	1.18415	+	0.683666i	0.227175	+	0.973854i	$0.427051\pi$
$348$	−7.75141	−	7.30659i	−0.415519	−	0.391674i
$349$	12.8258	−	12.8258i	0.686551	−	0.686551i	−0.274917	−	0.961468i	$-0.588650\pi$
$349$	12.8258	−	12.8258i	0.686551	−	0.686551i	0.961468	+	0.274917i	$0.0886505\pi$
$350$	3.00161	−	0.242968i	0.160443	−	0.0129872i
$351$	16.4432	−	8.97899i	0.877671	−	0.479263i
$352$	−1.48994	−	2.58066i	−0.0794143	−	0.137550i
$353$	5.27871	+	19.7004i	0.280957	+	1.04855i	0.951743	+	0.306896i	$0.0992902\pi$
$353$	5.27871	+	19.7004i	0.280957	+	1.04855i	−0.670786	+	0.741651i	$0.734043\pi$
$354$	1.06694	−	4.51067i	0.0567071	−	0.239740i
$355$	−18.4041	+	10.6256i	−0.976787	+	0.563948i
$356$	−8.86347	+	8.86347i	−0.469763	+	0.469763i
$357$	−9.28607	+	1.02845i	−0.491471	+	0.0544311i
$358$	7.51140	−	7.51140i	0.396990	−	0.396990i
$359$	5.92711	−	22.1203i	0.312821	−	1.16746i	−0.613181	−	0.789943i	$-0.710110\pi$
$359$	5.92711	−	22.1203i	0.312821	−	1.16746i	0.926001	−	0.377520i	$-0.123223\pi$
$360$	−0.348008	−	5.88515i	−0.0183416	−	0.310175i
$361$	−0.0359416	−	0.0207509i	−0.00189167	−	0.00109215i
$362$	−5.09738	+	19.0237i	−0.267912	+	0.999862i
$363$	1.05482	+	3.51766i	0.0553636	+	0.184629i
$364$	−9.53463	−	0.301498i	−0.499750	−	0.0158028i
$365$			23.2234i			1.21557i
$366$	−9.43784	+	0.278801i	−0.493324	+	0.0145732i
$367$	−4.41938	+	7.65459i	−0.230690	+	0.399566i	−0.958011	−	0.286731i	$-0.907432\pi$
$367$	−4.41938	+	7.65459i	−0.230690	+	0.399566i	0.727322	+	0.686297i	$0.240765\pi$
$368$	1.60906	−	2.78697i	0.0838780	−	0.145281i
$369$	29.0907	−	9.66825i	1.51440	−	0.503309i
$370$	5.65026	+	5.65026i	0.293743	+	0.293743i
$371$	−10.8674	+	3.87563i	−0.564206	+	0.201213i
$372$	−2.51289	+	4.66539i	−0.130287	+	0.241889i
$373$	15.7801	+	27.3320i	0.817065	+	1.41520i	0.907836	+	0.419326i	$0.137734\pi$
$373$	15.7801	+	27.3320i	0.817065	+	1.41520i	−0.0907705	+	0.995872i	$0.528933\pi$
$374$	−3.03766	+	5.26139i	−0.157074	+	0.272060i
$375$	17.7773	−	10.9761i	0.918018	−	0.566804i
$376$	−0.679782	+	0.392473i	−0.0350571	+	0.0202402i
$377$	−8.10496	+	20.6401i	−0.417427	+	1.06302i
$378$	1.26894	−	13.6890i	0.0652671	−	0.704088i
$379$	−2.07577	−	2.07577i	−0.106625	−	0.106625i	0.651782	−	0.758407i	$-0.274022\pi$
$379$	−2.07577	−	2.07577i	−0.106625	−	0.106625i	−0.758407	+	0.651782i	$0.774022\pi$
$380$	7.42635	−	4.28760i	0.380964	−	0.219949i
$381$	−12.7206	−	3.00888i	−0.651696	−	0.154150i
$382$	−23.3493	+	6.25642i	−1.19465	+	0.320106i
$383$	−14.1117	−	3.78122i	−0.721074	−	0.193211i	−0.120423	−	0.992723i	$-0.538425\pi$
$383$	−14.1117	−	3.78122i	−0.721074	−	0.193211i	−0.600651	+	0.799511i	$0.705092\pi$
$384$	−1.52492	−	0.821356i	−0.0778181	−	0.0419146i
$385$	−10.0358	+	11.8036i	−0.511471	+	0.601566i
$386$		−	7.15556i		−	0.364209i
$387$	2.59099	−	5.17051i	0.131707	−	0.262832i
$388$	2.65880	+	9.92278i	0.134980	+	0.503753i
$389$	−12.8526	+	22.2613i	−0.651652	+	1.12869i	0.331070	+	0.943606i	$0.392590\pi$
$389$	−12.8526	+	22.2613i	−0.651652	+	1.12869i	−0.982722	+	0.185088i	$0.940743\pi$
$390$	−11.0995	+	5.23559i	−0.562043	+	0.265115i
$391$	−6.56103			−0.331805
$392$	−4.08920	+	5.68141i	−0.206536	+	0.286955i
$393$	−0.301246	−	1.00461i	−0.0151959	−	0.0506760i
$394$	18.0548	−	10.4239i	0.909587	−	0.525150i
$395$	4.98023	+	18.5865i	0.250582	+	0.935186i
$396$	−6.68342	−	5.93713i	−0.335855	−	0.298352i
$397$	−26.5243	−	7.10715i	−1.33121	−	0.356698i	−0.478047	−	0.878334i	$-0.658655\pi$
$397$	−26.5243	−	7.10715i	−1.33121	−	0.356698i	−0.853168	+	0.521637i	$0.825322\pi$
$398$	−3.16978	−	3.16978i	−0.158887	−	0.158887i
$399$	18.6283	−	7.27031i	0.932582	−	0.363971i
$400$		−	1.13821i		−	0.0569107i
$401$	−4.48360	+	16.7330i	−0.223900	+	0.835608i	0.758942	+	0.651159i	$0.225717\pi$
$401$	−4.48360	+	16.7330i	−0.223900	+	0.835608i	−0.982842	+	0.184449i	$0.940950\pi$
$402$	0.270712	−	1.14449i	0.0135019	−	0.0570818i
$403$	10.9614	+	1.23706i	0.546025	+	0.0616222i
$404$	4.12046	−	2.37895i	0.205000	−	0.118357i
$405$	−6.55903	−	16.4251i	−0.325921	−	0.816170i
$406$	9.24621	+	13.3893i	0.458882	+	0.664498i
$407$	12.1168			0.600609
$408$	0.104271	+	3.52972i	0.00516218	+	0.174747i
$409$	8.62264	−	2.31043i	0.426362	−	0.114243i	−0.0392560	−	0.999229i	$-0.512499\pi$
$409$	8.62264	−	2.31043i	0.426362	−	0.114243i	0.465618	+	0.884986i	$0.345832\pi$
$410$	−19.3964	+	5.19726i	−0.957921	+	0.256674i
$411$	−0.238712	−	8.08076i	−0.0117748	−	0.398595i
$412$	10.3960			0.512174
$413$	−3.03389	+	6.39735i	−0.149288	+	0.314793i
$414$	1.94390	−	9.45663i	0.0955373	−	0.464768i
$415$	−11.6343	+	6.71709i	−0.571108	+	0.329729i
$416$	−0.404341	+	3.58281i	−0.0198245	+	0.175662i
$417$	0.480695	−	2.03223i	0.0235397	−	0.0995186i
$418$	3.36548	−	12.5601i	0.164611	−	0.614336i
$419$			2.60621i			0.127322i	0.997972	+	0.0636609i	$0.0202776\pi$
$419$			2.60621i			0.127322i	−0.997972	+	0.0636609i	$0.979722\pi$
$420$	−1.35909	+	8.90227i	−0.0663166	+	0.434386i
$421$	11.8588	+	11.8588i	0.577963	+	0.577963i	0.934342	−	0.356379i	$-0.115989\pi$
$421$	11.8588	+	11.8588i	0.577963	+	0.577963i	−0.356379	+	0.934342i	$0.615989\pi$
$422$	20.5600	+	5.50904i	1.00085	+	0.268176i
$423$	−1.56392	+	1.76051i	−0.0760406	+	0.0855989i
$424$	1.12868	+	4.21228i	0.0548134	+	0.204566i
$425$	−2.00967	+	1.16028i	−0.0974832	+	0.0562819i
$426$	5.37993	+	17.9413i	0.260659	+	0.869257i
$427$	14.1871	+	2.59672i	0.686564	+	0.125664i
$428$	14.8771			0.719113
$429$	−6.28747	+	17.5151i	−0.303562	+	0.845635i
$430$	−1.89419	+	3.28084i	−0.0913460	+	0.158216i
$431$	−5.13915	−	19.1796i	−0.247544	−	0.923848i	−0.972087	−	0.234619i	$-0.924616\pi$
$431$	−5.13915	−	19.1796i	−0.247544	−	0.923848i	0.724543	−	0.689229i	$-0.242051\pi$
$432$	−5.11841	−	0.895495i	−0.246259	−	0.0430845i
$433$		−	8.74957i		−	0.420477i	−0.977650	−	0.210239i	$-0.932576\pi$
