LMFDB - Embedded newform 425.2.p.a.16.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (of order $10$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.19
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.372964 - 0.270974i) q^{2} +(-2.68354 + 0.871936i) q^{3} +(-0.552359 - 1.69999i) q^{4} +(1.94832 - 1.09729i) q^{5} +(1.23714 + 0.401971i) q^{6} +3.02747i q^{7} +(-0.539562 + 1.66060i) q^{8} +(4.01408 - 2.91640i) q^{9} +(-1.02399 - 0.118696i) q^{10} +(-0.156731 + 0.215722i) q^{11} +(2.96456 + 4.08036i) q^{12} +(-0.531467 + 0.386133i) q^{13} +(0.820368 - 1.12914i) q^{14} +(-4.27164 + 4.64343i) q^{15} +(-2.24097 + 1.62816i) q^{16} +(0.184780 - 4.11896i) q^{17} -2.28738 q^{18} +(1.80483 - 5.55471i) q^{19} +(-2.94155 - 2.70602i) q^{20} +(-2.63976 - 8.12436i) q^{21} +(0.116910 - 0.0379864i) q^{22} +(1.41686 - 1.95014i) q^{23} -4.92676i q^{24} +(2.59192 - 4.27574i) q^{25} +0.302850 q^{26} +(-3.25348 + 4.47803i) q^{27} +(5.14666 - 1.67225i) q^{28} +(5.21795 - 1.69542i) q^{29} +(2.85142 - 0.574329i) q^{30} +(0.984390 + 0.319848i) q^{31} +4.76911 q^{32} +(0.232499 - 0.715558i) q^{33} +(-1.18505 + 1.48616i) q^{34} +(3.32201 + 5.89849i) q^{35} +(-7.17505 - 5.21298i) q^{36} +(-4.61435 - 6.35111i) q^{37} +(-2.17832 + 1.58264i) q^{38} +(1.08953 - 1.49961i) q^{39} +(0.770917 + 3.82744i) q^{40} +(-6.82123 - 9.38861i) q^{41} +(-1.21696 + 3.74540i) q^{42} +0.404623 q^{43} +(0.453296 + 0.147285i) q^{44} +(4.62059 - 10.0867i) q^{45} +(-1.05688 + 0.343400i) q^{46} +(1.19487 + 3.67742i) q^{47} +(4.59409 - 6.32322i) q^{48} -2.16560 q^{49} +(-2.12531 + 0.892356i) q^{50} +(3.09561 + 11.2145i) q^{51} +(0.949981 + 0.690202i) q^{52} +(0.0806292 + 0.248151i) q^{53} +(2.42686 - 0.788536i) q^{54} +(-0.0686536 + 0.592275i) q^{55} +(-5.02742 - 1.63351i) q^{56} +16.4800i q^{57} +(-2.40552 - 0.781602i) q^{58} +(3.57007 - 2.59380i) q^{59} +(10.2532 + 4.69689i) q^{60} +(-1.06269 + 1.46267i) q^{61} +(-0.280472 - 0.386036i) q^{62} +(8.82932 + 12.1525i) q^{63} +(2.70323 + 1.96401i) q^{64} +(-0.611769 + 1.33548i) q^{65} +(-0.280612 + 0.203876i) q^{66} +(4.63850 - 14.2758i) q^{67} +(-7.10424 + 1.96102i) q^{68} +(-2.10181 + 6.46871i) q^{69} +(0.359349 - 3.10011i) q^{70} +(-5.71409 + 1.85662i) q^{71} +(2.67713 + 8.23936i) q^{72} +(2.79384 - 3.84540i) q^{73} +3.61911i q^{74} +(-3.22735 + 13.7341i) q^{75} -10.4398 q^{76} +(-0.653092 - 0.474499i) q^{77} +(-0.812712 + 0.264066i) q^{78} +(-6.64764 + 2.15995i) q^{79} +(-2.57957 + 5.63117i) q^{80} +(0.226570 - 0.697311i) q^{81} +5.35000i q^{82} +(-2.05279 + 6.31783i) q^{83} +(-12.3532 + 8.97512i) q^{84} +(-4.15968 - 8.22782i) q^{85} +(-0.150910 - 0.109643i) q^{86} +(-12.5243 + 9.09944i) q^{87} +(-0.273662 - 0.376663i) q^{88} +(10.8570 + 7.88805i) q^{89} +(-4.45655 + 2.50991i) q^{90} +(-1.16901 - 1.60900i) q^{91} +(-4.09783 - 1.33147i) q^{92} -2.92054 q^{93} +(0.550844 - 1.69532i) q^{94} +(-2.57872 - 12.8028i) q^{95} +(-12.7981 + 4.15836i) q^{96} +(13.5820 - 4.41306i) q^{97} +(0.807690 + 0.586821i) q^{98} +1.32301i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.372964	−	0.270974i	−0.263726	−	0.191608i	0.448062	−	0.894002i	$-0.352114\pi$
$2$	−0.372964	−	0.270974i	−0.263726	−	0.191608i	−0.711788	+	0.702394i	$0.752114\pi$
$3$	−2.68354	+	0.871936i	−1.54934	+	0.503412i	−0.953936	−	0.300011i	$-0.903010\pi$
$3$	−2.68354	+	0.871936i	−1.54934	+	0.503412i	−0.595408	+	0.803423i	$0.703010\pi$
$4$	−0.552359	−	1.69999i	−0.276179	−	0.849993i
$5$	1.94832	−	1.09729i	0.871316	−	0.490722i
$5$	1.94832	−	1.09729i	0.871316	−	0.490722i
$6$	1.23714	+	0.401971i	0.505059	+	0.164104i
$7$			3.02747i			1.14428i	0.820157	+	0.572139i	$0.193886\pi$
$7$			3.02747i			1.14428i	−0.820157	+	0.572139i	$0.806114\pi$
$8$	−0.539562	+	1.66060i	−0.190764	+	0.587111i
$9$	4.01408	−	2.91640i	1.33803	−	0.972133i
$10$	−1.02399	−	0.118696i	−0.323815	−	0.0375350i
$11$	−0.156731	+	0.215722i	−0.0472562	+	0.0650426i	−0.831991	−	0.554789i	$-0.812799\pi$
$11$	−0.156731	+	0.215722i	−0.0472562	+	0.0650426i	0.784735	+	0.619831i	$0.212799\pi$
$12$	2.96456	+	4.08036i	0.855794	+	1.17790i
$13$	−0.531467	+	0.386133i	−0.147402	+	0.107094i	−0.659042	−	0.752106i	$-0.729038\pi$
$13$	−0.531467	+	0.386133i	−0.147402	+	0.107094i	0.511640	+	0.859200i	$0.329038\pi$
$14$	0.820368	−	1.12914i	0.219253	−	0.301775i
$15$	−4.27164	+	4.64343i	−1.10293	+	1.19893i
$16$	−2.24097	+	1.62816i	−0.560243	+	0.407040i
$17$	0.184780	−	4.11896i	0.0448158	−	0.998995i
$17$	0.184780	−	4.11896i	0.0448158	−	0.998995i
$18$	−2.28738			−0.539140
$19$	1.80483	−	5.55471i	0.414057	−	1.27434i	−0.499034	−	0.866582i	$-0.666312\pi$
$19$	1.80483	−	5.55471i	0.414057	−	1.27434i	0.913092	−	0.407755i	$-0.133688\pi$
$20$	−2.94155	−	2.70602i	−0.657750	−	0.605085i
$21$	−2.63976	−	8.12436i	−0.576044	−	1.77288i
$22$	0.116910	−	0.0379864i	0.0249253	−	0.00809873i
$23$	1.41686	−	1.95014i	0.295436	−	0.406633i	−0.635334	−	0.772237i	$-0.719138\pi$
$23$	1.41686	−	1.95014i	0.295436	−	0.406633i	0.930770	+	0.365604i	$0.119138\pi$
$24$		−	4.92676i		−	1.00567i
$25$	2.59192	−	4.27574i	0.518383	−	0.855148i
$26$	0.302850			0.0593938
$27$	−3.25348	+	4.47803i	−0.626132	+	0.861797i
$28$	5.14666	−	1.67225i	0.972628	−	0.316026i
$29$	5.21795	−	1.69542i	0.968950	−	0.314831i	0.218558	−	0.975824i	$-0.429865\pi$
$29$	5.21795	−	1.69542i	0.968950	−	0.314831i	0.750392	+	0.660993i	$0.229865\pi$
$30$	2.85142	−	0.574329i	0.520596	−	0.104858i
$31$	0.984390	+	0.319848i	0.176802	+	0.0574464i	0.396080	−	0.918216i	$-0.370370\pi$
$31$	0.984390	+	0.319848i	0.176802	+	0.0574464i	−0.219278	+	0.975662i	$0.570370\pi$
$32$	4.76911			0.843067
$33$	0.232499	−	0.715558i	0.0404729	−	0.124563i
$34$	−1.18505	+	1.48616i	−0.203234	+	0.254874i
$35$	3.32201	+	5.89849i	0.561522	+	0.997027i
$36$	−7.17505	−	5.21298i	−1.19584	−	0.868830i
$37$	−4.61435	−	6.35111i	−0.758595	−	1.04412i	−0.997330	−	0.0730313i	$-0.976733\pi$
$37$	−4.61435	−	6.35111i	−0.758595	−	1.04412i	0.238735	−	0.971085i	$-0.423267\pi$
$38$	−2.17832	+	1.58264i	−0.353370	+	0.256739i
$39$	1.08953	−	1.49961i	0.174465	−	0.240130i
$40$	0.770917	+	3.82744i	0.121893	+	0.605171i
$41$	−6.82123	−	9.38861i	−1.06530	−	1.46626i	−0.874748	−	0.484577i	$-0.838973\pi$
$41$	−6.82123	−	9.38861i	−1.06530	−	1.46626i	−0.190548	−	0.981678i	$-0.561027\pi$
$42$	−1.21696	+	3.74540i	−0.187780	+	0.577928i
$43$	0.404623			0.0617045			0.0308522	−	0.999524i	$-0.490178\pi$
$43$	0.404623			0.0617045			0.0308522	+	0.999524i	$0.490178\pi$
$44$	0.453296	+	0.147285i	0.0683369	+	0.0222040i
$45$	4.62059	−	10.0867i	0.688797	−	1.50363i
$46$	−1.05688	+	0.343400i	−0.155828	+	0.0506316i
$47$	1.19487	+	3.67742i	0.174289	+	0.536407i	0.999600	−	0.0282713i	$-0.00900025\pi$
$47$	1.19487	+	3.67742i	0.174289	+	0.536407i	−0.825311	+	0.564678i	$0.809000\pi$
$48$	4.59409	−	6.32322i	0.663100	−	0.912678i
$49$	−2.16560			−0.309371
$50$	−2.12531	+	0.892356i	−0.300564	+	0.126198i
$51$	3.09561	+	11.2145i	0.433472	+	1.57035i
$52$	0.949981	+	0.690202i	0.131739	+	0.0957138i
$53$	0.0806292	+	0.248151i	0.0110753	+	0.0340862i	0.956441	−	0.291924i	$-0.0942955\pi$
