LMFDB - Embedded newform 880.2.bk.b.243.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(243,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.243"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.20
Character	$\chi$	$=$	880.243
Dual form			880.2.bk.b.507.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23415 + 0.690563i) q^{2} -1.48151 q^{3} +(1.04624 - 1.70452i) q^{4} +(-1.55039 + 1.61130i) q^{5} +(1.82841 - 1.02308i) q^{6} +(2.89237 - 2.89237i) q^{7} +(-0.114146 + 2.82612i) q^{8} -0.805118 q^{9} +(0.800715 - 3.05922i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-1.55003 + 2.52526i) q^{12} +3.15509i q^{13} +(-1.57225 + 5.56697i) q^{14} +(2.29693 - 2.38716i) q^{15} +(-1.81074 - 3.56668i) q^{16} +(-1.30571 + 1.30571i) q^{17} +(0.993635 - 0.555985i) q^{18} +(-3.06068 - 3.06068i) q^{19} +(1.12439 + 4.32848i) q^{20} +(-4.28508 + 4.28508i) q^{21} +(-1.36098 - 0.384373i) q^{22} +(-0.293363 - 0.293363i) q^{23} +(0.169109 - 4.18694i) q^{24} +(-0.192552 - 4.99629i) q^{25} +(-2.17879 - 3.89385i) q^{26} +5.63733 q^{27} +(-1.90396 - 7.95620i) q^{28} +(3.64395 - 3.64395i) q^{29} +(-1.18627 + 4.53228i) q^{30} -5.61108i q^{31} +(4.69774 + 3.15138i) q^{32} +(-1.04759 - 1.04759i) q^{33} +(0.709763 - 2.51311i) q^{34} +(0.176150 + 9.14477i) q^{35} +(-0.842351 + 1.37234i) q^{36} -0.849705i q^{37} +(5.89093 + 1.66374i) q^{38} -4.67431i q^{39} +(-4.37675 - 4.56553i) q^{40} +0.0766293i q^{41} +(2.32930 - 8.24754i) q^{42} +12.3051i q^{43} +(1.94508 - 0.465467i) q^{44} +(1.24825 - 1.29728i) q^{45} +(0.564639 + 0.159468i) q^{46} +(4.95296 + 4.95296i) q^{47} +(2.68264 + 5.28408i) q^{48} -9.73155i q^{49} +(3.68789 + 6.03320i) q^{50} +(1.93442 - 1.93442i) q^{51} +(5.37790 + 3.30100i) q^{52} +3.15026 q^{53} +(-6.95731 + 3.89294i) q^{54} +(-2.23565 + 0.0430640i) q^{55} +(7.84403 + 8.50433i) q^{56} +(4.53444 + 4.53444i) q^{57} +(-1.98080 + 7.01356i) q^{58} +(4.56405 - 4.56405i) q^{59} +(-1.66579 - 6.41270i) q^{60} +(3.06868 + 3.06868i) q^{61} +(3.87481 + 6.92491i) q^{62} +(-2.32870 + 2.32870i) q^{63} +(-7.97394 - 0.645180i) q^{64} +(-5.08379 - 4.89164i) q^{65} +(2.01631 + 0.569453i) q^{66} +3.46931i q^{67} +(0.859508 + 3.59169i) q^{68} +(0.434621 + 0.434621i) q^{69} +(-6.53243 - 11.1644i) q^{70} +5.88208 q^{71} +(0.0919009 - 2.27536i) q^{72} +(10.2695 - 10.2695i) q^{73} +(0.586775 + 1.04866i) q^{74} +(0.285269 + 7.40207i) q^{75} +(-8.41920 + 2.01476i) q^{76} +4.09042 q^{77} +(3.22791 + 5.76879i) q^{78} +16.9605 q^{79} +(8.55435 + 2.61212i) q^{80} -5.93643 q^{81} +(-0.0529173 - 0.0945719i) q^{82} +14.7531 q^{83} +(2.82074 + 11.7872i) q^{84} +(-0.0795198 - 4.12824i) q^{85} +(-8.49743 - 15.1863i) q^{86} +(-5.39857 + 5.39857i) q^{87} +(-2.07908 + 1.91766i) q^{88} +0.571426 q^{89} +(-0.644670 + 2.46304i) q^{90} +(9.12568 + 9.12568i) q^{91} +(-0.806971 + 0.193112i) q^{92} +8.31289i q^{93} +(-9.53302 - 2.69235i) q^{94} +(9.67693 - 0.186401i) q^{95} +(-6.95977 - 4.66881i) q^{96} +(2.26353 - 2.26353i) q^{97} +(6.72025 + 12.0102i) q^{98} +(-0.569305 - 0.569305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.23415	+	0.690563i	−0.872675	+	0.488302i
$2$	−1.23415	+	0.690563i	−0.872675	+	0.488302i
$3$	−1.48151			−0.855352			−0.427676	−	0.903932i	$-0.640668\pi$
$3$	−1.48151			−0.855352			−0.427676	+	0.903932i	$0.640668\pi$
$4$	1.04624	−	1.70452i	0.523122	−	0.852258i
$5$	−1.55039	+	1.61130i	−0.693358	+	0.720594i
$5$	−1.55039	+	1.61130i	−0.693358	+	0.720594i
$6$	1.82841	−	1.02308i	0.746444	−	0.417670i
$7$	2.89237	−	2.89237i	1.09321	−	1.09321i	0.0980276	−	0.995184i	$-0.468747\pi$
$7$	2.89237	−	2.89237i	1.09321	−	1.09321i	0.995184	−	0.0980276i	$-0.0312533\pi$
$8$	−0.114146	+	2.82612i	−0.0403566	+	0.999185i
$9$	−0.805118			−0.268373
$10$	0.800715	−	3.05922i	0.253208	−	0.967412i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	−1.55003	+	2.52526i	−0.447454	+	0.728980i
$13$			3.15509i			0.875065i	0.899203	+	0.437532i	$0.144147\pi$
$13$			3.15509i			0.875065i	−0.899203	+	0.437532i	$0.855853\pi$
$14$	−1.57225	+	5.56697i	−0.420201	+	1.48784i
$15$	2.29693	−	2.38716i	0.593065	−	0.616361i
$16$	−1.81074	−	3.56668i	−0.452686	−	0.891670i
$17$	−1.30571	+	1.30571i	−0.316680	+	0.316680i	−0.847491	−	0.530810i	$-0.821888\pi$
$17$	−1.30571	+	1.30571i	−0.316680	+	0.316680i	0.530810	+	0.847491i	$0.321888\pi$
$18$	0.993635	−	0.555985i	0.234202	−	0.131047i
$19$	−3.06068	−	3.06068i	−0.702169	−	0.702169i	0.262707	−	0.964876i	$-0.415385\pi$
$19$	−3.06068	−	3.06068i	−0.702169	−	0.702169i	−0.964876	+	0.262707i	$0.915385\pi$
$20$	1.12439	+	4.32848i	0.251421	+	0.967878i
$21$	−4.28508	+	4.28508i	−0.935081	+	0.935081i
$22$	−1.36098	−	0.384373i	−0.290161	−	0.0819485i
$23$	−0.293363	−	0.293363i	−0.0611704	−	0.0611704i	0.675860	−	0.737030i	$-0.263772\pi$
$23$	−0.293363	−	0.293363i	−0.0611704	−	0.0611704i	−0.737030	+	0.675860i	$0.763772\pi$
$24$	0.169109	−	4.18694i	0.0345191	−	0.854655i
$25$	−0.192552	−	4.99629i	−0.0385105	−	0.999258i
$26$	−2.17879	−	3.89385i	−0.427296	−	0.763647i
$27$	5.63733			1.08491
$28$	−1.90396	−	7.95620i	−0.359814	−	1.50358i
$29$	3.64395	−	3.64395i	0.676665	−	0.676665i	−0.282579	−	0.959244i	$-0.591190\pi$
$29$	3.64395	−	3.64395i	0.676665	−	0.676665i	0.959244	+	0.282579i	$0.0911899\pi$
$30$	−1.18627	+	4.53228i	−0.216582	+	0.827478i
$31$		−	5.61108i		−	1.00778i	−0.863768	−	0.503890i	$-0.831902\pi$
$31$		−	5.61108i		−	1.00778i	0.863768	−	0.503890i	$-0.168098\pi$
$32$	4.69774	+	3.15138i	0.830452	+	0.557090i
$33$	−1.04759	−	1.04759i	−0.182362	−	0.182362i
$34$	0.709763	−	2.51311i	0.121723	−	0.430995i
$35$	0.176150	+	9.14477i	0.0297748	+	1.54575i
$36$	−0.842351	+	1.37234i	−0.140392	+	0.228723i
$37$		−	0.849705i		−	0.139691i	−0.997558	−	0.0698453i	$-0.977749\pi$
$37$		−	0.849705i		−	0.139691i	0.997558	−	0.0698453i	$-0.0222506\pi$
$38$	5.89093	+	1.66374i	0.955635	+	0.269895i
$39$		−	4.67431i		−	0.748489i
$40$	−4.37675	−	4.56553i	−0.692025	−	0.721873i
$41$			0.0766293i			0.0119675i	0.999982	+	0.00598374i	$0.00190469\pi$
$41$			0.0766293i			0.0119675i	−0.999982	+	0.00598374i	$0.998095\pi$
$42$	2.32930	−	8.24754i	0.359420	−	1.27262i
$43$			12.3051i			1.87651i	0.345950	+	0.938253i	$0.387557\pi$
$43$			12.3051i			1.87651i	−0.345950	+	0.938253i	$0.612443\pi$
$44$	1.94508	−	0.465467i	0.293232	−	0.0701719i
$45$	1.24825	−	1.29728i	0.186078	−	0.193388i
$46$	0.564639	+	0.159468i	0.0832515	+	0.0235122i
$47$	4.95296	+	4.95296i	0.722463	+	0.722463i	0.969106	−	0.246643i	$-0.0793275\pi$
$47$	4.95296	+	4.95296i	0.722463	+	0.722463i	−0.246643	+	0.969106i	$0.579328\pi$
$48$	2.68264	+	5.28408i	0.387206	+	0.762692i
$49$		−	9.73155i		−	1.39022i
$50$	3.68789	+	6.03320i	0.521547	+	0.853223i
$51$	1.93442	−	1.93442i	0.270873	−	0.270873i
$52$	5.37790	+	3.30100i	0.745781	+	0.457766i
$53$	3.15026			0.432722			0.216361	−	0.976313i	$-0.430581\pi$
$53$	3.15026			0.432722			0.216361	+	0.976313i	$0.430581\pi$
$54$	−6.95731	+	3.89294i	−0.946769	+	0.529761i
$55$	−2.23565	+	0.0430640i	−0.301455	+	0.00580675i
$56$	7.84403	+	8.50433i	1.04820	+	1.13644i
$57$	4.53444	+	4.53444i	0.600602	+	0.600602i
$58$	−1.98080	+	7.01356i	−0.260092	+	0.920925i
$59$	4.56405	−	4.56405i	0.594189	−	0.594189i	−0.344571	−	0.938760i	$-0.611976\pi$
$59$	4.56405	−	4.56405i	0.594189	−	0.594189i	0.938760	+	0.344571i	$0.111976\pi$
$60$	−1.66579	−	6.41270i	−0.215053	−	0.827876i
$61$	3.06868	+	3.06868i	0.392904	+	0.392904i	0.875721	−	0.482817i	$-0.160386\pi$
$61$	3.06868	+	3.06868i	0.392904	+	0.392904i	−0.482817	+	0.875721i	$0.660386\pi$
$62$	3.87481	+	6.92491i	0.492101	+	0.879464i
$63$	−2.32870	+	2.32870i	−0.293388	+	0.293388i
$64$	−7.97394	−	0.645180i	−0.996743	−	0.0806475i
$65$	−5.08379	−	4.89164i	−0.630566	−	0.606733i
$66$	2.01631	+	0.569453i	0.248190	+	0.0700949i
$67$			3.46931i			0.423844i	0.977287	+	0.211922i	$0.0679722\pi$
$67$			3.46931i			0.423844i	−0.977287	+	0.211922i	$0.932028\pi$
$68$	0.859508	+	3.59169i	0.104231	+	0.435556i
$69$	0.434621	+	0.434621i	0.0523222	+	0.0523222i
$70$	−6.53243	−	11.1644i	−0.780775	−	1.33440i
$71$	5.88208			0.698074			0.349037	−	0.937109i	$-0.386509\pi$
$71$	5.88208			0.698074			0.349037	+	0.937109i	$0.386509\pi$
$72$	0.0919009	−	2.27536i	0.0108306	−	0.268154i
$73$	10.2695	−	10.2695i	1.20195	−	1.20195i	0.228375	−	0.973573i	$-0.426659\pi$
$73$	10.2695	−	10.2695i	1.20195	−	1.20195i	0.973573	−	0.228375i	$-0.0733413\pi$
$74$	0.586775	+	1.04866i	0.0682112	+	0.121904i
$75$	0.285269	+	7.40207i	0.0329400	+	0.854718i
$76$	−8.41920	+	2.01476i	−0.965749	+	0.231108i
$77$	4.09042			0.466147
$78$	3.22791	+	5.76879i	0.365488	+	0.653187i
$79$	16.9605			1.90821			0.954103	−	0.299478i	$-0.0968126\pi$
