LMFDB - Embedded newform 672.2.bs.a.155.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.9
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21431 - 0.724880i) q^{2} +(-1.31477 - 1.12755i) q^{3} +(0.949098 + 1.76046i) q^{4} +(0.733476 - 1.77077i) q^{5} +(0.779205 + 2.32225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.123621 - 2.82572i) q^{8} +(0.457262 + 2.96495i) q^{9} +O(q^{10})$	\(q+(-1.21431 - 0.724880i) q^{2} +(-1.31477 - 1.12755i) q^{3} +(0.949098 + 1.76046i) q^{4} +(0.733476 - 1.77077i) q^{5} +(0.779205 + 2.32225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.123621 - 2.82572i) q^{8} +(0.457262 + 2.96495i) q^{9} +(-2.17426 + 1.61858i) q^{10} +(0.219221 - 0.529247i) q^{11} +(0.737155 - 3.38476i) q^{12} +(5.66926 - 2.34828i) q^{13} +(1.37121 - 0.346079i) q^{14} +(-2.96098 + 1.50113i) q^{15} +(-2.19842 + 3.34170i) q^{16} +0.0922529 q^{17} +(1.59397 - 3.93183i) q^{18} +(-1.63700 - 3.95206i) q^{19} +(3.81350 - 0.389379i) q^{20} +(1.72698 - 0.132387i) q^{21} +(-0.649843 + 0.483761i) q^{22} +(1.32228 - 1.32228i) q^{23} +(-3.34868 + 3.57580i) q^{24} +(0.937904 + 0.937904i) q^{25} +(-8.58646 - 1.25799i) q^{26} +(2.74193 - 4.41382i) q^{27} +(-1.91595 - 0.573718i) q^{28} +(2.81672 - 1.16673i) q^{29} +(4.68369 + 0.323522i) q^{30} -0.629905i q^{31} +(5.09190 - 2.46426i) q^{32} +(-0.884979 + 0.448658i) q^{33} +(-0.112024 - 0.0668723i) q^{34} +(0.733476 + 1.77077i) q^{35} +(-4.78568 + 3.61902i) q^{36} +(-0.995577 - 0.412381i) q^{37} +(-0.876947 + 5.98565i) q^{38} +(-10.1016 - 3.30491i) q^{39} +(-4.91303 - 2.29150i) q^{40} +(-8.34848 - 8.34848i) q^{41} +(-2.19306 - 1.09110i) q^{42} +(2.69663 + 1.11698i) q^{43} +(1.13978 - 0.116378i) q^{44} +(5.58562 + 1.36501i) q^{45} +(-2.56415 + 0.647162i) q^{46} +3.09832i q^{47} +(6.65836 - 1.91474i) q^{48} -1.00000i q^{49} +(-0.459038 - 1.81877i) q^{50} +(-0.121292 - 0.104020i) q^{51} +(9.51473 + 7.75174i) q^{52} +(-1.53979 - 0.637803i) q^{53} +(-6.52904 + 3.37218i) q^{54} +(-0.776380 - 0.776380i) q^{55} +(1.91068 + 2.08550i) q^{56} +(-2.30386 + 7.04186i) q^{57} +(-4.26611 - 0.625020i) q^{58} +(-10.1572 - 4.20725i) q^{59} +(-5.45294 - 3.78797i) q^{60} +(-1.88016 - 4.53912i) q^{61} +(-0.456606 + 0.764900i) q^{62} +(-2.41987 - 1.77320i) q^{63} +(-7.96944 - 0.698638i) q^{64} -11.7613i q^{65} +(1.39986 + 0.0966944i) q^{66} +(-13.7897 + 5.71188i) q^{67} +(0.0875571 + 0.162407i) q^{68} +(-3.22943 + 0.247562i) q^{69} +(0.392927 - 2.68194i) q^{70} +(-8.75458 - 8.75458i) q^{71} +(8.43465 - 0.925567i) q^{72} +(5.82153 - 5.82153i) q^{73} +(0.910012 + 1.22243i) q^{74} +(-0.175598 - 2.29066i) q^{75} +(5.40376 - 6.63276i) q^{76} +(0.219221 + 0.529247i) q^{77} +(9.87081 + 11.3356i) q^{78} -9.22448 q^{79} +(4.30487 + 6.34395i) q^{80} +(-8.58182 + 2.71152i) q^{81} +(4.08600 + 16.1893i) q^{82} +(15.3286 - 6.34931i) q^{83} +(1.87214 + 2.91463i) q^{84} +(0.0676653 - 0.163358i) q^{85} +(-2.46487 - 3.31109i) q^{86} +(-5.01890 - 1.64202i) q^{87} +(-1.46841 - 0.684885i) q^{88} +(0.611762 - 0.611762i) q^{89} +(-5.79321 - 5.70645i) q^{90} +(-2.34828 + 5.66926i) q^{91} +(3.58278 + 1.07284i) q^{92} +(-0.710250 + 0.828183i) q^{93} +(2.24591 - 3.76232i) q^{94} -8.19888 q^{95} +(-9.47327 - 2.50142i) q^{96} +14.3946 q^{97} +(-0.724880 + 1.21431i) q^{98} +(1.66943 + 0.407975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

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 $

$2$	−1.21431	−	0.724880i	−0.858647	−	0.512567i
$2$	−1.21431	−	0.724880i	−0.858647	−	0.512567i
$3$	−1.31477	−	1.12755i	−0.759085	−	0.650991i
$3$	−1.31477	−	1.12755i	−0.759085	−	0.650991i
$4$	0.949098	+	1.76046i	0.474549	+	0.880229i
$5$	0.733476	−	1.77077i	0.328020	−	0.791911i	−0.670719	−	0.741712i	$-0.734014\pi$
$5$	0.733476	−	1.77077i	0.328020	−	0.791911i	0.998739	−	0.0501996i	$-0.0159857\pi$
$6$	0.779205	+	2.32225i	0.318109	+	0.948054i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.123621	−	2.82572i	0.0437066	−	0.999044i
$9$	0.457262	+	2.96495i	0.152421	+	0.988316i
$10$	−2.17426	+	1.61858i	−0.687562	+	0.511840i
$11$	0.219221	−	0.529247i	0.0660977	−	0.159574i	−0.887379	−	0.461041i	$-0.847476\pi$
$11$	0.219221	−	0.529247i	0.0660977	−	0.159574i	0.953477	+	0.301467i	$0.0974762\pi$
$12$	0.737155	−	3.38476i	0.212798	−	0.977096i
$13$	5.66926	−	2.34828i	1.57237	−	0.651296i	0.585187	−	0.810898i	$-0.301021\pi$
$13$	5.66926	−	2.34828i	1.57237	−	0.651296i	0.987181	+	0.159602i	$0.0510211\pi$
$14$	1.37121	−	0.346079i	0.366472	−	0.0924936i
$15$	−2.96098	+	1.50113i	−0.764523	+	0.387590i
$16$	−2.19842	+	3.34170i	−0.549606	+	0.835424i
$17$	0.0922529			0.0223746			0.0111873	−	0.999937i	$-0.496439\pi$
$17$	0.0922529			0.0223746			0.0111873	+	0.999937i	$0.496439\pi$
$18$	1.59397	−	3.93183i	0.375703	−	0.926740i
$19$	−1.63700	−	3.95206i	−0.375553	−	0.906665i	−0.992788	−	0.119886i	$-0.961747\pi$
$19$	−1.63700	−	3.95206i	−0.375553	−	0.906665i	0.617235	−	0.786779i	$-0.288253\pi$
$20$	3.81350	−	0.389379i	0.852725	−	0.0870677i
$21$	1.72698	−	0.132387i	0.376859	−	0.0288893i
$22$	−0.649843	+	0.483761i	−0.138547	+	0.103138i
$23$	1.32228	−	1.32228i	0.275714	−	0.275714i	−0.555681	−	0.831395i	$-0.687543\pi$
$23$	1.32228	−	1.32228i	0.275714	−	0.275714i	0.831395	+	0.555681i	$0.187543\pi$
$24$	−3.34868	+	3.57580i	−0.683546	+	0.729907i
$25$	0.937904	+	0.937904i	0.187581	+	0.187581i
$26$	−8.58646	−	1.25799i	−1.68394	−	0.246711i
$27$	2.74193	−	4.41382i	0.527685	−	0.849440i
$28$	−1.91595	−	0.573718i	−0.362080	−	0.108423i
$29$	2.81672	−	1.16673i	0.523053	−	0.216655i	−0.105505	−	0.994419i	$-0.533646\pi$
$29$	2.81672	−	1.16673i	0.523053	−	0.216655i	0.628557	+	0.777763i	$0.283646\pi$
$30$	4.68369	+	0.323522i	0.855121	+	0.0590668i
$31$		−	0.629905i		−	0.113134i	−0.998399	−	0.0565672i	$-0.981985\pi$
$31$		−	0.629905i		−	0.113134i	0.998399	−	0.0565672i	$-0.0180155\pi$
$32$	5.09190	−	2.46426i	0.900129	−	0.435624i
$33$	−0.884979	+	0.448658i	−0.154055	+	0.0781013i
$34$	−0.112024	−	0.0668723i	−0.0192119	−	0.0114685i
$35$	0.733476	+	1.77077i	0.123980	+	0.299314i
$36$	−4.78568	+	3.61902i	−0.797613	+	0.603169i
$37$	−0.995577	−	0.412381i	−0.163672	−	0.0677951i	0.299343	−	0.954145i	$-0.403232\pi$
$37$	−0.995577	−	0.412381i	−0.163672	−	0.0677951i	−0.463015	+	0.886350i	$0.653232\pi$
$38$	−0.876947	+	5.98565i	−0.142260	+	0.971001i
$39$	−10.1016	−	3.30491i	−1.61755	−	0.529209i
$40$	−4.91303	−	2.29150i	−0.776818	−	0.362319i
$41$	−8.34848	−	8.34848i	−1.30381	−	1.30381i	−0.925800	−	0.378014i	$-0.876607\pi$
$41$	−8.34848	−	8.34848i	−1.30381	−	1.30381i	−0.378014	−	0.925800i	$-0.623393\pi$
$42$	−2.19306	−	1.09110i	−0.338396	−	0.168360i
$43$	2.69663	+	1.11698i	0.411232	+	0.170338i	0.578702	−	0.815539i	$-0.303560\pi$
$43$	2.69663	+	1.11698i	0.411232	+	0.170338i	−0.167470	+	0.985877i	$0.553560\pi$
$44$	1.13978	−	0.116378i	0.171828	−	0.0175446i
$45$	5.58562	+	1.36501i	0.832655	+	0.203484i
$46$	−2.56415	+	0.647162i	−0.378063	+	0.0954189i
$47$			3.09832i			0.451937i	0.974135	+	0.225968i	$0.0725546\pi$
$47$			3.09832i			0.451937i	−0.974135	+	0.225968i	$0.927445\pi$
$48$	6.65836	−	1.91474i	0.961052	−	0.276369i
$49$		−	1.00000i		−	0.142857i
$50$	−0.459038	−	1.81877i	−0.0649178	−	0.257213i
$51$	−0.121292	−	0.104020i	−0.0169842	−	0.0145657i
$52$	9.51473	+	7.75174i	1.31946	+	1.07497i
$53$	−1.53979	−	0.637803i	−0.211507	−	0.0876090i	0.274415	−	0.961611i	$-0.411516\pi$
$53$	−1.53979	−	0.637803i	−0.211507	−	0.0876090i	−0.485921	+	0.874002i	$0.661516\pi$
$54$	−6.52904	+	3.37218i	−0.888490	+	0.458895i
$55$	−0.776380	−	0.776380i	−0.104687	−	0.104687i
$56$	1.91068	+	2.08550i	0.255325	+	0.278687i
$57$	−2.30386	+	7.04186i	−0.305154	+	0.932717i
$58$	−4.26611	−	0.625020i	−0.560168	−	0.0820692i
$59$	−10.1572	−	4.20725i	−1.32235	−	0.547737i	−0.393889	−	0.919158i	$-0.628871\pi$
$59$	−10.1572	−	4.20725i	−1.32235	−	0.547737i	−0.928465	+	0.371421i	$0.878871\pi$
$60$	−5.45294	−	3.78797i	−0.703971	−	0.489025i
$61$	−1.88016	−	4.53912i	−0.240730	−	0.581174i	0.756625	−	0.653849i	$-0.226847\pi$
$61$	−1.88016	−	4.53912i	−0.240730	−	0.581174i	−0.997356	+	0.0726742i	$0.976847\pi$
$62$	−0.456606	+	0.764900i	−0.0579890	+	0.0971424i
$63$	−2.41987	−	1.77320i	−0.304875	−	0.223402i
$64$	−7.96944	−	0.698638i	−0.996179	−	0.0873297i
$65$		−	11.7613i		−	1.45881i
$66$	1.39986	+	0.0966944i	0.172311	+	0.0119023i
$67$	−13.7897	+	5.71188i	−1.68468	+	0.697817i	−0.999532	−	0.0305887i	$-0.990262\pi$
$67$	−13.7897	+	5.71188i	−1.68468	+	0.697817i	−0.685146	+	0.728405i	$0.740262\pi$
$68$	0.0875571	+	0.162407i	0.0106179	+	0.0196948i
$69$	−3.22943	+	0.247562i	−0.388778	+	0.0298030i
$70$	0.392927	−	2.68194i	0.0469637	−	0.320553i
$71$	−8.75458	−	8.75458i	−1.03898	−	1.03898i	−0.999209	−	0.0397688i	$-0.987338\pi$
$71$	−8.75458	−	8.75458i	−1.03898	−	1.03898i	−0.0397688	−	0.999209i	$-0.512662\pi$
$72$	8.43465	−	0.925567i	0.994033	−	0.109079i
$73$	5.82153	−	5.82153i	0.681358	−	0.681358i	−0.278948	−	0.960306i	$-0.589986\pi$
$73$	5.82153	−	5.82153i	0.681358	−	0.681358i	0.960306	+	0.278948i	$0.0899857\pi$
$74$	0.910012	+	1.22243i	0.105787	+	0.142105i
$75$	−0.175598	−	2.29066i	−0.0202763	−	0.264503i
$76$	5.40376	−	6.63276i	0.619854	−	0.760829i
