LMFDB - Embedded newform 55.2.j.a.14.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,2,Mod(4,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.4
Root			$-1.92464 + 0.625353i$ of defining polynomial
Character	$\chi$	$=$	55.14
Dual form			55.2.j.a.4.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18949 + 1.63719i) q^{2} +(-2.49233 + 0.809808i) q^{3} +(-0.647481 + 1.99274i) q^{4} +(1.54147 - 1.61983i) q^{5} +(-4.29042 - 3.11717i) q^{6} +(0.918552 + 0.298456i) q^{7} +(-0.183406 + 0.0595923i) q^{8} +(3.12889 - 2.27327i) q^{9} +(4.48555 + 0.596911i) q^{10} +(-3.31118 + 0.189896i) q^{11} -5.49092i q^{12} +(-2.65978 - 3.66088i) q^{13} +(0.603980 + 1.85886i) q^{14} +(-2.53011 + 5.28546i) q^{15} +(3.07453 + 2.23378i) q^{16} +(-1.96126 + 2.69944i) q^{17} +(7.44357 + 2.41856i) q^{18} +(-1.01283 - 3.11717i) q^{19} +(2.22984 + 4.12057i) q^{20} -2.53103 q^{21} +(-4.24952 - 5.19517i) q^{22} +3.36643i q^{23} +(0.408851 - 0.297048i) q^{24} +(-0.247725 - 4.99386i) q^{25} +(2.82978 - 8.70916i) q^{26} +(-1.33628 + 1.83923i) q^{27} +(-1.18949 + 1.63719i) q^{28} +(-1.51820 + 4.67254i) q^{29} +(-11.6629 + 2.14473i) q^{30} +(0.338464 - 0.245909i) q^{31} +8.07636i q^{32} +(8.09880 - 3.15471i) q^{33} -6.75241 q^{34} +(1.89937 - 1.02784i) q^{35} +(2.50415 + 7.70697i) q^{36} +(6.02737 + 1.95841i) q^{37} +(3.89867 - 5.36605i) q^{38} +(9.59368 + 6.97021i) q^{39} +(-0.186186 + 0.388948i) q^{40} +(1.78786 + 5.50247i) q^{41} +(-3.01064 - 4.14379i) q^{42} +2.26205i q^{43} +(1.76552 - 6.72129i) q^{44} +(1.14077 - 8.57246i) q^{45} +(-5.51149 + 4.00433i) q^{46} +(-4.11260 + 1.33626i) q^{47} +(-9.47169 - 3.07754i) q^{48} +(-4.90846 - 3.56620i) q^{49} +(7.88125 - 6.34573i) q^{50} +(2.70208 - 8.31615i) q^{51} +(9.01735 - 2.92991i) q^{52} +(-1.56392 - 2.15255i) q^{53} -4.60066 q^{54} +(-4.79650 + 5.65629i) q^{55} -0.186254 q^{56} +(5.04863 + 6.94884i) q^{57} +(-9.45574 + 3.07235i) q^{58} +(3.12889 - 9.62972i) q^{59} +(-8.89437 - 8.46410i) q^{60} +(1.99897 + 1.45233i) q^{61} +(0.805201 + 0.261626i) q^{62} +(3.55252 - 1.15428i) q^{63} +(-7.07350 + 5.13920i) q^{64} +(-10.0300 - 1.33473i) q^{65} +(14.7983 + 9.50680i) q^{66} -9.60059i q^{67} +(-4.10941 - 5.65612i) q^{68} +(-2.72616 - 8.39026i) q^{69} +(3.94206 + 1.88703i) q^{70} +(4.41166 + 3.20526i) q^{71} +(-0.438388 + 0.603390i) q^{72} +(-1.36528 - 0.443607i) q^{73} +(3.96321 + 12.1975i) q^{74} +(4.66148 + 12.2458i) q^{75} +6.86752 q^{76} +(-3.09817 - 0.813812i) q^{77} +23.9977i q^{78} +(0.812218 - 0.590111i) q^{79} +(8.35766 - 1.53692i) q^{80} +(-1.74436 + 5.36858i) q^{81} +(-6.88197 + 9.47221i) q^{82} +(-4.34692 + 5.98302i) q^{83} +(1.63880 - 5.04369i) q^{84} +(1.34942 + 7.33802i) q^{85} +(-3.70342 + 2.69069i) q^{86} -12.8750i q^{87} +(0.595976 - 0.232149i) q^{88} +12.1964 q^{89} +(15.3917 - 8.32920i) q^{90} +(-1.35054 - 4.15654i) q^{91} +(-6.70842 - 2.17970i) q^{92} +(-0.644427 + 0.886978i) q^{93} +(-7.07962 - 5.14365i) q^{94} +(-6.61056 - 3.16442i) q^{95} +(-6.54030 - 20.1290i) q^{96} +(1.77467 + 2.44262i) q^{97} -12.2781i q^{98} +(-9.92863 + 8.12138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.18949	+	1.63719i	0.841097	+	1.15767i	0.985755	+	0.168189i	$0.0537920\pi$
$2$	1.18949	+	1.63719i	0.841097	+	1.15767i	−0.144657	+	0.989482i	$0.546208\pi$
$3$	−2.49233	+	0.809808i	−1.43895	+	0.467543i	−0.921570	−	0.388213i	$-0.873093\pi$
$3$	−2.49233	+	0.809808i	−1.43895	+	0.467543i	−0.517380	+	0.855756i	$0.673093\pi$
$4$	−0.647481	+	1.99274i	−0.323741	+	0.996371i
$5$	1.54147	−	1.61983i	0.689367	−	0.724412i
$5$	1.54147	−	1.61983i	0.689367	−	0.724412i
$6$	−4.29042	−	3.11717i	−1.75156	−	1.27258i
$7$	0.918552	+	0.298456i	0.347180	+	0.112806i	0.477416	−	0.878677i	$-0.341573\pi$
$7$	0.918552	+	0.298456i	0.347180	+	0.112806i	−0.130236	+	0.991483i	$0.541573\pi$
$8$	−0.183406	+	0.0595923i	−0.0648439	+	0.0210691i
$9$	3.12889	−	2.27327i	1.04296	−	0.757756i
$10$	4.48555	+	0.596911i	1.41846	+	0.188760i
$11$	−3.31118	+	0.189896i	−0.998360	+	0.0572559i
$11$	−3.31118	+	0.189896i	−0.998360	+	0.0572559i
$12$		−	5.49092i		−	1.58509i
$13$	−2.65978	−	3.66088i	−0.737691	−	1.01534i	−0.998748	−	0.0500213i	$-0.984071\pi$
$13$	−2.65978	−	3.66088i	−0.737691	−	1.01534i	0.261057	−	0.965323i	$-0.415929\pi$
$14$	0.603980	+	1.85886i	0.161420	+	0.496801i
$15$	−2.53011	+	5.28546i	−0.653271	+	1.36470i
$16$	3.07453	+	2.23378i	0.768633	+	0.558445i
$17$	−1.96126	+	2.69944i	−0.475675	+	0.654710i	−0.977667	−	0.210162i	$-0.932601\pi$
$17$	−1.96126	+	2.69944i	−0.475675	+	0.654710i	0.501992	+	0.864872i	$0.332601\pi$
$18$	7.44357	+	2.41856i	1.75447	+	0.570060i
$19$	−1.01283	−	3.11717i	−0.232359	−	0.715129i	−0.997461	−	0.0712189i	$-0.977311\pi$
$19$	−1.01283	−	3.11717i	−0.232359	−	0.715129i	0.765101	−	0.643910i	$-0.222689\pi$
