LMFDB - Embedded newform 140.2.w.a.123.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(23,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("140.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.12745506816.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 49x^{4} + 2401 $ x^8 - 49*x^4 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			123.2
Root			$0.684771 + 2.55560i$ of defining polynomial
Character	$\chi$	$=$	140.123
Dual form			140.2.w.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(0.684771 + 2.55560i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.23205 - 0.133975i) q^{5} -3.74166i q^{6} +(-2.55560 + 0.684771i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.46410 + 2.00000i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(3.24037 + 1.87083i) q^{11} +(-1.36954 + 5.11120i) q^{12} +(-2.00000 - 2.00000i) q^{13} +3.74166 q^{14} +(1.87083 + 5.61249i) q^{15} +(2.00000 + 3.46410i) q^{16} +(0.732051 + 2.73205i) q^{17} +(5.46410 - 1.46410i) q^{18} +(-1.87083 - 3.24037i) q^{19} +(4.00000 + 2.00000i) q^{20} +(-3.50000 - 6.06218i) q^{21} +(-3.74166 - 3.74166i) q^{22} +(2.55560 + 0.684771i) q^{23} +(3.74166 - 6.48074i) q^{24} +(4.96410 - 0.598076i) q^{25} +(2.00000 + 3.46410i) q^{26} +(-1.87083 - 1.87083i) q^{27} +(-5.11120 - 1.36954i) q^{28} -3.00000i q^{29} +(-0.501287 - 8.35157i) q^{30} +(-6.48074 - 3.74166i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-2.56218 + 9.56218i) q^{33} -4.00000i q^{34} +(-5.61249 + 1.87083i) q^{35} -8.00000 q^{36} +(1.36954 + 5.11120i) q^{38} +(3.74166 - 6.48074i) q^{39} +(-4.73205 - 4.19615i) q^{40} +3.00000 q^{41} +(2.56218 + 9.56218i) q^{42} +(5.61249 - 5.61249i) q^{43} +(3.74166 + 6.48074i) q^{44} +(-7.46410 + 4.92820i) q^{45} +(-3.24037 - 1.87083i) q^{46} +(2.73908 - 10.2224i) q^{47} +(-7.48331 + 7.48331i) q^{48} +(6.06218 - 3.50000i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-6.48074 + 3.74166i) q^{51} +(-1.46410 - 5.46410i) q^{52} +(6.83013 - 1.83013i) q^{53} +(1.87083 + 3.24037i) q^{54} +(7.48331 + 3.74166i) q^{55} +(6.48074 + 3.74166i) q^{56} +(7.00000 - 7.00000i) q^{57} +(-1.09808 + 4.09808i) q^{58} +(-1.87083 + 3.24037i) q^{59} +(-2.37212 + 11.5919i) q^{60} +(1.50000 + 2.59808i) q^{61} +(7.48331 + 7.48331i) q^{62} +(7.48331 - 7.48331i) q^{63} +8.00000i q^{64} +(-4.73205 - 4.19615i) q^{65} +(7.00000 - 12.1244i) q^{66} +(-12.7780 + 3.42385i) q^{67} +(-1.46410 + 5.46410i) q^{68} +7.00000i q^{69} +(8.35157 - 0.501287i) q^{70} -3.74166i q^{71} +(10.9282 + 2.92820i) q^{72} +(-2.73205 + 0.732051i) q^{73} +(4.92772 + 12.2767i) q^{75} -7.48331i q^{76} +(-9.56218 - 2.56218i) q^{77} +(-7.48331 + 7.48331i) q^{78} +(1.87083 + 3.24037i) q^{79} +(4.92820 + 7.46410i) q^{80} +(-2.50000 + 4.33013i) q^{81} +(-4.09808 - 1.09808i) q^{82} +(-1.87083 + 1.87083i) q^{83} -14.0000i q^{84} +(2.00000 + 6.00000i) q^{85} +(-9.72111 + 5.61249i) q^{86} +(7.66680 - 2.05431i) q^{87} +(-2.73908 - 10.2224i) q^{88} +(2.59808 - 1.50000i) q^{89} +(12.0000 - 4.00000i) q^{90} +(6.48074 + 3.74166i) q^{91} +(3.74166 + 3.74166i) q^{92} +(5.12436 - 19.1244i) q^{93} +(-7.48331 + 12.9615i) q^{94} +(-4.60991 - 6.98203i) q^{95} +(12.9615 - 7.48331i) q^{96} +(-9.00000 + 9.00000i) q^{97} +(-9.56218 + 2.56218i) q^{98} -14.9666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8} - 4 q^{10} - 16 q^{13} + 16 q^{16} - 8 q^{17} + 16 q^{18} + 32 q^{20} - 28 q^{21} + 12 q^{25} + 16 q^{26} + 16 q^{32} + 28 q^{33} - 64 q^{36} - 24 q^{40} + 24 q^{41} - 28 q^{42}+ \cdots - 28 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8 - 4 * q^10 - 16 * q^13 + 16 * q^16 - 8 * q^17 + 16 * q^18 + 32 * q^20 - 28 * q^21 + 12 * q^25 + 16 * q^26 + 16 * q^32 + 28 * q^33 - 64 * q^36 - 24 * q^40 + 24 * q^41 - 28 * q^42 - 32 * q^45 - 56 * q^50 + 16 * q^52 + 20 * q^53 + 56 * q^57 + 12 * q^58 + 12 * q^61 - 24 * q^65 + 56 * q^66 + 16 * q^68 + 32 * q^72 - 8 * q^73 - 28 * q^77 - 16 * q^80 - 20 * q^81 - 12 * q^82 + 16 * q^85 + 96 * q^90 - 56 * q^93 - 72 * q^97 - 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$	0.684771	+	2.55560i	0.395353	+	1.47548i	0.821179	+	0.570671i	$0.193317\pi$
$3$	0.684771	+	2.55560i	0.395353	+	1.47548i	−0.425826	+	0.904805i	$0.640016\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$		−	3.74166i		−	1.52753i
$7$	−2.55560	+	0.684771i	−0.965926	+	0.258819i
$7$	−2.55560	+	0.684771i	−0.965926	+	0.258819i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−3.46410	+	2.00000i	−1.15470	+	0.666667i
$10$	−3.09808	−	0.633975i	−0.979698	−	0.200480i
$11$	3.24037	+	1.87083i	0.977008	+	0.564076i	0.901366	−	0.433059i	$-0.142566\pi$
$11$	3.24037	+	1.87083i	0.977008	+	0.564076i	0.0756428	+	0.997135i	$0.475899\pi$
$12$	−1.36954	+	5.11120i	−0.395353	+	1.47548i
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$	3.74166			1.00000
$15$	1.87083	+	5.61249i	0.483046	+	1.44914i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	0.732051	+	2.73205i	0.177548	+	0.662620i	0.996104	+	0.0881917i	$0.0281088\pi$
$17$	0.732051	+	2.73205i	0.177548	+	0.662620i	−0.818555	+	0.574428i	$0.805225\pi$
$18$	5.46410	−	1.46410i	1.28790	−	0.345092i
$19$	−1.87083	−	3.24037i	−0.429198	−	0.743392i	0.567605	−	0.823301i	$-0.307870\pi$
$19$	−1.87083	−	3.24037i	−0.429198	−	0.743392i	−0.996802	+	0.0799094i	$0.974537\pi$
$20$	4.00000	+	2.00000i	0.894427	+	0.447214i
$21$	−3.50000	−	6.06218i	−0.763763	−	1.32288i
$22$	−3.74166	−	3.74166i	−0.797724	−	0.797724i
$23$	2.55560	+	0.684771i	0.532879	+	0.142785i	0.515218	−	0.857059i	$-0.327711\pi$
$23$	2.55560	+	0.684771i	0.532879	+	0.142785i	0.0176618	+	0.999844i	$0.494378\pi$
$24$	3.74166	−	6.48074i	0.763763	−	1.32288i
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	−1.87083	−	1.87083i	−0.360041	−	0.360041i
$28$	−5.11120	−	1.36954i	−0.965926	−	0.258819i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	−0.501287	−	8.35157i	−0.0915221	−	1.52478i
$31$	−6.48074	−	3.74166i	−1.16398	−	0.672022i	−0.211722	−	0.977330i	$-0.567907\pi$
$31$	−6.48074	−	3.74166i	−1.16398	−	0.672022i	−0.952254	+	0.305308i	$0.901240\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$	−2.56218	+	9.56218i	−0.446018	+	1.66456i
$34$		−	4.00000i		−	0.685994i
$35$	−5.61249	+	1.87083i	−0.948683	+	0.316228i
$36$	−8.00000			−1.33333
$37$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$37$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$38$	1.36954	+	5.11120i	0.222169	+	0.829146i
$39$	3.74166	−	6.48074i	0.599145	−	1.03775i
$40$	−4.73205	−	4.19615i	−0.748203	−	0.663470i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	2.56218	+	9.56218i	0.395353	+	1.47548i
$43$	5.61249	−	5.61249i	0.855896	−	0.855896i	−0.134956	−	0.990852i	$-0.543089\pi$
$43$	5.61249	−	5.61249i	0.855896	−	0.855896i	0.990852	+	0.134956i	$0.0430892\pi$
$44$	3.74166	+	6.48074i	0.564076	+	0.977008i
$45$	−7.46410	+	4.92820i	−1.11268	+	0.734653i
$46$	−3.24037	−	1.87083i	−0.477767	−	0.275839i
$47$	2.73908	−	10.2224i	0.399536	−	1.49109i	−0.414378	−	0.910105i	$-0.636001\pi$
$47$	2.73908	−	10.2224i	0.399536	−	1.49109i	0.813914	−	0.580985i	$-0.197333\pi$
$48$	−7.48331	+	7.48331i	−1.08012	+	1.08012i
$49$	6.06218	−	3.50000i	0.866025	−	0.500000i
$50$	−7.00000	−	1.00000i	−0.989949	−	0.141421i
$51$	−6.48074	+	3.74166i	−0.907485	+	0.523937i
$52$	−1.46410	−	5.46410i	−0.203034	−	0.757735i
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.242846	−	0.970065i	$-0.421919\pi$
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.695344	+	0.718677i	$0.255252\pi$
$54$	1.87083	+	3.24037i	0.254588	+	0.440959i
$55$	7.48331	+	3.74166i	1.00905	+	0.504525i
$56$	6.48074	+	3.74166i	0.866025	+	0.500000i
$57$	7.00000	−	7.00000i	0.927173	−	0.927173i
$58$	−1.09808	+	4.09808i	−0.144184	+	0.538104i
$59$	−1.87083	+	3.24037i	−0.243561	+	0.421860i	−0.961726	−	0.274013i	$-0.911649\pi$
$59$	−1.87083	+	3.24037i	−0.243561	+	0.421860i	0.718165	+	0.695873i	$0.244982\pi$
$60$	−2.37212	+	11.5919i	−0.306239	+	1.49651i
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	0.945931	−	0.324367i	$-0.105151\pi$
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	−0.753876	+	0.657017i	$0.771818\pi$
$62$	7.48331	+	7.48331i	0.950382	+	0.950382i
$63$	7.48331	−	7.48331i	0.942809	−	0.942809i
$64$			8.00000i			1.00000i
$65$	−4.73205	−	4.19615i	−0.586939	−	0.520469i
$66$	7.00000	−	12.1244i	0.861640	−	1.49241i
$67$	−12.7780	+	3.42385i	−1.56108	+	0.418290i	−0.933005	−	0.359862i	$-0.882824\pi$
$67$	−12.7780	+	3.42385i	−1.56108	+	0.418290i	−0.628075	+	0.778153i	$0.716157\pi$
$68$	−1.46410	+	5.46410i	−0.177548	+	0.662620i
$69$			7.00000i			0.842701i
$70$	8.35157	−	0.501287i	0.998203	−	0.0599153i
$71$		−	3.74166i		−	0.444053i	−0.975041	−	0.222027i	$-0.928733\pi$
$71$		−	3.74166i		−	0.444053i	0.975041	−	0.222027i	$-0.0712672\pi$
$72$	10.9282	+	2.92820i	1.28790	+	0.345092i
$73$	−2.73205	+	0.732051i	−0.319762	+	0.0856801i	−0.415130	−	0.909762i	$-0.636264\pi$