$77$	0.219221	+	0.529247i	0.0249826	+	0.0603133i
$78$	9.87081	+	11.3356i	1.11765	+	1.28351i
$79$	−9.22448			−1.03783			−0.518917	−	0.854824i	$-0.673665\pi$
$79$	−9.22448			−1.03783			−0.518917	+	0.854824i	$0.673665\pi$
$80$	4.30487	+	6.34395i	0.481299	+	0.709275i
$81$	−8.58182	+	2.71152i	−0.953536	+	0.301279i
$82$	4.08600	+	16.1893i	0.451223	+	1.78781i
$83$	15.3286	−	6.34931i	1.68253	−	0.696928i	0.683090	−	0.730334i	$-0.260635\pi$
$83$	15.3286	−	6.34931i	1.68253	−	0.696928i	0.999442	+	0.0334061i	$0.0106355\pi$
$84$	1.87214	+	2.91463i	0.204267	+	0.318013i
$85$	0.0676653	−	0.163358i	0.00733933	−	0.0177187i
$86$	−2.46487	−	3.31109i	−0.265793	−	0.357044i
$87$	−5.01890	−	1.64202i	−0.538082	−	0.176043i
$88$	−1.46841	−	0.684885i	−0.156533	−	0.0730090i
$89$	0.611762	−	0.611762i	0.0648466	−	0.0648466i	−0.673940	−	0.738786i	$-0.735399\pi$
$89$	0.611762	−	0.611762i	0.0648466	−	0.0648466i	0.738786	+	0.673940i	$0.235399\pi$
$90$	−5.79321	−	5.70645i	−0.610658	−	0.601513i
$91$	−2.34828	+	5.66926i	−0.246167	+	0.594299i
$92$	3.58278	+	1.07284i	0.373531	+	0.111852i
$93$	−0.710250	+	0.828183i	−0.0736494	+	0.0858786i
$94$	2.24591	−	3.76232i	0.231648	−	0.388054i
$95$	−8.19888			−0.841187
$96$	−9.47327	−	2.50142i	−0.966862	−	0.255300i
$97$	14.3946			1.46155			0.730775	−	0.682619i	$-0.239159\pi$
$97$	14.3946			1.46155			0.730775	+	0.682619i	$0.239159\pi$
$98$	−0.724880	+	1.21431i	−0.0732239	+	0.122664i
$99$	1.66943	+	0.407975i	0.167784	+	0.0410030i
$100$	−0.760977	+	2.54130i	−0.0760977	+	0.254130i
$101$	−6.31165	+	15.2377i	−0.628033	+	1.51620i	0.214031	+	0.976827i	$0.431341\pi$
$101$	−6.31165	+	15.2377i	−0.628033	+	1.51620i	−0.842064	+	0.539378i	$0.818659\pi$
$102$	0.0718840	+	0.214234i	0.00711757	+	0.0212123i
$103$	0.0978990	−	0.0978990i	0.00964627	−	0.00964627i	−0.702267	−	0.711913i	$-0.747829\pi$
$103$	0.0978990	−	0.0978990i	0.00964627	−	0.00964627i	0.711913	+	0.702267i	$0.247829\pi$
$104$	−5.93476	−	16.3100i	−0.581951	−	1.59933i
$105$	1.03227	−	3.15519i	0.100740	−	0.307915i
$106$	1.40745	+	1.89065i	0.136704	+	0.183637i
$107$	1.87659	−	4.53049i	0.181417	−	0.437979i	−0.806842	−	0.590767i	$-0.798825\pi$
$107$	1.87659	−	4.53049i	0.181417	−	0.437979i	0.988259	+	0.152788i	$0.0488253\pi$
$108$	10.3727	+	0.637902i	0.998114	+	0.0613821i
$109$	11.7310	−	4.85913i	1.12362	−	0.465421i	0.258016	−	0.966141i	$-0.416931\pi$
$109$	11.7310	−	4.85913i	1.12362	−	0.465421i	0.865609	+	0.500720i	$0.166931\pi$
$110$	0.379984	+	1.50555i	0.0362300	+	0.143548i
$111$	0.843978	+	1.66475i	0.0801068	+	0.158011i
$112$	−0.808414	−	3.91746i	−0.0763880	−	0.370165i
$113$	−5.44869			−0.512570			−0.256285	−	0.966601i	$-0.582499\pi$
$113$	−5.44869			−0.512570			−0.256285	+	0.966601i	$0.582499\pi$
$114$	7.90211	−	6.88098i	0.740100	−	0.644463i
$115$	−1.37159	−	3.31130i	−0.127901	−	0.308781i
$116$	4.72732	+	3.85139i	0.438921	+	0.357592i
$117$	9.55487	+	15.7353i	0.883348	+	1.45473i
$118$	9.28423	+	12.4716i	0.854683	+	1.14811i
$119$	−0.0652327	+	0.0652327i	−0.00597987	+	0.00597987i
$120$	3.87574	+	8.55250i	0.353805	+	0.780732i
$121$	7.54613	+	7.54613i	0.686012	+	0.686012i
$122$	−1.00721	+	6.87479i	−0.0911887	+	0.622414i
$123$	1.56304	+	20.3897i	0.140934	+	1.83848i
$124$	1.10892	−	0.597842i	0.0995841	−	0.0536878i
$125$	11.2026	−	4.64026i	1.00199	−	0.415037i
$126$	1.65311	+	3.90733i	0.147271	+	0.348093i
$127$		−	9.21197i		−	0.817430i	−0.912662	−	0.408715i	$-0.865977\pi$
$127$		−	9.21197i		−	0.817430i	0.912662	−	0.408715i	$-0.134023\pi$
$128$	9.17094	+	6.62525i	0.810604	+	0.585595i
$129$	−2.28601	−	4.50916i	−0.201272	−	0.397009i
$130$	−8.52556	+	14.2819i	−0.747741	+	1.25261i
$131$	3.41265	+	8.23886i	0.298164	+	0.719832i	0.999972	+	0.00746607i	$0.00237655\pi$
$131$	3.41265	+	8.23886i	0.298164	+	0.719832i	−0.701808	+	0.712366i	$0.747623\pi$
$132$	−1.62978	−	1.13215i	−0.141854	−	0.0985409i
$133$	3.95206	+	1.63700i	0.342687	+	0.141946i
$134$	20.8854	+	3.05988i	1.80422	+	0.264333i
$135$	−5.80471	−	8.09275i	−0.499590	−	0.696513i
$136$	0.0114044	−	0.260681i	0.000977919	−	0.0223532i
$137$	−5.52576	−	5.52576i	−0.472097	−	0.472097i	0.430495	−	0.902593i	$-0.358339\pi$
$137$	−5.52576	−	5.52576i	−0.472097	−	0.472097i	−0.902593	+	0.430495i	$0.858339\pi$
$138$	4.10098	+	2.04033i	0.349099	+	0.173684i
$139$	18.9803	+	7.86189i	1.60989	+	0.666837i	0.992770	−	0.120035i	$-0.0383007\pi$
$139$	18.9803	+	7.86189i	1.60989	+	0.666837i	0.617116	+	0.786872i	$0.288301\pi$
$140$	−2.42122	+	2.97189i	−0.204631	+	0.251170i
$141$	3.49351	−	4.07359i	0.294207	−	0.343059i
$142$	4.28476	+	16.9768i	0.359569	+	1.42466i
$143$		−	3.51523i		−	0.293958i
$144$	−10.9132	−	4.99018i	−0.909434	−	0.415849i
$145$		−	5.84353i		−	0.485279i
$146$	−11.2890	+	2.84923i	−0.934288	+	0.235804i
$147$	−1.12755	+	1.31477i	−0.0929988	+	0.108441i
$148$	−0.218920	−	2.14406i	−0.0179951	−	0.176241i
$149$	2.64866	+	1.09711i	0.216987	+	0.0898790i	0.488529	−	0.872548i	$-0.337534\pi$
$149$	2.64866	+	1.09711i	0.216987	+	0.0898790i	−0.271542	+	0.962427i	$0.587534\pi$
$150$	−1.44723	+	2.90886i	−0.118165	+	0.237508i
$151$	−3.25307	−	3.25307i	−0.264731	−	0.264731i	0.562242	−	0.826973i	$-0.309939\pi$
$151$	−3.25307	−	3.25307i	−0.264731	−	0.264731i	−0.826973	+	0.562242i	$0.809939\pi$
$152$	−11.3698	+	4.13714i	−0.922212	+	0.335567i
$153$	0.0421838	+	0.273525i	0.00341035	+	0.0221132i
$154$	0.117438	−	0.801580i	0.00946342	−	0.0645931i
$155$	−1.11542	−	0.462020i	−0.0895923	−	0.0371104i
$156$	−3.76926	−	20.9201i	−0.301782	−	1.67495i
$157$	−7.93451	−	19.1556i	−0.633243	−	1.52878i	−0.835523	−	0.549456i	$-0.814835\pi$
$157$	−7.93451	−	19.1556i	−0.633243	−	1.52878i	0.202280	−	0.979328i	$-0.435165\pi$
$158$	11.2014	+	6.68664i	0.891134	+	0.531960i
$159$	1.30532	+	2.57476i	0.103519	+	0.204192i
$160$	−0.628848	−	10.8240i	−0.0497148	−	0.855716i
$161$			1.86998i			0.147375i
$162$	12.3865	+	2.92817i	0.973177	+	0.230059i
$163$	19.7196	−	8.16813i	1.54456	−	0.639777i	0.562237	−	0.826976i	$-0.309941\pi$
$163$	19.7196	−	8.16813i	1.54456	−	0.639777i	0.982322	+	0.187199i	$0.0599408\pi$
$164$	6.77362	−	22.6207i	0.528931	−	1.76638i
$165$	0.145357	+	1.89617i	0.0113160	+	0.147617i
$166$	−23.2162	−	3.40136i	−1.80192	−	0.263997i
$167$	9.86165	+	9.86165i	0.763117	+	0.763117i	0.976885	−	0.213768i	$-0.0685735\pi$
$167$	9.86165	+	9.86165i	0.763117	+	0.763117i	−0.213768	+	0.976885i	$0.568574\pi$
$168$	−0.160599	−	4.89635i	−0.0123905	−	0.377761i
$169$	17.4336	−	17.4336i	1.34105	−	1.34105i
$170$	−0.200582	+	0.149319i	−0.0153839	+	0.0114522i
$171$	10.9691	−	6.66073i	0.838829	−	0.509359i
$172$	0.592969	+	5.80742i	0.0452134	+	0.442812i
$173$	−1.52226	−	3.67506i	−0.115735	−	0.279410i	0.855388	−	0.517988i	$-0.173319\pi$
$173$	−1.52226	−	3.67506i	−0.115735	−	0.279410i	−0.971123	+	0.238578i	$0.923319\pi$
$174$	4.90423	+	5.63202i	0.371789	+	0.426962i
$175$	−1.32640			−0.100266
$176$	1.28664	+	1.89608i	0.0969842	+	0.142923i
$177$	8.61053	+	16.9843i	0.647207	+	1.27662i
$178$	−1.18632	+	0.299415i	−0.0889186	+	0.0224421i
$179$	−1.65842	+	0.686941i	−0.123956	+	0.0513444i	−0.443799	−	0.896126i	$-0.646370\pi$
$179$	−1.65842	+	0.686941i	−0.123956	+	0.0513444i	0.319843	+	0.947470i	$0.396370\pi$
$180$	2.89826	+	11.1288i	0.216023	+	0.829491i
$181$	−1.99051	+	4.80551i	−0.147953	+	0.357191i	−0.980430	−	0.196870i	$-0.936922\pi$
$181$	−1.99051	+	4.80551i	−0.147953	+	0.357191i	0.832476	+	0.554061i	$0.186922\pi$
$182$	6.96107	−	5.18201i	0.515989	−	0.384116i
$183$	−2.64609	+	8.08789i	−0.195605	+	0.597874i
$184$	−3.57293	−	3.89985i	−0.263400	−	0.287501i
$185$	−1.46046	+	1.46046i	−0.107375	+	0.107375i
$186$	1.46280	−	0.490825i	0.107257	−	0.0359891i
$187$	0.0202238	−	0.0488246i	0.00147891	−	0.00357041i
$188$	−5.45447	+	2.94061i	−0.397808	+	0.214466i
$189$	1.18221	+	5.05988i	0.0859928	+	0.368052i
$190$	9.95598	+	5.94320i	0.722283	+	0.431165i
$191$	7.38971			0.534701			0.267350	−	0.963599i	$-0.413852\pi$
$191$	7.38971			0.534701			0.267350	+	0.963599i	$0.413852\pi$
$192$	9.69026	+	9.90449i	0.699334	+	0.714795i
$193$	−5.24194			−0.377323			−0.188662	−	0.982042i	$-0.560415\pi$
$193$	−5.24194			−0.377323			−0.188662	+	0.982042i	$0.560415\pi$
$194$	−17.4795	−	10.4343i	−1.25495	−	0.749143i
$195$	−13.2615	+	15.4635i	−0.949676	+	1.10736i
$196$	1.76046	−	0.949098i	0.125747	−	0.0677927i
$197$	−6.11869	+	14.7718i	−0.435939	+	1.05245i	0.541399	+	0.840766i	$0.317895\pi$
$197$	−6.11869	+	14.7718i	−0.435939	+	1.05245i	−0.977338	+	0.211684i	$0.932105\pi$
$198$	−1.73147	−	1.70555i	−0.123051	−	0.121208i
$199$	3.20398	−	3.20398i	0.227124	−	0.227124i	−0.584366	−	0.811490i	$-0.698657\pi$
$199$	3.20398	−	3.20398i	0.227124	−	0.227124i	0.811490	+	0.584366i	$0.198657\pi$
$200$	2.76620	−	2.53431i	0.195600	−	0.179203i
$201$	24.5707	+	8.03874i	1.73309	+	0.567009i
$202$	18.7098	−	13.9281i	1.31642	−	0.979976i
$203$	−1.16673	+	2.81672i	−0.0818881	+	0.197695i
$204$	0.0680047	−	0.312254i	0.00476128	−	0.0218622i
$205$	−20.9066	+	8.65981i	−1.46018	+	0.604827i
$206$	−0.189845	+	0.0479147i	−0.0132271	+	0.00333838i
$207$	4.52511	+	3.31585i	0.314517	+	0.230468i
$208$	−4.61619	+	24.1074i	−0.320075	+	1.67155i
$209$	−2.45048			−0.169503
$210$	−3.54063	+	3.08310i	−0.244327	+	0.212754i