$20$	2.22984	+	4.12057i	0.498607	+	0.921388i
$21$	−2.53103			−0.552316
$22$	−4.24952	−	5.19517i	−0.906001	−	1.10761i
$23$			3.36643i			0.701948i	0.936385	+	0.350974i	$0.114149\pi$
$23$			3.36643i			0.701948i	−0.936385	+	0.350974i	$0.885851\pi$
$24$	0.408851	−	0.297048i	0.0834565	−	0.0606347i
$25$	−0.247725	−	4.99386i	−0.0495450	−	0.998772i
$26$	2.82978	−	8.70916i	0.554965	−	1.70801i
$27$	−1.33628	+	1.83923i	−0.257167	+	0.353959i
$28$	−1.18949	+	1.63719i	−0.224793	+	0.309401i
$29$	−1.51820	+	4.67254i	−0.281923	+	0.867668i	0.705382	+	0.708828i	$0.250776\pi$
$29$	−1.51820	+	4.67254i	−0.281923	+	0.867668i	−0.987304	+	0.158841i	$0.949224\pi$
$30$	−11.6629	+	2.14473i	−2.12934	+	0.391573i
$31$	0.338464	−	0.245909i	0.0607900	−	0.0441665i	−0.556975	−	0.830529i	$-0.688038\pi$
$31$	0.338464	−	0.245909i	0.0607900	−	0.0441665i	0.617765	+	0.786363i	$0.288038\pi$
$32$			8.07636i			1.42771i
$33$	8.09880	−	3.15471i	1.40982	−	0.549164i
$34$	−6.75241			−1.15803
$35$	1.89937	−	1.02784i	0.321052	−	0.173737i
$36$	2.50415	+	7.70697i	0.417358	+	1.28449i
$37$	6.02737	+	1.95841i	0.990894	+	0.321961i	0.759221	−	0.650833i	$-0.225580\pi$
$37$	6.02737	+	1.95841i	0.990894	+	0.321961i	0.231673	+	0.972794i	$0.425580\pi$
$38$	3.89867	−	5.36605i	0.632447	−	0.870489i
$39$	9.59368	+	6.97021i	1.53622	+	1.11613i
$40$	−0.186186	+	0.388948i	−0.0294386	+	0.0614980i
$41$	1.78786	+	5.50247i	0.279217	+	0.859341i	0.988073	+	0.153988i	$0.0492117\pi$
$41$	1.78786	+	5.50247i	0.279217	+	0.859341i	−0.708856	+	0.705353i	$0.750788\pi$
$42$	−3.01064	−	4.14379i	−0.464552	−	0.639401i
$43$			2.26205i			0.344960i	0.985013	+	0.172480i	$0.0551780\pi$
$43$			2.26205i			0.344960i	−0.985013	+	0.172480i	$0.944822\pi$
$44$	1.76552	−	6.72129i	0.266161	−	1.01327i
$45$	1.14077	−	8.57246i	0.170057	−	1.27791i
$46$	−5.51149	+	4.00433i	−0.812625	+	0.590407i
$47$	−4.11260	+	1.33626i	−0.599884	+	0.194914i	−0.593189	−	0.805063i	$-0.702131\pi$
$47$	−4.11260	+	1.33626i	−0.599884	+	0.194914i	−0.00669531	+	0.999978i	$0.502131\pi$
$48$	−9.47169	−	3.07754i	−1.36712	−	0.444205i
$49$	−4.90846	−	3.56620i	−0.701208	−	0.509457i
$50$	7.88125	−	6.34573i	1.11458	−	0.897421i
$51$	2.70208	−	8.31615i	0.378367	−	1.16449i
$52$	9.01735	−	2.92991i	1.25048	−	0.406306i
$53$	−1.56392	−	2.15255i	−0.214821	−	0.295676i	0.687984	−	0.725726i	$-0.258496\pi$
$53$	−1.56392	−	2.15255i	−0.214821	−	0.295676i	−0.902805	+	0.430050i	$0.858496\pi$
$54$	−4.60066			−0.626071
$55$	−4.79650	+	5.65629i	−0.646760	+	0.762694i
$56$	−0.186254			−0.0248892
$57$	5.04863	+	6.94884i	0.668707	+	0.920396i
$58$	−9.45574	+	3.07235i	−1.24160	+	0.403420i
$59$	3.12889	−	9.62972i	0.407346	−	1.25368i	−0.511574	−	0.859239i	$-0.670937\pi$
$59$	3.12889	−	9.62972i	0.407346	−	1.25368i	0.918920	−	0.394444i	$-0.129063\pi$
$60$	−8.89437	−	8.46410i	−1.14826	−	1.09271i
$61$	1.99897	+	1.45233i	0.255941	+	0.185952i	0.708356	−	0.705856i	$-0.249437\pi$
$61$	1.99897	+	1.45233i	0.255941	+	0.185952i	−0.452414	+	0.891808i	$0.649437\pi$
$62$	0.805201	+	0.261626i	0.102261	+	0.0332265i
$63$	3.55252	−	1.15428i	0.447575	−	0.145426i
$64$	−7.07350	+	5.13920i	−0.884187	+	0.642400i
$65$	−10.0300	−	1.33473i	−1.24407	−	0.165553i
$66$	14.7983	+	9.50680i	1.82155	+	1.17021i
$67$		−	9.60059i		−	1.17290i	−0.809986	−	0.586449i	$-0.800525\pi$
$67$		−	9.60059i		−	1.17290i	0.809986	−	0.586449i	$-0.199475\pi$
$68$	−4.10941	−	5.65612i	−0.498339	−	0.685905i
$69$	−2.72616	−	8.39026i	−0.328191	−	1.01007i
$70$	3.94206	+	1.88703i	0.471166	+	0.225544i
$71$	4.41166	+	3.20526i	0.523567	+	0.380394i	0.817946	−	0.575295i	$-0.195113\pi$
$71$	4.41166	+	3.20526i	0.523567	+	0.380394i	−0.294379	+	0.955689i	$0.595113\pi$
$72$	−0.438388	+	0.603390i	−0.0516646	+	0.0711102i
$73$	−1.36528	−	0.443607i	−0.159794	−	0.0519203i	0.228028	−	0.973655i	$-0.426772\pi$
$73$	−1.36528	−	0.443607i	−0.159794	−	0.0519203i	−0.387822	+	0.921734i	$0.626772\pi$
$74$	3.96321	+	12.1975i	0.460713	+	1.41793i
$75$	4.66148	+	12.2458i	0.538262	+	1.41402i
$76$	6.86752			0.787758
$77$	−3.09817	−	0.813812i	−0.353069	−	0.0927425i
$78$			23.9977i			2.71721i
$79$	0.812218	−	0.590111i	0.0913817	−	0.0663927i	−0.541156	−	0.840922i	$-0.682013\pi$
$79$	0.812218	−	0.590111i	0.0913817	−	0.0663927i	0.632538	+	0.774529i	$0.282013\pi$
$80$	8.35766	−	1.53692i	0.934415	−	0.171833i
$81$	−1.74436	+	5.36858i	−0.193818	+	0.596509i
$82$	−6.88197	+	9.47221i	−0.759986	+	1.04603i
$83$	−4.34692	+	5.98302i	−0.477136	+	0.656721i	−0.977951	−	0.208833i	$-0.933034\pi$
$83$	−4.34692	+	5.98302i	−0.477136	+	0.656721i	0.500815	+	0.865554i	$0.333034\pi$
$84$	1.63880	−	5.04369i	0.178807	−	0.550312i
$85$	1.34942	+	7.33802i	0.146365	+	0.795920i
$86$	−3.70342	+	2.69069i	−0.399350	+	0.290145i
$87$		−	12.8750i		−	1.38034i
$88$	0.595976	−	0.232149i	0.0635312	−	0.0247472i
