LMFDB - Embedded newform 546.2.bv.a.515.31

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			515.31
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(1.26037 - 1.18805i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.89818 + 0.508616i) q^{5} +(1.52492 - 0.821356i) q^{6} +(1.71379 - 2.01567i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.177090 - 2.99477i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(1.26037 - 1.18805i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.89818 + 0.508616i) q^{5} +(1.52492 - 0.821356i) q^{6} +(1.71379 - 2.01567i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.177090 - 2.99477i) q^{9} +(1.70186 + 0.982571i) q^{10} +(-2.87835 + 0.771252i) q^{11} +(1.68554 - 0.398691i) q^{12} +(-3.35607 - 1.31786i) q^{13} +(2.17709 - 1.50343i) q^{14} +(2.99668 - 1.61408i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.01939 + 1.76563i) q^{17} +(0.946159 - 2.84689i) q^{18} +(-1.12940 + 4.21497i) q^{19} +(1.38957 + 1.38957i) q^{20} +(-0.234697 - 4.57656i) q^{21} -2.97989 q^{22} +(1.60906 + 2.78697i) q^{23} +(1.73130 + 0.0511439i) 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} +(3.31233 - 0.783485i) q^{30} +(-2.95519 + 0.791840i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.71152 + 4.39168i) 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} +(-5.79559 + 2.32617i) q^{39} +(0.982571 + 1.70186i) q^{40} +(7.22551 - 7.22551i) q^{41} +(0.957802 - 4.48136i) q^{42} +1.92779i q^{43} +(-2.87835 - 0.771252i) q^{44} +(1.85934 - 5.59455i) 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} +(0.812842 + 3.43644i) q^{51} +(-2.24751 - 2.81934i) q^{52} +(3.77663 + 2.18044i) q^{53} +(-2.18972 - 4.71223i) q^{54} -5.85591 q^{55} +(2.63713 - 0.213464i) q^{56} +(3.58412 + 6.65422i) q^{57} +(-1.59176 + 5.94052i) q^{58} +(2.58491 - 0.692626i) q^{59} +(3.40224 + 0.100505i) q^{60} +(2.72566 + 4.72098i) q^{61} -3.05944 q^{62} +(-5.73297 - 5.48935i) q^{63} +1.00000i q^{64} +(-5.70016 - 4.20850i) q^{65} +(-3.75578 + 3.54025i) 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} +(2.24284 - 1.99240i) q^{72} +(-3.05864 - 11.4150i) q^{73} +(3.52144 + 2.03310i) q^{74} +(-1.91850 + 0.453796i) q^{75} +(-3.08557 + 3.08557i) q^{76} +(-3.37829 + 7.12357i) q^{77} +(-6.20017 + 0.746900i) q^{78} +(-4.89586 - 8.47987i) q^{79} +(0.508616 + 1.89818i) q^{80} +(-8.93728 - 1.06069i) q^{81} +(8.84941 - 5.10921i) q^{82} +(-4.83395 + 4.83395i) q^{83} +(2.08503 - 4.08077i) q^{84} +(-2.83301 + 2.83301i) q^{85} +(-0.498949 + 1.86210i) q^{86} +(7.30659 + 7.75141i) 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} +(-2.78390 + 4.50892i) q^{93} +(-0.392473 + 0.679782i) q^{94} +(-4.28760 + 7.42635i) q^{95} +(1.47377 + 0.909940i) q^{96} +(7.26398 + 7.26398i) q^{97} +(0.700646 - 6.96485i) q^{98} +(1.79999 + 8.75658i) 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
$3$	1.26037	−	1.18805i	0.727678	−	0.685919i
$3$	1.26037	−	1.18805i	0.727678	−	0.685919i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.89818	+	0.508616i	0.848893	+	0.227460i	0.656939	−	0.753944i	$-0.271851\pi$
$5$	1.89818	+	0.508616i	0.848893	+	0.227460i	0.191954	+	0.981404i	$0.438518\pi$
$6$	1.52492	−	0.821356i	0.622545	−	0.335317i
$7$	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
$9$	0.177090	−	2.99477i	0.0590301	−	0.998256i
$10$	1.70186	+	0.982571i	0.538177	+	0.310716i
$11$	−2.87835	+	0.771252i	−0.867856	+	0.232541i	−0.665160	−	0.746701i	$-0.731637\pi$
$11$	−2.87835	+	0.771252i	−0.867856	+	0.232541i	−0.202695	+	0.979242i	$0.564970\pi$
$12$	1.68554	−	0.398691i	0.486574	−	0.115092i
$13$	−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
$15$	2.99668	−	1.61408i	0.773740	−	0.416754i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.01939	+	1.76563i	−0.247238	+	0.428229i	−0.962758	−	0.270363i	$-0.912856\pi$
$17$	−1.01939	+	1.76563i	−0.247238	+	0.428229i	0.715520	+	0.698592i	$0.246190\pi$
$18$	0.946159	−	2.84689i	0.223012	−	0.671018i
$19$	−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
$21$	−0.234697	−	4.57656i	−0.0512150	−	0.998688i
$22$	−2.97989			−0.635314
$23$	1.60906	+	2.78697i	0.335512	+	0.581124i	0.983583	−	0.180456i	$-0.0577573\pi$
$23$	1.60906	+	2.78697i	0.335512	+	0.581124i	−0.648071	+	0.761580i	$0.724424\pi$
$24$	1.73130	+	0.0511439i	0.353399	+	0.0104397i
$25$	−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	$0.193452\pi$
$29$			6.15008i			1.14204i	−0.820935	+	0.571021i	$0.806548\pi$
$30$	3.31233	−	0.783485i	0.604745	−	0.143044i
$31$	−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
$33$	−2.71152	+	4.39168i	−0.472015	+	0.764494i
$34$	−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
$39$	−5.79559	+	2.32617i	−0.928038	+	0.372486i
$40$	0.982571	+	1.70186i	0.155358	+	0.269088i
$41$	7.22551	−	7.22551i	1.12844	−	1.12844i	0.138004	−	0.990432i	$-0.455931\pi$
$41$	7.22551	−	7.22551i	1.12844	−	1.12844i	0.990432	−	0.138004i	$-0.0440687\pi$
$42$	0.957802	−	4.48136i	0.147792	−	0.691489i
$43$			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
$45$	1.85934	−	5.59455i	0.277174	−	0.833986i
$46$	0.832911	+	3.10846i	0.122806	+	0.458318i
$47$	−0.203159	+	0.758199i	−0.0296338	+	0.110595i	−0.979159	−	0.203097i	$-0.934899\pi$
$47$	−0.203159	+	0.758199i	−0.0296338	+	0.110595i	0.949525	+	0.313692i	$0.101566\pi$
$48$	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
$51$	0.812842	+	3.43644i	0.113821	+	0.481198i
$52$	−2.24751	−	2.81934i	−0.311674	−	0.390972i
$53$	3.77663	+	2.18044i	0.518759	+	0.299506i	0.736427	−	0.676517i	$-0.236512\pi$
$53$	3.77663	+	2.18044i	0.518759	+	0.299506i	−0.217667	+	0.976023i	$0.569845\pi$
$54$	−2.18972	−	4.71223i	−0.297984	−	0.641253i
$55$	−5.85591			−0.789610
$56$	2.63713	−	0.213464i	0.352401	−	0.0285253i
$57$	3.58412	+	6.65422i	0.474728	+	0.881373i
$58$	−1.59176	+	5.94052i	−0.209008	+	0.780029i
$59$	2.58491	−	0.692626i	0.336527	−	0.0901722i	−0.0865982	−	0.996243i	$-0.527600\pi$
$59$	2.58491	−	0.692626i	0.336527	−	0.0901722i	0.423125	+	0.906071i	$0.360933\pi$
$60$	3.40224	+	0.100505i	0.439228	+	0.0129751i
$61$	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
$63$	−5.73297	−	5.48935i	−0.722287	−	0.691594i
$64$			1.00000i			0.125000i
$65$	−5.70016	−	4.20850i	−0.707017	−	0.522000i
$66$	−3.75578	+	3.54025i	−0.462304	+	0.435774i
$67$	−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	−0.996070	−	0.0885725i	$-0.971769\pi$
$71$	−7.64671	+	7.64671i	−0.907497	+	0.907497i	0.0885725	+	0.996070i	$0.471769\pi$
$72$	2.24284	−	1.99240i	0.264322	−	0.234807i
$73$	−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
$75$	−1.91850	+	0.453796i	−0.221530	+	0.0523998i
$76$	−3.08557	+	3.08557i	−0.353939	+	0.353939i