$79$	16.9605			1.90821			0.954103	+	0.299478i	$0.0968126\pi$
$80$	8.55435	+	2.61212i	0.956405	+	0.292044i
$81$	−5.93643			−0.659603
$82$	−0.0529173	−	0.0945719i	−0.00584374	−	0.0104437i
$83$	14.7531			1.61936			0.809680	−	0.586872i	$-0.199641\pi$
$83$	14.7531			1.61936			0.809680	+	0.586872i	$0.199641\pi$
$84$	2.82074	+	11.7872i	0.307768	+	1.28609i
$85$	−0.0795198	−	4.12824i	−0.00862513	−	0.447771i
$86$	−8.49743	−	15.1863i	−0.916302	−	1.63758i
$87$	−5.39857	+	5.39857i	−0.578787	+	0.578787i
$88$	−2.07908	+	1.91766i	−0.221631	+	0.204423i
$89$	0.571426			0.0605711			0.0302855	−	0.999541i	$-0.490358\pi$
$89$	0.571426			0.0605711			0.0302855	+	0.999541i	$0.490358\pi$
$90$	−0.644670	+	2.46304i	−0.0679542	+	0.259627i
$91$	9.12568	+	9.12568i	0.956631	+	0.956631i
$92$	−0.806971	+	0.193112i	−0.0841325	+	0.0201333i
$93$			8.31289i			0.862007i
$94$	−9.53302	−	2.69235i	−0.983256	−	0.277695i
$95$	9.67693	−	0.186401i	0.992832	−	0.0191243i
$96$	−6.95977	−	4.66881i	−0.710329	−	0.476509i
$97$	2.26353	−	2.26353i	0.229827	−	0.229827i	−0.582794	−	0.812620i	$-0.698040\pi$
$97$	2.26353	−	2.26353i	0.229827	−	0.229827i	0.812620	+	0.582794i	$0.198040\pi$
$98$	6.72025	+	12.0102i	0.678848	+	1.21321i
$99$	−0.569305	−	0.569305i	−0.0572173	−	0.0572173i
$100$	−8.71771	−	4.89913i	−0.871771	−	0.489913i
$101$	−13.4033	+	13.4033i	−1.33368	+	1.33368i	−0.431627	+	0.902052i	$0.642060\pi$
$101$	−13.4033	+	13.4033i	−1.33368	+	1.33368i	−0.902052	+	0.431627i	$0.857940\pi$
$102$	−1.05152	+	3.72321i	−0.104116	+	0.368652i
$103$	6.38559	+	6.38559i	0.629190	+	0.629190i	0.947864	−	0.318674i	$-0.103238\pi$
$103$	6.38559	+	6.38559i	0.629190	+	0.629190i	−0.318674	+	0.947864i	$0.603238\pi$
$104$	−8.91668	−	0.360140i	−0.874352	−	0.0353147i
$105$	−0.260969	−	13.5481i	−0.0254679	−	1.32216i
$106$	−3.88789	+	2.17546i	−0.377625	+	0.211299i
$107$	−1.32856			−0.128437			−0.0642184	−	0.997936i	$-0.520455\pi$
$107$	−1.32856			−0.128437			−0.0642184	+	0.997936i	$0.520455\pi$
$108$	5.89803	−	9.60892i	0.567538	−	0.924619i
$109$	13.0761	−	13.0761i	1.25246	−	1.25246i	0.297849	−	0.954613i	$-0.403731\pi$
$109$	13.0761	−	13.0761i	1.25246	−	1.25246i	0.954613	−	0.297849i	$-0.0962692\pi$
$110$	2.72939	−	1.59701i	0.260237	−	0.152269i
$111$			1.25885i			0.119485i
$112$	−15.5535	−	5.07881i	−1.46967	−	0.479902i
$113$	3.37196	+	3.37196i	0.317207	+	0.317207i	0.847694	−	0.530486i	$-0.177991\pi$
$113$	3.37196	+	3.37196i	0.317207	+	0.317207i	−0.530486	+	0.847694i	$0.677991\pi$
$114$	−8.72749	−	2.46486i	−0.817405	−	0.230855i
$115$	0.927523	−	0.0178663i	0.0864919	−	0.00166604i
$116$	−2.39871	−	10.0236i	−0.222714	−	0.930672i
$117$		−	2.54022i		−	0.234844i
$118$	−2.48095	+	8.78449i	−0.228390	+	0.808678i
$119$			7.55316i			0.692397i
$120$	6.48421	+	6.76389i	0.591925	+	0.617456i
$121$			1.00000i			0.0909091i
$122$	−5.90633	−	1.66809i	−0.534734	−	0.151022i
$123$		−	0.113527i		−	0.0102364i
$124$	−9.56417	−	5.87056i	−0.858888	−	0.527192i
$125$	8.34904	+	7.43596i	0.746761	+	0.665093i
$126$	1.26584	−	4.48207i	0.112770	−	0.399294i
$127$	−14.1632	−	14.1632i	−1.25678	−	1.25678i	−0.952623	−	0.304155i	$-0.901626\pi$
$127$	−14.1632	−	14.1632i	−1.25678	−	1.25678i	−0.304155	−	0.952623i	$-0.598374\pi$
$128$	10.2866	−	4.71026i	0.909213	−	0.416332i
$129$		−	18.2301i		−	1.60507i
$130$	9.65213	+	2.52633i	0.846548	+	0.221574i
$131$	4.96880	−	4.96880i	0.434126	−	0.434126i	−0.455903	−	0.890029i	$-0.650684\pi$
$131$	4.96880	−	4.96880i	0.434126	−	0.434126i	0.890029	+	0.455903i	$0.150684\pi$
$132$	−2.88166	+	0.689596i	−0.250817	+	0.0600216i
$133$	−17.7052			−1.53524
$134$	−2.39578	−	4.28164i	−0.206964	−	0.369878i
$135$	−8.74009	+	9.08342i	−0.752227	+	0.781776i
$136$	−3.54105	−	3.83913i	−0.303642	−	0.329203i
$137$	−6.53817	−	6.53817i	−0.558594	−	0.558594i	0.370313	−	0.928907i	$-0.379250\pi$
$137$	−6.53817	−	6.53817i	−0.558594	−	0.558594i	−0.928907	+	0.370313i	$0.879250\pi$
$138$	−0.836520	−	0.236254i	−0.0712093	−	0.0201112i
$139$	−6.53886	+	6.53886i	−0.554619	+	0.554619i	−0.927770	−	0.373151i	$-0.878277\pi$
$139$	−6.53886	+	6.53886i	−0.554619	+	0.554619i	0.373151	+	0.927770i	$0.378277\pi$
$140$	15.7717	+	9.26741i	1.33295	+	0.783239i
$141$	−7.33787	−	7.33787i	−0.617960	−	0.617960i
$142$	−7.25936	+	4.06195i	−0.609192	+	0.340871i
$143$	−2.23099	+	2.23099i	−0.186564	+	0.186564i
$144$	1.45786	+	2.87160i	0.121489	+	0.239300i
$145$	0.221923	+	11.5211i	0.0184297	+	0.956771i
$146$	−5.58232	+	19.7657i	−0.461996	+	1.63582i
$147$			14.4174i			1.18913i
$148$	−1.44833	−	0.888999i	−0.119052	−	0.0730753i
$149$	−7.47260	−	7.47260i	−0.612180	−	0.612180i	0.331334	−	0.943514i	$-0.392501\pi$
$149$	−7.47260	−	7.47260i	−0.612180	−	0.612180i	−0.943514	+	0.331334i	$0.892501\pi$
$150$	−5.46366	−	8.93826i	−0.446106	−	0.729806i
$151$	9.48714			0.772052			0.386026	−	0.922488i	$-0.373847\pi$
$151$	9.48714			0.772052			0.386026	+	0.922488i	$0.373847\pi$
$152$	8.99923	−	8.30050i	0.729934	−	0.673260i
$153$	1.05125	−	1.05125i	0.0849884	−	0.0849884i
$154$	−5.04819	+	2.82470i	−0.406795	+	0.227620i
$155$	9.04111	+	8.69939i	0.726200	+	0.698752i
$156$	−7.96743	−	4.89047i	−0.637905	−	0.391551i
$157$	9.98223			0.796669			0.398334	−	0.917240i	$-0.369588\pi$
$157$	9.98223			0.796669			0.398334	+	0.917240i	$0.369588\pi$
$158$	−20.9318	+	11.7123i	−1.66524	+	0.931781i
$159$	−4.66716			−0.370130
$160$	−12.3612	+	2.68358i	−0.977236	+	0.212155i
$161$	−1.69702			−0.133744
$162$	7.32644	−	4.09948i	0.575619	−	0.322086i
$163$	19.5974			1.53499			0.767494	−	0.641056i	$-0.221503\pi$
$163$	19.5974			1.53499			0.767494	+	0.641056i	$0.221503\pi$
$164$	0.130616	+	0.0801730i	0.0101994	+	0.00626046i
$165$	3.31215	−	0.0637999i	0.257851	−	0.00496682i
$166$	−18.2075	+	10.1879i	−1.41317	+	0.790736i
$167$	−12.3245	+	12.3245i	−0.953695	+	0.953695i	−0.998974	−	0.0452795i	$-0.985582\pi$
$167$	−12.3245	+	12.3245i	−0.953695	+	0.953695i	0.0452795	+	0.998974i	$0.485582\pi$
$168$	−11.6210	−	12.5993i	−0.896582	−	0.972056i
$169$	3.04540			0.234261
$170$	2.94895	+	5.03995i	0.226174	+	0.386547i
$171$	2.46421	+	2.46421i	0.188443	+	0.188443i
$172$	20.9742	+	12.8741i	1.59927	+	0.981642i
$173$		−	5.34557i		−	0.406416i	−0.979136	−	0.203208i	$-0.934863\pi$
$173$		−	5.34557i		−	0.406416i	0.979136	−	0.203208i	$-0.0651368\pi$
$174$	2.93458	−	10.3907i	0.222470	−	0.787716i
$175$	−15.0080	−	13.8942i	−1.13450	−	1.05030i
$176$	1.24163	−	3.80241i	0.0935917	−	0.286618i
$177$	−6.76171	+	6.76171i	−0.508241	+	0.508241i
$178$	−0.705225	+	0.394606i	−0.0528588	+	0.0295770i
$179$	1.30147	+	1.30147i	0.0972763	+	0.0972763i	0.754070	−	0.656794i	$-0.228088\pi$
$179$	1.30147	+	1.30147i	0.0972763	+	0.0972763i	−0.656794	+	0.754070i	$0.728088\pi$
$180$	−0.905264	−	3.48494i	−0.0674744	−	0.259752i
$181$	−13.9447	+	13.9447i	−1.03650	+	1.03650i	−0.0371901	+	0.999308i	$0.511841\pi$
$181$	−13.9447	+	13.9447i	−1.03650	+	1.03650i	−0.999308	+	0.0371901i	$0.988159\pi$
$182$	−17.5643	−	4.96058i	−1.30195	−	0.367703i
$183$	−4.54629	−	4.54629i	−0.336072	−	0.336072i
$184$	0.862566	−	0.795593i	0.0635892	−	0.0586519i
$185$	1.36913	+	1.31738i	0.100660	+	0.0968555i
$186$	−5.74058	−	10.2593i	−0.420920	−	0.752251i
$187$	−1.84655			−0.135033
$188$	13.6244	−	3.26039i	0.993661	−	0.237788i
$189$	16.3052	−	16.3052i	1.18603	−	1.18603i
$190$	−11.8141	+	6.91258i	−0.857081	+	0.501491i
$191$		−	7.86548i		−	0.569126i	−0.958657	−	0.284563i	$-0.908151\pi$
$191$		−	7.86548i		−	0.569126i	0.958657	−	0.284563i	$-0.0918485\pi$
$192$	11.8135	+	0.955843i	0.852566	+	0.0689820i
$193$	2.45386	+	2.45386i	0.176632	+	0.176632i	0.789886	−	0.613254i	$-0.210140\pi$
$193$	2.45386	+	2.45386i	0.176632	+	0.176632i	−0.613254	+	0.789886i	$0.710140\pi$
$194$	−1.23042	+	4.35664i	−0.0883391	+	0.312789i
$195$	7.53170	+	7.24703i	0.539356	+	0.518970i
$196$	−16.5876	−	10.1816i	−1.18483	−	0.727256i
$197$		−	23.3992i		−	1.66713i	−0.552425	−	0.833563i	$-0.686297\pi$
$197$		−	23.3992i		−	1.66713i	0.552425	−	0.833563i	$-0.313703\pi$
$198$	1.09575	+	0.309465i	0.0778714	+	0.0219928i
$199$		−	17.5047i		−	1.24088i	−0.784255	−	0.620439i	$-0.786955\pi$
$199$		−	17.5047i		−	1.24088i	0.784255	−	0.620439i	$-0.213045\pi$
$200$	14.1421	+	0.0261290i	0.999998	+	0.00184760i
$201$		−	5.13983i		−	0.362536i
$202$	7.28584	−	25.7975i	0.512630	−	1.81511i
$203$		−	21.0793i		−	1.47948i
$204$	−1.27337	−	5.32113i	−0.0891539	−	0.372554i
$205$	−0.123472	−	0.118806i	−0.00862369	−	0.00829774i
$206$	−12.2904	−	3.47111i	−0.856313	−	0.241844i
$207$	0.236192	+	0.236192i	0.0164165	+	0.0164165i
$208$	11.2532	−	5.71306i	0.780269	−	0.396130i
$209$		−	4.32846i		−	0.299406i
$210$	9.67789	+	16.5401i	0.667838	+	1.14138i
$211$	12.3456	−	12.3456i	0.849905	−	0.849905i	−0.140216	−	0.990121i	$-0.544780\pi$