$73$	−2.73205	+	0.732051i	−0.319762	+	0.0856801i	0.0953678	+	0.995442i	$0.469597\pi$
$74$		0			0
$75$	4.92772	+	12.2767i	0.569004	+	1.41759i
$76$		−	7.48331i		−	0.858395i
$77$	−9.56218	−	2.56218i	−1.08971	−	0.291987i
$78$	−7.48331	+	7.48331i	−0.847319	+	0.847319i
$79$	1.87083	+	3.24037i	0.210485	+	0.364570i	0.951866	−	0.306514i	$-0.0991625\pi$
$79$	1.87083	+	3.24037i	0.210485	+	0.364570i	−0.741382	+	0.671084i	$0.765829\pi$
$80$	4.92820	+	7.46410i	0.550990	+	0.834512i
$81$	−2.50000	+	4.33013i	−0.277778	+	0.481125i
$82$	−4.09808	−	1.09808i	−0.452557	−	0.121262i
$83$	−1.87083	+	1.87083i	−0.205350	+	0.205350i	−0.802288	−	0.596938i	$-0.796384\pi$
$83$	−1.87083	+	1.87083i	−0.205350	+	0.205350i	0.596938	+	0.802288i	$0.296384\pi$
$84$		−	14.0000i		−	1.52753i
$85$	2.00000	+	6.00000i	0.216930	+	0.650791i
$86$	−9.72111	+	5.61249i	−1.04825	+	0.605210i
$87$	7.66680	−	2.05431i	0.821967	−	0.220245i
$88$	−2.73908	−	10.2224i	−0.291987	−	1.08971i
$89$	2.59808	−	1.50000i	0.275396	−	0.159000i	−0.355942	−	0.934508i	$-0.615840\pi$
$89$	2.59808	−	1.50000i	0.275396	−	0.159000i	0.631337	+	0.775509i	$0.282506\pi$
$90$	12.0000	−	4.00000i	1.26491	−	0.421637i
$91$	6.48074	+	3.74166i	0.679366	+	0.392232i
$92$	3.74166	+	3.74166i	0.390095	+	0.390095i
$93$	5.12436	−	19.1244i	0.531371	−	1.98310i
$94$	−7.48331	+	12.9615i	−0.771845	+	1.33687i
$95$	−4.60991	−	6.98203i	−0.472967	−	0.716341i
$96$	12.9615	−	7.48331i	1.32288	−	0.763763i
$97$	−9.00000	+	9.00000i	−0.913812	+	0.913812i	−0.996570	−	0.0827581i	$-0.973627\pi$
$97$	−9.00000	+	9.00000i	−0.913812	+	0.913812i	0.0827581	+	0.996570i	$0.473627\pi$
$98$	−9.56218	+	2.56218i	−0.965926	+	0.258819i
$99$	−14.9666			−1.50420
$100$	9.19615	+	3.92820i	0.919615	+	0.392820i
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$	10.2224	−	2.73908i	1.01217	−	0.271210i
$103$	−2.55560	−	0.684771i	−0.251811	−	0.0674725i	0.130706	−	0.991421i	$-0.458276\pi$
$103$	−2.55560	−	0.684771i	−0.251811	−	0.0674725i	−0.382516	+	0.923949i	$0.624942\pi$
$104$			8.00000i			0.784465i
$105$	−8.62436	−	13.0622i	−0.841651	−	1.27474i
$106$	−10.0000			−0.971286
$107$	3.42385	−	12.7780i	0.330996	−	1.23530i	−0.577148	−	0.816639i	$-0.695835\pi$
$107$	3.42385	−	12.7780i	0.330996	−	1.23530i	0.908145	−	0.418656i	$-0.137499\pi$
$108$	−1.36954	−	5.11120i	−0.131784	−	0.491825i
$109$	−12.9904	−	7.50000i	−1.24425	−	0.718370i	−0.274296	−	0.961645i	$-0.588445\pi$
$109$	−12.9904	−	7.50000i	−1.24425	−	0.718370i	−0.969957	+	0.243276i	$0.921778\pi$
$110$	−8.85286	−	7.85028i	−0.844087	−	0.748495i
$111$		0			0
$112$	−7.48331	−	7.48331i	−0.707107	−	0.707107i
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	0.658505	−	0.752577i	$-0.271189\pi$
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	−12.1244	+	7.00000i	−1.13555	+	0.655610i
$115$	5.79597	+	1.18606i	0.540477	+	0.110600i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	10.9282	+	2.92820i	1.01031	+	0.270712i
$118$	3.74166	−	3.74166i	0.344447	−	0.344447i
$119$	−3.74166	−	6.48074i	−0.342997	−	0.594089i
$120$	7.48331	−	14.9666i	0.683130	−	1.36626i
$121$	1.50000	+	2.59808i	0.136364	+	0.236189i
$122$	−1.09808	−	4.09808i	−0.0994151	−	0.371022i
$123$	2.05431	+	7.66680i	0.185231	+	0.691292i
$124$	−7.48331	−	12.9615i	−0.672022	−	1.16398i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−12.9615	+	7.48331i	−1.15470	+	0.666667i
$127$	7.48331	+	7.48331i	0.664037	+	0.664037i	0.956329	−	0.292292i	$-0.0944180\pi$
$127$	7.48331	+	7.48331i	0.664037	+	0.664037i	−0.292292	+	0.956329i	$0.594418\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$	18.1865	+	10.5000i	1.60123	+	0.924473i
$130$	4.92820	+	7.46410i	0.432232	+	0.654645i
$131$	−12.9615	+	7.48331i	−1.13245	+	0.653820i	−0.944550	−	0.328368i	$-0.893501\pi$
$131$	−12.9615	+	7.48331i	−1.13245	+	0.653820i	−0.187900	+	0.982188i	$0.560168\pi$
$132$	−14.0000	+	14.0000i	−1.21854	+	1.21854i
$133$	7.00000	+	7.00000i	0.606977	+	0.606977i
$134$	18.7083			1.61615
$135$	−4.42643	−	3.92514i	−0.380966	−	0.337822i
$136$	4.00000	−	6.92820i	0.342997	−	0.594089i
$137$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$137$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$138$	2.56218	−	9.56218i	0.218107	−	0.813987i
$139$	−11.2250			−0.952090			−0.476045	−	0.879421i	$-0.657930\pi$
$139$	−11.2250			−0.952090			−0.476045	+	0.879421i	$0.657930\pi$
$140$	−11.5919	−	2.37212i	−0.979698	−	0.200480i
$141$	28.0000			2.35803
$142$	−1.36954	+	5.11120i	−0.114929	+	0.428922i
$143$	−2.73908	−	10.2224i	−0.229054	−	0.854840i
$144$	−13.8564	−	8.00000i	−1.15470	−	0.666667i
$145$	−0.401924	−	6.69615i	−0.0333780	−	0.556085i
$146$	4.00000			0.331042
$147$	13.0958	+	13.0958i	1.08012	+	1.08012i
$148$		0			0
$149$	−6.06218	+	3.50000i	−0.496633	+	0.286731i	−0.727322	−	0.686296i	$-0.759235\pi$
$149$	−6.06218	+	3.50000i	−0.496633	+	0.286731i	0.230689	+	0.973028i	$0.425902\pi$
$150$	−2.23780	−	18.5740i	−0.182715	−	1.51656i
$151$	19.4422	+	11.2250i	1.58219	+	0.913475i	0.994540	+	0.104357i	$0.0332784\pi$
$151$	19.4422	+	11.2250i	1.58219	+	0.913475i	0.587646	+	0.809118i	$0.300055\pi$
$152$	−2.73908	+	10.2224i	−0.222169	+	0.829146i
$153$	−8.00000	−	8.00000i	−0.646762	−	0.646762i
$154$	12.1244	+	7.00000i	0.977008	+	0.564076i
$155$	−14.9666	−	7.48331i	−1.20215	−	0.601074i
$156$	12.9615	−	7.48331i	1.03775	−	0.599145i
$157$	−3.29423	−	12.2942i	−0.262908	−	0.981186i	−0.963518	−	0.267642i	$-0.913756\pi$
$157$	−3.29423	−	12.2942i	−0.262908	−	0.981186i	0.700610	−	0.713544i	$-0.252911\pi$
$158$	−1.36954	−	5.11120i	−0.108955	−	0.406625i
$159$	9.35414	+	16.2019i	0.741832	+	1.28489i
$160$	−4.00000	−	12.0000i	−0.316228	−	0.948683i
$161$	−7.00000			−0.551677
$162$	5.00000	−	5.00000i	0.392837	−	0.392837i
$163$	10.2224	+	2.73908i	0.800680	+	0.214542i	0.635883	−	0.771786i	$-0.280636\pi$
$163$	10.2224	+	2.73908i	0.800680	+	0.214542i	0.164797	+	0.986327i	$0.447303\pi$
$164$	5.19615	+	3.00000i	0.405751	+	0.234261i
$165$	−4.43782	+	21.6865i	−0.345484	+	1.68829i
$166$	3.24037	−	1.87083i	0.251502	−	0.145204i
$167$	−5.61249	−	5.61249i	−0.434307	−	0.434307i	0.455783	−	0.890091i	$-0.349359\pi$
$167$	−5.61249	−	5.61249i	−0.434307	−	0.434307i	−0.890091	+	0.455783i	$0.849359\pi$
$168$	−5.12436	+	19.1244i	−0.395353	+	1.47548i
$169$		−	5.00000i		−	0.384615i
$170$	−0.535898	−	8.92820i	−0.0411015	−	0.684762i
$171$	12.9615	+	7.48331i	0.991189	+	0.572263i
$172$	15.3336	−	4.10862i	1.16918	−	0.313280i
$173$	−2.92820	+	10.9282i	−0.222627	+	0.830856i	0.760714	+	0.649087i	$0.224849\pi$
$173$	−2.92820	+	10.9282i	−0.222627	+	0.830856i	−0.983341	+	0.181769i	$0.941818\pi$
$174$	−11.2250			−0.850963
$175$	−12.2767	+	4.92772i	−0.928032	+	0.372500i
$176$			14.9666i			1.12815i
$177$	−9.56218	−	2.56218i	−0.718737	−	0.192585i
$178$	−4.09808	+	1.09808i	−0.307164	+	0.0823043i
$179$	−3.74166	+	6.48074i	−0.279665	+	0.484393i	−0.971301	−	0.237852i	$-0.923557\pi$
$179$	−3.74166	+	6.48074i	−0.279665	+	0.484393i	0.691637	+	0.722246i	$0.256890\pi$
$180$	−17.8564	+	1.07180i	−1.33094	+	0.0798870i
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$	−7.48331	−	7.48331i	−0.554700	−	0.554700i
$183$	−5.61249	+	5.61249i	−0.414887	+	0.414887i
$184$	−3.74166	−	6.48074i	−0.275839	−	0.477767i
$185$		0			0
$186$	−14.0000	+	24.2487i	−1.02653	+	1.77800i
$187$	−2.73908	+	10.2224i	−0.200302	+	0.747536i
$188$	14.9666	−	14.9666i	1.09155	−	1.09155i
$189$	6.06218	+	3.50000i	0.440959	+	0.254588i
$190$	3.74166	+	11.2250i	0.271448	+	0.814345i
$191$	−3.24037	+	1.87083i	−0.234465	+	0.135368i	−0.612630	−	0.790370i	$-0.709888\pi$
$191$	−3.24037	+	1.87083i	−0.234465	+	0.135368i	0.378165	+	0.925738i	$0.376555\pi$
$192$	−20.4448	+	5.47817i	−1.47548	+	0.395353i
$193$	−6.83013	+	1.83013i	−0.491643	+	0.131735i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−6.83013	+	1.83013i	−0.491643	+	0.131735i	0.00447566	+	0.999990i	$0.498575\pi$
$194$	15.5885	−	9.00000i	1.11919	−	0.646162i
$195$	7.48331	−	14.9666i	0.535891	−	1.07178i
$196$	14.0000			1.00000
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	−0.741832	−	0.670585i	$-0.766043\pi$
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	0.670585	+	0.741832i	$0.266043\pi$
$198$	20.4448	+	5.47817i	1.45295	+	0.389316i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−11.1244	−	8.73205i	−0.786611	−	0.617449i
$201$	−17.5000	−	30.3109i	−1.23435	−	2.13797i
$202$	15.0000	−	15.0000i	1.05540	−	1.05540i
$203$	2.05431	+	7.66680i	0.144184	+	0.538104i
$204$	−14.9666			−1.04787
$205$	6.69615	−	0.401924i	0.467680	−	0.0280716i
$206$	3.24037	+	1.87083i	0.225767	+	0.130347i
$207$	−10.2224	+	2.73908i	−0.710506	+	0.190379i
$208$	2.92820	−	10.9282i	0.203034	−	0.757735i
$209$		−	14.0000i		−	0.968400i
$210$	7.00000	+	21.0000i	0.483046	+	1.44914i
$211$		−	11.2250i		−	0.772759i	−0.922340	−	0.386379i	$-0.873726\pi$
$211$		−	11.2250i		−	0.772759i	0.922340	−	0.386379i	$-0.126274\pi$
$212$	13.6603	+	3.66025i	0.938190	+	0.251387i
$213$	9.56218	−	2.56218i	0.655190	−	0.175558i