$211$	−5.14238	−	12.4148i	−0.354016	−	0.854670i	−0.996116	−	0.0880493i	$-0.971937\pi$
$211$	−5.14238	−	12.4148i	−0.354016	−	0.854670i	0.642100	−	0.766621i	$-0.278063\pi$
$212$	−0.338589	−	3.31608i	−0.0232544	−	0.227749i
$213$	1.63907	+	21.3815i	0.112307	+	1.46504i
$214$	−5.56282	+	4.14111i	−0.380267	+	0.283081i
$215$	3.95582	−	3.95582i	0.269785	−	0.269785i
$216$	−12.1333	−	8.29358i	−0.825565	−	0.564307i
$217$	0.445410	+	0.445410i	0.0302364	+	0.0302364i
$218$	−17.7673	−	2.60306i	−1.20336	−	0.176302i
$219$	−14.2181	+	1.08993i	−0.960767	+	0.0736507i
$220$	0.629924	−	2.10365i	0.0424694	−	0.141828i
$221$	0.523005	−	0.216636i	0.0351811	−	0.0145725i
$222$	0.181894	−	2.63331i	0.0122079	−	0.176736i
$223$			19.4790i			1.30441i	0.758043	+	0.652205i	$0.226156\pi$
$223$			19.4790i			1.30441i	−0.758043	+	0.652205i	$0.773844\pi$
$224$	−1.85802	+	5.34301i	−0.124144	+	0.356995i
$225$	−2.35197	+	3.20970i	−0.156798	+	0.213980i
$226$	6.61640	+	3.94965i	0.440116	+	0.262727i
$227$	−2.78555	−	6.72492i	−0.184884	−	0.446348i	0.804077	−	0.594525i	$-0.202660\pi$
$227$	−2.78555	−	6.72492i	−0.184884	−	0.446348i	−0.988961	+	0.148176i	$0.952660\pi$
$228$	−14.5835	+	2.62756i	−0.965815	+	0.174015i
$229$	−8.82936	−	3.65724i	−0.583460	−	0.241677i	0.0713740	−	0.997450i	$-0.477262\pi$
$229$	−8.82936	−	3.65724i	−0.583460	−	0.241677i	−0.654834	+	0.755772i	$0.727262\pi$
$230$	−0.734765	+	5.01518i	−0.0484490	+	0.330691i
$231$	0.308526	−	0.943024i	0.0202995	−	0.0620464i
$232$	−2.94864	−	8.10352i	−0.193588	−	0.532022i
$233$	2.09576	+	2.09576i	0.137298	+	0.137298i	0.772415	−	0.635118i	$-0.219048\pi$
$233$	2.09576	+	2.09576i	0.137298	+	0.137298i	−0.635118	+	0.772415i	$0.719048\pi$
$234$	−0.196399	−	26.0336i	−0.0128390	−	1.70187i
$235$	5.48641	+	2.27254i	0.357894	+	0.148244i
$236$	−2.23349	−	21.8744i	−0.145388	−	1.42390i
$237$	12.1281	+	10.4011i	0.787805	+	0.675621i
$238$	0.126499	−	0.0319268i	0.00819968	−	0.00206951i
$239$			9.62336i			0.622483i	0.950331	+	0.311242i	$0.100745\pi$
$239$			9.62336i			0.622483i	−0.950331	+	0.311242i	$0.899255\pi$
$240$	1.49319	−	13.1948i	0.0963848	−	0.851722i
$241$			3.82092i			0.246127i	0.992399	+	0.123064i	$0.0392719\pi$
$241$			3.82092i			0.246127i	−0.992399	+	0.123064i	$0.960728\pi$
$242$	−3.69330	−	14.6334i	−0.237415	−	0.940669i
$243$	14.3405	+	6.11140i	0.919945	+	0.392047i
$244$	6.20646	−	7.61802i	0.397328	−	0.487694i
$245$	−1.77077	−	0.733476i	−0.113130	−	0.0468601i
$246$	12.8821	−	25.8924i	0.821331	−	1.65084i
$247$	−18.5611	−	18.5611i	−1.18101	−	1.18101i
$248$	−1.77994	−	0.0778695i	−0.113026	−	0.00494472i
$249$	−27.3128	−	8.93585i	−1.73088	−	0.566286i
$250$	−16.9670	−	2.48581i	−1.07309	−	0.157216i
$251$	14.0770	+	5.83088i	0.888532	+	0.368042i	0.779800	−	0.626029i	$-0.215321\pi$
$251$	14.0770	+	5.83088i	0.888532	+	0.368042i	0.108733	+	0.994071i	$0.465321\pi$
$252$	0.824954	−	5.94302i	0.0519672	−	0.374375i
$253$	−0.409940	−	0.989683i	−0.0257727	−	0.0622208i
$254$	−6.67757	+	11.1862i	−0.418988	+	0.701884i
$255$	−0.273159	+	0.138483i	−0.0171059	+	0.00867217i
$256$	−6.33386	−	14.6929i	−0.395866	−	0.918308i
$257$			1.37611i			0.0858394i	0.999079	+	0.0429197i	$0.0136660\pi$
$257$			1.37611i			0.0858394i	−0.999079	+	0.0429197i	$0.986334\pi$
$258$	−0.492679	+	7.13260i	−0.0306728	+	0.444056i
$259$	0.995577	−	0.412381i	0.0618621	−	0.0256241i
$260$	20.7053	−	11.1627i	1.28409	−	0.692279i
$261$	4.74726	+	7.81794i	0.293848	+	0.483918i
$262$	1.82817	−	12.4783i	0.112945	−	0.770911i
$263$	−9.03903	−	9.03903i	−0.557371	−	0.557371i	0.371187	−	0.928558i	$-0.378951\pi$
$263$	−9.03903	−	9.03903i	−0.557371	−	0.557371i	−0.928558	+	0.371187i	$0.878951\pi$
$264$	1.15838	+	2.55617i	0.0712934	+	0.157321i
$265$	−2.25880	+	2.25880i	−0.138757	+	0.138757i
$266$	−3.61240	−	4.85259i	−0.221490	−	0.297531i
$267$	−1.49412	+	0.114537i	−0.0914387	+	0.00700952i
$268$	−23.1433	−	18.8550i	−1.41370	−	1.15175i
$269$	8.58962	+	20.7372i	0.523718	+	1.26437i	0.935578	+	0.353121i	$0.114880\pi$
$269$	8.58962	+	20.7372i	0.523718	+	1.26437i	−0.411859	+	0.911247i	$0.635120\pi$
$270$	1.18245	+	14.0348i	0.0719615	+	0.854133i
$271$	−15.4663			−0.939508			−0.469754	−	0.882797i	$-0.655657\pi$
$271$	−15.4663			−0.939508			−0.469754	+	0.882797i	$0.655657\pi$
$272$	−0.202811	+	0.308281i	−0.0122972	+	0.0186923i
$273$	9.47983	−	4.80598i	0.573745	−	0.290871i
$274$	2.70447	+	10.7155i	0.163383	+	0.647347i
$275$	0.701991	−	0.290774i	0.0423317	−	0.0175344i
$276$	−3.50087	−	5.45031i	−0.210727	−	0.328070i
$277$	−3.49065	+	8.42718i	−0.209733	+	0.506340i	−0.993381	−	0.114865i	$-0.963357\pi$
$277$	−3.49065	+	8.42718i	−0.209733	+	0.506340i	0.783648	+	0.621205i	$0.213357\pi$
$278$	−17.3490	−	23.3052i	−1.04052	−	1.39775i
$279$	1.86764	−	0.288032i	0.111812	−	0.0172440i
$280$	5.09437	−	1.85370i	0.304447	−	0.110780i
$281$	6.21227	−	6.21227i	0.370593	−	0.370593i	−0.497100	−	0.867693i	$-0.665602\pi$
$281$	6.21227	−	6.21227i	0.370593	−	0.370593i	0.867693	+	0.497100i	$0.165602\pi$
$282$	−7.19508	+	2.41423i	−0.428461	+	0.143765i
$283$	4.29804	−	10.3764i	0.255492	−	0.616812i	−0.743138	−	0.669138i	$-0.766664\pi$
$283$	4.29804	−	10.3764i	0.255492	−	0.616812i	0.998630	+	0.0523262i	$0.0166635\pi$
$284$	7.10312	−	23.7210i	0.421492	−	1.40758i
$285$	10.7797	+	9.24464i	0.638532	+	0.547605i
$286$	−2.54812	+	4.26858i	−0.150674	+	0.252407i
$287$	11.8065			0.696918
$288$	9.63473	+	13.9704i	0.567732	+	0.823213i
$289$	−16.9915			−0.999499
$290$	−4.23586	+	7.09586i	−0.248738	+	0.416683i
$291$	−18.9256	−	16.2306i	−1.10944	−	0.951456i
$292$	15.7738	+	4.72335i	0.923089	+	0.276413i
$293$	−6.74010	+	16.2720i	−0.393761	+	0.950623i	0.595352	+	0.803465i	$0.297013\pi$
$293$	−6.74010	+	16.2720i	−0.393761	+	0.950623i	−0.989113	+	0.147158i	$0.952987\pi$
$294$	2.32225	−	0.779205i	0.135436	−	0.0454442i
$295$	−14.9001	+	14.9001i	−0.867518	+	0.867518i
$296$	−1.28835	+	2.76225i	−0.0748838	+	0.160552i
$297$	−1.73491	−	2.41876i	−0.100670	−	0.140351i
$298$	−2.42102	−	3.25220i	−0.140246	−	0.188395i
$299$	4.39125	−	10.6014i	0.253952	−	0.613095i
$300$	3.86596	−	2.48320i	0.223201	−	0.143368i
$301$	−2.69663	+	1.11698i	−0.155431	+	0.0643817i
$302$	1.59215	+	6.30832i	0.0916180	+	0.363003i
$303$	25.4796	−	12.9174i	1.46377	−	0.742085i
$304$	16.8054	+	3.21796i	0.963855	+	0.184563i
$305$	−9.41677			−0.539203
$306$	0.147049	−	0.362722i	0.00840621	−	0.0207355i
$307$	−8.55754	−	20.6597i	−0.488404	−	1.17911i	−0.955523	−	0.294918i	$-0.904708\pi$
$307$	−8.55754	−	20.6597i	−0.488404	−	1.17911i	0.467118	−	0.884195i	$-0.345292\pi$
$308$	−0.723655	+	0.888238i	−0.0412341	+	0.0506120i
$309$	−0.239101	+	0.0183291i	−0.0136020	+	0.00104270i
$310$	1.01955	+	1.36958i	0.0579066	+	0.0777868i
$311$	−19.0362	+	19.0362i	−1.07944	+	1.07944i	−0.0828859	+	0.996559i	$0.526414\pi$
$311$	−19.0362	+	19.0362i	−1.07944	+	1.07944i	−0.996559	+	0.0828859i	$0.973586\pi$
$312$	−10.5875	+	28.1358i	−0.599401	+	1.59287i
$313$	22.0609	+	22.0609i	1.24696	+	1.24696i	0.957057	+	0.289900i	$0.0936221\pi$
$313$	22.0609	+	22.0609i	1.24696	+	1.24696i	0.289900	+	0.957057i	$0.406378\pi$
$314$	−4.25055	+	29.0124i	−0.239873	+	1.63726i
$315$	−4.91484	+	2.98442i	−0.276920	+	0.168153i
$316$	−8.75493	−	16.2393i	−0.492504	−	0.913532i
$317$	−8.59494	+	3.56014i	−0.482740	+	0.199957i	−0.610762	−	0.791814i	$-0.709137\pi$
$317$	−8.59494	+	3.56014i	−0.482740	+	0.199957i	0.128023	+	0.991771i	$0.459137\pi$
$318$	0.281323	−	4.07276i	0.0157758	−	0.228389i
$319$		−	1.74651i		−	0.0977861i
$320$	−7.08251	+	13.5996i	−0.395925	+	0.760240i
$321$	−7.57564	+	3.84062i	−0.422831	+	0.214362i
$322$	1.35551	−	2.27074i	0.0755397	−	0.126543i
$323$	−0.151018	−	0.364589i	−0.00840285	−	0.0202863i
$324$	−12.9185	−	12.5344i	−0.717695	−	0.696358i
$325$	7.51968	+	3.11475i	0.417117	+	0.172775i
$326$	−29.8666	−	4.37571i	−1.65416	−	0.242348i
$327$	−20.9025	−	6.83861i	−1.15591	−	0.378176i
$328$	−24.6226	+	22.5585i	−1.35955	+	1.24558i
$329$	−2.19084	−	2.19084i	−0.120785	−	0.120785i
$330$	1.19799	−	2.40791i	0.0659471	−	0.132551i
$331$	24.6823	+	10.2237i	1.35666	+	0.561948i	0.938139	−	0.346258i	$-0.112548\pi$
$331$	24.6823	+	10.2237i	1.35666	+	0.561948i	0.418523	+	0.908206i	$0.362548\pi$
$332$	25.7260	+	20.9592i	1.41190	+	1.15029i
$333$	0.767450	−	3.14040i	0.0420560	−	0.172093i
$334$	−4.82659	−	19.1236i	−0.264099	−	1.04640i
$335$			28.6079i			1.56301i
$336$	−3.35425	+	6.06210i	−0.182989	+	0.330715i
$337$		−	8.08667i		−	0.440509i	−0.975442	−	0.220254i	$-0.929311\pi$
$337$		−	8.08667i		−	0.440509i	0.975442	−	0.220254i	$-0.0706888\pi$
$338$	−33.8071	+	8.53255i	−1.83887	+	0.464109i
$339$	7.16380	+	6.14367i	0.389084	+	0.333678i
$340$	0.351807	−	0.0359213i	0.0190794	−	0.00194811i
$341$	−0.333376	−	0.138089i	−0.0180533	−	0.00747792i
$342$	−18.1481	+	0.136910i	−0.981339	+	0.00740326i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	3.48964	−	7.48185i	0.188149	−	0.403394i
$345$	−1.93033	+	5.90015i	−0.103926	+	0.317653i
$346$	−0.815482	+	5.56612i	−0.0438406	+	0.299236i
$347$	29.9925	+	12.4233i	1.61008	+	0.666917i	0.992795	−	0.119824i	$-0.0382329\pi$
$347$	29.9925	+	12.4233i	1.61008	+	0.666917i	0.617284	+	0.786740i	$0.288233\pi$
$348$	−1.87272	−	10.3940i	−0.100389	−	0.557177i