$89$	12.1964			1.29282			0.646410	−	0.762991i	$-0.276270\pi$
$89$	12.1964			1.29282			0.646410	+	0.762991i	$0.276270\pi$
$90$	15.3917	−	8.32920i	1.62243	−	0.877974i
$91$	−1.35054	−	4.15654i	−0.141575	−	0.435723i
$92$	−6.70842	−	2.17970i	−0.699401	−	0.227249i
$93$	−0.644427	+	0.886978i	−0.0668240	+	0.0919754i
$94$	−7.07962	−	5.14365i	−0.730207	−	0.530527i
$95$	−6.61056	−	3.16442i	−0.678229	−	0.324663i
$96$	−6.54030	−	20.1290i	−0.667517	−	2.05440i
$97$	1.77467	+	2.44262i	0.180190	+	0.248010i	0.889552	−	0.456834i	$-0.151017\pi$
$97$	1.77467	+	2.44262i	0.180190	+	0.248010i	−0.709362	+	0.704844i	$0.751017\pi$
$98$		−	12.2781i		−	1.24027i
$99$	−9.92863	+	8.12138i	−0.997865	+	0.816229i
$100$	10.1119	+	2.73978i	1.01119	+	0.273978i
$101$	−12.2940	+	8.93210i	−1.22330	+	0.888777i	−0.996369	−	0.0851342i	$-0.972868\pi$
$101$	−12.2940	+	8.93210i	−1.22330	+	0.888777i	−0.226928	+	0.973912i	$0.572868\pi$
$102$	16.8292	−	5.46815i	1.66634	−	0.541428i
$103$	9.26987	+	3.01196i	0.913387	+	0.296778i	0.727751	−	0.685841i	$-0.240565\pi$
$103$	9.26987	+	3.01196i	0.913387	+	0.296778i	0.185636	+	0.982619i	$0.440565\pi$
$104$	0.705981	+	0.512925i	0.0692272	+	0.0502965i
$105$	−3.90151	+	4.09985i	−0.380749	+	0.400104i
$106$	1.66387	−	5.12088i	0.161610	−	0.497384i
$107$	−7.26778	+	2.36144i	−0.702602	+	0.228289i	−0.638464	−	0.769652i	$-0.720430\pi$
$107$	−7.26778	+	2.36144i	−0.702602	+	0.228289i	−0.0641384	+	0.997941i	$0.520430\pi$
$108$	−2.79989	−	3.85372i	−0.269420	−	0.370825i
$109$	9.85576			0.944010			0.472005	−	0.881596i	$-0.343530\pi$
$109$	9.85576			0.944010			0.472005	+	0.881596i	$0.343530\pi$
$110$	−14.9658	−	1.12469i	−1.42694	−	0.107235i
$111$	−16.6082			−1.57638
$112$	2.15743	+	2.96945i	0.203858	+	0.280587i
$113$	4.77298	−	1.55084i	0.449004	−	0.145890i	−0.0757819	−	0.997124i	$-0.524145\pi$
$113$	4.77298	−	1.55084i	0.449004	−	0.145890i	0.524786	+	0.851234i	$0.324145\pi$
$114$	−5.37130	+	16.5312i	−0.503068	+	1.54829i
$115$	5.45305	+	5.18925i	0.508500	+	0.483900i
$116$	−8.32816	−	6.05076i	−0.773250	−	0.561799i
$117$	−16.6443	−	5.40807i	−1.53877	−	0.499976i
$118$	19.4875	−	6.33188i	1.79397	−	0.582896i
$119$	−2.60718	+	1.89423i	−0.239000	+	0.173644i
$120$	0.149065	−	1.12016i	0.0136077	−	0.102256i
$121$	10.9279	−	1.25756i	0.993444	−	0.114324i
$122$			5.00023i			0.452700i
$123$	−8.91189	−	12.2662i	−0.803558	−	1.10600i
$124$	0.270884	+	0.833694i	0.0243261	+	0.0748679i
$125$	−8.47108	−	7.29662i	−0.757677	−	0.652630i
$126$	6.11547	+	4.44315i	0.544810	+	0.395827i
$127$	4.16764	−	5.73626i	0.369818	−	0.509011i	−0.583033	−	0.812448i	$-0.698134\pi$
$127$	4.16764	−	5.73626i	0.369818	−	0.509011i	0.952851	+	0.303438i	$0.0981344\pi$
$128$	−1.46559	−	0.476198i	−0.129541	−	0.0420903i
$129$	−1.83183	−	5.63779i	−0.161284	−	0.496380i
$130$	−9.74537	−	18.0087i	−0.854726	−	1.57947i
$131$	7.21704			0.630556			0.315278	−	0.948999i	$-0.397902\pi$
$131$	7.21704			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$132$	1.04271	+	18.1814i	0.0907559	+	1.58249i
$133$		−	3.16557i		−	0.274490i
$134$	15.7180	−	11.4198i	1.35783	−	0.986521i
$135$	0.919409	+	4.99967i	0.0791301	+	0.430303i
$136$	0.198841	−	0.611970i	0.0170505	−	0.0524760i
$137$	4.99076	−	6.86920i	0.426390	−	0.586875i	−0.540730	−	0.841196i	$-0.681852\pi$
$137$	4.99076	−	6.86920i	0.426390	−	0.586875i	0.967120	+	0.254321i	$0.0818520\pi$
$138$	10.4937	−	14.4434i	0.893286	−	1.22950i
$139$	−2.39184	+	7.36133i	−0.202873	+	0.624380i	0.796921	+	0.604084i	$0.206461\pi$
$139$	−2.39184	+	7.36133i	−0.202873	+	0.624380i	−0.999794	+	0.0202958i	$0.993539\pi$
$140$	0.818415	+	4.45047i	0.0691687	+	0.376133i
$141$	9.16785	−	6.66083i	0.772072	−	0.560943i
$142$			11.0354i			0.926067i
$143$	9.50222	+	11.6168i	0.794615	+	0.971442i
$144$	14.6978			1.22482
$145$	5.22847	+	9.66182i	0.434201	+	0.802370i
$146$	−0.897720	−	2.76290i	−0.0742958	−	0.228659i
$147$	15.1215	+	4.91326i	1.24720	+	0.405239i
$148$	−7.80522	+	10.7430i	−0.641585	+	0.883067i
$149$	−13.6589	−	9.92376i	−1.11898	−	0.812986i	−0.134925	−	0.990856i	$-0.543079\pi$
$149$	−13.6589	−	9.92376i	−1.11898	−	0.812986i	−0.984054	+	0.177870i	$0.943079\pi$
$150$	−14.5039	+	22.1980i	−1.18424	+	1.81246i
$151$	−3.79555	−	11.6815i	−0.308877	−	0.950626i	−0.978202	−	0.207656i	$-0.933416\pi$
$151$	−3.79555	−	11.6815i	−0.308877	−	0.950626i	0.669325	−	0.742970i	$-0.266584\pi$
$152$	0.371519	+	0.511353i	0.0301342	+	0.0414762i
$153$			12.9047i			1.04328i
$154$	−2.35288	−	6.04033i	−0.189600	−	0.486744i
$155$	0.123402	−	0.927318i	0.00991190	−	0.0744840i
$156$	−20.1016	+	14.6046i	−1.60941	+	1.16931i
$157$	−4.00368	+	1.30087i	−0.319528	+	0.103821i	−0.464390	−	0.885631i	$-0.653726\pi$
$157$	−4.00368	+	1.30087i	−0.319528	+	0.103821i	0.144862	+	0.989452i	$0.453726\pi$
$158$	1.93225	+	0.627827i	0.153722	+	0.0499472i