$211$	12.3456	−	12.3456i	0.849905	−	0.849905i	0.990121	+	0.140216i	$0.0447796\pi$
$212$	3.29595	−	5.36967i	0.226366	−	0.368790i
$213$	−8.71438			−0.597099
$214$	1.63964	−	0.917456i	0.112084	−	0.0627160i
$215$	−19.8271	−	19.0777i	−1.35220	−	1.30109i
$216$	−0.643478	+	15.9318i	−0.0437831	+	1.08402i
$217$	−16.2293	−	16.2293i	−1.10172	−	1.10172i
$218$	−7.10797	+	25.1677i	−0.481412	+	1.70457i
$219$	−15.2143	+	15.2143i	−1.02809	+	1.02809i
$220$	−2.26564	+	3.85576i	−0.152749	+	0.259955i
$221$	−4.11963	−	4.11963i	−0.277116	−	0.277116i
$222$	−0.869315	−	1.55361i	−0.0583446	−	0.104271i
$223$	−18.9155	+	18.9155i	−1.26668	+	1.26668i	−0.318883	+	0.947794i	$0.603308\pi$
$223$	−18.9155	+	18.9155i	−1.26668	+	1.26668i	−0.947794	+	0.318883i	$0.896692\pi$
$224$	22.7025	−	4.47265i	1.51688	−	0.298842i
$225$	0.155027	+	4.02260i	0.0103352	+	0.268174i
$226$	−6.49005	−	1.83295i	−0.431712	−	0.121926i
$227$			3.01644i			0.200208i	0.994977	+	0.100104i	$0.0319176\pi$
$227$			3.01644i			0.200208i	−0.994977	+	0.100104i	$0.968082\pi$
$228$	12.4732	−	2.98489i	0.826055	−	0.197679i
$229$	10.8003	+	10.8003i	0.713705	+	0.713705i	0.967308	−	0.253604i	$-0.0816159\pi$
$229$	10.8003	+	10.8003i	0.713705	+	0.713705i	−0.253604	+	0.967308i	$0.581616\pi$
$230$	−1.13236	+	0.662563i	−0.0746658	+	0.0436881i
$231$	−6.06001			−0.398720
$232$	9.88232	+	10.7142i	0.648806	+	0.703422i
$233$	11.1011	−	11.1011i	0.727255	−	0.727255i	−0.242817	−	0.970072i	$-0.578072\pi$
$233$	11.1011	−	11.1011i	0.727255	−	0.727255i	0.970072	+	0.242817i	$0.0780715\pi$
$234$	1.75418	+	3.13501i	0.114675	+	0.204942i
$235$	−15.6597	+	0.301644i	−1.02153	+	0.0196771i
$236$	−3.00438	−	12.5546i	−0.195569	−	0.817236i
$237$	−25.1272			−1.63219
$238$	−5.21594	−	9.32172i	−0.338099	−	0.604238i
$239$	−7.52700			−0.486881			−0.243441	−	0.969916i	$-0.578276\pi$
$239$	−7.52700			−0.486881			−0.243441	+	0.969916i	$0.578276\pi$
$240$	−12.6734	−	3.86989i	−0.818063	−	0.249800i
$241$	6.17299			0.397638			0.198819	−	0.980036i	$-0.436289\pi$
$241$	6.17299			0.397638			0.198819	+	0.980036i	$0.436289\pi$
$242$	−0.690563	−	1.23415i	−0.0443911	−	0.0793341i
$243$	−8.11710			−0.520712
$244$	8.44121	−	2.02002i	0.540393	−	0.129319i
$245$	15.6804	+	15.0877i	1.00179	+	0.963921i
$246$	0.0783978	+	0.140109i	0.00499846	+	0.00893306i
$247$	9.65673	−	9.65673i	0.614443	−	0.614443i
$248$	15.8576	+	0.640481i	1.00696	+	0.0406706i
$249$	−21.8569			−1.38512
$250$	−15.4390	−	3.41154i	−0.976445	−	0.215765i
$251$	−9.71239	−	9.71239i	−0.613041	−	0.613041i	0.330697	−	0.943737i	$-0.392716\pi$
$251$	−9.71239	−	9.71239i	−0.613041	−	0.613041i	−0.943737	+	0.330697i	$0.892716\pi$
$252$	1.53291	+	6.40568i	0.0965643	+	0.403520i
$253$		−	0.414878i		−	0.0260831i
$254$	27.2600	+	7.69889i	1.71045	+	0.483071i
$255$	0.117810	+	6.11605i	0.00737753	+	0.383002i
$256$	−9.44241	+	12.9167i	−0.590151	+	0.807293i
$257$	−6.14195	+	6.14195i	−0.383125	+	0.383125i	−0.872227	−	0.489102i	$-0.837325\pi$
$257$	−6.14195	+	6.14195i	−0.383125	+	0.383125i	0.489102	+	0.872227i	$0.337325\pi$
$258$	12.5891	+	22.4987i	0.783761	+	1.40071i
$259$	−2.45766	−	2.45766i	−0.152711	−	0.152711i
$260$	−13.6568	+	3.54754i	−0.846956	+	0.220009i
$261$	−2.93381	+	2.93381i	−0.181598	+	0.181598i
$262$	−2.70096	+	9.56350i	−0.166866	+	0.590835i
$263$	−5.26324	−	5.26324i	−0.324545	−	0.324545i	0.525963	−	0.850508i	$-0.323705\pi$
$263$	−5.26324	−	5.26324i	−0.324545	−	0.324545i	−0.850508	+	0.525963i	$0.823705\pi$
$264$	3.08019	−	2.84104i	0.189573	−	0.174854i
$265$	−4.88415	+	5.07601i	−0.300031	+	0.311817i
$266$	21.8509	−	12.2266i	1.33976	−	0.749660i
$267$	−0.846576			−0.0518096
$268$	5.91349	+	3.62975i	0.361224	+	0.221722i
$269$	−20.1781	+	20.1781i	−1.23028	+	1.23028i	−0.266424	+	0.963856i	$0.585842\pi$
$269$	−20.1781	+	20.1781i	−1.23028	+	1.23028i	−0.963856	+	0.266424i	$0.914158\pi$
$270$	4.51390	−	17.2459i	0.274707	−	1.04955i
$271$			7.09237i			0.430831i	0.976523	+	0.215415i	$0.0691105\pi$
$271$			7.09237i			0.430831i	−0.976523	+	0.215415i	$0.930889\pi$
$272$	7.02134	+	2.29274i	0.425731	+	0.139018i
$273$	−13.5198	−	13.5198i	−0.818256	−	0.818256i
$274$	12.5841	+	3.55405i	0.760233	+	0.214708i
$275$	3.39676	−	3.66907i	0.204832	−	0.221253i
$276$	1.19554	−	0.286098i	0.0719629	−	0.0172211i
$277$			2.69961i			0.162204i	0.996706	+	0.0811020i	$0.0258440\pi$
$277$			2.69961i			0.162204i	−0.996706	+	0.0811020i	$0.974156\pi$
$278$	3.55443	−	12.5854i	0.213181	−	0.754824i
$279$			4.51758i			0.270461i
$280$	−25.8643	−	0.546015i	−1.54569	−	0.0326306i
$281$		−	3.18063i		−	0.189741i	−0.995490	−	0.0948704i	$-0.969756\pi$
$281$		−	3.18063i		−	0.189741i	0.995490	−	0.0948704i	$-0.0302437\pi$
$282$	14.1233	+	3.98876i	0.841030	+	0.237527i
$283$		−	23.1925i		−	1.37865i	−0.724453	−	0.689324i	$-0.757907\pi$
$283$		−	23.1925i		−	1.37865i	0.724453	−	0.689324i	$-0.242093\pi$
$284$	6.15410	−	10.0261i	0.365178	−	0.594939i
$285$	−14.3365	+	0.276155i	−0.849221	+	0.0163580i
$286$	1.21273	−	4.29401i	0.0717103	−	0.253910i
$287$	0.221640	+	0.221640i	0.0130830	+	0.0130830i
$288$	−3.78224	−	2.53723i	−0.222871	−	0.149508i
$289$			13.5903i			0.799427i
$290$	−8.22990	−	14.0654i	−0.483277	−	0.825951i
$291$	−3.35345	+	3.35345i	−0.196583	+	0.196583i
$292$	−6.76008	−	28.2488i	−0.395603	−	1.65314i
$293$	−22.6517			−1.32333			−0.661664	−	0.749801i	$-0.730149\pi$
$293$	−22.6517			−1.32333			−0.661664	+	0.749801i	$0.730149\pi$
$294$	−9.95614	−	17.7932i	−0.580654	−	1.03772i
$295$	0.277959	+	14.4301i	0.0161834	+	0.840155i
$296$	2.40137	+	0.0969902i	0.139577	+	0.00563744i
$297$	3.98620	+	3.98620i	0.231303	+	0.231303i
$298$	14.3826	+	4.06200i	0.833162	+	0.235305i
$299$	0.925587	−	0.925587i	0.0535281	−	0.0535281i
$300$	12.9154	+	7.25813i	0.745671	+	0.419049i
$301$	35.5908	+	35.5908i	2.05142	+	2.05142i
$302$	−11.7085	+	6.55147i	−0.673750	+	0.376995i
$303$	19.8572	−	19.8572i	1.14077	−	1.14077i
$304$	−5.37436	+	16.4586i	−0.308241	+	0.943965i
$305$	−9.70222	+	0.186888i	−0.555548	+	0.0107012i
$306$	−0.571443	+	2.02335i	−0.0326672	+	0.115667i
$307$		−	16.9039i		−	0.964759i	−0.875962	−	0.482379i	$-0.839773\pi$
$307$		−	16.9039i		−	0.964759i	0.875962	−	0.482379i	$-0.160227\pi$
$308$	4.27958	−	6.97219i	0.243852	−	0.397277i
$309$	−9.46033	−	9.46033i	−0.538179	−	0.538179i
$310$	−17.1656	−	4.49288i	−0.974938	−	0.255178i
$311$	27.8539			1.57945			0.789724	−	0.613463i	$-0.210224\pi$
$311$	27.8539			1.57945			0.789724	+	0.613463i	$0.210224\pi$
$312$	13.2102	+	0.533553i	0.747879	+	0.0302065i
$313$	−14.0290	+	14.0290i	−0.792965	+	0.792965i	−0.981975	−	0.189010i	$-0.939472\pi$
$313$	−14.0290	+	14.0290i	−0.792965	+	0.792965i	0.189010	+	0.981975i	$0.439472\pi$
$314$	−12.3196	+	6.89336i	−0.695233	+	0.389015i
$315$	−0.141822	−	7.36262i	−0.00799074	−	0.414836i
$316$	17.7448	−	28.9094i	0.998225	−	1.62628i
$317$	−11.6983			−0.657043			−0.328521	−	0.944497i	$-0.606550\pi$
$317$	−11.6983			−0.657043			−0.328521	+	0.944497i	$0.606550\pi$
$318$	5.75996	−	3.22297i	0.323003	−	0.180735i
$319$	5.15333			0.288531
$320$	13.4023	−	11.8481i	0.749213	−	0.662329i
$321$	1.96828			0.109859
$322$	2.09438	−	1.17190i	0.116715	−	0.0653076i
$323$	7.99271			0.444726
$324$	−6.21096	+	10.1187i	−0.345053	+	0.562152i
$325$	15.7638	−	0.607520i	0.874416	−	0.0336992i
$326$	−24.1861	+	13.5333i	−1.33955	+	0.749538i
$327$	−19.3724	+	19.3724i	−1.07130	+	1.07130i
$328$	−0.216564	−	0.00874691i	−0.0119577	−	0.000482967i
$329$	28.6515			1.57961
$330$	−4.04363	+	2.36599i	−0.222594	+	0.130243i
$331$	8.29523	+	8.29523i	0.455947	+	0.455947i	0.897323	−	0.441375i	$-0.145509\pi$
$331$	8.29523	+	8.29523i	0.455947	+	0.455947i	−0.441375	+	0.897323i	$0.645509\pi$
$332$	15.4353	−	25.1468i	0.847123	−	1.38011i
$333$			0.684113i			0.0374891i
$334$	6.69939	−	23.7210i	0.366574	−	1.29796i
$335$	−5.59009	−	5.37880i	−0.305419	−	0.293875i
$336$	23.0427	+	7.52432i	1.25708	+	0.410486i
$337$	7.80621	−	7.80621i	0.425231	−	0.425231i	−0.461769	−	0.887000i	$-0.652785\pi$
$337$	7.80621	−	7.80621i	0.425231	−	0.425231i	0.887000	+	0.461769i	$0.152785\pi$
$338$	−3.75847	+	2.10304i	−0.204434	+	0.114390i
$339$	−4.99561	−	4.99561i	−0.271324	−	0.271324i
$340$	−7.11985	−	4.18361i	−0.386128	−	0.226888i
$341$	3.96763	−	3.96763i	0.214859	−	0.214859i
$342$	−4.74290	−	1.33951i	−0.256466	−	0.0724323i
$343$	−7.90065	−	7.90065i	−0.426595	−	0.426595i
$344$	−34.7757	−	1.40457i	−1.87498	−	0.0757295i
$345$	−1.37414	+	0.0264692i	−0.0739811	+	0.00142505i
$346$	3.69146	+	6.59723i	0.198454	+	0.354669i
$347$	26.6040			1.42818			0.714088	−	0.700056i	$-0.246841\pi$
$347$	26.6040			1.42818			0.714088	+	0.700056i	$0.246841\pi$
$348$	3.55372	+	14.8502i	0.190499	+	0.796052i