$53$	0.0806292	+	0.248151i	0.0110753	+	0.0340862i	−0.945366	+	0.326010i	$0.894296\pi$
$54$	2.42686	−	0.788536i	0.330254	−	0.107306i
$55$	−0.0686536	+	0.592275i	−0.00925725	+	0.0798623i
$56$	−5.02742	−	1.63351i	−0.671818	−	0.218287i
$57$			16.4800i			2.18283i
$58$	−2.40552	−	0.781602i	−0.315861	−	0.102629i
$59$	3.57007	−	2.59380i	0.464783	−	0.337685i	−0.330622	−	0.943763i	$-0.607258\pi$
$59$	3.57007	−	2.59380i	0.464783	−	0.337685i	0.795405	+	0.606079i	$0.207258\pi$
$60$	10.2532	+	4.69689i	1.32369	+	0.606366i
$61$	−1.06269	+	1.46267i	−0.136064	+	0.187276i	−0.871612	−	0.490197i	$-0.836925\pi$
$61$	−1.06269	+	1.46267i	−0.136064	+	0.187276i	0.735548	+	0.677473i	$0.236925\pi$
$62$	−0.280472	−	0.386036i	−0.0356200	−	0.0490267i
$63$	8.82932	+	12.1525i	1.11239	+	1.53107i
$64$	2.70323	+	1.96401i	0.337904	+	0.245502i
$65$	−0.611769	+	1.33548i	−0.0758806	+	0.165646i
$66$	−0.280612	+	0.203876i	−0.0345409	+	0.0250954i
$67$	4.63850	−	14.2758i	0.566683	−	1.74407i	−0.0962161	−	0.995360i	$-0.530674\pi$
$67$	4.63850	−	14.2758i	0.566683	−	1.74407i	0.662899	−	0.748709i	$-0.269326\pi$
$68$	−7.10424	+	1.96102i	−0.861516	+	0.237809i
$69$	−2.10181	+	6.46871i	−0.253028	+	0.778741i
$70$	0.359349	−	3.10011i	0.0429505	−	0.370534i
$71$	−5.71409	+	1.85662i	−0.678138	+	0.220340i	−0.627780	−	0.778391i	$-0.716036\pi$
$71$	−5.71409	+	1.85662i	−0.678138	+	0.220340i	−0.0503582	+	0.998731i	$0.516036\pi$
$72$	2.67713	+	8.23936i	0.315503	+	0.971018i
$73$	2.79384	−	3.84540i	0.326995	−	0.450069i	−0.613592	−	0.789623i	$-0.710276\pi$
$73$	2.79384	−	3.84540i	0.326995	−	0.450069i	0.940587	+	0.339554i	$0.110276\pi$
$74$			3.61911i			0.420713i
$75$	−3.22735	+	13.7341i	−0.372662	+	1.58588i
$76$	−10.4398			−1.19753
$77$	−0.653092	−	0.474499i	−0.0744267	−	0.0540742i
$78$	−0.812712	+	0.264066i	−0.0920215	+	0.0298996i
$79$	−6.64764	+	2.15995i	−0.747918	+	0.243013i	−0.658085	−	0.752944i	$-0.728633\pi$
$79$	−6.64764	+	2.15995i	−0.747918	+	0.243013i	−0.0898328	+	0.995957i	$0.528633\pi$
$80$	−2.57957	+	5.63117i	−0.288405	+	0.629584i
$81$	0.226570	−	0.697311i	0.0251745	−	0.0774790i
$82$			5.35000i			0.590808i
$83$	−2.05279	+	6.31783i	−0.225323	+	0.693471i	0.772936	+	0.634484i	$0.218787\pi$
$83$	−2.05279	+	6.31783i	−0.225323	+	0.693471i	−0.998259	+	0.0589877i	$0.981213\pi$
$84$	−12.3532	+	8.97512i	−1.34784	+	0.979266i
$85$	−4.15968	−	8.22782i	−0.451180	−	0.892433i
$86$	−0.150910	−	0.109643i	−0.0162730	−	0.0118231i
$87$	−12.5243	+	9.09944i	−1.34275	+	0.975563i
$88$	−0.273662	−	0.376663i	−0.0291724	−	0.0401524i
$89$	10.8570	+	7.88805i	1.15084	+	0.836131i	0.988592	−	0.150619i	$-0.0481267\pi$
$89$	10.8570	+	7.88805i	1.15084	+	0.836131i	0.162244	+	0.986751i	$0.448127\pi$
$90$	−4.45655	+	2.50991i	−0.469761	+	0.264568i
$91$	−1.16901	−	1.60900i	−0.122545	−	0.168669i
$92$	−4.09783	−	1.33147i	−0.427229	−	0.138815i
$93$	−2.92054			−0.302846
$94$	0.550844	−	1.69532i	0.0568153	−	0.174859i
$95$	−2.57872	−	12.8028i	−0.264571	−	1.31354i
$96$	−12.7981	+	4.15836i	−1.30620	+	0.424411i
$97$	13.5820	−	4.41306i	1.37904	−	0.448078i	0.476689	−	0.879072i	$-0.341837\pi$
$97$	13.5820	−	4.41306i	1.37904	−	0.448078i	0.902355	+	0.430994i	$0.141837\pi$
$98$	0.807690	+	0.586821i	0.0815891	+	0.0592779i
$99$			1.32301i			0.132968i
$100$	−8.70037	−	2.04448i	−0.870037	−	0.204448i
$101$	11.7076			1.16495			0.582477	−	0.812847i	$-0.302084\pi$
$101$	11.7076			1.16495			0.582477	+	0.812847i	$0.302084\pi$
$102$	1.88430	−	5.02145i	0.186574	−	0.497198i
$103$	1.48436	+	4.56838i	0.146258	+	0.450136i	0.997171	−	0.0751712i	$-0.0239503\pi$
$103$	1.48436	+	4.56838i	0.146258	+	0.450136i	−0.850913	+	0.525307i	$0.823950\pi$
$104$	−0.354454	−	1.09090i	−0.0347571	−	0.106971i
$105$	−14.0579	−	12.9323i	−1.37191	−	1.26206i
$106$	0.0371708	−	0.114400i	0.00361035	−	0.0111115i
$107$			16.4427i			1.58958i	0.606886	+	0.794789i	$0.292419\pi$
$107$			16.4427i			1.58958i	−0.606886	+	0.794789i	$0.707581\pi$
$108$	9.40967	+	3.05739i	0.905446	+	0.294197i
$109$	−8.44550	−	11.6242i	−0.808933	−	1.11340i	−0.991487	−	0.130204i	$-0.958437\pi$
$109$	−8.44550	−	11.6242i	−0.808933	−	1.11340i	0.182555	−	0.983196i	$-0.441563\pi$
$110$	0.186097	−	0.202294i	0.0177436	−	0.0192880i
$111$	17.9206	+	13.0201i	1.70095	+	1.23581i
$112$	−4.92921	−	6.78448i	−0.465767	−	0.641073i
$113$	4.14113	+	5.69977i	0.389565	+	0.536190i	0.958087	−	0.286478i	$-0.0924846\pi$
$113$	4.14113	+	5.69977i	0.389565	+	0.536190i	−0.568522	+	0.822668i	$0.692485\pi$
$114$	4.46566	−	6.14645i	0.418247	−	0.575668i
$115$	0.620634	−	5.35421i	0.0578745	−	0.499283i
$116$	−5.76436	−	7.93397i	−0.535208	−	0.736650i
$117$	−1.00723	+	3.09994i	−0.0931186	+	0.286590i
$118$	−2.03436			−0.187278
$119$	12.4701	+	0.559417i	1.14313	+	0.0512817i
$120$	−5.40607	−	9.59891i	−0.493505	−	0.876256i
$121$	3.37722	+	10.3940i	0.307020	+	0.944909i
$122$	0.792693	−	0.257562i	0.0717671	−	0.0233185i
$123$	26.4913	+	19.2471i	2.38864	+	1.73545i
$124$		−	1.85012i		−	0.166146i
$125$	0.358169	−	11.1746i	0.0320356	−	0.999487i
$126$		−	6.92498i		−	0.616926i
$127$	−17.3414	−	12.5992i	−1.53880	−	1.11800i	−0.951084	−	0.308931i	$-0.900029\pi$
$127$	−17.3414	−	12.5992i	−1.53880	−	1.11800i	−0.587712	−	0.809070i	$-0.699971\pi$
$128$	−3.42348	−	10.5364i	−0.302596	−	0.931295i
$129$	−1.08582	+	0.352806i	−0.0956014	+	0.0310628i
$130$	0.590050	−	0.332314i	0.0517508	−	0.0291459i
$131$	18.1321	+	5.89149i	1.58421	+	0.514741i	0.963137	−	0.269010i	$-0.0866966\pi$
$131$	18.1321	+	5.89149i	1.58421	+	0.514741i	0.621074	+	0.783752i	$0.286697\pi$
$132$	−1.34486			−0.117055
$133$	16.8167	+	5.46408i	1.45819	+	0.473796i
$134$	−5.59838	+	4.06746i	−0.483626	+	0.351375i
$135$	−1.42514	+	12.2946i	−0.122656	+	1.05815i
$136$	6.74025	+	2.52928i	0.577972	+	0.216884i
$137$	−4.81506	+	3.49834i	−0.411378	+	0.298884i	−0.774160	−	0.632991i	$-0.781827\pi$
$137$	−4.81506	+	3.49834i	−0.411378	+	0.298884i	0.362781	+	0.931874i	$0.381827\pi$
$138$	2.53675	−	1.84306i	0.215943	−	0.156892i
$139$	11.0652	−	15.2299i	0.938537	−	1.29179i	−0.0178976	−	0.999840i	$-0.505697\pi$
$139$	11.0652	−	15.2299i	0.938537	−	1.29179i	0.956435	−	0.291946i	$-0.0943027\pi$
$140$	8.19241	−	8.90546i	0.692385	−	0.752648i
$141$	−6.41295	−	8.82667i	−0.540068	−	0.743340i
$142$	2.63425	+	0.855920i	0.221061	+	0.0718272i
$143$		−	0.175168i		−	0.0146483i
$144$	−4.24707	+	13.0711i	−0.353922	+	1.08926i
$145$	8.30589	−	9.02881i	0.689767	−	0.749802i
$146$	−2.08401	+	0.677135i	−0.172474	+	0.0560401i
$147$	5.81147	−	1.88826i	0.479322	−	0.155741i
$148$	−8.24802	+	11.3524i	−0.677983	+	0.933163i
$149$	11.8704			0.972462			0.486231	−	0.873830i	$-0.338371\pi$
$149$	11.8704			0.972462			0.486231	+	0.873830i	$0.338371\pi$
$150$	4.92528	−	4.24781i	0.402148	−	0.346832i
$151$	−1.37128			−0.111594			−0.0557968	−	0.998442i	$-0.517770\pi$
$151$	−1.37128			−0.111594			−0.0557968	+	0.998442i	$0.517770\pi$
$152$	8.25033	+	5.99421i	0.669190	+	0.486195i
$153$	−11.2708	−	17.0727i	−0.911192	−	1.38025i
$154$	0.115003	+	0.353942i	0.00926719	+	0.0285215i
$155$	2.26887	−	0.456993i	0.182240	−	0.0367066i
$156$	−3.15113	−	1.02386i	−0.252292	−	0.0819747i
$157$	−14.7812			−1.17967			−0.589835	−	0.807524i	$-0.700807\pi$