$214$	−9.35414	+	16.2019i	−0.639436	+	1.10754i
$215$	11.7754	−	13.2793i	0.803077	−	0.905640i
$216$			7.48331i			0.509175i
$217$	19.1244	+	5.12436i	1.29825	+	0.347864i
$218$	15.0000	+	15.0000i	1.01593	+	1.01593i
$219$	−3.74166	−	6.48074i	−0.252838	−	0.437928i
$220$	9.21982	+	13.9641i	0.621600	+	0.941456i
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$		0			0
$223$	−3.74166	+	3.74166i	−0.250560	+	0.250560i	−0.821200	−	0.570640i	$-0.806695\pi$
$223$	−3.74166	+	3.74166i	−0.250560	+	0.250560i	0.570640	+	0.821200i	$0.306695\pi$
$224$	7.48331	+	12.9615i	0.500000	+	0.866025i
$225$	−16.0000	+	12.0000i	−1.06667	+	0.800000i
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$227$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$228$	19.1244	−	5.12436i	1.26654	−	0.339369i
$229$	−13.8564	+	8.00000i	−0.915657	+	0.528655i	−0.882247	−	0.470787i	$-0.843970\pi$
$229$	−13.8564	+	8.00000i	−0.915657	+	0.528655i	−0.0334101	+	0.999442i	$0.510637\pi$
$230$	−7.48331	−	3.74166i	−0.493435	−	0.246718i
$231$		−	26.1916i		−	1.72328i
$232$	−6.00000	+	6.00000i	−0.393919	+	0.393919i
$233$	−5.12436	+	19.1244i	−0.335708	+	1.25288i	0.567392	+	0.823448i	$0.307952\pi$
$233$	−5.12436	+	19.1244i	−0.335708	+	1.25288i	−0.903100	+	0.429431i	$0.858714\pi$
$234$	−13.8564	−	8.00000i	−0.905822	−	0.522976i
$235$	4.74423	−	23.1839i	0.309480	−	1.51235i
$236$	−6.48074	+	3.74166i	−0.421860	+	0.243561i
$237$	−7.00000	+	7.00000i	−0.454699	+	0.454699i
$238$	2.73908	+	10.2224i	0.177548	+	0.662620i
$239$	22.4499			1.45217			0.726083	−	0.687607i	$-0.241339\pi$
$239$	22.4499			1.45217			0.726083	+	0.687607i	$0.241339\pi$
$240$	−15.7006	+	17.7057i	−1.01347	+	1.14290i
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	−0.605481	−	0.795860i	$-0.707019\pi$
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	0.991975	+	0.126432i	$0.0403527\pi$
$242$	−1.09808	−	4.09808i	−0.0705870	−	0.263434i
$243$	−20.4448	−	5.47817i	−1.31153	−	0.351425i
$244$			6.00000i			0.384111i
$245$	13.0622	−	8.62436i	0.834512	−	0.550990i
$246$		−	11.2250i		−	0.715678i
$247$	−2.73908	+	10.2224i	−0.174284	+	0.650436i
$248$	5.47817	+	20.4448i	0.347864	+	1.29825i
$249$	−6.06218	−	3.50000i	−0.384175	−	0.221803i
$250$	−15.7583	−	1.29423i	−0.996644	−	0.0818542i
$251$			7.48331i			0.472343i	0.971711	+	0.236171i	$0.0758927\pi$
$251$			7.48331i			0.472343i	−0.971711	+	0.236171i	$0.924107\pi$
$252$	20.4448	−	5.47817i	1.28790	−	0.345092i
$253$	7.00000	+	7.00000i	0.440086	+	0.440086i
$254$	−7.48331	−	12.9615i	−0.469545	−	0.813276i
$255$	−13.9641	+	9.21982i	−0.874463	+	0.577368i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	27.3205	+	7.32051i	1.70421	+	0.456641i	0.973993	−	0.226578i	$-0.0727539\pi$
$257$	27.3205	+	7.32051i	1.70421	+	0.456641i	0.730214	+	0.683219i	$0.239421\pi$
$258$	−21.0000	−	21.0000i	−1.30740	−	1.30740i
$259$		0			0
$260$	−4.00000	−	12.0000i	−0.248069	−	0.744208i
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$	20.4448	−	5.47817i	1.26308	−	0.338442i
$263$	0.684771	+	2.55560i	0.0422248	+	0.157585i	0.983819	−	0.179164i	$-0.0573393\pi$
$263$	0.684771	+	2.55560i	0.0422248	+	0.157585i	−0.941594	+	0.336749i	$0.890673\pi$
$264$	24.2487	−	14.0000i	1.49241	−	0.861640i
$265$	15.0000	−	5.00000i	0.921443	−	0.307148i
$266$	−7.00000	−	12.1244i	−0.429198	−	0.743392i
$267$	5.61249	+	5.61249i	0.343479	+	0.343479i
$268$	−25.5560	−	6.84771i	−1.56108	−	0.418290i
$269$	−11.2583	−	6.50000i	−0.686433	−	0.396312i	0.115842	−	0.993268i	$-0.463043\pi$
$269$	−11.2583	−	6.50000i	−0.686433	−	0.396312i	−0.802274	+	0.596956i	$0.796377\pi$
$270$	4.60991	+	6.98203i	0.280550	+	0.424913i
$271$	9.72111	−	5.61249i	0.590515	−	0.340934i	−0.174786	−	0.984606i	$-0.555923\pi$
$271$	9.72111	−	5.61249i	0.590515	−	0.340934i	0.765301	+	0.643672i	$0.222590\pi$
$272$	−8.00000	+	8.00000i	−0.485071	+	0.485071i
$273$	−5.12436	+	19.1244i	−0.310140	+	1.15746i
$274$		0			0
$275$	17.2044	+	7.34900i	1.03747	+	0.443161i
$276$	−7.00000	+	12.1244i	−0.421350	+	0.729800i
$277$	0.732051	+	2.73205i	0.0439847	+	0.164153i	0.984425	−	0.175806i	$-0.0562533\pi$
$277$	0.732051	+	2.73205i	0.0439847	+	0.164153i	−0.940440	+	0.339959i	$0.889587\pi$
$278$	15.3336	+	4.10862i	0.919648	+	0.246419i
$279$	29.9333			1.79206
$280$	14.9666	+	7.48331i	0.894427	+	0.447214i
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	−38.2487	−	10.2487i	−2.27768	−	0.610302i
$283$	−2.73908	−	10.2224i	−0.162822	−	0.607658i	−0.998308	−	0.0581474i	$-0.981481\pi$
$283$	−2.73908	−	10.2224i	−0.162822	−	0.607658i	0.835486	−	0.549511i	$-0.185186\pi$
$284$	3.74166	−	6.48074i	0.222027	−	0.384561i
$285$	14.6865	−	16.5622i	0.869955	−	0.981059i
$286$			14.9666i			0.884995i
$287$	−7.66680	+	2.05431i	−0.452557	+	0.121262i
$288$	16.0000	+	16.0000i	0.942809	+	0.942809i
$289$	7.79423	−	4.50000i	0.458484	−	0.264706i
$290$	−1.90192	+	9.29423i	−0.111685	+	0.545776i
$291$	−29.1633	−	16.8375i	−1.70958	−	0.987029i
$292$	−5.46410	−	1.46410i	−0.319762	−	0.0856801i
$293$	−20.0000	−	20.0000i	−1.16841	−	1.16841i	−0.982582	−	0.185831i	$-0.940502\pi$
$293$	−20.0000	−	20.0000i	−1.16841	−	1.16841i	−0.185831	−	0.982582i	$-0.559498\pi$
$294$	−13.0958	−	22.6826i	−0.763763	−	1.32288i
$295$	−3.74166	+	7.48331i	−0.217848	+	0.435695i
$296$		0			0
$297$	−2.56218	−	9.56218i	−0.148673	−	0.554854i
$298$	9.56218	−	2.56218i	0.553922	−	0.148423i
$299$	−3.74166	−	6.48074i	−0.216386	−	0.374791i
$300$	−3.74166	+	26.1916i	−0.216025	+	1.51217i
$301$	−10.5000	+	18.1865i	−0.605210	+	1.04825i
$302$	−22.4499	−	22.4499i	−1.29185	−	1.29185i
$303$	−38.3340	−	10.2716i	−2.20223	−	0.590086i
$304$	7.48331	−	12.9615i	0.429198	−	0.743392i
$305$	3.69615	+	5.59808i	0.211641	+	0.320545i
$306$	8.00000	+	13.8564i	0.457330	+	0.792118i
$307$	9.35414	+	9.35414i	0.533869	+	0.533869i	0.921722	−	0.387852i	$-0.126783\pi$
$307$	9.35414	+	9.35414i	0.533869	+	0.533869i	−0.387852	+	0.921722i	$0.626783\pi$
$308$	−14.0000	−	14.0000i	−0.797724	−	0.797724i
$309$		−	7.00000i		−	0.398216i
$310$	17.7057	+	15.7006i	1.00562	+	0.891732i
$311$	−16.2019	−	9.35414i	−0.918723	−	0.530425i	−0.0354954	−	0.999370i	$-0.511301\pi$
$311$	−16.2019	−	9.35414i	−0.918723	−	0.530425i	−0.883227	+	0.468945i	$0.844634\pi$
$312$	−20.4448	+	5.47817i	−1.15746	+	0.310140i
$313$	1.46410	−	5.46410i	0.0827559	−	0.308849i	−0.912124	−	0.409915i	$-0.865558\pi$
$313$	1.46410	−	5.46410i	0.0827559	−	0.308849i	0.994880	+	0.101065i	$0.0322251\pi$
$314$			18.0000i			1.01580i
$315$	15.7006	−	17.7057i	0.884627	−	0.997604i
$316$			7.48331i			0.420969i
$317$	−13.6603	−	3.66025i	−0.767236	−	0.205580i	−0.146086	−	0.989272i	$-0.546668\pi$
$317$	−13.6603	−	3.66025i	−0.767236	−	0.205580i	−0.621150	+	0.783692i	$0.713334\pi$
$318$	−6.84771	−	25.5560i	−0.384000	−	1.43311i
$319$	5.61249	−	9.72111i	0.314239	−	0.544278i
$320$	1.07180	+	17.8564i	0.0599153	+	0.998203i
$321$	35.0000			1.95351
$322$	9.56218	+	2.56218i	0.532879	+	0.142785i
$323$	7.48331	−	7.48331i	0.416383	−	0.416383i
$324$	−8.66025	+	5.00000i	−0.481125	+	0.277778i
$325$	−11.1244	−	8.73205i	−0.617068	−	0.484367i
$326$	−12.9615	−	7.48331i	−0.717870	−	0.414462i
$327$	10.2716	−	38.3340i	0.568019	−	2.11987i
$328$	−6.00000	−	6.00000i	−0.331295	−	0.331295i
$329$			28.0000i			1.54369i
$330$	14.0000	−	28.0000i	0.770675	−	1.54135i
$331$	19.4422	−	11.2250i	1.06864	−	0.616980i	0.140831	−	0.990034i	$-0.455022\pi$
$331$	19.4422	−	11.2250i	1.06864	−	0.616980i	0.927810	+	0.373053i	$0.121689\pi$
$332$	−5.11120	+	1.36954i	−0.280513	+	0.0751634i
$333$		0			0
$334$	5.61249	+	9.72111i	0.307102	+	0.531916i
$335$	−28.0624	+	9.35414i	−1.53321	+	0.511071i
$336$	14.0000	−	24.2487i	0.763763	−	1.32288i
$337$	−21.0000	+	21.0000i	−1.14394	+	1.14394i	−0.156221	+	0.987722i	$0.549931\pi$
$337$	−21.0000	+	21.0000i	−1.14394	+	1.14394i	−0.987722	+	0.156221i	$0.950069\pi$
$338$	−1.83013	+	6.83013i	−0.0995458	+	0.371510i
$339$	1.87083	−	3.24037i	0.101609	−	0.175993i
$340$	−2.53590	+	12.3923i	−0.137528	+	0.672067i
$341$	−14.0000	−	24.2487i	−0.758143	−	1.31314i
$342$	−14.9666	−	14.9666i	−0.809303	−	0.809303i
$343$	−13.0958	+	13.0958i	−0.707107	+	0.707107i
$344$	−22.4499			−1.21042
$345$	0.937822	+	15.6244i	0.0504906	+	0.841187i
$346$	8.00000	−	13.8564i	0.430083	−	0.744925i
$347$	17.8892	−	4.79340i	0.960342	−	0.257323i	0.255597	−	0.966783i	$-0.417728\pi$
$347$	17.8892	−	4.79340i	0.960342	−	0.257323i	0.704745	+	0.709460i	$0.251061\pi$
$348$	15.3336	+	4.10862i	0.821967	+	0.220245i
$349$			11.0000i			0.588817i	0.955680	+	0.294408i	$0.0951225\pi$
$349$			11.0000i			0.588817i	−0.955680	+	0.294408i	$0.904877\pi$
$350$	18.5740	−	2.23780i	0.992820	−	0.119615i
$351$			7.48331i			0.399430i
$352$	5.47817	−	20.4448i	0.291987	−	1.08971i
$353$	23.2224	−	6.22243i	1.23601	−	0.331187i	0.419090	−	0.907945i	$-0.362349\pi$
$353$	23.2224	−	6.22243i	1.23601	−	0.331187i	0.816915	+	0.576758i	$0.195682\pi$
$354$	12.1244	+	7.00000i	0.644402	+	0.372046i
$355$	−0.501287	−	8.35157i	−0.0266056	−	0.443255i
$356$	6.00000			0.317999
