LMFDB - Embedded newform 425.2.p.a.16.20

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			16.20
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +(2.27158 - 3.44092i) 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} +(-1.77962 + 0.667802i) 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} +(-0.650077 + 9.19660i) 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	0.595408	−	0.803423i	$-0.296990\pi$
$3$	2.68354	−	0.871936i	1.54934	−	0.503412i	0.953936	+	0.300011i	$0.0969903\pi$
$4$	−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	$-0.806114\pi$
$7$		−	3.02747i		−	1.14428i	0.820157	−	0.572139i	$-0.193886\pi$
$8$	−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	−0.784735	−	0.619831i	$-0.787201\pi$
$11$	0.156731	−	0.215722i	0.0472562	−	0.0650426i	0.831991	+	0.554789i	$0.187201\pi$
$12$	−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
$17$	2.27158	−	3.44092i	0.550938	−	0.834546i
$17$	2.27158	−	3.44092i	0.550938	−	0.834546i
$18$	−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	−0.930770	−	0.365604i	$-0.880862\pi$
$23$	−1.41686	+	1.95014i	−0.295436	+	0.406633i	0.635334	+	0.772237i	$0.280862\pi$
$24$			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	−0.750392	−	0.660993i	$-0.770135\pi$
$29$	−5.21795	+	1.69542i	−0.968950	+	0.314831i	−0.218558	+	0.975824i	$0.570135\pi$
$30$	2.85142	−	0.574329i	0.520596	−	0.104858i
$31$	−0.984390	−	0.319848i	−0.176802	−	0.0574464i	0.219278	−	0.975662i	$-0.429630\pi$
$31$	−0.984390	−	0.319848i	−0.176802	−	0.0574464i	−0.396080	+	0.918216i	$0.629630\pi$
$32$	4.76911			0.843067
$33$	0.232499	−	0.715558i	0.0404729	−	0.124563i
$34$	−1.77962	+	0.667802i	−0.305202	+	0.114527i
$35$	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	$0.0232673\pi$
$37$	4.61435	+	6.35111i	0.758595	+	1.04412i	−0.238735	+	0.971085i	$0.576733\pi$
$38$	−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	$0.161027\pi$
$41$	6.82123	+	9.38861i	1.06530	+	1.46626i	0.190548	+	0.981678i	$0.438973\pi$
$42$	−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	−0.735548	−	0.677473i	$-0.763075\pi$
$61$	1.06269	−	1.46267i	0.136064	−	0.187276i	0.871612	+	0.490197i	$0.163075\pi$
$62$	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	0.0503582	−	0.998731i	$-0.483964\pi$
$71$	5.71409	−	1.85662i	0.678138	−	0.220340i	0.627780	+	0.778391i	$0.283964\pi$
$72$	2.67713	+	8.23936i	0.315503	+	0.971018i
$73$	−2.79384	+	3.84540i	−0.326995	+	0.450069i	−0.940587	−	0.339554i	$-0.889724\pi$
$73$	−2.79384	+	3.84540i	−0.326995	+	0.450069i	0.613592	+	0.789623i	$0.289724\pi$
$74$		−	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	0.0898328	−	0.995957i	$-0.471367\pi$
$79$	6.64764	−	2.15995i	0.747918	−	0.243013i	0.658085	+	0.752944i	$0.271367\pi$
$80$	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
$85$	−0.650077	+	9.19660i	−0.0705107	+	0.997511i
$86$	−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	−0.902355	−	0.430994i	$-0.858163\pi$
$97$	−13.5820	+	4.41306i	−1.37904	+	0.448078i	−0.476689	+	0.879072i	$0.658163\pi$
$98$	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	$0.302084\pi$
$102$	−4.19340	+	3.34379i	−0.415209	+	0.331084i
$103$	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	$-0.707581\pi$
$107$		−	16.4427i		−	1.58958i	0.606886	−	0.794789i	$-0.292419\pi$
$108$	−9.40967	−	3.05739i	−0.905446	−	0.294197i
$109$	8.44550	+	11.6242i	0.808933	+	1.11340i	0.991487	+	0.130204i	$0.0415634\pi$
$109$	8.44550	+	11.6242i	0.808933	+	1.11340i	−0.182555	+	0.983196i	$0.558437\pi$
$110$	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	0.568522	−	0.822668i	$-0.307515\pi$
$113$	−4.14113	−	5.69977i	−0.389565	−	0.536190i	−0.958087	+	0.286478i	$0.907515\pi$
$114$	−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
$119$	−10.4173	−	6.87713i	−0.954952	−	0.630426i
$120$	−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	−0.621074	−	0.783752i	$-0.713303\pi$
$131$	−18.1321	−	5.89149i	−1.58421	−	0.514741i	−0.963137	+	0.269010i	$0.913303\pi$