$157$	−14.7812			−1.17967			−0.589835	+	0.807524i	$0.700807\pi$
$158$	3.06462	+	0.995756i	0.243808	+	0.0792181i
$159$	−0.432744	−	0.595621i	−0.0343188	−	0.0472358i
$160$	9.29176	−	5.23309i	0.734578	−	0.413712i
$161$	5.90401	+	4.28951i	0.465301	+	0.338061i
$162$	−0.273456	+	0.198677i	−0.0214847	+	0.0156096i
$163$	−5.75379	−	7.91942i	−0.450672	−	0.620296i	0.521870	−	0.853025i	$-0.325235\pi$
$163$	−5.75379	−	7.91942i	−0.450672	−	0.620296i	−0.972542	+	0.232729i	$0.925235\pi$
$164$	−12.1927	+	16.7819i	−0.952093	+	1.31044i
$165$	−0.332191	−	1.64926i	−0.0258610	−	0.128394i
$166$	2.47758	−	1.80007i	0.192298	−	0.139713i
$167$	−4.92170	−	1.59916i	−0.380853	−	0.123746i	0.112333	−	0.993671i	$-0.464168\pi$
$167$	−4.92170	−	1.59916i	−0.380853	−	0.123746i	−0.493186	+	0.869924i	$0.664168\pi$
$168$	14.9156			1.15077
$169$	−3.88386	+	11.9533i	−0.298759	+	0.919485i
$170$	−0.678118	+	4.19585i	−0.0520093	+	0.321807i
$171$	−8.95500	−	27.5606i	−0.684806	−	2.10762i
$172$	−0.223497	−	0.687854i	−0.0170415	−	0.0524483i
$173$	−9.23281	+	12.7079i	−0.701957	+	0.966161i	0.297976	+	0.954573i	$0.403689\pi$
$173$	−9.23281	+	12.7079i	−0.701957	+	0.966161i	−0.999933	+	0.0115877i	$0.996311\pi$
$174$	7.13684			0.541042
$175$	12.9447	+	7.84696i	0.978527	+	0.593175i
$176$		−	0.738609i		−	0.0556748i
$177$	−7.31879	+	10.0735i	−0.550114	+	0.757167i
$178$	−1.91180	−	5.88392i	−0.143296	−	0.441018i
$179$	−3.67342	−	11.3056i	−0.274564	−	0.845022i	−0.989334	−	0.145663i	$-0.953469\pi$
$179$	−3.67342	−	11.3056i	−0.274564	−	0.845022i	0.714770	−	0.699360i	$-0.246531\pi$
$180$	−19.6994	−	2.28346i	−1.46831	−	0.170199i
$181$	−5.99537	−	1.94801i	−0.445632	−	0.144795i	0.0776004	−	0.996985i	$-0.475274\pi$
$181$	−5.99537	−	1.94801i	−0.445632	−	0.144795i	−0.523233	+	0.852190i	$0.675274\pi$
$182$			0.916872i			0.0679630i
$183$	1.57643	−	4.85174i	0.116533	−	0.358651i
$184$	2.47392	+	3.40507i	0.182380	+	0.251025i
$185$	−15.9592	−	7.31073i	−1.17335	−	0.537496i
$186$	1.08926	+	0.791392i	0.0798682	+	0.0580277i
$187$	0.859589	+	0.685430i	0.0628594	+	0.0501236i
$188$	5.59157	−	4.06251i	0.407807	−	0.296289i
$189$	−13.5571	−	9.84982i	−0.986135	−	0.716469i
$190$	−2.50746	+	5.47374i	−0.181910	+	0.397107i
$191$	−12.5873	+	9.14521i	−0.910785	+	0.661724i	−0.941213	−	0.337813i	$-0.890313\pi$
$191$	−12.5873	+	9.14521i	−0.910785	+	0.661724i	0.0304284	+	0.999537i	$0.490313\pi$
$192$	−8.96674	−	2.91347i	−0.647119	−	0.210262i
$193$		−	10.3300i		−	0.743567i	−0.928319	−	0.371784i	$-0.878746\pi$
$193$		−	10.3300i		−	0.743567i	0.928319	−	0.371784i	$-0.121254\pi$
$194$	−6.26143	−	2.03446i	−0.449544	−	0.146066i
$195$	0.477252	−	4.11725i	0.0341767	−	0.294843i
$196$	1.19619	+	3.68148i	0.0854419	+	0.262963i
$197$	14.5785	−	4.73686i	1.03868	−	0.337487i	0.260462	−	0.965484i	$-0.416125\pi$
$197$	14.5785	−	4.73686i	1.03868	−	0.337487i	0.778216	+	0.627997i	$0.216125\pi$
$198$	0.358503	−	0.493437i	0.0254777	−	0.0350671i
$199$		−	0.376574i		−	0.0266947i	−0.999911	−	0.0133473i	$-0.995751\pi$
$199$		−	0.376574i		−	0.0266947i	0.999911	−	0.0133473i	$-0.00424871\pi$
$200$	5.70180	+	6.61117i	0.403178	+	0.467480i
$201$			42.3543i			2.98744i
$202$	−4.36653	−	3.17247i	−0.307228	−	0.223214i
$203$	5.13283	+	15.7972i	0.360254	+	1.10875i
$204$	17.3547	−	11.4569i	1.21507	−	0.802146i
$205$	−23.5920	−	10.8072i	−1.64773	−	0.754807i
$206$	0.684303	−	2.10607i	0.0476776	−	0.146737i
$207$		−	11.9602i		−	0.831289i
$208$	0.562315	−	1.73063i	0.0389895	−	0.119997i
$209$	0.915397	+	1.25994i	0.0633194	+	0.0871516i
$210$	1.73877	+	8.63260i	0.119986	+	0.595706i
$211$	−11.8037	+	16.2464i	−0.812600	+	1.11845i	0.178317	+	0.983973i	$0.442935\pi$
$211$	−11.8037	+	16.2464i	−0.812600	+	1.11845i	−0.990917	+	0.134475i	$0.957065\pi$
$212$	0.377317	−	0.274137i	0.0259143	−	0.0188278i
$213$	13.7152	−	9.96465i	0.939747	−	0.682766i
$214$	4.45556	−	6.13255i	0.304576	−	0.419212i
$215$	0.788336	−	0.443988i	0.0537641	−	0.0302797i
$216$	−5.68077	−	7.81890i	−0.386527	−	0.532009i
$217$	−0.968331	+	2.98022i	−0.0657346	+	0.202310i
$218$			6.62394i			0.448630i
$219$	−4.14446	+	12.7553i	−0.280057	+	0.861926i
$220$	1.04478	−	0.210438i	0.0704390	−	0.0141877i
$221$	1.49226	+	2.26044i	0.100381	+	0.152054i
$222$	−3.15563	−	9.71203i	−0.211792	−	0.651829i
$223$	−12.1520	−	8.82892i	−0.813756	−	0.591228i	0.101161	−	0.994870i	$-0.467744\pi$
$223$	−12.1520	−	8.82892i	−0.813756	−	0.591228i	−0.914917	+	0.403642i	$0.867744\pi$
$224$			14.4384i			0.964703i
$225$	−2.06561	−	24.7222i	−0.137707	−	1.64815i
$226$		−	3.24795i		−	0.216051i
$227$	0.268998	−	0.370244i	0.0178540	−	0.0245739i	−0.799997	−	0.600004i	$-0.795165\pi$
$227$	0.268998	−	0.370244i	0.0178540	−	0.0245739i	0.817851	+	0.575430i	$0.195165\pi$
$228$	28.0157	−	9.10287i	1.85539	−	0.602852i
$229$	−5.54580	−	17.0682i	−0.366477	−	1.12790i	−0.949051	−	0.315122i	$-0.897955\pi$
$229$	−5.54580	−	17.0682i	−0.366477	−	1.12790i	0.582575	−	0.812777i	$-0.302045\pi$
$230$	−1.68233	+	1.82875i	−0.110930	+	0.120585i
$231$	2.16633	+	0.703884i	0.142534	+	0.0463122i
$232$			9.57972i			0.628939i
$233$	5.59757	+	1.81876i	0.366709	+	0.119151i	0.486574	−	0.873639i	$-0.338246\pi$
$233$	5.59757	+	1.81876i	0.366709	+	0.119151i	−0.119865	+	0.992790i	$0.538246\pi$
$234$	1.21567	−	0.883233i	0.0794705	−	0.0577387i
$235$	6.36318	+	5.85369i	0.415088	+	0.381852i
$236$	−6.38139	−	4.63635i	−0.415393	−	0.301801i
$237$	15.9559	−	11.5926i	1.03645	−	0.753022i
$238$	−4.49930	−	3.58771i	−0.291646	−	0.232557i
$239$	3.04521	+	2.21248i	0.196978	+	0.143113i	0.681903	−	0.731443i	$-0.261153\pi$
$239$	3.04521	+	2.21248i	0.196978	+	0.143113i	−0.484924	+	0.874556i	$0.661153\pi$
$240$	2.01237	−	17.3607i	0.129898	−	1.12063i
$241$	12.6137	+	17.3612i	0.812517	+	1.11833i	0.990930	+	0.134378i	$0.0429037\pi$
$241$	12.6137	+	17.3612i	0.812517	+	1.11833i	−0.178413	+	0.983956i	$0.557096\pi$
$242$	1.55693	−	4.79173i	0.100083	−	0.308024i
$243$		−	14.5366i		−	0.932525i
$244$	3.07351	+	0.998644i	0.196761	+	0.0639316i
$245$	−4.21928	+	2.37628i	−0.269560	+	0.151815i
$246$	−4.66485	−	14.3569i	−0.297420	−	0.915365i
$247$	1.18565	+	3.64905i	0.0754409	+	0.232183i
$248$	−1.06228	+	1.46210i	−0.0674548	+	0.0928435i
$249$		−	18.7441i		−	1.18786i
$250$	−3.16162	+	4.07067i	−0.199958	+	0.257452i
$251$	21.7753			1.37444			0.687222	−	0.726447i	$-0.258830\pi$
$251$	21.7753			1.37444			0.687222	+	0.726447i	$0.258830\pi$
$252$	15.7822	−	21.7223i	0.994182	−	1.36837i
$253$	0.198622	+	0.611296i	0.0124873	+	0.0384319i
$254$	3.05364	+	9.39813i	0.191602	+	0.589691i
$255$	18.3368	+	18.4527i	1.14830	+	1.15556i
$256$	0.486829	−	1.49831i	0.0304268	−	0.0936442i
$257$	−24.4173			−1.52311			−0.761556	−	0.648099i	$-0.775564\pi$
$257$	−24.4173			−1.52311			−0.761556	+	0.648099i	$0.775564\pi$
$258$	0.500575	+	0.162647i	0.0311644	+	0.0101259i
$259$	19.2278	−	13.9698i	1.19476	−	0.868043i
$260$	2.60822	+	0.302332i	0.161755	+	0.0187498i
$261$	16.0008	−	22.0232i	0.990423	−	1.36320i
$262$	−5.16619	−	7.11066i	−0.319169	−	0.439298i
$263$	−22.7290	+	16.5136i	−1.40153	+	1.01827i	−0.407041	+	0.913410i	$0.633439\pi$