$357$	14.0000	−	14.0000i	0.740959	−	0.740959i
$358$	7.48331	−	7.48331i	0.395505	−	0.395505i
$359$	11.2250	+	19.4422i	0.592431	+	1.02612i	0.993904	+	0.110250i	$0.0351652\pi$
$359$	11.2250	+	19.4422i	0.592431	+	1.02612i	−0.401472	+	0.915871i	$0.631501\pi$
$360$	24.7846	+	5.07180i	1.30626	+	0.267307i
$361$	2.50000	−	4.33013i	0.131579	−	0.227901i
$362$	17.7583	+	4.75833i	0.933357	+	0.250092i
$363$	−5.61249	+	5.61249i	−0.294579	+	0.294579i
$364$	7.48331	+	12.9615i	0.392232	+	0.679366i
$365$	−6.00000	+	2.00000i	−0.314054	+	0.104685i
$366$	9.72111	−	5.61249i	0.508131	−	0.293369i
$367$	−17.8892	+	4.79340i	−0.933808	+	0.250213i	−0.693478	−	0.720478i	$-0.743923\pi$
$367$	−17.8892	+	4.79340i	−0.933808	+	0.250213i	−0.240331	+	0.970691i	$0.577256\pi$
$368$	2.73908	+	10.2224i	0.142785	+	0.532879i
$369$	−10.3923	+	6.00000i	−0.541002	+	0.312348i
$370$		0			0
$371$	−16.2019	+	9.35414i	−0.841158	+	0.485643i
$372$	28.0000	−	28.0000i	1.45173	−	1.45173i
$373$	8.78461	−	32.7846i	0.454850	−	1.69752i	−0.233679	−	0.972314i	$-0.575076\pi$
$373$	8.78461	−	32.7846i	0.454850	−	1.69752i	0.688529	−	0.725209i	$-0.258257\pi$
$374$	7.48331	−	12.9615i	0.386953	−	0.670222i
$375$	12.6437	+	26.7421i	0.652917	+	1.38095i
$376$	−25.9230	+	14.9666i	−1.33687	+	0.771845i
$377$	−6.00000	+	6.00000i	−0.309016	+	0.309016i
$378$	−7.00000	−	7.00000i	−0.360041	−	0.360041i
$379$	11.2250			0.576588			0.288294	−	0.957542i	$-0.406912\pi$
$379$	11.2250			0.576588			0.288294	+	0.957542i	$0.406912\pi$
$380$	−1.00257	−	16.7031i	−0.0514310	−	0.856853i
$381$	−14.0000	+	24.2487i	−0.717242	+	1.24230i
$382$	5.11120	−	1.36954i	0.261512	−	0.0700718i
$383$	12.7780	+	3.42385i	0.652925	+	0.174951i	0.570051	−	0.821609i	$-0.306923\pi$
$383$	12.7780	+	3.42385i	0.652925	+	0.174951i	0.0828741	+	0.996560i	$0.473590\pi$
$384$	29.9333			1.52753
$385$	−21.6865	−	4.43782i	−1.10525	−	0.226172i
$386$	10.0000			0.508987
$387$	−8.21725	+	30.6672i	−0.417706	+	1.55890i
$388$	−24.5885	+	6.58846i	−1.24829	+	0.334478i
$389$	6.92820	+	4.00000i	0.351274	+	0.202808i	0.665246	−	0.746624i	$-0.268327\pi$
$389$	6.92820	+	4.00000i	0.351274	+	0.202808i	−0.313972	+	0.949432i	$0.601660\pi$
$390$	−15.7006	+	17.7057i	−0.795029	+	0.896564i
$391$			7.48331i			0.378447i
$392$	−19.1244	−	5.12436i	−0.965926	−	0.258819i
$393$	−28.0000	−	28.0000i	−1.41241	−	1.41241i
$394$	1.73205	−	1.00000i	0.0872595	−	0.0503793i
$395$	4.60991	+	6.98203i	0.231950	+	0.351304i
$396$	−25.9230	−	14.9666i	−1.30268	−	0.752101i
$397$	−15.0263	−	4.02628i	−0.754147	−	0.202073i	−0.138790	−	0.990322i	$-0.544321\pi$
$397$	−15.0263	−	4.02628i	−0.754147	−	0.202073i	−0.615357	+	0.788249i	$0.710988\pi$
$398$		0			0
$399$	−13.0958	+	22.6826i	−0.655610	+	1.13555i
$400$	12.0000	+	16.0000i	0.600000	+	0.800000i
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	0.996119	+	0.0880147i	$0.0280523\pi$
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	−0.421837	+	0.906672i	$0.638614\pi$
$402$	12.8109	+	47.8109i	0.638949	+	2.38459i
$403$	5.47817	+	20.4448i	0.272887	+	1.01843i
$404$	−25.9808	+	15.0000i	−1.29259	+	0.746278i
$405$	−5.00000	+	10.0000i	−0.248452	+	0.496904i
$406$		−	11.2250i		−	0.557086i
$407$		0			0
$408$	20.4448	+	5.47817i	1.01217	+	0.271210i
$409$	4.33013	+	2.50000i	0.214111	+	0.123617i	0.603220	−	0.797574i	$-0.293884\pi$
$409$	4.33013	+	2.50000i	0.214111	+	0.123617i	−0.389109	+	0.921192i	$0.627217\pi$
$410$	−9.29423	−	1.90192i	−0.459009	−	0.0939293i
$411$		0			0
$412$	−3.74166	−	3.74166i	−0.184338	−	0.184338i
$413$	2.56218	−	9.56218i	0.126077	−	0.470524i
$414$	14.9666			0.735570
$415$	−3.92514	+	4.42643i	−0.192678	+	0.217285i
$416$	−8.00000	+	13.8564i	−0.392232	+	0.679366i
$417$	−7.68653	−	28.6865i	−0.376411	−	1.40479i
$418$	−5.12436	+	19.1244i	−0.250640	+	0.935403i
$419$	14.9666			0.731168			0.365584	−	0.930778i	$-0.380869\pi$
$419$	14.9666			0.731168			0.365584	+	0.930778i	$0.380869\pi$
$420$	−1.87564	−	31.2487i	−0.0915221	−	1.52478i
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	−4.10862	+	15.3336i	−0.200005	+	0.746428i
$423$	10.9563	+	40.8896i	0.532715	+	1.98812i
$424$	−17.3205	−	10.0000i	−0.841158	−	0.485643i
$425$	5.26795	+	13.1244i	0.255533	+	0.636625i
$426$	−14.0000			−0.678302
$427$	−5.61249	−	5.61249i	−0.271607	−	0.271607i
$428$	18.7083	−	18.7083i	0.904299	−	0.904299i
$429$	24.2487	−	14.0000i	1.17074	−	0.675926i
$430$	−20.9461	+	13.8297i	−1.01011	+	0.666929i
$431$	9.72111	+	5.61249i	0.468249	+	0.270344i	0.715507	−	0.698606i	$-0.246196\pi$
$431$	9.72111	+	5.61249i	0.468249	+	0.270344i	−0.247257	+	0.968950i	$0.579529\pi$
$432$	2.73908	−	10.2224i	0.131784	−	0.491825i
$433$	23.0000	+	23.0000i	1.10531	+	1.10531i	0.993759	+	0.111551i	$0.0355818\pi$
$433$	23.0000	+	23.0000i	1.10531	+	1.10531i	0.111551	+	0.993759i	$0.464418\pi$
$434$	−24.2487	−	14.0000i	−1.16398	−	0.672022i
$435$	16.8375	−	5.61249i	0.807294	−	0.269098i
$436$	−15.0000	−	25.9808i	−0.718370	−	1.24425i
$437$	−2.56218	−	9.56218i	−0.122566	−	0.457421i
$438$	2.73908	+	10.2224i	0.130878	+	0.488445i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−7.48331	−	22.4499i	−0.356753	−	1.07026i
$441$	−14.0000	+	24.2487i	−0.666667	+	1.15470i
$442$	−8.00000	+	8.00000i	−0.380521	+	0.380521i
$443$	−7.66680	−	2.05431i	−0.364261	−	0.0976033i	0.0720462	−	0.997401i	$-0.477047\pi$
$443$	−7.66680	−	2.05431i	−0.364261	−	0.0976033i	−0.436307	+	0.899798i	$0.643714\pi$
$444$		0			0
$445$	5.59808	−	3.69615i	0.265374	−	0.175214i
$446$	6.48074	−	3.74166i	0.306872	−	0.177173i
$447$	−13.0958	−	13.0958i	−0.619410	−	0.619410i
$448$	−5.47817	−	20.4448i	−0.258819	−	0.965926i
$449$		−	35.0000i		−	1.65175i	−0.563852	−	0.825876i	$-0.690681\pi$
$449$		−	35.0000i		−	1.65175i	0.563852	−	0.825876i	$-0.309319\pi$
$450$	26.2487	−	10.5359i	1.23738	−	0.496667i
$451$	9.72111	+	5.61249i	0.457749	+	0.264282i
$452$	−0.732051	−	2.73205i	−0.0344328	−	0.128505i
$453$	−15.3731	+	57.3731i	−0.722290	+	2.69562i
$454$		0			0
$455$	14.9666	+	7.48331i	0.701646	+	0.350823i
$456$	−28.0000			−1.31122
$457$	32.7846	+	8.78461i	1.53360	+	0.410927i	0.924191	−	0.381930i	$-0.124740\pi$
$457$	32.7846	+	8.78461i	1.53360	+	0.410927i	0.609408	+	0.792857i	$0.291407\pi$
$458$	21.8564	−	5.85641i	1.02128	−	0.273652i
$459$	3.74166	−	6.48074i	0.174646	−	0.302495i
$460$	8.85286	+	7.85028i	0.412767	+	0.366021i
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$	−9.58679	+	35.7784i	−0.446018	+	1.66456i
$463$	−24.3208	+	24.3208i	−1.13028	+	1.13028i	−0.140152	+	0.990130i	$0.544759\pi$
$463$	−24.3208	+	24.3208i	−1.13028	+	1.13028i	−0.990130	+	0.140152i	$0.955241\pi$
$464$	10.3923	−	6.00000i	0.482451	−	0.278543i
$465$	8.87564	−	43.3731i	0.411598	−	2.01138i
$466$	14.0000	−	24.2487i	0.648537	−	1.12330i
$467$	−10.2716	+	38.3340i	−0.475311	+	1.77389i	0.144895	+	0.989447i	$0.453715\pi$
$467$	−10.2716	+	38.3340i	−0.475311	+	1.77389i	−0.620206	+	0.784439i	$0.712951\pi$
$468$	16.0000	+	16.0000i	0.739600	+	0.739600i
$469$	30.3109	−	17.5000i	1.39963	−	0.808075i
$470$	−14.9666	+	29.9333i	−0.690359	+	1.38072i
$471$	29.1633	−	16.8375i	1.34378	−	0.775829i
$472$	10.2224	−	2.73908i	0.470524	−	0.126077i
$473$	28.6865	−	7.68653i	1.31901	−	0.353427i
$474$	12.1244	−	7.00000i	0.556890	−	0.321521i
$475$	−11.2250	−	14.9666i	−0.515037	−	0.686716i
$476$		−	14.9666i		−	0.685994i
$477$	−20.0000	+	20.0000i	−0.915737	+	0.915737i
$478$	−30.6672	−	8.21725i	−1.40268	−	0.375848i
$479$	3.74166	−	6.48074i	0.170961	−	0.296113i	−0.767795	−	0.640695i	$-0.778646\pi$
$479$	3.74166	−	6.48074i	0.170961	−	0.296113i	0.938756	+	0.344583i	$0.111980\pi$
$480$	27.9281	−	18.4396i	1.27474	−	0.841651i
$481$		0			0
$482$	−12.0000	+	12.0000i	−0.546585	+	0.546585i
$483$	−4.79340	−	17.8892i	−0.218107	−	0.813987i
$484$			6.00000i			0.272727i
$485$	−18.8827	+	21.2942i	−0.857419	+	0.966921i
$486$	25.9230	+	14.9666i	1.17589	+	0.678900i
$487$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$487$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$488$	2.19615	−	8.19615i	0.0994151	−	0.371022i
$489$			28.0000i			1.26620i
$490$	−21.0000	+	7.00000i	−0.948683	+	0.316228i
$491$			22.4499i			1.01315i	0.862195	+	0.506576i	$0.169089\pi$
$491$			22.4499i			1.01315i	−0.862195	+	0.506576i	$0.830911\pi$
$492$	−4.10862	+	15.3336i	−0.185231	+	0.691292i
$493$	8.19615	−	2.19615i	0.369136	−	0.0989097i
$494$	7.48331	−	12.9615i	0.336690	−	0.583165i
$495$	−33.4063	+	2.00515i	−1.50150	+	0.0901247i
$496$		−	29.9333i		−	1.34404i
$497$	2.56218	+	9.56218i	0.114929	+	0.428922i
$498$	7.00000	+	7.00000i	0.313678	+	0.313678i
$499$	−20.5791	−	35.6441i	−0.921248	−	1.59565i	−0.797487	−	0.603336i	$-0.793838\pi$
$499$	−20.5791	−	35.6441i	−0.921248	−	1.59565i	−0.123760	−	0.992312i	$-0.539495\pi$
$500$	21.0526	+	7.53590i	0.941499	+	0.337016i
$501$	10.5000	−	18.1865i	0.469105	−	0.812514i
$502$	2.73908	−	10.2224i	0.122251	−	0.456248i
$503$	16.8375	−	16.8375i	0.750745	−	0.750745i	−0.223873	−	0.974618i	$-0.571870\pi$