$433$		−	8.74957i		−	0.420477i	0.977650	−	0.210239i	$-0.0674241\pi$
$434$	5.24322	−	6.16682i	0.251683	−	0.296017i
$435$	18.4298	+	9.92674i	0.883643	+	0.475951i
$436$	10.5021	+	2.81402i	0.502958	+	0.134767i
$437$	13.5643	−	3.63454i	0.648867	−	0.173863i
$438$	19.9191	+	4.71160i	0.951774	+	0.225129i
$439$	−18.0150	+	10.4010i	−0.859808	+	0.496410i	−0.863948	−	0.503581i	$-0.832015\pi$
$439$	−18.0150	+	10.4010i	−0.859808	+	0.496410i	0.00414009	+	0.999991i	$0.498682\pi$
$440$	4.14075	+	4.14075i	0.197403	+	0.197403i
$441$	−6.26598	+	20.0434i	−0.298380	+	0.954447i
$442$	6.73810	−	2.93835i	0.320499	−	0.139763i
$443$	2.35905	−	1.36200i	0.112082	−	0.0647106i	−0.442911	−	0.896566i	$-0.646054\pi$
$443$	2.35905	−	1.36200i	0.112082	−	0.0647106i	0.554993	+	0.831855i	$0.312721\pi$
$444$	5.99267	−	3.70000i	0.284399	−	0.175594i
$445$	12.3164	−	21.3326i	0.583852	−	1.01126i
$446$	11.6057	+	20.1017i	0.549546	+	0.951841i
$447$	16.2995	−	30.2614i	0.770939	−	1.43132i
$448$	2.01567	+	1.71379i	0.0952315	+	0.0809689i
$449$	−22.4174	−	22.4174i	−1.05794	−	1.05794i	−0.998215	−	0.0597270i	$-0.980977\pi$
$449$	−22.4174	−	22.4174i	−1.05794	−	1.05794i	−0.0597270	−	0.998215i	$-0.519023\pi$
$450$	−1.07693	−	3.24037i	−0.0507670	−	0.152752i
$451$	−15.2249	+	26.3703i	−0.716911	+	1.24173i
$452$	8.06919	−	13.9762i	0.379543	−	0.657387i
$453$	−12.3801	+	0.365720i	−0.581670	+	0.0171830i
$454$			4.31617i			0.202568i
$455$	18.2518	−	4.27717i	0.855658	−	0.200517i
$456$	−2.17089	−	7.23960i	−0.101661	−	0.339025i
$457$	−4.85785	+	18.1297i	−0.227241	+	0.848074i	0.754254	+	0.656583i	$0.227999\pi$
$457$	−4.85785	+	18.1297i	−0.227241	+	0.848074i	−0.981494	+	0.191491i	$0.938668\pi$
$458$	−16.5571	−	9.55923i	−0.773661	−	0.446674i
$459$	3.63653	+	9.95008i	0.169739	+	0.464430i
$460$	−1.63679	+	6.10858i	−0.0763157	+	0.284814i
$461$	25.1394	−	25.1394i	1.17086	−	1.17086i	0.188852	−	0.982006i	$-0.439523\pi$
$461$	25.1394	−	25.1394i	1.17086	−	1.17086i	0.982006	−	0.188852i	$-0.0604765\pi$
$462$	8.08808	+	11.0026i	0.376292	+	0.511888i
$463$	16.7958	−	16.7958i	0.780567	−	0.780567i	−0.199359	−	0.979926i	$-0.563886\pi$
$463$	16.7958	−	16.7958i	0.780567	−	0.780567i	0.979926	+	0.199359i	$0.0638860\pi$
$464$	5.32613	−	3.07504i	0.247259	−	0.142755i
$465$	2.39702	−	10.1339i	0.111159	−	0.469946i
$466$	4.06551	+	15.1727i	0.188331	+	0.702862i
$467$	6.43406	+	11.1441i	0.297733	+	0.515688i	0.975617	−	0.219480i	$-0.0704362\pi$
$467$	6.43406	+	11.1441i	0.297733	+	0.515688i	−0.677884	+	0.735169i	$0.737103\pi$
$468$	2.23879	+	10.5824i	0.103488	+	0.489173i
$469$	−0.769784	+	1.62319i	−0.0355453	+	0.0749519i
$470$	1.09073	−	1.09073i	0.0503118	−	0.0503118i
$471$	−23.6092	−	22.2544i	−1.08785	−	1.02543i
$472$	2.31757	+	1.33805i	0.106675	+	0.0615887i
$473$	1.48681	+	5.54886i	0.0683637	+	0.255137i
$474$	16.9524	−	0.500786i	0.778647	−	0.0230019i
$475$	3.51204	−	3.51204i	0.161143	−	0.161143i
$476$	0.971167	−	5.30595i	0.0445134	−	0.243198i
$477$	7.19870	+	10.9240i	0.329606	+	0.500175i
$478$	22.4047	−	12.9354i	1.02477	−	0.591650i
$479$	20.8166	−	5.57779i	0.951135	−	0.254856i	0.250291	−	0.968171i	$-0.419474\pi$
$479$	20.8166	−	5.57779i	0.951135	−	0.254856i	0.700844	+	0.713315i	$0.252807\pi$
$480$	3.31233	+	0.783485i	0.151186	+	0.0357610i
$481$	−11.7946	−	8.70808i	−0.537786	−	0.397054i
$482$			29.0777i			1.32445i
$483$	−5.92296	+	13.5056i	−0.269504	+	0.614525i
$484$	−2.12026			−0.0963756
$485$	−10.0938	−	17.4829i	−0.458335	−	0.793859i
$486$	−15.4188	+	2.29345i	−0.699412	+	0.104033i
$487$	−6.76544	+	1.81279i	−0.306571	+	0.0821455i	−0.408825	−	0.912613i	$-0.634061\pi$
$487$	−6.76544	+	1.81279i	−0.306571	+	0.0821455i	0.102254	+	0.994758i	$0.467395\pi$
$488$	1.41090	−	5.26556i	0.0638686	−	0.238361i
$489$	3.92016	−	7.27812i	0.177276	−	0.329128i
$490$	4.87239	−	12.8642i	0.220112	−	0.581145i
$491$	−4.58195			−0.206780			−0.103390	−	0.994641i	$-0.532969\pi$
$491$	−4.58195			−0.206780			−0.103390	+	0.994641i	$0.532969\pi$
$492$	0.522609	+	17.6911i	0.0235611	+	0.797577i
$493$	−10.8588	−	6.26932i	−0.489055	−	0.282356i
$494$	−12.3026	+	9.80738i	−0.553522	+	0.441255i
$495$	15.7061	+	7.87045i	0.705936	+	0.353751i
$496$	−2.16335	−	2.16335i	−0.0971372	−	0.0971372i
$497$	−2.30842	−	28.5181i	−0.103547	−	1.27921i
$498$	3.40098	+	11.3418i	0.152402	+	0.508237i
$499$	−2.71651	+	10.1382i	−0.121608	+	0.453846i	−0.999696	−	0.0246524i	$-0.992152\pi$
$499$	−2.71651	+	10.1382i	−0.121608	+	0.453846i	0.878088	+	0.478498i	$0.158819\pi$
$500$	3.12200	+	11.6514i	0.139620	+	0.521069i
$501$	31.7988	−	19.6333i	1.42067	−	0.877151i
$502$	28.6302	+	7.67144i	1.27783	+	0.342393i
$503$			6.06721i			0.270524i	0.990810	+	0.135262i	$0.0431876\pi$
$503$			6.06721i			0.270524i	−0.990810	+	0.135262i	$0.956812\pi$
$504$	7.35991	+	2.97182i	0.327836	+	0.132375i
$505$	−6.61141	+	6.61141i	−0.294204	+	0.294204i
$506$	4.79482	+	8.30487i	0.213156	+	0.369197i
$507$	18.7079	−	12.5306i	0.830846	−	0.556502i
$508$	3.77345	−	6.53581i	0.167420	−	0.289980i
$509$	−24.4905	−	6.56221i	−1.08552	−	0.290865i	−0.328666	−	0.944446i	$-0.606599\pi$
$509$	−24.4905	−	6.56221i	−1.08552	−	0.290865i	−0.756856	+	0.653582i	$0.773266\pi$
$510$	−1.99320	−	6.64703i	−0.0882604	−	0.294335i
$511$	−28.2507	−	13.3977i	−1.24974	−	0.592677i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−13.0301	−	18.5563i	−0.575293	−	0.819282i
$514$	7.62785	+	28.4675i	0.336450	+	1.25565i
$515$	−19.7335	+	5.28758i	−0.869562	+	0.232999i
$516$	2.42974	+	2.29031i	0.106963	+	0.100825i
$517$		−	2.33905i		−	0.102871i
$518$	−10.1331	+	3.61375i	−0.445221	+	0.158779i
$519$	11.3258	−	3.39618i	0.497145	−	0.149076i
$520$	−1.05476	−	7.00648i	−0.0462543	−	0.307254i
$521$	26.8303	+	15.4905i	1.17546	+	0.678650i	0.954959	−	0.296737i	$-0.0958986\pi$