$349$	1.21594	−	1.21594i	0.0650878	−	0.0650878i	−0.673814	−	0.738901i	$-0.735345\pi$
$349$	1.21594	−	1.21594i	0.0650878	−	0.0650878i	0.738901	+	0.673814i	$0.235345\pi$
$350$	28.1169	+	6.78347i	1.50291	+	0.362592i
$351$			17.7863i			0.949363i
$352$	1.09345	+	5.55017i	0.0582808	+	0.295825i
$353$	21.0331	+	21.0331i	1.11948	+	1.11948i	0.991818	+	0.127659i	$0.0407464\pi$
$353$	21.0331	+	21.0331i	1.11948	+	1.11948i	0.127659	+	0.991818i	$0.459254\pi$
$354$	3.67556	−	13.0143i	0.195354	−	0.691704i
$355$	−9.11955	+	9.47777i	−0.484015	+	0.503028i
$356$	0.597852	−	0.974005i	0.0316861	−	0.0516221i
$357$		−	11.1901i		−	0.592244i
$358$	−2.50495	−	0.707459i	−0.132391	−	0.0373904i
$359$			27.3352i			1.44270i	0.692571	+	0.721349i	$0.256478\pi$
$359$			27.3352i			1.44270i	−0.692571	+	0.721349i	$0.743522\pi$
$360$	3.52380	+	3.67579i	0.185721	+	0.193731i
$361$		−	0.264442i		−	0.0139180i
$362$	7.58011	−	26.8394i	0.398402	−	1.41065i
$363$		−	1.48151i		−	0.0777593i
$364$	25.1025	−	6.00716i	1.31573	−	0.314861i
$365$	0.625427	+	32.4688i	0.0327364	+	1.69950i
$366$	8.75030	+	2.47130i	0.457386	+	0.129177i
$367$	2.80960	+	2.80960i	0.146660	+	0.146660i	0.776624	−	0.629964i	$-0.216930\pi$
$367$	2.80960	+	2.80960i	0.146660	+	0.146660i	−0.629964	+	0.776624i	$0.716930\pi$
$368$	−0.515126	+	1.57754i	−0.0268528	+	0.0822348i
$369$		−	0.0616956i		−	0.00321174i
$370$	−2.59944	−	0.680371i	−0.135138	−	0.0353708i
$371$	9.11171	−	9.11171i	0.473056	−	0.473056i
$372$	14.1694	+	8.69732i	0.734652	+	0.450935i
$373$	−18.8843			−0.977794			−0.488897	−	0.872341i	$-0.662601\pi$
$373$	−18.8843			−0.977794			−0.488897	+	0.872341i	$0.662601\pi$
$374$	2.27892	−	1.27516i	0.117840	−	0.0659369i
$375$	−12.3692	−	11.0165i	−0.638743	−	0.568889i
$376$	−14.5630	+	13.4323i	−0.751031	+	0.692719i
$377$	11.4970	+	11.4970i	0.592126	+	0.592126i
$378$	−8.86328	+	31.3829i	−0.455878	+	1.61416i
$379$	0.772930	−	0.772930i	0.0397028	−	0.0397028i	−0.686977	−	0.726679i	$-0.741063\pi$
$379$	0.772930	−	0.772930i	0.0397028	−	0.0397028i	0.726679	+	0.686977i	$0.241063\pi$
$380$	9.80672	−	16.6895i	0.503074	−	0.856153i
$381$	20.9829	+	20.9829i	1.07499	+	1.07499i
$382$	5.43161	+	9.70717i	0.277905	+	0.496662i
$383$	−23.8262	+	23.8262i	−1.21746	+	1.21746i	−0.248947	+	0.968517i	$0.580084\pi$
$383$	−23.8262	+	23.8262i	−1.21746	+	1.21746i	−0.968517	+	0.248947i	$0.919916\pi$
$384$	−15.2397	+	6.97832i	−0.777697	+	0.356111i
$385$	−6.34177	+	6.59088i	−0.323206	+	0.335902i
$386$	−4.72297	−	1.33388i	−0.240393	−	0.0678927i
$387$		−	9.90704i		−	0.503603i
$388$	−1.49001	−	6.22643i	−0.0756440	−	0.316099i
$389$	−2.75557	−	2.75557i	−0.139713	−	0.139713i	0.633791	−	0.773504i	$-0.281498\pi$
$389$	−2.75557	−	2.75557i	−0.139713	−	0.139713i	−0.773504	+	0.633791i	$0.781498\pi$
$390$	−14.2998	−	3.74279i	−0.724097	−	0.189524i
$391$	0.766092			0.0387429
$392$	27.5026	+	1.11082i	1.38909	+	0.0561047i
$393$	−7.36134	+	7.36134i	−0.371330	+	0.371330i
$394$	16.1586	+	28.8781i	0.814061	+	1.45486i
$395$	−26.2955	+	27.3284i	−1.32307	+	1.37504i
$396$	−1.56602	+	0.374756i	−0.0786955	+	0.0188322i
$397$	−15.8149			−0.793729			−0.396865	−	0.917877i	$-0.629902\pi$
$397$	−15.8149			−0.793729			−0.396865	+	0.917877i	$0.629902\pi$
$398$	12.0881	+	21.6034i	0.605923	+	1.08288i
$399$	26.2305			1.31317
$400$	−17.4715	+	9.73378i	−0.873575	+	0.486689i
$401$	12.3269			0.615574			0.307787	−	0.951455i	$-0.400412\pi$
$401$	12.3269			0.615574			0.307787	+	0.951455i	$0.400412\pi$
$402$	3.54938	+	6.34331i	0.177027	+	0.316376i
$403$	17.7035			0.881873
$404$	8.82300	+	36.8693i	0.438961	+	1.83432i
$405$	9.20381	−	9.56535i	0.457341	−	0.475306i
$406$	14.5566	+	26.0150i	0.722431	+	1.29110i
$407$	0.600832	−	0.600832i	0.0297821	−	0.0297821i
$408$	5.24611	+	5.68772i	0.259721	+	0.281584i
$409$	4.28692			0.211974			0.105987	−	0.994367i	$-0.466200\pi$
$409$	4.28692			0.211974			0.105987	+	0.994367i	$0.466200\pi$
$410$	0.234426	+	0.0613582i	0.0115775	+	0.00303027i
$411$	9.68639	+	9.68639i	0.477795	+	0.477795i
$412$	17.5652	−	4.20344i	0.865376	−	0.207089i
$413$		−	26.4018i		−	1.29915i
$414$	−0.454601	−	0.128390i	−0.0223424	−	0.00631004i
$415$	−22.8731	+	23.7716i	−1.12279	+	1.16690i
$416$	−9.94289	+	14.8218i	−0.487490	+	0.726699i
$417$	9.68741	−	9.68741i	0.474395	−	0.474395i
$418$	2.98907	+	5.34196i	0.146200	+	0.261284i
$419$	−3.66585	−	3.66585i	−0.179088	−	0.179088i	0.611870	−	0.790958i	$-0.290418\pi$
$419$	−3.66585	−	3.66585i	−0.179088	−	0.179088i	−0.790958	+	0.611870i	$0.790418\pi$
$420$	−23.3660	−	13.7298i	−1.14014	−	0.669945i
$421$	−13.3808	+	13.3808i	−0.652140	+	0.652140i	−0.953508	−	0.301368i	$-0.902557\pi$
$421$	−13.3808	+	13.3808i	−0.652140	+	0.652140i	0.301368	+	0.953508i	$0.402557\pi$
$422$	−6.71088	+	23.7617i	−0.326680	+	1.15670i
$423$	−3.98772	−	3.98772i	−0.193889	−	0.193889i
$424$	−0.359589	+	8.90303i	−0.0174632	+	0.432369i
$425$	6.77511	+	6.27228i	0.328641	+	0.304250i
$426$	10.7548	−	6.01783i	0.521074	−	0.291565i
$427$	17.7515			0.859055
$428$	−1.39000	+	2.26455i	−0.0671882	+	0.109461i
$429$	3.30524	−	3.30524i	0.159578	−	0.159578i
$430$	37.6440	+	9.85286i	1.81535	+	0.475147i
$431$		−	16.9286i		−	0.815421i	−0.913111	−	0.407710i	$-0.866327\pi$
$431$		−	16.9286i		−	0.815421i	0.913111	−	0.407710i	$-0.133673\pi$
$432$	−10.2078	−	20.1066i	−0.491121	−	0.967378i
$433$	14.7943	+	14.7943i	0.710968	+	0.710968i	0.966738	−	0.255770i	$-0.0823289\pi$
$433$	14.7943	+	14.7943i	0.710968	+	0.710968i	−0.255770	+	0.966738i	$0.582329\pi$
$434$	31.2367	+	8.82200i	1.49941	+	0.423470i
$435$	−0.328782	−	17.0686i	−0.0157639	−	0.818377i
$436$	−8.60760	−	35.9692i	−0.412229	−	1.72261i
$437$			1.79578i			0.0859039i
$438$	8.27028	−	29.2832i	0.395169	−	1.39921i
$439$		−	14.0052i		−	0.668433i	−0.942496	−	0.334216i	$-0.891528\pi$
$439$		−	14.0052i		−	0.668433i	0.942496	−	0.334216i	$-0.108472\pi$
$440$	0.133486	−	6.32315i	0.00636371	−	0.301444i
$441$			7.83505i			0.373098i
$442$	7.92909	+	2.23937i	0.377148	+	0.106516i
$443$			11.1114i			0.527920i	0.964534	+	0.263960i	$0.0850287\pi$
$443$			11.1114i			0.527920i	−0.964534	+	0.263960i	$0.914971\pi$
$444$	2.14573	+	1.31706i	0.101832	+	0.0625051i
$445$	−0.885936	+	0.920737i	−0.0419974	+	0.0436471i
$446$	10.2822	−	36.4069i	0.486876	−	1.72392i
$447$	11.0708	+	11.0708i	0.523629	+	0.523629i
$448$	−24.9296	+	21.1975i	−1.17782	+	1.00149i
$449$		−	21.5211i		−	1.01564i	−0.861462	−	0.507822i	$-0.830451\pi$
$449$		−	21.5211i		−	1.01564i	0.861462	−	0.507822i	$-0.169549\pi$
$450$	−2.96919	−	4.85743i	−0.139969	−	0.228982i
$451$	−0.0541851	+	0.0541851i	−0.00255148	+	0.00255148i
$452$	9.27546	−	2.21966i	0.436281	−	0.104404i
$453$	−14.0553			−0.660376
$454$	−2.08304	−	3.72273i	−0.0977620	−	0.174716i
$455$	−28.8526	+	0.555769i	−1.35263	+	0.0260549i
$456$	−13.3325	+	12.2973i	−0.624351	+	0.575874i
$457$	−6.80915	−	6.80915i	−0.318519	−	0.318519i	0.529679	−	0.848198i	$-0.322312\pi$
$457$	−6.80915	−	6.80915i	−0.318519	−	0.318519i	−0.848198	+	0.529679i	$0.822312\pi$
$458$	−20.7875	−	5.87089i	−0.971335	−	0.274329i
$459$	−7.36071	+	7.36071i	−0.343568	+	0.343568i
$460$	0.939962	−	1.59967i	0.0438260	−	0.0745850i
$461$	−1.86893	−	1.86893i	−0.0870446	−	0.0870446i	0.662244	−	0.749288i	$-0.269604\pi$
$461$	−1.86893	−	1.86893i	−0.0870446	−	0.0870446i	−0.749288	+	0.662244i	$0.769604\pi$
$462$	7.47896	−	4.18482i	0.347953	−	0.194696i
$463$	7.98057	−	7.98057i	0.370889	−	0.370889i	−0.496912	−	0.867801i	$-0.665533\pi$
$463$	7.98057	−	7.98057i	0.370889	−	0.370889i	0.867801	+	0.496912i	$0.165533\pi$
$464$	−19.5951	−	6.39855i	−0.909679	−	0.297045i
$465$	−13.3945	−	12.8883i	−0.621157	−	0.597679i
$466$	−6.03437	+	21.3663i	−0.279537	+	0.989777i
$467$		−	15.8301i		−	0.732531i	−0.930510	−	0.366266i	$-0.880636\pi$
$467$		−	15.8301i		−	0.732531i	0.930510	−	0.366266i	$-0.119364\pi$
$468$	−4.32985	−	2.65769i	−0.200147	−	0.122852i
$469$	10.0345	+	10.0345i	0.463351	+	0.463351i
$470$	19.1181	−	11.1863i	0.881853	−	0.515986i
$471$	−14.7888			−0.681432
$472$	12.3776	+	13.4195i	0.569726	+	0.617685i
$473$	−8.70100	+	8.70100i	−0.400072	+	0.400072i
$474$	31.0107	−	17.3519i	1.42437	−	0.797001i
$475$	−14.7027	+	15.8814i	−0.674607	+	0.728689i
$476$	12.8745	+	7.90246i	0.590101	+	0.362209i
$477$	−2.53633			−0.116131
$478$	9.28944	−	5.19787i	0.424889	−	0.237745i
$479$	27.4005			1.25196			0.625981	−	0.779838i	$-0.284699\pi$
$479$	27.4005			1.25196			0.625981	+	0.779838i	$0.284699\pi$
$480$	18.3132	−	3.97576i	0.835881	−	0.181468i
$481$	2.68090			0.122238
$482$	−7.61839	+	4.26284i	−0.347008	+	0.194167i
$483$	2.51417			0.114398
$484$	1.70452	+	1.04624i	0.0774780	+	0.0475566i
$485$	0.137853	+	7.15658i	0.00625957	+	0.324964i