$503$	16.8375	−	16.8375i	0.750745	−	0.750745i	0.974618	+	0.223873i	$0.0718701\pi$
$504$	−29.9333			−1.33333
$505$	−15.0000	+	30.0000i	−0.667491	+	1.33498i
$506$	−7.00000	−	12.1244i	−0.311188	−	0.538993i
$507$	12.7780	−	3.42385i	0.567491	−	0.152059i
$508$	5.47817	+	20.4448i	0.243054	+	0.907091i
$509$	9.52628	−	5.50000i	0.422245	−	0.243783i	−0.273792	−	0.961789i	$-0.588278\pi$
$509$	9.52628	−	5.50000i	0.422245	−	0.243783i	0.696037	+	0.718006i	$0.254945\pi$
$510$	22.4499	−	7.48331i	0.994100	−	0.331367i
$511$	6.48074	−	3.74166i	0.286691	−	0.165521i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−2.56218	+	9.56218i	−0.113123	+	0.422180i
$514$	−34.6410	−	20.0000i	−1.52795	−	0.882162i
$515$	−5.79597	−	1.18606i	−0.255401	−	0.0522640i
$516$	21.0000	+	36.3731i	0.924473	+	1.60123i
$517$	28.0000	−	28.0000i	1.23144	−	1.23144i
$518$		0			0
$519$	−29.9333			−1.31392
$520$	1.07180	+	17.8564i	0.0470014	+	0.783055i
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$	−4.39230	−	16.3923i	−0.192246	−	0.717472i
$523$	20.4448	+	5.47817i	0.893989	+	0.239544i	0.676433	−	0.736504i	$-0.263525\pi$
$523$	20.4448	+	5.47817i	0.893989	+	0.239544i	0.217556	+	0.976048i	$0.430192\pi$
$524$	−29.9333			−1.30764
$525$	−21.0000	−	28.0000i	−0.916515	−	1.22202i
$526$		−	3.74166i		−	0.163144i
$527$	5.47817	−	20.4448i	0.238633	−	0.890589i
$528$	−38.2487	+	10.2487i	−1.66456	+	0.446018i
$529$	−13.8564	−	8.00000i	−0.602452	−	0.347826i
$530$	−22.3205	+	1.33975i	−0.969541	+	0.0581948i
$531$		−	14.9666i		−	0.649496i
$532$	5.12436	+	19.1244i	0.222169	+	0.829146i
$533$	−6.00000	−	6.00000i	−0.259889	−	0.259889i
$534$	−5.61249	−	9.72111i	−0.242876	−	0.420674i
$535$	5.93029	−	28.9798i	0.256389	−	1.25291i
$536$	32.4037	+	18.7083i	1.39963	+	0.808075i
$537$	−19.1244	−	5.12436i	−0.825277	−	0.221132i
$538$	13.0000	+	13.0000i	0.560470	+	0.560470i
$539$	26.1916			1.12815
$540$	−3.74166	−	11.2250i	−0.161015	−	0.483046i
$541$	−3.50000	−	6.06218i	−0.150477	−	0.260633i	0.780926	−	0.624623i	$-0.214748\pi$
$541$	−3.50000	−	6.06218i	−0.150477	−	0.260633i	−0.931403	+	0.363990i	$0.881414\pi$
$542$	−15.3336	+	4.10862i	−0.658634	+	0.176481i
$543$	−8.90202	−	33.2228i	−0.382022	−	1.42573i
$544$	13.8564	−	8.00000i	0.594089	−	0.342997i
$545$	−30.0000	−	15.0000i	−1.28506	−	0.642529i
$546$	14.0000	−	24.2487i	0.599145	−	1.03775i
$547$	−20.5791	−	20.5791i	−0.879899	−	0.879899i	0.113624	−	0.993524i	$-0.463754\pi$
$547$	−20.5791	−	20.5791i	−0.879899	−	0.879899i	−0.993524	+	0.113624i	$0.963754\pi$
$548$		0			0
$549$	−10.3923	−	6.00000i	−0.443533	−	0.256074i
$550$	−20.8118	−	16.3362i	−0.887417	−	0.696577i
$551$	−9.72111	+	5.61249i	−0.414133	+	0.239100i
$552$	14.0000	−	14.0000i	0.595880	−	0.595880i
$553$	−7.00000	−	7.00000i	−0.297670	−	0.297670i
$554$		−	4.00000i		−	0.169944i
$555$		0			0
$556$	−19.4422	−	11.2250i	−0.824534	−	0.476045i
$557$	6.95448	+	25.9545i	0.294671	+	1.09973i	0.941478	+	0.337073i	$0.109437\pi$
$557$	6.95448	+	25.9545i	0.294671	+	1.09973i	−0.646807	+	0.762653i	$0.723896\pi$
$558$	−40.8896	−	10.9563i	−1.73099	−	0.463819i
$559$	−22.4499			−0.949531
$560$	−17.7057	−	15.7006i	−0.748203	−	0.663470i
$561$	−28.0000			−1.18216
$562$	5.46410	+	1.46410i	0.230489	+	0.0617594i
$563$	−6.16294	−	23.0004i	−0.259737	−	0.969351i	−0.965394	−	0.260797i	$-0.916015\pi$
$563$	−6.16294	−	23.0004i	−0.259737	−	0.969351i	0.705657	−	0.708554i	$-0.250652\pi$
$564$	48.4974	+	28.0000i	2.04211	+	1.17901i
$565$	−2.36603	−	2.09808i	−0.0995394	−	0.0882667i
$566$			14.9666i			0.629094i
$567$	3.42385	−	12.7780i	0.143788	−	0.536625i
$568$	−7.48331	+	7.48331i	−0.313993	+	0.313993i
$569$	−10.3923	+	6.00000i	−0.435668	+	0.251533i	−0.701758	−	0.712415i	$-0.747601\pi$
$569$	−10.3923	+	6.00000i	−0.435668	+	0.251533i	0.266090	+	0.963948i	$0.414268\pi$
$570$	−26.1244	+	17.2487i	−1.09423	+	0.722469i
$571$	−16.2019	−	9.35414i	−0.678026	−	0.391459i	0.121085	−	0.992642i	$-0.461363\pi$
$571$	−16.2019	−	9.35414i	−0.678026	−	0.391459i	−0.799111	+	0.601183i	$0.794696\pi$
$572$	5.47817	−	20.4448i	0.229054	−	0.854840i
$573$	−7.00000	−	7.00000i	−0.292429	−	0.292429i
$574$	11.2250			0.468521
$575$	13.0958	+	1.87083i	0.546133	+	0.0780189i
$576$	−16.0000	−	27.7128i	−0.666667	−	1.15470i
$577$	−1.09808	−	4.09808i	−0.0457135	−	0.170605i	0.939295	−	0.343110i	$-0.111480\pi$
$577$	−1.09808	−	4.09808i	−0.0457135	−	0.170605i	−0.985009	+	0.172505i	$0.944814\pi$
$578$	−12.2942	+	3.29423i	−0.511372	+	0.137022i
$579$	−9.35414	−	16.2019i	−0.388745	−	0.673326i
$580$	6.00000	−	12.0000i	0.249136	−	0.498273i
$581$	3.50000	−	6.06218i	0.145204	−	0.251502i
$582$	33.6749	+	33.6749i	1.39587	+	1.39587i
$583$	25.5560	+	6.84771i	1.05842	+	0.283603i
$584$	6.92820	+	4.00000i	0.286691	+	0.165521i
$585$	24.7846	+	5.07180i	1.02472	+	0.209693i
$586$	20.0000	+	34.6410i	0.826192	+	1.43101i
$587$	14.9666	+	14.9666i	0.617739	+	0.617739i	0.944951	−	0.327212i	$-0.106109\pi$
$587$	14.9666	+	14.9666i	0.617739	+	0.617739i	−0.327212	+	0.944951i	$0.606109\pi$
$588$	9.58679	+	35.7784i	0.395353	+	1.47548i
$589$			28.0000i			1.15372i
$590$	7.85028	−	8.85286i	0.323191	−	0.364466i
$591$	−3.24037	−	1.87083i	−0.133291	−	0.0769556i
$592$		0			0
$593$	5.49038	−	20.4904i	0.225463	−	0.841439i	−0.756756	−	0.653698i	$-0.773217\pi$
$593$	5.49038	−	20.4904i	0.225463	−	0.841439i	0.982219	−	0.187741i	$-0.0601166\pi$
$594$			14.0000i			0.574427i
$595$	−9.21982	−	13.9641i	−0.377976	−	0.572470i
$596$	−14.0000			−0.573462
$597$		0			0
$598$	2.73908	+	10.2224i	0.112009	+	0.418025i
$599$	−22.4499	+	38.8844i	−0.917280	+	1.58878i	−0.113751	+	0.993509i	$0.536287\pi$
$599$	−22.4499	+	38.8844i	−0.917280	+	1.58878i	−0.803529	+	0.595266i	$0.797047\pi$
$600$	14.6980	−	34.4089i	0.600043	−	1.40474i
$601$	4.00000			0.163163			0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000			0.163163			0.0815817	+	0.996667i	$0.474003\pi$
$602$	21.0000	−	21.0000i	0.855896	−	0.855896i
$603$	37.4166	−	37.4166i	1.52372	−	1.52372i
$604$	22.4499	+	38.8844i	0.913475	+	1.58219i
$605$	3.69615	+	5.59808i	0.150270	+	0.227594i
$606$	48.6056	+	28.0624i	1.97447	+	1.13996i
$607$	−11.6411	+	43.4452i	−0.472498	+	1.76339i	0.158251	+	0.987399i	$0.449414\pi$
$607$	−11.6411	+	43.4452i	−0.472498	+	1.76339i	−0.630749	+	0.775987i	$0.717252\pi$
$608$	−14.9666	+	14.9666i	−0.606977	+	0.606977i
$609$	−18.1865	+	10.5000i	−0.736956	+	0.425481i
$610$	−3.00000	−	9.00000i	−0.121466	−	0.364399i
$611$	−25.9230	+	14.9666i	−1.04873	+	0.605485i
$612$	−5.85641	−	21.8564i	−0.236731	−	0.883493i
$613$	−30.0526	+	8.05256i	−1.21381	+	0.325240i	−0.808256	−	0.588831i	$-0.799588\pi$
$613$	−30.0526	+	8.05256i	−1.21381	+	0.325240i	−0.405555	+	0.914071i	$0.632922\pi$
$614$	−9.35414	−	16.2019i	−0.377503	−	0.653854i
$615$	5.61249	+	16.8375i	0.226317	+	0.678952i
$616$	14.0000	+	24.2487i	0.564076	+	0.977008i
$617$	4.00000	−	4.00000i	0.161034	−	0.161034i	−0.621991	−	0.783025i	$-0.713676\pi$
$617$	4.00000	−	4.00000i	0.161034	−	0.161034i	0.783025	+	0.621991i	$0.213676\pi$
$618$	−2.56218	+	9.56218i	−0.103066	+	0.384647i
$619$	5.61249	−	9.72111i	0.225585	−	0.390724i	−0.730910	−	0.682474i	$-0.760904\pi$
$619$	5.61249	−	9.72111i	0.225585	−	0.390724i	0.956495	+	0.291750i	$0.0942374\pi$
$620$	−18.4396	−	27.9281i	−0.740554	−	1.12162i
$621$	−3.50000	−	6.06218i	−0.140450	−	0.243267i
$622$	18.7083	+	18.7083i	0.750134	+	0.750134i
$623$	−5.61249	+	5.61249i	−0.224860	+	0.224860i
$624$	29.9333			1.19829
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$	35.7784	−	9.58679i	1.42885	−	0.382860i
$628$	6.58846	−	24.5885i	0.262908	−	0.981186i
$629$		0			0
$630$	−27.9281	+	18.4396i	−1.11268	+	0.734653i
$631$		−	33.6749i		−	1.34058i	−0.742101	−	0.670289i	$-0.766170\pi$
$631$		−	33.6749i		−	1.34058i	0.742101	−	0.670289i	$-0.233830\pi$
$632$	2.73908	−	10.2224i	0.108955	−	0.406625i
$633$	28.6865	−	7.68653i	1.14019	−	0.305512i
$634$	17.3205	+	10.0000i	0.687885	+	0.397151i
$635$	17.7057	+	15.7006i	0.702630	+	0.623058i
$636$			37.4166i			1.48366i
$637$	−19.1244	−	5.12436i	−0.757735	−	0.203034i
$638$	−11.2250	+	11.2250i	−0.444401	+	0.444401i
$639$	7.48331	+	12.9615i	0.296035	+	0.512748i
$640$	5.07180	−	24.7846i	0.200480	−	0.979698i
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	−0.708631	−	0.705580i	$-0.750687\pi$
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	0.965365	+	0.260902i	$0.0840201\pi$
$642$	−47.8109	−	12.8109i	−1.88695	−	0.505605i
$643$	14.9666	−	14.9666i	0.590226	−	0.590226i	−0.347466	−	0.937692i	$-0.612958\pi$
$643$	14.9666	−	14.9666i	0.590226	−	0.590226i	0.937692	+	0.347466i	$0.112958\pi$
$644$	−12.1244	−	7.00000i	−0.477767	−	0.275839i
$645$	42.0000	+	21.0000i	1.65375	+	0.826874i
$646$	−12.9615	+	7.48331i	−0.509963	+	0.294427i
$647$	12.7780	−	3.42385i	0.502355	−	0.134606i	0.00126221	−	0.999999i	$-0.499598\pi$
$647$	12.7780	−	3.42385i	0.502355	−	0.134606i	0.501093	+	0.865394i	$0.332932\pi$
$648$	13.6603	−	3.66025i	0.536625	−	0.143788i
$649$	−12.1244	+	7.00000i	−0.475923	+	0.274774i