$521$	26.8303	+	15.4905i	1.17546	+	0.678650i	0.220497	+	0.975388i	$0.429232\pi$
$522$	12.2534	−	13.7937i	0.536318	−	0.603733i
$523$	0.968980	+	1.67832i	0.0423705	+	0.0733879i	0.886433	−	0.462857i	$-0.153176\pi$
$523$	0.968980	+	1.67832i	0.0423705	+	0.0733879i	−0.844062	+	0.536245i	$0.819842\pi$
$524$	0.605528			0.0264526
$525$	0.574163	+	5.18425i	0.0250585	+	0.226259i
$526$	12.1246	+	12.1246i	0.528658	+	0.528658i
$527$	−1.61439	+	6.02497i	−0.0703237	+	0.262452i
$528$	4.39168	−	2.71152i	0.191123	−	0.118004i
$529$	6.32185	−	10.9498i	0.274863	−	0.476077i
$530$	−4.28487	−	7.42161i	−0.186123	−	0.322374i
$531$	7.86388	+	1.61649i	0.341263	+	0.0701497i
$532$	0.931484	+	11.5075i	0.0403850	+	0.498914i
$533$	33.7716	−	14.7271i	1.46281	−	0.637903i
$534$	−15.7986	−	14.8920i	−0.683672	−	0.644439i
$535$	−28.2395	+	7.56675i	−1.22090	+	0.327139i
$536$	0.588033	+	0.339501i	0.0253992	+	0.0146642i
$537$	13.3886	+	12.6203i	0.577761	+	0.544605i
$538$	8.24468	+	8.24468i	0.355453	+	0.355453i
$539$	−8.56911	−	19.0178i	−0.369098	−	0.819155i
$540$	10.1711	−	0.903493i	0.437696	−	0.0388802i
$541$	10.5211	+	2.81912i	0.452337	+	0.121203i	0.477793	−	0.878473i	$-0.341437\pi$
$541$	10.5211	+	2.81912i	0.452337	+	0.121203i	−0.0254556	+	0.999676i	$0.508104\pi$
$542$	21.9619	+	12.6797i	0.943344	+	0.544640i
$543$	−33.1963	−	7.85212i	−1.42459	−	0.336967i
$544$	−1.96931	−	0.527674i	−0.0844333	−	0.0226238i
$545$	−21.3661			−0.915224
$546$	0.0343447	−	16.5227i	0.00146982	−	0.707105i
$547$	−34.1078			−1.45834			−0.729171	−	0.684331i	$-0.760094\pi$
$547$	−34.1078			−1.45834			−0.729171	+	0.684331i	$0.760094\pi$
$548$	4.50842	+	1.20803i	0.192590	+	0.0516044i
$549$	−0.965375	−	16.3254i	−0.0412012	−	0.696752i
$550$	2.93734	+	1.69587i	0.125249	+	0.0723123i
$551$	25.9224	+	6.94589i	1.10433	+	0.295905i
$552$	4.90737	+	2.64322i	0.208871	+	0.112503i
$553$	−25.4831	−	4.66426i	−1.08365	−	0.198345i
$554$	−20.2268	−	20.2268i	−0.859356	−	0.859356i
$555$	−9.49329	+	10.0712i	−0.402968	+	0.427500i
$556$	1.04415	+	0.602841i	0.0442819	+	0.0255662i
$557$	21.8948	−	5.86670i	0.927713	−	0.248580i	0.236834	−	0.971550i	$-0.423890\pi$
$557$	21.8948	−	5.86670i	0.927713	−	0.248580i	0.690879	+	0.722970i	$0.257224\pi$
$558$	−8.20568	−	4.11194i	−0.347374	−	0.174072i
$559$	2.54056	−	6.46981i	0.107454	−	0.273644i
$560$	−4.69777	−	2.22788i	−0.198517	−	0.0941450i
$561$	−9.26437	−	4.99001i	−0.391142	−	0.210678i
$562$	0.317310	+	0.549597i	0.0133849	+	0.0231834i
$563$	12.6747	−	21.9532i	0.534175	−	0.925218i	−0.465028	−	0.885296i	$-0.653956\pi$
$563$	12.6747	−	21.9532i	0.534175	−	0.925218i	0.999203	−	0.0399219i	$-0.0127109\pi$
$564$	−0.714253	−	1.15683i	−0.0300755	−	0.0487114i
$565$	−8.20824	+	30.6336i	−0.345323	+	1.28876i
$566$	−20.3790	−	20.3790i	−0.856594	−	0.856594i
$567$	23.7647	+	1.49679i	0.998022	+	0.0628594i
$568$	−10.8141			−0.453749
$569$	11.4337	+	19.8037i	0.479325	+	0.830215i	0.999719	−	0.0237110i	$-0.00754816\pi$
$569$	11.4337	+	19.8037i	0.479325	+	0.830215i	−0.520394	+	0.853926i	$0.674215\pi$
$570$	7.80292	+	12.6379i	0.326828	+	0.529344i
$571$	39.5683	+	22.8448i	1.65588	+	0.956023i	0.974586	+	0.224015i	$0.0719164\pi$
$571$	39.5683	+	22.8448i	1.65588	+	0.956023i	0.681295	+	0.732009i	$0.261417\pi$
$572$	−8.64356	−	6.38165i	−0.361405	−	0.266830i
$573$	−12.0259	−	40.1045i	−0.502388	−	1.67539i
$574$	4.86752	−	26.5936i	0.203166	−	1.11000i
$575$			3.66291i			0.152754i
$576$	1.34402	−	2.68209i	0.0560008	−	0.111754i
$577$	4.20984	−	1.12802i	0.175258	−	0.0469602i	−0.170123	−	0.985423i	$-0.554416\pi$
$577$	4.20984	−	1.12802i	0.175258	−	0.0469602i	0.345381	+	0.938463i	$0.387750\pi$
$578$	−3.32411	−	12.4058i	−0.138265	−	0.516012i
$579$	12.3884	−	0.365963i	0.514844	−	0.0152089i
$580$	−8.54595	+	8.54595i	−0.354851	+	0.354851i
$581$	−1.45929	−	18.0280i	−0.0605416	−	0.747929i
$582$	−17.0433	+	5.11066i	−0.706467	+	0.211844i
$583$	−12.5521	−	3.36333i	−0.519856	−	0.139295i
$584$	−5.90883	+	10.2344i	−0.244509	+	0.423502i
$585$	−9.63203	−	18.9487i	−0.398235	−	0.783432i
$586$	1.85243	+	3.20850i	0.0765231	+	0.132542i
$587$	7.29612	−	7.29612i	0.301143	−	0.301143i	−0.540318	−	0.841461i	$-0.681696\pi$
$587$	7.29612	−	7.29612i	0.301143	−	0.301143i	0.841461	+	0.540318i	$0.181696\pi$
$588$	−10.0453	−	6.78905i	−0.414263	−	0.279976i
$589$		−	13.3503i		−	0.550091i
$590$	−5.07973	−	1.36111i	−0.209129	−	0.0560359i
$591$	18.9703	+	30.7251i	0.780334	+	1.26386i
$592$	1.05241	+	3.92765i	0.0432538	+	0.161425i
$593$	6.45528	−	24.0914i	0.265086	−	0.989316i	−0.697111	−	0.716963i	$-0.745532\pi$
$593$	6.45528	−	24.0914i	0.265086	−	0.989316i	0.962197	−	0.272353i	$-0.0878018\pi$
$594$	9.93711	−	11.8746i	0.407724	−	0.487222i
$595$	0.855241	+	10.5656i	0.0350615	+	0.433148i
$596$	14.0323	+	14.0323i	0.574784	+	0.574784i
$597$	5.32571	−	5.64993i	0.217967	−	0.231236i
$598$	1.30122	−	11.5299i	0.0532108	−	0.471493i
$599$	−23.3553	−	13.4842i	−0.954273	−	0.550950i	−0.0598673	−	0.998206i	$-0.519068\pi$
$599$	−23.3553	−	13.4842i	−0.954273	−	0.550950i	−0.894406	+	0.447257i	$0.852401\pi$
$600$	1.97058	−	0.0582126i	0.0804488	−	0.00237652i
$601$	2.30129			0.0938717			0.0469358	−	0.998898i	$-0.485054\pi$
$601$	2.30129			0.0938717			0.0469358	+	0.998898i	$0.485054\pi$
$602$	−2.89829	−	4.19697i	−0.118126	−	0.171056i
$603$	1.99529	+	0.410150i	0.0812544	+	0.0167026i
$604$	1.85076	−	6.90714i	0.0753065	−	0.281048i
$605$	4.02465	−	1.07840i	0.163625	−	0.0438432i
$606$	4.32940	+	7.01206i	0.175870	+	0.284846i
$607$	6.18973	+	10.7209i	0.251233	+	0.435149i	0.963866	−	0.266389i	$-0.0858305\pi$
$607$	6.18973	+	10.7209i	0.251233	+	0.435149i	−0.712632	+	0.701538i	$0.752497\pi$
$608$	4.36366			0.176970
$609$	−22.7079	+	16.6927i	−0.920170	+	0.676422i
$610$			10.7126i			0.433741i
$611$	−1.68102	+	2.27684i	−0.0680067	+	0.0921110i