$77$	−3.37829	+	7.12357i	−0.384992	+	0.811806i
$78$	−6.20017	+	0.746900i	−0.702031	+	0.0845698i
$79$	−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
$81$	−8.93728	−	1.06069i	−0.993031	−	0.117854i
$82$	8.84941	−	5.10921i	0.977254	−	0.564218i
$83$	−4.83395	+	4.83395i	−0.530595	+	0.530595i	−0.920749	−	0.390154i	$-0.872422\pi$
$83$	−4.83395	+	4.83395i	−0.530595	+	0.530595i	0.390154	+	0.920749i	$0.372422\pi$
$84$	2.08503	−	4.08077i	0.227495	−	0.445248i
$85$	−2.83301	+	2.83301i	−0.307284	+	0.307284i
$86$	−0.498949	+	1.86210i	−0.0538030	+	0.200796i
$87$	7.30659	+	7.75141i	0.783348	+	0.831039i
$88$	−2.58066	−	1.48994i	−0.275099	−	0.158829i
$89$	3.24426	−	12.1077i	0.343890	−	1.28342i	−0.550013	−	0.835156i	$-0.685377\pi$
$89$	3.24426	−	12.1077i	0.343890	−	1.28342i	0.893903	−	0.448260i	$-0.147956\pi$
$90$	3.24396	−	4.92268i	0.341943	−	0.518896i
$91$	−8.40798	+	4.50621i	−0.881396	+	0.472379i
$92$			3.21812i			0.335512i
$93$	−2.78390	+	4.50892i	−0.288677	+	0.467553i
$94$	−0.392473	+	0.679782i	−0.0404805	+	0.0701142i
$95$	−4.28760	+	7.42635i	−0.439899	+	0.761927i
$96$	1.47377	+	0.909940i	0.150416	+	0.0928703i
$97$	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
$99$	1.79999	+	8.75658i	0.180906	+	0.880069i
$100$	−0.569107	−	0.985722i	−0.0569107	−	0.0985722i
$101$	−2.37895	+	4.12046i	−0.236714	+	0.410001i	−0.959769	−	0.280789i	$-0.909404\pi$
$101$	−2.37895	+	4.12046i	−0.236714	+	0.410001i	0.723055	+	0.690790i	$0.242737\pi$
$102$	−0.104271	+	3.52972i	−0.0103244	+	0.349495i
$103$	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
$105$	1.88222	−	8.80652i	0.183686	−	0.859428i
$106$	3.08360	+	3.08360i	0.299506	+	0.299506i
$107$	−12.8840	+	7.43856i	−1.24554	+	0.719113i	−0.970217	−	0.242238i	$-0.922118\pi$
$107$	−12.8840	+	7.43856i	−1.24554	+	0.719113i	−0.275324	+	0.961352i	$0.588785\pi$
$108$	−0.895495	−	5.11841i	−0.0861690	−	0.492519i
$109$	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
$111$	6.20063	−	3.33980i	0.588538	−	0.317000i
$112$	2.60252	+	0.476348i	0.245915	+	0.0450106i
$113$			16.1384i			1.51817i	0.650991	+	0.759085i	$0.274353\pi$
$113$			16.1384i			1.51817i	−0.650991	+	0.759085i	$0.725647\pi$
$114$	1.73975	+	7.35512i	0.162943	+	0.688870i
$115$	1.63679	+	6.10858i	0.152631	+	0.569628i
$116$	−3.07504	+	5.32613i	−0.285510	+	0.494519i
$117$	−4.54102	+	9.81729i	−0.419818	+	0.907609i
$118$	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
$123$	0.522609	−	17.6911i	0.0471221	−	1.59515i
$124$	−2.95519	−	0.791840i	−0.265384	−	0.0711094i
$125$	−8.52945	−	8.52945i	−0.762897	−	0.762897i
$126$	−4.11688	−	6.78611i	−0.366761	−	0.604555i
$127$		−	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
$129$	2.29031	+	2.42974i	0.201650	+	0.213927i
$130$	−4.41669	−	5.54041i	−0.387369	−	0.485926i
$131$	−0.524403	+	0.302764i	−0.0458173	+	0.0264526i	−0.522734	−	0.852496i	$-0.675088\pi$
$131$	−0.524403	+	0.302764i	−0.0458173	+	0.0264526i	0.476916	+	0.878949i	$0.341754\pi$
$132$	−4.54409	+	2.44755i	−0.395512	+	0.213032i
$133$	6.56045	+	9.50006i	0.568863	+	0.823759i
$134$	−0.679003			−0.0586569
$135$	−4.30312	−	9.26021i	−0.370353	−	0.796992i
$136$	−1.96931	+	0.527674i	−0.168867	+	0.0452477i
$137$	−4.50842	+	1.20803i	−0.385181	+	0.103209i	−0.446213	−	0.894927i	$-0.647228\pi$
$137$	−4.50842	+	1.20803i	−0.385181	+	0.103209i	0.0610320	+	0.998136i	$0.480561\pi$
$138$	4.74278	+	2.92829i	0.403732	+	0.249273i
$139$	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
$141$	0.644719	+	1.19698i	0.0542952	+	0.100804i
$142$	−9.36527	+	5.40704i	−0.785916	+	0.453749i
$143$	10.6764	+	1.20489i	0.892803	+	0.100758i
$144$	2.68209	−	1.34402i	0.223508	−	0.112002i
$145$	−3.12803	+	11.6740i	−0.259769	+	0.969471i
$146$		−	11.8177i		−	0.978037i
$147$	−9.62707	−	7.37018i	−0.794027	−	0.607883i
$148$	2.87524	+	2.87524i	0.236343	+	0.236343i
$149$	−19.1684	−	5.13616i	−1.57034	−	0.420771i	−0.634420	−	0.772988i	$-0.718761\pi$
$149$	−19.1684	−	5.13616i	−1.57034	−	0.420771i	−0.935918	+	0.352218i	$0.885428\pi$
$150$	−1.97058	−	0.0582126i	−0.160898	−	0.00475304i
$151$	−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
$156$	−6.18222	−	0.883273i	−0.494974	−	0.0707184i
$157$	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
$159$	7.35042	−	1.73864i	0.582927	−	0.137883i
$160$			1.96514i			0.155358i
$161$	8.37521	+	1.53294i	0.660059	+	0.120813i
$162$	−8.35822	−	3.33768i	−0.656684	−	0.262233i
$163$	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
$165$	−7.38064	+	6.95709i	−0.574582	+	0.541609i
$166$	−5.92036	+	3.41812i	−0.459509	+	0.265298i
$167$	−15.2569	−	15.2569i	−1.18061	−	1.18061i	−0.979586	−	0.201026i	$-0.935572\pi$
$167$	−15.2569	−	15.2569i	−1.18061	−	1.18061i	−0.201026	−	0.979586i	$-0.564428\pi$
$168$	3.07016	−	3.40207i	0.236868	−	0.262476i
$169$	9.52648	+	8.84569i	0.732806	+	0.680438i
$170$	−3.46972	+	2.00324i	−0.266115	+	0.153642i
$171$	12.4229	+	4.12871i	0.949999	+	0.315731i
$172$	−0.963895	+	1.66952i	−0.0734963	+	0.127299i
$173$	−3.41329	−	5.91199i	−0.259508	−	0.449481i	0.706602	−	0.707611i	$-0.250227\pi$
$173$	−3.41329	−	5.91199i	−0.259508	−	0.449481i	−0.966110	+	0.258130i	$0.916894\pi$
$174$	5.05141	+	9.37837i	0.382946	+	0.710973i
$175$	−2.83645	+	1.01156i	−0.214415	+	0.0764670i
$176$	−2.10710	−	2.10710i	−0.158829	−	0.158829i
$177$	2.43509	−	3.94397i	0.183033	−	0.296447i
$178$	6.26742	−	10.8555i	0.469763	−	0.813654i
$179$	5.31136	−	9.19954i	0.396990	−	0.687606i	−0.596363	−	0.802715i	$-0.703388\pi$
$179$	5.31136	−	9.19954i	0.396990	−	0.687606i	0.993353	+	0.115108i	$0.0367216\pi$
$180$	4.40751	−	3.91535i	0.328516	−	0.291833i
$181$		−	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
$186$	−3.85604	+	3.63475i	−0.282738	+	0.266513i
$187$	1.57241	−	5.86832i	0.114986	−	0.429134i
$188$	−0.555040	+	0.555040i	−0.0404805	+	0.0404805i
$189$	−13.7473	−	0.107602i	−0.999969	−	0.00782691i
$190$	−6.06359	+	6.06359i	−0.439899	+	0.439899i
$191$	−20.9344	+	12.0865i	−1.51476	+	0.874546i	−0.514908	+	0.857245i	$0.672174\pi$
$191$	−20.9344	+	12.0865i	−1.51476	+	0.874546i	−0.999850	+	0.0173008i	$0.994493\pi$
$192$	1.18805	+	1.26037i	0.0857399	+	0.0909597i
$193$	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
$195$	−12.1842	+	1.46777i	−0.872530	+	0.105109i
$196$	2.47941	−	6.54619i	0.177100	−	0.467585i
$197$	14.7417	−	14.7417i	1.05030	−	1.05030i	0.0516350	−	0.998666i	$-0.483557\pi$
$197$	14.7417	−	14.7417i	1.05030	−	1.05030i	0.998666	−	0.0516350i	$-0.0164432\pi$
$198$	−0.527709	+	8.92408i	−0.0375027	+	0.634207i
$199$	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
$201$	−0.617851	+	1.00070i	−0.0435799	+	0.0705837i
$202$	−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
$207$	8.63129	−	4.32522i	0.599916	−	0.300623i