$349$	−9.23693	−	22.2999i	−0.494442	−	1.19369i	−0.952438	−	0.304734i	$-0.901433\pi$
$349$	−9.23693	−	22.2999i	−0.494442	−	1.19369i	0.457996	−	0.888954i	$-0.348567\pi$
$350$	1.61066	+	0.961478i	0.0860932	+	0.0513931i
$351$	5.17980	−	31.4619i	0.276477	−	1.67931i
$352$	−0.187950	−	3.23509i	−0.0100178	−	0.172431i
$353$		−	21.2234i		−	1.12961i	−0.825225	−	0.564804i	$-0.808952\pi$
$353$		−	21.2234i		−	1.12961i	0.825225	−	0.564804i	$-0.191048\pi$
$354$	1.85574	−	26.8658i	0.0986313	−	1.42790i
$355$	−21.9236	+	9.08105i	−1.16358	+	0.481972i
$356$	1.65760	+	0.496359i	0.0878527	+	0.0263070i
$357$	0.159319	−	0.0122131i	0.00843207	−	0.000646387i
$358$	2.51179	+	0.367997i	0.132752	+	0.0194493i
$359$	19.2385	+	19.2385i	1.01537	+	1.01537i	0.999880	+	0.0154916i	$0.00493134\pi$
$359$	19.2385	+	19.2385i	1.01537	+	1.01537i	0.0154916	+	0.999880i	$0.495069\pi$
$360$	4.54765	−	15.6147i	0.239682	−	0.822966i
$361$	0.496014	−	0.496014i	0.0261060	−	0.0261060i
$362$	5.90051	−	4.39250i	0.310124	−	0.230865i
$363$	−1.41282	−	18.4301i	−0.0741537	−	0.967329i
$364$	−12.2092	+	1.24663i	−0.639938	+	0.0653410i
$365$	−6.03862	−	14.5785i	−0.316076	−	0.763074i
$366$	9.07592	−	7.90311i	0.474406	−	0.413102i
$367$	25.4305			1.32746			0.663729	−	0.747973i	$-0.268973\pi$
$367$	25.4305			1.32746			0.663729	+	0.747973i	$0.268973\pi$
$368$	1.51172	+	7.32557i	0.0788038	+	0.381872i
$369$	20.9354	−	28.5703i	1.08985	−	1.48731i
$370$	2.83212	−	0.714795i	0.147235	−	0.0371604i
$371$	1.53979	−	0.637803i	0.0799420	−	0.0331131i
$372$	−2.13208	−	0.464337i	−0.110543	−	0.0240748i
$373$	−11.9534	+	28.8581i	−0.618925	+	1.49422i	0.234027	+	0.972230i	$0.424809\pi$
$373$	−11.9534	+	28.8581i	−0.618925	+	1.49422i	−0.852953	+	0.521988i	$0.825191\pi$
$374$	−0.0599500	+	0.0446284i	−0.00309994	+	0.00230768i
$375$	−19.9610	−	6.53057i	−1.03078	−	0.337237i
$376$	8.75501	+	0.383018i	0.451505	+	0.0197526i
$377$	13.2289	−	13.2289i	0.681324	−	0.681324i
$378$	2.23224	−	7.00122i	0.114814	−	0.360104i
$379$	0.936111	−	2.25997i	0.0480848	−	0.116087i	−0.898012	−	0.439971i	$-0.854989\pi$
$379$	0.936111	−	2.25997i	0.0480848	−	0.116087i	0.946097	+	0.323884i	$0.104989\pi$
$380$	−7.78154	−	14.4338i	−0.399184	−	0.740437i
$381$	−10.3870	+	12.1117i	−0.532140	+	0.620499i
$382$	−8.97340	−	5.35666i	−0.459119	−	0.274070i
$383$	−20.5474			−1.04992			−0.524962	−	0.851126i	$-0.675920\pi$
$383$	−20.5474			−1.04992			−0.524962	+	0.851126i	$0.675920\pi$
$384$	−4.58742	−	19.0514i	−0.234101	−	0.972212i
$385$	1.09797			0.0559576
$386$	6.36534	+	3.79978i	0.323987	+	0.193404i
$387$	−2.07872	+	8.50611i	−0.105667	+	0.432390i
$388$	13.6619	+	25.3411i	0.693577	+	1.28650i
$389$	12.1896	−	29.4282i	0.618036	−	1.49207i	−0.235945	−	0.971766i	$-0.575819\pi$
$389$	12.1896	−	29.4282i	0.618036	−	1.49207i	0.853981	−	0.520304i	$-0.174181\pi$
$390$	27.3128	−	9.16450i	1.38304	−	0.464062i
$391$	0.121984	−	0.121984i	0.00616899	−	0.00616899i
$392$	−2.82572	−	0.123621i	−0.142721	−	0.00624380i
$393$	4.80287	−	14.6802i	0.242273	−	0.740517i
$394$	18.1378	−	13.5023i	0.913769	−	0.680235i
$395$	−6.76593	+	16.3344i	−0.340431	+	0.821873i
$396$	0.866232	+	3.32617i	0.0435298	+	0.167146i
$397$	−2.21670	+	0.918186i	−0.111253	+	0.0460824i	−0.437616	−	0.899162i	$-0.644177\pi$
$397$	−2.21670	+	0.918186i	−0.111253	+	0.0460824i	0.326363	+	0.945245i	$0.394177\pi$
$398$	−6.21312	+	1.56812i	−0.311436	+	0.0786030i
$399$	−3.35027	−	6.60843i	−0.167723	−	0.330835i
$400$	−5.19610	+	1.07228i	−0.259805	+	0.0536139i
$401$	3.78293			0.188910			0.0944552	−	0.995529i	$-0.469889\pi$
$401$	3.78293			0.188910			0.0944552	+	0.995529i	$0.469889\pi$
$402$	−24.0094	−	27.5724i	−1.19748	−	1.37518i
$403$	−1.47920	−	3.57109i	−0.0736840	−	0.177889i
$404$	−32.8157	+	3.35065i	−1.63264	+	0.166701i
$405$	−1.49310	+	17.1852i	−0.0741926	+	0.853942i
$406$	3.45855	−	2.57464i	0.171645	−	0.127777i
$407$	−0.436503	+	0.436503i	−0.0216367	+	0.0216367i
$408$	−0.308925	+	0.329878i	−0.0152941	+	0.0163314i
$409$	−16.8547	−	16.8547i	−0.833412	−	0.833412i	0.154570	−	0.987982i	$-0.450601\pi$
$409$	−16.8547	−	16.8547i	−0.833412	−	0.833412i	−0.987982	+	0.154570i	$0.950601\pi$
$410$	31.6645	+	4.63910i	1.56380	+	0.229109i
$411$	1.03456	+	13.4957i	0.0510309	+	0.665694i
$412$	0.265263	+	0.0794313i	0.0130686	+	0.00391330i
$413$	10.1572	−	4.20725i	0.499803	−	0.207025i
$414$	−3.09129	−	7.30663i	−0.151929	−	0.359101i
$415$		−	31.8005i		−	1.56102i
$416$	23.0805	−	25.9277i	1.13161	−	1.27121i
$417$	−16.0901	−	31.7378i	−0.787936	−	1.55421i
$418$	2.97564	+	1.77630i	0.145544	+	0.0868819i
$419$	−12.1847	−	29.4165i	−0.595262	−	1.43709i	−0.878360	−	0.478000i	$-0.841362\pi$
$419$	−12.1847	−	29.4165i	−0.595262	−	1.43709i	0.283098	−	0.959091i	$-0.408638\pi$
$420$	6.53431	−	1.17731i	0.318842	−	0.0574469i
$421$	−30.0312	−	12.4393i	−1.46363	−	0.606256i	−0.498235	−	0.867042i	$-0.666018\pi$
$421$	−30.0312	−	12.4393i	−1.46363	−	0.606256i	−0.965397	+	0.260785i	$0.916018\pi$
$422$	−2.75480	+	18.8030i	−0.134101	+	0.915317i
$423$	−9.18636	+	1.41675i	−0.446656	+	0.0688845i
$424$	−1.99261	+	4.27218i	−0.0967695	+	0.207476i
$425$	0.0865243	+	0.0865243i	0.00419705	+	0.00419705i
$426$	13.5087	−	27.1519i	0.654499	−	1.31552i
$427$	4.53912	+	1.88016i	0.219663	+	0.0909875i
$428$	9.75680	−	0.996221i	0.471613	−	0.0481542i
$429$	−3.96360	+	4.62174i	−0.191364	+	0.223139i
$430$	−7.67109	+	1.93610i	−0.369933	+	0.0933670i
$431$			36.0100i			1.73454i	0.497837	+	0.867271i	$0.334128\pi$
$431$			36.0100i			1.73454i	−0.497837	+	0.867271i	$0.665872\pi$
$432$	8.72172	+	18.8661i	0.419624	+	0.907698i
$433$			9.78384i			0.470181i	0.971973	+	0.235091i	$0.0755387\pi$
$433$			9.78384i			0.470181i	−0.971973	+	0.235091i	$0.924461\pi$
$434$	−0.217997	−	0.863735i	−0.0104642	−	0.0414606i
$435$	−6.58887	+	7.68292i	−0.315912	+	0.368368i
$436$	19.6882	+	16.0401i	0.942892	+	0.768182i
$437$	−7.39028	−	3.06115i	−0.353525	−	0.146435i
$438$	18.0552	+	8.98287i	0.862711	+	0.429218i
$439$	22.1447	+	22.1447i	1.05691	+	1.05691i	0.998280	+	0.0586291i	$0.0186729\pi$
$439$	22.1447	+	22.1447i	1.05691	+	1.05691i	0.0586291	+	0.998280i	$0.481327\pi$
$440$	−2.28981	+	2.09786i	−0.109163	+	0.100012i
$441$	2.96495	−	0.457262i	0.141188	−	0.0217744i
$442$	−0.792126	−	0.116053i	−0.0376776	−	0.00552007i
$443$	32.0355	+	13.2695i	1.52205	+	0.630454i	0.978001	−	0.208599i	$-0.0668902\pi$
$443$	32.0355	+	13.2695i	1.52205	+	0.630454i	0.544050	+	0.839053i	$0.316890\pi$
$444$	−2.12971	+	3.06580i	−0.101071	+	0.145496i
$445$	−0.634575	−	1.53200i	−0.0300817	−	0.0726237i
$446$	14.1199	−	23.6535i	0.668598	−	1.12003i
$447$	−2.24535	−	4.42896i	−0.106201	−	0.209482i
$448$	6.12925	−	5.14123i	0.289580	−	0.242900i
$449$		−	17.0456i		−	0.804432i	−0.915545	−	0.402216i	$-0.868240\pi$
$449$		−	17.0456i		−	0.804432i	0.915545	−	0.402216i	$-0.131760\pi$
$450$	5.18267	−	2.19268i	0.244313	−	0.103364i
$451$	−6.24858	+	2.58825i	−0.294234	+	0.121876i
$452$	−5.17134	−	9.59219i	−0.243240	−	0.451179i
$453$	0.609053	+	7.94505i	0.0286158	+	0.373291i
$454$	−1.49223	+	10.1853i	−0.0700340	+	0.478021i
$455$	8.31652	+	8.31652i	0.389885	+	0.389885i
$456$	19.6136	+	7.38061i	0.918489	+	0.345629i
$457$	−7.94994	+	7.94994i	−0.371883	+	0.371883i	−0.868163	−	0.496280i	$-0.834699\pi$
$457$	−7.94994	+	7.94994i	−0.371883	+	0.371883i	0.496280	+	0.868163i	$0.334699\pi$
$458$	8.07052	+	10.8412i	0.377111	+	0.506578i
$459$	0.252951	−	0.407188i	0.0118067	−	0.0190059i
$460$	4.52764	−	5.55737i	0.211102	−	0.259114i
$461$	6.01950	+	14.5324i	0.280356	+	0.676840i	0.999844	−	0.0176655i	$-0.00562339\pi$
$461$	6.01950	+	14.5324i	0.280356	+	0.676840i	−0.719488	+	0.694505i	$0.755623\pi$
$462$	−1.05823	+	0.921479i	−0.0492331	+	0.0428711i
$463$	5.24499			0.243756			0.121878	−	0.992545i	$-0.461108\pi$
$463$	5.24499			0.243756			0.121878	+	0.992545i	$0.461108\pi$
$464$	−2.29352	+	11.9776i	−0.106474	+	0.556046i
$465$	0.945569	+	1.86514i	0.0438497	+	0.0864937i
$466$	−1.02573	−	4.06407i	−0.0475159	−	0.188265i
$467$	23.3660	−	9.67853i	1.08125	−	0.447869i	0.230303	−	0.973119i	$-0.426028\pi$
$467$	23.3660	−	9.67853i	1.08125	−	0.447869i	0.850948	+	0.525250i	$0.176028\pi$
$468$	−18.6328	+	31.7553i	−0.861300	+	1.46789i
$469$	5.71188	−	13.7897i	0.263750	−	0.636749i
$470$	−5.01488	−	6.73656i	−0.231319	−	0.310734i
$471$	−11.1668	+	34.1318i	−0.514539	+	1.57271i
$472$	−13.1442	+	28.1813i	−0.605009	+	1.29715i
$473$	1.18232	−	1.18232i	0.0543630	−	0.0543630i
$474$	−7.18776	−	21.4215i	−0.330145	−	0.983923i
$475$	2.17131	−	5.24200i	0.0996263	−	0.240519i
$476$	−0.176752	−	0.0529272i	−0.00810140	−	0.00242591i
$477$	1.18696	−	4.85705i	0.0543473	−	0.222389i
$478$	6.97578	−	11.6857i	0.319065	−	0.534493i
$479$	6.68418			0.305408			0.152704	−	0.988272i	$-0.451202\pi$
$479$	6.68418			0.305408			0.152704	+	0.988272i	$0.451202\pi$
$480$	−11.3779	+	14.9402i	−0.519326	+	0.681925i
$481$	−6.61257			−0.301507
$482$	2.76971	−	4.63979i	0.126157	−	0.211336i
$483$	2.10850	−	2.45860i	0.0959400	−	0.111870i
$484$	−6.12263	+	20.4467i	−0.278301	+	0.929394i
$485$	10.5581	−	25.4895i	0.479418	−	1.15742i
$486$	−12.9838	−	17.8163i	−0.588958	−	0.808164i
$487$	−13.5118	+	13.5118i	−0.612277	+	0.612277i	−0.943539	−	0.331262i	$-0.892526\pi$