$159$	5.64096	+	4.09840i	0.447357	+	0.325024i
$160$	13.0824	+	12.4495i	1.03425	+	0.984218i
$161$	−1.00473	+	3.09224i	−0.0791837	+	0.243702i
$162$	−10.8643	+	3.53003i	−0.853581	+	0.277345i
$163$	−9.74169	−	13.4083i	−0.763028	−	1.05022i	−0.996956	−	0.0779643i	$-0.975158\pi$
$163$	−9.74169	−	13.4083i	−0.763028	−	1.05022i	0.233928	−	0.972254i	$-0.424842\pi$
$164$	−12.1226			−0.946617
$165$	7.37397	−	17.9816i	0.574062	−	1.39987i
$166$	−14.9660			−1.16159
$167$	−5.38810	−	7.41608i	−0.416944	−	0.573874i	0.547951	−	0.836510i	$-0.315408\pi$
$167$	−5.38810	−	7.41608i	−0.416944	−	0.573874i	−0.964895	+	0.262637i	$0.915408\pi$
$168$	0.464207	−	0.150830i	0.0358144	−	0.0116368i
$169$	−2.31036	+	7.11055i	−0.177720	+	0.546965i
$170$	−10.4086	+	10.9378i	−0.798307	+	0.838889i
$171$	−10.2552	−	7.45085i	−0.784236	−	0.569781i
$172$	−4.50769	−	1.46464i	−0.343708	−	0.111678i
$173$	−3.90853	+	1.26996i	−0.297160	+	0.0965531i	−0.453803	−	0.891102i	$-0.649933\pi$
$173$	−3.90853	+	1.26996i	−0.297160	+	0.0965531i	0.156643	+	0.987655i	$0.449933\pi$
$174$	21.0788	−	15.3147i	1.59798	−	1.16100i
$175$	1.26290	−	4.66106i	0.0954661	−	0.352343i
$176$	−10.6045	−	6.81261i	−0.799346	−	0.513520i
$177$			26.5343i			1.99444i
$178$	14.5075	+	19.9679i	1.08739	+	1.49666i
$179$	5.03576	+	15.4985i	0.376390	+	1.15841i	0.942536	+	0.334105i	$0.108434\pi$
$179$	5.03576	+	15.4985i	0.376390	+	1.15841i	−0.566145	+	0.824305i	$0.691566\pi$
$180$	16.3441	+	7.82378i	1.21822	+	0.583150i
$181$	4.48753	+	3.26038i	0.333555	+	0.242342i	0.741938	−	0.670469i	$-0.233907\pi$
$181$	4.48753	+	3.26038i	0.333555	+	0.242342i	−0.408382	+	0.912811i	$0.633907\pi$
$182$	5.19860	−	7.15526i	0.385346	−	0.530383i
$183$	−6.15820	−	2.00092i	−0.455227	−	0.147912i
$184$	−0.200613	−	0.617424i	−0.0147894	−	0.0455171i
$185$	12.4633	−	6.74451i	0.916322	−	0.495866i
$186$	−2.21870			−0.162683
$187$	5.98147	−	9.31078i	0.437408	−	0.680871i
$188$		−	9.06056i		−	0.660809i
$189$	−1.77637	+	1.29061i	−0.129212	+	0.0938779i
$190$	−2.68243	−	14.5868i	−0.194604	−	1.05824i
$191$	6.74155	−	20.7484i	0.487802	−	1.50130i	−0.340080	−	0.940396i	$-0.610454\pi$
$191$	6.74155	−	20.7484i	0.487802	−	1.50130i	0.827882	−	0.560903i	$-0.189546\pi$
$192$	13.4678	−	18.5368i	0.971951	−	1.33778i
$193$	−13.2128	+	18.1858i	−0.951076	+	1.30904i	−2.83481e−5		1.00000i	$0.500009\pi$
$193$	−13.2128	+	18.1858i	−0.951076	+	1.30904i	−0.951048	+	0.309044i	$0.899991\pi$
$194$	−1.88809	+	5.81094i	−0.135557	+	0.417201i
$195$	26.0790	−	4.79577i	1.86755	−	0.343432i
$196$	10.2847	−	7.47224i	0.734619	−	0.533732i
$197$		−	25.7479i		−	1.83446i	−0.398358	−	0.917230i	$-0.630420\pi$
$197$		−	25.7479i		−	1.83446i	0.398358	−	0.917230i	$-0.369580\pi$
$198$	−25.1063	−	6.59480i	−1.78423	−	0.468672i
$199$	−16.9671			−1.20277			−0.601385	−	0.798960i	$-0.705384\pi$
$199$	−16.9671			−1.20277			−0.601385	+	0.798960i	$0.705384\pi$
$200$	0.343030	+	0.901143i	0.0242559	+	0.0637204i
$201$	7.77463	+	23.9279i	0.548380	+	1.68774i
$202$	−29.2472	−	9.50298i	−2.05782	−	0.668627i
$203$	−2.78909	+	3.83886i	−0.195756	+	0.269435i
$204$	14.8224	+	10.7691i	1.03778	+	0.753988i
$205$	11.6690	+	5.58587i	0.815000	+	0.390134i
$206$	6.09526	+	18.7593i	0.424677	+	1.30702i
$207$	7.65279	+	10.5332i	0.531906	+	0.732106i
$208$		−	17.1969i		−	1.19239i
$209$	3.94561	+	10.1292i	0.272924	+	0.700652i
$210$	−11.3531	−	1.51080i	−0.783436	−	0.104255i
$211$	4.71363	−	3.42465i	0.324500	−	0.235763i	−0.413593	−	0.910462i	$-0.635726\pi$
$211$	4.71363	−	3.42465i	0.324500	−	0.235763i	0.738093	+	0.674699i	$0.235726\pi$
$212$	5.30209	−	1.72275i	0.364149	−	0.118319i
$213$	−13.5910	−	4.41597i	−0.931238	−	0.302577i
$214$	−12.5111	−	9.08984i	−0.855241	−	0.621369i
$215$	3.66415	+	3.48689i	0.249893	+	0.237804i
$216$	0.135478	−	0.416958i	0.00921810	−	0.0283704i
$217$	0.384290	−	0.124863i	0.0260873	−	0.00847628i
$218$	11.7233	+	16.1358i	0.794005	+	1.09285i
$219$	3.76197			0.254211
$220$	−8.16589	−	13.2205i	−0.550544	−	0.891328i
$221$	15.0988			1.01566
$222$	−19.7553	−	27.1908i	−1.32589	−	1.82493i
$223$	18.0913	−	5.87820i	1.21148	−	0.393634i	0.367508	−	0.930020i	$-0.380211\pi$
$223$	18.0913	−	5.87820i	1.21148	−	0.393634i	0.843972	+	0.536387i	$0.180211\pi$
$224$	−2.41043	+	7.41856i	−0.161054	+	0.495673i
$225$	−12.1275	−	15.0621i	−0.808499	−	1.00414i
$226$	8.21644	+	5.96959i	0.546549	+	0.397091i
$227$	27.0727	+	8.79646i	1.79688	+	0.583841i	0.999799	−	0.0200332i	$-0.00637719\pi$
$227$	27.0727	+	8.79646i	1.79688	+	0.583841i	0.797079	+	0.603874i	$0.206377\pi$
$228$	−17.1161	+	5.56137i	−1.13354	+	0.368311i
$229$	−20.5420	+	14.9247i	−1.35746	+	0.986250i	−0.358854	+	0.933394i	$0.616832\pi$
$229$	−20.5420	+	14.9247i	−1.35746	+	0.986250i	−0.998602	+	0.0528558i	$0.983168\pi$
$230$	−2.00946	+	15.1003i	−0.132500	+	0.995682i
$231$	8.38071	−	0.480634i	0.551410	−	0.0316234i