$208$	−0.536735	−	3.56538i	−0.0372159	−	0.247214i
$209$		−	13.0032i		−	0.899451i
$210$	4.09738	−	8.01929i	0.282746	−	0.553384i
$211$	−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
$213$	−0.553074	+	18.7224i	−0.0378960	+	1.28284i
$214$	−14.3702	+	3.85048i	−0.982327	+	0.263214i
$215$	−0.980506	+	3.65930i	−0.0668699	+	0.249562i
$216$	0.459760	−	5.17577i	0.0312827	−	0.352167i
$217$	−3.46848	+	7.31373i	−0.235455	+	0.496489i
$218$	10.8726			0.736382
$219$	−17.4166	−	10.7534i	−1.17690	−	0.726645i
$220$	−5.07136	−	2.92795i	−0.341911	−	0.197403i
$221$	5.74800	−	4.58218i	0.386653	−	0.308231i
$222$	6.85375	−	1.62116i	0.459994	−	0.108805i
$223$	−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	0.993038	−	0.117794i	$-0.0375822\pi$
$227$	1.11711	+	4.16910i	0.0741449	+	0.276713i	−0.918893	+	0.394507i	$0.870916\pi$
$228$	−0.223174	+	7.55478i	−0.0147801	+	0.500328i
$229$	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
$231$	4.20522	+	12.9919i	0.276683	+	0.854807i
$232$	−4.34877	+	4.34877i	−0.285510	+	0.285510i
$233$	7.85397	+	13.6035i	0.514530	+	0.891193i	0.999858	+	0.0168603i	$0.00536707\pi$
$233$	7.85397	+	13.6035i	0.514530	+	0.891193i	−0.485327	+	0.874332i	$0.661300\pi$
$234$	−6.92719	+	8.30747i	−0.452845	+	0.543076i
$235$	−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	$-0.434470\pi$
$239$	18.2934	−	18.2934i	1.18330	−	1.18330i	0.978884	−	0.204417i	$-0.0655299\pi$
$240$	2.89618	+	1.78816i	0.186947	+	0.115425i
$241$	−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
$243$	−12.5245	+	9.28104i	−0.803445	+	0.595379i
$244$			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
$249$	−0.349632	+	11.8356i	−0.0221570	+	0.750048i
$250$	−6.03123	−	10.4464i	−0.381449	−	0.660689i
$251$	29.6402			1.87087			0.935436	−	0.353497i	$-0.115007\pi$
$251$	29.6402			1.87087			0.935436	+	0.353497i	$0.115007\pi$
$252$	−2.22023	−	7.62041i	−0.139861	−	0.480041i
$253$	−6.78090	−	6.78090i	−0.426311	−	0.426311i
$254$	1.95328	−	7.28975i	0.122560	−	0.457399i
$255$	−0.204907	+	6.93641i	−0.0128318	+	0.434375i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.7359	+	25.5233i	0.919199	+	1.59210i	0.800635	+	0.599153i	$0.204496\pi$
$257$	14.7359	+	25.5233i	0.919199	+	1.59210i	0.118564	+	0.992946i	$0.462171\pi$
$258$	1.58340	+	2.93972i	0.0985783	+	0.183019i
$259$	8.85248	−	6.11325i	0.550066	−	0.379859i
$260$	−2.83223	−	6.49474i	−0.175647	−	0.402787i
$261$	18.4181	+	1.08912i	1.14005	+	0.0674148i
$262$	−0.584896	+	0.156722i	−0.0361350	+	0.00968234i
$263$	14.8496	+	8.57339i	0.915663	+	0.528658i	0.882249	−	0.470784i	$-0.156029\pi$
$263$	14.8496	+	8.57339i	0.915663	+	0.528658i	0.0334138	+	0.999442i	$0.489362\pi$
$264$	−5.02272	+	1.18806i	−0.309127	+	0.0731197i
$265$	6.05972	+	6.05972i	0.372246	+	0.372246i
$266$	3.87811	+	10.8743i	0.237782	+	0.666747i
$267$	−10.2956	−	19.1146i	−0.630078	−	1.16979i
$268$	−0.655866	−	0.175739i	−0.0400634	−	0.0107350i
$269$	10.0976	+	5.82987i	0.615663	+	0.355453i	0.775179	−	0.631742i	$-0.217660\pi$
$269$	10.0976	+	5.82987i	0.615663	+	0.355453i	−0.159515	+	0.987195i	$0.550993\pi$
$270$	−1.75978	−	10.0584i	−0.107097	−	0.612135i
$271$	−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
$273$	−5.24362	+	15.6686i	−0.317358	+	0.948306i
$274$	−4.66746			−0.281972
$275$	3.27618	+	0.877849i	0.197561	+	0.0529363i
$276$	3.82328	+	4.05604i	0.230134	+	0.244145i
$277$	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
$279$	1.84804	+	8.99033i	0.110639	+	0.538237i
$280$	5.11432	+	0.936092i	0.305639	+	0.0559422i
$281$	0.448744	+	0.448744i	0.0267698	+	0.0267698i	0.720365	−	0.693595i	$-0.243974\pi$
$281$	0.448744	+	0.448744i	0.0267698	+	0.0267698i	−0.693595	+	0.720365i	$0.743974\pi$
$282$	0.312951	+	1.32306i	0.0186359	+	0.0787869i
$283$	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
$285$	3.41886	+	14.4539i	0.202516	+	0.856173i
$286$	10.0007	+	3.92708i	0.591356	+	0.232213i
$287$	−2.18127	−	26.9473i	−0.128756	−	1.59065i
$288$	2.93856	−	0.604047i	0.173156	−	0.0355938i
$289$	6.42170	+	11.1227i	0.377747	+	0.654277i
$290$	−6.04290	+	10.4666i	−0.354851	+	0.614620i
$291$	17.7853	+	0.525392i	1.04259	+	0.0307990i
$292$	3.05864	−	11.4150i	0.178993	−	0.668012i
$293$	2.61973	+	2.61973i	0.153046	+	0.153046i	0.779477	−	0.626431i	$-0.215485\pi$
$293$	2.61973	+	2.61973i	0.153046	+	0.153046i	−0.626431	+	0.779477i	$0.715485\pi$
$294$	−7.39149	−	9.61072i	−0.431080	−	0.560509i
$295$	5.25892			0.306186
$296$	2.03310	+	3.52144i	0.118172	+	0.204679i
$297$	12.6719	+	8.89810i	0.735298	+	0.516320i
$298$	−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
$303$	1.89693	+	8.01962i	0.108976	+	0.460715i
$304$	−4.21497	+	1.12940i	−0.241745	+	0.0647754i
$305$	2.77263	+	10.3476i	0.158760	+	0.592501i
$306$	4.06206	+	4.57266i	0.232212	+	0.261401i
$307$	−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	−0.587531	−	0.809202i	$-0.699900\pi$
$311$	7.17794	−	12.4326i	0.407024	−	0.704986i	0.994555	+	0.104216i	$0.0332333\pi$
$312$	−5.74296	−	2.45325i	−0.325131	−	0.138888i
$313$	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
$315$	−8.09026	−	13.3357i	−0.455834	−	0.751380i
$316$		−	9.79172i		−	0.550827i
$317$	−31.6985	−	8.49358i	−1.78036	−	0.477047i	−0.789714	−	0.613475i	$-0.789771\pi$
$317$	−31.6985	−	8.49358i	−1.78036	−	0.477047i	−0.990650	+	0.136428i	$0.956438\pi$
$318$	7.54996	+	0.223032i	0.423381	+	0.0125070i
$319$	−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
$324$	−7.20957	−	5.38722i	−0.400531	−	0.299290i
$325$	2.55815	+	3.20901i	0.141901	+	0.178004i
$326$	4.13336	+	2.38640i	0.228926	+	0.132170i
$327$	9.89337	−	16.0237i	0.547105	−	0.886112i
$328$	10.2184			0.564218
$329$	1.18011	+	1.70889i	0.0650615	+	0.0942143i
$330$	−8.92978	+	4.80978i	−0.491568	+	0.264770i
$331$	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
$333$	3.84728	−	11.5760i	0.210829	−	0.634363i
$334$	−10.7882	−	18.6858i	−0.590306	−	1.02244i
$335$	−1.33434			−0.0729026
$336$	3.84607	−	2.49153i	0.209820	−	0.135924i
$337$			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
$339$	19.1731	+	20.3404i	1.04134	+	1.10474i
$340$	−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
$345$	9.32024	+	5.75452i	0.501785	+	0.309813i
$346$	−1.76685	−	6.59397i	−0.0949864	−	0.354494i
$347$	−22.0582	−	12.7353i	−1.18415	−	0.683666i	−0.227175	−	0.973854i	$-0.572949\pi$
$347$	−22.0582	−	12.7353i	−1.18415	−	0.683666i	−0.956970	+	0.290187i	$0.906282\pi$
$348$	2.45198	+	10.3662i	0.131440	+	0.555687i
$349$	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
$351$	5.94001	+	17.7684i	0.317054	+	0.948407i
$352$	−1.48994	−	2.58066i	−0.0794143	−	0.137550i
$353$	−5.27871	−	19.7004i	−0.280957	−	1.04855i	−0.951743	−	0.306896i	$-0.900710\pi$