$487$	−13.5118	+	13.5118i	−0.612277	+	0.612277i	0.331262	+	0.943539i	$0.392526\pi$
$488$	−13.0587	+	4.75169i	−0.591140	+	0.215099i
$489$	−35.1368	−	11.4956i	−1.58894	−	0.519849i
$490$	1.61858	+	2.17426i	0.0731199	+	0.0982231i
$491$	−12.6297	+	30.4907i	−0.569969	+	1.37603i	0.331613	+	0.943416i	$0.392407\pi$
$491$	−12.6297	+	30.4907i	−0.569969	+	1.37603i	−0.901581	+	0.432610i	$0.857593\pi$
$492$	−34.4117	+	22.1035i	−1.55140	+	0.996502i
$493$	0.259851	−	0.107634i	0.0117031	−	0.00484758i
$494$	9.08436	+	35.9935i	0.408725	+	1.61942i
$495$	1.94692	−	2.65694i	0.0875074	−	0.119420i
$496$	2.10495	+	1.38480i	0.0945151	+	0.0621793i
$497$	12.3808			0.555357
$498$	26.6888	+	30.6494i	1.19595	+	1.37343i
$499$	−7.90474	−	19.0837i	−0.353865	−	0.854305i	−0.996136	−	0.0878272i	$-0.972008\pi$
$499$	−7.90474	−	19.0837i	−0.353865	−	0.854305i	0.642271	−	0.766478i	$-0.277992\pi$
$500$	18.8013	+	15.3176i	0.840821	+	0.685024i
$501$	−1.84634	−	24.0853i	−0.0824883	−	1.07605i
$502$	−12.8672	−	17.2846i	−0.574289	−	0.771451i
$503$	−2.77192	+	2.77192i	−0.123594	+	0.123594i	−0.766198	−	0.642604i	$-0.777854\pi$
$503$	−2.77192	+	2.77192i	−0.123594	+	0.123594i	0.642604	+	0.766198i	$0.277854\pi$
$504$	−5.30972	+	6.61867i	−0.236514	+	0.294819i
$505$	22.3529	+	22.3529i	0.994692	+	0.994692i
$506$	−0.219607	+	1.49894i	−0.00976271	+	0.0666360i
$507$	−42.5786	+	3.26400i	−1.89098	+	0.144959i
$508$	16.2173	−	8.74306i	0.719526	−	0.387911i
$509$	4.03159	−	1.66994i	0.178697	−	0.0740188i	−0.291541	−	0.956558i	$-0.594168\pi$
$509$	4.03159	−	1.66994i	0.178697	−	0.0740188i	0.470238	+	0.882540i	$0.344168\pi$
$510$	0.432084	+	0.0298459i	0.0191330	+	0.00132160i
$511$			8.23288i			0.364201i
$512$	−2.95935	+	22.4331i	−0.130786	+	0.991411i
$513$	−21.9322	−	3.61086i	−0.968331	−	0.159423i
$514$	0.997514	−	1.67102i	0.0439985	−	0.0737057i
$515$	−0.101550	−	0.245163i	−0.00447482	−	0.0108032i
$516$	5.76854	−	8.30405i	0.253946	−	0.365566i
$517$	1.63978	+	0.679219i	0.0721174	+	0.0298720i
$518$	−1.50787	−	0.220915i	−0.0662518	−	0.00970643i
$519$	−2.14239	+	6.54830i	−0.0940403	+	0.287438i
$520$	−33.2343	−	1.45395i	−1.45742	−	0.0637599i
$521$	12.2715	+	12.2715i	0.537623	+	0.537623i	0.922830	−	0.385207i	$-0.125870\pi$
$521$	12.2715	+	12.2715i	0.537623	+	0.537623i	−0.385207	+	0.922830i	$0.625870\pi$
$522$	−0.0975792	−	12.9346i	−0.00427092	−	0.566132i
$523$	7.76551	+	3.21658i	0.339562	+	0.140651i	0.545947	−	0.837820i	$-0.316170\pi$
$523$	7.76551	+	3.21658i	0.339562	+	0.140651i	−0.206385	+	0.978471i	$0.566170\pi$
$524$	−11.2652	+	13.8273i	−0.492124	+	0.604049i
$525$	1.74391	+	1.49558i	0.0761105	+	0.0652724i
$526$	4.42398	+	17.5284i	0.192895	+	0.764275i
$527$		−	0.0581106i		−	0.00253134i
$528$	0.446284	−	3.94367i	0.0194220	−	0.171626i
$529$			19.5032i			0.847964i
$530$	4.38024	−	1.10553i	0.190266	−	0.0480210i
$531$	7.82977	−	32.0394i	0.339783	−	1.39039i
$532$	0.869029	+	8.51111i	0.0376772	+	0.369003i
$533$	−66.9343	−	27.7251i	−2.89925	−	1.20091i
$534$	1.89735	+	0.943975i	0.0821064	+	0.0408498i
$535$	−6.64601	−	6.64601i	−0.287332	−	0.287332i
$536$	14.4355	+	39.6720i	0.623518	+	1.71357i
$537$	2.95501	+	0.966782i	0.127518	+	0.0417197i
$538$	4.60150	−	31.4078i	0.198385	−	1.35409i
$539$	−0.529247	−	0.219221i	−0.0227963	−	0.00944253i
$540$	8.73771	−	17.8998i	0.376011	−	0.770283i
$541$	6.01360	+	14.5181i	0.258545	+	0.624183i	0.998843	−	0.0480964i	$-0.0153155\pi$
$541$	6.01360	+	14.5181i	0.258545	+	0.624183i	−0.740298	+	0.672279i	$0.765315\pi$
$542$	18.7808	+	11.2112i	0.806706	+	0.481561i
$543$	8.03552	−	4.07377i	0.344837	−	0.174822i
$544$	0.469742	−	0.227335i	0.0201400	−	0.00974692i
$545$		−	24.3369i		−	1.04248i
$546$	−14.9952	−	1.03578i	−0.641736	−	0.0443274i
$547$	19.2999	−	7.99428i	0.825204	−	0.341811i	0.0702016	−	0.997533i	$-0.477636\pi$
$547$	19.2999	−	7.99428i	0.825204	−	0.341811i	0.755002	+	0.655722i	$0.227636\pi$
$548$	4.48338	−	14.9724i	0.191520	−	0.639587i
$549$	12.5985	−	7.65015i	0.537691	−	0.326501i
$550$	−1.06321	−	0.155769i	−0.0453355	−	0.00664202i
$551$	−9.22194	−	9.22194i	−0.392868	−	0.392868i
$552$	0.300317	+	9.15608i	0.0127824	+	0.389709i
$553$	6.52269	−	6.52269i	0.277373	−	0.277373i
$554$	10.3474	−	7.70291i	0.439620	−	0.327265i
$555$	3.56692	−	0.273434i	0.151407	−	0.0116066i
$556$	4.17362	+	40.8757i	0.177001	+	1.73352i
$557$	14.0219	+	33.8519i	0.594128	+	1.43435i	0.879483	+	0.475930i	$0.157889\pi$
$557$	14.0219	+	33.8519i	0.594128	+	1.43435i	−0.285355	+	0.958422i	$0.592111\pi$
$558$	−2.47668	−	1.00405i	−0.104846	−	0.0425049i
$559$	17.9109			0.757549
$560$	−7.52986	−	1.44185i	−0.318195	−	0.0609291i
$561$	−0.0816419	+	0.0413900i	−0.00344693	+	0.00174749i
$562$	−12.0468	+	3.04047i	−0.508162	+	0.128255i
$563$	7.21758	−	2.98962i	0.304185	−	0.125997i	−0.225370	−	0.974273i	$-0.572359\pi$
$563$	7.21758	−	2.98962i	0.304185	−	0.125997i	0.529555	+	0.848276i	$0.322359\pi$
$564$	10.4871	+	2.28394i	0.441586	+	0.0961713i
$565$	−3.99648	+	9.64837i	−0.168133	+	0.405910i
$566$	−12.7408	+	9.48458i	−0.535535	+	0.398667i
$567$	4.15093	−	7.98560i	0.174323	−	0.335364i
$568$	−25.8203	+	23.6558i	−1.08340	+	0.992575i
$569$	−24.8980	+	24.8980i	−1.04378	+	1.04378i	−0.0447816	+	0.998997i	$0.514259\pi$
$569$	−24.8980	+	24.8980i	−1.04378	+	1.04378i	−0.998997	+	0.0447816i	$0.985741\pi$
$570$	−6.38861	−	19.0398i	−0.267589	−	0.797491i
$571$	−10.0351	+	24.2270i	−0.419957	+	1.01387i	0.562402	+	0.826864i	$0.309877\pi$
$571$	−10.0351	+	24.2270i	−0.419957	+	1.01387i	−0.982359	+	0.187003i	$0.940123\pi$
$572$	6.18842	−	3.33630i	0.258751	−	0.139498i
$573$	−9.71581	−	8.33227i	−0.405884	−	0.348086i
$574$	−14.3368	−	8.55832i	−0.598406	−	0.357217i
$575$	2.48034			0.103437
$576$	−1.57270	−	23.9484i	−0.0655290	−	0.997851i
$577$	7.46199			0.310647			0.155323	−	0.987864i	$-0.450358\pi$
$577$	7.46199			0.310647			0.155323	+	0.987864i	$0.450358\pi$
$578$	20.6329	+	12.3168i	0.858217	+	0.512311i
$579$	6.89197	+	5.91055i	0.286420	+	0.245634i
$580$	10.2873	−	5.54608i	0.427156	−	0.230289i
$581$	−6.34931	+	15.3286i	−0.263414	+	0.635937i
$582$	11.2163	+	33.4278i	0.464932	+	1.38563i
$583$	−0.675111	+	0.675111i	−0.0279602	+	0.0279602i
$584$	−15.7304	−	17.1697i	−0.650927	−	0.710487i
$585$	34.8718	−	5.37801i	1.44177	−	0.222354i
$586$	19.9798	−	14.8735i	0.825360	−	0.614420i
$587$	−7.50250	+	18.1126i	−0.309661	+	0.747588i	0.690055	+	0.723757i	$0.257586\pi$
$587$	−7.50250	+	18.1126i	−0.309661	+	0.747588i	−0.999716	+	0.0238311i	$0.992414\pi$
$588$	−3.38476	−	0.737155i	−0.139585	−	0.0303997i
$589$	−2.48942	+	1.03115i	−0.102575	+	0.0424879i
$590$	28.8942	−	7.29257i	1.18955	−	0.300230i
$591$	24.7007	−	12.5225i	1.01605	−	0.515107i
$592$	3.56675	−	2.42032i	0.146593	−	0.0994747i
$593$	−24.3162			−0.998546			−0.499273	−	0.866445i	$-0.666399\pi$
$593$	−24.3162			−0.998546			−0.499273	+	0.866445i	$0.666399\pi$
$594$	0.353410	+	4.19473i	0.0145006	+	0.172112i
$595$	0.0676653	+	0.163358i	0.00277401	+	0.00669704i
$596$	0.582422	+	5.70413i	0.0238569	+	0.233650i
$597$	−7.82515	+	0.599862i	−0.320262	+	0.0245507i
$598$	−13.0171	+	9.69027i	−0.532308	+	0.396264i
$599$	5.51316	−	5.51316i	0.225262	−	0.225262i	−0.585448	−	0.810710i	$-0.699081\pi$
$599$	5.51316	−	5.51316i	0.225262	−	0.225262i	0.810710	+	0.585448i	$0.199081\pi$
$600$	−6.49449	+	0.213018i	−0.265137	+	0.00869642i
$601$	30.4317	+	30.4317i	1.24133	+	1.24133i	0.959448	+	0.281886i	$0.0909600\pi$
$601$	30.4317	+	30.4317i	1.24133	+	1.24133i	0.281886	+	0.959448i	$0.409040\pi$
$602$	4.08422	+	0.598371i	0.166460	+	0.0243878i
$603$	−23.2409	−	38.2739i	−0.946443	−	1.55863i
$604$	2.63941	−	8.81437i	0.107396	−	0.358652i
$605$	18.8973	−	7.82754i	0.768286	−	0.318235i
$606$	−40.3037	−	2.78395i	−1.63723	−	0.113090i
$607$			4.68349i			0.190097i	0.995473	+	0.0950484i	$0.0303006\pi$
$607$			4.68349i			0.190097i	−0.995473	+	0.0950484i	$0.969699\pi$
$608$	−18.0743	−	16.0895i	−0.733011	−	0.652515i
$609$	4.70998	−	2.38781i	0.190858	−	0.0967591i
$610$	11.4349	+	6.82603i	0.462985	+	0.276378i
$611$	7.27574	+	17.5652i	0.294345	+	0.710611i
$612$	−0.441493	+	0.333865i	−0.0178463	+	0.0134957i
$613$	38.5691	+	15.9758i	1.55779	+	0.645258i	0.984704	−	0.174236i	$-0.0557456\pi$
$613$	38.5691	+	15.9758i	1.55779	+	0.645258i	0.573087	+	0.819494i	$0.305746\pi$
$614$	−4.58431	+	31.2905i	−0.185008	+	1.26278i
$615$	37.2519	+	12.1876i	1.50214	+	0.491451i
$616$	1.52261	−	0.554033i	0.0613476	−	0.0223226i
$617$	−13.6254	−	13.6254i	−0.548537	−	0.548537i	0.377480	−	0.926018i	$-0.376791\pi$
$617$	−13.6254	−	13.6254i	−0.548537	−	0.548537i	−0.926018	+	0.377480i	$0.876791\pi$
$618$	0.303629	+	0.151062i	0.0122138	+	0.00607662i
$619$	0.581709	+	0.240952i	0.0233809	+	0.00968467i	0.394343	−	0.918963i	$-0.370972\pi$
$619$	0.581709	+	0.240952i	0.0233809	+	0.00968467i	−0.370962	+	0.928648i	$0.620972\pi$
$620$	−0.245272	−	2.40214i	−0.00985035	−	0.0964725i
$621$	−2.21070	−	9.46188i	−0.0887125	−	0.379692i
$622$	36.9148	−	9.31690i	1.48015	−	0.373574i
$623$			0.865161i			0.0346620i
$624$	33.2516	−	26.4909i	1.33113	−	1.06048i
$625$		−	16.6087i		−	0.664348i
$626$	−10.7973	−	42.7803i	−0.431546	−	1.70985i
$627$	3.22183	+	2.76304i	0.128667	+	0.110345i
$628$	26.1920	−	32.1489i	1.04517	−	1.28288i