$263$	−22.7290	+	16.5136i	−1.40153	+	1.01827i	−0.994487	+	0.104859i	$0.966561\pi$
$264$	1.06281	+	0.772176i	0.0654113	+	0.0475241i
$265$	0.429385	+	0.395005i	0.0263769	+	0.0242650i
$266$	−4.79141	−	6.59481i	−0.293780	−	0.404354i
$267$	−36.0130	−	11.7013i	−2.20396	−	0.716110i
$268$	−26.8308			−1.63895
$269$	−3.06694	−	0.996509i	−0.186995	−	0.0607582i	0.214023	−	0.976829i	$-0.431343\pi$
$269$	−3.06694	−	0.996509i	−0.186995	−	0.0607582i	−0.401017	+	0.916070i	$0.631343\pi$
$270$	3.86306	−	4.19929i	0.235098	−	0.255561i
$271$	−5.25967	−	16.1876i	−0.319502	−	0.983327i	−0.973861	−	0.227143i	$-0.927062\pi$
$271$	−5.25967	−	16.1876i	−0.319502	−	0.983327i	0.654359	−	0.756184i	$-0.272938\pi$
$272$	6.29225	+	9.53133i	0.381523	+	0.577922i
$273$	4.54003	+	3.29853i	0.274775	+	0.199636i
$274$	2.74381			0.165759
$275$	0.516137	+	1.22927i	0.0311242	+	0.0741280i
$276$	12.1577			0.731805
$277$	−9.76161	+	13.4357i	−0.586519	+	0.807274i	−0.994391	−	0.105765i	$-0.966271\pi$
$277$	−9.76161	+	13.4357i	−0.586519	+	0.807274i	0.407873	+	0.913039i	$0.366271\pi$
$278$	−8.25384	+	2.68184i	−0.495033	+	0.160846i
$279$	4.88423	−	1.58698i	0.292411	−	0.0950101i
$280$	−11.5875	+	2.33393i	−0.692484	+	0.139479i
$281$	−8.32622	+	25.6255i	−0.496700	+	1.52869i	0.317590	+	0.948228i	$0.397127\pi$
$281$	−8.32622	+	25.6255i	−0.496700	+	1.52869i	−0.814290	+	0.580458i	$0.802873\pi$
$282$			5.02978i			0.299519i
$283$	−20.8179	−	6.76414i	−1.23750	−	0.402087i	−0.384071	−	0.923304i	$-0.625478\pi$
$283$	−20.8179	−	6.76414i	−1.23750	−	0.402087i	−0.853424	+	0.521217i	$0.825478\pi$
$284$	6.31246	+	8.68836i	0.374576	+	0.515559i
$285$	18.0833	+	32.1083i	1.07116	+	1.90193i
$286$	−0.0474660	+	0.0653314i	−0.00280673	+	0.00386313i
$287$	28.4238	−	20.6511i	1.67780	−	1.21900i
$288$	19.1436	−	13.9086i	1.12805	−	0.819574i
$289$	−16.9317	−	1.52221i	−0.995983	−	0.0895415i
$290$	−5.54438	+	1.11674i	−0.325577	+	0.0655773i
$291$	−32.6000	+	23.6853i	−1.91104	+	1.38846i
$292$	−8.08032	−	2.62546i	−0.472865	−	0.153643i
$293$	−5.64597			−0.329841			−0.164921	−	0.986307i	$-0.552737\pi$
$293$	−5.64597			−0.329841			−0.164921	+	0.986307i	$0.552737\pi$
$294$	−2.67914	−	0.870506i	−0.156251	−	0.0507690i
$295$	4.10949	−	8.97096i	0.239264	−	0.522309i
$296$	13.0364	−	4.23578i	0.757725	−	0.246200i
$297$	−0.456087	−	1.40369i	−0.0264649	−	0.0814505i
$298$	−4.42724	−	3.21658i	−0.256463	−	0.186331i
$299$			1.58353i			0.0915782i
$300$	25.1305	−	2.09972i	1.45091	−	0.121227i
$301$			1.22499i			0.0706070i
$302$	0.511440	+	0.371583i	0.0294301	+	0.0213822i
$303$	−31.4179	+	10.2083i	−1.80491	+	0.586452i
$304$	4.99937	+	15.3865i	0.286734	+	0.882476i
$305$	−0.465496	+	4.01584i	−0.0266542	+	0.229946i
$306$	−0.422662	+	9.42163i	−0.0241620	+	0.538598i
$307$	29.5669			1.68747			0.843735	−	0.536759i	$-0.180352\pi$
$307$	29.5669			1.68747			0.843735	+	0.536759i	$0.180352\pi$
$308$	−0.445900	+	1.37234i	−0.0254075	+	0.0781964i
$309$	−7.96668	−	10.9652i	−0.453208	−	0.623788i
$310$	−0.970043	−	0.444365i	−0.0550947	−	0.0252382i
$311$	16.4822	−	22.6858i	0.934619	−	1.28639i	−0.0234118	−	0.999726i	$-0.507453\pi$
$311$	16.4822	−	22.6858i	0.934619	−	1.28639i	0.958030	−	0.286666i	$-0.0925471\pi$
$312$	1.90238	+	2.61841i	0.107701	+	0.148238i
$313$	4.12608	+	5.67907i	0.233220	+	0.321000i	0.909546	−	0.415602i	$-0.136429\pi$
$313$	4.12608	+	5.67907i	0.233220	+	0.321000i	−0.676327	+	0.736602i	$0.736429\pi$
$314$	5.51287	+	4.00533i	0.311109	+	0.226034i
$315$	30.5372	+	13.9887i	1.72058	+	0.788175i
$316$	7.34376	+	10.1078i	0.413119	+	0.568610i
$317$	19.5259	+	6.34434i	1.09668	+	0.356334i	0.800825	−	0.598898i	$-0.204395\pi$
$317$	19.5259	+	6.34434i	1.09668	+	0.356334i	0.295857	+	0.955232i	$0.404395\pi$
$318$			0.339408i			0.0190331i
$319$	−0.452077	+	1.39135i	−0.0253115	+	0.0779007i
$320$	7.42186	+	0.860306i	0.414895	+	0.0480926i
$321$	−14.3370	−	44.1248i	−0.800214	−	2.46280i
$322$	−1.03964	−	3.19967i	−0.0579366	−	0.178311i
$323$	−22.5461	−	8.46044i	−1.25450	−	0.470752i
$324$	−1.31057			−0.0728093
$325$	0.273488	+	3.27324i	0.0151704	+	0.181567i
$326$			4.51279i			0.249940i
$327$	32.7995	+	23.8302i	1.81381	+	1.31781i
$328$	19.2712	−	6.26160i	1.06407	−	0.345739i
$329$	−11.1333	+	3.61743i	−0.613798	+	0.199435i
$330$	−0.323011	+	0.705129i	−0.0177812	+	0.0388161i
$331$	−4.42478	+	13.6181i	−0.243208	+	0.748517i	0.752718	+	0.658343i	$0.228742\pi$
$331$	−4.42478	+	13.6181i	−0.243208	+	0.748517i	−0.995926	+	0.0901738i	$0.971258\pi$
$332$	11.8741			0.651675
$333$	−37.0448	−	12.0366i	−2.03004	−	0.659600i
$334$	1.40229	+	1.93008i	0.0767298	+	0.105609i
$335$	−6.62741	−	32.9037i	−0.362094	−	1.79772i
$336$	19.1434	+	13.9085i	1.04436	+	0.758770i
$337$	−0.765556	−	1.05370i	−0.0417025	−	0.0573986i	0.787657	−	0.616115i	$-0.211294\pi$
$337$	−0.765556	−	1.05370i	−0.0417025	−	0.0573986i	−0.829359	+	0.558716i	$0.811294\pi$
$338$	4.68758	−	3.40573i	0.254971	−	0.185247i
$339$	−16.0827	−	11.6848i	−0.873494	−	0.634631i
$340$	−11.6895	+	11.6161i	−0.633955	+	0.629972i
$341$	−0.223283	+	0.162224i	−0.0120914	+	0.00878494i
$342$	−4.12834	+	12.7057i	−0.223235	+	0.687046i
$343$			14.6360i			0.790271i
$344$	−0.218319	+	0.671917i	−0.0117710	+	0.0362274i
$345$	3.00303	+	14.9094i	0.161678	+	0.802696i
$346$	6.88701	−	2.23773i	0.370248	−	0.120301i
$347$	−1.21213	+	0.393844i	−0.0650704	+	0.0211427i	−0.341371	−	0.939929i	$-0.610891\pi$
$347$	−1.21213	+	0.393844i	−0.0650704	+	0.0211427i	0.276301	+	0.961071i	$0.410891\pi$
$348$	22.3868	+	16.2650i	1.20006	+	0.871895i
$349$	30.6374			1.63998			0.819991	−	0.572376i	$-0.193978\pi$
$349$	30.6374			1.63998			0.819991	+	0.572376i	$0.193978\pi$
$350$	−2.70158	−	6.43432i	−0.144406	−	0.343929i
$351$		−	3.63620i		−	0.194086i
$352$	−0.747467	+	1.02880i	−0.0398401	+	0.0548353i
$353$	−6.31810	−	19.4451i	−0.336278	−	1.03496i	−0.966089	−	0.258209i	$-0.916868\pi$
$353$	−6.31810	−	19.4451i	−0.336278	−	1.03496i	0.629811	−	0.776749i	$-0.283132\pi$
$354$	5.45930	−	1.77383i	0.290158	−	0.0942782i
$355$	−9.09565	+	9.88731i	−0.482747	+	0.524764i
$356$	7.41263	−	22.8137i	0.392868	−	1.20912i
$357$	−33.9517	+	9.37187i	−1.79691	+	0.496012i
$358$	−1.69348	+	5.21200i	−0.0895033	+	0.275463i
$359$	12.4377	−	9.03653i	0.656438	−	0.476930i	−0.209020	−	0.977911i	$-0.567027\pi$
$359$	12.4377	−	9.03653i	0.656438	−	0.476930i	0.865458	+	0.500981i	$0.167027\pi$
$360$	14.2569	+	13.1153i	0.751403	+	0.691239i
$361$	−12.2260	−	8.88271i	−0.643474	−	0.467511i
$362$	1.70820	+	2.35113i	0.0897809	+	0.123573i
$363$	−18.1258	−	24.9480i	−0.951358	−	1.30943i
$364$	−2.08957	+	2.87604i	−0.109523	+	0.150746i
$365$	1.22380	−	10.5577i	0.0640566	−	0.552616i
$366$	−1.90265	+	1.38236i	−0.0994531	+	0.0722569i
$367$	24.2169	+	7.86855i	1.26411	+	0.410735i	0.862958	−	0.505275i	$-0.168609\pi$
$367$	24.2169	+	7.86855i	1.26411	+	0.410735i	0.401155	+	0.916010i	$0.368609\pi$
$368$			6.67709i			0.348068i
$369$	−54.7619	−	17.7932i	−2.85079	−	0.926278i
$370$	3.97121	+	7.05119i	0.206453	+	0.366574i
$371$	−0.751272	+	0.244103i	−0.0390041	+	0.0126732i
$372$	1.61319	+	4.96488i	0.0836398	+	0.257417i
$373$	9.95435	+	7.23226i	0.515417	+	0.374472i	0.814874	−	0.579637i	$-0.196806\pi$