$650$	12.0000	+	16.0000i	0.470679	+	0.627572i
$651$			52.3832i			2.05306i
$652$	14.9666	+	14.9666i	0.586138	+	0.586138i
$653$	−10.9808	+	40.9808i	−0.429710	+	1.60370i	0.323706	+	0.946158i	$0.395071\pi$
$653$	−10.9808	+	40.9808i	−0.429710	+	1.60370i	−0.753417	+	0.657543i	$0.771596\pi$
$654$	−28.0624	+	48.6056i	−1.09733	+	1.90063i
$655$	−27.9281	+	18.4396i	−1.09124	+	0.720497i
$656$	6.00000	+	10.3923i	0.234261	+	0.405751i
$657$	8.00000	−	8.00000i	0.312110	−	0.312110i
$658$	10.2487	−	38.2487i	0.399536	−	1.49109i
$659$	−11.2250			−0.437263			−0.218631	−	0.975808i	$-0.570159\pi$
$659$	−11.2250			−0.437263			−0.218631	+	0.975808i	$0.570159\pi$
$660$	−29.3731	+	33.1244i	−1.14335	+	1.28936i
$661$	7.50000	−	12.9904i	0.291716	−	0.505267i	−0.682499	−	0.730886i	$-0.739107\pi$
$661$	7.50000	−	12.9904i	0.291716	−	0.505267i	0.974216	+	0.225619i	$0.0724404\pi$
$662$	−30.6672	+	8.21725i	−1.19191	+	0.319372i
$663$	20.4448	+	5.47817i	0.794010	+	0.212754i
$664$	7.48331			0.290409
$665$	16.5622	+	14.6865i	0.642254	+	0.569519i
$666$		0			0
$667$	2.05431	−	7.66680i	0.0795433	−	0.296860i
$668$	−4.10862	−	15.3336i	−0.158967	−	0.593275i
$669$	−12.1244	−	7.00000i	−0.468755	−	0.270636i
$670$	41.7578	−	2.50644i	1.61325	−	0.0968320i
$671$			11.2250i			0.433335i
$672$	−28.0000	+	28.0000i	−1.08012	+	1.08012i
$673$	−24.0000	−	24.0000i	−0.925132	−	0.925132i	0.0722542	−	0.997386i	$-0.476981\pi$
$673$	−24.0000	−	24.0000i	−0.925132	−	0.925132i	−0.997386	+	0.0722542i	$0.976981\pi$
$674$	36.3731	−	21.0000i	1.40104	−	0.808890i
$675$	−10.4059	−	8.16809i	−0.400523	−	0.314390i
$676$	5.00000	−	8.66025i	0.192308	−	0.333087i
$677$	24.5885	+	6.58846i	0.945011	+	0.253215i	0.698244	−	0.715860i	$-0.253965\pi$
$677$	24.5885	+	6.58846i	0.945011	+	0.253215i	0.246767	+	0.969075i	$0.420632\pi$
$678$	−3.74166	+	3.74166i	−0.143697	+	0.143697i
$679$	16.8375	−	29.1633i	0.646162	−	1.11919i
$680$	8.00000	−	16.0000i	0.306786	−	0.613572i
$681$		0			0
$682$	10.2487	+	38.2487i	0.392443	+	1.46462i
$683$	−8.90202	−	33.2228i	−0.340626	−	1.27123i	−0.897639	−	0.440731i	$-0.854719\pi$
$683$	−8.90202	−	33.2228i	−0.340626	−	1.27123i	0.557013	−	0.830504i	$-0.311947\pi$
$684$	14.9666	+	25.9230i	0.572263	+	0.991189i
$685$		0			0
$686$	22.6826	−	13.0958i	0.866025	−	0.500000i
$687$	−29.9333	−	29.9333i	−1.14203	−	1.14203i
$688$	30.6672	+	8.21725i	1.16918	+	0.313280i
$689$	−17.3205	−	10.0000i	−0.659859	−	0.380970i
$690$	4.43782	−	21.6865i	0.168945	−	0.825592i
$691$	35.6441	−	20.5791i	1.35596	−	0.782866i	0.366887	−	0.930265i	$-0.380423\pi$
$691$	35.6441	−	20.5791i	1.35596	−	0.782866i	0.989077	+	0.147399i	$0.0470901\pi$
$692$	−16.0000	+	16.0000i	−0.608229	+	0.608229i
$693$	38.2487	−	10.2487i	1.45295	−	0.389316i
$694$	−26.1916			−0.994220
$695$	−25.0547	+	1.50386i	−0.950379	+	0.0570447i
$696$	−19.4422	−	11.2250i	−0.736956	−	0.425481i
$697$	2.19615	+	8.19615i	0.0831852	+	0.310451i
$698$	4.02628	−	15.0263i	0.152397	−	0.568753i
$699$	−52.3832			−1.98131
$700$	−26.1916	−	3.74166i	−0.989949	−	0.141421i
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$	2.73908	−	10.2224i	0.103380	−	0.385820i
$703$		0			0
$704$	−14.9666	+	25.9230i	−0.564076	+	0.977008i
$705$	62.4974	−	3.75129i	2.35379	−	0.141282i
$706$	−34.0000			−1.27961
$707$	10.2716	−	38.3340i	0.386302	−	1.44170i
$708$	−14.0000	−	14.0000i	−0.526152	−	0.526152i
$709$	−4.33013	+	2.50000i	−0.162621	+	0.0938895i	−0.579102	−	0.815255i	$-0.696597\pi$
$709$	−4.33013	+	2.50000i	−0.162621	+	0.0938895i	0.416481	+	0.909145i	$0.363263\pi$
$710$	−2.37212	+	11.5919i	−0.0890239	+	0.435038i
$711$	−12.9615	−	7.48331i	−0.486094	−	0.280646i
$712$	−8.19615	−	2.19615i	−0.307164	−	0.0823043i
$713$	−14.0000	−	14.0000i	−0.524304	−	0.524304i
$714$	−24.2487	+	14.0000i	−0.907485	+	0.523937i
$715$	−7.48331	−	22.4499i	−0.279860	−	0.839580i
$716$	−12.9615	+	7.48331i	−0.484393	+	0.279665i
$717$	15.3731	+	57.3731i	0.574118	+	2.14264i
$718$	−8.21725	−	30.6672i	−0.306665	−	1.14449i
$719$	9.35414	+	16.2019i	0.348851	+	0.604227i	0.986046	−	0.166476i	$-0.0532387\pi$
$719$	9.35414	+	16.2019i	0.348851	+	0.604227i	−0.637195	+	0.770703i	$0.719905\pi$
$720$	−32.0000	−	16.0000i	−1.19257	−	0.596285i
$721$	7.00000			0.260694
$722$	−5.00000	+	5.00000i	−0.186081	+	0.186081i
$723$	30.6672	+	8.21725i	1.14053	+	0.305603i
$724$	−22.5167	−	13.0000i	−0.836825	−	0.483141i
$725$	−1.79423	−	14.8923i	−0.0666360	−	0.553086i
$726$	9.72111	−	5.61249i	0.360784	−	0.208299i
$727$	5.61249	+	5.61249i	0.208156	+	0.208156i	0.803483	−	0.595328i	$-0.202978\pi$
$727$	5.61249	+	5.61249i	0.208156	+	0.208156i	−0.595328	+	0.803483i	$0.702978\pi$
$728$	−5.47817	−	20.4448i	−0.203034	−	0.757735i
$729$		−	41.0000i		−	1.51852i
$730$	8.92820	−	0.535898i	0.330448	−	0.0198345i
$731$	19.4422	+	11.2250i	0.719097	+	0.415171i
$732$	−15.3336	+	4.10862i	−0.566746	+	0.151859i
$733$	−9.15064	+	34.1506i	−0.337986	+	1.26138i	0.562609	+	0.826723i	$0.309798\pi$
$733$	−9.15064	+	34.1506i	−0.337986	+	1.26138i	−0.900595	+	0.434659i	$0.856869\pi$
$734$	26.1916			0.966750
$735$	30.9850	+	27.4760i	1.14290	+	1.01347i
$736$		−	14.9666i		−	0.551677i
$737$	−47.8109	−	12.8109i	−1.76114	−	0.471895i
$738$	16.3923	−	4.39230i	0.603409	−	0.161683i
$739$	−20.5791	+	35.6441i	−0.757015	+	1.31119i	0.187351	+	0.982293i	$0.440010\pi$
$739$	−20.5791	+	35.6441i	−0.757015	+	1.31119i	−0.944366	+	0.328895i	$0.893324\pi$
$740$		0			0
$741$	−28.0000			−1.02861
$742$	25.5560	−	6.84771i	0.938190	−	0.251387i
$743$	−28.0624	+	28.0624i	−1.02951	+	1.02951i	−0.0299596	+	0.999551i	$0.509538\pi$
$743$	−28.0624	+	28.0624i	−1.02951	+	1.02951i	−0.999551	+	0.0299596i	$0.990462\pi$
$744$	−48.4974	+	28.0000i	−1.77800	+	1.02653i
$745$	−13.0622	+	8.62436i	−0.478561	+	0.315972i
$746$	−24.0000	+	41.5692i	−0.878702	+	1.52196i
$747$	2.73908	−	10.2224i	0.100218	−	0.374018i
$748$	−14.9666	+	14.9666i	−0.547234	+	0.547234i
$749$			35.0000i			1.27887i
$750$	−7.48331	−	41.1582i	−0.273252	−	1.50289i
$751$	−38.8844	+	22.4499i	−1.41891	+	0.819210i	−0.996204	−	0.0870549i	$-0.972254\pi$
$751$	−38.8844	+	22.4499i	−1.41891	+	0.819210i	−0.422710	+	0.906265i	$0.638921\pi$
$752$	40.8896	−	10.9563i	1.49109	−	0.399536i
$753$	−19.1244	+	5.12436i	−0.696930	+	0.186742i
$754$	10.3923	−	6.00000i	0.378465	−	0.218507i
$755$	44.8999	+	22.4499i	1.63407	+	0.817037i
$756$	7.00000	+	12.1244i	0.254588	+	0.440959i
$757$	10.0000	−	10.0000i	0.363456	−	0.363456i	−0.501628	−	0.865084i	$-0.667265\pi$
$757$	10.0000	−	10.0000i	0.363456	−	0.363456i	0.865084	+	0.501628i	$0.167265\pi$
$758$	−15.3336	−	4.10862i	−0.556941	−	0.149232i
$759$	−13.0958	+	22.6826i	−0.475347	+	0.823326i
$760$	−4.74423	+	23.1839i	−0.172091	+	0.840968i
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	−0.998684	−	0.0512772i	$-0.983671\pi$
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	0.454935	−	0.890525i	$-0.349663\pi$
$762$	28.0000	−	28.0000i	1.01433	−	1.01433i
$763$	38.3340	+	10.2716i	1.38778	+	0.371856i
$764$	−7.48331			−0.270737
$765$	−18.9282	−	16.7846i	−0.684351	−	0.606849i
$766$	−16.2019	−	9.35414i	−0.585397	−	0.337979i
$767$	10.2224	−	2.73908i	0.369109	−	0.0989026i
$768$	−40.8896	−	10.9563i	−1.47548	−	0.395353i
$769$		−	8.00000i		−	0.288487i	−0.989542	−	0.144244i	$-0.953925\pi$
$769$		−	8.00000i		−	0.288487i	0.989542	−	0.144244i	$-0.0460749\pi$
$770$	28.0000	+	14.0000i	1.00905	+	0.504525i
$771$			74.8331i			2.69505i
$772$	−13.6603	−	3.66025i	−0.491643	−	0.131735i
$773$	−35.5167	+	9.51666i	−1.27745	+	0.342290i	−0.832879	−	0.553455i	$-0.813309\pi$
$773$	−35.5167	+	9.51666i	−1.27745	+	0.342290i	−0.444567	+	0.895746i	$0.646642\pi$
$774$	22.4499	−	38.8844i	0.806947	−	1.39767i
$775$	−34.4089	−	14.6980i	−1.23600	−	0.527967i
$776$	36.0000			1.29232
$777$		0			0
$778$	−8.00000	−	8.00000i	−0.286814	−	0.286814i
$779$	−5.61249	−	9.72111i	−0.201088	−	0.348295i
$780$	27.9281	−	18.4396i	0.999987	−	0.660245i
$781$	7.00000	−	12.1244i	0.250480	−	0.433844i
$782$	2.73908	−	10.2224i	0.0979494	−	0.365552i
$783$	−5.61249	+	5.61249i	−0.200574	+	0.200574i
$784$	24.2487	+	14.0000i	0.866025	+	0.500000i
$785$	−9.00000	−	27.0000i	−0.321224	−	0.963671i
$786$	28.0000	+	48.4974i	0.998727	+	1.72985i
$787$	−38.3340	+	10.2716i	−1.36646	+	0.366142i	−0.866184	−	0.499725i	$-0.833434\pi$
$787$	−38.3340	+	10.2716i	−1.36646	+	0.366142i	−0.500275	+	0.865867i	$0.666768\pi$
$788$	−2.73205	+	0.732051i	−0.0973253	+	0.0260782i
$789$	−6.06218	+	3.50000i	−0.215819	+	0.124603i
$790$	−3.74166	−	11.2250i	−0.133122	−	0.399367i
$791$	3.24037	+	1.87083i	0.115214	+	0.0665190i
$792$	29.9333	+	29.9333i	1.06363	+	1.06363i
$793$	2.19615	−	8.19615i	0.0779877	−	0.291054i
$794$	19.0526	+	11.0000i	0.676150	+	0.390375i
$795$	23.0496	+	34.9101i	0.817484	+	1.23814i
$796$		0			0
$797$	8.00000	−	8.00000i	0.283375	−	0.283375i	−0.551079	−	0.834453i	$-0.685784\pi$
$797$	8.00000	−	8.00000i	0.283375	−	0.283375i	0.834453	+	0.551079i	$0.185784\pi$
$798$	26.1916	−	26.1916i	0.927173	−	0.927173i
$799$	29.9333			1.05896