$232$		−	0.947446i		−	0.0622029i
$233$	7.35755	+	10.1268i	0.482009	+	0.663429i	0.978890	−	0.204390i	$-0.0655211\pi$
$233$	7.35755	+	10.1268i	0.482009	+	0.663429i	−0.496880	+	0.867819i	$0.665521\pi$
$234$	−10.9442	−	33.6828i	−0.715446	−	2.20192i
$235$	−4.17493	+	8.72154i	−0.272342	+	0.568931i
$236$	17.1637	+	12.4701i	1.11726	+	0.811737i
$237$	−1.54644	+	2.12849i	−0.100452	+	0.138261i
$238$	−6.20244	−	2.01529i	−0.402044	−	0.130632i
$239$	−6.30011	−	19.3897i	−0.407520	−	1.25422i	−0.918773	−	0.394787i	$-0.870818\pi$
$239$	−6.30011	−	19.3897i	−0.407520	−	1.25422i	0.511252	−	0.859431i	$-0.329182\pi$
$240$	−19.5855	+	10.5986i	−1.26424	+	0.684139i
$241$	−22.7935			−1.46826			−0.734129	−	0.679010i	$-0.762409\pi$
$241$	−22.7935			−1.46826			−0.734129	+	0.679010i	$0.762409\pi$
$242$	15.0575	+	16.3952i	0.967932	+	1.05392i
$243$		−	21.6131i		−	1.38648i
$244$	−4.18842	+	3.04307i	−0.268136	+	0.194812i
$245$	−13.3429	+	2.45368i	−0.852447	+	0.156760i
$246$	9.48148	−	29.1810i	0.604517	−	1.86051i
$247$	−8.71768	+	11.9989i	−0.554693	+	0.763469i
$248$	−0.0474222	+	0.0652711i	−0.00301132	+	0.00414472i
$249$	5.98887	−	18.4318i	0.379529	−	1.16807i
$250$	1.86971	−	22.5481i	0.118251	−	1.42607i
$251$	−13.7151	+	9.96460i	−0.865689	+	0.628960i	−0.929427	−	0.369007i	$-0.879698\pi$
$251$	−13.7151	+	9.96460i	−0.865689	+	0.628960i	0.0637374	+	0.997967i	$0.479698\pi$
$252$			7.82663i			0.493031i
$253$	−0.639272	−	11.1469i	−0.0401907	−	0.700797i
$254$	14.3487			0.900320
$255$	−9.30560	−	17.1960i	−0.582739	−	1.07686i
$256$	4.44000	+	13.6649i	0.277500	+	0.854057i
$257$	4.50405	+	1.46346i	0.280955	+	0.0912879i	0.446105	−	0.894981i	$-0.352811\pi$
$257$	4.50405	+	1.46346i	0.280955	+	0.0912879i	−0.165150	+	0.986268i	$0.552811\pi$
$258$	7.05121	−	9.70516i	0.438989	−	0.604217i
$259$	4.95196	+	3.59781i	0.307700	+	0.223557i
$260$	9.15402	−	19.1230i	0.567708	−	1.18596i
$261$	5.87166	+	18.0711i	0.363447	+	1.11857i
$262$	8.58461	+	11.8157i	0.530359	+	0.729976i
$263$			18.1037i			1.11632i	0.829732	+	0.558162i	$0.188493\pi$
$263$			18.1037i			1.11632i	−0.829732	+	0.558162i	$0.811507\pi$
$264$	−1.29737	+	1.06122i	−0.0798479	+	0.0653136i
$265$	−5.89751	−	0.784807i	−0.362281	−	0.0482103i
$266$	5.18266	−	3.76542i	0.317769	−	0.230873i
$267$	−30.3976	+	9.87677i	−1.86030	+	0.604449i
$268$	19.1315	+	6.21620i	1.16864	+	0.379715i
$269$	−1.85914	−	1.35074i	−0.113354	−	0.0823562i	0.529664	−	0.848207i	$-0.322318\pi$
$269$	−1.85914	−	1.35074i	−0.113354	−	0.0823562i	−0.643018	+	0.765851i	$0.722318\pi$
$270$	−7.09179	+	7.45231i	−0.431593	+	0.453533i
$271$	0.248971	−	0.766255i	0.0151239	−	0.0465467i	−0.943210	−	0.332198i	$-0.892210\pi$
$271$	0.248971	−	0.766255i	0.0151239	−	0.0465467i	0.958334	+	0.285651i	$0.0922098\pi$
$272$	−12.0599	+	3.91850i	−0.731239	+	0.237594i
$273$	6.73199	+	9.26579i	0.407439	+	0.560791i
$274$	17.1827			1.03804
$275$	1.76858	+	16.4885i	0.106649	+	0.994297i
$276$	18.4848			1.11265
$277$	6.95521	+	9.57302i	0.417898	+	0.575187i	0.965122	−	0.261799i	$-0.0843157\pi$
$277$	6.95521	+	9.57302i	0.417898	+	0.575187i	−0.547225	+	0.836986i	$0.684316\pi$
$278$	−14.8970	+	4.84033i	−0.893462	+	0.290304i
$279$	0.500000	−	1.53884i	0.0299342	−	0.0921280i
$280$	−0.287105	+	0.301701i	−0.0171578	+	0.0180301i
$281$	−5.03960	−	3.66148i	−0.300637	−	0.218426i	0.427231	−	0.904142i	$-0.359489\pi$
$281$	−5.03960	−	3.66148i	−0.300637	−	0.218426i	−0.727869	+	0.685717i	$0.759489\pi$
$282$	21.8101	+	7.08655i	1.29878	+	0.421998i
$283$	−8.22250	+	2.67165i	−0.488777	+	0.158813i	−0.543029	−	0.839714i	$-0.682723\pi$
$283$	−8.22250	+	2.67165i	−0.488777	+	0.158813i	0.0542519	+	0.998527i	$0.482723\pi$
$284$	−9.24372	+	6.71596i	−0.548514	+	0.398519i
$285$	19.0383	+	2.53351i	1.12773	+	0.150072i
$286$	−7.71608	+	29.3750i	−0.456261	+	1.73698i
$287$			5.58790i			0.329843i
$288$	18.3597	+	25.2700i	1.08186	+	1.48905i
$289$	1.81285	+	5.57937i	0.106638	+	0.328198i
$290$	−9.59905	+	20.0527i	−0.563676	+	1.17753i
$291$	−6.40111	−	4.65068i	−0.375240	−	0.272628i
$292$	1.76799	−	2.43343i	0.103464	−	0.142406i
$293$	−5.52610	−	1.79554i	−0.322838	−	0.104896i	0.143115	−	0.989706i	$-0.454288\pi$
$293$	−5.52610	−	1.79554i	−0.322838	−	0.104896i	−0.465953	+	0.884810i	$0.654288\pi$
$294$	9.94288	+	30.6010i	0.579880	+	1.78469i
$295$	−10.7755	−	19.9122i	−0.627372	−	1.15933i
$296$	−1.22216			−0.0710369
$297$	4.07540	−	6.34377i	0.236478	−	0.368103i
$298$		−	34.1665i		−	1.97921i
$299$	12.3241	−	8.95396i	0.712719	−	0.517821i
$300$	−27.4209	+	1.36024i	−1.58314	+	0.0785333i
$301$	−0.675123	+	2.07781i	−0.0389134	+	0.119763i
$302$	14.6101	−	20.1091i	0.840717	−	1.15715i
$303$	23.4074	−	32.2176i	1.34472	−	1.85085i
$304$	3.84909	−	11.8463i	0.220761	−	0.679432i
$305$	5.43389	−	0.999260i	0.311144	−	0.0572175i