$629$	−0.0918449	−	0.0380434i	−0.00366209	−	0.00151689i
$630$	8.13149	−	0.0613443i	0.323966	−	0.00244402i
$631$	14.3322	+	14.3322i	0.570555	+	0.570555i	0.932283	−	0.361729i	$-0.117813\pi$
$631$	14.3322	+	14.3322i	0.570555	+	0.570555i	−0.361729	+	0.932283i	$0.617813\pi$
$632$	−1.14034	+	26.0658i	−0.0453602	+	1.03684i
$633$	−7.23724	+	22.1209i	−0.287655	+	0.879229i
$634$	13.0176	+	1.90718i	0.516995	+	0.0757439i
$635$	−16.3123	−	6.75676i	−0.647332	−	0.268134i
$636$	−3.29387	+	4.74167i	−0.130611	+	0.188019i
$637$	−2.34828	−	5.66926i	−0.0930423	−	0.224624i
$638$	−1.26601	+	2.12081i	−0.0501220	+	0.0839637i
$639$	21.9537	−	29.9600i	0.868476	−	1.18520i
$640$	18.4584	−	11.3801i	0.729634	−	0.449840i
$641$			38.3845i			1.51610i	0.652198	+	0.758049i	$0.273847\pi$
$641$			38.3845i			1.51610i	−0.652198	+	0.758049i	$0.726153\pi$
$642$	11.9832	+	0.827728i	0.472938	+	0.0326678i
$643$	21.0792	−	8.73127i	0.831281	−	0.344328i	0.0738713	−	0.997268i	$-0.476465\pi$
$643$	21.0792	−	8.73127i	0.831281	−	0.344328i	0.757410	+	0.652940i	$0.226465\pi$
$644$	−3.29202	+	1.77480i	−0.129724	+	0.0699368i
$645$	−9.66140	+	0.740626i	−0.380417	+	0.0291621i
$646$	−0.0809009	+	0.552194i	−0.00318300	+	0.0217258i
$647$	−3.95866	−	3.95866i	−0.155631	−	0.155631i	0.624997	−	0.780628i	$-0.285100\pi$
$647$	−3.95866	−	3.95866i	−0.155631	−	0.155631i	−0.780628	+	0.624997i	$0.785100\pi$
$648$	6.60110	+	24.5851i	0.259316	+	0.965793i
$649$	−4.45335	+	4.45335i	−0.174809	+	0.174809i
$650$	−6.87340	−	9.23314i	−0.269597	−	0.362153i
$651$	−0.0833915	−	1.08784i	−0.00326837	−	0.0426357i
$652$	33.0955	+	26.9632i	1.29612	+	1.05596i
$653$	−2.38016	−	5.74622i	−0.0931429	−	0.224867i	0.870441	−	0.492273i	$-0.163834\pi$
$653$	−2.38016	−	5.74622i	−0.0931429	−	0.224867i	−0.963584	+	0.267406i	$0.913834\pi$
$654$	20.4250	+	23.4560i	0.798679	+	0.917203i
$655$	17.0922			0.667847
$656$	46.2516	−	9.54457i	1.80582	−	0.372653i
$657$	19.9225	+	14.5986i	0.777250	+	0.569544i
$658$	1.07227	+	4.24846i	0.0418013	+	0.165622i
$659$	−17.1001	+	7.08309i	−0.666125	+	0.275918i	−0.690014	−	0.723796i	$-0.742395\pi$
$659$	−17.1001	+	7.08309i	−0.666125	+	0.275918i	0.0238882	+	0.999715i	$0.492395\pi$
$660$	−3.20017	+	2.05555i	−0.124567	+	0.0800121i
$661$	11.8710	−	28.6592i	0.461730	−	1.11471i	−0.505957	−	0.862559i	$-0.668860\pi$
$661$	11.8710	−	28.6592i	0.461730	−	1.11471i	0.967687	−	0.252156i	$-0.0811396\pi$
$662$	−22.5610	−	30.3065i	−0.876858	−	1.17790i
$663$	−0.931902	−	0.304887i	−0.0361921	−	0.0118408i
$664$	−16.0465	−	44.0993i	−0.622724	−	1.71138i
$665$	5.79748	−	5.79748i	0.224817	−	0.224817i
$666$	−3.20833	+	3.25711i	−0.124320	+	0.126210i
$667$	2.18176	−	5.26722i	0.0844779	−	0.203948i
$668$	−8.00134	+	26.7207i	−0.309581	+	1.03385i
$669$	21.9635	−	25.6105i	0.849160	−	0.990158i
$670$	20.7373	−	34.7388i	0.801150	−	1.34208i
$671$	−2.81449			−0.108652
$672$	8.46739	−	4.92984i	0.326637	−	0.190173i
$673$	−17.7553			−0.684416			−0.342208	−	0.939624i	$-0.611175\pi$
$673$	−17.7553			−0.684416			−0.342208	+	0.939624i	$0.611175\pi$
$674$	−5.86186	+	9.81973i	−0.225791	+	0.378242i
$675$	6.71140	−	1.56807i	0.258322	−	0.0603552i
$676$	47.2374	+	14.1450i	1.81682	+	0.544037i
$677$	13.1278	−	31.6934i	0.504543	−	1.21808i	−0.442441	−	0.896797i	$-0.645888\pi$
$677$	13.1278	−	31.6934i	0.504543	−	1.21808i	0.946985	−	0.321278i	$-0.104112\pi$
$678$	−4.24565	−	12.6532i	−0.163053	−	0.485944i
$679$	−10.1785	+	10.1785i	−0.390615	+	0.390615i
$680$	−0.453241	−	0.211398i	−0.0173810	−	0.00810674i
$681$	−3.92031	+	11.9826i	−0.150227	+	0.459174i
$682$	0.304724	+	0.409340i	0.0116685	+	0.0156744i
$683$	8.30627	−	20.0531i	0.317831	−	0.767311i	−0.681538	−	0.731783i	$-0.738689\pi$
$683$	8.30627	−	20.0531i	0.317831	−	0.767311i	0.999369	−	0.0355285i	$-0.0113115\pi$
$684$	22.1367	+	12.9890i	0.846418	+	0.496646i
$685$	−13.8378	+	5.73182i	−0.528717	+	0.219002i
$686$	−0.346079	−	1.37121i	−0.0132134	−	0.0523532i
$687$	7.48489	+	14.7640i	0.285566	+	0.563281i
$688$	−9.66094	+	6.55571i	−0.368320	+	0.249934i
$689$	−10.2272			−0.389626
$690$	6.62092	−	5.76535i	0.252054	−	0.219483i
$691$	−0.0957300	−	0.231113i	−0.00364174	−	0.00879194i	0.922048	−	0.387075i	$-0.126515\pi$
$691$	−0.0957300	−	0.231113i	−0.00364174	−	0.00879194i	−0.925690	+	0.378283i	$0.876515\pi$
$692$	5.02502	−	6.16787i	0.191022	−	0.234467i
$693$	−1.46895	+	0.891985i	−0.0558007	+	0.0338837i
$694$	−27.4148	−	36.8266i	−1.04065	−	1.39792i
$695$	27.8432	−	27.8432i	1.05615	−	1.05615i
$696$	−5.26033	+	13.9790i	−0.199392	+	0.529874i
$697$	−0.770172	−	0.770172i	−0.0291723	−	0.0291723i
$698$	−4.94827	+	33.7747i	−0.187295	+	1.27839i
$699$	−0.392377	−	5.11852i	−0.0148410	−	0.193600i
$700$	−1.25888	−	2.33506i	−0.0475812	−	0.0882571i
$701$	−40.3179	+	16.7002i	−1.52278	+	0.630758i	−0.978147	−	0.207913i	$-0.933333\pi$
$701$	−40.3179	+	16.7002i	−1.52278	+	0.630758i	−0.544638	+	0.838672i	$0.683333\pi$
$702$	−29.0960	+	34.4498i	−1.09816	+	1.30022i
$703$			4.60965i			0.173856i
$704$	−2.11682	+	4.06465i	−0.0797808	+	0.153192i
$705$	−4.65098	−	9.17408i	−0.175166	−	0.345516i
$706$	−15.3844	+	25.7718i	−0.579000	+	0.969935i
$707$	−6.31165	−	15.2377i	−0.237374	−	0.573072i
$708$	−21.7279	+	31.2783i	−0.816586	+	1.17551i
$709$	5.81578	+	2.40897i	0.218416	+	0.0904709i	0.489209	−	0.872167i	$-0.337286\pi$
$709$	5.81578	+	2.40897i	0.218416	+	0.0904709i	−0.270792	+	0.962638i	$0.587286\pi$
$710$	33.2047	+	4.86476i	1.24615	+	0.182571i
$711$	−4.21800	−	27.3501i	−0.158187	−	1.02571i
$712$	−1.65304	−	1.80430i	−0.0619504	−	0.0676188i
$713$	−0.832909	−	0.832909i	−0.0311927	−	0.0311927i
$714$	−0.202316	−	0.100657i	−0.00757149	−	0.00376699i
$715$	−6.22466	−	2.57834i	−0.232789	−	0.0964244i
$716$	−2.78334	−	2.26761i	−0.104018	−	0.0847445i
$717$	10.8508	−	12.6525i	0.405231	−	0.472518i
$718$	−9.41593	−	37.3072i	−0.351399	−	1.39229i
$719$			2.78813i			0.103980i	0.998648	+	0.0519899i	$0.0165564\pi$
$719$			2.78813i			0.103980i	−0.998648	+	0.0519899i	$0.983444\pi$
$720$	−16.8410	+	15.6646i	−0.627628	+	0.583784i
$721$			0.138450i			0.00515615i
$722$	−0.961865	+	0.242764i	−0.0357969	+	0.00903475i
$723$	4.30828	−	5.02365i	0.160227	−	0.186832i
$724$	−10.3491	+	1.05670i	−0.384621	+	0.0392718i
$725$	3.73609	+	1.54754i	0.138755	+	0.0574742i
$726$	−11.6440	+	23.4040i	−0.432150	+	0.868603i
$727$	21.3359	+	21.3359i	0.791303	+	0.791303i	0.981706	−	0.190403i	$-0.0609794\pi$
$727$	21.3359	+	21.3359i	0.791303	+	0.791303i	−0.190403	+	0.981706i	$0.560979\pi$
$728$	15.7295	+	7.33644i	0.582972	+	0.271906i
$729$	−11.9636	−	24.2048i	−0.443098	−	0.896473i
$730$	−3.23492	+	22.0801i	−0.119730	+	0.817222i
$731$	0.248772	+	0.103045i	0.00920116	+	0.00381124i
$732$	−16.7498	+	3.01787i	−0.619090	+	0.111544i
$733$	−15.6463	−	37.7735i	−0.577909	−	1.39520i	−0.894686	−	0.446695i	$-0.852601\pi$
$733$	−15.6463	−	37.7735i	−0.577909	−	1.39520i	0.316778	−	0.948500i	$-0.397399\pi$
$734$	−30.8805	−	18.4340i	−1.13982	−	0.680412i
$735$	1.50113	+	2.96098i	0.0553700	+	0.109218i
$736$	3.47446	−	9.99133i	0.128070	−	0.368285i
$737$			8.55032i			0.314955i
$738$	−46.1320	+	19.5175i	−1.69814	+	0.718450i
$739$	40.9690	−	16.9699i	1.50707	−	0.624249i	0.532119	−	0.846670i	$-0.321396\pi$
$739$	40.9690	−	16.9699i	1.50707	−	0.624249i	0.974951	+	0.222421i	$0.0713960\pi$
$740$	−3.95721	−	1.18496i	−0.145470	−	0.0435600i
$741$	3.47509	+	45.3322i	0.127660	+	1.66532i
$742$	−2.33212	−	0.341674i	−0.0856147	−	0.0125432i
$743$	−4.49913	−	4.49913i	−0.165057	−	0.165057i	0.619746	−	0.784803i	$-0.287236\pi$
$743$	−4.49913	−	4.49913i	−0.165057	−	0.165057i	−0.784803	+	0.619746i	$0.787236\pi$
$744$	2.25242	+	2.10935i	0.0825775	+	0.0773325i
$745$	3.88546	−	3.88546i	0.142352	−	0.142352i
$746$	35.4339	−	26.3779i	1.29733	−	0.965765i
$747$	25.8346	+	42.5452i	0.945237	+	1.55665i
$748$	0.105148	−	0.0107362i	0.00384459	−	0.000392553i
$749$	1.87659	+	4.53049i	0.0685691	+	0.165540i
$750$	19.5049	+	22.3995i	0.712220	+	0.817912i
$751$	31.4711			1.14840			0.574199	−	0.818716i	$-0.305314\pi$
$751$	31.4711			1.14840			0.574199	+	0.818716i	$0.305314\pi$
$752$	−10.3536	−	6.81143i	−0.377559	−	0.248387i
$753$	−11.9335	−	23.5388i	−0.434880	−	0.857802i
$754$	−25.6534	+	6.47464i	−0.934242	+	0.235792i
$755$	−8.14648	+	3.37438i	−0.296481	+	0.122806i
$756$	−7.78568	+	6.88355i	−0.283162	+	0.250352i
$757$	−17.3946	+	41.9943i	−0.632218	+	1.52631i	0.204611	+	0.978843i	$0.434407\pi$
$757$	−17.3946	+	41.9943i	−0.632218	+	1.52631i	−0.836829	+	0.547465i	$0.815593\pi$
$758$	−2.77494	+	2.06574i	−0.100790	+	0.0750310i
$759$	−0.576938	+	1.76344i	−0.0209415	+	0.0640087i
$760$	−1.01355	+	23.1678i	−0.0367654	+	0.840383i
$761$	−7.55754	+	7.55754i	−0.273961	+	0.273961i	−0.830692	−	0.556732i	$-0.812055\pi$
$761$	−7.55754	+	7.55754i	−0.273961	+	0.273961i	0.556732	+	0.830692i	$0.312055\pi$
$762$	21.3925	−	7.17801i	0.774968	−	0.260032i
$763$	−4.85913	+	11.7310i	−0.175912	+	0.424690i
$764$	7.01356	+	13.0093i	0.253742	+	0.470659i
$765$	0.515290	+	0.125926i	0.0186303	+	0.00455288i
$766$	24.9509	+	14.8944i	0.901514	+	0.538157i
$767$	−67.4635			−2.43597
$768$	−8.23943	+	26.4596i	−0.297315	+	0.954780i
$769$	−45.6580			−1.64647			−0.823235	−	0.567701i	$-0.807833\pi$