$612$	−6.10566	+	0.361047i	−0.246807	+	0.0145945i
$613$	6.16430	−	1.65172i	0.248974	−	0.0667123i	−0.132174	−	0.991227i	$-0.542196\pi$
$613$	6.16430	−	1.65172i	0.248974	−	0.0667123i	0.381147	+	0.924514i	$0.375529\pi$
$614$	13.0208	−	7.51756i	0.525476	−	0.303384i
$615$	−9.98999	−	33.3151i	−0.402835	−	1.34340i
$616$	−7.42594	+	2.64831i	−0.299200	+	0.106704i
$617$	−8.49833	+	8.49833i	−0.342130	+	0.342130i	−0.857168	−	0.515038i	$-0.827778\pi$
$617$	−8.49833	+	8.49833i	−0.342130	+	0.342130i	0.515038	+	0.857168i	$0.327778\pi$
$618$	0.531692	+	17.9986i	0.0213878	+	0.724008i
$619$	1.19950	+	4.47660i	0.0482120	+	0.179930i	0.985833	−	0.167729i	$-0.0536434\pi$
$619$	1.19950	+	4.47660i	0.0482120	+	0.179930i	−0.937621	+	0.347659i	$0.886977\pi$
$620$	5.20674	+	3.00611i	0.209108	+	0.120728i
$621$	16.4716	+	2.88181i	0.660984	+	0.115643i
$622$	10.1511	−	10.1511i	0.407024	−	0.407024i
$623$	18.8452	+	27.2894i	0.755018	+	1.09333i
$624$	−6.22358	−	0.516796i	−0.249143	−	0.0206884i
$625$	−9.00670	−	15.6001i	−0.360268	−	0.624003i
$626$	−3.31837	−	12.3843i	−0.132629	−	0.494978i
$627$	21.9174	+	5.18426i	0.875298	+	0.207040i
$628$	16.2223	−	9.36594i	0.647340	−	0.373742i
$629$	5.86197	−	5.86197i	0.233732	−	0.233732i
$630$	−15.4820	−	1.89768i	−0.616816	−	0.0756055i
$631$	−2.19609	+	2.19609i	−0.0874251	+	0.0874251i	−0.749467	−	0.662042i	$-0.769690\pi$
$631$	−2.19609	+	2.19609i	−0.0874251	+	0.0874251i	0.662042	+	0.749467i	$0.269690\pi$
$632$	−2.53428	+	9.45807i	−0.100808	+	0.376222i
$633$	−8.48626	+	35.8772i	−0.337298	+	1.42599i
$634$	−28.4201	−	16.4083i	−1.12871	−	0.651659i
$635$	−3.83848	+	14.3254i	−0.152325	+	0.568486i
$636$	−7.23497	+	2.16951i	−0.286885	+	0.0860265i
$637$	−5.32645	+	24.6704i	−0.211042	+	0.977477i
$638$			18.3266i			0.725556i
$639$	−30.7865	+	10.2318i	−1.21789	+	0.404765i
$640$	−0.982571	+	1.70186i	−0.0388395	+	0.0672721i
$641$	12.7864	−	22.1467i	0.505032	−	0.874741i	−0.494951	−	0.868921i	$-0.664814\pi$
$641$	12.7864	−	22.1467i	0.505032	−	0.874741i	0.999983	−	0.00582025i	$-0.00185265\pi$
$642$	0.760874	+	25.7567i	0.0300293	+	1.01654i
$643$	−3.48176	−	3.48176i	−0.137307	−	0.137307i	0.635112	−	0.772420i	$-0.280954\pi$
$643$	−3.48176	−	3.48176i	−0.137307	−	0.137307i	−0.772420	+	0.635112i	$0.780954\pi$
$644$	−6.48667	−	5.51517i	−0.255611	−	0.217328i
$645$	−5.77697	−	3.11161i	−0.227468	−	0.122520i
$646$	−4.44826	−	7.70461i	−0.175014	−	0.303134i
$647$	3.72444	−	6.45091i	0.146423	−	0.253612i	−0.783480	−	0.621417i	$-0.786557\pi$
$647$	3.72444	−	6.45091i	0.146423	−	0.253612i	0.929903	+	0.367805i	$0.119891\pi$
$648$	1.28859	−	8.90727i	0.0506206	−	0.349911i
$649$	−6.90610	+	3.98724i	−0.271088	+	0.156513i
$650$	−1.64043	−	3.76176i	−0.0643430	−	0.147549i
$651$	10.9447	+	8.76217i	0.428958	+	0.343417i
$652$	3.37488	+	3.37488i	0.132170	+	0.132170i
$653$	−25.0837	+	14.4821i	−0.981603	+	0.566729i	−0.902754	−	0.430158i	$-0.858458\pi$
$653$	−25.0837	+	14.4821i	−0.981603	+	0.566729i	−0.0788492	+	0.996887i	$0.525125\pi$
$654$	−4.33479	+	18.3261i	−0.169504	+	0.716608i
$655$	−1.14940	+	0.307982i	−0.0449109	+	0.0120338i
$656$	−9.87024	−	2.64472i	−0.385368	−	0.103259i
$657$	−7.13843	+	34.7269i	−0.278496	+	1.35483i
$658$	0.697603	+	1.95610i	0.0271954	+	0.0762567i
$659$		−	14.9624i		−	0.582853i	−0.956593	−	0.291427i	$-0.905870\pi$
$659$		−	14.9624i		−	0.582853i	0.956593	−	0.291427i	$-0.0941299\pi$
$660$	−6.95709	+	7.38064i	−0.270804	+	0.287291i
$661$	−9.14717	−	34.1377i	−0.355784	−	1.32780i	−0.879495	−	0.475907i	$-0.842120\pi$
$661$	−9.14717	−	34.1377i	−0.355784	−	1.32780i	0.523712	−	0.851896i	$-0.324547\pi$
$662$	−3.29084	+	5.69990i	−0.127902	+	0.221533i
$663$	5.43177	+	11.5154i	0.210953	+	0.447220i
$664$	−6.83624			−0.265298
$665$	−7.62104	−	21.3696i	−0.295531	−	0.828677i
$666$	6.71228	+	10.1858i	0.260096	+	0.394693i
$667$	−17.1401	+	9.89585i	−0.663668	+	0.383169i
$668$	5.58440	+	20.8413i	0.216067	+	0.806373i
$669$	−34.2083	+	21.1210i	−1.32257	+	0.816584i
$670$	−1.28887	−	0.345352i	−0.0497934	−	0.0133421i
$671$	11.4865	+	11.4865i	0.443430	+	0.443430i
$672$	−2.86398	+	3.57737i	−0.110481	+	0.138000i
$673$		−	0.983033i		−	0.0378931i	−0.999820	−	0.0189466i	$-0.993969\pi$
$673$		−	0.983033i		−	0.0378931i	0.999820	−	0.0189466i	$-0.00603124\pi$
$674$	2.80781	−	10.4789i	0.108153	−	0.403632i
$675$	5.55496	−	2.03021i	0.213810	−	0.0781429i
$676$	3.82733	+	12.4238i	0.147205	+	0.477840i
$677$	21.1055	−	12.1853i	0.811151	−	0.468318i	−0.0362043	−	0.999344i	$-0.511527\pi$
$677$	21.1055	−	12.1853i	0.811151	−	0.468318i	0.847356	+	0.531026i	$0.178193\pi$
$678$	24.6097	+	13.2553i	0.945130	+	0.509069i
$679$	27.0907	−	2.19288i	1.03965	−	0.0841550i
$680$	4.00649			0.153642
$681$	−7.47256	+	0.220745i	−0.286349	+	0.00845898i
$682$	8.80613	−	2.35960i	0.337204	−	0.0903536i
$683$	−40.5076	+	10.8540i	−1.54998	+	0.415316i	−0.929475	−	0.368885i	$-0.879739\pi$
$683$	−40.5076	+	10.8540i	−1.54998	+	0.415316i	−0.620506	+	0.784202i	$0.713073\pi$
$684$	12.4229	−	4.12871i	0.475000	−	0.157865i
$685$	−9.17223			−0.350453
$686$	12.8381	+	13.3485i	0.490160	+	0.509650i
$687$	15.7031	−	29.1541i	0.599109	−	1.11230i
$688$	−1.66952	+	0.963895i	−0.0636497	+	0.0367482i
$689$	9.80112	+	12.2948i	0.373393	+	0.468394i
$690$	−10.6595	−	2.52135i	−0.405799	−	0.0959861i
$691$	−4.84751	+	18.0912i	−0.184408	+	0.688220i	0.810348	+	0.585948i	$0.199278\pi$
$691$	−4.84751	+	18.0912i	−0.184408	+	0.688220i	−0.994756	+	0.102272i	$0.967389\pi$
$692$			6.82658i			0.259508i
$693$	−18.6351	+	14.5656i	−0.707889	+	0.553301i
$694$	−18.0104	−	18.0104i	−0.683666	−	0.683666i
$695$	−2.28861	−	0.613230i	−0.0868118	−	0.0232611i
$696$	5.59621	+	9.06383i	0.212124	+	0.343564i
$697$	5.39200	+	20.1232i	0.204236	+	0.762221i
$698$	−15.7084	+	9.06923i	−0.594570	+	0.343275i
$699$	−26.0605	+	7.81459i	−0.985699	+	0.295575i