$306$	−21.1275	+	15.3500i	−1.20778	+	0.877503i
$307$			18.4721i			1.05426i	0.849785	+	0.527130i	$0.176732\pi$
$307$			18.4721i			1.05426i	−0.849785	+	0.527130i	$0.823268\pi$
$308$	3.62773	−	5.64693i	0.206709	−	0.321764i
$309$	−25.5427			−1.45307
$310$	1.66499	−	0.901003i	0.0945648	−	0.0511735i
$311$	−3.50158	−	10.7768i	−0.198557	−	0.611094i	−0.999917	−	0.0129120i	$-0.995890\pi$
$311$	−3.50158	−	10.7768i	−0.198557	−	0.611094i	0.801360	−	0.598182i	$-0.204110\pi$
$312$	−2.17491	−	0.706672i	−0.123130	−	0.0400074i
$313$	3.00651	−	4.13811i	0.169938	−	0.233900i	−0.715550	−	0.698561i	$-0.753824\pi$
$313$	3.00651	−	4.13811i	0.169938	−	0.233900i	0.885488	+	0.464661i	$0.153824\pi$
$314$	−6.89212	−	5.00742i	−0.388945	−	0.282585i
$315$	3.60636	−	7.53378i	0.203195	−	0.424481i
$316$	0.650043	+	2.00063i	0.0365678	+	0.112544i
$317$	−6.94368	−	9.55715i	−0.389996	−	0.536783i	0.568202	−	0.822889i	$-0.307639\pi$
$317$	−6.94368	−	9.55715i	−0.389996	−	0.536783i	−0.958198	+	0.286106i	$0.907639\pi$
$318$			14.1104i			0.791270i
$319$	4.13974	−	15.7599i	0.231781	−	0.882387i
$320$	−2.57896	+	19.3798i	−0.144168	+	1.08337i
$321$	16.2014	−	11.7710i	0.904274	−	0.656994i
$322$	−6.25771	+	2.03325i	−0.348729	+	0.113309i
$323$	10.4010	+	3.37951i	0.578730	+	0.188041i
$324$	−9.56877	−	6.95212i	−0.531598	−	0.386229i
$325$	−17.6230	+	14.1895i	−0.977549	+	0.787090i
$326$	10.3643	−	31.8981i	0.574026	−	1.76667i
$327$	−24.5638	+	7.98127i	−1.35838	+	0.441365i
$328$	−0.655810	−	0.902645i	−0.0362110	−	0.0498402i
$329$	−4.17645			−0.230255
$330$	38.2106	−	9.31635i	2.10343	−	0.512848i
$331$	29.2692			1.60878			0.804391	−	0.594100i	$-0.202492\pi$
$331$	29.2692			1.60878			0.804391	+	0.594100i	$0.202492\pi$
$332$	−9.10807	−	12.5362i	−0.499870	−	0.688012i
$333$	23.3110	−	7.57419i	1.27743	−	0.415063i
$334$	5.73247	−	17.6427i	0.313667	−	0.965367i
$335$	−15.5514	−	14.7990i	−0.849661	−	0.808558i
$336$	−7.78174	−	5.65376i	−0.424529	−	0.308438i
$337$	−25.3400	−	8.23348i	−1.38036	−	0.448506i	−0.477572	−	0.878593i	$-0.658483\pi$
$337$	−25.3400	−	8.23348i	−1.38036	−	0.448506i	−0.902788	+	0.430087i	$0.858483\pi$
$338$	−14.3895	+	4.67543i	−0.782685	+	0.254310i
$339$	−10.6400	+	7.73040i	−0.577885	+	0.419858i
$340$	−15.4965	−	2.06219i	−0.840417	−	0.111838i
$341$	−1.07402	+	0.878523i	−0.0581615	+	0.0475747i
$342$		−	25.6525i		−	1.38713i
$343$	−7.41820	−	10.2103i	−0.400545	−	0.551303i
$344$	−0.134801	−	0.414875i	−0.00726798	−	0.0223686i
$345$	−17.7931	−	8.51742i	−0.957949	−	0.458563i
$346$	−6.72833	−	4.88842i	−0.361717	−	0.262803i
$347$	2.53411	−	3.48790i	0.136038	−	0.187240i	−0.735563	−	0.677457i	$-0.763082\pi$
$347$	2.53411	−	3.48790i	0.136038	−	0.187240i	0.871601	+	0.490216i	$0.163082\pi$
$348$	25.6565	+	8.33631i	1.37533	+	0.446873i
$349$	4.06960	+	12.5249i	0.217841	+	0.670444i	0.998940	+	0.0460373i	$0.0146593\pi$
$349$	4.06960	+	12.5249i	0.217841	+	0.670444i	−0.781099	+	0.624407i	$0.785341\pi$
$350$	9.13326	−	3.47668i	0.488193	−	0.185836i
$351$	10.2874			0.549100
$352$	−1.53367	−	26.7423i	−0.0817449	−	1.42537i
$353$		−	25.4904i		−	1.35672i	−0.734732	−	0.678358i	$-0.762692\pi$
$353$		−	25.4904i		−	1.35672i	0.734732	−	0.678358i	$-0.237308\pi$
$354$	−43.4418	+	31.5623i	−2.30890	+	1.67752i
$355$	11.9924	−	2.20534i	0.636492	−	0.117047i
$356$	−7.89696	+	24.3044i	−0.418538	+	1.28813i
$357$	4.96400	−	6.83237i	0.262723	−	0.361607i
$358$	−19.3840	+	26.6798i	−1.02448	+	1.41007i
$359$	−8.11915	+	24.9882i	−0.428512	+	1.31883i	0.471078	+	0.882091i	$0.343865\pi$
$359$	−8.11915	+	24.9882i	−0.428512	+	1.31883i	−0.899591	+	0.436734i	$0.856135\pi$
$360$	0.301628	+	1.64022i	0.0158972	+	0.0864474i
$361$	6.68037	−	4.85358i	0.351599	−	0.255451i
$362$			11.2252i			0.589981i
$363$	−26.2175	+	11.9838i	−1.37606	+	0.628984i
$364$	9.15736			0.479976
$365$	−2.82311	+	1.52772i	−0.147769	+	0.0799646i
$366$	−4.04923	−	12.4622i	−0.211657	−	0.651412i
$367$	1.91993	+	0.623823i	0.100220	+	0.0325633i	0.358698	−	0.933454i	$-0.383221\pi$
$367$	1.91993	+	0.623823i	0.100220	+	0.0325633i	−0.258478	+	0.966017i	$0.583221\pi$
$368$	−7.51985	+	10.3502i	−0.391999	+	0.539541i
$369$	18.1026	+	13.1523i	0.942384	+	0.684682i
$370$	25.8671	+	12.3824i	1.34477	+	0.643729i
$371$	−0.794101	−	2.44399i	−0.0412277	−	0.126886i
$372$	−1.35026	−	1.85848i	−0.0700080	−	0.0963577i
$373$			8.87153i			0.459351i	0.973267	+	0.229675i	$0.0737664\pi$
$373$			8.87153i			0.459351i	−0.973267	+	0.229675i	$0.926234\pi$
$374$	22.3585	−	1.28226i	1.15613	−	0.0663040i
$375$	27.0216	+	11.3257i	1.39539	+	0.584855i
$376$	0.674645	−	0.490159i	0.0347922	−	0.0252780i
$377$	21.1437	−	6.86999i	1.08895	−	0.353823i
$378$	−4.22595	−	1.37309i	−0.217359	−	0.0706243i
$379$	17.0412	+	12.3812i	0.875348	+	0.635978i	0.932017	−	0.362415i	$-0.118048\pi$
$379$	17.0412	+	12.3812i	0.875348	+	0.635978i	−0.0566685	+	0.998393i	$0.518048\pi$