$800$	−10.5359	−	26.2487i	−0.372500	−	0.928032i
$801$	−6.00000	+	10.3923i	−0.212000	+	0.367194i
$802$	−8.41858	−	31.4186i	−0.297271	−	1.10943i
$803$	−10.2224	−	2.73908i	−0.360741	−	0.0966602i
$804$		−	70.0000i		−	2.46871i
$805$	−15.6244	+	0.937822i	−0.550686	+	0.0330539i
$806$		−	29.9333i		−	1.05435i
$807$	8.90202	−	33.2228i	0.313366	−	1.16950i
$808$	40.9808	−	10.9808i	1.44170	−	0.386302i
$809$	42.4352	+	24.5000i	1.49194	+	0.861374i	0.999957	−	0.00922879i	$-0.00293766\pi$
$809$	42.4352	+	24.5000i	1.49194	+	0.861374i	0.491986	+	0.870603i	$0.336271\pi$
$810$	10.4904	−	11.8301i	0.368594	−	0.415668i
$811$		−	22.4499i		−	0.788324i	−0.919041	−	0.394162i	$-0.871035\pi$
$811$		−	22.4499i		−	0.788324i	0.919041	−	0.394162i	$-0.128965\pi$
$812$	−4.10862	+	15.3336i	−0.144184	+	0.538104i
$813$	21.0000	+	21.0000i	0.736502	+	0.736502i
$814$		0			0
$815$	23.1839	+	4.74423i	0.812096	+	0.166183i
$816$	−25.9230	−	14.9666i	−0.907485	−	0.523937i
$817$	−28.6865	−	7.68653i	−1.00361	−	0.268918i
$818$	−5.00000	−	5.00000i	−0.174821	−	0.174821i
$819$	−29.9333			−1.04595
$820$	12.0000	+	6.00000i	0.419058	+	0.209529i
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	0.511311	−	0.859396i	$-0.329160\pi$
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	−0.999914	+	0.0131101i	$0.995827\pi$
$822$		0			0
$823$	−6.16294	−	23.0004i	−0.214826	−	0.801743i	−0.986228	−	0.165394i	$-0.947110\pi$
$823$	−6.16294	−	23.0004i	−0.214826	−	0.801743i	0.771401	−	0.636349i	$-0.219556\pi$
$824$	3.74166	+	6.48074i	0.130347	+	0.225767i
$825$	−7.00000	+	49.0000i	−0.243709	+	1.70596i
$826$	−7.00000	+	12.1244i	−0.243561	+	0.421860i
$827$	9.35414	+	9.35414i	0.325275	+	0.325275i	0.850787	−	0.525511i	$-0.176126\pi$
$827$	9.35414	+	9.35414i	0.325275	+	0.325275i	−0.525511	+	0.850787i	$0.676126\pi$
$828$	−20.4448	−	5.47817i	−0.710506	−	0.190379i
$829$	17.3205	+	10.0000i	0.601566	+	0.347314i	0.769657	−	0.638457i	$-0.220427\pi$
$829$	17.3205	+	10.0000i	0.601566	+	0.347314i	−0.168091	+	0.985771i	$0.553760\pi$
$830$	6.98203	−	4.60991i	0.242350	−	0.160012i
$831$	−6.48074	+	3.74166i	−0.224814	+	0.129797i
$832$	16.0000	−	16.0000i	0.554700	−	0.554700i
$833$	14.0000	+	14.0000i	0.485071	+	0.485071i
$834$			42.0000i			1.45434i
$835$	−13.2793	−	11.7754i	−0.459549	−	0.407505i
$836$	14.0000	−	24.2487i	0.484200	−	0.838659i
$837$	5.12436	+	19.1244i	0.177124	+	0.661034i
$838$	−20.4448	−	5.47817i	−0.706254	−	0.189240i
$839$	−18.7083			−0.645882			−0.322941	−	0.946419i	$-0.604672\pi$
$839$	−18.7083			−0.645882			−0.322941	+	0.946419i	$0.604672\pi$
$840$	−8.87564	+	43.3731i	−0.306239	+	1.49651i
$841$	20.0000			0.689655
$842$	9.56218	+	2.56218i	0.329534	+	0.0882985i
$843$	−2.73908	−	10.2224i	−0.0943390	−	0.352078i
$844$	11.2250	−	19.4422i	0.386379	−	0.669229i
$845$	−0.669873	−	11.1603i	−0.0230443	−	0.383924i
$846$		−	59.8665i		−	2.05825i
$847$	−5.61249	−	5.61249i	−0.192847	−	0.192847i
$848$	20.0000	+	20.0000i	0.686803	+	0.686803i
$849$	24.2487	−	14.0000i	0.832214	−	0.480479i
$850$	−2.39230	−	19.8564i	−0.0820554	−	0.681069i
$851$		0			0
$852$	19.1244	+	5.12436i	0.655190	+	0.175558i
$853$	9.00000	+	9.00000i	0.308154	+	0.308154i	0.844193	−	0.536039i	$-0.180080\pi$
$853$	9.00000	+	9.00000i	0.308154	+	0.308154i	−0.536039	+	0.844193i	$0.680080\pi$
$854$	5.61249	+	9.72111i	0.192055	+	0.332650i
$855$	29.9333	+	14.9666i	1.02370	+	0.511848i
$856$	−32.4037	+	18.7083i	−1.10754	+	0.639436i
$857$	−9.15064	−	34.1506i	−0.312580	−	1.16656i	−0.926222	−	0.376979i	$-0.876963\pi$
$857$	−9.15064	−	34.1506i	−0.312580	−	1.16656i	0.613642	−	0.789584i	$-0.289704\pi$
$858$	−38.2487	+	10.2487i	−1.30579	+	0.349885i
$859$	−22.4499	−	38.8844i	−0.765982	−	1.32672i	−0.939726	−	0.341929i	$-0.888920\pi$
$859$	−22.4499	−	38.8844i	−0.765982	−	1.32672i	0.173744	−	0.984791i	$-0.444414\pi$
$860$	33.6749	−	11.2250i	1.14831	−	0.382768i
$861$	−10.5000	−	18.1865i	−0.357839	−	0.619795i
$862$	−11.2250	−	11.2250i	−0.382324	−	0.382324i
$863$	48.5564	+	13.0106i	1.65288	+	0.442888i	0.960417	−	0.278567i	$-0.0898594\pi$
$863$	48.5564	+	13.0106i	1.65288	+	0.442888i	0.692462	+	0.721454i	$0.256526\pi$
$864$	−7.48331	+	12.9615i	−0.254588	+	0.440959i
$865$	−5.07180	+	24.7846i	−0.172446	+	0.842702i
$866$	−23.0000	−	39.8372i	−0.781572	−	1.35372i
$867$	16.8375	+	16.8375i	0.571830	+	0.571830i
$868$	28.0000	+	28.0000i	0.950382	+	0.950382i
$869$			14.0000i			0.474917i
$870$	−25.0547	+	1.50386i	−0.849434	+	0.0509857i
$871$	32.4037	+	18.7083i	1.09796	+	0.633906i
$872$	10.9808	+	40.9808i	0.371856	+	1.38778i
$873$	13.1769	−	49.1769i	0.445971	−	1.66439i
$874$			14.0000i			0.473557i
$875$	−26.7421	+	12.6437i	−0.904046	+	0.427434i
$876$		−	14.9666i		−	0.505676i
$877$	12.2942	+	3.29423i	0.415147	+	0.111238i	0.460346	−	0.887740i	$-0.347726\pi$
$877$	12.2942	+	3.29423i	0.415147	+	0.111238i	−0.0451990	+	0.998978i	$0.514392\pi$
$878$		0			0
$879$	37.4166	−	64.8074i	1.26203	−	2.18590i
$880$	2.00515	+	33.4063i	0.0675935	+	1.12613i
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	28.0000	−	28.0000i	0.942809	−	0.942809i
$883$	−29.9333	+	29.9333i	−1.00733	+	1.00733i	−0.00736147	+	0.999973i	$0.502343\pi$
$883$	−29.9333	+	29.9333i	−1.00733	+	1.00733i	−0.999973	+	0.00736147i	$0.997657\pi$
$884$	13.8564	−	8.00000i	0.466041	−	0.269069i
$885$	−21.6865	−	4.43782i	−0.728985	−	0.149176i
$886$	9.72111	+	5.61249i	0.326587	+	0.188555i
$887$	3.42385	−	12.7780i	0.114962	−	0.429043i	−0.884322	−	0.466877i	$-0.845379\pi$
$887$	3.42385	−	12.7780i	0.114962	−	0.429043i	0.999284	+	0.0378338i	$0.0120458\pi$
$888$		0			0
$889$	−24.2487	−	14.0000i	−0.813276	−	0.469545i
$890$	−9.00000	+	3.00000i	−0.301681	+	0.100560i
$891$	−16.2019	+	9.35414i	−0.542782	+	0.313376i
$892$	−10.2224	+	2.73908i	−0.342271	+	0.0917113i
$893$	−38.2487	+	10.2487i	−1.27994	+	0.342960i
$894$	13.0958	+	22.6826i	0.437989	+	0.758619i
$895$	−7.48331	+	14.9666i	−0.250140	+	0.500279i
$896$			29.9333i			1.00000i
$897$	14.0000	−	14.0000i	0.467446	−	0.467446i
$898$	−12.8109	+	47.8109i	−0.427505	+	1.59547i
$899$	−11.2250	+	19.4422i	−0.374374	+	0.648434i
$900$	−39.7128	+	4.78461i	−1.32376	+	0.159487i
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$	−11.2250	−	11.2250i	−0.373751	−	0.373751i
$903$	−53.6676	−	14.3802i	−1.78595	−	0.478543i
$904$			4.00000i			0.133038i
$905$	−29.0167	+	1.74167i	−0.964546	+	0.0578951i
$906$	42.0000	−	72.7461i	1.39536	−	2.41683i
$907$	12.7780	−	3.42385i	0.424286	−	0.113687i	−0.0403565	−	0.999185i	$-0.512849\pi$
$907$	12.7780	−	3.42385i	0.424286	−	0.113687i	0.464643	+	0.885498i	$0.346183\pi$
$908$		0			0
$909$		−	60.0000i		−	1.99007i
$910$	−17.7057	−	15.7006i	−0.586939	−	0.520469i
$911$		−	48.6415i		−	1.61157i	−0.592211	−	0.805783i	$-0.701745\pi$
$911$		−	48.6415i		−	1.61157i	0.592211	−	0.805783i	$-0.298255\pi$
$912$	38.2487	+	10.2487i	1.26654	+	0.339369i
$913$	−9.56218	+	2.56218i	−0.316462	+	0.0847957i
$914$	−41.5692	−	24.0000i	−1.37499	−	0.793849i
$915$	−11.7754	+	13.2793i	−0.389283	+	0.439000i
$916$	−32.0000			−1.05731
$917$	28.0000	−	28.0000i	0.924641	−	0.924641i
$918$	−7.48331	+	7.48331i	−0.246986	+	0.246986i
$919$	5.61249	+	9.72111i	0.185139	+	0.320670i	0.943623	−	0.331021i	$-0.107393\pi$
$919$	5.61249	+	9.72111i	0.185139	+	0.320670i	−0.758484	+	0.651691i	$0.774060\pi$
$920$	−9.21982	−	13.9641i	−0.303969	−	0.460381i
$921$	−17.5000	+	30.3109i	−0.576645	+	0.998778i
$922$	−27.3205	−	7.32051i	−0.899753	−	0.241088i
$923$	−7.48331	+	7.48331i	−0.246316	+	0.246316i
$924$	26.1916	−	45.3652i	0.861640	−	1.49241i
$925$		0			0
$926$	42.1248	−	24.3208i	1.38431	−	0.799230i
$927$	10.2224	−	2.73908i	0.335748	−	0.0899633i
$928$	−16.3923	+	4.39230i	−0.538104	+	0.144184i
$929$	−28.5788	+	16.5000i	−0.937641	+	0.541347i	−0.889220	−	0.457480i	$-0.848752\pi$
$929$	−28.5788	+	16.5000i	−0.937641	+	0.541347i	−0.0484211	+	0.998827i	$0.515419\pi$
$930$	−28.0000	+	56.0000i	−0.918156	+	1.83631i
$931$	−22.6826	−	13.0958i	−0.743392	−	0.429198i
$932$	−28.0000	+	28.0000i	−0.917170	+	0.917170i
$933$	12.8109	−	47.8109i	0.419410	−	1.56526i
$934$	28.0624	−	48.6056i	0.918231	−	1.59042i
$935$	−4.74423	+	23.1839i	−0.155153	+	0.758194i
$936$	−16.0000	−	27.7128i	−0.522976	−	0.905822i
$937$	−12.0000	+	12.0000i	−0.392023	+	0.392023i	−0.875408	−	0.483385i	$-0.839407\pi$
$937$	−12.0000	+	12.0000i	−0.392023	+	0.392023i	0.483385	+	0.875408i	$0.339407\pi$
$938$	−47.8109	+	12.8109i	−1.56108	+	0.418290i
$939$	14.9666			0.488417
$940$	31.4011	−	35.4114i	1.02419	−	1.15499i
$941$	−24.0000	+	41.5692i	−0.782378	+	1.35512i	0.148176	+	0.988961i	$0.452660\pi$
$941$	−24.0000	+	41.5692i	−0.782378	+	1.35512i	−0.930553	+	0.366157i	$0.880673\pi$
$942$	−46.0008	+	12.3259i	−1.49879	+	0.401599i
$943$	7.66680	+	2.05431i	0.249665	+	0.0668976i
$944$	−14.9666			−0.487122
$945$	14.0000	+	7.00000i	0.455420	+	0.227710i
$946$	−42.0000			−1.36554
$947$	−4.79340	+	17.8892i	−0.155764	+	0.581321i	0.843274	+	0.537484i	$0.180625\pi$