$700$	−2.96222	−	0.542186i	−0.111961	−	0.0204927i
$701$	12.5994			0.475874			0.237937	−	0.971281i	$-0.423529\pi$
$701$	12.5994			0.475874			0.237937	+	0.971281i	$0.423529\pi$
$702$	−18.2068	+	4.41724i	−0.687172	+	0.166718i
$703$	−8.87176	+	15.3663i	−0.334605	+	0.579552i
$704$	0.771252	+	2.87835i	0.0290677	+	0.108482i
$705$	1.94417	+	1.83260i	0.0732215	+	0.0690196i
$706$		−	20.3954i		−	0.767589i
$707$	−4.22848	−	11.8568i	−0.159028	−	0.445920i
$708$	−2.19803	+	4.08083i	−0.0826070	+	0.153367i
$709$	−25.8508	−	6.92669i	−0.970846	−	0.260137i	−0.261661	−	0.965160i	$-0.584270\pi$
$709$	−25.8508	−	6.92669i	−0.970846	−	0.260137i	−0.709185	+	0.705022i	$0.750937\pi$
$710$	20.5271	−	5.50022i	0.770368	−	0.206419i
$711$	1.73402	+	29.3239i	0.0650307	+	1.09973i
$712$	10.8555	−	6.26742i	0.406827	−	0.234882i
$713$	6.96191	+	6.96191i	0.260726	+	0.260726i
$714$	9.23584	+	1.41001i	0.345642	+	0.0527683i
$715$	19.6529	+	7.71728i	0.734975	+	0.288610i
$716$	−9.19954	+	5.31136i	−0.343803	+	0.198495i
$717$	23.5408	+	38.1277i	0.879148	+	1.42390i
$718$	−11.4503	+	19.8325i	−0.427321	+	0.740142i
$719$	3.39194	+	5.87502i	0.126498	+	0.219101i	0.922318	−	0.386433i	$-0.126293\pi$
$719$	3.39194	+	5.87502i	0.126498	+	0.219101i	−0.795819	+	0.605534i	$0.792960\pi$
$720$	−1.18704	+	5.77469i	−0.0442383	+	0.215210i
$721$	4.95212	−	27.0558i	0.184426	−	1.00761i
$722$	0.0293462	+	0.0293462i	0.00109215	+	0.00109215i
$723$	−50.3420	+	1.48714i	−1.87224	+	0.0553075i
$724$	9.84737	−	17.0562i	0.365975	−	0.633887i
$725$	−3.50005	+	6.06227i	−0.129989	+	0.225147i
$726$	−0.108438	−	3.67080i	−0.00402453	−	0.136236i
$727$		−	28.5848i		−	1.06015i	−0.847951	−	0.530075i	$-0.822164\pi$
$727$		−	28.5848i		−	1.06015i	0.847951	−	0.530075i	$-0.177836\pi$
$728$	9.13171	+	2.75897i	0.338444	+	0.102254i
$729$	−4.75922	−	26.5772i	−0.176267	−	0.984342i
$730$	6.01066	−	22.4321i	0.222464	−	0.830248i
$731$	3.40377	+	1.96517i	0.125893	+	0.0726843i
$732$	9.18841	+	2.17339i	0.339613	+	0.0803308i
$733$	12.0661	−	45.0312i	0.445671	−	1.66327i	−0.268488	−	0.963283i	$-0.586524\pi$
$733$	12.0661	−	45.0312i	0.445671	−	1.66327i	0.714159	−	0.699984i	$-0.246809\pi$
$734$	6.24995	−	6.24995i	0.230690	−	0.230690i
$735$	22.5209	+	7.77762i	0.830696	+	0.286882i
$736$	−2.27555	+	2.27555i	−0.0838780	+	0.0838780i
$737$	−1.75227	+	1.01168i	−0.0645458	+	0.0372656i
$738$	−30.6018	+	1.80958i	−1.12647	+	0.0666117i
$739$	−1.72812	−	6.44941i	−0.0635698	−	0.237246i	0.926829	−	0.375483i	$-0.122523\pi$
$739$	−1.72812	−	6.44941i	−0.0635698	−	0.237246i	−0.990399	+	0.138237i	$0.955856\pi$
$740$	−3.99534	−	6.92013i	−0.146871	−	0.254389i
$741$	−17.6087	−	20.7979i	−0.646871	−	0.764030i
$742$	11.5002	−	0.930890i	0.422184	−	0.0341740i
$743$	−1.78670	+	1.78670i	−0.0655478	+	0.0655478i	−0.739121	−	0.673573i	$-0.764759\pi$
$743$	−1.78670	+	1.78670i	−0.0655478	+	0.0655478i	0.673573	+	0.739121i	$0.264759\pi$
$744$	3.63475	−	3.85604i	0.133256	−	0.141369i
$745$	−33.7728	−	19.4987i	−1.23734	−	0.714379i
$746$	−8.16841	−	30.4849i	−0.299067	−	1.11613i
$747$	−19.4620	+	6.46817i	−0.712078	+	0.236658i
$748$	4.29590	−	4.29590i	0.157074	−	0.157074i
$749$	7.08669	−	38.7180i	0.258942	−	1.41472i
$750$	−20.0124	+	6.00100i	−0.730751	+	0.219125i
$751$	−9.91617	+	5.72510i	−0.361846	+	0.208912i	−0.669890	−	0.742460i	$-0.733659\pi$
$751$	−9.91617	+	5.72510i	−0.361846	+	0.208912i	0.308044	+	0.951372i	$0.400326\pi$
$752$	0.758199	−	0.203159i	0.0276487	−	0.00740844i
$753$	−11.8173	+	49.9597i	−0.430645	+	1.82063i
$754$	13.1709	−	17.8391i	0.479654	−	0.649663i
$755$			14.0523i			0.511417i
$756$	−4.76868	+	12.8942i	−0.173435	+	0.468956i
$757$	9.06839			0.329596			0.164798	−	0.986327i	$-0.447303\pi$
$757$	9.06839			0.329596			0.164798	+	0.986327i	$0.447303\pi$
$758$	1.46779	+	2.54228i	0.0533125	+	0.0923399i
$759$	−14.1330	+	8.72599i	−0.512994	+	0.316733i
$760$	−8.28302	+	2.21943i	−0.300457	+	0.0805071i
$761$	−7.13113	+	26.6137i	−0.258503	+	0.964747i	0.707605	+	0.706608i	$0.249776\pi$
$761$	−7.13113	+	26.6137i	−0.258503	+	0.964747i	−0.966108	+	0.258138i	$0.916891\pi$
$762$	11.5084	+	6.19869i	0.416906	+	0.224555i
$763$	12.3262	−	25.9914i	0.446238	−	0.940951i
$764$	24.1729			0.874546
$765$	11.4060	−	3.79077i	0.412386	−	0.137056i
$766$	12.6522	+	7.30475i	0.457143	+	0.263931i
$767$	9.58795	+	1.08206i	0.346201	+	0.0390708i
$768$	1.26037	+	1.18805i	0.0454799	+	0.0428699i
$769$	33.1971	+	33.1971i	1.19712	+	1.19712i	0.975025	+	0.222093i	$0.0712889\pi$
$769$	33.1971	+	33.1971i	1.19712	+	1.19712i	0.222093	+	0.975025i	$0.428711\pi$
$770$	12.7488	−	8.80394i	0.459435	−	0.317272i
$771$	−48.8956	+	14.6620i	−1.76093	+	0.528039i
$772$	−1.85200	+	6.91174i	−0.0666548	+	0.248759i
$773$	3.73452	+	13.9374i	0.134321	+	0.501294i	1.00000		0.000693289i	$0.000220681\pi$
$773$	3.73452	+	13.9374i	0.134321	+	0.501294i	−0.865679	+	0.500600i	$0.833113\pi$
$774$	−3.84093	+	4.32373i	−0.138059	+	0.155413i
$775$	3.36364	+	0.901283i	0.120825	+	0.0323751i
$776$		−	10.2728i		−	0.368773i
$777$	−6.77472	−	17.3585i	−0.243042	−	0.622733i
$778$	18.1763	−	18.1763i	0.651652	−	0.651652i
$779$	−22.2948	−	38.6158i	−0.798796	−	1.38355i
$780$	12.0763	−	2.18444i	0.432402	−	0.0782156i
$781$	16.1124	−	27.9074i	0.576546	−	0.998607i
$782$	6.33747	+	1.69812i	0.226627	+	0.0607246i
$783$	24.5076	+	20.5088i	0.875831	+	0.732926i
$784$	5.42032	−	4.42946i	0.193583	−	0.158195i
$785$	−26.0292	+	26.0292i	−0.929022	+	0.929022i
$786$	0.0309691	+	1.04835i	0.00110463	+	0.0373934i
$787$	14.1227	+	52.7068i	0.503421	+	1.87879i	0.476537	+	0.879155i	$0.341892\pi$
$787$	14.1227	+	52.7068i	0.503421	+	1.87879i	0.0268843	+	0.999639i	$0.491441\pi$
$788$	−20.1375	+	5.39583i	−0.717369	+	0.192218i
$789$	−20.3712	+	21.6114i	−0.725233	+	0.769385i
$790$		−	19.2421i		−	0.684604i