$769$	−45.6580			−1.64647			−0.823235	+	0.567701i	$0.807833\pi$
$770$	−1.33327	−	0.795895i	−0.0480478	−	0.0286820i
$771$	1.55163	−	1.80927i	0.0558807	−	0.0651594i
$772$	−4.97512	−	9.22822i	−0.179058	−	0.332131i
$773$	9.23234	−	22.2888i	0.332064	−	0.801674i	−0.666364	−	0.745627i	$-0.732150\pi$
$773$	9.23234	−	22.2888i	0.332064	−	0.801674i	0.998428	−	0.0560473i	$-0.0178498\pi$
$774$	8.69012	−	8.82224i	0.312360	−	0.317109i
$775$	0.590790	−	0.590790i	0.0212218	−	0.0212218i
$776$	1.77947	−	40.6751i	0.0638794	−	1.46015i
$777$	−1.77394	−	0.580374i	−0.0636397	−	0.0208208i
$778$	−36.1339	+	26.8990i	−1.29546	+	0.964377i
$779$	−19.3273	+	46.6601i	−0.692471	+	1.67177i
$780$	−39.8093	−	8.66993i	−1.42540	−	0.310433i
$781$	−6.55253	+	2.71415i	−0.234468	+	0.0971198i
$782$	−0.236550	+	0.0597026i	−0.00845901	+	0.00213496i
$783$	2.57354	−	15.6316i	0.0919709	−	0.558628i
$784$	3.34170	+	2.19842i	0.119346	+	0.0785152i
$785$	−39.7399			−1.41838
$786$	−16.4735	+	14.3448i	−0.587591	+	0.511661i
$787$	−6.62820	−	16.0019i	−0.236270	−	0.570406i	0.760621	−	0.649196i	$-0.224894\pi$
$787$	−6.62820	−	16.0019i	−0.236270	−	0.570406i	−0.996891	+	0.0787897i	$0.974894\pi$
$788$	−31.8124	+	3.24822i	−1.13327	+	0.115713i
$789$	1.69233	+	22.0763i	0.0602484	+	0.785935i
$790$	20.0564	−	14.9305i	0.713575	−	0.531205i
$791$	3.85281	−	3.85281i	0.136990	−	0.136990i
$792$	1.35920	−	4.66692i	0.0482971	−	0.165832i
$793$	−21.3183	−	21.3183i	−0.757033	−	0.757033i
$794$	3.35733	+	0.491876i	0.119147	+	0.0174560i
$795$	5.51672	−	0.422902i	0.195658	−	0.0149988i
$796$	8.68136	+	2.59958i	0.307703	+	0.0921396i
$797$	50.7843	−	21.0356i	1.79887	−	0.745118i	0.811993	−	0.583668i	$-0.198383\pi$
$797$	50.7843	−	21.0356i	1.79887	−	0.745118i	0.986881	−	0.161450i	$-0.0516171\pi$
$798$	−0.722048	+	10.4532i	−0.0255602	+	0.370040i
$799$			0.285829i			0.0101119i
$800$	7.08695	+	2.46447i	0.250561	+	0.0871322i
$801$	2.09358	+	1.53411i	0.0739729	+	0.0542049i
$802$	−4.59365	−	2.74217i	−0.162207	−	0.0968294i
$803$	−1.80482	−	4.35723i	−0.0636908	−	0.153763i
$804$	9.16820	+	50.8853i	0.323337	+	1.79459i
$805$	3.31130	+	1.37159i	0.116708	+	0.0483421i
$806$	−0.792412	+	5.40865i	−0.0279115	+	0.190512i
$807$	12.0888	−	36.9499i	0.425546	−	1.30070i
$808$	42.2772	+	19.7187i	1.48731	+	0.693701i
$809$	−2.60429	−	2.60429i	−0.0915621	−	0.0915621i	0.659842	−	0.751404i	$-0.270623\pi$
$809$	−2.60429	−	2.60429i	−0.0915621	−	0.0915621i	−0.751404	+	0.659842i	$0.770623\pi$
$810$	14.2703	−	19.7859i	0.501408	−	0.695206i
$811$	−14.2954	−	5.92134i	−0.501979	−	0.207927i	0.117301	−	0.993096i	$-0.462576\pi$
$811$	−14.2954	−	5.92134i	−0.501979	−	0.207927i	−0.619280	+	0.785170i	$0.712576\pi$
$812$	−6.06606	+	0.619377i	−0.212877	+	0.0217359i
$813$	20.3346	+	17.4390i	0.713167	+	0.611611i
$814$	0.846463	−	0.213638i	0.0296685	−	0.00748801i
$815$		−	40.9100i		−	1.43301i
$816$	0.614253	−	0.176640i	0.0215032	−	0.00618365i
$817$		−	12.4857i		−	0.436820i
$818$	8.24920	+	32.6845i	0.288427	+	1.14279i
$819$	−17.8828	−	4.37020i	−0.624876	−	0.152707i
$820$	−35.0877	−	28.5862i	−1.22531	−	0.998275i
$821$	−38.1533	−	15.8036i	−1.33156	−	0.551550i	−0.400460	−	0.916314i	$-0.631150\pi$
$821$	−38.1533	−	15.8036i	−1.33156	−	0.551550i	−0.931100	+	0.364764i	$0.881150\pi$
$822$	8.52649	−	17.1379i	0.297395	−	0.597752i
$823$	2.00686	+	2.00686i	0.0699546	+	0.0699546i	0.741218	−	0.671264i	$-0.234248\pi$
$823$	2.00686	+	2.00686i	0.0699546	+	0.0699546i	−0.671264	+	0.741218i	$0.734248\pi$
$824$	−0.264533	−	0.288738i	−0.00921545	−	0.0100587i
$825$	−1.25082	−	0.409228i	−0.0435481	−	0.0142475i
$826$	−15.3837	−	2.25384i	−0.535269	−	0.0784212i
$827$	17.4699	+	7.23627i	0.607488	+	0.251630i	0.665154	−	0.746706i	$-0.268366\pi$
$827$	17.4699	+	7.23627i	0.607488	+	0.251630i	−0.0576662	+	0.998336i	$0.518366\pi$
$828$	−1.54265	+	11.1133i	−0.0536108	+	0.386215i
$829$	−20.0269	−	48.3492i	−0.695562	−	1.67924i	−0.733261	−	0.679947i	$-0.762003\pi$
$829$	−20.0269	−	48.3492i	−0.695562	−	1.67924i	0.0376987	−	0.999289i	$-0.487997\pi$
$830$	−23.0515	+	38.6156i	−0.800130	+	1.34037i
$831$	14.0915	−	7.14395i	0.488828	−	0.247821i
$832$	−46.8214	+	14.7537i	−1.62324	+	0.511494i
$833$		−	0.0922529i		−	0.00319637i
$834$	−3.46773	+	50.2029i	−0.120078	+	1.73839i
$835$	24.6960	−	10.2294i	0.854639	−	0.354003i
$836$	−2.32575	−	4.31397i	−0.0804377	−	0.149202i
$837$	−2.78029	−	1.72716i	−0.0961008	−	0.0596992i
$838$	−6.52741	+	44.5532i	−0.225486	+	1.53907i
$839$	−15.3743	−	15.3743i	−0.530780	−	0.530780i	0.390024	−	0.920805i	$-0.372467\pi$
$839$	−15.3743	−	15.3743i	−0.530780	−	0.530780i	−0.920805	+	0.390024i	$0.872467\pi$
$840$	−8.78809	−	3.30697i	−0.303218	−	0.114101i
$841$	−13.9334	+	13.9334i	−0.480462	+	0.480462i
$842$	27.4502	+	36.8742i	0.945996	+	1.27077i
$843$	−15.1724	+	1.16309i	−0.522564	+	0.0400588i
$844$	16.9751	−	20.8358i	0.584307	−	0.717198i
$845$	−18.0838	−	43.6581i	−0.622100	−	1.50188i
$846$	12.1821	+	4.93864i	0.418828	+	0.169794i
$847$	−10.6718			−0.366689
$848$	5.51646	−	3.74335i	0.189436	−	0.128547i
$849$	−17.3508	+	8.79634i	−0.595479	+	0.301890i
$850$	−0.0423476	−	0.167787i	−0.00145251	−	0.00575505i
$851$	−1.86171	+	0.771146i	−0.0638186	+	0.0264345i
$852$	−36.0856	+	23.1787i	−1.23627	+	0.794089i
$853$	−6.05428	+	14.6163i	−0.207295	+	0.500453i	−0.992995	−	0.118153i	$-0.962303\pi$
$853$	−6.05428	+	14.6163i	−0.207295	+	0.500453i	0.785701	+	0.618607i	$0.212303\pi$
$854$	−4.14900	−	5.57342i	−0.141976	−	0.190718i
$855$	−3.74903	−	24.3092i	−0.128214	−	0.831358i
$856$	−12.5699	−	5.86279i	−0.429631	−	0.200386i
$857$	19.4458	−	19.4458i	0.664258	−	0.664258i	−0.292123	−	0.956381i	$-0.594362\pi$
$857$	19.4458	−	19.4458i	0.664258	−	0.664258i	0.956381	+	0.292123i	$0.0943617\pi$
$858$	8.16324	−	2.73909i	0.278688	−	0.0935109i
$859$	10.2701	−	24.7943i	0.350412	−	0.845971i	−0.646157	−	0.763205i	$-0.723625\pi$
$859$	10.2701	−	24.7943i	0.350412	−	0.845971i	0.996569	−	0.0827657i	$-0.0263753\pi$
$860$	10.7185	+	3.20960i	0.365499	+	0.109446i
$861$	−15.5229	−	13.3125i	−0.529020	−	0.453687i
$862$	26.1029	−	43.7273i	0.889070	−	1.48936i
$863$	17.4226			0.593071			0.296536	−	0.955022i	$-0.404169\pi$
$863$	17.4226			0.593071			0.296536	+	0.955022i	$0.404169\pi$
$864$	3.08482	−	29.2316i	0.104948	−	0.994478i
$865$	−7.62422			−0.259231
$866$	7.09211	−	11.8806i	0.241000	−	0.403720i
$867$	22.3400	+	19.1588i	0.758705	+	0.650665i
$868$	−0.361388	+	1.20686i	−0.0122663	+	0.0409636i
$869$	−2.02220	+	4.88203i	−0.0685985	+	0.165611i
$870$	13.5701	−	4.55331i	0.460070	−	0.154372i
$871$	−64.7642	+	64.7642i	−2.19445	+	2.19445i
$872$	−12.2804	−	33.7492i	−0.415866	−	1.14289i
$873$	6.58210	+	42.6792i	0.222770	+	1.44447i
$874$	6.75512	+	9.07425i	0.228495	+	0.306941i
$875$	−4.64026	+	11.2026i	−0.156869	+	0.378716i
$876$	−15.4131	−	23.9958i	−0.520761	−	0.810744i
$877$	−26.4620	+	10.9609i	−0.893558	+	0.370124i	−0.781740	−	0.623605i	$-0.785667\pi$
$877$	−26.4620	+	10.9609i	−0.893558	+	0.370124i	−0.111818	+	0.993729i	$0.535667\pi$
$878$	−10.8383	−	42.9428i	−0.365774	−	1.44925i
$879$	27.2092	−	13.7943i	0.917745	−	0.465269i
$880$	4.30124	−	0.887613i	0.144995	−	0.0299214i
$881$	−20.0866			−0.676735			−0.338368	−	0.941014i	$-0.609875\pi$
$881$	−20.0866			−0.676735			−0.338368	+	0.941014i	$0.609875\pi$
$882$	−3.93183	−	1.59397i	−0.132391	−	0.0536719i
$883$	19.3803	+	46.7881i	0.652198	+	1.57455i	0.809581	+	0.587008i	$0.199694\pi$
$883$	19.3803	+	46.7881i	0.652198	+	1.57455i	−0.157383	+	0.987538i	$0.550306\pi$
$884$	0.877762	+	0.715120i	0.0295223	+	0.0240521i
$885$	36.3909	−	2.78966i	1.22327	−	0.0937734i
$886$	−29.2822	−	39.3352i	−0.983754	−	1.32149i
$887$	24.3258	−	24.3258i	0.816780	−	0.816780i	−0.168860	−	0.985640i	$-0.554009\pi$
$887$	24.3258	−	24.3258i	0.816780	−	0.816780i	0.985640	+	0.168860i	$0.0540087\pi$
$888$	4.80846	−	2.17905i	0.161361	−	0.0731242i
$889$	6.51384	+	6.51384i	0.218467	+	0.218467i
$890$	−0.339945	+	2.32031i	−0.0113950	+	0.0777771i
$891$	−0.446257	+	5.13633i	−0.0149502	+	0.172073i
$892$	−34.2920	+	18.4875i	−1.14818	+	0.619007i
$893$	12.2448	−	5.07194i	0.409755	−	0.169726i
$894$	−0.483915	+	7.00573i	−0.0161845	+	0.234307i
$895$			3.44053i			0.115004i
$896$	−11.1696	+	1.80008i	−0.373150	+	0.0601363i
$897$	−17.7271	+	8.98710i	−0.591891	+	0.300071i
$898$	−12.3560	+	20.6987i	−0.412326	+	0.690723i
$899$	−0.734926	−	1.77427i	−0.0245112	−	0.0591752i
$900$	−7.88279	−	1.09422i	−0.262760	−	0.0364739i
$901$	−0.142050	−	0.0588392i	−0.00473238	−	0.00196022i
$902$	9.46388	+	1.38654i	0.315113	+	0.0461666i
$903$	4.80491	+	1.57201i	0.159897	+	0.0523131i
$904$	−0.673573	+	15.3965i	−0.0224027	+	0.512080i
$905$	7.04945	+	7.04945i	0.234332	+	0.234332i
$906$	5.01963	−	10.0892i	0.166766	−	0.335193i
$907$	−4.13594	−	1.71316i	−0.137332	−	0.0568847i	0.312959	−	0.949767i	$-0.398680\pi$
$907$	−4.13594	−	1.71316i	−0.137332	−	0.0568847i	−0.450291	+	0.892882i	$0.648680\pi$
$908$	9.19517	−	11.2865i	0.305152	−	0.374554i
$909$	−48.0650	−	11.7461i	−1.59421	−	0.389594i
$910$	−4.07036	−	16.1273i	−0.134931	−	0.534615i
$911$			13.0208i			0.431398i	0.976460	+	0.215699i	$0.0692030\pi$
$911$			13.0208i			0.431398i	−0.976460	+	0.215699i	$0.930797\pi$
$912$	−18.4669	−	23.1798i	−0.611500	−	0.767560i