$132$	−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
$136$	4.48834	+	5.62877i	0.384872	+	0.482663i
$137$	−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	$0.494303\pi$
$139$	−11.0652	+	15.2299i	−0.938537	+	1.29179i	−0.956435	+	0.291946i	$0.905697\pi$
$140$	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
$153$	−0.916820	−	20.4370i	−0.0741205	−	1.65223i
$154$	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	0.972542	−	0.232729i	$-0.0747654\pi$
$163$	5.75379	+	7.91942i	0.450672	+	0.620296i	−0.521870	+	0.853025i	$0.674765\pi$
$164$	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	0.493186	−	0.869924i	$-0.335832\pi$
$167$	4.92170	+	1.59916i	0.380853	+	0.123746i	−0.112333	+	0.993671i	$0.535832\pi$
$168$	14.9156			1.15077
$169$	−3.88386	+	11.9533i	−0.298759	+	0.919485i
$170$	2.73450	−	3.25385i	0.209726	−	0.249559i
$171$	−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	$-0.596311\pi$
$173$	9.23281	−	12.7079i	0.701957	−	0.966161i	0.999933	−	0.0115877i	$-0.00368858\pi$
$174$	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	0.523233	−	0.852190i	$-0.324726\pi$
$181$	5.99537	+	1.94801i	0.445632	+	0.144795i	−0.0776004	+	0.996985i	$0.524726\pi$
$182$		−	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
$187$	−0.386255	−	1.02933i	−0.0282458	−	0.0752719i
$188$	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	$0.121254\pi$
$193$			10.3300i			0.743567i	−0.928319	+	0.371784i	$0.878746\pi$
$194$	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	−0.778216	−	0.627997i	$-0.783875\pi$
$197$	−14.5785	+	4.73686i	−1.03868	+	0.337487i	−0.260462	+	0.965484i	$0.583875\pi$
$198$	−0.358503	+	0.493437i	−0.0254777	+	0.0350671i
$199$			0.376574i			0.0266947i	0.999911	+	0.0133473i	$0.00424871\pi$
$199$			0.376574i			0.0266947i	−0.999911	+	0.0133473i	$0.995751\pi$
$200$	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
$204$	−20.7744	+	0.931959i	−1.45450	+	0.0652502i
$205$	−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	$-0.557065\pi$
$211$	11.8037	−	16.2464i	0.812600	−	1.11845i	0.990917	−	0.134475i	$-0.0429349\pi$
$212$	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
$221$	0.121388	+	2.70587i	0.00816541	+	0.182016i
$222$	−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	−0.817851	−	0.575430i	$-0.804835\pi$
$227$	−0.268998	+	0.370244i	−0.0178540	+	0.0245739i	0.799997	+	0.600004i	$0.204835\pi$
$228$	−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	0.119865	−	0.992790i	$-0.461754\pi$
$233$	−5.59757	−	1.81876i	−0.366709	−	0.119151i	−0.486574	+	0.873639i	$0.661754\pi$
$234$	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
$238$	2.02175	+	5.38775i	0.131051	+	0.349236i
$239$	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	$-0.957096\pi$
$241$	−12.6137	−	17.3612i	−0.812517	−	1.11833i	0.178413	−	0.983956i	$-0.442904\pi$
$242$	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
$255$	6.27433	+	25.2463i	0.392914	+	1.58098i
$256$	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	0.401017	−	0.916070i	$-0.368657\pi$
$269$	3.06694	+	0.996509i	0.186995	+	0.0607582i	−0.214023	+	0.976829i	$0.568657\pi$
$270$	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	$-0.272938\pi$
$272$	0.511840	+	11.4095i	0.0310349	+	0.691802i
$273$	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	−0.407873	−	0.913039i	$-0.633729\pi$
$277$	9.76161	−	13.4357i	0.586519	−	0.807274i	0.994391	+	0.105765i	$0.0337292\pi$
$278$	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	0.853424	−	0.521217i	$-0.174522\pi$
$283$	20.8179	+	6.76414i	1.23750	+	0.402087i	0.384071	+	0.923304i	$0.374522\pi$
$284$	−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
$289$	−6.67989	−	15.6326i	−0.392935	−	0.919566i
$290$	−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
$306$	−5.19595	+	7.87069i	−0.297033	+	0.449937i
$307$	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	$0.492547\pi$
$311$	−16.4822	+	22.6858i	−0.934619	+	1.28639i	−0.958030	+	0.286666i	$0.907453\pi$