$373$	9.95435	+	7.23226i	0.515417	+	0.374472i	−0.299458	+	0.954110i	$0.596806\pi$
$374$	−0.134862	−	0.488568i	−0.00697354	−	0.0252632i
$375$	8.78237	+	30.2998i	0.453520	+	1.56468i
$376$	−6.75143			−0.348178
$377$	−2.11851	+	2.91588i	−0.109109	+	0.150176i
$378$	2.38727	+	7.34726i	0.122788	+	0.377903i
$379$	−5.58154	+	1.81355i	−0.286704	+	0.0931559i	−0.448839	−	0.893613i	$-0.648162\pi$
$379$	−5.58154	+	1.81355i	−0.286704	+	0.0931559i	0.162134	+	0.986769i	$0.448162\pi$
$380$	−20.3402	+	11.4555i	−1.04343	+	0.587655i
$381$	57.5220	+	18.6900i	2.94694	+	0.957519i
$382$	7.17273			0.366989
$383$	−10.3983	+	32.0028i	−0.531330	+	1.63527i	0.220119	+	0.975473i	$0.429356\pi$
$383$	−10.3983	+	32.0028i	−0.531330	+	1.63527i	−0.751448	+	0.659792i	$0.770644\pi$
$384$	18.3741	+	25.2898i	0.937651	+	1.29057i
$385$	−1.79310	−	0.207847i	−0.0913846	−	0.0105929i
$386$	−2.79916	+	3.85271i	−0.142473	+	0.196098i
$387$	1.62419	−	1.18004i	0.0825622	−	0.0599850i
$388$	−15.0043	−	20.6516i	−0.761727	−	1.04843i
$389$	4.91071	+	3.56784i	0.248983	+	0.180897i	0.705276	−	0.708933i	$-0.250823\pi$
$389$	4.91071	+	3.56784i	0.248983	+	0.180897i	−0.456293	+	0.889830i	$0.650823\pi$
$390$	−1.29367	+	1.40627i	−0.0655074	+	0.0712090i
$391$	−7.77076	−	6.19635i	−0.392984	−	0.313363i
$392$	1.16847	−	3.59619i	0.0590168	−	0.181635i
$393$	−53.7953			−2.71362
$394$	−6.72084	−	2.18373i	−0.338591	−	0.110015i
$395$	−10.5817	+	11.5027i	−0.532421	+	0.578761i
$396$	2.24911	−	0.730779i	0.113022	−	0.0367230i
$397$	8.54349	−	2.77595i	0.428785	−	0.139321i	−0.0866704	−	0.996237i	$-0.527623\pi$
$397$	8.54349	−	2.77595i	0.428785	−	0.139321i	0.515456	+	0.856916i	$0.327623\pi$
$398$	−0.102042	+	0.140449i	−0.00511490	+	0.00704006i
$399$	−49.8927			−2.49776
$400$	1.15318	+	13.8019i	0.0576591	+	0.690093i
$401$		−	18.4804i		−	0.922868i	−0.887175	−	0.461434i	$-0.847335\pi$
$401$		−	18.4804i		−	0.922868i	0.887175	−	0.461434i	$-0.152665\pi$
$402$	11.4769	−	15.7966i	0.572417	−	0.787864i
$403$	−0.646675	+	0.210117i	−0.0322132	+	0.0104667i
$404$	−6.46682	−	19.9028i	−0.321736	−	0.990202i
$405$	−0.323720	−	1.60720i	−0.0160858	−	0.0798624i
$406$	2.36628	−	7.28266i	0.117437	−	0.361432i
$407$	2.09328			0.103760
$408$	−20.2931	−	0.910367i	−1.00466	−	0.0450699i
$409$	−11.2900	+	8.20267i	−0.558255	+	0.405596i	−0.830820	−	0.556541i	$-0.812128\pi$
$409$	−11.2900	+	8.20267i	−0.558255	+	0.405596i	0.272565	+	0.962137i	$0.412128\pi$
$410$	5.87049	+	10.4235i	0.289923	+	0.514781i
$411$	9.87108	−	13.5864i	0.486905	−	0.670167i
$412$	6.94629	−	5.04677i	0.342219	−	0.248637i
$413$	7.85267	+	10.8083i	0.386405	+	0.531841i
$414$	−3.24090	+	4.46072i	−0.159282	+	0.219232i
$415$	2.93299	+	14.5617i	0.143975	+	0.714804i
$416$	−2.53462	+	1.84151i	−0.124270	+	0.0902875i
$417$	−16.4144	+	50.5183i	−0.803816	+	2.47389i
$418$		−	0.717960i		−	0.0351166i
$419$	12.1942	+	3.96214i	0.595726	+	0.193563i	0.591333	−	0.806427i	$-0.298602\pi$
$419$	12.1942	+	3.96214i	0.595726	+	0.193563i	0.00439272	+	0.999990i	$0.498602\pi$
$420$	−14.2197	+	31.0414i	−0.693850	+	1.51467i
$421$	2.50033	+	7.69521i	0.121858	+	0.375042i	0.993316	−	0.115430i	$-0.0368245\pi$
$421$	2.50033	+	7.69521i	0.121858	+	0.375042i	−0.871457	+	0.490472i	$0.836825\pi$
$422$	8.80472	−	2.86083i	0.428607	−	0.139263i
$423$	15.5211	+	11.2768i	0.754663	+	0.548294i
$424$	−0.455585			−0.0221251
$425$	−17.1327	−	11.4661i	−0.831057	−	0.556187i
$426$	−7.81543			−0.378659
$427$	−4.42820	−	3.21728i	−0.214296	−	0.155695i
$428$	27.9524	−	9.08228i	1.35113	−	0.439009i
$429$	0.152735	+	0.470071i	0.00737413	+	0.0226952i
$430$	−0.414331	−	0.0480272i	−0.0199808	−	0.00231608i
$431$	−29.3274	−	9.52903i	−1.41265	−	0.458997i	−0.499390	−	0.866377i	$-0.666443\pi$
$431$	−29.3274	−	9.52903i	−1.41265	−	0.458997i	−0.913259	+	0.407380i	$0.866443\pi$
$432$		−	15.3323i		−	0.737677i
$433$	6.68529	−	20.5752i	0.321274	−	0.988781i	−0.651820	−	0.758374i	$-0.725994\pi$
$433$	6.68529	−	20.5752i	0.321274	−	0.988781i	0.973094	−	0.230407i	$-0.0740058\pi$
$434$	1.16872	−	0.849121i	0.0561001	−	0.0407591i
$435$	−14.4167	+	31.4714i	−0.691227	+	1.50894i
$436$	−15.0961	+	20.7780i	−0.722972	+	0.995085i
$437$	−8.27527	−	11.3899i	−0.395860	−	0.544855i
$438$	5.00211	−	3.63424i	0.239010	−	0.173651i
$439$	−15.0949	+	20.7763i	−0.720440	+	0.991601i	0.279069	+	0.960271i	$0.409974\pi$
$439$	−15.0949	+	20.7763i	−0.720440	+	0.991601i	−0.999509	+	0.0313299i	$0.990026\pi$
$440$	−0.946489	−	0.433575i	−0.0451221	−	0.0206699i
$441$	−8.69288	+	6.31575i	−0.413947	+	0.300750i
$442$	0.0559608	−	1.24743i	0.00266178	−	0.0593342i
$443$	1.90524			0.0905208			0.0452604	−	0.998975i	$-0.485588\pi$
$443$	1.90524			0.0905208			0.0452604	+	0.998975i	$0.485588\pi$
$444$	12.2353	−	37.6565i	0.580663	−	1.78710i
$445$	29.8083	+	3.45524i	1.41305	+	0.163794i
$446$	2.13984	+	6.58574i	0.101324	+	0.311844i
$447$	−31.8548	+	10.3502i	−1.50668	+	0.489550i
$448$	−5.94600	+	8.18397i	−0.280922	+	0.386656i
$449$			27.9678i			1.31988i	0.751317	+	0.659942i	$0.229419\pi$
$449$			27.9678i			1.31988i	−0.751317	+	0.659942i	$0.770581\pi$
$450$	−5.92869	+	9.78024i	−0.279481	+	0.461045i
$451$	3.09443			0.145711
$452$	7.40215	−	10.1882i	0.348168	−	0.479212i
$453$	3.67990	−	1.19567i	0.172897	−	0.0561776i
$454$	−0.200653	+	0.0651962i	−0.00941712	+	0.00305981i
$455$	−4.04314	−	1.85211i	−0.189545	−	0.0868285i
$456$	−27.3667	−	8.89197i	−1.28156	−	0.416405i
$457$	31.5816			1.47732			0.738662	−	0.674076i	$-0.235458\pi$
$457$	31.5816			1.47732			0.738662	+	0.674076i	$0.235458\pi$
$458$	−2.55666	+	7.86860i	−0.119465	+	0.367676i
$459$	17.8437	+	14.2284i	0.832871	+	0.664125i
$460$	−9.44490	+	1.90238i	−0.440371	+	0.0886988i
$461$	17.1394	+	12.4525i	0.798262	+	0.579971i	0.910404	−	0.413721i	$-0.135771\pi$
$461$	17.1394	+	12.4525i	0.798262	+	0.579971i	−0.112142	+	0.993692i	$0.535771\pi$
$462$	−0.617230	−	0.849544i	−0.0287161	−	0.0395244i
$463$	1.69136	−	1.22885i	0.0786043	−	0.0571094i	−0.547789	−	0.836616i	$-0.684530\pi$
$463$	1.69136	−	1.22885i	0.0786043	−	0.0571094i	0.626393	+	0.779507i	$0.284530\pi$
$464$	−8.93287	+	12.2950i	−0.414698	+	0.570783i
$465$	−5.69015	+	3.20467i	−0.263875	+	0.148613i
$466$	−1.59486	−	2.19513i	−0.0738802	−	0.101687i
$467$	2.08182	−	6.40717i	0.0963349	−	0.296488i	−0.891264	−	0.453484i	$-0.850181\pi$
$467$	2.08182	−	6.40717i	0.0963349	−	0.296488i	0.987599	+	0.156996i	$0.0501809\pi$
$468$	5.82621			0.269316
$469$	43.2197	+	14.0429i	1.99570	+	0.648442i
$470$	−0.787038	−	3.90747i	−0.0363033	−	0.180238i
$471$	39.6660	−	12.8883i	1.82771	−	0.593860i
$472$	2.38100	+	7.32797i	0.109594	+	0.337297i
$473$	−0.0634170	+	0.0872860i	−0.00291592	+	0.00401342i
$474$	−9.09228			−0.417622
$475$	−19.0725	−	22.1143i	−0.875107	−	1.01468i
$476$	−5.93694	−	21.5079i	−0.272119	−	0.985813i
$477$	1.04736	+	0.760952i	0.0479553	+	0.0348416i
$478$	−0.536231	−	1.65035i	−0.0245266	−	0.0754852i
$479$	−8.07738	+	2.62450i	−0.369065	+	0.119916i	−0.487677	−	0.873024i	$-0.662156\pi$
$479$	−8.07738	+	2.62450i	−0.369065	+	0.119916i	0.118612	+	0.992941i	$0.462156\pi$
$480$	−20.3719	+	22.1450i	−0.929847	+	1.01078i
$481$	4.90475	+	1.59365i	0.223637	+	0.0726642i