$913$		−	9.50452i		−	0.314554i
$914$	15.4164	−	3.89094i	0.509931	−	0.128701i
$915$	12.3809	+	10.6179i	0.409301	+	0.351016i
$916$	−1.94151	−	19.0148i	−0.0641493	−	0.628266i
$917$	−8.23886	−	3.41265i	−0.272071	−	0.112696i
$918$	−0.602323	+	0.311093i	−0.0198796	+	0.0102676i
$919$	−36.1064	−	36.1064i	−1.19104	−	1.19104i	−0.976775	−	0.214266i	$-0.931264\pi$
$919$	−36.1064	−	36.1064i	−1.19104	−	1.19104i	−0.214266	−	0.976775i	$-0.568736\pi$
$920$	−9.52639	+	3.46638i	−0.314076	+	0.114283i
$921$	−12.0436	+	36.8119i	−0.396851	+	1.21299i
$922$	3.22468	−	22.0102i	0.106199	−	0.724868i
$923$	−70.1902	−	29.0737i	−2.31034	−	0.956973i
$924$	1.95298	−	0.351875i	0.0642482	−	0.0115758i
$925$	−0.546981	−	1.32053i	−0.0179846	−	0.0434187i
$926$	−6.36905	−	3.80199i	−0.209300	−	0.124941i
$927$	0.335031	+	0.245500i	0.0110039	+	0.00806327i
$928$	11.4674	−	12.8820i	0.376434	−	0.422872i
$929$			53.3222i			1.74944i	0.484624	+	0.874722i	$0.338956\pi$
$929$			53.3222i			1.74944i	−0.484624	+	0.874722i	$0.661044\pi$
$930$	0.203788	−	2.95028i	0.00668248	−	0.0967435i
$931$	−3.95206	+	1.63700i	−0.129524	+	0.0536504i
$932$	−1.70041	+	5.67858i	−0.0556989	+	0.186008i
$933$	46.4926	−	3.56404i	1.52210	−	0.116681i
$934$	−35.3894	−	5.18483i	−1.15798	−	0.169653i
$935$	−0.0716233	−	0.0716233i	−0.00234233	−	0.00234233i
$936$	45.6447	−	25.0542i	1.49194	−	0.818923i
$937$	−21.0185	+	21.0185i	−0.686646	+	0.686646i	−0.961489	−	0.274843i	$-0.911374\pi$
$937$	−21.0185	+	21.0185i	−0.686646	+	0.686646i	0.274843	+	0.961489i	$0.411374\pi$
$938$	−16.9319	+	12.6045i	−0.552845	+	0.411553i
$939$	−4.13034	−	53.8799i	−0.134788	−	1.75830i
$940$	1.20642	+	11.8155i	0.0393491	+	0.385378i
$941$	11.1727	+	26.9732i	0.364218	+	0.879301i	0.994674	+	0.103075i	$0.0328682\pi$
$941$	11.1727	+	26.9732i	0.364218	+	0.879301i	−0.630455	+	0.776226i	$0.717132\pi$
$942$	38.3015	−	33.3521i	1.24793	−	1.08667i
$943$	−22.0780			−0.718959
$944$	36.3892	−	24.6929i	1.18437	−	0.803686i
$945$	9.82699	+	1.61789i	0.319672	+	0.0526299i
$946$	−2.29274	+	0.578662i	−0.0745433	+	0.0188139i
$947$	33.2749	−	13.7829i	1.08129	−	0.447884i	0.230327	−	0.973113i	$-0.426020\pi$
$947$	33.2749	−	13.7829i	1.08129	−	0.447884i	0.850961	+	0.525229i	$0.176020\pi$
$948$	−6.79987	+	31.2226i	−0.220849	+	1.01406i
$949$	19.3331	−	46.6743i	0.627580	−	1.51511i
$950$	−6.43646	+	4.79147i	−0.208826	+	0.155456i
$951$	15.3146	+	5.01044i	0.496611	+	0.162475i
$952$	0.176265	+	0.192394i	0.00571279	+	0.00623551i
$953$	24.3943	−	24.3943i	0.790208	−	0.790208i	−0.191320	−	0.981528i	$-0.561277\pi$
$953$	24.3943	−	24.3943i	0.790208	−	0.790208i	0.981528	+	0.191320i	$0.0612767\pi$
$954$	−4.96212	+	5.03755i	−0.160654	+	0.163097i
$955$	5.42018	−	13.0855i	0.175393	−	0.423436i
$956$	−16.9415	+	9.13351i	−0.547928	+	0.295399i
$957$	−1.96928	+	2.29627i	−0.0636579	+	0.0742279i
$958$	−8.11667	−	4.84523i	−0.262238	−	0.156542i
$959$	7.81460			0.252347
$960$	24.6461	−	9.89449i	0.795450	−	0.319343i
$961$	30.6032			0.987201
$962$	8.02971	+	4.79332i	0.258888	+	0.154543i
$963$	14.2907	+	3.49237i	0.460513	+	0.112540i
$964$	−6.72658	+	3.62643i	−0.216648	+	0.116800i
$965$	−3.84484	+	9.28226i	−0.123770	+	0.298806i
$966$	−4.34256	+	1.45710i	−0.139720	+	0.0468814i
$967$	−10.9328	+	10.9328i	−0.351576	+	0.351576i	−0.860696	−	0.509120i	$-0.829971\pi$
$967$	−10.9328	+	10.9328i	−0.351576	+	0.351576i	0.509120	+	0.860696i	$0.329971\pi$
$968$	22.2561	−	20.3904i	0.715340	−	0.655373i
$969$	−0.212538	+	0.649632i	−0.00682771	+	0.0208692i
$970$	−31.2976	+	23.2988i	−1.00491	+	0.748079i
$971$	−9.32368	+	22.5093i	−0.299211	+	0.722359i	0.700749	+	0.713408i	$0.252849\pi$
$971$	−9.32368	+	22.5093i	−0.299211	+	0.722359i	−0.999960	+	0.00895125i	$0.997151\pi$
$972$	2.85170	+	31.0462i	0.0914683	+	0.995808i
$973$	−18.9803	+	7.86189i	−0.608480	+	0.252041i
$974$	26.2019	−	6.61308i	0.839564	−	0.211897i
$975$	−6.37464	−	12.5740i	−0.204152	−	0.402690i
$976$	19.3017	+	3.69597i	0.617834	+	0.118305i
$977$	54.6751			1.74921			0.874605	−	0.484836i	$-0.161121\pi$
$977$	54.6751			1.74921			0.874605	+	0.484836i	$0.161121\pi$
$978$	34.3341	+	39.4292i	1.09788	+	1.26081i
$979$	−0.189662	−	0.457884i	−0.00606162	−	0.0146340i
$980$	−0.389379	−	3.81350i	−0.0124382	−	0.121818i
$981$	19.7712	+	32.5599i	0.631246	+	1.03956i
$982$	37.4384	−	27.8702i	1.19471	−	0.889373i
$983$	−4.37715	+	4.37715i	−0.139609	+	0.139609i	−0.773458	−	0.633848i	$-0.781474\pi$
$983$	−4.37715	+	4.37715i	−0.139609	+	0.139609i	0.633848	+	0.773458i	$0.281474\pi$
$984$	57.8089	−	1.89612i	1.84288	−	0.0604460i
$985$	21.6696	+	21.6696i	0.690450	+	0.690450i
$986$	−0.393561	−	0.0576599i	−0.0125335	−	0.00183627i
$987$	0.410179	+	5.35075i	0.0130561	+	0.170316i
$988$	15.0597	−	50.2924i	0.479114	−	1.60001i
$989$	5.04265	−	2.08873i	0.160347	−	0.0664178i
$990$	−4.29012	+	1.81506i	−0.136349	+	0.0576865i
$991$		−	24.5953i		−	0.781294i	−0.920540	−	0.390647i	$-0.872251\pi$
$991$		−	24.5953i		−	0.781294i	0.920540	−	0.390647i	$-0.127749\pi$
$992$	−1.55225	−	3.20741i	−0.0492840	−	0.101835i
$993$	−20.9239	−	41.2724i	−0.663999	−	1.30974i
$994$	−15.0342	−	8.97463i	−0.476856	−	0.284658i
$995$	−3.32346	−	8.02354i	−0.105361	−	0.254363i
$996$	−10.1914	−	56.5641i	−0.322926	−	1.79230i
$997$	−40.4599	−	16.7590i	−1.28138	−	0.530764i	−0.364974	−	0.931018i	$-0.618922\pi$
$997$	−40.4599	−	16.7590i	−1.28138	−	0.530764i	−0.916404	+	0.400254i	$0.868922\pi$
$998$	−4.23460	+	28.9035i	−0.134044	+	0.914926i
$999$	−4.54998	+	3.26358i	−0.143955	+	0.103255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.9	✓	192
3.2	odd	2	inner	672.2.bs.a.155.40	yes	192
32.19	odd	8	inner	672.2.bs.a.659.40	yes	192
96.83	even	8	inner	672.2.bs.a.659.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.9	✓	192	1.1	even	1	trivial
672.2.bs.a.155.40	yes	192	3.2	odd	2	inner
672.2.bs.a.659.9	yes	192	96.83	even	8	inner
672.2.bs.a.659.40	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21431 - 0.724880i) q^{2} +(-1.31477 - 1.12755i) q^{3} +(0.949098 + 1.76046i) q^{4} +(0.733476 - 1.77077i) q^{5} +(0.779205 + 2.32225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.123621 - 2.82572i) q^{8} +(0.457262 + 2.96495i) q^{9} +O(q^{10})\)	\(q+(-1.21431 - 0.724880i) q^{2} +(-1.31477 - 1.12755i) q^{3} +(0.949098 + 1.76046i) q^{4} +(0.733476 - 1.77077i) q^{5} +(0.779205 + 2.32225i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.123621 - 2.82572i) q^{8} +(0.457262 + 2.96495i) q^{9} +(-2.17426 + 1.61858i) q^{10} +(0.219221 - 0.529247i) q^{11} +(0.737155 - 3.38476i) q^{12} +(5.66926 - 2.34828i) q^{13} +(1.37121 - 0.346079i) q^{14} +(-2.96098 + 1.50113i) q^{15} +(-2.19842 + 3.34170i) q^{16} +0.0922529 q^{17} +(1.59397 - 3.93183i) q^{18} +(-1.63700 - 3.95206i) q^{19} +(3.81350 - 0.389379i) q^{20} +(1.72698 - 0.132387i) q^{21} +(-0.649843 + 0.483761i) q^{22} +(1.32228 - 1.32228i) q^{23} +(-3.34868 + 3.57580i) q^{24} +(0.937904 + 0.937904i) q^{25} +(-8.58646 - 1.25799i) q^{26} +(2.74193 - 4.41382i) q^{27} +(-1.91595 - 0.573718i) q^{28} +(2.81672 - 1.16673i) q^{29} +(4.68369 + 0.323522i) q^{30} -0.629905i q^{31} +(5.09190 - 2.46426i) q^{32} +(-0.884979 + 0.448658i) q^{33} +(-0.112024 - 0.0668723i) q^{34} +(0.733476 + 1.77077i) q^{35} +(-4.78568 + 3.61902i) q^{36} +(-0.995577 - 0.412381i) q^{37} +(-0.876947 + 5.98565i) q^{38} +(-10.1016 - 3.30491i) q^{39} +(-4.91303 - 2.29150i) q^{40} +(-8.34848 - 8.34848i) q^{41} +(-2.19306 - 1.09110i) q^{42} +(2.69663 + 1.11698i) q^{43} +(1.13978 - 0.116378i) q^{44} +(5.58562 + 1.36501i) q^{45} +(-2.56415 + 0.647162i) q^{46} +3.09832i q^{47} +(6.65836 - 1.91474i) q^{48} -1.00000i q^{49} +(-0.459038 - 1.81877i) q^{50} +(-0.121292 - 0.104020i) q^{51} +(9.51473 + 7.75174i) q^{52} +(-1.53979 - 0.637803i) q^{53} +(-6.52904 + 3.37218i) q^{54} +(-0.776380 - 0.776380i) q^{55} +(1.91068 + 2.08550i) q^{56} +(-2.30386 + 7.04186i) q^{57} +(-4.26611 - 0.625020i) q^{58} +(-10.1572 - 4.20725i) q^{59} +(-5.45294 - 3.78797i) q^{60} +(-1.88016 - 4.53912i) q^{61} +(-0.456606 + 0.764900i) q^{62} +(-2.41987 - 1.77320i) q^{63} +(-7.96944 - 0.698638i) q^{64} -11.7613i q^{65} +(1.39986 + 0.0966944i) q^{66} +(-13.7897 + 5.71188i) q^{67} +(0.0875571 + 0.162407i) q^{68} +(-3.22943 + 0.247562i) q^{69} +(0.392927 - 2.68194i) q^{70} +(-8.75458 - 8.75458i) q^{71} +(8.43465 - 0.925567i) q^{72} +(5.82153 - 5.82153i) q^{73} +(0.910012 + 1.22243i) q^{74} +(-0.175598 - 2.29066i) q^{75} +(5.40376 - 6.63276i) q^{76} +(0.219221 + 0.529247i) q^{77} +(9.87081 + 11.3356i) q^{78} -9.22448 q^{79} +(4.30487 + 6.34395i) q^{80} +(-8.58182 + 2.71152i) q^{81} +(4.08600 + 16.1893i) q^{82} +(15.3286 - 6.34931i) q^{83} +(1.87214 + 2.91463i) q^{84} +(0.0676653 - 0.163358i) q^{85} +(-2.46487 - 3.31109i) q^{86} +(-5.01890 - 1.64202i) q^{87} +(-1.46841 - 0.684885i) q^{88} +(0.611762 - 0.611762i) q^{89} +(-5.79321 - 5.70645i) q^{90} +(-2.34828 + 5.66926i) q^{91} +(3.58278 + 1.07284i) q^{92} +(-0.710250 + 0.828183i) q^{93} +(2.24591 - 3.76232i) q^{94} -8.19888 q^{95} +(-9.47327 - 2.50142i) q^{96} +14.3946 q^{97} +(-0.724880 + 1.21431i) q^{98} +(1.66943 + 0.407975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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