$312$	−1.90238	−	2.61841i	−0.107701	−	0.148238i
$313$	−4.12608	−	5.67907i	−0.233220	−	0.321000i	0.676327	−	0.736602i	$-0.263571\pi$
$313$	−4.12608	−	5.67907i	−0.233220	−	0.321000i	−0.909546	+	0.415602i	$0.863571\pi$
$314$	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	−0.295857	−	0.955232i	$-0.595605\pi$
$317$	−19.5259	−	6.34434i	−1.09668	−	0.356334i	−0.800825	+	0.598898i	$0.795605\pi$
$318$		−	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
$323$	−15.0135	−	18.8282i	−0.835373	−	1.04763i
$324$	−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	0.829359	−	0.558716i	$-0.188706\pi$
$337$	0.765556	+	1.05370i	0.0417025	+	0.0573986i	−0.787657	+	0.616115i	$0.788706\pi$
$338$	4.68758	−	3.40573i	0.254971	−	0.185247i
$339$	−16.0827	−	11.6848i	−0.873494	−	0.634631i
$340$	15.9932	−	3.97470i	0.867351	−	0.215558i
$341$	−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	−0.276301	−	0.961071i	$-0.589109\pi$
$347$	1.21213	−	0.393844i	0.0650704	−	0.0211427i	0.341371	+	0.939929i	$0.389109\pi$
$348$	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	−0.401155	−	0.916010i	$-0.631391\pi$
$367$	−24.2169	−	7.86855i	−1.26411	−	0.410735i	−0.862958	+	0.505275i	$0.831391\pi$
$368$		−	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	−0.162134	−	0.986769i	$-0.551838\pi$
$379$	5.58154	−	1.81355i	0.286704	−	0.0931559i	0.448839	+	0.893613i	$0.351838\pi$
$380$	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
$391$	3.49178	+	9.30521i	0.176587	+	0.470585i
$392$	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	−0.515456	−	0.856916i	$-0.672377\pi$
$397$	−8.54349	+	2.77595i	−0.428785	+	0.139321i	0.0866704	+	0.996237i	$0.472377\pi$
$398$	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	$0.152665\pi$
$401$			18.4804i			0.922868i	−0.887175	+	0.461434i	$0.847335\pi$
$402$	−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
$408$	16.9526	+	11.1915i	0.839278	+	0.554062i
$409$	−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	−0.00439272	−	0.999990i	$-0.501398\pi$
$419$	−12.1942	−	3.96214i	−0.595726	−	0.193563i	−0.591333	+	0.806427i	$0.701398\pi$
$420$	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
$425$	−8.82476	−	18.6313i	−0.428064	−	0.903749i
$426$	−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	0.913259	−	0.407380i	$-0.133557\pi$
$431$	29.3274	+	9.52903i	1.41265	+	0.458997i	0.499390	+	0.866377i	$0.333557\pi$
$432$			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	$-0.590026\pi$
$439$	15.0949	−	20.7763i	0.720440	−	0.991601i	0.999509	−	0.0313299i	$-0.00997425\pi$
$440$	−0.946489	−	0.433575i	−0.0451221	−	0.0206699i
$441$	−8.69288	+	6.31575i	−0.413947	+	0.300750i
$442$	0.687947	−	1.04208i	0.0327223	−	0.0495669i
$443$	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	$-0.770581\pi$
$449$		−	27.9678i		−	1.31988i	0.751317	−	0.659942i	$-0.229419\pi$
$450$	−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
$459$	−8.01803	−	21.3672i	−0.374250	−	0.997333i
$460$	−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	−0.118612	−	0.992941i	$-0.537844\pi$
$479$	8.07738	−	2.62450i	0.369065	−	0.119916i	0.487677	+	0.873024i	$0.337844\pi$
$480$	−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	$0.0500134\pi$
$487$	18.3449	+	25.2497i	0.831289	+	1.14417i	−0.156393	+	0.987695i	$0.549987\pi$
$488$	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	$0.0354274\pi$
$499$			4.96217i			0.222137i	−0.993813	+	0.111069i	$0.964573\pi$
$500$	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	−0.325202	−	0.945644i	$-0.605432\pi$
$503$	−0.728023	+	0.236549i	−0.0324610	+	0.0105472i	0.292742	+	0.956192i	$0.405432\pi$
$504$	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	$0.569141\pi$
$510$	4.50100	−	11.1161i	0.199307	−	0.492231i
$511$	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	−0.268155	−	0.963376i	$-0.586414\pi$
$521$	1.85253	−	0.601923i	0.0811608	−	0.0263707i	0.349316	+	0.937005i	$0.386414\pi$
$522$	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