$486$	10.0177	−	5.60537i	0.454412	−	0.254265i
$487$	1.99789	−	1.99789i	0.0905329	−	0.0905329i	−0.660390	−	0.750923i	$-0.729609\pi$
$487$	1.99789	−	1.99789i	0.0905329	−	0.0905329i	0.750923	+	0.660390i	$0.229609\pi$
$488$	−9.02275	+	8.32219i	−0.408441	+	0.376728i
$489$	−29.0338			−1.31296
$490$	−29.7710	−	7.79220i	−1.34492	−	0.352016i
$491$	30.7971	+	30.7971i	1.38985	+	1.38985i	0.825607	+	0.564245i	$0.190833\pi$
$491$	30.7971	+	30.7971i	1.38985	+	1.38985i	0.564245	+	0.825607i	$0.309167\pi$
$492$	−0.193509	−	0.118777i	−0.00872406	−	0.00535489i
$493$			9.51587i			0.428573i
$494$	−5.24926	+	18.5864i	−0.236175	+	0.836243i
$495$	1.79997	−	0.0346716i	0.0809024	−	0.00155837i
$496$	−20.0129	+	10.1602i	−0.898607	+	0.456208i
$497$	17.0131	−	17.0131i	0.763143	−	0.763143i
$498$	26.9746	−	15.0935i	1.20876	−	0.676358i
$499$	−14.7637	−	14.7637i	−0.660913	−	0.660913i	0.294682	−	0.955595i	$-0.404786\pi$
$499$	−14.7637	−	14.7637i	−0.660913	−	0.660913i	−0.955595	+	0.294682i	$0.904786\pi$
$500$	21.4099	−	6.45122i	0.957478	−	0.288507i
$501$	18.2588	−	18.2588i	0.815745	−	0.815745i
$502$	18.6936	+	5.27951i	0.834334	+	0.235636i
$503$	−8.57296	−	8.57296i	−0.382249	−	0.382249i	0.489663	−	0.871912i	$-0.337120\pi$
$503$	−8.57296	−	8.57296i	−0.382249	−	0.382249i	−0.871912	+	0.489663i	$0.837120\pi$
$504$	−6.31537	−	6.84699i	−0.281309	−	0.304989i
$505$	−0.816284	−	42.3771i	−0.0363242	−	1.88576i
$506$	0.286499	+	0.512021i	0.0127364	+	0.0227621i
$507$	−4.51180			−0.200376
$508$	−38.9595	+	9.32319i	−1.72855	+	0.413650i
$509$	−2.76247	+	2.76247i	−0.122444	+	0.122444i	−0.765674	−	0.643229i	$-0.777594\pi$
$509$	−2.76247	+	2.76247i	−0.122444	+	0.122444i	0.643229	+	0.765674i	$0.277594\pi$
$510$	−4.36891	−	7.46675i	−0.193459	−	0.330633i
$511$		−	59.4060i		−	2.62797i
$512$	2.73355	−	22.4617i	0.120807	−	0.992676i
$513$	−17.2541	−	17.2541i	−0.761787	−	0.761787i
$514$	3.33867	−	11.8215i	0.147263	−	0.521424i
$515$	−20.1892	+	0.388893i	−0.889645	+	0.0171367i
$516$	−31.0735	−	19.0732i	−1.36794	−	0.839650i
$517$			7.00454i			0.308059i
$518$	4.73028	+	1.33595i	0.207837	+	0.0586981i
$519$			7.91954i			0.347629i
$520$	14.4047	−	13.8090i	0.631686	−	0.605567i
$521$		−	25.1306i		−	1.10099i	−0.834838	−	0.550495i	$-0.814439\pi$
$521$		−	25.1306i		−	1.10099i	0.834838	−	0.550495i	$-0.185561\pi$
$522$	1.59478	−	5.64674i	0.0698015	−	0.247151i
$523$			21.8562i			0.955705i	0.878440	+	0.477852i	$0.158585\pi$
$523$			21.8562i			0.955705i	−0.878440	+	0.477852i	$0.841415\pi$
$524$	−3.27081	−	13.6680i	−0.142886	−	0.597088i
$525$	22.2346	+	20.5844i	0.970397	+	0.898377i
$526$	10.1302	+	2.86102i	0.441698	+	0.124746i
$527$	7.32643	+	7.32643i	0.319144	+	0.319144i
$528$	−1.83950	+	5.63333i	−0.0800539	+	0.245159i
$529$		−	22.8279i		−	0.992516i
$530$	2.52246	−	9.63736i	0.109569	−	0.418620i
$531$	−3.67460	+	3.67460i	−0.159464	+	0.159464i
$532$	−18.5240	+	30.1788i	−0.803117	+	1.30842i
$533$	−0.241772			−0.0104723
$534$	1.04480	−	0.584614i	0.0452129	−	0.0252987i
$535$	2.05979	−	2.14071i	0.0890527	−	0.0925508i
$536$	−9.80470	−	0.396007i	−0.423498	−	0.0171049i
$537$	−1.92814	−	1.92814i	−0.0832055	−	0.0832055i
$538$	10.9685	−	38.8370i	0.472886	−	1.67438i
$539$	6.88125	−	6.88125i	0.296396	−	0.296396i
$540$	6.33854	+	24.4011i	0.272767	+	1.05006i
$541$	−30.4868	−	30.4868i	−1.31073	−	1.31073i	−0.920877	−	0.389854i	$-0.872525\pi$
$541$	−30.4868	−	30.4868i	−1.31073	−	1.31073i	−0.389854	−	0.920877i	$-0.627475\pi$
$542$	−4.89773	−	8.75304i	−0.210376	−	0.375975i
$543$	20.6592	−	20.6592i	0.886571	−	0.886571i
$544$	−10.2487	+	2.01910i	−0.439408	+	0.0865682i
$545$	0.796356	+	41.3425i	0.0341121	+	1.77092i
$546$	26.0217	+	7.34917i	1.11363	+	0.314515i
$547$		−	4.71953i		−	0.201793i	−0.994897	−	0.100896i	$-0.967829\pi$
$547$		−	4.71953i		−	0.201793i	0.994897	−	0.100896i	$-0.0321710\pi$
$548$	−17.9849	+	4.30389i	−0.768279	+	0.183853i
$549$	−2.47065	−	2.47065i	−0.105445	−	0.105445i
$550$	−1.65838	+	6.87385i	−0.0707135	+	0.293102i
$551$	−22.3060			−0.950266
$552$	−1.27790	+	1.17868i	−0.0543911	+	0.0501680i
$553$	49.0560	−	49.0560i	2.08607	−	2.08607i
$554$	−1.86425	−	3.33172i	−0.0792046	−	0.141551i
$555$	−2.02838	−	1.95171i	−0.0860999	−	0.0828456i
$556$	4.30434	+	17.9868i	0.182545	+	0.762812i
$557$	−38.3455			−1.62475			−0.812375	−	0.583136i	$-0.801825\pi$
$557$	−38.3455			−1.62475			−0.812375	+	0.583136i	$0.801825\pi$
$558$	−3.11968	−	5.57537i	−0.132066	−	0.236024i
$559$	−38.8236			−1.64206
$560$	32.2975	−	17.1871i	1.36482	−	0.726287i
$561$	2.73569			0.115501
$562$	2.19643	+	3.92537i	0.0926508	+	0.165582i
$563$	42.2358			1.78003			0.890013	−	0.455936i	$-0.150695\pi$
$563$	42.2358			1.78003			0.890013	+	0.455936i	$0.150695\pi$
$564$	−20.1847	+	4.83031i	−0.849930	+	0.203393i
$565$	−10.6611	+	0.205358i	−0.448516	+	0.00863949i
$566$	16.0159	+	28.6229i	0.673197	+	1.20311i
$567$	−17.1703	+	17.1703i	−0.721086	+	0.721086i
$568$	−0.671415	+	16.6235i	−0.0281719	+	0.697506i
$569$	1.49200			0.0625478			0.0312739	−	0.999511i	$-0.490044\pi$
$569$	1.49200			0.0625478			0.0312739	+	0.999511i	$0.490044\pi$
$570$	17.5027	−	10.2411i	0.733106	−	0.428952i
$571$	−16.1387	−	16.1387i	−0.675382	−	0.675382i	0.283569	−	0.958952i	$-0.408481\pi$
$571$	−16.1387	−	16.1387i	−0.675382	−	0.675382i	−0.958952	+	0.283569i	$0.908481\pi$
$572$	1.46859	+	6.13691i	0.0614049	+	0.256597i
$573$			11.6528i			0.486803i
$574$	−0.426593	−	0.120480i	−0.0178056	−	0.00502874i
$575$	−1.40924	+	1.52221i	−0.0587693	+	0.0634807i
$576$	6.41997	+	0.519446i	0.267499	+	0.0216436i
$577$	12.2291	−	12.2291i	0.509106	−	0.509106i	−0.405146	−	0.914252i	$-0.632779\pi$
$577$	12.2291	−	12.2291i	0.509106	−	0.509106i	0.914252	+	0.405146i	$0.132779\pi$
$578$	−9.38493	−	16.7724i	−0.390362	−	0.697640i
$579$	−3.63542	−	3.63542i	−0.151083	−	0.151083i
$580$	19.8700	+	11.6756i	0.825057	+	0.484802i
$581$	42.6712	−	42.6712i	1.77030	−	1.77030i
$582$	1.82289	−	6.45442i	0.0755610	−	0.267544i
$583$	2.22757	+	2.22757i	0.0922566	+	0.0922566i
$584$	27.8505	+	30.1949i	1.15246	+	1.24948i
$585$	4.09305	+	3.93835i	0.169227	+	0.162831i
$586$	27.9556	−	15.6424i	1.15483	−	0.646183i
$587$	−20.4112			−0.842462			−0.421231	−	0.906953i	$-0.638402\pi$
$587$	−20.4112			−0.842462			−0.421231	+	0.906953i	$0.638402\pi$
$588$	24.5747	+	15.0842i	1.01344	+	0.622060i
$589$	−17.1737	+	17.1737i	−0.707632	+	0.707632i
$590$	−10.3080	−	17.6170i	−0.424372	−	0.725279i
$591$			34.6663i			1.42598i
$592$	−3.03063	+	1.53860i	−0.124558	+	0.0632360i
$593$	−7.70227	−	7.70227i	−0.316294	−	0.316294i	0.531048	−	0.847342i	$-0.321798\pi$
$593$	−7.70227	−	7.70227i	−0.316294	−	0.316294i	−0.847342	+	0.531048i	$0.821798\pi$
$594$	−7.67228	−	2.16684i	−0.314797	−	0.0889064i
$595$	−12.1704	−	11.7104i	−0.498937	−	0.480079i
$596$	−20.5553	+	4.91899i	−0.841980	+	0.201490i
$597$			25.9335i			1.06139i
$598$	−0.503135	+	1.78149i	−0.0205747	+	0.0728504i
$599$			1.05486i			0.0431004i	0.999768	+	0.0215502i	$0.00686018\pi$
$599$			1.05486i			0.0431004i	−0.999768	+	0.0215502i	$0.993140\pi$
$600$	−20.9517	−	0.0387104i	−0.855351	−	0.00158035i
$601$			23.9274i			0.976020i	0.872838	+	0.488010i	$0.162277\pi$
$601$			23.9274i			0.976020i	−0.872838	+	0.488010i	$0.837723\pi$
$602$	−68.5020	−	19.3466i	−2.79193	−	0.788509i
$603$		−	2.79320i		−	0.113748i
$604$	9.92587	−	16.1710i	0.403878	−	0.657987i
$605$	−1.61130	−	1.55039i	−0.0655085	−	0.0630325i
$606$	−10.7941	+	38.2194i	−0.438479	+	1.55256i
$607$	19.0611	+	19.0611i	0.773664	+	0.773664i	0.978745	−	0.205081i	$-0.0657457\pi$
$607$	19.0611	+	19.0611i	0.773664	+	0.773664i	−0.205081	+	0.978745i	$0.565746\pi$
$608$	−4.73293	−	24.0237i	−0.191946	−	0.974289i
$609$			31.2292i			1.26547i
$610$	11.8449	−	6.93065i	0.479587	−	0.280614i
$611$	−15.6270	+	15.6270i	−0.632202	+	0.632202i
$612$	−0.692006	−	2.89173i	−0.0279727	−	0.116891i
$613$	17.3805			0.701991			0.350995	−	0.936377i	$-0.385843\pi$
$613$	17.3805			0.701991			0.350995	+	0.936377i	$0.385843\pi$
$614$	11.6732	+	20.8620i	0.471094	+	0.841920i
$615$	0.182926	+	0.176012i	0.00737629	+	0.00709749i
$616$	−0.466905	+	11.5600i	−0.0188121	+	0.465767i
$617$	6.12592	+	6.12592i	0.246620	+	0.246620i	0.819582	−	0.572962i	$-0.194206\pi$
$617$	6.12592	+	6.12592i	0.246620	+	0.246620i	−0.572962	+	0.819582i	$0.694206\pi$
$618$	18.2084	+	5.14250i	0.732450	+	0.206861i
$619$	17.2117	−	17.2117i	0.691797	−	0.691797i	−0.270830	−	0.962627i	$-0.587298\pi$
$619$	17.2117	−	17.2117i	0.691797	−	0.691797i	0.962627	+	0.270830i	$0.0872983\pi$
$620$	24.2875	−	6.30902i	0.975408	−	0.253377i
$621$	−1.65378	−	1.65378i	−0.0663641	−	0.0663641i
$622$	−34.3758	+	19.2348i	−1.37834	+	0.771247i
$623$	1.65277	−	1.65277i	0.0662170	−	0.0662170i