$947$	−4.79340	+	17.8892i	−0.155764	+	0.581321i	−0.999039	+	0.0438373i	$0.986042\pi$
$948$	−19.1244	+	5.12436i	−0.621130	+	0.166431i
$949$	6.92820	+	4.00000i	0.224899	+	0.129845i
$950$	9.85543	+	24.5534i	0.319752	+	0.796618i
$951$		−	37.4166i		−	1.21332i
$952$	−5.47817	+	20.4448i	−0.177548	+	0.662620i
$953$	36.0000	+	36.0000i	1.16615	+	1.16615i	0.983103	+	0.183051i	$0.0585973\pi$
$953$	36.0000	+	36.0000i	1.16615	+	1.16615i	0.183051	+	0.983103i	$0.441403\pi$
$954$	34.6410	−	20.0000i	1.12154	−	0.647524i
$955$	−6.98203	+	4.60991i	−0.225933	+	0.149173i
$956$	38.8844	+	22.4499i	1.25761	+	0.726083i
$957$	28.6865	+	7.68653i	0.927304	+	0.248470i
$958$	−7.48331	+	7.48331i	−0.241775	+	0.241775i
$959$		0			0
$960$	−44.8999	+	14.9666i	−1.44914	+	0.483046i
$961$	12.5000	+	21.6506i	0.403226	+	0.698408i
$962$		0			0
$963$	13.6954	+	51.1120i	0.441329	+	1.64706i
$964$	20.7846	−	12.0000i	0.669427	−	0.386494i
$965$	−15.0000	+	5.00000i	−0.482867	+	0.160956i
$966$			26.1916i			0.842701i
$967$	24.3208	+	24.3208i	0.782103	+	0.782103i	0.980185	−	0.198082i	$-0.0634713\pi$
$967$	24.3208	+	24.3208i	0.782103	+	0.782103i	−0.198082	+	0.980185i	$0.563471\pi$
$968$	2.19615	−	8.19615i	0.0705870	−	0.263434i
$969$	24.2487	+	14.0000i	0.778981	+	0.449745i
$970$	33.5885	−	22.1769i	1.07846	−	0.712058i
$971$	38.8844	−	22.4499i	1.24786	−	0.720453i	0.277179	−	0.960818i	$-0.410601\pi$
$971$	38.8844	−	22.4499i	1.24786	−	0.720453i	0.970682	+	0.240365i	$0.0772673\pi$
$972$	−29.9333	−	29.9333i	−0.960110	−	0.960110i
$973$	28.6865	−	7.68653i	0.919648	−	0.246419i
$974$		0			0
$975$	14.6980	−	34.4089i	0.470712	−	1.10197i
$976$	−6.00000	+	10.3923i	−0.192055	+	0.332650i
$977$	−0.366025	−	1.36603i	−0.0117102	−	0.0437030i	0.959824	−	0.280604i	$-0.0905349\pi$
$977$	−0.366025	−	1.36603i	−0.0117102	−	0.0437030i	−0.971534	+	0.236901i	$0.923868\pi$
$978$	10.2487	−	38.2487i	0.327718	−	1.22306i
$979$	11.2250			0.358752
$980$	31.2487	−	1.87564i	0.998203	−	0.0599153i
$981$	60.0000			1.91565
$982$	8.21725	−	30.6672i	0.262223	−	0.978629i
$983$	2.05431	+	7.66680i	0.0655224	+	0.244533i	0.990918	−	0.134471i	$-0.0429334\pi$
$983$	2.05431	+	7.66680i	0.0655224	+	0.244533i	−0.925395	+	0.379004i	$0.876267\pi$
$984$	11.2250	−	19.4422i	0.357839	−	0.619795i
$985$	−2.09808	+	2.36603i	−0.0668503	+	0.0753878i
$986$	−12.0000			−0.382158
$987$	−71.5568	+	19.1736i	−2.27768	+	0.610302i
$988$	−14.9666	+	14.9666i	−0.476152	+	0.476152i
$989$	18.1865	−	10.5000i	0.578298	−	0.333881i
$990$	46.3678	+	9.48846i	1.47366	+	0.301563i
$991$	32.4037	+	18.7083i	1.02934	+	0.594288i	0.916795	−	0.399359i	$-0.130767\pi$
$991$	32.4037	+	18.7083i	1.02934	+	0.594288i	0.112543	+	0.993647i	$0.464100\pi$
$992$	−10.9563	+	40.8896i	−0.347864	+	1.29825i
$993$	42.0000	+	42.0000i	1.33283	+	1.33283i
$994$		−	14.0000i		−	0.444053i
$995$		0			0
$996$	−7.00000	−	12.1244i	−0.221803	−	0.384175i
$997$	1.09808	+	4.09808i	0.0347764	+	0.129787i	0.981132	−	0.193341i	$-0.0619322\pi$
$997$	1.09808	+	4.09808i	0.0347764	+	0.129787i	−0.946355	+	0.323128i	$0.895266\pi$
$998$	15.0650	+	56.2232i	0.476873	+	1.77971i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.a.123.2	yes	8
4.3	odd	2	inner	140.2.w.a.123.1	yes	8
5.2	odd	4	inner	140.2.w.a.67.2	yes	8
5.3	odd	4		700.2.be.c.207.1		8
5.4	even	2		700.2.be.c.543.1		8
7.2	even	3	inner	140.2.w.a.23.1	✓	8
7.3	odd	6		980.2.k.g.883.1		4
7.4	even	3		980.2.k.e.883.2		4
7.5	odd	6		980.2.x.f.863.2		8
7.6	odd	2		980.2.x.f.263.1		8
20.3	even	4		700.2.be.c.207.2		8
20.7	even	4	inner	140.2.w.a.67.1	yes	8
20.19	odd	2		700.2.be.c.543.2		8
28.3	even	6		980.2.k.g.883.2		4
28.11	odd	6		980.2.k.e.883.1		4
28.19	even	6		980.2.x.f.863.1		8
28.23	odd	6	inner	140.2.w.a.23.2	yes	8
28.27	even	2		980.2.x.f.263.2		8
35.2	odd	12	inner	140.2.w.a.107.1	yes	8
35.9	even	6		700.2.be.c.443.2		8
35.12	even	12		980.2.x.f.667.2		8
35.17	even	12		980.2.k.g.687.2		4
35.23	odd	12		700.2.be.c.107.2		8
35.27	even	4		980.2.x.f.67.1		8
35.32	odd	12		980.2.k.e.687.1		4
140.23	even	12		700.2.be.c.107.1		8
140.27	odd	4		980.2.x.f.67.2		8
140.47	odd	12		980.2.x.f.667.1		8
140.67	even	12		980.2.k.e.687.2		4
140.79	odd	6		700.2.be.c.443.1		8
140.87	odd	12		980.2.k.g.687.1		4
140.107	even	12	inner	140.2.w.a.107.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.a.23.1	✓	8	7.2	even	3	inner
140.2.w.a.23.2	yes	8	28.23	odd	6	inner
140.2.w.a.67.1	yes	8	20.7	even	4	inner
140.2.w.a.67.2	yes	8	5.2	odd	4	inner
140.2.w.a.107.1	yes	8	35.2	odd	12	inner
140.2.w.a.107.2	yes	8	140.107	even	12	inner
140.2.w.a.123.1	yes	8	4.3	odd	2	inner
140.2.w.a.123.2	yes	8	1.1	even	1	trivial
700.2.be.c.107.1		8	140.23	even	12
700.2.be.c.107.2		8	35.23	odd	12
700.2.be.c.207.1		8	5.3	odd	4
700.2.be.c.207.2		8	20.3	even	4
700.2.be.c.443.1		8	140.79	odd	6
700.2.be.c.443.2		8	35.9	even	6
700.2.be.c.543.1		8	5.4	even	2
700.2.be.c.543.2		8	20.19	odd	2
980.2.k.e.687.1		4	35.32	odd	12
980.2.k.e.687.2		4	140.67	even	12
980.2.k.e.883.1		4	28.11	odd	6
980.2.k.e.883.2		4	7.4	even	3
980.2.k.g.687.1		4	140.87	odd	12
980.2.k.g.687.2		4	35.17	even	12
980.2.k.g.883.1		4	7.3	odd	6
980.2.k.g.883.2		4	28.3	even	6
980.2.x.f.67.1		8	35.27	even	4
980.2.x.f.67.2		8	140.27	odd	4
980.2.x.f.263.1		8	7.6	odd	2
980.2.x.f.263.2		8	28.27	even	2
980.2.x.f.667.1		8	140.47	odd	12
980.2.x.f.667.2		8	35.12	even	12
980.2.x.f.863.1		8	28.19	even	6
980.2.x.f.863.2		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(0.684771 + 2.55560i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.23205 - 0.133975i) q^{5} -3.74166i q^{6} +(-2.55560 + 0.684771i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.46410 + 2.00000i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(3.24037 + 1.87083i) q^{11} +(-1.36954 + 5.11120i) q^{12} +(-2.00000 - 2.00000i) q^{13} +3.74166 q^{14} +(1.87083 + 5.61249i) q^{15} +(2.00000 + 3.46410i) q^{16} +(0.732051 + 2.73205i) q^{17} +(5.46410 - 1.46410i) q^{18} +(-1.87083 - 3.24037i) q^{19} +(4.00000 + 2.00000i) q^{20} +(-3.50000 - 6.06218i) q^{21} +(-3.74166 - 3.74166i) q^{22} +(2.55560 + 0.684771i) q^{23} +(3.74166 - 6.48074i) q^{24} +(4.96410 - 0.598076i) q^{25} +(2.00000 + 3.46410i) q^{26} +(-1.87083 - 1.87083i) q^{27} +(-5.11120 - 1.36954i) q^{28} -3.00000i q^{29} +(-0.501287 - 8.35157i) q^{30} +(-6.48074 - 3.74166i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-2.56218 + 9.56218i) q^{33} -4.00000i q^{34} +(-5.61249 + 1.87083i) q^{35} -8.00000 q^{36} +(1.36954 + 5.11120i) q^{38} +(3.74166 - 6.48074i) q^{39} +(-4.73205 - 4.19615i) q^{40} +3.00000 q^{41} +(2.56218 + 9.56218i) q^{42} +(5.61249 - 5.61249i) q^{43} +(3.74166 + 6.48074i) q^{44} +(-7.46410 + 4.92820i) q^{45} +(-3.24037 - 1.87083i) q^{46} +(2.73908 - 10.2224i) q^{47} +(-7.48331 + 7.48331i) q^{48} +(6.06218 - 3.50000i) q^{49} +(-7.00000 - 1.00000i) q^{50} +(-6.48074 + 3.74166i) q^{51} +(-1.46410 - 5.46410i) q^{52} +(6.83013 - 1.83013i) q^{53} +(1.87083 + 3.24037i) q^{54} +(7.48331 + 3.74166i) q^{55} +(6.48074 + 3.74166i) q^{56} +(7.00000 - 7.00000i) q^{57} +(-1.09808 + 4.09808i) q^{58} +(-1.87083 + 3.24037i) q^{59} +(-2.37212 + 11.5919i) q^{60} +(1.50000 + 2.59808i) q^{61} +(7.48331 + 7.48331i) q^{62} +(7.48331 - 7.48331i) q^{63} +8.00000i q^{64} +(-4.73205 - 4.19615i) q^{65} +(7.00000 - 12.1244i) q^{66} +(-12.7780 + 3.42385i) q^{67} +(-1.46410 + 5.46410i) q^{68} +7.00000i q^{69} +(8.35157 - 0.501287i) q^{70} -3.74166i q^{71} +(10.9282 + 2.92820i) q^{72} +(-2.73205 + 0.732051i) q^{73} +(4.92772 + 12.2767i) q^{75} -7.48331i q^{76} +(-9.56218 - 2.56218i) q^{77} +(-7.48331 + 7.48331i) q^{78} +(1.87083 + 3.24037i) q^{79} +(4.92820 + 7.46410i) q^{80} +(-2.50000 + 4.33013i) q^{81} +(-4.09808 - 1.09808i) q^{82} +(-1.87083 + 1.87083i) q^{83} -14.0000i q^{84} +(2.00000 + 6.00000i) q^{85} +(-9.72111 + 5.61249i) q^{86} +(7.66680 - 2.05431i) q^{87} +(-2.73908 - 10.2224i) q^{88} +(2.59808 - 1.50000i) q^{89} +(12.0000 - 4.00000i) q^{90} +(6.48074 + 3.74166i) q^{91} +(3.74166 + 3.74166i) q^{92} +(5.12436 - 19.1244i) q^{93} +(-7.48331 + 12.9615i) q^{94} +(-4.60991 - 6.98203i) q^{95} +(12.9615 - 7.48331i) q^{96} +(-9.00000 + 9.00000i) q^{97} +(-9.56218 + 2.56218i) q^{98} -14.9666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8} - 4 q^{10} - 16 q^{13} + 16 q^{16} - 8 q^{17} + 16 q^{18} + 32 q^{20} - 28 q^{21} + 12 q^{25} + 16 q^{26} + 16 q^{32} + 28 q^{33} - 64 q^{36} - 24 q^{40} + 24 q^{41} - 28 q^{42}+ \cdots - 28 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8 - 4 * q^10 - 16 * q^13 + 16 * q^16 - 8 * q^17 + 16 * q^18 + 32 * q^20 - 28 * q^21 + 12 * q^25 + 16 * q^26 + 16 * q^32 + 28 * q^33 - 64 * q^36 - 24 * q^40 + 24 * q^41 - 28 * q^42 - 32 * q^45 - 56 * q^50 + 16 * q^52 + 20 * q^53 + 56 * q^57 + 12 * q^58 + 12 * q^61 - 24 * q^65 + 56 * q^66 + 16 * q^68 + 32 * q^72 - 8 * q^73 - 28 * q^77 - 16 * q^80 - 20 * q^81 - 12 * q^82 + 16 * q^85 + 96 * q^90 - 56 * q^93 - 72 * q^97 - 28 * q^98

Introduction

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