$527$	−3.33669	+	2.66065i	−0.145348	+	0.115900i
$528$	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	0.535992	−	0.844223i	$-0.319938\pi$
$541$	−10.0607	−	13.8474i	−0.432543	−	0.595345i	−0.968535	+	0.248879i	$0.919938\pi$
$542$	−2.42476	+	7.46263i	−0.104152	+	0.320548i
$543$	17.7874			0.763329
$544$	10.8334	−	16.4101i	0.464478	−	0.703579i
$545$	−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	−0.537859	−	0.843035i	$-0.680767\pi$
$547$	−11.1672	+	3.62843i	−0.477473	+	0.155140i	0.0603862	+	0.998175i	$0.480767\pi$
$548$	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
$561$	−1.93404	−	2.42545i	−0.0816553	−	0.102403i
$562$	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	−0.719370	−	0.694627i	$-0.755569\pi$
$571$	−21.3402	+	6.93386i	−0.893061	+	0.290173i	−0.173691	+	0.984800i	$0.555569\pi$
$572$	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	$0.616719\pi$
$578$	−1.74468	+	7.64049i	−0.0725692	+	0.317803i
$579$	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
$595$	27.8425	+	1.96809i	1.14143	+	0.0806839i
$596$	−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	$-0.760958\pi$
$601$		−	33.4560i		−	1.36470i	0.731026	−	0.682350i	$-0.239042\pi$
$602$	−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	$0.190310\pi$
$607$			27.7362i			1.12578i	−0.826533	+	0.562889i	$0.809690\pi$
$608$	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
$612$	−34.2361	+	12.8471i	−1.38391	+	0.519314i
$613$	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	0.256856	−	0.966450i	$-0.417313\pi$
$617$	−2.56858	−	0.834581i	−0.103407	−	0.0335990i	−0.360264	+	0.932851i	$0.617313\pi$
$618$		−	6.24839i		−	0.251347i
$619$	36.7223	+	11.9318i	1.47600	+	0.479580i	0.932914	−	0.360100i	$-0.117257\pi$
$619$	36.7223	+	11.9318i	1.47600	+	0.479580i	0.543082	+	0.839680i	$0.317257\pi$
$620$	−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
$629$	32.3355	−	1.45060i	1.28930	−	0.0578392i
$630$	−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	0.982881	−	0.184241i	$-0.0589826\pi$
$641$	12.7585	+	17.5606i	0.503931	+	0.693601i	−0.478950	+	0.877842i	$0.658983\pi$
$642$	−6.60949	+	20.3419i	−0.260856	+	0.802832i
$643$			9.73870i			0.384057i	0.981389	+	0.192028i	$0.0615066\pi$
$643$			9.73870i			0.384057i	−0.981389	+	0.192028i	$0.938493\pi$
$644$	4.03098	−	12.4061i	0.158843	−	0.488868i
$645$	−1.72840	+	1.87884i	−0.0680559	+	0.0739793i
$646$	0.497531	+	11.0905i	0.0195751	+	0.436351i
$647$	−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	−0.597963	−	0.801524i	$-0.704023\pi$
$653$	−15.6032	+	5.06980i	−0.610602	+	0.198397i	−0.0126387	+	0.999920i	$0.504023\pi$
$654$	−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
$663$	2.68509	+	7.15547i	0.104280	+	0.277895i
$664$	−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	−0.933587	−	0.358350i	$-0.883340\pi$
$673$	−7.89377	+	10.8648i	−0.304282	+	0.418809i	0.629305	+	0.777158i	$0.283340\pi$
$674$		−	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	−0.972357	−	0.233501i	$-0.924982\pi$
$677$	−11.7037	+	16.1088i	−0.449810	+	0.619110i	0.522547	+	0.852610i	$0.324982\pi$
$678$	2.83201	+	8.71602i	0.108763	+	0.334737i
$679$	13.3604	+	41.1192i	0.512726	+	1.57801i
$680$	−14.9211	−	6.04165i	−0.572199	−	0.231687i
$681$	−0.399038	+	1.22811i	−0.0152912	+	0.0470614i
$682$	0.127235			0.00487208
$683$	−12.0019	−	3.89966i	−0.459241	−	0.149217i	0.0702545	−	0.997529i	$-0.477619\pi$
$683$	−12.0019	−	3.89966i	−0.459241	−	0.149217i	−0.529496	+	0.848313i	$0.677619\pi$
$684$	−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	0.449419	−	0.893321i	$-0.351631\pi$
$691$	−14.1702	−	19.5036i	−0.539059	−	0.741950i	−0.988477	+	0.151371i	$0.951631\pi$
$692$	−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
$697$	47.8004	−	2.14437i	1.81057	−	0.0812238i
$698$	−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	0.992262	−	0.124165i	$-0.0396251\pi$
$709$	15.1121	+	20.8001i	0.567548	+	0.781163i	−0.424713	+	0.905328i	$0.639625\pi$