$624$	−16.6718	+	8.46398i	−0.667405	+	0.338830i
$625$	−24.9258	+	1.92410i	−0.997034	+	0.0769638i
$626$	7.62595	−	27.0018i	0.304794	−	1.07921i
$627$			6.41267i			0.256097i
$628$	10.4439	−	17.0149i	0.416755	−	0.678967i
$629$	1.10947	+	1.10947i	0.0442373	+	0.0442373i
$630$	5.25938	+	8.98863i	0.209539	+	0.358115i
$631$	27.7765			1.10576			0.552882	−	0.833259i	$-0.313528\pi$
$631$	27.7765			1.10576			0.552882	+	0.833259i	$0.313528\pi$
$632$	−1.93597	+	47.9325i	−0.0770088	+	1.90665i
$633$	−18.2902	+	18.2902i	−0.726968	+	0.726968i
$634$	14.4375	−	8.07843i	0.573385	−	0.320835i
$635$	44.7796	−	0.862561i	1.77702	−	0.0342297i
$636$	−4.88299	+	7.95524i	−0.193623	+	0.315446i
$637$	30.7039			1.21653
$638$	−6.35997	+	3.55870i	−0.251794	+	0.140890i
$639$	−4.73577			−0.187344
$640$	−8.35861	+	23.8775i	−0.330403	+	0.943840i
$641$	−14.2633			−0.563367			−0.281683	−	0.959507i	$-0.590893\pi$
$641$	−14.2633			−0.563367			−0.281683	+	0.959507i	$0.590893\pi$
$642$	−2.42915	+	1.35922i	−0.0958710	+	0.0536442i
$643$	−8.84820			−0.348939			−0.174470	−	0.984663i	$-0.555821\pi$
$643$	−8.84820			−0.348939			−0.174470	+	0.984663i	$0.555821\pi$
$644$	−1.77550	+	2.89260i	−0.0699646	+	0.113985i
$645$	29.3741	+	28.2639i	1.15661	+	1.11289i
$646$	−9.86419	+	5.51947i	−0.388101	+	0.217161i
$647$	6.56354	−	6.56354i	0.258040	−	0.258040i	−0.566217	−	0.824256i	$-0.691594\pi$
$647$	6.56354	−	6.56354i	0.258040	−	0.258040i	0.824256	+	0.566217i	$0.191594\pi$
$648$	0.677619	−	16.7771i	0.0266194	−	0.659066i
$649$	6.45455			0.253363
$650$	−19.0353	+	11.6356i	−0.746625	+	0.456387i
$651$	24.0439	+	24.0439i	0.942355	+	0.942355i
$652$	20.5037	−	33.4041i	0.802987	−	1.30821i
$653$			26.2559i			1.02747i	0.857949	+	0.513736i	$0.171739\pi$
$653$			26.2559i			1.02747i	−0.857949	+	0.513736i	$0.828261\pi$
$654$	10.5305	−	37.2863i	0.411777	−	1.45801i
$655$	0.302608	+	15.7098i	0.0118239	+	0.613833i
$656$	0.273312	−	0.138756i	0.0106710	−	0.00541751i
$657$	−8.26812	+	8.26812i	−0.322570	+	0.322570i
$658$	−35.3602	+	19.7857i	−1.37849	+	0.771327i
$659$	−26.6116	−	26.6116i	−1.03664	−	1.03664i	−0.999303	−	0.0373371i	$-0.988112\pi$
$659$	−26.6116	−	26.6116i	−1.03664	−	1.03664i	−0.0373371	−	0.999303i	$-0.511888\pi$
$660$	3.35657	−	5.71236i	0.130654	−	0.222353i
$661$	−21.1931	+	21.1931i	−0.824315	+	0.824315i	−0.986724	−	0.162408i	$-0.948074\pi$
$661$	−21.1931	+	21.1931i	−0.824315	+	0.824315i	0.162408	+	0.986724i	$0.448074\pi$
$662$	−15.9659	−	4.50916i	−0.620533	−	0.175254i
$663$	6.10328	+	6.10328i	0.237032	+	0.237032i
$664$	−1.68400	+	41.6940i	−0.0653519	+	1.61804i
$665$	27.4501	−	28.5284i	1.06447	−	1.10628i
$666$	−0.472423	−	0.844297i	−0.0183060	−	0.0327158i
$667$	−2.13800			−0.0827837
$668$	8.11282	+	33.9016i	0.313895	+	1.31169i
$669$	28.0236	−	28.0236i	1.08346	−	1.08346i
$670$	10.6134	+	2.77793i	0.410031	+	0.107321i
$671$			4.33977i			0.167535i
$672$	−33.6341	+	6.62630i	−1.29746	+	0.255615i
$673$	−22.2740	−	22.2740i	−0.858601	−	0.858601i	0.132572	−	0.991173i	$-0.457676\pi$
$673$	−22.2740	−	22.2740i	−0.858601	−	0.858601i	−0.991173	+	0.132572i	$0.957676\pi$
$674$	−4.24334	+	15.0247i	−0.163447	+	0.578730i
$675$	−1.08548	−	28.1658i	−0.0417802	−	1.08410i
$676$	3.18623	−	5.19093i	0.122547	−	0.199651i
$677$			27.4482i			1.05492i	0.849580	+	0.527460i	$0.176856\pi$
$677$			27.4482i			1.05492i	−0.849580	+	0.527460i	$0.823144\pi$
$678$	9.61510	+	2.71554i	0.369266	+	0.104290i
$679$		−	13.0939i		−	0.502498i
$680$	11.6760	+	0.246489i	0.447754	+	0.00945242i
$681$		−	4.46889i		−	0.171248i
$682$	−2.15675	+	7.63655i	−0.0825861	+	0.292419i
$683$			28.5470i			1.09232i	0.837681	+	0.546160i	$0.183911\pi$
$683$			28.5470i			1.09232i	−0.837681	+	0.546160i	$0.816089\pi$
$684$	6.77845	−	1.62212i	0.259181	−	0.0620232i
$685$	20.6717	−	0.398186i	0.789825	−	0.0152139i
$686$	15.2065	+	4.29467i	0.580586	+	0.163971i
$687$	−16.0008	−	16.0008i	−0.610469	−	0.610469i
$688$	43.8883	−	22.2813i	1.67322	−	0.849468i
$689$			9.93937i			0.378660i
$690$	1.67761	−	0.981596i	0.0638655	−	0.0373687i
$691$	18.7853	−	18.7853i	0.714625	−	0.714625i	−0.252874	−	0.967499i	$-0.581376\pi$
$691$	18.7853	−	18.7853i	0.714625	−	0.714625i	0.967499	+	0.252874i	$0.0813759\pi$
$692$	−9.11161	−	5.59278i	−0.346371	−	0.212605i
$693$	−3.29327			−0.125101
$694$	−32.8333	+	18.3717i	−1.24633	+	0.697382i
$695$	−0.398228	−	20.6739i	−0.0151056	−	0.784204i
$696$	−14.6408	−	15.8732i	−0.554958	−	0.601673i
$697$	−0.100055	−	0.100055i	−0.00378987	−	0.00378987i
$698$	−0.660967	+	2.34033i	−0.0250180	+	0.0885830i
$699$	−16.4464	+	16.4464i	−0.622059	+	0.622059i
$700$	−39.3849	+	11.0447i	−1.48861	+	0.417451i
$701$	−35.5160	−	35.5160i	−1.34142	−	1.34142i	−0.894645	−	0.446777i	$-0.852572\pi$
$701$	−35.5160	−	35.5160i	−1.34142	−	1.34142i	−0.446777	−	0.894645i	$-0.647428\pi$
$702$	−12.2826	−	21.9509i	−0.463576	−	0.828485i
$703$	−2.60068	+	2.60068i	−0.0980864	+	0.0980864i
$704$	−5.18222	−	6.09464i	−0.195312	−	0.229700i
$705$	23.2001	−	0.446889i	0.873766	−	0.0168308i
$706$	−40.4826	−	11.4333i	−1.52358	−	0.430297i
$707$			77.5345i			2.91599i
$708$	4.45103	+	18.5998i	0.167280	+	0.699025i
$709$	9.43396	+	9.43396i	0.354300	+	0.354300i	0.861707	−	0.507407i	$-0.169396\pi$
$709$	9.43396	+	9.43396i	0.354300	+	0.354300i	−0.507407	+	0.861707i	$0.669396\pi$
$710$	4.70987	−	17.9946i	0.176758	−	0.675325i
$711$	−13.6552			−0.512110
$712$	−0.0652259	+	1.61492i	−0.00244444	+	0.0605217i
$713$	−1.64608	+	1.64608i	−0.0616463	+	0.0616463i
$714$	7.72748	+	13.8103i	0.289194	+	0.516836i
$715$	−0.135871	−	7.05369i	−0.00508128	−	0.263793i
$716$	3.58003	−	0.856718i	0.133792	−	0.0320171i
$717$	11.1514			0.416455
$718$	−18.8767	−	33.7357i	−0.704473	−	1.25901i
$719$	34.7155			1.29467			0.647334	−	0.762206i	$-0.275884\pi$
$719$	34.7155			1.29467			0.647334	+	0.762206i	$0.275884\pi$
$720$	−6.88726	−	2.10306i	−0.256673	−	0.0783765i
$721$	36.9389			1.37568
$722$	0.182614	+	0.326361i	0.00679619	+	0.0121459i
$723$	−9.14537			−0.340120
$724$	9.17936	+	38.3584i	0.341148	+	1.42558i
$725$	−18.9079	−	17.5046i	−0.702222	−	0.650104i
$726$	1.02308	+	1.82841i	0.0379700	+	0.0678586i
$727$	8.19846	−	8.19846i	0.304064	−	0.304064i	−0.538537	−	0.842602i	$-0.681023\pi$
$727$	8.19846	−	8.19846i	0.304064	−	0.304064i	0.842602	+	0.538537i	$0.181023\pi$
$728$	−26.8319	+	24.7486i	−0.994458	+	0.917245i
$729$	29.8349			1.10500
$730$	−23.1937	−	39.6395i	−0.858436	−	1.46712i
$731$	−16.0668	−	16.0668i	−0.594253	−	0.594253i
$732$	−12.5058	+	2.99269i	−0.462226	+	0.110613i
$733$		−	31.1798i		−	1.15165i	−0.817572	−	0.575827i	$-0.804680\pi$
$733$		−	31.1798i		−	1.15165i	0.817572	−	0.575827i	$-0.195320\pi$
$734$	−5.40767	−	1.52726i	−0.199601	−	0.0563721i
$735$	−23.2307	−	22.3527i	−0.856879	−	0.824492i
$736$	−0.453646	−	2.30264i	−0.0167216	−	0.0848765i
$737$	−2.45317	+	2.45317i	−0.0903638	+	0.0903638i
$738$	0.0426047	+	0.0761415i	0.00156830	+	0.00280281i
$739$	1.89949	+	1.89949i	0.0698740	+	0.0698740i	0.741180	−	0.671306i	$-0.234266\pi$
$739$	1.89949	+	1.89949i	0.0698740	+	0.0698740i	−0.671306	+	0.741180i	$0.734266\pi$
$740$	3.67793	−	0.955397i	0.135203	−	0.0351211i
$741$	−14.3066	+	14.3066i	−0.525565	+	0.525565i
$742$	−4.95299	+	17.5374i	−0.181830	+	0.643819i
$743$	−25.4178	−	25.4178i	−0.932488	−	0.932488i	0.0653732	−	0.997861i	$-0.479176\pi$
$743$	−25.4178	−	25.4178i	−0.932488	−	0.932488i	−0.997861	+	0.0653732i	$0.979176\pi$
$744$	−23.4933	−	0.948882i	−0.861304	−	0.0347877i
$745$	23.6261	−	0.455094i	0.865592	−	0.0166734i
$746$	23.3061	−	13.0408i	0.853296	−	0.477459i
$747$	−11.8780			−0.434592
$748$	−1.93194	+	3.14747i	−0.0706388	+	0.115083i
$749$	−3.84268	+	3.84268i	−0.140409	+	0.140409i
$750$	22.8730	+	5.05425i	0.835205	+	0.184555i
$751$		−	20.8704i		−	0.761572i	−0.924663	−	0.380786i	$-0.875654\pi$
$751$		−	20.8704i		−	0.761572i	0.924663	−	0.380786i	$-0.124346\pi$
$752$	8.69708	−	26.6342i	0.317150	−	0.971248i
$753$	14.3890	+	14.3890i	0.524366	+	0.524366i
$754$	−22.1284	−	6.24960i	−0.805870	−	0.227597i
$755$	−14.7088	+	15.2866i	−0.535308	+	0.556336i
$756$	−10.7332	−	44.8518i	−0.390364	−	1.63124i
$757$			31.7309i			1.15328i	0.816999	+	0.576639i	$0.195636\pi$
$757$			31.7309i			1.15328i	−0.816999	+	0.576639i	$0.804364\pi$
$758$	−0.420154	+	1.48767i	−0.0152607	+	0.0540345i
$759$			0.614647i			0.0223103i
$760$	−0.577790	+	27.3695i	−0.0209586	+	0.992795i
$761$			26.9647i			0.977469i	0.872433	+	0.488735i	$0.162541\pi$
$761$			26.9647i			0.977469i	−0.872433	+	0.488735i	$0.837459\pi$
$762$	−40.3861	−	11.4060i	−1.46303	−	0.413196i
$763$		−	75.6416i		−	2.73841i
$764$	−13.4068	−	8.22922i	−0.485042	−	0.297723i
$765$	0.0640228	+	3.32372i	0.00231475	+	0.120169i
$766$	12.9516	−	45.8586i	0.467960	−	1.65694i