$353$	−5.27871	−	19.7004i	−0.280957	−	1.04855i	0.670786	−	0.741651i	$-0.265957\pi$
$354$	3.37289	−	3.17933i	0.179267	−	0.168980i
$355$	−18.4041	+	10.6256i	−0.976787	+	0.563948i
$356$	8.86347	−	8.86347i	0.469763	−	0.469763i
$357$	8.31977	+	4.25091i	0.440329	+	0.224982i
$358$	7.51140	−	7.51140i	0.396990	−	0.396990i
$359$	−5.92711	+	22.1203i	−0.312821	+	1.16746i	0.613181	+	0.789943i	$0.289890\pi$
$359$	−5.92711	+	22.1203i	−0.312821	+	1.16746i	−0.926001	+	0.377520i	$0.876777\pi$
$360$	5.27069	−	2.64119i	0.277790	−	0.139203i
$361$	−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
$366$	8.03400	+	4.96037i	0.419944	+	0.259283i
$367$	−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
$369$	−20.3592	−	22.9183i	−1.05986	−	1.19308i
$370$	5.65026	+	5.65026i	0.293743	+	0.293743i
$371$	10.8674	−	3.87563i	0.564206	−	0.201213i
$372$	−4.66539	+	2.51289i	−0.241889	+	0.130287i
$373$	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
$375$	−20.8837	−	0.616921i	−1.07843	−	0.0318577i
$376$	−0.679782	+	0.392473i	−0.0350571	+	0.0202402i
$377$	8.10496	−	20.6401i	0.417427	−	1.06302i
$378$	−13.2510	−	3.66200i	−0.681559	−	0.188353i
$379$	−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
$381$	−8.96607	−	9.51193i	−0.459346	−	0.487311i
$382$	−23.3493	+	6.25642i	−1.19465	+	0.320106i
$383$	14.1117	+	3.78122i	0.721074	+	0.193211i	0.600651	−	0.799511i	$-0.294908\pi$
$383$	14.1117	+	3.78122i	0.721074	+	0.193211i	0.120423	+	0.992723i	$0.461575\pi$
$384$	0.821356	+	1.52492i	0.0419146	+	0.0778181i
$385$	−10.0358	+	11.8036i	−0.511471	+	0.601566i
$386$			7.15556i			0.364209i
$387$	5.77329	+	0.341393i	0.293473	+	0.0173540i
$388$	2.65880	+	9.92278i	0.134980	+	0.503753i
$389$	12.8526	−	22.2613i	0.651652	−	1.12869i	−0.331070	−	0.943606i	$-0.607410\pi$
$389$	12.8526	−	22.2613i	0.651652	−	1.12869i	0.982722	−	0.185088i	$-0.0592569\pi$
$390$	−12.1489	−	1.73576i	−0.615186	−	0.0878935i
$391$	−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
$396$	−2.81945	+	8.48342i	−0.141683	+	0.426308i
$397$	−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
$399$	19.5551	+	4.17952i	0.978981	+	0.209238i
$400$		−	1.13821i		−	0.0569107i
$401$	4.48360	−	16.7330i	0.223900	−	0.835608i	−0.758942	−	0.651159i	$-0.774283\pi$
$401$	4.48360	−	16.7330i	0.223900	−	0.835608i	0.982842	−	0.184449i	$-0.0590501\pi$
$402$	−0.855798	+	0.806687i	−0.0426833	+	0.0402339i
$403$	10.9614	+	1.23706i	0.546025	+	0.0616222i
$404$	−4.12046	+	2.37895i	−0.205000	+	0.118357i
$405$	−16.4251	−	6.55903i	−0.816170	−	0.325921i
$406$	9.24621	+	13.3893i	0.458882	+	0.664498i
$407$	−12.1168			−0.600609
$408$	−1.85516	+	3.00470i	−0.0918443	+	0.148755i
$409$	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
$411$	−4.24711	+	6.87879i	−0.209495	+	0.339306i
$412$	10.3960			0.512174
$413$	3.03389	−	6.39735i	0.149288	−	0.314793i
$414$	9.45663	−	1.94390i	0.464768	−	0.0955373i
$415$	−11.6343	+	6.71709i	−0.571108	+	0.329729i
$416$	0.404341	−	3.58281i	0.0198245	−	0.175662i
$417$	1.51961	−	1.43241i	0.0744157	−	0.0701453i
$418$	3.36548	−	12.5601i	0.164611	−	0.614336i
$419$		−	2.60621i		−	0.127322i	−0.997972	−	0.0636609i	$-0.979722\pi$
$419$		−	2.60621i		−	0.127322i	0.997972	−	0.0636609i	$-0.0202776\pi$
$420$	6.03331	−	6.68556i	0.294395	−	0.326222i
$421$	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
$423$	2.23465	+	0.742683i	0.108653	+	0.0361105i
$424$	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
$429$	14.8877	−	11.1654i	0.718785	−	0.539071i
$430$	−1.89419	+	3.28084i	−0.0913460	+	0.158216i
$431$	5.13915	+	19.1796i	0.247544	+	0.923848i	0.972087	+	0.234619i	$0.0753841\pi$
$431$	5.13915	+	19.1796i	0.247544	+	0.923848i	−0.724543	+	0.689229i	$0.757949\pi$
$432$	1.78368	−	4.88042i	0.0858174	−	0.234809i
$433$		−	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
$435$	9.92674	+	18.4298i	0.475951	+	0.883643i
$436$	10.5021	+	2.81402i	0.502958	+	0.134767i
$437$	−13.5643	+	3.63454i	−0.648867	+	0.173863i
$438$	−14.0399	−	14.8947i	−0.670854	−	0.711696i
$439$	−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
$441$	−20.8898	+	2.14821i	−0.994754	+	0.102296i
$442$	6.73810	−	2.93835i	0.320499	−	0.139763i
$443$	−2.35905	+	1.36200i	−0.112082	+	0.0647106i	−0.554993	−	0.831855i	$-0.687279\pi$
$443$	−2.35905	+	1.36200i	−0.112082	+	0.0647106i	0.442911	+	0.896566i	$0.353946\pi$
$444$	7.03980	+	0.207961i	0.334094	+	0.00986941i
$445$	12.3164	−	21.3326i	0.583852	−	1.01126i
$446$	−11.6057	−	20.1017i	−0.549546	−	0.951841i
$447$	−30.2614	+	16.2995i	−1.43132	+	0.770939i
$448$	2.01567	+	1.71379i	0.0952315	+	0.0809689i
$449$	22.4174	+	22.4174i	1.05794	+	1.05794i	0.998215	+	0.0597270i	$0.0190230\pi$
$449$	22.4174	+	22.4174i	1.05794	+	1.05794i	0.0597270	+	0.998215i	$0.480977\pi$
$450$	−2.55283	+	2.26778i	−0.120342	+	0.106904i
$451$	−15.2249	+	26.3703i	−0.716911	+	1.24173i
$452$	−8.06919	+	13.9762i	−0.379543	+	0.657387i
$453$	−10.5387	−	6.50680i	−0.495150	−	0.305716i
$454$			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
$459$	10.4353	−	1.82571i	0.487078	−	0.0852170i
$460$	−1.63679	+	6.10858i	−0.0763157	+	0.284814i
$461$	−25.1394	+	25.1394i	−1.17086	+	1.17086i	−0.188852	+	0.982006i	$0.560477\pi$
$461$	−25.1394	+	25.1394i	−1.17086	+	1.17086i	−0.982006	+	0.188852i	$0.939523\pi$
$462$	0.699370	+	13.6376i	0.0325376	+	0.634481i
$463$	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
$465$	−7.57766	+	7.14281i	−0.351406	+	0.331240i
$466$	4.06551	+	15.1727i	0.188331	+	0.702862i
$467$	−6.43406	−	11.1441i	−0.297733	−	0.515688i	0.677884	−	0.735169i	$-0.262897\pi$
$467$	−6.43406	−	11.1441i	−0.297733	−	0.515688i	−0.975617	+	0.219480i	$0.929564\pi$
$468$	−8.84128	+	6.23151i	−0.408688	+	0.288052i
$469$	−0.769784	+	1.62319i	−0.0355453	+	0.0749519i
$470$	−1.09073	+	1.09073i	−0.0503118	+	0.0503118i
$471$	−7.46824	−	31.5733i	−0.344118	−	1.45482i
$472$	2.31757	+	1.33805i	0.106675	+	0.0615887i
$473$	−1.48681	−	5.54886i	−0.0683637	−	0.255137i
$474$	−14.4308	−	8.90987i	−0.662827	−	0.409244i
$475$	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	−0.700844	−	0.713315i	$-0.747193\pi$
$479$	−20.8166	+	5.57779i	−0.951135	+	0.254856i	−0.250291	+	0.968171i	$0.580526\pi$
$480$	2.33468	+	2.47682i	0.106563	+	0.113051i
$481$	−11.7946	−	8.70808i	−0.537786	−	0.397054i
$482$		−	29.0777i		−	1.32445i
$483$	12.3771	−	8.01806i	0.563178	−	0.364834i
$484$	−2.12026			−0.0963756
$485$	10.0938	+	17.4829i	0.458335	+	0.793859i
$486$	−14.4998	+	5.72322i	−0.657725	+	0.259611i
$487$	−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
$489$	7.27812	−	3.92016i	0.329128	−	0.177276i
$490$	4.87239	−	12.8642i	0.220112	−	0.581145i
$491$	4.58195			0.206780			0.103390	−	0.994641i	$-0.467031\pi$