$791$	−32.5297	−	27.6577i	−1.15662	−	0.983396i
$792$	4.91905	+	7.46462i	0.174791	+	0.265244i
$793$	−2.92591	−	19.4360i	−0.103902	−	0.690192i
$794$	23.7810	+	13.7300i	0.843956	+	0.487258i
$795$	12.6299	−	7.79794i	0.447935	−	0.276565i
$796$	2.24137	+	3.88217i	0.0794433	+	0.137600i
$797$	8.06678			0.285740			0.142870	−	0.989741i	$-0.454367\pi$
$797$	8.06678			0.285740			0.142870	+	0.989741i	$0.454367\pi$
$798$	−19.8753	+	2.20121i	−0.703577	+	0.0779221i
$799$	−1.13160	−	1.13160i	−0.0400332	−	0.0400332i
$800$	−0.294591	+	1.09943i	−0.0104154	+	0.0388707i
$801$	24.9744	−	28.1137i	0.882428	−	0.993348i
$802$	8.66165	−	15.0024i	0.305854	−	0.529754i
$803$	−17.6077	−	30.4974i	−0.621361	−	1.07623i
$804$	−0.557703	+	1.03542i	−0.0196687	+	0.0365166i
$805$	15.1180	+	7.16958i	0.532839	+	0.252694i
$806$	−10.2677	−	4.03192i	−0.361664	−	0.142018i
$807$	−13.8523	+	14.6956i	−0.487625	+	0.517311i
$808$	−4.59577	+	1.23143i	−0.161679	+	0.0433217i
$809$	1.41612	+	0.817598i	0.0497882	+	0.0287452i	0.524687	−	0.851295i	$-0.324182\pi$
$809$	1.41612	+	0.817598i	0.0497882	+	0.0287452i	−0.474899	+	0.880040i	$0.657516\pi$
$810$	2.08440	+	17.5630i	0.0732385	+	0.617102i
$811$	30.0246	+	30.0246i	1.05431	+	1.05431i	0.998438	+	0.0558683i	$0.0177927\pi$
$811$	30.0246	+	30.0246i	1.05431	+	1.05431i	0.0558683	+	0.998438i	$0.482207\pi$
$812$	−5.46576	−	15.3261i	−0.191810	−	0.537842i
$813$	−20.8291	+	38.6710i	−0.730508	+	1.35625i
$814$	−11.7040	−	3.13607i	−0.410224	−	0.109919i
$815$	−8.12265	−	4.68961i	−0.284524	−	0.164270i
$816$	0.812842	−	3.43644i	0.0284552	−	0.120299i
$817$	−8.12558	−	2.17724i	−0.284278	−	0.0761720i
$818$	−8.92681			−0.312119
$819$	28.6074	−	0.785573i	0.999623	−	0.0274501i
$820$	20.0807			0.701247
$821$	−10.3146	−	2.76379i	−0.359982	−	0.0964570i	0.0742948	−	0.997236i	$-0.476329\pi$
$821$	−10.3146	−	2.76379i	−0.359982	−	0.0964570i	−0.434277	+	0.900779i	$0.642996\pi$
$822$	−1.86088	+	7.86720i	−0.0649055	+	0.274400i
$823$	−11.5585	−	6.67330i	−0.402904	−	0.232617i	0.284832	−	0.958577i	$-0.408062\pi$
$823$	−11.5585	−	6.67330i	−0.402904	−	0.232617i	−0.687736	+	0.725961i	$0.741395\pi$
$824$	−10.0418	−	2.69068i	−0.349822	−	0.0937344i
$825$	−2.78583	+	5.17214i	−0.0969903	+	0.180071i
$826$	4.58627	−	5.39414i	0.159577	−	0.187686i
$827$	22.7698	+	22.7698i	0.791784	+	0.791784i	0.981784	−	0.190000i	$-0.0608489\pi$
$827$	22.7698	+	22.7698i	0.791784	+	0.791784i	−0.190000	+	0.981784i	$0.560849\pi$
$828$	−4.32522	+	8.63129i	−0.150312	+	0.299958i
$829$	12.3778	+	7.14635i	0.429900	+	0.248203i	0.699304	−	0.714824i	$-0.253493\pi$
$829$	12.3778	+	7.14635i	0.429900	+	0.248203i	−0.269404	+	0.963027i	$0.586827\pi$
$830$	12.9764	−	3.47702i	0.450418	−	0.120689i
$831$	33.9841	−	36.0531i	1.17890	−	1.25067i
$832$	1.31786	−	3.35607i	0.0456887	−	0.116351i
$833$	−13.3462	−	5.05496i	−0.462419	−	0.175144i
$834$	−0.990295	+	1.83857i	−0.0342911	+	0.0636644i
$835$	−21.2004	−	36.7202i	−0.733671	−	1.27076i
$836$	−6.50161	+	11.2611i	−0.224863	+	0.389474i
$837$	6.69932	−	14.4168i	0.231562	−	0.498316i
$838$	0.674538	−	2.51741i	0.0233015	−	0.0869624i
$839$	−14.2522	−	14.2522i	−0.492039	−	0.492039i	0.416909	−	0.908948i	$-0.363113\pi$
$839$	−14.2522	−	14.2522i	−0.492039	−	0.492039i	−0.908948	+	0.416909i	$0.863113\pi$
$840$	3.61685	−	8.24717i	0.124793	−	0.284555i
$841$	−8.82353			−0.304260
$842$	−8.38544	−	14.5240i	−0.288981	−	0.500530i
$843$	−0.935286	+	0.577466i	−0.0322130	+	0.0198890i
$844$	−18.4336	−	10.6426i	−0.634511	−	0.366335i
$845$	−13.5839	−	21.6361i	−0.467301	−	0.744303i
$846$	1.96629	−	1.29575i	0.0676024	−	0.0445487i
$847$	−1.00998	+	5.51802i	−0.0347034	+	0.189601i
$848$		−	4.36087i		−	0.149753i
$849$	34.2398	−	36.3244i	1.17511	−	1.24665i
$850$	2.24149	−	0.600606i	0.0768825	−	0.0206006i
$851$	−3.38678	−	12.6397i	−0.116097	−	0.433282i
$852$	−0.553074	−	18.7224i	−0.0189480	−	0.641418i
$853$	−5.05730	+	5.05730i	−0.173159	+	0.173159i	−0.788366	−	0.615207i	$-0.789072\pi$
$853$	−5.05730	+	5.05730i	−0.173159	+	0.173159i	0.615207	+	0.788366i	$0.289072\pi$
$854$	−13.0316	−	6.18014i	−0.445933	−	0.211480i
$855$	−21.4809	+	14.1555i	−0.734631	+	0.484108i
$856$	−14.3702	−	3.85048i	−0.491163	−	0.131607i
$857$	19.7039	−	34.1282i	0.673074	−	1.16580i	−0.303954	−	0.952687i	$-0.598307\pi$
$857$	19.7039	−	34.1282i	0.673074	−	1.16580i	0.977028	−	0.213112i	$-0.0683598\pi$
$858$	10.6065	−	15.2909i	0.362098	−	0.522024i
$859$	4.30239	+	7.45195i	0.146796	+	0.254257i	0.930041	−	0.367455i	$-0.119771\pi$
$859$	4.30239	+	7.45195i	0.146796	+	0.254257i	−0.783246	+	0.621712i	$0.786437\pi$
$860$	2.67879	−	2.67879i	0.0913460	−	0.0913460i
$861$	46.2903	+	7.06702i	1.57757	+	0.240843i
$862$			19.8562i			0.676304i
$863$	−18.7890	−	5.03450i	−0.639585	−	0.171376i	−0.0755695	−	0.997141i	$-0.524077\pi$
$863$	−18.7890	−	5.03450i	−0.639585	−	0.171376i	−0.564015	+	0.825764i	$0.690744\pi$
$864$	4.71223	+	2.18972i	0.160313	+	0.0744959i
$865$	−3.47211	−	12.9581i	−0.118055	−	0.440589i
$866$	−2.26456	+	8.45143i	−0.0769527	+	0.287191i
$867$	21.3080	−	6.38950i	0.723659	−	0.216999i
$868$	−6.66066	+	4.59964i	−0.226077	+	0.156122i
$869$	−20.6321	−	20.6321i	−0.699897	−	0.699897i
$870$	−15.2326	−	14.3585i	−0.516435	−	0.486798i
$871$	2.43274	+	0.274549i	0.0824301	+	0.00930273i
$872$	−9.41591	−	5.43628i	−0.318863	−	0.184096i
$873$	−9.71972	−	29.2456i	−0.328963	−	0.989813i
$874$	−14.0428			−0.475004
$875$	31.8102	−	2.57490i	1.07538	−	0.0870476i
$876$	−18.0210	−	9.70651i	−0.608872	−	0.327952i
$877$	11.7179	−	43.7318i	0.395686	−	1.47672i	−0.424923	−	0.905229i	$-0.639699\pi$
$877$	11.7179	−	43.7318i	0.395686	−	1.47672i	0.820609	−	0.571490i	$-0.193634\pi$
$878$	20.0931	−	5.38393i	0.678109	−	0.181699i
$879$	−5.46012	+	3.37120i	−0.184165	+	0.113708i
$880$	−2.92795	−	5.07136i	−0.0987013	−	0.170956i