$767$	14.4000	+	14.4000i	0.519954	+	0.519954i
$768$	13.9891	−	19.1362i	0.504787	−	0.690520i
$769$			29.6864i			1.07052i	0.844687	+	0.535260i	$0.179787\pi$
$769$			29.6864i			1.07052i	−0.844687	+	0.535260i	$0.820213\pi$
$770$	3.27526	−	12.5135i	0.118032	−	0.450956i
$771$	9.09939	−	9.09939i	0.327706	−	0.327706i
$772$	6.74997	−	1.61530i	0.242937	−	0.0581359i
$773$	−25.4587			−0.915686			−0.457843	−	0.889033i	$-0.651378\pi$
$773$	−25.4587			−0.915686			−0.457843	+	0.889033i	$0.651378\pi$
$774$	6.84144	+	12.2268i	0.245910	+	0.439482i
$775$	−28.0346	+	1.08043i	−1.00703	+	0.0388101i
$776$	6.13864	+	6.65539i	0.220364	+	0.238914i
$777$	3.64105	+	3.64105i	0.130622	+	0.130622i
$778$	5.30368	+	1.49789i	0.190146	+	0.0537019i
$779$	0.234538	−	0.234538i	0.00840319	−	0.00840319i
$780$	20.2327	−	5.25573i	0.724446	−	0.188185i
$781$	4.15926	+	4.15926i	0.148830	+	0.148830i
$782$	−0.945471	+	0.529035i	−0.0338100	+	0.0189182i
$783$	20.5422	−	20.5422i	0.734118	−	0.734118i
$784$	−34.7093	+	17.6213i	−1.23962	+	0.629334i
$785$	−15.4764	+	16.0843i	−0.552376	+	0.574075i
$786$	4.00151	−	14.1685i	0.142729	−	0.505372i
$787$			35.0861i			1.25068i	0.780351	+	0.625342i	$0.215040\pi$
$787$			35.0861i			1.25068i	−0.780351	+	0.625342i	$0.784960\pi$
$788$	−39.8843	−	24.4813i	−1.42082	−	0.872111i
$789$	7.79756	+	7.79756i	0.277600	+	0.277600i
$790$	13.5805	−	51.8860i	0.483174	−	1.84602i
$791$	19.5059			0.693550
$792$	1.67391	−	1.54394i	0.0594797	−	0.0548615i
$793$	−9.68197	+	9.68197i	−0.343817	+	0.343817i
$794$	19.5180	−	10.9212i	0.692668	−	0.387580i
$795$	7.23593	−	7.52017i	0.256632	−	0.266713i
$796$	−29.8371	−	18.3142i	−1.05755	−	0.649131i
$797$	−9.53566			−0.337770			−0.168885	−	0.985636i	$-0.554017\pi$
$797$	−9.53566			−0.337770			−0.168885	+	0.985636i	$0.554017\pi$
$798$	−32.3724	+	18.1138i	−1.14597	+	0.641223i
$799$	−12.9342			−0.457580
$800$	14.8406	−	24.0781i	0.524696	−	0.851290i
$801$	−0.460066			−0.0162556
$802$	−15.2132	+	8.51247i	−0.537196	+	0.300586i
$803$	14.5232			0.512512
$804$	−8.76092	−	5.37752i	−0.308974	−	0.189651i
$805$	2.63106	−	2.73441i	0.0927326	−	0.0963753i
$806$	−21.8487	+	12.2254i	−0.769588	+	0.430620i
$807$	29.8941	−	29.8941i	1.05232	−	1.05232i
$808$	−36.3495	−	39.4093i	−1.27877	−	1.38642i
$809$	15.6353			0.549708			0.274854	−	0.961486i	$-0.411370\pi$
$809$	15.6353			0.549708			0.274854	+	0.961486i	$0.411370\pi$
$810$	−4.75339	+	18.1609i	−0.167017	+	0.638108i
$811$	−7.73722	−	7.73722i	−0.271691	−	0.271691i	0.558090	−	0.829781i	$-0.311534\pi$
$811$	−7.73722	−	7.73722i	−0.271691	−	0.271691i	−0.829781	+	0.558090i	$0.811534\pi$
$812$	−35.9300	−	22.0541i	−1.26089	−	0.773947i
$813$		−	10.5074i		−	0.368512i
$814$	−0.326603	+	1.15643i	−0.0114474	+	0.0405328i
$815$	−30.3837	+	31.5773i	−1.06430	+	1.10610i
$816$	−10.4022	−	3.39672i	−0.364150	−	0.118909i
$817$	37.6619	−	37.6619i	1.31762	−	1.31762i
$818$	−5.29069	+	2.96039i	−0.184985	+	0.103508i
$819$	−7.34725	−	7.34725i	−0.256734	−	0.256734i
$820$	−0.331688	+	0.0861609i	−0.0115831	+	0.00300887i
$821$	11.5270	−	11.5270i	0.402296	−	0.402296i	−0.476745	−	0.879041i	$-0.658184\pi$
$821$	11.5270	−	11.5270i	0.402296	−	0.402296i	0.879041	+	0.476745i	$0.158184\pi$
$822$	−18.6435	−	5.26538i	−0.650267	−	0.183651i
$823$	16.9733	+	16.9733i	0.591653	+	0.591653i	0.938078	−	0.346425i	$-0.112604\pi$
$823$	16.9733	+	16.9733i	0.591653	+	0.591653i	−0.346425	+	0.938078i	$0.612604\pi$
$824$	−18.7753	+	17.3176i	−0.654070	+	0.603286i
$825$	−5.03234	+	5.43577i	−0.175204	+	0.189249i
$826$	18.2321	+	32.5838i	0.634377	+	1.13373i
$827$	3.34289			0.116244			0.0581218	−	0.998309i	$-0.481489\pi$
$827$	3.34289			0.116244			0.0581218	+	0.998309i	$0.481489\pi$
$828$	0.649707	−	0.155478i	0.0225789	−	0.00540324i
$829$	−33.0586	+	33.0586i	−1.14817	+	1.14817i	−0.161259	+	0.986912i	$0.551555\pi$
$829$	−33.0586	+	33.0586i	−1.14817	+	1.14817i	−0.986912	+	0.161259i	$0.948445\pi$
$830$	11.8130	−	45.1329i	0.410035	−	1.56659i
$831$		−	3.99951i		−	0.138742i
$832$	2.03560	−	25.1585i	0.0705718	−	0.872215i
$833$	12.7066	+	12.7066i	0.440256	+	0.440256i
$834$	−5.26593	+	18.6455i	−0.182344	+	0.645640i
$835$	−0.750580	−	38.9661i	−0.0259749	−	1.34848i
$836$	−7.37792	−	4.52863i	−0.255171	−	0.156626i
$837$		−	31.6315i		−	1.09335i
$838$	7.05570	+	1.99270i	0.243735	+	0.0688367i
$839$			10.0892i			0.348318i	0.984718	+	0.174159i	$0.0557206\pi$
$839$			10.0892i			0.348318i	−0.984718	+	0.174159i	$0.944279\pi$
$840$	38.3184	+	0.808929i	1.32211	+	0.0279107i
$841$			2.44321i			0.0842486i
$842$	7.27360	−	25.7542i	0.250665	−	0.887548i
$843$			4.71215i			0.162295i
$844$	−8.12674	−	33.9598i	−0.279734	−	1.16894i
$845$	−4.72157	+	4.90704i	−0.162427	+	0.168807i
$846$	7.67521	+	2.16766i	0.263879	+	0.0745258i
$847$	2.89237	+	2.89237i	0.0993828	+	0.0993828i
$848$	−5.70432	−	11.2360i	−0.195887	−	0.385845i
$849$			34.3599i			1.17923i
$850$	−12.6929	−	3.06228i	−0.435363	−	0.105035i
$851$	−0.249272	+	0.249272i	−0.00854493	+	0.00854493i
$852$	−9.11737	+	14.8538i	−0.312356	+	0.508883i
$853$	1.93972			0.0664149			0.0332074	−	0.999448i	$-0.489428\pi$
$853$	1.93972			0.0664149			0.0332074	+	0.999448i	$0.489428\pi$
$854$	−21.9080	+	12.2585i	−0.749676	+	0.419478i
$855$	−7.79107	+	0.150075i	−0.266449	+	0.00513245i
$856$	0.151650	−	3.75468i	0.00518328	−	0.128332i
$857$	−30.4341	−	30.4341i	−1.03961	−	1.03961i	−0.999182	−	0.0404274i	$-0.987128\pi$
$857$	−30.4341	−	30.4341i	−1.03961	−	1.03961i	−0.0404274	−	0.999182i	$-0.512872\pi$
$858$	−1.79668	+	6.36163i	−0.0613376	+	0.217182i
$859$	34.6172	−	34.6172i	1.18112	−	1.18112i	0.201671	−	0.979453i	$-0.435363\pi$
$859$	34.6172	−	34.6172i	1.18112	−	1.18112i	0.979453	−	0.201671i	$-0.0646372\pi$
$860$	−53.2623	+	13.8357i	−1.81623	+	0.471792i
$861$	−0.328362	−	0.328362i	−0.0111906	−	0.0111906i
$862$	11.6903	+	20.8924i	0.398172	+	0.711597i
$863$	−22.8307	+	22.8307i	−0.777167	+	0.777167i	−0.979348	−	0.202181i	$-0.935197\pi$
$863$	−22.8307	+	22.8307i	−0.777167	+	0.777167i	0.202181	+	0.979348i	$0.435197\pi$
$864$	26.4828	+	17.7654i	0.900962	+	0.604390i
$865$	8.61330	+	8.28775i	0.292861	+	0.281792i
$866$	−28.4747	−	8.04195i	−0.967611	−	0.273277i
$867$		−	20.1341i		−	0.683792i
$868$	−44.6429	+	10.6833i	−1.51528	+	0.362614i
$869$	11.9929	+	11.9929i	0.406831	+	0.406831i
$870$	12.1927	+	20.8381i	0.413372	+	0.706479i
$871$	−10.9460			−0.370891
$872$	35.4620	+	38.4472i	1.20090	+	1.30199i
$873$	−1.82241	+	1.82241i	−0.0616792	+	0.0616792i
$874$	−1.24010	−	2.21626i	−0.0419470	−	0.0749661i
$875$	45.6560	−	2.64094i	1.54345	−	0.0892802i
$876$	10.0151	+	41.8510i	0.338380	+	1.41401i
$877$	−35.8585			−1.21086			−0.605428	−	0.795900i	$-0.706998\pi$
$877$	−35.8585			−1.21086			−0.605428	+	0.795900i	$0.706998\pi$
$878$	9.67149	+	17.2845i	0.326397	+	0.583324i
$879$	33.5588			1.13191
$880$	4.20179	+	7.89588i	0.141642	+	0.266170i
$881$	18.6467			0.628224			0.314112	−	0.949386i	$-0.398293\pi$
$881$	18.6467			0.628224			0.314112	+	0.949386i	$0.398293\pi$
$882$	−5.41060	−	9.66961i	−0.182184	−	0.325593i
$883$	−16.0468			−0.540018			−0.270009	−	0.962858i	$-0.587027\pi$
$883$	−16.0468			−0.540018			−0.270009	+	0.962858i	$0.587027\pi$
$884$	−11.3321	+	2.71183i	−0.381140	+	0.0912086i
$885$	−0.411800	−	21.3784i	−0.0138425	−	0.718628i
$886$	−7.67315	−	13.7132i	−0.257784	−	0.460702i
$887$	25.5256	−	25.5256i	0.857067	−	0.857067i	−0.133925	−	0.990992i	$-0.542758\pi$
$887$	25.5256	−	25.5256i	0.857067	−	0.857067i	0.990992	+	0.133925i	$0.0427580\pi$
$888$	−3.55766	−	0.143692i	−0.119387	−	0.00482200i
$889$	−81.9301			−2.74785
$890$	0.457550	−	1.74812i	0.0153371	−	0.0585971i
$891$	−4.19769	−	4.19769i	−0.140628	−	0.140628i
$892$	12.4515	+	52.0321i	0.416908	+	1.74216i
$893$		−	30.3189i		−	1.01458i
$894$	−21.3080	−	6.01790i	−0.712647	−	0.201269i
$895$	−4.11484	+	0.0792616i	−0.137544	+	0.00264942i
$896$	16.1287	−	43.3763i	0.538822	−	1.44910i
$897$	−1.37127	+	1.37127i	−0.0457853	+	0.0457853i
$898$	14.8617	+	26.5602i	0.495941	+	0.886326i
$899$	−20.4465	−	20.4465i	−0.681929	−	0.681929i
$900$	7.01879	+	3.94438i	0.233960	+	0.131479i
$901$	−4.11332	+	4.11332i	−0.137035	+	0.137035i
$902$	0.0294542	−	0.104291i	0.000980718	−	0.00347250i
$903$	−52.7282	−	52.7282i	−1.75468	−	1.75468i
$904$	−9.91447	+	9.14468i	−0.329750	+	0.304148i
$905$	−0.849253	−	44.0887i	−0.0282301	−	1.46556i
$906$	17.3463	−	9.70609i	0.576294	−	0.322463i
$907$	−14.0890			−0.467817			−0.233908	−	0.972259i	$-0.575152\pi$
$907$	−14.0890			−0.467817			−0.233908	+	0.972259i	$0.575152\pi$
$908$	5.14156	+	3.15593i	0.170629	+	0.104733i
$909$	10.7912	−	10.7912i	0.357923	−	0.357923i
$910$	35.2246	−	20.6104i	1.16768	−	0.683229i