$491$	4.58195			0.206780			0.103390	+	0.994641i	$0.467031\pi$
$492$	9.29815	−	15.0596i	0.419193	−	0.678941i
$493$	−10.8588	−	6.26932i	−0.489055	−	0.282356i
$494$	12.3026	−	9.80738i	0.553522	−	0.441255i
$495$	−1.03702	+	17.5371i	−0.0466108	+	0.788233i
$496$	−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
$501$	−37.3553	−	1.10350i	−1.66891	−	0.0493009i
$502$	28.6302	+	7.67144i	1.27783	+	0.342393i
$503$		−	6.06721i		−	0.270524i	−0.990810	−	0.135262i	$-0.956812\pi$
$503$		−	6.06721i		−	0.270524i	0.990810	−	0.135262i	$-0.0431876\pi$
$504$	−0.172266	−	7.93538i	−0.00767335	−	0.353470i
$505$	−6.61141	+	6.61141i	−0.294204	+	0.294204i
$506$	−4.79482	−	8.30487i	−0.213156	−	0.369197i
$507$	22.5160	−	0.169013i	0.999972	−	0.00750613i
$508$	3.77345	−	6.53581i	0.167420	−	0.289980i
$509$	24.4905	+	6.56221i	1.08552	+	0.290865i	0.756856	−	0.653582i	$-0.226734\pi$
$509$	24.4905	+	6.56221i	1.08552	+	0.290865i	0.328666	+	0.944446i	$0.393401\pi$
$510$	−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
$513$	20.5626	−	9.55520i	0.907859	−	0.421872i
$514$	7.62785	+	28.4675i	0.336450	+	1.25565i
$515$	19.7335	−	5.28758i	0.869562	−	0.232999i
$516$	0.768593	+	3.24937i	0.0338354	+	0.143045i
$517$		−	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	−0.220497	−	0.975388i	$-0.570768\pi$
$521$	−26.8303	−	15.4905i	−1.17546	−	0.678650i	−0.954959	+	0.296737i	$0.904101\pi$
$522$	17.5086	+	5.81896i	0.766331	+	0.254689i
$523$	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
$525$	−2.37321	+	4.64478i	−0.103575	+	0.202715i
$526$	12.1246	+	12.1246i	0.528658	+	0.528658i
$527$	1.61439	−	6.02497i	0.0703237	−	0.262452i
$528$	−5.15907	−	0.152403i	−0.224520	−	0.00663249i
$529$	6.32185	−	10.9498i	0.274863	−	0.476077i
$530$	4.28487	+	7.42161i	0.186123	+	0.322374i
$531$	−1.61649	−	7.86388i	−0.0701497	−	0.341263i
$532$	0.931484	+	11.5075i	0.0403850	+	0.498914i
$533$	−33.7716	+	14.7271i	−1.46281	+	0.637903i
$534$	−4.99753	−	21.1280i	−0.216264	−	0.914297i
$535$	−28.2395	+	7.56675i	−1.22090	+	0.327139i
$536$	−0.588033	−	0.339501i	−0.0253992	−	0.0146642i
$537$	−4.23518	−	17.9050i	−0.182762	−	0.772658i
$538$	8.24468	+	8.24468i	0.355453	+	0.355453i
$539$	8.56911	+	19.0178i	0.369098	+	0.819155i
$540$	0.903493	−	10.1711i	0.0388802	−	0.437696i
$541$	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
$543$	−23.3983	−	24.8228i	−1.00412	−	1.06525i
$544$	−1.96931	−	0.527674i	−0.0844333	−	0.0226238i
$545$	21.3661			0.915224
$546$	−9.12027	+	13.7775i	−0.390312	+	0.589624i
$547$	−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
$549$	14.6209	−	7.32667i	0.624006	−	0.312695i
$550$	2.93734	+	1.69587i	0.125249	+	0.0723123i
$551$	−25.9224	−	6.94589i	−1.10433	−	0.295905i
$552$	2.64322	+	4.90737i	0.112503	+	0.208871i
$553$	−25.4831	−	4.66426i	−1.08365	−	0.198345i
$554$	20.2268	+	20.2268i	0.859356	+	0.859356i
$555$	13.4686	−	3.18581i	0.571710	−	0.135230i
$556$	1.04415	+	0.602841i	0.0442819	+	0.0255662i
$557$	−21.8948	+	5.86670i	−0.927713	+	0.248580i	−0.690879	−	0.722970i	$-0.742776\pi$
$557$	−21.8948	+	5.86670i	−0.927713	+	0.248580i	−0.236834	+	0.971550i	$0.576110\pi$
$558$	−0.541796	+	9.16230i	−0.0229361	+	0.387871i
$559$	2.54056	−	6.46981i	0.107454	−	0.273644i
$560$	4.69777	+	2.22788i	0.198517	+	0.0941450i
$561$	−4.99001	−	9.26437i	−0.210678	−	0.391142i
$562$	0.317310	+	0.549597i	0.0133849	+	0.0231834i
$563$	−12.6747	+	21.9532i	−0.534175	+	0.925218i	0.465028	+	0.885296i	$0.346044\pi$
$563$	−12.6747	+	21.9532i	−0.534175	+	0.925218i	−0.999203	+	0.0399219i	$0.987289\pi$
$564$	−0.0401451	+	1.35897i	−0.00169041	+	0.0572230i
$565$	−8.20824	+	30.6336i	−0.345323	+	1.28876i
$566$	20.3790	+	20.3790i	0.856594	+	0.856594i
$567$	−17.4546	+	16.1968i	−0.733024	+	0.680203i
$568$	−10.8141			−0.453749
$569$	−11.4337	−	19.8037i	−0.479325	−	0.830215i	0.520394	−	0.853926i	$-0.325785\pi$
$569$	−11.4337	−	19.8037i	−0.479325	−	0.830215i	−0.999719	+	0.0237110i	$0.992452\pi$
$570$	−0.438569	+	14.8462i	−0.0183696	+	0.621840i
$571$	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
$576$	2.99477	+	0.177090i	0.124782	+	0.00737876i
$577$	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
$579$	10.5457	+	6.51113i	0.438264	+	0.270593i
$580$	−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
$585$	−13.6129	+	16.3254i	−0.562825	+	0.674971i
$586$	1.85243	+	3.20850i	0.0765231	+	0.132542i
$587$	−7.29612	+	7.29612i	−0.301143	+	0.301143i	−0.841461	−	0.540318i	$-0.818304\pi$
$587$	−7.29612	+	7.29612i	−0.301143	+	0.301143i	0.540318	+	0.841461i	$0.318304\pi$
$588$	−4.65219	−	11.1963i	−0.191853	−	0.461728i
$589$		−	13.3503i		−	0.550091i
$590$	5.07973	+	1.36111i	0.209129	+	0.0560359i
$591$	1.06624	−	36.0938i	0.0438593	−	1.48470i
$592$	1.05241	+	3.92765i	0.0432538	+	0.161425i
$593$	−6.45528	+	24.0914i	−0.265086	+	0.989316i	0.697111	+	0.716963i	$0.254468\pi$
$593$	−6.45528	+	24.0914i	−0.265086	+	0.989316i	−0.962197	+	0.272353i	$0.912198\pi$
$594$	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
$597$	7.55584	−	1.78723i	0.309240	−	0.0731464i
$598$	1.30122	−	11.5299i	0.0532108	−	0.471493i
$599$	23.3553	+	13.4842i	0.954273	+	0.550950i	0.894406	−	0.447257i	$-0.147599\pi$
$599$	23.3553	+	13.4842i	0.954273	+	0.550950i	0.0598673	+	0.998206i	$0.480932\pi$
$600$	−1.67747	−	1.03571i	−0.0684824	−	0.0422825i
$601$	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
$603$	0.410150	+	1.99529i	0.0167026	+	0.0812544i
$604$	1.85076	−	6.90714i	0.0753065	−	0.281048i
$605$	−4.02465	+	1.07840i	−0.163625	+	0.0438432i
$606$	−0.243337	+	8.23732i	−0.00988489	+	0.334618i
$607$	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
$609$	28.1462	−	1.44340i	1.14054	−	0.0584897i
$610$			10.7126i			0.433741i
$611$	1.68102	−	2.27684i	0.0680067	−	0.0921110i
$612$	2.74016	+	5.46818i	0.110764	+	0.221038i
$613$	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	−0.515038	−	0.857168i	$-0.672222\pi$
$617$	8.49833	−	8.49833i	0.342130	−	0.342130i	0.857168	+	0.515038i	$0.172222\pi$
$618$	9.45974	−	15.3214i	0.380526	−	0.616316i
$619$	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
$621$	5.74010	−	15.7058i	0.230342	−	0.630251i
$622$	10.1511	−	10.1511i	0.407024	−	0.407024i
$623$	−18.8452	−	27.2894i	−0.755018	−	1.09333i
$624$	−4.91232	−	3.85605i	−0.196650	−	0.154365i
$625$	−9.00670	−	15.6001i	−0.360268	−	0.624003i
$626$	3.31837	+	12.3843i	0.132629	+	0.494978i
$627$	−15.4484	−	16.3889i	−0.616951	−	0.654511i
$628$	16.2223	−	9.36594i	0.647340	−	0.373742i
$629$	−5.86197	+	5.86197i	−0.233732	+	0.233732i
$630$	−4.36306	−	14.9752i	−0.173828	−	0.596626i
$631$	−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
$633$	−26.8274	+	25.2879i	−1.06630	+	1.00510i
$634$	−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