$482$		−	9.89309i		−	0.450618i
$483$	−19.5838	−	6.36318i	−0.891096	−	0.289535i
$484$	15.8042	−	11.4824i	0.718373	−	0.521929i
$485$	21.6197	−	23.5014i	0.981701	−	1.06715i
$486$	−3.93905	+	5.42164i	−0.178679	+	0.245931i
$487$	−18.3449	−	25.2497i	−0.831289	−	1.14417i	−0.987682	−	0.156476i	$-0.949987\pi$
$487$	−18.3449	−	25.2497i	−0.831289	−	1.14417i	0.156393	−	0.987695i	$-0.450013\pi$
$488$	−1.85553	−	2.55391i	−0.0839957	−	0.115610i
$489$	22.3458	+	16.2352i	1.01051	+	0.734179i
$490$	2.21755	+	0.257048i	0.100179	+	0.0116122i
$491$	−2.71675	+	1.97383i	−0.122605	+	0.0890778i	−0.647398	−	0.762152i	$-0.724143\pi$
$491$	−2.71675	+	1.97383i	−0.122605	+	0.0890778i	0.524793	+	0.851230i	$0.324143\pi$
$492$	18.0870	−	55.6662i	0.815426	−	2.50962i
$493$	−6.01918	−	21.8058i	−0.271090	−	0.982085i
$494$	0.546594	−	1.68224i	0.0245924	−	0.0756878i
$495$	1.45173	+	2.57766i	0.0652503	+	0.115857i
$496$	−2.72675	+	0.885976i	−0.122435	+	0.0397815i
$497$	−5.62087	−	17.2993i	−0.252131	−	0.775978i
$498$	−5.07916	+	6.99086i	−0.227603	+	0.313268i
$499$		−	4.96217i		−	0.222137i	−0.993813	−	0.111069i	$-0.964573\pi$
$499$		−	4.96217i		−	0.222137i	0.993813	−	0.111069i	$-0.0354274\pi$
$500$	−19.1945	+	5.56351i	−0.858404	+	0.248808i
$501$	14.6020			0.652367
$502$	−8.12141	−	5.90055i	−0.362476	−	0.263354i
$503$	0.728023	−	0.236549i	0.0324610	−	0.0105472i	−0.292742	−	0.956192i	$-0.594568\pi$
$503$	0.728023	−	0.236549i	0.0324610	−	0.0105472i	0.325202	+	0.945644i	$0.394568\pi$
$504$	−24.9444	+	8.10494i	−1.11111	+	0.361023i
$505$	22.8102	−	12.8467i	1.01504	−	0.571669i
$506$	0.0915666	−	0.281813i	0.00407063	−	0.0125281i
$507$		−	35.4637i		−	1.57500i
$508$	−11.8399	+	36.4394i	−0.525309	+	1.61673i
$509$	−27.3172	+	19.8471i	−1.21081	+	0.879707i	−0.995304	−	0.0967956i	$-0.969141\pi$
$509$	−27.3172	+	19.8471i	−1.21081	+	0.879707i	−0.215508	+	0.976502i	$0.569141\pi$
$510$	−1.83875	−	11.8510i	−0.0814214	−	0.524772i
$511$	11.6418	+	8.45829i	0.515004	+	0.374173i
$512$	−18.5132	+	13.4506i	−0.818174	+	0.594438i
$513$	19.0022	+	26.1542i	0.838965	+	1.15474i
$514$	9.10680	+	6.61648i	0.401684	+	0.291840i
$515$	7.90484	+	7.27191i	0.348329	+	0.320439i
$516$	1.19953	+	1.65101i	0.0528063	+	0.0726816i
$517$	−0.980572	−	0.318607i	−0.0431255	−	0.0140123i
$518$	−10.9568			−0.481412
$519$	13.6962	−	42.1525i	0.601196	−	1.85029i
$520$	−1.88762	−	1.73648i	−0.0827776	−	0.0761497i
$521$	−1.85253	+	0.601923i	−0.0811608	+	0.0263707i	−0.349316	−	0.937005i	$-0.613586\pi$
$521$	−1.85253	+	0.601923i	−0.0811608	+	0.0263707i	0.268155	+	0.963376i	$0.413586\pi$
$522$	−11.9354	+	3.87806i	−0.522400	+	0.169738i
$523$	25.4091	+	18.4608i	1.11106	+	0.807235i	0.982831	−	0.184509i	$-0.0590695\pi$
$523$	25.4091	+	18.4608i	1.11106	+	0.807235i	0.128233	+	0.991744i	$0.459070\pi$
$524$		−	34.0786i		−	1.48873i
$525$	−41.5797	−	9.77071i	−1.81469	−	0.426429i
$526$	12.9518			0.564727
$527$	1.49934	−	3.99557i	0.0653122	−	0.174050i
$528$	0.644020	+	1.98209i	0.0280274	+	0.0862594i
$529$	5.31183	+	16.3481i	0.230949	+	0.710788i
$530$	−0.0531091	−	0.263675i	−0.00230691	−	0.0114533i
$531$	6.76596	−	20.8235i	0.293618	−	0.903662i
$532$		−	31.6063i		−	1.37031i
$533$	7.25051	+	2.35583i	0.314055	+	0.102043i
$534$	10.2608	+	14.1228i	0.444028	+	0.611153i
$535$	18.0424	+	32.0357i	0.780041	+	1.38503i
$536$	21.2037	+	15.4054i	0.915860	+	0.665411i
$537$	19.7156	+	27.1362i	0.850790	+	1.17101i
$538$	0.873830	+	1.20272i	0.0376735	+	0.0518531i
$539$	0.339416	−	0.467166i	0.0146197	−	0.0201223i
$540$	21.6879	−	4.36835i	0.933299	−	0.187984i
$541$	10.0607	+	13.8474i	0.432543	+	0.595345i	0.968535	−	0.248879i	$-0.0800621\pi$
$541$	10.0607	+	13.8474i	0.432543	+	0.595345i	−0.535992	+	0.844223i	$0.680062\pi$
$542$	−2.42476	+	7.46263i	−0.104152	+	0.320548i
$543$	17.7874			0.763329
$544$	0.881237	−	19.6438i	0.0377827	−	0.842220i
$545$	−29.2097	−	13.3806i	−1.25121	−	0.573162i
$546$	−0.799453	−	2.46046i	−0.0342134	−	0.105298i
$547$	11.1672	−	3.62843i	0.477473	−	0.155140i	−0.0603862	−	0.998175i	$-0.519233\pi$
$547$	11.1672	−	3.62843i	0.477473	−	0.155140i	0.537859	+	0.843035i	$0.319233\pi$
$548$	8.60678	+	6.25319i	0.367663	+	0.267123i
$549$			8.97052i			0.382852i
$550$	0.140601	−	0.598335i	0.00599526	−	0.0255131i
$551$		−	32.0441i		−	1.36513i
$552$	−9.60788	−	6.98054i	−0.408939	−	0.297111i
$553$	−6.53919	−	20.1256i	−0.278075	−	0.855826i
$554$	7.28147	−	2.36589i	0.309360	−	0.100517i
$555$	49.2018	+	5.70323i	2.08850	+	0.242089i
$556$	−32.0026	−	10.3983i	−1.35721	−	0.440985i
$557$	−4.58343			−0.194206			−0.0971030	−	0.995274i	$-0.530958\pi$
$557$	−4.58343			−0.194206			−0.0971030	+	0.995274i	$0.530958\pi$
$558$	−2.25167	−	0.731613i	−0.0953209	−	0.0309716i
$559$	−0.215044	+	0.156238i	−0.00909538	+	0.00660818i
$560$	−17.0482	−	7.80958i	−0.720419	−	0.330015i
$561$	−2.90440	−	1.08988i	−0.122624	−	0.0460146i
$562$	10.0492	−	7.30119i	0.423901	−	0.307982i
$563$	15.0489	−	10.9337i	0.634236	−	0.460800i	−0.223629	−	0.974674i	$-0.571790\pi$
$563$	15.0489	−	10.9337i	0.634236	−	0.460800i	0.857865	+	0.513875i	$0.171790\pi$
$564$	−11.4630	+	15.7774i	−0.482678	+	0.664349i
$565$	14.3225	+	6.56099i	0.602554	+	0.276023i
$566$	5.93142	+	8.16390i	0.249316	+	0.343154i
$567$	2.11109	+	0.685935i	0.0886575	+	0.0288066i
$568$		−	10.4906i		−	0.440175i
$569$	−7.84605	+	24.1477i	−0.328923	+	1.01232i	0.640715	+	0.767779i	$0.278638\pi$
$569$	−7.84605	+	24.1477i	−0.328923	+	1.01232i	−0.969638	+	0.244543i	$0.921362\pi$
$570$	1.95611	−	16.8754i	0.0819325	−	0.706831i
$571$	21.3402	−	6.93386i	0.893061	−	0.290173i	0.173691	−	0.984800i	$-0.444431\pi$
$571$	21.3402	−	6.93386i	0.893061	−	0.290173i	0.719370	+	0.694627i	$0.244431\pi$
$572$	−0.297783	+	0.0967556i	−0.0124509	+	0.00404555i
$573$	25.8045	−	35.5169i	1.07800	−	1.48374i
$574$	−16.1970			−0.676049
$575$	−4.66592	−	11.1127i	−0.194582	−	0.463434i
$576$	16.5788			0.690785
$577$	10.0532	+	7.30406i	0.418519	+	0.304072i	0.777042	−	0.629449i	$-0.216719\pi$
$577$	10.0532	+	7.30406i	0.418519	+	0.304072i	−0.358523	+	0.933521i	$0.616719\pi$
$578$	5.90244	+	5.15579i	0.245509	+	0.214453i
$579$	9.00707	+	27.7209i	0.374321	+	1.15204i
$580$	−19.9367	−	9.13275i	−0.827826	−	0.379217i
$581$	−19.1271	−	6.21476i	−0.793524	−	0.257832i
$582$	18.5767			0.770030
$583$	−0.0661687	−	0.0214995i	−0.00274043	−	0.000890419i
$584$	4.87821	+	6.71429i	0.201862	+	0.277839i
$585$	1.43912	+	7.14490i	0.0595001	+	0.295405i
$586$	2.10575	+	1.52991i	0.0869876	+	0.0632002i
$587$	−26.2984	+	19.1069i	−1.08545	+	0.788627i	−0.978625	−	0.205651i	$-0.934069\pi$
$587$	−26.2984	+	19.1069i	−1.08545	+	0.788627i	−0.106826	+	0.994278i	$0.534069\pi$
$588$	−6.42004	−	8.83642i	−0.264758	−	0.364408i
$589$	3.55332	−	4.89073i	0.146412	−	0.201519i
$590$	−3.96359	+	2.23228i	−0.163178	+	0.0919015i
$591$	−34.9919	+	25.4231i	−1.43938	+	1.04577i
$592$	20.6813	+	6.71975i	0.849994	+	0.276180i
$593$	35.7041			1.46619			0.733096	−	0.680126i	$-0.238075\pi$
$593$	35.7041			1.46619			0.733096	+	0.680126i	$0.238075\pi$
$594$	−0.210260	+	0.647115i	−0.00862709	+	0.0265515i
$595$	24.9095	−	12.5933i	1.02119	−	0.516276i