$710$	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
$714$	10.1232	+	12.6954i	0.378853	+	0.475114i
$715$	−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	0.171420	−	0.985198i	$-0.445165\pi$
$719$	−7.21257	−	2.34351i	−0.268983	−	0.0873980i	−0.440403	+	0.897800i	$0.645165\pi$
$720$	−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
$731$	0.919132	−	1.39228i	0.0339953	−	0.0514952i
$732$	−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	$-0.932803\pi$
$743$		−	11.4234i		−	0.419085i	0.977800	−	0.209543i	$-0.0671975\pi$
$744$	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
$748$	−1.53649	+	1.22519i	−0.0561796	+	0.0447973i
$749$	−49.7799			−1.81892
$750$	4.93496	−	13.6806i	0.180199	−	0.499543i
$751$			32.9687i			1.20304i	0.798856	+	0.601522i	$0.205439\pi$
$751$			32.9687i			1.20304i	−0.798856	+	0.601522i	$0.794561\pi$
$752$	−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
$765$	24.2115	+	38.8118i	0.875368	+	1.40324i
$766$	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
$772$	17.5608	−	5.70585i	0.632027	−	0.205358i
$773$	24.6815	+	17.9322i	0.887732	+	0.644975i	0.935286	−	0.353894i	$-0.115142\pi$
$773$	24.6815	+	17.9322i	0.887732	+	0.644975i	−0.0475536	+	0.998869i	$0.515142\pi$
$774$	−0.925526			−0.0332674
$775$	−3.91905	+	3.37998i	−0.140776	+	0.121412i
$776$		−	24.9354i		−	0.895129i
$777$	39.4179	−	54.2541i	1.41411	−	1.94635i
$778$	−0.864727	−	2.66136i	−0.0310020	−	0.0954142i
$779$	64.4622	−	20.9450i	2.30960	−	0.750433i
$780$	−7.26288	+	1.46288i	−0.260053	+	0.0523795i
$781$	0.495062	−	1.52364i	0.0177147	−	0.0545203i
$782$	1.21916	−	4.41670i	0.0435972	−	0.157941i
$783$	−9.38438	+	28.8822i	−0.335370	+	1.03216i
$784$	4.85304	−	3.52594i	0.173323	−	0.125926i
$785$	28.7986	−	16.2193i	1.02787	−	0.578890i
$786$	20.0637	+	14.5772i	0.715650	+	0.519950i
$787$	−7.00688	−	9.64414i	−0.249768	−	0.343777i	0.665662	−	0.746254i	$-0.268149\pi$
$787$	−7.00688	−	9.64414i	−0.249768	−	0.343777i	−0.915430	+	0.402477i	$0.868149\pi$
$788$	16.1052	+	22.1669i	0.573723	+	0.789662i
$789$	−46.5954	+	64.1330i	−1.65884	+	2.28320i
$790$	7.06350	−	1.42272i	0.251308	−	0.0506181i
$791$	−17.2559	+	12.5372i	−0.613550	+	0.445770i
$792$	2.19700	+	0.713848i	0.0780669	+	0.0253655i
$793$			1.18770i			0.0421766i
$794$	3.93863	+	1.27974i	0.139777	+	0.0454162i
$795$	−1.49669	−	0.685617i	−0.0530822	−	0.0243163i
$796$	0.640171	−	0.208004i	0.0226903	−	0.00737251i
$797$	−16.5751	−	51.0130i	−0.587121	−	1.80697i	−0.590580	−	0.806979i	$-0.701101\pi$
$797$	−16.5751	−	51.0130i	−0.587121	−	1.80697i	0.00345897	−	0.999994i	$-0.498899\pi$
$798$	18.6082	+	13.5197i	0.658723	+	0.478591i
$799$	15.3679	+	4.24210i	0.543679	+	0.150075i
$800$	12.3611	−	20.3915i	0.437032	−	0.720948i
$801$	66.5854			2.35268
$802$	5.00772	−	6.89253i	0.176829	−	0.243384i
$803$	0.391653	+	1.20539i	0.0138212	+	0.0425371i
$804$	−72.0016	+	23.3947i	−2.53930	+	0.825069i
$805$	−16.2097	−	1.87895i	−0.571318	−	0.0662244i
$806$	−0.298123	−	0.0968660i	−0.0105009	−	0.00341196i
$807$	9.09915			0.320305
$808$	−6.31699	+	19.4417i	−0.222231	+	0.683957i
$809$	11.6730	+	16.0666i	0.410402	+	0.564870i	0.963316	−	0.268368i	$-0.0864843\pi$
$809$	11.6730	+	16.0666i	0.410402	+	0.564870i	−0.552914	+	0.833238i	$0.686484\pi$
$810$	0.314774	−	0.687148i	0.0110600	−	0.0241439i
$811$	16.7706	−	23.0828i	0.588897	−	0.810547i	−0.405739	−	0.913989i	$-0.632986\pi$
$811$	16.7706	−	23.0828i	0.588897	−	0.810547i	0.994635	+	0.103442i	$0.0329856\pi$
$812$	24.0199	−	17.4515i	0.842932	−	0.612426i
$813$	−28.2291	−	38.8540i	−0.990038	−	1.36267i
$814$	−0.780720	−	0.567227i	−0.0273642	−	0.0198813i
$815$	−19.9001	−	9.11600i	−0.697071	−	0.319320i
$816$	11.3219	+	30.1716i	0.396346	+	1.05622i
$817$	0.730277	−	2.24756i	0.0255492	−	0.0786323i
$818$	6.43348			0.224941
$819$	9.38499	+	3.04937i	0.327938	+	0.106553i
$820$	−5.34084	+	46.0754i	−0.186510	+	1.60902i
$821$	−10.2273	+	3.32307i	−0.356937	+	0.115976i	−0.481996	−	0.876173i	$-0.660088\pi$
$821$	−10.2273	+	3.32307i	−0.356937	+	0.115976i	0.125059	+	0.992149i	$0.460088\pi$