$911$		−	12.0656i		−	0.399753i	−0.979821	−	0.199876i	$-0.935946\pi$
$911$		−	12.0656i		−	0.399753i	0.979821	−	0.199876i	$-0.0640540\pi$
$912$	7.96219	−	24.3836i	0.263655	−	0.807422i
$913$	10.4320	+	10.4320i	0.345249	+	0.345249i
$914$	13.1056	+	3.70135i	0.433496	+	0.122430i
$915$	14.3740	−	0.276877i	0.475189	−	0.00915327i
$916$	29.7091	−	7.10952i	0.981615	−	0.234905i
$917$		−	28.7431i		−	0.949182i
$918$	4.00117	−	14.1672i	0.132058	−	0.467589i
$919$			13.5317i			0.446371i	0.974776	+	0.223186i	$0.0716456\pi$
$919$			13.5317i			0.446371i	−0.974776	+	0.223186i	$0.928354\pi$
$920$	−0.0553805	+	2.62333i	−0.00182584	+	0.0864887i
$921$			25.0434i			0.825208i
$922$	3.59715	+	1.01592i	0.118466	+	0.0334576i
$923$			18.5585i			0.610860i
$924$	−6.34026	+	10.3294i	−0.208579	+	0.339812i
$925$	−4.24537	+	0.163613i	−0.139587	+	0.00537955i
$926$	−4.33812	+	15.3603i	−0.142559	+	0.504771i
$927$	−5.14115	−	5.14115i	−0.168858	−	0.168858i
$928$	28.6018	−	5.63488i	0.938901	−	0.184974i
$929$		−	23.1897i		−	0.760828i	−0.924816	−	0.380414i	$-0.875781\pi$
$929$		−	23.1897i		−	0.760828i	0.924816	−	0.380414i	$-0.124219\pi$
$930$	25.4310	+	6.65626i	0.833915	+	0.218267i
$931$	−29.7852	+	29.7852i	−0.976170	+	0.976170i
$932$	−7.30750	−	30.5364i	−0.239365	−	1.00025i
$933$	−41.2659			−1.35098
$934$	10.9317	+	19.5367i	0.357696	+	0.639262i
$935$	2.86288	−	2.97534i	0.0936262	−	0.0973039i
$936$	7.17898	+	0.289956i	0.234652	+	0.00947750i
$937$	39.7908	+	39.7908i	1.29991	+	1.29991i	0.928450	+	0.371458i	$0.121142\pi$
$937$	39.7908	+	39.7908i	1.29991	+	1.29991i	0.371458	+	0.928450i	$0.378858\pi$
$938$	−19.3135	−	5.45461i	−0.630610	−	0.178099i
$939$	20.7841	−	20.7841i	0.678265	−	0.678265i
$940$	−15.8697	+	27.0078i	−0.517614	+	0.880898i
$941$	1.43026	+	1.43026i	0.0466253	+	0.0466253i	0.730035	−	0.683410i	$-0.239504\pi$
$941$	1.43026	+	1.43026i	0.0466253	+	0.0466253i	−0.683410	+	0.730035i	$0.739504\pi$
$942$	18.2516	−	10.2126i	0.594669	−	0.332745i
$943$	0.0224802	−	0.0224802i	0.000732055	−	0.000732055i
$944$	−24.5429	−	8.01419i	−0.798802	−	0.260840i
$945$	0.993016	+	51.5521i	0.0323028	+	1.67699i
$946$	4.72974	−	16.7469i	0.153777	−	0.544489i
$947$			19.7585i			0.642066i	0.947068	+	0.321033i	$0.104030\pi$
$947$			19.7585i			0.642066i	−0.947068	+	0.321033i	$0.895970\pi$
$948$	−26.2892	+	42.8297i	−0.853834	+	1.39104i
$949$	32.4011	+	32.4011i	1.05178	+	1.05178i
$950$	7.17823	−	29.7532i	0.232892	−	0.965320i
$951$	17.3312			0.562003
$952$	−21.3462	−	0.862162i	−0.691833	−	0.0279428i
$953$	20.8735	−	20.8735i	0.676160	−	0.676160i	−0.282969	−	0.959129i	$-0.591319\pi$
$953$	20.8735	−	20.8735i	0.676160	−	0.676160i	0.959129	+	0.282969i	$0.0913194\pi$
$954$	3.13021	−	1.75150i	0.101344	−	0.0567069i
$955$	12.6736	+	12.1946i	0.410109	+	0.394608i
$956$	−7.87508	+	12.8299i	−0.254698	+	0.414948i
$957$	−7.63472			−0.246796
$958$	−33.8163	+	18.9218i	−1.09256	+	0.611336i
$959$	−37.8216			−1.22132
$960$	−19.8557	+	17.5531i	−0.640841	+	0.566524i
$961$	−0.484224			−0.0156201
$962$	−3.30862	+	1.85133i	−0.106674	+	0.0596892i
$963$	1.06965			0.0344690
$964$	6.45846	−	10.5220i	0.208013	−	0.338890i
$965$	−7.75833	+	0.149444i	−0.249750	+	0.00481077i
$966$	−3.10285	+	1.73619i	−0.0998327	+	0.0558610i
$967$	−20.8535	+	20.8535i	−0.670602	+	0.670602i	−0.957855	−	0.287253i	$-0.907258\pi$
$967$	−20.8535	+	20.8535i	−0.670602	+	0.670602i	0.287253	+	0.957855i	$0.407258\pi$
$968$	−2.82612	−	0.114146i	−0.0908350	−	0.00366879i
$969$	−11.8413			−0.380398
$970$	−5.11220	−	8.73709i	−0.164143	−	0.280531i
$971$	−11.6225	−	11.6225i	−0.372983	−	0.372983i	0.495580	−	0.868562i	$-0.334956\pi$
$971$	−11.6225	−	11.6225i	−0.372983	−	0.372983i	−0.868562	+	0.495580i	$0.834956\pi$
$972$	−8.49247	+	13.8357i	−0.272396	+	0.443781i
$973$			37.8256i			1.21263i
$974$	−1.08602	+	3.84536i	−0.0347984	+	0.123213i
$975$	−23.3542	+	0.900050i	−0.747933	+	0.0288247i
$976$	5.38841	−	16.5016i	0.172479	−	0.528203i
$977$	21.5641	−	21.5641i	0.689898	−	0.689898i	−0.272311	−	0.962209i	$-0.587788\pi$
$977$	21.5641	−	21.5641i	0.689898	−	0.689898i	0.962209	+	0.272311i	$0.0877880\pi$
$978$	35.8321	−	20.0497i	1.14578	−	0.641119i
$979$	0.404059	+	0.404059i	0.0129138	+	0.0129138i
$980$	42.1228	−	10.9420i	1.34557	−	0.349530i
$981$	−10.5278	+	10.5278i	−0.336127	+	0.336127i
$982$	−59.2755	−	16.7408i	−1.89156	−	0.534221i
$983$	−37.2725	−	37.2725i	−1.18881	−	1.18881i	−0.977397	−	0.211412i	$-0.932194\pi$
$983$	−37.2725	−	37.2725i	−1.18881	−	1.18881i	−0.211412	−	0.977397i	$-0.567806\pi$
$984$	0.320842	+	0.0129587i	0.0102281	+	0.000413107i
$985$	37.7031	+	36.2780i	1.20132	+	1.15591i
$986$	−6.57131	−	11.7440i	−0.209273	−	0.374005i
$987$	−42.4476			−1.35112
$988$	−6.35674	−	26.5634i	−0.202235	−	0.845093i
$989$	3.60985	−	3.60985i	0.114787	−	0.114787i
$990$	−2.19748	+	1.28578i	−0.0698405	+	0.0408648i
$991$		−	45.6153i		−	1.44902i	−0.689266	−	0.724508i	$-0.742067\pi$
$991$		−	45.6153i		−	1.44902i	0.689266	−	0.724508i	$-0.257933\pi$
$992$	17.6826	−	26.3594i	0.561425	−	0.836913i
$993$	−12.2895	−	12.2895i	−0.389995	−	0.389995i
$994$	−9.24808	+	32.7454i	−0.293331	+	1.03862i
$995$	28.2053	+	27.1392i	0.894168	+	0.860372i
$996$	−22.8676	+	37.2554i	−0.724588	+	1.18048i
$997$		−	33.3810i		−	1.05719i	−0.848875	−	0.528593i	$-0.822720\pi$
$997$		−	33.3810i		−	1.05719i	0.848875	−	0.528593i	$-0.177280\pi$
$998$	28.4158	+	8.02532i	0.899487	+	0.254037i
$999$		−	4.79007i		−	0.151551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bk.b.243.20	yes	236
5.2	odd	4		880.2.s.b.67.40	✓	236
16.11	odd	4		880.2.s.b.683.40	yes	236
80.27	even	4	inner	880.2.bk.b.507.20	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.40	✓	236	5.2	odd	4
880.2.s.b.683.40	yes	236	16.11	odd	4
880.2.bk.b.243.20	yes	236	1.1	even	1	trivial
880.2.bk.b.507.20	yes	236	80.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23415 + 0.690563i) q^{2} -1.48151 q^{3} +(1.04624 - 1.70452i) q^{4} +(-1.55039 + 1.61130i) q^{5} +(1.82841 - 1.02308i) q^{6} +(2.89237 - 2.89237i) q^{7} +(-0.114146 + 2.82612i) q^{8} -0.805118 q^{9} +(0.800715 - 3.05922i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-1.55003 + 2.52526i) q^{12} +3.15509i q^{13} +(-1.57225 + 5.56697i) q^{14} +(2.29693 - 2.38716i) q^{15} +(-1.81074 - 3.56668i) q^{16} +(-1.30571 + 1.30571i) q^{17} +(0.993635 - 0.555985i) q^{18} +(-3.06068 - 3.06068i) q^{19} +(1.12439 + 4.32848i) q^{20} +(-4.28508 + 4.28508i) q^{21} +(-1.36098 - 0.384373i) q^{22} +(-0.293363 - 0.293363i) q^{23} +(0.169109 - 4.18694i) q^{24} +(-0.192552 - 4.99629i) q^{25} +(-2.17879 - 3.89385i) q^{26} +5.63733 q^{27} +(-1.90396 - 7.95620i) q^{28} +(3.64395 - 3.64395i) q^{29} +(-1.18627 + 4.53228i) q^{30} -5.61108i q^{31} +(4.69774 + 3.15138i) q^{32} +(-1.04759 - 1.04759i) q^{33} +(0.709763 - 2.51311i) q^{34} +(0.176150 + 9.14477i) q^{35} +(-0.842351 + 1.37234i) q^{36} -0.849705i q^{37} +(5.89093 + 1.66374i) q^{38} -4.67431i q^{39} +(-4.37675 - 4.56553i) q^{40} +0.0766293i q^{41} +(2.32930 - 8.24754i) q^{42} +12.3051i q^{43} +(1.94508 - 0.465467i) q^{44} +(1.24825 - 1.29728i) q^{45} +(0.564639 + 0.159468i) q^{46} +(4.95296 + 4.95296i) q^{47} +(2.68264 + 5.28408i) q^{48} -9.73155i q^{49} +(3.68789 + 6.03320i) q^{50} +(1.93442 - 1.93442i) q^{51} +(5.37790 + 3.30100i) q^{52} +3.15026 q^{53} +(-6.95731 + 3.89294i) q^{54} +(-2.23565 + 0.0430640i) q^{55} +(7.84403 + 8.50433i) q^{56} +(4.53444 + 4.53444i) q^{57} +(-1.98080 + 7.01356i) q^{58} +(4.56405 - 4.56405i) q^{59} +(-1.66579 - 6.41270i) q^{60} +(3.06868 + 3.06868i) q^{61} +(3.87481 + 6.92491i) q^{62} +(-2.32870 + 2.32870i) q^{63} +(-7.97394 - 0.645180i) q^{64} +(-5.08379 - 4.89164i) q^{65} +(2.01631 + 0.569453i) q^{66} +3.46931i q^{67} +(0.859508 + 3.59169i) q^{68} +(0.434621 + 0.434621i) q^{69} +(-6.53243 - 11.1644i) q^{70} +5.88208 q^{71} +(0.0919009 - 2.27536i) q^{72} +(10.2695 - 10.2695i) q^{73} +(0.586775 + 1.04866i) q^{74} +(0.285269 + 7.40207i) q^{75} +(-8.41920 + 2.01476i) q^{76} +4.09042 q^{77} +(3.22791 + 5.76879i) q^{78} +16.9605 q^{79} +(8.55435 + 2.61212i) q^{80} -5.93643 q^{81} +(-0.0529173 - 0.0945719i) q^{82} +14.7531 q^{83} +(2.82074 + 11.7872i) q^{84} +(-0.0795198 - 4.12824i) q^{85} +(-8.49743 - 15.1863i) q^{86} +(-5.39857 + 5.39857i) q^{87} +(-2.07908 + 1.91766i) q^{88} +0.571426 q^{89} +(-0.644670 + 2.46304i) q^{90} +(9.12568 + 9.12568i) q^{91} +(-0.806971 + 0.193112i) q^{92} +8.31289i q^{93} +(-9.53302 - 2.69235i) q^{94} +(9.67693 - 0.186401i) q^{95} +(-6.95977 - 4.66881i) q^{96} +(2.26353 - 2.26353i) q^{97} +(6.72025 + 12.0102i) q^{98} +(-0.569305 - 0.569305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

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