$596$	−6.55673	−	20.1795i	−0.268574	−	0.826586i
$597$	0.328349	+	1.01055i	0.0134384	+	0.0413592i
$598$	0.429097	−	0.590602i	0.0175471	−	0.0241515i
$599$	−37.6671			−1.53904			−0.769518	−	0.638625i	$-0.779503\pi$
$599$	−37.6671			−1.53904			−0.769518	+	0.638625i	$0.779503\pi$
$600$	−21.0655	−	12.7697i	−0.859997	−	0.521323i
$601$			33.4560i			1.36470i	0.731026	+	0.682350i	$0.239042\pi$
$601$			33.4560i			1.36470i	−0.731026	+	0.682350i	$0.760958\pi$
$602$	0.331940	−	0.456876i	0.0135289	−	0.0186209i
$603$	−23.0147	−	70.8320i	−0.937232	−	2.88450i
$604$	0.757441	+	2.33116i	0.0308198	+	0.0948537i
$605$	17.9851	+	16.5451i	0.731199	+	0.672653i
$606$	14.4840	+	4.70613i	0.588371	+	0.191173i
$607$		−	27.7362i		−	1.12578i	−0.826533	−	0.562889i	$-0.809690\pi$
$607$		−	27.7362i		−	1.12578i	0.826533	−	0.562889i	$-0.190310\pi$
$608$	8.60745	−	26.4910i	0.349078	−	1.07435i
$609$	−27.5483	−	37.9170i	−1.11631	−	1.53647i
$610$	1.26180	−	1.37163i	0.0510889	−	0.0555355i
$611$	−2.05501	−	1.49305i	−0.0831367	−	0.0604023i
$612$	−22.7979	+	28.5905i	−0.921549	+	1.15570i
$613$	10.7180	−	7.78708i	0.432896	−	0.314517i	−0.349910	−	0.936783i	$-0.613788\pi$
$613$	10.7180	−	7.78708i	0.432896	−	0.314517i	0.782806	+	0.622266i	$0.213788\pi$
$614$	−11.0274	−	8.01187i	−0.445029	−	0.323333i
$615$	72.7332	+	8.43088i	2.93289	+	0.339966i
$616$	1.14034	−	0.828503i	0.0459455	−	0.0333813i
$617$	2.56858	+	0.834581i	0.103407	+	0.0335990i	0.360264	−	0.932851i	$-0.382687\pi$
$617$	2.56858	+	0.834581i	0.103407	+	0.0335990i	−0.256856	+	0.966450i	$0.582687\pi$
$618$			6.24839i			0.251347i
$619$	−36.7223	−	11.9318i	−1.47600	−	0.479580i	−0.543082	−	0.839680i	$-0.682743\pi$
$619$	−36.7223	−	11.9318i	−1.47600	−	0.479580i	−0.932914	+	0.360100i	$0.882743\pi$
$620$	−2.03011	−	3.60463i	−0.0815314	−	0.144765i
$621$	4.12307	+	12.6895i	0.165453	+	0.509212i
$622$	−12.2945	+	3.99473i	−0.492966	+	0.160174i
$623$	−23.8809	+	32.8692i	−0.956766	+	1.31688i
$624$			5.13451i			0.205545i
$625$	−11.5639	−	22.1647i	−0.462557	−	0.886589i
$626$		−	3.23615i		−	0.129343i
$627$	−3.55509	−	2.58293i	−0.141977	−	0.103152i
$628$	8.16453	+	25.1279i	0.325800	+	1.00271i
$629$	−27.0126	+	17.8328i	−1.07706	+	0.711040i
$630$	−7.59870	−	13.4921i	−0.302739	−	0.537538i
$631$	−1.66010	+	5.10926i	−0.0660875	+	0.203396i	−0.978647	−	0.205547i	$-0.934103\pi$
$631$	−1.66010	+	5.10926i	−0.0660875	+	0.203396i	0.912560	+	0.408943i	$0.134103\pi$
$632$		−	12.2045i		−	0.485469i
$633$	17.5099	−	53.8900i	0.695957	−	2.14193i
$634$	−5.56330	−	7.65722i	−0.220947	−	0.304107i
$635$	−47.6115	−	5.51890i	−1.88941	−	0.219011i
$636$	−0.773517	+	1.06466i	−0.0306720	+	0.0422163i
$637$	1.15094	−	0.836209i	0.0456020	−	0.0331318i
$638$	0.545629	−	0.396423i	0.0216017	−	0.0156945i
$639$	−17.5222	+	24.1172i	−0.693167	+	0.954062i
$640$	−18.2315	−	16.7718i	−0.720664	−	0.662962i
$641$	−12.7585	−	17.5606i	−0.503931	−	0.693601i	0.478950	−	0.877842i	$-0.341017\pi$
$641$	−12.7585	−	17.5606i	−0.503931	−	0.693601i	−0.982881	+	0.184241i	$0.941017\pi$
$642$	−6.60949	+	20.3419i	−0.260856	+	0.802832i
$643$		−	9.73870i		−	0.384057i	−0.981389	−	0.192028i	$-0.938493\pi$
$643$		−	9.73870i		−	0.384057i	0.981389	−	0.192028i	$-0.0615066\pi$
$644$	4.03098	−	12.4061i	0.158843	−	0.488868i
$645$	−1.72840	+	1.87884i	−0.0680559	+	0.0739793i
$646$	6.11634	+	9.26487i	0.240644	+	0.364521i
$647$	−5.92018	−	18.2204i	−0.232746	−	0.716319i	−0.997412	−	0.0718926i	$-0.977096\pi$
$647$	−5.92018	−	18.2204i	−0.232746	−	0.716319i	0.764666	−	0.644427i	$-0.222904\pi$
$648$	1.03571	+	0.752485i	0.0406864	+	0.0295604i
$649$			1.17667i			0.0461884i
$650$	0.784963	−	1.29491i	0.0307888	−	0.0507905i
$651$		−	8.84186i		−	0.346540i
$652$	−10.2847	+	14.1557i	−0.402781	+	0.554381i
$653$	15.6032	−	5.06980i	0.610602	−	0.198397i	0.0126387	−	0.999920i	$-0.495977\pi$
$653$	15.6032	−	5.06980i	0.610602	−	0.198397i	0.597963	+	0.801524i	$0.295977\pi$
$654$	−5.77565	−	17.7756i	−0.225846	−	0.695082i
$655$	41.7919	−	8.41766i	1.63294	−	0.328905i
$656$	30.5723	+	9.93356i	1.19365	+	0.387840i
$657$		−	23.5837i		−	0.920087i
$658$	5.13255	+	1.66767i	0.200088	+	0.0650124i
$659$	16.4046	−	11.9186i	0.639033	−	0.464284i	−0.220485	−	0.975390i	$-0.570764\pi$
$659$	16.4046	−	11.9186i	0.639033	−	0.464284i	0.859518	+	0.511106i	$0.170764\pi$
$660$	−2.62022	+	1.47570i	−0.101992	+	0.0574415i
$661$	−24.5954	−	17.8696i	−0.956651	−	0.695048i	−0.00428034	−	0.999991i	$-0.501362\pi$
$661$	−24.5954	−	17.8696i	−0.956651	−	0.695048i	−0.952371	+	0.304943i	$0.901362\pi$
$662$	5.34043	−	3.88005i	0.207562	−	0.150802i
$663$	−5.97552	−	4.76483i	−0.232070	−	0.185051i
$664$	−9.38378	−	6.81772i	−0.364161	−	0.264579i
$665$	38.7601	−	7.80700i	1.50305	−	0.302742i
$666$	10.5548	+	14.5274i	0.408989	+	0.562925i
$667$	4.08682	−	12.5779i	0.158242	−	0.487019i
$668$			9.25013i			0.357898i
$669$	40.3086	+	13.0970i	1.55842	+	0.506361i
$670$	−6.44427	+	14.0678i	−0.248964	+	0.543485i
$671$	−0.148973	−	0.458492i	−0.00575104	−	0.0176999i
$672$	−12.5893	−	38.7459i	−0.485644	−	1.49466i
$673$	7.89377	−	10.8648i	0.304282	−	0.418809i	−0.629305	−	0.777158i	$-0.716660\pi$
$673$	7.89377	−	10.8648i	0.304282	−	0.418809i	0.933587	+	0.358350i	$0.116660\pi$
$674$			0.600438i			0.0231280i
$675$	10.7141	+	25.5177i	0.412388	+	0.982178i
$676$	22.4657			0.864066
$677$	11.7037	−	16.1088i	0.449810	−	0.619110i	−0.522547	−	0.852610i	$-0.675018\pi$
$677$	11.7037	−	16.1088i	0.449810	−	0.619110i	0.972357	+	0.233501i	$0.0750181\pi$
$678$	2.83201	+	8.71602i	0.108763	+	0.334737i
$679$	13.3604	+	41.1192i	0.512726	+	1.57801i
$680$	15.9075	−	2.46814i	0.610026	−	0.0946490i
$681$	−0.399038	+	1.22811i	−0.0152912	+	0.0470614i
$682$	0.127235			0.00487208
$683$	12.0019	+	3.89966i	0.459241	+	0.149217i	0.529496	−	0.848313i	$-0.322381\pi$
$683$	12.0019	+	3.89966i	0.459241	+	0.149217i	−0.0702545	+	0.997529i	$0.522381\pi$
$684$	−41.9063	+	30.4467i	−1.60233	+	1.16416i
$685$	−5.54259	+	12.0994i	−0.211772	+	0.462295i
$686$	3.96599	−	5.45872i	0.151422	−	0.208415i
$687$	29.7648	+	40.9677i	1.13560	+	1.56302i
$688$	−0.906749	+	0.658791i	−0.0345695	+	0.0251162i
$689$	−0.138671	−	0.100751i	−0.00528295	−	0.00383829i
$690$	2.92005	−	6.37442i	0.111164	−	0.242670i
$691$	14.1702	+	19.5036i	0.539059	+	0.741950i	0.988477	−	0.151371i	$-0.0483688\pi$
$691$	14.1702	+	19.5036i	0.539059	+	0.741950i	−0.449419	+	0.893321i	$0.648369\pi$
$692$	26.7030	+	8.67633i	1.01510	+	0.329825i
$693$	−4.00539			−0.152152
$694$	0.558802	+	0.181566i	0.0212118	+	0.00689215i
$695$	4.84693	−	41.8145i	0.183855	−	1.58611i
$696$	−8.35290	−	25.7076i	−0.316616	−	0.974443i
$697$	−39.9318	+	26.3616i	−1.51252	+	0.998515i
$698$	−11.4267	−	8.30195i	−0.432505	−	0.314234i
$699$	−16.6072			−0.628140
$700$	6.18961	−	26.3401i	0.233945	−	0.995563i
$701$	20.7718			0.784540			0.392270	−	0.919850i	$-0.371690\pi$
$701$	20.7718			0.784540			0.392270	+	0.919850i	$0.371690\pi$
$702$	−0.985317	+	1.35617i	−0.0371884	+	0.0511855i
$703$	−43.6067	+	14.1687i	−1.64466	+	0.534381i
$704$	−0.847361	+	0.275324i	−0.0319361	+	0.0103767i
$705$	−22.1799	−	10.1603i	−0.835343	−	0.382661i