$822$	7.36312	−	2.39242i	0.256818	−	0.0834454i
$823$	25.4311	−	35.0029i	0.886473	−	1.22013i	−0.0881124	−	0.996111i	$-0.528083\pi$
$823$	25.4311	−	35.0029i	0.886473	−	1.22013i	0.974586	−	0.224015i	$-0.0719165\pi$
$824$	−8.38716			−0.292181
$825$	−2.45692	−	2.84877i	−0.0855391	−	0.0991815i
$826$			6.15898i			0.214298i
$827$	−30.1950	+	41.5598i	−1.04998	+	1.44518i	−0.161158	+	0.986929i	$0.551523\pi$
$827$	−30.1950	+	41.5598i	−1.04998	+	1.44518i	−0.888824	+	0.458248i	$0.848477\pi$
$828$	20.3321	−	6.60630i	0.706590	−	0.229585i
$829$	−9.53823	−	29.3557i	−0.331276	−	1.01956i	−0.968527	−	0.248908i	$-0.919928\pi$
$829$	−9.53823	−	29.3557i	−0.331276	−	1.01956i	0.637251	−	0.770657i	$-0.280072\pi$
$830$	−2.85194	+	6.22574i	−0.0989922	+	0.216099i
$831$	14.4806	−	44.5668i	0.502328	−	1.54601i
$832$	−2.19505			−0.0760997
$833$	−4.91932	+	7.45165i	−0.170444	+	0.258184i
$834$	19.8112	−	14.3936i	0.686004	−	0.498411i
$835$	−11.3438	+	2.28485i	−0.392568	+	0.0790705i
$836$	−1.63625	+	2.25210i	−0.0565907	+	0.0778905i
$837$	−4.63498	+	3.36751i	−0.160208	+	0.116398i
$838$	3.47437	+	4.78205i	0.120020	+	0.165193i
$839$	−15.9897	+	22.0079i	−0.552024	+	0.759796i	−0.990285	−	0.139051i	$-0.955595\pi$
$839$	−15.9897	+	22.0079i	−0.552024	+	0.759796i	0.438261	+	0.898848i	$0.355595\pi$
$840$	−29.0604	+	16.3667i	−1.00268	+	0.564706i
$841$	0.891108	−	0.647428i	0.0307278	−	0.0223251i
$842$	1.15267	−	3.54756i	0.0397238	−	0.122257i
$843$			76.0269i			2.61851i
$844$	−34.1385	−	11.0923i	−1.17510	−	0.381812i
$845$	−5.54920	−	27.5506i	−0.190898	−	0.947769i
$846$	−2.73311	−	8.41165i	−0.0939663	−	0.289199i
$847$	31.4676	−	10.2244i	1.08124	−	0.351316i
$848$	−0.584718	−	0.424822i	−0.0200793	−	0.0145885i
$849$	61.7636			2.11972
$850$	−1.75727	+	9.34008i	−0.0602740	+	0.320362i
$851$	−18.9235			−0.648688
$852$	−24.5154	−	17.8115i	−0.839885	−	0.610212i
$853$	11.8621	−	3.85423i	0.406150	−	0.131966i	−0.0988152	−	0.995106i	$-0.531505\pi$
$853$	11.8621	−	3.85423i	0.406150	−	0.131966i	0.504965	+	0.863140i	$0.331505\pi$
$854$	0.779761	+	2.39986i	0.0266829	+	0.0821215i
$855$	47.6892	+	43.8708i	1.63094	+	1.50035i
$856$	27.3048	+	8.87187i	0.933259	+	0.303234i
$857$			27.0221i			0.923056i	0.887126	+	0.461528i	$0.152699\pi$
$857$			27.0221i			0.923056i	−0.887126	+	0.461528i	$0.847301\pi$
$858$	0.0704124	−	0.216707i	0.00240384	−	0.00739826i
$859$	27.6329	−	20.0765i	0.942821	−	0.685000i	−0.00627671	−	0.999980i	$-0.501998\pi$
$859$	27.6329	−	20.0765i	0.942821	−	0.685000i	0.949098	+	0.314980i	$0.101998\pi$
$860$	1.19022	+	1.09492i	0.0405861	+	0.0373364i
$861$	58.2700	−	80.2018i	1.98584	−	2.73327i
$862$	−8.35593	−	11.5010i	−0.284604	−	0.391724i
$863$	−9.92804	+	7.21314i	−0.337954	+	0.245538i	−0.743798	−	0.668404i	$-0.766978\pi$
$863$	−9.92804	+	7.21314i	−0.337954	+	0.245538i	0.405844	+	0.913942i	$0.366978\pi$
$864$	15.5162	−	21.3562i	0.527872	−	0.726553i
$865$	−4.04429	+	34.8901i	−0.137510	+	1.18630i
$866$	−8.06873	+	5.86227i	−0.274187	+	0.199208i
$867$	−31.5564	−	36.1264i	−1.07171	−	1.22692i
$868$	5.60119			0.190117
$869$	0.575943	−	1.77257i	0.0195375	−	0.0601304i
$870$	−13.9049	+	7.83116i	−0.471419	+	0.265501i
$871$	3.04716	+	9.37821i	0.103249	+	0.317768i
$872$	−23.8601	+	7.75261i	−0.808005	+	0.262537i
$873$	−41.6490	+	57.3249i	−1.40960	+	1.94015i
$874$		−	6.49043i		−	0.219542i
$875$	33.8308	+	1.08435i	1.14369	+	0.0366576i
$876$	23.9731			0.809976
$877$	2.38195	−	3.27847i	0.0804327	−	0.110706i	−0.766905	−	0.641761i	$-0.778204\pi$
$877$	2.38195	−	3.27847i	0.0804327	−	0.110706i	0.847337	+	0.531055i	$0.178204\pi$
$878$	−11.2597	+	3.65850i	−0.379997	+	0.123469i
$879$	−15.1512	+	4.92293i	−0.511038	+	0.166046i
$880$	−0.810467	−	1.43905i	−0.0273208	−	0.0485103i
$881$	5.74921	+	1.86803i	0.193696	+	0.0629355i	0.404258	−	0.914645i	$-0.367530\pi$
$881$	5.74921	+	1.86803i	0.193696	+	0.0629355i	−0.210563	+	0.977580i	$0.567530\pi$
$882$	4.95354			0.166794
$883$	−13.8747	+	42.7018i	−0.466920	+	1.43703i	0.389632	+	0.920970i	$0.372602\pi$