$380$	10.5861	−	11.1242i	0.543055	−	0.570661i
$381$	−5.74187	+	17.6717i	−0.294165	+	0.905346i
$382$	41.9881	−	13.6428i	2.14830	−	0.698025i
$383$	15.2704	+	21.0179i	0.780281	+	1.07396i	0.995251	+	0.0973436i	$0.0310346\pi$
$383$	15.2704	+	21.0179i	0.780281	+	1.07396i	−0.214970	+	0.976621i	$0.568965\pi$
$384$	4.03836			0.206082
$385$	−6.09399	+	3.76405i	−0.310578	+	0.191834i
$386$	−45.4902			−2.31539
$387$	5.14225	+	7.07771i	0.261396	+	0.359780i
$388$	−6.01657	+	1.95490i	−0.305445	+	0.0992451i
$389$	0.507965	−	1.56335i	0.0257548	−	0.0792652i	−0.937353	−	0.348381i	$-0.886731\pi$
$389$	0.507965	−	1.56335i	0.0257548	−	0.0792652i	0.963108	+	0.269116i	$0.0867315\pi$
$390$	38.8723	+	36.9918i	1.96838	+	1.87315i
$391$	−9.08746	−	6.60243i	−0.459573	−	0.333899i
$392$	1.11276	+	0.361558i	0.0562029	+	0.0182614i
$393$	−17.9873	+	5.84442i	−0.907338	+	0.294812i
$394$	42.1543	−	30.6269i	2.12370	−	1.54296i
$395$	0.296130	−	2.22530i	0.0148999	−	0.111967i
$396$	−9.75521	−	25.0437i	−0.490218	−	1.25849i
$397$			16.7088i			0.838588i	0.907850	+	0.419294i	$0.137722\pi$
$397$			16.7088i			0.838588i	−0.907850	+	0.419294i	$0.862278\pi$
$398$	−20.1823	−	27.7785i	−1.01165	−	1.39241i
$399$	2.56351	+	7.88966i	0.128336	+	0.394977i
$400$	10.3935	−	15.9071i	0.519677	−	0.795357i
$401$	−22.4842	−	16.3357i	−1.12281	−	0.815766i	−0.138174	−	0.990408i	$-0.544123\pi$
$401$	−22.4842	−	16.3357i	−1.12281	−	0.815766i	−0.984632	+	0.174641i	$0.944123\pi$
$402$	−29.9267	+	41.1906i	−1.49261	+	2.05440i
$403$	−1.80048	−	0.585013i	−0.0896885	−	0.0291416i
$404$	−9.83926	−	30.2821i	−0.489521	−	1.50659i
$405$	6.00733	+	11.1011i	0.298507	+	0.551618i
$406$	−9.60255			−0.476567
$407$	−20.3296	−	5.34009i	−1.00770	−	0.264698i
$408$			1.68626i			0.0834822i
$409$	31.9019	−	23.1781i	1.57745	−	1.14608i	0.657902	−	0.753104i	$-0.271444\pi$
$409$	31.9019	−	23.1781i	1.57745	−	1.14608i	0.919547	−	0.392980i	$-0.128556\pi$
$410$	4.73505	+	25.7488i	0.233848	+	1.27164i
$411$	−6.87591	+	21.1619i	−0.339164	+	1.04384i
$412$	−12.0041	+	16.5223i	−0.591401	+	0.813994i
$413$	5.74809	−	7.91157i	0.282845	−	0.389303i
$414$	−8.14191	+	25.0582i	−0.400153	+	1.23154i
$415$	2.99084	+	16.2639i	0.146815	+	0.798365i
$416$	29.5665	−	21.4814i	1.44962	−	1.05321i
$417$		−	20.2838i		−	0.993303i
$418$	−11.8902	+	18.5083i	−0.581569	+	0.905272i
$419$	−14.7812			−0.722111			−0.361055	−	0.932544i	$-0.617583\pi$
$419$	−14.7812			−0.722111			−0.361055	+	0.932544i	$0.617583\pi$
$420$	−5.64379	−	10.4293i	−0.275389	−	0.508897i
$421$	−3.33036	−	10.2498i	−0.162312	−	0.499545i	0.836516	−	0.547942i	$-0.184589\pi$
$421$	−3.33036	−	10.2498i	−0.162312	−	0.499545i	−0.998828	+	0.0483974i	$0.984589\pi$
$422$	11.2136	+	3.64354i	0.545872	+	0.177365i
$423$	−9.83016	+	13.5301i	−0.477959	+	0.657854i
$424$	0.415108	+	0.301594i	0.0201594	+	0.0146467i
$425$	13.9665	+	9.12553i	0.677474	+	0.442653i
$426$	−8.93653	−	27.5038i	−0.432976	−	1.33256i
$427$	1.40270	+	1.93065i	0.0678813	+	0.0934306i
$428$		−	16.0118i		−	0.773960i
$429$	−33.0900	−	21.2579i	−1.59760	−	1.02634i
$430$	−1.35025	+	10.1466i	−0.0651146	+	0.489310i
$431$	−26.0435	+	18.9217i	−1.25447	+	0.911428i	−0.998473	−	0.0552489i	$-0.982405\pi$
$431$	−26.0435	+	18.9217i	−1.25447	+	0.911428i	−0.256000	+	0.966677i	$0.582405\pi$
$432$	−8.21685	+	2.66982i	−0.395334	+	0.128452i
$433$	−0.363904	−	0.118240i	−0.0174881	−	0.00568223i	0.300260	−	0.953857i	$-0.402927\pi$
$433$	−0.363904	−	0.118240i	−0.0174881	−	0.00568223i	−0.317748	+	0.948175i	$0.602927\pi$
$434$	0.661536	+	0.480634i	0.0317547	+	0.0230712i
$435$	−20.8553	−	19.8464i	−0.999936	−	0.951563i
$436$	−6.38142	+	19.6400i	−0.305615	+	0.940585i
$437$	10.4937	−	3.40962i	0.501983	−	0.163104i
$438$	4.47484	+	6.15908i	0.213816	+	0.294292i
$439$	−26.5331			−1.26635			−0.633177	−	0.774007i	$-0.718249\pi$
$439$	−26.5331			−1.26635			−0.633177	+	0.774007i	$0.718249\pi$
$440$	0.542637	−	1.32323i	0.0258692	−	0.0630827i
$441$	−23.4649			−1.11738
$442$	17.9599	+	24.7197i	0.854267	+	1.17580i
$443$	−13.7913	+	4.48106i	−0.655243	+	0.212901i	−0.617725	−	0.786395i	$-0.711945\pi$
$443$	−13.7913	+	4.48106i	−0.655243	+	0.212901i	−0.0375185	+	0.999296i	$0.511945\pi$
$444$	10.7535	−	33.0958i	0.510337	−	1.57066i
$445$	18.8005	−	19.7562i	0.891228	−	0.936534i
$446$	31.1432	+	22.6268i	1.47467	+	1.07141i
$447$	42.0788	+	13.6722i	1.99026	+	0.646675i
$448$	−8.03120	+	2.60950i	−0.379439	+	0.123287i
$449$	8.18240	−	5.94486i	0.386151	−	0.280555i	−0.377725	−	0.925918i	$-0.623294\pi$
$449$	8.18240	−	5.94486i	0.386151	−	0.280555i	0.763876	+	0.645362i	$0.223294\pi$
$450$	10.2340	−	37.7713i	0.482435	−	1.78055i
$451$	−6.96483	−	17.8802i	−0.327961	−	0.841945i
$452$			10.5155i			0.494606i
$453$	18.9195	+	26.0405i	0.888917	+	1.22349i