$639$	21.5460	+	24.2543i	0.852345	+	0.959484i
$640$	−0.982571	+	1.70186i	−0.0388395	+	0.0672721i
$641$	−12.7864	+	22.1467i	−0.505032	+	0.874741i	0.494951	+	0.868921i	$0.335186\pi$
$641$	−12.7864	+	22.1467i	−0.505032	+	0.874741i	−0.999983	+	0.00582025i	$0.998147\pi$
$642$	−13.5373	+	21.9255i	−0.534274	+	0.865332i
$643$	−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
$645$	3.11161	+	5.77697i	0.122520	+	0.227468i
$646$	−4.44826	−	7.70461i	−0.175014	−	0.303134i
$647$	−3.72444	+	6.45091i	−0.146423	+	0.253612i	−0.929903	−	0.367805i	$-0.880109\pi$
$647$	−3.72444	+	6.45091i	−0.146423	+	0.253612i	0.783480	+	0.621417i	$0.213443\pi$
$648$	−5.56959	−	7.06963i	−0.218794	−	0.277721i
$649$	−6.90610	+	3.98724i	−0.271088	+	0.156513i
$650$	1.64043	+	3.76176i	0.0643430	+	0.147549i
$651$	4.31748	+	13.3388i	0.169215	+	0.522787i
$652$	3.37488	+	3.37488i	0.132170	+	0.132170i
$653$	25.0837	−	14.4821i	0.981603	−	0.566729i	0.0788492	−	0.996887i	$-0.474875\pi$
$653$	25.0837	−	14.4821i	0.981603	−	0.566729i	0.902754	+	0.430158i	$0.141542\pi$
$654$	13.7035	−	12.9171i	0.535849	−	0.505099i
$655$	−1.14940	+	0.307982i	−0.0449109	+	0.0120338i
$656$	9.87024	+	2.64472i	0.385368	+	0.103259i
$657$	−34.7269	+	7.13843i	−1.35483	+	0.278496i
$658$	0.697603	+	1.95610i	0.0271954	+	0.0762567i
$659$			14.9624i			0.582853i	0.956593	+	0.291427i	$0.0941299\pi$
$659$			14.9624i			0.582853i	−0.956593	+	0.291427i	$0.905870\pi$
$660$	−9.87037	+	2.33470i	−0.384203	+	0.0908780i
$661$	−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
$663$	1.80080	−	12.6042i	0.0699371	−	0.489505i
$664$	−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
$669$	−40.1858	−	1.18712i	−1.55367	−	0.0458967i
$670$	−1.28887	−	0.345352i	−0.0497934	−	0.0133421i
$671$	−11.4865	−	11.4865i	−0.443430	−	0.443430i
$672$	4.35988	−	1.41120i	0.168186	−	0.0544383i
$673$		−	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
$675$	1.01926	+	5.82584i	0.0392315	+	0.224237i
$676$	3.82733	+	12.4238i	0.147205	+	0.477840i
$677$	−21.1055	+	12.1853i	−0.811151	+	0.468318i	−0.847356	−	0.531026i	$-0.821807\pi$
$677$	−21.1055	+	12.1853i	−0.811151	+	0.468318i	0.0362043	+	0.999344i	$0.488473\pi$
$678$	13.2553	+	24.6097i	0.509069	+	0.945130i
$679$	27.0907	−	2.19288i	1.03965	−	0.0841550i
$680$	−4.00649			−0.153642
$681$	6.36105	+	3.92745i	0.243756	+	0.150500i
$682$	8.80613	−	2.35960i	0.337204	−	0.0903536i
$683$	40.5076	−	10.8540i	1.54998	−	0.415316i	0.620506	−	0.784202i	$-0.286927\pi$
$683$	40.5076	−	10.8540i	1.54998	−	0.415316i	0.929475	+	0.368885i	$0.120261\pi$
$684$	8.69415	+	9.78700i	0.332429	+	0.374215i
$685$	−9.17223			−0.350453
$686$	−12.8381	−	13.3485i	−0.490160	−	0.509650i
$687$	29.1541	−	15.7031i	1.11230	−	0.599109i
$688$	−1.66952	+	0.963895i	−0.0636497	+	0.0367482i
$689$	−9.80112	−	12.2948i	−0.373393	−	0.468394i
$690$	7.51328	+	7.97069i	0.286026	+	0.303439i
$691$	−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
$693$	20.7352	+	11.3787i	0.787665	+	0.432242i
$694$	−18.0104	−	18.0104i	−0.683666	−	0.683666i
$695$	2.28861	+	0.613230i	0.0868118	+	0.0232611i
$696$	−0.314539	+	10.6476i	−0.0119226	+	0.403597i
$697$	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	$-0.576471\pi$
$701$	−12.5994			−0.475874			−0.237937	+	0.971281i	$0.576471\pi$
$702$	1.13880	+	18.7004i	0.0429813	+	0.705799i
$703$	−8.87176	+	15.3663i	−0.334605	+	0.579552i
$704$	−0.771252	−	2.87835i	−0.0290677	−	0.108482i
$705$	0.614993	+	2.60000i	0.0231620	+	0.0979215i
$706$		−	20.3954i		−	0.767589i
$707$	4.22848	+	11.8568i	0.159028	+	0.445920i
$708$	4.08083	−	2.19803i	0.153367	−	0.0826070i
$709$	−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
$711$	−26.2623	+	13.1603i	−0.984912	+	0.493548i
$712$	10.8555	−	6.26742i	0.406827	−	0.234882i
$713$	−6.96191	−	6.96191i	−0.260726	−	0.260726i
$714$	6.93607	+	6.25937i	0.259576	+	0.234251i
$715$	19.6529	+	7.71728i	0.734975	+	0.288610i
$716$	9.19954	−	5.31136i	0.343803	−	0.198495i
$717$	1.32313	−	44.7899i	0.0494132	−	1.67271i
$718$	−11.4503	+	19.8325i	−0.427321	+	0.740142i
$719$	−3.39194	−	5.87502i	−0.126498	−	0.219101i	0.795819	−	0.605534i	$-0.207040\pi$
$719$	−3.39194	−	5.87502i	−0.126498	−	0.219101i	−0.922318	+	0.386433i	$0.873707\pi$
$720$	5.77469	−	1.18704i	0.215210	−	0.0442383i
$721$	4.95212	−	27.0558i	0.184426	−	1.00761i
$722$	−0.0293462	−	0.0293462i	−0.00109215	−	0.00109215i
$723$	−42.8539	−	26.4589i	−1.59375	−	0.984018i
$724$	9.84737	−	17.0562i	0.365975	−	0.633887i
$725$	3.50005	−	6.06227i	0.129989	−	0.225147i
$726$	−1.92931	+	3.12479i	−0.0716035	+	0.115972i
$727$		−	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
$732$	6.47641	+	6.87070i	0.239375	+	0.253948i
$733$	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
$735$	−14.5253	−	18.8864i	−0.535775	−	0.696637i
$736$	−2.27555	+	2.27555i	−0.0838780	+	0.0838780i
$737$	1.75227	−	1.01168i	0.0645458	−	0.0372656i
$738$	−13.7338	−	27.4067i	−0.505547	−	1.00886i
$739$	−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
$741$	−3.25922	−	27.0554i	−0.119730	−	0.993906i
$742$	11.5002	−	0.930890i	0.422184	−	0.0341740i
$743$	1.78670	−	1.78670i	0.0655478	−	0.0655478i	−0.673573	−	0.739121i	$-0.735241\pi$
$743$	1.78670	−	1.78670i	0.0655478	−	0.0655478i	0.739121	+	0.673573i	$0.235241\pi$
$744$	−5.15680	+	1.21977i	−0.189058	+	0.0447189i
$745$	−33.7728	−	19.4987i	−1.23734	−	0.714379i
$746$	8.16841	+	30.4849i	0.299067	+	1.11613i
$747$	13.6205	+	15.3326i	0.498349	+	0.560991i
$748$	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
$753$	37.3577	−	35.2139i	1.36139	−	1.28327i
$754$	13.1709	−	17.8391i	0.479654	−	0.649663i
$755$		−	14.0523i		−	0.511417i
$756$	−11.8517	−	6.96684i	−0.431043	−	0.253381i
$757$	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
$759$	−16.6025	−	0.490451i	−0.602632	−	0.0178022i
$760$	−8.28302	+	2.21943i	−0.300457	+	0.0805071i
$761$	7.13113	−	26.6137i	0.258503	−	0.964747i	−0.707605	−	0.706608i	$-0.750224\pi$
$761$	7.13113	−	26.6137i	0.258503	−	0.964747i	0.966108	−	0.258138i	$-0.0831091\pi$
$762$	−6.19869	−	11.5084i	−0.224555	−	0.416906i
$763$	12.3262	−	25.9914i	0.446238	−	0.940951i
$764$	−24.1729			−0.874546
$765$	7.98252	+	8.98592i	0.288609	+	0.324887i
$766$	12.6522	+	7.30475i	0.457143	+	0.263931i
$767$	−9.58795	−	1.08206i	−0.346201	−	0.0390708i
$768$	0.398691	+	1.68554i	0.0143865	+	0.0608217i
$769$	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	$-0.999779\pi$
$773$	−3.73452	−	13.9374i	−0.134321	−	0.501294i	0.865679	−	0.500600i	$-0.166887\pi$
$774$	5.48821	+	1.82400i	0.197270	+	0.0655622i
$775$	3.36364	+	0.901283i	0.120825	+	0.0323751i
$776$			10.2728i			0.368773i
$777$	3.89462	−	18.2221i	0.139719	−	0.653716i
$778$	18.1763	−	18.1763i	0.651652	−	0.651652i