$881$	14.0771			0.474270			0.237135	−	0.971477i	$-0.423792\pi$
$881$	14.0771			0.474270			0.237135	+	0.971477i	$0.423792\pi$
$882$	11.2401	−	17.7387i	0.378473	−	0.597292i
$883$			14.6606i			0.493369i	0.969096	+	0.246684i	$0.0793411\pi$
$883$			14.6606i			0.493369i	−0.969096	+	0.246684i	$0.920659\pi$
$884$	−7.26901	+	1.09428i	−0.244483	+	0.0368047i
$885$	2.09668	−	8.86412i	0.0704793	−	0.297964i
$886$	−2.63118	+	0.705024i	−0.0883963	+	0.0236857i
$887$	−29.8300	+	17.2224i	−1.00159	+	0.578270i	−0.908719	−	0.417408i	$-0.862939\pi$
$887$	−29.8300	+	17.2224i	−1.00159	+	0.578270i	−0.0928742	+	0.995678i	$0.529605\pi$
$888$	−6.74610	+	2.02291i	−0.226384	+	0.0678844i
$889$	−15.2121	−	12.9338i	−0.510197	−	0.433785i
$890$	−17.4180	+	17.4180i	−0.583852	+	0.583852i
$891$	21.0667	+	16.5968i	0.705761	+	0.556012i
$892$	−6.00755	−	22.4205i	−0.201148	−	0.750693i
$893$	2.96634	+	1.71262i	0.0992647	+	0.0573105i
$894$	−23.5763	+	25.0117i	−0.788510	+	0.836515i
$895$	14.7610	−	14.7610i	0.493405	−	0.493405i
$896$	−1.50343	−	2.17709i	−0.0502260	−	0.0727313i
$897$	20.0282	+	1.66311i	0.668723	+	0.0555296i
$898$	15.8515	+	27.4556i	0.528971	+	0.916204i
$899$	4.86988	+	18.1747i	0.162420	+	0.606159i
$900$	0.201567	+	3.40869i	0.00671888	+	0.113623i
$901$	−7.69970	+	4.44542i	−0.256514	+	0.148098i
$902$	21.5312	−	21.5312i	0.716911	−	0.716911i
$903$	7.11796	−	5.23245i	0.236871	−	0.174125i
$904$	−11.4116	+	11.4116i	−0.379543	+	0.379543i
$905$	−10.0171	+	37.3842i	−0.332979	+	1.24269i
$906$	12.0530	+	2.85096i	0.400433	+	0.0947168i
$907$	32.7408	+	18.9029i	1.08714	+	0.627661i	0.932814	−	0.360358i	$-0.117346\pi$
$907$	32.7408	+	18.9029i	1.08714	+	0.627661i	0.154328	+	0.988020i	$0.450679\pi$
$908$	1.11711	−	4.16910i	0.0370725	−	0.138356i
$909$	−11.9185	+	7.85409i	−0.395313	+	0.260504i
$910$	−18.7369	−	0.592487i	−0.621122	−	0.0196407i
$911$			21.3678i			0.707946i	0.935256	+	0.353973i	$0.115169\pi$
$911$			21.3678i			0.707946i	−0.935256	+	0.353973i	$0.884831\pi$
$912$	0.223174	+	7.55478i	0.00739004	+	0.250164i
$913$	10.1856	−	17.6420i	0.337095	−	0.583865i
$914$	9.38465	−	16.2547i	0.310417	−	0.537657i
$915$	−18.5467	+	0.547884i	−0.613135	+	0.0181125i
$916$	13.5188	+	13.5188i	0.446674	+	0.446674i
$917$	0.288442	−	1.57590i	0.00952520	−	0.0520407i
$918$	−0.937347	−	10.5522i	−0.0309371	−	0.348276i
$919$	16.8905	+	29.2552i	0.557165	+	0.965039i	0.997732	+	0.0673187i	$0.0214444\pi$
$919$	16.8905	+	29.2552i	0.557165	+	0.965039i	−0.440566	+	0.897720i	$0.645222\pi$
$920$	3.16203	−	5.47680i	0.104249	−	0.180565i
$921$	13.6810	+	22.1584i	0.450806	+	0.730143i
$922$	−30.7893	+	17.7762i	−1.01399	+	0.585429i
$923$	−35.7402	+	15.5856i	−1.17640	+	0.513007i
$924$	−4.96480	−	12.7211i	−0.163330	−	0.418492i
$925$	−3.27264	−	3.27264i	−0.107604	−	0.107604i
$926$	−20.5706	+	11.8764i	−0.675991	+	0.390284i
$927$	−31.1336	+	1.84103i	−1.02256	+	0.0604674i
$928$	−5.94052	+	1.59176i	−0.195007	+	0.0522520i
$929$	29.4538	+	7.89212i	0.966347	+	0.258932i	0.707285	−	0.706929i	$-0.249920\pi$
$929$	29.4538	+	7.89212i	0.966347	+	0.258932i	0.259062	+	0.965861i	$0.416587\pi$
$930$	−4.93818	+	9.16815i	−0.161929	+	0.300636i
$931$	30.3922	+	3.05738i	0.996064	+	0.100201i
$932$		−	15.7079i		−	0.514530i
$933$	18.0938	+	17.0555i	0.592364	+	0.558371i
$934$	−3.33052	−	12.4297i	−0.108978	−	0.406711i
$935$	−5.96944	+	10.3394i	−0.195222	+	0.338134i
$936$	0.576428	−	10.8013i	0.0188411	−	0.353051i
$937$	−57.8553			−1.89005			−0.945025	−	0.326997i	$-0.893963\pi$
$937$	−57.8553			−1.89005			−0.945025	+	0.326997i	$0.893963\pi$
$938$	1.16367	−	1.36865i	0.0379950	−	0.0446879i
$939$	21.2712	−	6.37847i	0.694160	−	0.208153i
$940$	−1.33587	+	0.771265i	−0.0435713	+	0.0251559i
$941$	6.01742	+	22.4573i	0.196162	+	0.732088i	0.991963	+	0.126529i	$0.0403838\pi$
$941$	6.01742	+	22.4573i	0.196162	+	0.732088i	−0.795800	+	0.605559i	$0.792950\pi$
$942$	17.0449	+	27.6066i	0.555352	+	0.899471i
$943$	31.7636	+	8.51103i	1.03437	+	0.277157i
$944$	−1.89229	−	1.89229i	−0.0615887	−	0.0615887i
$945$	2.49364	−	26.9009i	0.0811182	−	0.875087i
$946$		−	5.74460i		−	0.186773i
$947$	1.45149	−	5.41704i	0.0471671	−	0.176030i	−0.938324	−	0.345757i	$-0.887622\pi$
$947$	1.45149	−	5.41704i	0.0471671	−	0.176030i	0.985491	+	0.169727i	$0.0542887\pi$
$948$	−16.5043	−	3.90387i	−0.536036	−	0.126792i
$949$	−4.77837	+	42.3404i	−0.155112	+	1.37443i
$950$	−4.30135	+	2.48339i	−0.139554	+	0.0805717i
$951$	26.9542	−	50.0427i	0.874049	−	1.62275i
$952$	−2.31136	+	4.87380i	−0.0749115	+	0.157961i
$953$	56.2129			1.82091			0.910457	−	0.413605i	$-0.135730\pi$
$953$	56.2129			1.82091			0.910457	+	0.413605i	$0.135730\pi$
$954$	−4.12608	−	12.4149i	−0.133587	−	0.401948i
$955$	−45.8846	+	12.2948i	−1.48479	+	0.397849i
$956$	−24.9892	+	6.69585i	−0.808210	+	0.216559i
$957$	−31.7287	+	0.937291i	−1.02564	+	0.0302983i
$958$	−21.5509			−0.696279
$959$	5.29149	−	11.1578i	0.170871	−	0.360304i
$960$	−2.99668	−	1.61408i	−0.0967175	−	0.0520943i
$961$	−18.7407	+	10.8199i	−0.604537	+	0.349030i
$962$	9.13885	+	11.4640i	0.294649	+	0.369615i
$963$	−44.5536	+	2.63459i	−1.43572	+	0.0848986i
$964$	7.52585	−	28.0869i	0.242391	−	0.904617i
$965$		−	14.0617i		−	0.452662i
$966$	9.21664	−	11.5124i	0.296541	−	0.370406i
$967$	−15.9991	−	15.9991i	−0.514498	−	0.514498i	0.401403	−	0.915901i	$-0.368523\pi$
$967$	−15.9991	−	15.9991i	−0.514498	−	0.514498i	−0.915901	+	0.401403i	$0.868523\pi$
$968$	2.04802	+	0.548765i	0.0658258	+	0.0176380i
$969$	13.1115	−	8.09530i	0.421201	−	0.260058i
$970$	5.22493	+	19.4997i	0.167762	+	0.626097i
$971$	−52.6319	+	30.3870i	−1.68904	+	0.975166i	−0.733781	+	0.679386i	$0.762246\pi$
$971$	−52.6319	+	30.3870i	−1.68904	+	0.975166i	−0.955256	+	0.295780i	$0.904421\pi$
$972$	15.4870	+	1.77538i	0.496747	+	0.0569453i
$973$	2.06628	−	2.43026i	0.0662420	−	0.0779106i