$883$	−13.8747	+	42.7018i	−0.466920	+	1.43703i	−0.856552	+	0.516061i	$0.827398\pi$
$884$	4.53288	−	1.70097i	0.152457	−	0.0572097i
$885$	−3.20588	+	27.6572i	−0.107765	+	0.929685i
$886$	−0.710587	−	0.516272i	−0.0238726	−	0.0173445i
$887$	−31.2258	−	42.9787i	−1.04846	−	1.44308i	−0.890135	−	0.455696i	$-0.849390\pi$
$887$	−31.2258	−	42.9787i	−1.04846	−	1.44308i	−0.158326	−	0.987387i	$-0.550610\pi$
$888$	−31.2904	+	22.7338i	−1.05004	+	0.762896i
$889$	−38.1438	+	52.5005i	−1.27930	+	1.76081i
$890$	10.1812	+	9.36597i	0.341273	+	0.313948i
$891$	−0.114915	−	0.158166i	−0.00384979	−	0.00529877i
$892$	−8.29679	+	25.5349i	−0.277797	+	0.854971i
$893$	22.5835			0.755729
$894$	−14.6853	−	4.77156i	−0.491151	−	0.159585i
$895$	19.5625	+	17.9962i	0.653904	+	0.601547i
$896$	−31.8987	+	10.3645i	−1.06566	+	0.346254i
$897$	−1.38074	−	4.24948i	−0.0461016	−	0.141886i
$898$	−7.57857	+	10.4310i	−0.252900	+	0.348087i
$899$	5.67878			0.189398
$900$	−40.8865	+	17.1670i	−1.36288	+	0.572235i
$901$	1.03702	+	0.286255i	0.0345483	+	0.00953655i
$902$	−1.15411	−	0.838510i	−0.0384277	−	0.0279193i
$903$	−1.06811	−	3.28730i	−0.0355445	−	0.109395i
$904$	11.6994	−	3.80138i	0.389118	−	0.126432i
$905$	−13.8184	+	2.78329i	−0.459341	+	0.0925197i
$906$	1.69647	+	0.551216i	0.0563614	+	0.0183129i
$907$			9.59578i			0.318623i	0.987228	+	0.159311i	$0.0509274\pi$
$907$			9.59578i			0.318623i	−0.987228	+	0.159311i	$0.949073\pi$
$908$	0.777992	+	0.252785i	0.0258186	+	0.00838896i
$909$	46.9954	−	34.1442i	1.55874	−	1.13249i
$910$	1.00607	+	1.78636i	0.0333510	+	0.0592173i
$911$	−13.4464	+	18.5073i	−0.445498	+	0.613175i	−0.971423	−	0.237356i	$-0.923719\pi$
$911$	−13.4464	+	18.5073i	−0.445498	+	0.613175i	0.525925	+	0.850531i	$0.323719\pi$
$912$	26.8321	+	36.9312i	0.888498	+	1.22291i
$913$	1.04116	+	1.43303i	0.0344573	+	0.0474264i
$914$	−11.7788	−	8.55780i	−0.389608	−	0.283067i
$915$	2.25237	+	11.1826i	0.0744612	+	0.369684i
$916$	−25.9524	+	18.8556i	−0.857493	+	0.623005i
$917$	−17.8363	+	54.8945i	−0.589007	+	1.81278i
$918$	−2.79951	+	10.1419i	−0.0923977	+	0.334731i
$919$	−17.3490	+	53.3948i	−0.572291	+	1.76133i	0.0729311	+	0.997337i	$0.476765\pi$
$919$	−17.3490	+	53.3948i	−0.572291	+	1.76133i	−0.645222	+	0.763995i	$0.723235\pi$
$920$	8.55634	+	3.91956i	0.282094	+	0.129224i
$921$	79.3440	−	25.7804i	2.61447	−	0.849494i
$922$	−3.01808	−	9.28868i	−0.0993951	−	0.305907i
$923$	−2.31995	+	3.19313i	−0.0763620	+	0.105103i
$924$			4.07153i			0.133944i
$925$	39.1157	−	3.26822i	1.28612	−	0.107458i
$926$	−0.963805			−0.0316726
$927$	19.2816	+	14.0089i	0.633290	+	0.460112i
$928$	−24.8850	+	8.08562i	−0.816890	+	0.265424i
$929$	9.32839	−	3.03098i	0.306054	−	0.0994431i	−0.151963	−	0.988386i	$-0.548560\pi$
$929$	9.32839	−	3.03098i	0.306054	−	0.0994431i	0.458018	+	0.888943i	$0.348560\pi$
$930$	−2.99061	−	0.346657i	−0.0980659	−	0.0113673i
$931$	−3.90854	+	12.0293i	−0.128097	+	0.394243i
$932$			10.5204i			0.344607i
$933$	−24.4501	+	75.2497i	−0.800460	+	2.46356i
$934$	−2.51262	+	1.82553i	−0.0822155	+	0.0597330i
$935$	1.88202	+	1.58163i	0.0615486	+	0.0517248i
$936$	−4.60430	−	3.34522i	−0.150496	−	0.109342i
$937$	11.2648	−	8.18436i	0.368005	−	0.267371i	−0.388378	−	0.921500i	$-0.626965\pi$
$937$	11.2648	−	8.18436i	0.368005	−	0.267371i	0.756383	+	0.654129i	$0.226965\pi$
$938$	12.3141	+	16.9489i	0.402070	+	0.553402i
$939$	−16.0243	−	11.6423i	−0.522933	−	0.379933i
$940$	−6.43643	+	14.0506i	−0.209933	+	0.458281i
$941$	−21.6892	−	29.8527i	−0.707049	−	0.973169i	−0.999856	−	0.0169972i	$-0.994589\pi$
$941$	−21.6892	−	29.8527i	−0.707049	−	0.973169i	0.292807	−	0.956172i	$-0.405411\pi$
$942$	18.2864	+	5.94161i	0.595803	+	0.193588i
$943$	−27.9739			−0.910955
$944$	−3.77728	+	11.6253i	−0.122940	+	0.378371i
$945$	37.2217	+	4.31456i	1.21082	+	0.140353i
$946$	−0.0473046	+	0.0153702i	−0.00153800	+	0.000499728i
$947$	−24.2629	+	7.88348i	−0.788437	+	0.256179i	−0.675438	−	0.737416i	$-0.736046\pi$
$947$	−24.2629	+	7.88348i	−0.788437	+	0.256179i	−0.112999	+	0.993595i	$0.536046\pi$