$706$	−2.91270	+	8.96437i	−0.109621	+	0.337378i
$707$			35.4446i			1.33303i
$708$	21.1673	+	6.87768i	0.795517	+	0.258479i
$709$	−15.1121	−	20.8001i	−0.567548	−	0.781163i	0.424713	−	0.905328i	$-0.360375\pi$
$709$	−15.1121	−	20.8001i	−0.567548	−	0.781163i	−0.992262	+	0.124165i	$0.960375\pi$
$710$	6.07156	−	1.22292i	0.227862	−	0.0458955i
$711$	−20.3849	+	28.0574i	−0.764493	+	1.05223i
$712$	−18.9569	+	13.7730i	−0.710440	+	0.516165i
$713$	2.01849	−	1.46652i	0.0755932	−	0.0549217i
$714$	15.2023	+	5.70467i	0.568932	+	0.213492i
$715$	−0.192210	−	0.341284i	−0.00718824	−	0.0127633i
$716$	−17.1904	+	12.4895i	−0.642434	+	0.466756i
$717$	−10.1011	−	3.28204i	−0.377232	−	0.122570i
$718$	−7.08749			−0.264503
$719$	7.21257	+	2.34351i	0.268983	+	0.0873980i	0.440403	−	0.897800i	$-0.354835\pi$
$719$	7.21257	+	2.34351i	0.268983	+	0.0873980i	−0.171420	+	0.985198i	$0.554835\pi$
$720$	6.06814	+	30.1270i	0.226146	+	1.12277i
$721$	−13.8307	+	4.49385i	−0.515081	+	0.167360i
$722$	2.15288	+	6.62587i	0.0801217	+	0.246589i
$723$	−48.9872	−	35.5912i	−1.82185	−	1.32365i
$724$			11.2680i			0.418774i
$725$	6.27534	−	26.7050i	0.233060	−	0.991799i
$726$			14.2164i			0.527618i
$727$	11.4713	+	8.33439i	0.425447	+	0.309105i	0.779826	−	0.625997i	$-0.215308\pi$
$727$	11.4713	+	8.33439i	0.425447	+	0.309105i	−0.354379	+	0.935102i	$0.615308\pi$
$728$	3.30266	−	1.07310i	0.122405	−	0.0397717i
$729$	13.3547	+	41.1016i	0.494619	+	1.52228i
$730$	−3.31731	+	3.60603i	−0.122779	+	0.133465i
$731$	0.0747664	−	1.66663i	0.00276533	−	0.0616425i
$732$	−9.11865			−0.337035
$733$	5.41314	−	16.6599i	0.199939	−	0.615349i	−0.799944	−	0.600074i	$-0.795138\pi$
$733$	5.41314	−	16.6599i	0.199939	−	0.615349i	0.999883	−	0.0152746i	$-0.00486224\pi$
$734$	−6.89987	−	9.49685i	−0.254679	−	0.350535i
$735$	9.25065	−	10.0558i	0.341215	−	0.370914i
$736$	6.75717	−	9.30045i	0.249073	−	0.342819i
$737$	2.35261	+	3.23809i	0.0866595	+	0.119277i
$738$	15.6027	+	21.4753i	0.574344	+	0.790517i
$739$	−5.06544	−	3.68026i	−0.186335	−	0.135380i	0.490707	−	0.871325i	$-0.336739\pi$
$739$	−5.06544	−	3.68026i	−0.186335	−	0.135380i	−0.677042	+	0.735944i	$0.736739\pi$
$740$	−3.61292	+	31.1686i	−0.132813	+	1.14578i
$741$	−6.36347	−	8.75857i	−0.233768	−	0.321754i
$742$	0.346343	+	0.112534i	0.0127147	+	0.00413124i
$743$			11.4234i			0.419085i	0.977800	+	0.209543i	$0.0671975\pi$
$743$			11.4234i			0.419085i	−0.977800	+	0.209543i	$0.932803\pi$
$744$	1.57581	−	4.84985i	0.0577721	−	0.177804i
$745$	23.1274	−	13.0253i	0.847322	−	0.477209i
$746$	−1.75286	−	5.39475i	−0.0641767	−	0.197516i
$747$	10.1853	+	31.3470i	0.372659	+	1.14693i
$748$	0.690420	−	1.83989i	0.0252443	−	0.0672731i
$749$	−49.7799			−1.81892
$750$	4.93496	−	13.6806i	0.180199	−	0.499543i
$751$		−	32.9687i		−	1.20304i	−0.798856	−	0.601522i	$-0.794561\pi$
$751$		−	32.9687i		−	1.20304i	0.798856	−	0.601522i	$-0.205439\pi$
$752$	−8.66509	−	6.29556i	−0.315983	−	0.229575i
$753$	−58.4349	+	18.9867i	−2.12949	+	0.691912i
$754$	1.58026	−	0.513457i	0.0575496	−	0.0186990i
$755$	−2.67170	+	1.50469i	−0.0972332	+	0.0547614i
$756$	−9.25616	+	28.4875i	−0.336643	+	1.03608i
$757$	−43.3669			−1.57620			−0.788099	−	0.615549i	$-0.788934\pi$
$757$	−43.3669			−1.57620			−0.788099	+	0.615549i	$0.788934\pi$
$758$	2.57314	+	0.836064i	0.0934607	+	0.0303672i
$759$	−1.06602	−	1.46725i	−0.0386941	−	0.0532579i
$760$	22.6517	+	2.62567i	0.821663	+	0.0952431i
$761$	11.4839	+	8.34358i	0.416293	+	0.302454i	0.776144	−	0.630555i	$-0.217173\pi$
$761$	11.4839	+	8.34358i	0.416293	+	0.302454i	−0.359852	+	0.933010i	$0.617173\pi$
$762$	−16.3891	−	22.5577i	−0.593716	−	0.817179i
$763$	35.1921	−	25.5685i	1.27404	−	0.925643i
$764$	22.4994	+	16.3468i	0.814001	+	0.591406i
$765$	−40.6929	−	20.8959i	−1.47125	−	0.755491i
$766$	12.5501	−	9.11821i	0.453455	−	0.329454i
$767$	−0.895817	+	2.75704i	−0.0323461	+	0.0995510i
$768$			4.44525i			0.160404i
$769$	−7.23438	+	22.2651i	−0.260879	+	0.802901i	0.731736	+	0.681588i	$0.238711\pi$
$769$	−7.23438	+	22.2651i	−0.260879	+	0.802901i	−0.992614	+	0.121313i	$0.961289\pi$
$770$	0.612439	+	0.563402i	0.0220708	+	0.0203036i
$771$	65.5250	−	21.2904i	2.35983	−	0.766754i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.372964 - 0.270974i) q^{2} +(-2.68354 + 0.871936i) q^{3} +(-0.552359 - 1.69999i) q^{4} +(1.94832 - 1.09729i) q^{5} +(1.23714 + 0.401971i) q^{6} +3.02747i q^{7} +(-0.539562 + 1.66060i) q^{8} +(4.01408 - 2.91640i) q^{9} +(-1.02399 - 0.118696i) q^{10} +(-0.156731 + 0.215722i) q^{11} +(2.96456 + 4.08036i) q^{12} +(-0.531467 + 0.386133i) q^{13} +(0.820368 - 1.12914i) q^{14} +(-4.27164 + 4.64343i) q^{15} +(-2.24097 + 1.62816i) q^{16} +(0.184780 - 4.11896i) q^{17} -2.28738 q^{18} +(1.80483 - 5.55471i) q^{19} +(-2.94155 - 2.70602i) q^{20} +(-2.63976 - 8.12436i) q^{21} +(0.116910 - 0.0379864i) q^{22} +(1.41686 - 1.95014i) q^{23} -4.92676i q^{24} +(2.59192 - 4.27574i) q^{25} +0.302850 q^{26} +(-3.25348 + 4.47803i) q^{27} +(5.14666 - 1.67225i) q^{28} +(5.21795 - 1.69542i) q^{29} +(2.85142 - 0.574329i) q^{30} +(0.984390 + 0.319848i) q^{31} +4.76911 q^{32} +(0.232499 - 0.715558i) q^{33} +(-1.18505 + 1.48616i) q^{34} +(3.32201 + 5.89849i) q^{35} +(-7.17505 - 5.21298i) q^{36} +(-4.61435 - 6.35111i) q^{37} +(-2.17832 + 1.58264i) q^{38} +(1.08953 - 1.49961i) q^{39} +(0.770917 + 3.82744i) q^{40} +(-6.82123 - 9.38861i) q^{41} +(-1.21696 + 3.74540i) q^{42} +0.404623 q^{43} +(0.453296 + 0.147285i) q^{44} +(4.62059 - 10.0867i) q^{45} +(-1.05688 + 0.343400i) q^{46} +(1.19487 + 3.67742i) q^{47} +(4.59409 - 6.32322i) q^{48} -2.16560 q^{49} +(-2.12531 + 0.892356i) q^{50} +(3.09561 + 11.2145i) q^{51} +(0.949981 + 0.690202i) q^{52} +(0.0806292 + 0.248151i) q^{53} +(2.42686 - 0.788536i) q^{54} +(-0.0686536 + 0.592275i) q^{55} +(-5.02742 - 1.63351i) q^{56} +16.4800i q^{57} +(-2.40552 - 0.781602i) q^{58} +(3.57007 - 2.59380i) q^{59} +(10.2532 + 4.69689i) q^{60} +(-1.06269 + 1.46267i) q^{61} +(-0.280472 - 0.386036i) q^{62} +(8.82932 + 12.1525i) q^{63} +(2.70323 + 1.96401i) q^{64} +(-0.611769 + 1.33548i) q^{65} +(-0.280612 + 0.203876i) q^{66} +(4.63850 - 14.2758i) q^{67} +(-7.10424 + 1.96102i) q^{68} +(-2.10181 + 6.46871i) q^{69} +(0.359349 - 3.10011i) q^{70} +(-5.71409 + 1.85662i) q^{71} +(2.67713 + 8.23936i) q^{72} +(2.79384 - 3.84540i) q^{73} +3.61911i q^{74} +(-3.22735 + 13.7341i) q^{75} -10.4398 q^{76} +(-0.653092 - 0.474499i) q^{77} +(-0.812712 + 0.264066i) q^{78} +(-6.64764 + 2.15995i) q^{79} +(-2.57957 + 5.63117i) q^{80} +(0.226570 - 0.697311i) q^{81} +5.35000i q^{82} +(-2.05279 + 6.31783i) q^{83} +(-12.3532 + 8.97512i) q^{84} +(-4.15968 - 8.22782i) q^{85} +(-0.150910 - 0.109643i) q^{86} +(-12.5243 + 9.09944i) q^{87} +(-0.273662 - 0.376663i) q^{88} +(10.8570 + 7.88805i) q^{89} +(-4.45655 + 2.50991i) q^{90} +(-1.16901 - 1.60900i) q^{91} +(-4.09783 - 1.33147i) q^{92} -2.92054 q^{93} +(0.550844 - 1.69532i) q^{94} +(-2.57872 - 12.8028i) q^{95} +(-12.7981 + 4.15836i) q^{96} +(13.5820 - 4.41306i) q^{97} +(0.807690 + 0.586821i) q^{98} +1.32301i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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