$779$	22.2948	+	38.6158i	0.798796	+	1.38355i
$780$	−11.2857	−	4.82099i	−0.404094	−	0.172619i
$781$	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
$786$	−0.550994	+	0.892412i	−0.0196533	+	0.0318313i
$787$	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
$789$	28.9016	−	6.83627i	1.02892	−	0.243378i
$790$		−	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
$795$	14.8367	+	0.438289i	0.526205	+	0.0155445i
$796$	2.24137	+	3.88217i	0.0794433	+	0.137600i
$797$	−8.06678			−0.285740			−0.142870	−	0.989741i	$-0.545633\pi$
$797$	−8.06678			−0.285740			−0.142870	+	0.989741i	$0.545633\pi$
$798$	17.8071	+	9.09835i	0.630363	+	0.322078i
$799$	−1.13160	−	1.13160i	−0.0400332	−	0.0400332i
$800$	0.294591	−	1.09943i	0.0104154	−	0.0388707i
$801$	−35.6853	−	11.8600i	−1.26088	−	0.419051i
$802$	8.66165	−	15.0024i	0.305854	−	0.529754i
$803$	17.6077	+	30.4974i	0.621361	+	1.07623i
$804$	−1.03542	+	0.557703i	−0.0365166	+	0.0196687i
$805$	15.1180	+	7.16958i	0.532839	+	0.252694i
$806$	10.2677	+	4.03192i	0.361664	+	0.142018i
$807$	19.6530	−	4.64863i	0.691817	−	0.163640i
$808$	−4.59577	+	1.23143i	−0.161679	+	0.0433217i
$809$	−1.41612	−	0.817598i	−0.0497882	−	0.0287452i	0.474899	−	0.880040i	$-0.342484\pi$
$809$	−1.41612	−	0.817598i	−0.0497882	−	0.0287452i	−0.524687	+	0.851295i	$0.675818\pi$
$810$	−14.1678	−	10.5867i	−0.497807	−	0.371977i
$811$	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
$813$	−38.6710	+	20.8291i	−1.35625	+	0.730508i
$814$	−11.7040	−	3.13607i	−0.410224	−	0.109919i
$815$	8.12265	+	4.68961i	0.284524	+	0.164270i
$816$	−2.56962	+	2.42216i	−0.0899548	+	0.0847926i
$817$	−8.12558	−	2.17724i	−0.284278	−	0.0761720i
$818$	8.92681			0.312119
$819$	12.0061	+	25.9780i	0.419526	+	0.907743i
$820$	20.0807			0.701247
$821$	10.3146	+	2.76379i	0.359982	+	0.0964570i	0.434277	−	0.900779i	$-0.357004\pi$
$821$	10.3146	+	2.76379i	0.359982	+	0.0964570i	−0.0742948	+	0.997236i	$0.523671\pi$
$822$	−5.88276	+	5.54517i	−0.205185	+	0.193410i
$823$	−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
$825$	5.17214	−	2.78583i	0.180071	−	0.0969903i
$826$	4.58627	−	5.39414i	0.159577	−	0.187686i
$827$	−22.7698	−	22.7698i	−0.791784	−	0.791784i	0.190000	−	0.981784i	$-0.439151\pi$
$827$	−22.7698	−	22.7698i	−0.791784	−	0.791784i	−0.981784	+	0.190000i	$0.939151\pi$
$828$	9.63752	+	0.569898i	0.334927	+	0.0198053i
$829$	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
$831$	48.2150	−	11.4046i	1.67256	−	0.395621i
$832$	1.31786	−	3.35607i	0.0456887	−	0.116351i
$833$	13.3462	+	5.05496i	0.462419	+	0.175144i
$834$	1.83857	−	0.990295i	0.0636644	−	0.0342911i
$835$	−21.2004	−	36.7202i	−0.733671	−	1.27076i
$836$	6.50161	−	11.2611i	0.224863	−	0.389474i
$837$	13.0102	+	9.13563i	0.449697	+	0.315773i
$838$	0.674538	−	2.51741i	0.0233015	−	0.0869624i
$839$	14.2522	+	14.2522i	0.492039	+	0.492039i	0.908948	−	0.416909i	$-0.136887\pi$
$839$	14.2522	+	14.2522i	0.492039	+	0.492039i	−0.416909	+	0.908948i	$0.636887\pi$
$840$	7.55808	−	4.89622i	0.260778	−	0.168936i
$841$	−8.82353			−0.304260
$842$	8.38544	+	14.5240i	0.288981	+	0.500530i
$843$	1.09871	+	0.0324569i	0.0378417	+	0.00111788i
$844$	−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
$849$	48.5777	−	11.4904i	1.66718	−	0.394349i
$850$	2.24149	−	0.600606i	0.0768825	−	0.0206006i
$851$	3.38678	+	12.6397i	0.116097	+	0.433282i
$852$	−9.84016	+	15.9375i	−0.337118	+	0.546010i
$853$	−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	$0.401693\pi$
$857$	−19.7039	+	34.1282i	−0.673074	+	1.16580i	−0.977028	+	0.213112i	$0.931640\pi$
$858$	17.2702	−	6.93174i	0.589596	−	0.236646i
$859$	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
$861$	−34.7638	−	31.3722i	−1.18475	−	1.06916i
$862$			19.8562i			0.676304i
$863$	18.7890	+	5.03450i	0.639585	+	0.171376i	0.564015	−	0.825764i	$-0.309256\pi$
$863$	18.7890	+	5.03450i	0.639585	+	0.171376i	0.0755695	+	0.997141i	$0.475923\pi$
$864$	2.98605	−	4.25247i	0.101587	−	0.144672i
$865$	−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
$870$	4.81850	+	20.3711i	0.163362	+	0.690645i
$871$	2.43274	+	0.274549i	0.0824301	+	0.00930273i
$872$	9.41591	+	5.43628i	0.318863	+	0.184096i
$873$	23.0403	−	20.4676i	0.779797	−	0.692722i
$874$	−14.0428			−0.475004
$875$	−31.8102	+	2.57490i	−1.07538	+	0.0870476i
$876$	−9.70651	−	18.0210i	−0.327952	−	0.608872i
$877$	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
$879$	6.41420	+	0.189481i	0.216346	+	0.00639103i
$880$	−2.92795	−	5.07136i	−0.0987013	−	0.170956i
$881$	−14.0771			−0.474270			−0.237135	−	0.971477i	$-0.576208\pi$
$881$	−14.0771			−0.474270			−0.237135	+	0.971477i	$0.576208\pi$
$882$	−20.7340	−	3.33168i	−0.698151	−	0.112183i
$883$			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
$885$	6.62821	−	6.24784i	0.222805	−	0.210019i
$886$	−2.63118	+	0.705024i	−0.0883963	+	0.0236857i
$887$	29.8300	−	17.2224i	1.00159	−	0.578270i	0.0928742	−	0.995678i	$-0.470395\pi$
$887$	29.8300	−	17.2224i	1.00159	−	0.578270i	0.908719	+	0.417408i	$0.137061\pi$
$888$	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
$891$	26.5427	−	3.83986i	0.889213	−	0.128640i
$892$	−6.00755	−	22.4205i	−0.201148	−	0.750693i
$893$	−2.96634	−	1.71262i	−0.0992647	−	0.0573105i
$894$	−33.4489	+	7.91187i	−1.11870	+	0.264612i
$895$	14.7610	−	14.7610i	0.493405	−	0.493405i
$896$	1.50343	+	2.17709i	0.0502260	+	0.0727313i
$897$	−15.8084	−	12.4092i	−0.527828	−	0.414332i
$898$	15.8515	+	27.4556i	0.528971	+	0.916204i
$899$	−4.86988	−	18.1747i	−0.162420	−	0.606159i
$900$	−3.05279	+	1.52978i	−0.101760	+	0.0509927i
$901$	−7.69970	+	4.44542i	−0.256514	+	0.148098i
$902$	−21.5312	+	21.5312i	−0.716911	+	0.716911i
$903$	8.82265	−	0.452446i	0.293599	−	0.0150565i
$904$	−11.4116	+	11.4116i	−0.379543	+	0.379543i
$905$	10.0171	−	37.3842i	0.332979	−	1.24269i
$906$	−8.49549	−	9.01269i	−0.282244	−	0.299427i
$907$	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	$-0.884831\pi$
$911$		−	21.3678i		−	0.707946i	0.935256	−	0.353973i	$-0.115169\pi$
$912$	−3.97066	+	6.43104i	−0.131482	+	0.212953i
$913$	10.1856	−	17.6420i	0.337095	−	0.583865i
$914$	−9.38465	+	16.2547i	−0.310417	+	0.537657i
$915$	15.7880	+	9.74783i	0.521934	+	0.322253i
$916$	13.5188	+	13.5188i	0.446674	+	0.446674i
$917$	−0.288442	+	1.57590i	−0.00952520	+	0.0520407i
$918$	10.5522	+	0.937347i	0.348276	+	0.0309371i
$919$	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
$921$	−0.768954	+	26.0302i	−0.0253379	+	0.857725i
$922$	−30.7893	+	17.7762i	−1.01399	+	0.585429i
$923$	35.7402	−	15.5856i	1.17640	−	0.513007i
$924$	−2.85414	+	13.3540i	−0.0938944	+	0.439313i
$925$	−3.27264	−	3.27264i	−0.107604	−	0.107604i
$926$	20.5706	−	11.8764i	0.675991	−	0.390284i
$927$	−13.9724	−	27.8830i	−0.458915	−	0.915799i