$974$	7.00410			0.224426
$975$	6.42883	−	3.03246i	0.205887	−	0.0971166i
$976$	−2.72566	+	4.72098i	−0.0872461	+	0.151115i
$977$	5.40149	+	20.1587i	0.172809	+	0.644932i	0.996914	+	0.0784958i	$0.0250117\pi$
$977$	5.40149	+	20.1587i	0.172809	+	0.644932i	−0.824105	+	0.566437i	$0.808322\pi$
$978$	−5.67030	+	6.01551i	−0.181316	+	0.192355i
$979$			37.3524i			1.19379i
$980$	−8.03586	+	11.1648i	−0.256696	+	0.356646i
$981$	−31.9496	−	6.56753i	−1.02007	−	0.209685i
$982$	4.42582	+	1.18590i	0.141234	+	0.0378435i
$983$	−32.1403	+	8.61197i	−1.02512	+	0.274679i	−0.731933	−	0.681377i	$-0.761382\pi$
$983$	−32.1403	+	8.61197i	−1.02512	+	0.274679i	−0.293184	+	0.956056i	$0.594715\pi$
$984$	4.07399	−	17.2236i	0.129874	−	0.549067i
$985$	35.4802	−	20.4845i	1.13049	−	0.652691i
$986$	8.86616	+	8.86616i	0.282356	+	0.282356i
$987$	−3.35091	+	1.30780i	−0.106661	+	0.0416277i
$988$	14.4218	−	6.28905i	0.458818	−	0.200081i
$989$	5.37270	−	3.10193i	0.170842	−	0.0986356i
$990$	−13.1339	−	11.6673i	−0.417422	−	0.370811i
$991$	0.657213	−	1.13833i	0.0208771	−	0.0361601i	−0.855398	−	0.517971i	$-0.826687\pi$
$991$	0.657213	−	1.13833i	0.0208771	−	0.0361601i	0.876275	+	0.481811i	$0.160021\pi$
$992$	1.52972	+	2.64955i	0.0485686	+	0.0841233i
$993$	−10.0365	−	5.40590i	−0.318499	−	0.171551i
$994$	−5.15126	+	28.1438i	−0.163388	+	0.892668i
$995$	−6.22906	−	6.22906i	−0.197475	−	0.197475i
$996$	−0.349632	−	11.8356i	−0.0110785	−	0.375024i
$997$	8.63838	−	14.9621i	0.273580	−	0.473855i	−0.696196	−	0.717852i	$-0.745125\pi$
$997$	8.63838	−	14.9621i	0.273580	−	0.473855i	0.969776	+	0.243997i	$0.0784588\pi$
$998$	5.24789	−	9.08962i	0.166119	−	0.287727i
$999$	−17.2914	+	12.1419i	−0.547076	+	0.384152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.11	yes	144
3.2	odd	2	inner	546.2.bv.a.515.31	yes	144
7.2	even	3	inner	546.2.bv.a.359.31	yes	144
13.5	odd	4	inner	546.2.bv.a.473.11	yes	144
21.2	odd	6	inner	546.2.bv.a.359.11	yes	144
39.5	even	4	inner	546.2.bv.a.473.31	yes	144
91.44	odd	12	inner	546.2.bv.a.317.31	yes	144
273.44	even	12	inner	546.2.bv.a.317.11	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.11	✓	144	273.44	even	12	inner
546.2.bv.a.317.31	yes	144	91.44	odd	12	inner
546.2.bv.a.359.11	yes	144	21.2	odd	6	inner
546.2.bv.a.359.31	yes	144	7.2	even	3	inner
546.2.bv.a.473.11	yes	144	13.5	odd	4	inner
546.2.bv.a.473.31	yes	144	39.5	even	4	inner
546.2.bv.a.515.11	yes	144	1.1	even	1	trivial
546.2.bv.a.515.31	yes	144	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.398691 - 1.68554i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.89818 - 0.508616i) q^{5} +(-0.821356 + 1.52492i) q^{6} +(1.71379 - 2.01567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68209 - 1.34402i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.398691 - 1.68554i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.89818 - 0.508616i) q^{5} +(-0.821356 + 1.52492i) q^{6} +(1.71379 - 2.01567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68209 - 1.34402i) q^{9} +(1.70186 + 0.982571i) q^{10} +(2.87835 - 0.771252i) q^{11} +(1.18805 - 1.26037i) q^{12} +(-3.35607 - 1.31786i) q^{13} +(-2.17709 + 1.50343i) q^{14} +(-1.61408 + 2.99668i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.01939 - 1.76563i) q^{17} +(2.24284 + 1.99240i) q^{18} +(-1.12940 + 4.21497i) q^{19} +(-1.38957 - 1.38957i) q^{20} +(-2.71422 - 3.69229i) q^{21} -2.97989 q^{22} +(-1.60906 - 2.78697i) q^{23} +(-1.47377 + 0.909940i) q^{24} +(-0.985722 - 0.569107i) q^{25} +(2.90063 + 2.14157i) q^{26} +(-3.33472 + 3.98492i) q^{27} +(2.49202 - 0.888729i) q^{28} -6.15008i q^{29} +(2.33468 - 2.47682i) q^{30} +(-2.95519 + 0.791840i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.152403 - 5.15907i) q^{33} +(-1.44163 + 1.44163i) q^{34} +(-4.27828 + 2.95445i) q^{35} +(-1.65075 - 2.50500i) q^{36} +(3.92765 + 1.05241i) q^{37} +(2.18183 - 3.77904i) q^{38} +(-3.55935 + 5.13138i) q^{39} +(0.982571 + 1.70186i) q^{40} +(-7.22551 + 7.22551i) q^{41} +(1.66610 + 4.26897i) q^{42} +1.92779i q^{43} +(2.87835 + 0.771252i) q^{44} +(4.40751 + 3.91535i) q^{45} +(0.832911 + 3.10846i) q^{46} +(0.203159 - 0.758199i) q^{47} +(1.65907 - 0.497493i) q^{48} +(-1.12586 - 6.90887i) q^{49} +(0.804839 + 0.804839i) q^{50} +(-2.56962 - 2.42216i) q^{51} +(-2.24751 - 2.81934i) q^{52} +(-3.77663 - 2.18044i) q^{53} +(4.25247 - 2.98605i) q^{54} -5.85591 q^{55} +(-2.63713 + 0.213464i) q^{56} +(6.65422 + 3.58412i) q^{57} +(-1.59176 + 5.94052i) q^{58} +(-2.58491 + 0.692626i) q^{59} +(-2.89618 + 1.78816i) q^{60} +(2.72566 + 4.72098i) q^{61} +3.05944 q^{62} +(-7.30564 + 3.10285i) q^{63} +1.00000i q^{64} +(5.70016 + 4.20850i) q^{65} +(-1.18806 + 5.02272i) q^{66} +(-0.655866 + 0.175739i) q^{67} +(1.76563 - 1.01939i) q^{68} +(-5.33907 + 1.60099i) q^{69} +(4.89717 - 1.74648i) q^{70} +(7.64671 - 7.64671i) q^{71} +(0.946159 + 2.84689i) q^{72} +(-3.05864 - 11.4150i) q^{73} +(-3.52144 - 2.03310i) q^{74} +(-1.35225 + 1.43458i) q^{75} +(-3.08557 + 3.08557i) q^{76} +(3.37829 - 7.12357i) q^{77} +(4.76616 - 4.03530i) q^{78} +(-4.89586 - 8.47987i) q^{79} +(-0.508616 - 1.89818i) q^{80} +(5.38722 + 7.20957i) q^{81} +(8.84941 - 5.10921i) q^{82} +(4.83395 - 4.83395i) q^{83} +(-0.504442 - 4.55473i) q^{84} +(-2.83301 + 2.83301i) q^{85} +(0.498949 - 1.86210i) q^{86} +(-10.3662 - 2.45198i) q^{87} +(-2.58066 - 1.48994i) q^{88} +(-3.24426 + 12.1077i) q^{89} +(-3.24396 - 4.92268i) q^{90} +(-8.40798 + 4.50621i) q^{91} -3.21812i q^{92} +(0.156471 + 5.29679i) q^{93} +(-0.392473 + 0.679782i) q^{94} +(4.28760 - 7.42635i) q^{95} +(-1.73130 + 0.0511439i) q^{96} +(7.26398 + 7.26398i) q^{97} +(-0.700646 + 6.96485i) q^{98} +(-8.75658 - 1.79999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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