$948$	−28.5207	−	20.7215i	−0.926309	−	0.673003i
$949$		−	3.12250i		−	0.101361i
$950$	1.12094	+	13.4160i	0.0363682	+	0.435273i
$951$	−57.9304			−1.87852
$952$	17.0410	−	13.5883i	0.552300	−	0.440401i
$953$	2.79056	+	8.58845i	0.0903950	+	0.278207i	0.986026	−	0.166590i	$-0.0532757\pi$
$953$	2.79056	+	8.58845i	0.0903950	+	0.278207i	−0.895631	+	0.444797i	$0.853276\pi$
$954$	−0.184430	−	0.567616i	−0.00597113	−	0.0183772i
$955$	14.4892	−	31.6297i	0.468859	−	1.02351i
$956$	2.07913	−	6.39890i	0.0672438	−	0.206955i
$957$			4.12793i			0.133437i
$958$	−3.72375	−	1.20992i	−0.120309	−	0.0390907i
$959$	10.5911	+	14.5775i	0.342006	+	0.470731i
$960$	−20.6670	+	4.16272i	−0.667025	+	0.134351i
$961$	−24.2128	−	17.5916i	−0.781058	−	0.567472i
$962$	1.39746	+	1.92344i	0.0450559	+	0.0620141i
$963$	−47.9536	−	66.0024i	−1.54528	−	2.12690i
$964$	−22.5465	+	31.0326i	−0.726175	+	0.999494i
$965$	−11.3349	−	20.1261i	−0.364885	−	0.647882i
$966$	−5.57982	−	7.67996i	−0.179528	−	0.247099i
$967$	1.81576	−	5.58835i	0.0583910	−	0.179709i	−0.917607	−	0.397489i	$-0.869882\pi$
$967$	1.81576	−	5.58835i	0.0583910	−	0.179709i	0.975998	+	0.217780i	$0.0698816\pi$
$968$	−19.0825			−0.613335
$969$	−56.7064	−	37.4355i	−1.82167	−	1.20260i
$970$	−14.4317	+	2.90681i	−0.463373	+	0.0933319i
$971$	5.57101	+	17.1458i	0.178782	+	0.550235i	0.999786	−	0.0206875i	$-0.00658549\pi$
$971$	5.57101	+	17.1458i	0.178782	+	0.550235i	−0.821004	+	0.570923i	$0.806585\pi$
$972$	24.7121	−	8.02943i	0.792640	−	0.257544i
$973$	46.1082	+	33.4996i	1.47816	+	1.07395i
$974$		−	14.3882i		−	0.461029i
$975$	3.58797	+	8.54542i	0.114907	+	0.273672i
$976$			5.00804i			0.160303i
$977$	29.0942	+	21.1381i	0.930804	+	0.676269i	0.946190	−	0.323613i	$-0.104897\pi$
$977$	29.0942	+	21.1381i	0.930804	+	0.676269i	−0.0153853	+	0.999882i	$0.504897\pi$
$978$	−3.93486	−	12.1103i	−0.125823	−	0.387244i
$979$	3.40325	−	1.10578i	0.108768	−	0.0353409i
$980$	−6.37021	−	5.86015i	−0.203489	−	0.187196i
$981$	67.8019	+	22.0302i	2.16475	+	0.703369i
$982$	1.54811			0.0494021
$983$	−43.3405	−	14.0822i	−1.38235	−	0.449152i	−0.478907	−	0.877865i	$-0.658967\pi$
$983$	−43.3405	−	14.0822i	−1.38235	−	0.449152i	−0.903441	+	0.428713i	$0.858967\pi$
$984$	−46.2554	+	33.6065i	−1.47457	+	1.07134i
$985$	23.2060	−	25.2258i	0.739405	−	0.803760i
$986$	8.15376	−	6.50175i	0.259669	−	0.207058i
$987$	26.7225	−	19.4150i	0.850587	−	0.617988i
$988$	5.54843	−	4.03117i	0.176519	−	0.128249i
$989$	−0.573295	+	0.789073i	−0.0182297	+	0.0250911i
$990$	0.157037	−	1.35476i	0.00499095	−	0.0430570i
$991$	−3.37329	−	4.64293i	−0.107156	−	0.147488i	0.752071	−	0.659082i	$-0.229055\pi$
$991$	−3.37329	−	4.64293i	−0.107156	−	0.147488i	−0.859227	+	0.511594i	$0.829055\pi$
$992$	−4.69467	−	1.52539i	−0.149056	−	0.0484312i
$993$			40.4028i			1.28214i
$994$	−2.59127	+	7.97512i	−0.0821902	+	0.252956i
$995$	−0.413211	−	0.733688i	−0.0130997	−	0.0232595i
$996$	31.8646	−	10.3534i	1.00967	−	0.328061i
$997$	11.3036	−	3.67276i	0.357989	−	0.116318i	−0.124500	−	0.992220i	$-0.539733\pi$
$997$	11.3036	−	3.67276i	0.357989	−	0.116318i	0.482489	+	0.875902i	$0.339733\pi$
$998$	1.34462	−	1.85071i	0.0425633	−	0.0585833i
$999$	43.4532			1.37480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.p.a.16.20	yes	168
17.16	even	2	inner	425.2.p.a.16.19	✓	168
25.11	even	5	inner	425.2.p.a.186.19	yes	168
425.186	even	10	inner	425.2.p.a.186.20	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.p.a.16.19	✓	168	17.16	even	2	inner
425.2.p.a.16.20	yes	168	1.1	even	1	trivial
425.2.p.a.186.19	yes	168	25.11	even	5	inner
425.2.p.a.186.20	yes	168	425.186	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
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} +(2.27158 - 3.44092i) 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} +(-1.77962 + 0.667802i) 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} +(-0.650077 + 9.19660i) 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

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