$928$	−5.94052	+	1.59176i	−0.195007	+	0.0522520i
$929$	−29.4538	−	7.89212i	−0.966347	−	0.258932i	−0.259062	−	0.965861i	$-0.583413\pi$
$929$	−29.4538	−	7.89212i	−0.966347	−	0.258932i	−0.707285	+	0.706929i	$0.750080\pi$
$930$	−9.16815	+	4.93818i	−0.300636	+	0.161929i
$931$	30.3922	+	3.05738i	0.996064	+	0.100201i
$932$			15.7079i			0.514530i
$933$	−5.72356	−	24.1974i	−0.187381	−	0.792188i
$934$	−3.33052	−	12.4297i	−0.108978	−	0.406711i
$935$	5.96944	−	10.3394i	0.195222	−	0.338134i
$936$	−10.1529	+	3.73088i	−0.331857	+	0.121948i
$937$	−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	$-0.959616\pi$
$941$	−6.01742	−	22.4573i	−0.196162	−	0.732088i	0.795800	−	0.605559i	$-0.207050\pi$
$942$	0.958021	−	32.4304i	0.0312140	−	1.05664i
$943$	31.7636	+	8.51103i	1.03437	+	0.277157i
$944$	1.89229	+	1.89229i	0.0615887	+	0.0615887i
$945$	−26.0402	−	7.19635i	−0.847087	−	0.234097i
$946$		−	5.74460i		−	0.186773i
$947$	−1.45149	+	5.41704i	−0.0471671	+	0.176030i	−0.985491	−	0.169727i	$-0.945711\pi$
$947$	−1.45149	+	5.41704i	−0.0471671	+	0.176030i	0.938324	+	0.345757i	$0.112378\pi$
$948$	−11.6330	−	12.3412i	−0.377823	−	0.400825i
$949$	−4.77837	+	42.3404i	−0.155112	+	1.37443i
$950$	4.30135	−	2.48339i	0.139554	−	0.0805717i
$951$	−50.0427	+	26.9542i	−1.62275	+	0.874049i
$952$	−2.31136	+	4.87380i	−0.0749115	+	0.157961i
$953$	−56.2129			−1.82091			−0.910457	−	0.413605i	$-0.864270\pi$
$953$	−56.2129			−1.82091			−0.910457	+	0.413605i	$0.864270\pi$
$954$	9.78075	−	8.68860i	0.316664	−	0.281304i
$955$	−45.8846	+	12.2948i	−1.48479	+	0.397849i
$956$	24.9892	−	6.69585i	0.808210	−	0.216559i
$957$	−27.0092	−	16.6761i	−0.873084	−	0.539061i
$958$	−21.5509			−0.696279
$959$	−5.29149	+	11.1578i	−0.170871	+	0.360304i
$960$	1.61408	+	2.99668i	0.0520943	+	0.0967175i
$961$	−18.7407	+	10.8199i	−0.604537	+	0.349030i
$962$	−9.13885	−	11.4640i	−0.294649	−	0.369615i
$963$	19.9952	+	39.9018i	0.644335	+	1.28582i
$964$	7.52585	−	28.0869i	0.242391	−	0.904617i
$965$			14.0617i			0.452662i
$966$	14.0306	−	4.54141i	0.451427	−	0.146118i
$967$	−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
$969$	−15.4025	−	0.455002i	−0.494800	−	0.0146168i
$970$	5.22493	+	19.4997i	0.167762	+	0.626097i
$971$	52.6319	−	30.3870i	1.68904	−	0.975166i	0.733781	−	0.679386i	$-0.237754\pi$
$971$	52.6319	−	30.3870i	1.68904	−	0.975166i	0.955256	−	0.295780i	$-0.0955794\pi$
$972$	−15.4870	+	1.77538i	−0.496747	+	0.0569453i
$973$	2.06628	−	2.43026i	0.0662420	−	0.0779106i
$974$	−7.00410			−0.224426
$975$	7.03669	+	1.00535i	0.225354	+	0.0321971i
$976$	−2.72566	+	4.72098i	−0.0872461	+	0.151115i
$977$	−5.40149	−	20.1587i	−0.172809	−	0.644932i	−0.996914	−	0.0784958i	$-0.974988\pi$
$977$	−5.40149	−	20.1587i	−0.172809	−	0.644932i	0.824105	−	0.566437i	$-0.191678\pi$
$978$	8.04474	−	1.90287i	0.257242	−	0.0608471i
$979$			37.3524i			1.19379i
$980$	8.03586	−	11.1648i	0.256696	−	0.356646i
$981$	−6.56753	−	31.9496i	−0.209685	−	1.02007i
$982$	4.42582	+	1.18590i	0.141234	+	0.0378435i
$983$	32.1403	−	8.61197i	1.02512	−	0.274679i	0.293184	−	0.956056i	$-0.405285\pi$
$983$	32.1403	−	8.61197i	1.02512	−	0.274679i	0.731933	+	0.681377i	$0.238618\pi$
$984$	12.8790	−	12.1400i	0.410569	−	0.387008i
$985$	35.4802	−	20.4845i	1.13049	−	0.652691i
$986$	−8.86616	−	8.86616i	−0.282356	−	0.282356i
$987$	3.51762	+	0.751822i	0.111967	+	0.0239308i
$988$	14.4218	−	6.28905i	0.458818	−	0.200081i
$989$	−5.37270	+	3.10193i	−0.170842	+	0.0986356i
$990$	−5.54062	+	16.6711i	−0.176092	+	0.529843i
$991$	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
$993$	−5.40590	−	10.0365i	−0.171551	−	0.318499i
$994$	−5.15126	+	28.1438i	−0.163388	+	0.892668i
$995$	6.22906	+	6.22906i	0.197475	+	0.197475i
$996$	−6.22057	+	10.0751i	−0.197106	+	0.319241i
$997$	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
$999$	−8.90386	−	19.1609i	−0.281706	−	0.606224i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.26037 - 1.18805i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.89818 + 0.508616i) q^{5} +(1.52492 - 0.821356i) q^{6} +(1.71379 - 2.01567i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.177090 - 2.99477i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.26037 - 1.18805i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.89818 + 0.508616i) q^{5} +(1.52492 - 0.821356i) q^{6} +(1.71379 - 2.01567i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.177090 - 2.99477i) q^{9} +(1.70186 + 0.982571i) q^{10} +(-2.87835 + 0.771252i) q^{11} +(1.68554 - 0.398691i) q^{12} +(-3.35607 - 1.31786i) q^{13} +(2.17709 - 1.50343i) q^{14} +(2.99668 - 1.61408i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.01939 + 1.76563i) q^{17} +(0.946159 - 2.84689i) q^{18} +(-1.12940 + 4.21497i) q^{19} +(1.38957 + 1.38957i) q^{20} +(-0.234697 - 4.57656i) q^{21} -2.97989 q^{22} +(1.60906 + 2.78697i) q^{23} +(1.73130 + 0.0511439i) 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} +(3.31233 - 0.783485i) q^{30} +(-2.95519 + 0.791840i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.71152 + 4.39168i) 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} +(-5.79559 + 2.32617i) q^{39} +(0.982571 + 1.70186i) q^{40} +(7.22551 - 7.22551i) q^{41} +(0.957802 - 4.48136i) q^{42} +1.92779i q^{43} +(-2.87835 - 0.771252i) q^{44} +(1.85934 - 5.59455i) 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} +(0.812842 + 3.43644i) q^{51} +(-2.24751 - 2.81934i) q^{52} +(3.77663 + 2.18044i) q^{53} +(-2.18972 - 4.71223i) q^{54} -5.85591 q^{55} +(2.63713 - 0.213464i) q^{56} +(3.58412 + 6.65422i) q^{57} +(-1.59176 + 5.94052i) q^{58} +(2.58491 - 0.692626i) q^{59} +(3.40224 + 0.100505i) q^{60} +(2.72566 + 4.72098i) q^{61} -3.05944 q^{62} +(-5.73297 - 5.48935i) q^{63} +1.00000i q^{64} +(-5.70016 - 4.20850i) q^{65} +(-3.75578 + 3.54025i) 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} +(2.24284 - 1.99240i) q^{72} +(-3.05864 - 11.4150i) q^{73} +(3.52144 + 2.03310i) q^{74} +(-1.91850 + 0.453796i) q^{75} +(-3.08557 + 3.08557i) q^{76} +(-3.37829 + 7.12357i) q^{77} +(-6.20017 + 0.746900i) q^{78} +(-4.89586 - 8.47987i) q^{79} +(0.508616 + 1.89818i) q^{80} +(-8.93728 - 1.06069i) q^{81} +(8.84941 - 5.10921i) q^{82} +(-4.83395 + 4.83395i) q^{83} +(2.08503 - 4.08077i) q^{84} +(-2.83301 + 2.83301i) q^{85} +(-0.498949 + 1.86210i) q^{86} +(7.30659 + 7.75141i) 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} +(-2.78390 + 4.50892i) q^{93} +(-0.392473 + 0.679782i) q^{94} +(-4.28760 + 7.42635i) q^{95} +(1.47377 + 0.909940i) q^{96} +(7.26398 + 7.26398i) q^{97} +(0.700646 - 6.96485i) q^{98} +(1.79999 + 8.75658i) 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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