$454$	17.8012	+	54.7866i	0.835454	+	2.57126i
$455$	−8.81472	−	4.21953i	−0.413240	−	0.197815i
$456$	−1.34005	−	0.973602i	−0.0627535	−	0.0455931i
$457$	22.9758	−	31.6235i	1.07476	−	1.47928i	0.209602	−	0.977787i	$-0.432783\pi$
$457$	22.9758	−	31.6235i	1.07476	−	1.47928i	0.865160	−	0.501496i	$-0.167217\pi$
$458$	−48.8691	−	15.8785i	−2.28351	−	0.741956i
$459$	−2.34410	−	7.21440i	−0.109413	−	0.336739i
$460$	−13.8716	+	7.50658i	−0.646766	+	0.349996i
$461$	39.1322			1.82257			0.911285	−	0.411776i	$-0.135092\pi$
$461$	39.1322			1.82257			0.911285	+	0.411776i	$0.135092\pi$
$462$	10.7557	+	13.1491i	0.500399	+	0.611753i
$463$			12.9189i			0.600392i	0.953878	+	0.300196i	$0.0970521\pi$
$463$			12.9189i			0.600392i	−0.953878	+	0.300196i	$0.902948\pi$
$464$	−15.1052	+	10.9745i	−0.701240	+	0.509481i
$465$	0.443390	+	2.41112i	0.0205617	+	0.111813i
$466$	−7.82780	+	24.0915i	−0.362616	+	1.11602i
$467$	−6.61206	+	9.10071i	−0.305969	+	0.421131i	−0.934119	−	0.356962i	$-0.883813\pi$
$467$	−6.61206	+	9.10071i	−0.305969	+	0.421131i	0.628150	+	0.778093i	$0.283813\pi$
$468$	21.5538	−	29.6662i	0.996324	−	1.37132i
$469$	2.86535	−	8.81864i	0.132310	−	0.407207i
$470$	−19.2449	+	3.53902i	−0.887701	+	0.163243i
$471$	8.92504	−	6.48442i	0.411244	−	0.298786i
$472$			1.95261i			0.0898762i
$473$	−0.429556	−	7.49007i	−0.0197510	−	0.344394i
$474$	−5.32424			−0.244550
$475$	−15.3158	+	5.83014i	−0.702738	+	0.267505i
$476$	−2.08661	−	6.42192i	−0.0956395	−	0.294348i
$477$	−9.78665	−	3.17988i	−0.448100	−	0.145597i
$478$	24.2508	−	33.3784i	1.10921	−	1.52669i
$479$	16.9621	+	12.3237i	0.775017	+	0.563083i	0.903479	−	0.428632i	$-0.141004\pi$
$479$	16.9621	+	12.3237i	0.775017	+	0.563083i	−0.128462	+	0.991714i	$0.541004\pi$
$480$	−42.6873	−	20.4341i	−1.94840	−	0.932683i
$481$	−8.86200	−	27.2744i	−0.404072	−	1.24361i
$482$	−27.1126	−	37.3174i	−1.23495	−	1.69976i
$483$		−	8.52053i		−	0.387697i
$484$	−4.56960	+	22.5907i	−0.207709	+	1.02685i
$485$	6.69223	+	0.890564i	0.303879	+	0.0404384i
$486$	35.3849	−	25.7086i	1.60509	−	1.16617i
$487$	−21.4645	+	6.97424i	−0.972649	+	0.316033i	−0.751885	−	0.659294i	$-0.770855\pi$
$487$	−21.4645	+	6.97424i	−0.972649	+	0.316033i	−0.220764	+	0.975327i	$0.570855\pi$
$488$	−0.453171	−	0.147244i	−0.0205141	−	0.00666543i
$489$	35.1377	+	25.5290i	1.58898	+	1.15446i
$490$	−19.8884	−	18.9263i	−0.898467	−	0.855003i
$491$	−6.20389	+	19.0936i	−0.279977	+	0.861682i	0.707882	+	0.706331i	$0.249651\pi$
$491$	−6.20389	+	19.0936i	−0.279977	+	0.861682i	−0.987859	+	0.155351i	$0.950349\pi$
$492$	30.2136	−	9.81699i	1.36213	−	0.442584i
$493$	−9.63565	−	13.2623i	−0.433968	−	0.597306i
$494$	−30.0141			−1.35040
$495$	−2.14943	+	28.6016i	−0.0966098	+	1.28555i
$496$	1.58993			0.0713898
$497$	3.09571	+	4.26088i	0.138862	+	0.191127i
$498$	37.3002	−	12.1196i	1.67146	−	0.543091i
$499$	−1.43750	+	4.42417i	−0.0643513	+	0.198053i	−0.978063	−	0.208311i	$-0.933203\pi$
$499$	−1.43750	+	4.42417i	−0.0643513	+	0.198053i	0.913711	+	0.406364i	$0.133203\pi$
$500$	20.0252	−	12.1563i	0.895553	−	0.543645i
$501$	19.4346	+	14.1200i	0.868272	+	0.630836i
$502$	−32.6280	−	10.6015i	−1.45626	−	0.473167i
$503$	12.3611	−	4.01636i	0.551154	−	0.179081i	−0.0201833	−	0.999796i	$-0.506425\pi$
$503$	12.3611	−	4.01636i	0.551154	−	0.179081i	0.571337	+	0.820716i	$0.306425\pi$
$504$	−0.582768	+	0.423406i	−0.0259585	+	0.0188600i
$505$	−4.48232	+	33.6828i	−0.199460	+	1.49887i
$506$	17.4892	−	14.3057i	0.777488	−	0.635966i
$507$		−	19.5928i		−	0.870147i
$508$	8.73242	+	12.0191i	0.387439	+	0.533263i
$509$	−9.12976	−	28.0985i	−0.404669	−	1.24544i	−0.921171	−	0.389158i	$-0.872766\pi$
$509$	−9.12976	−	28.0985i	−0.404669	−	1.24544i	0.516501	−	0.856286i	$-0.327234\pi$
$510$	17.0843	−	35.6896i	0.756506	−	1.58036i
$511$	−1.12169	−	0.814952i	−0.0496205	−	0.0360514i
$512$	−18.9023	+	26.0168i	−0.835373	+	1.14979i
$513$	7.08662	+	2.30258i	0.312882	+	0.101661i
$514$	2.96157	+	9.11478i	0.130629	+	0.402036i
$515$	19.1681	−	10.3728i	0.844649	−	0.457080i
$516$	12.4207			0.546793
$517$	13.3638	−	5.20558i	0.587740	−	0.228941i
$518$			12.3869i			0.544248i
$519$	8.71293	−	6.33032i	0.382455	−	0.277870i
$520$	1.91910	−	0.352912i	0.0841583	−	0.0154762i
$521$	−9.71896	+	29.9119i	−0.425796	+	1.31046i	0.476435	+	0.879210i	$0.341929\pi$
$521$	−9.71896	+	29.9119i	−0.425796	+	1.31046i	−0.902230	+	0.431254i	$0.858071\pi$
$522$	−22.6016	+	31.1085i	−0.989247	+	1.36158i
$523$	−5.30194	+	7.29750i	−0.231838	+	0.319097i	−0.909047	−	0.416693i	$-0.863189\pi$
$523$	−5.30194	+	7.29750i	−0.231838	+	0.319097i	0.677210	+	0.735790i	$0.263189\pi$
$524$	−4.67290	+	14.3817i	−0.204137	+	0.628268i
$525$	0.626999	+	12.6396i	0.0273645	+	0.551638i
$526$	−29.6393	+	21.5342i	−1.29234	+	0.938937i
$527$			1.39595i			0.0608088i
$528$	31.9469	+	8.39166i	1.39031	+	0.365200i
$529$	11.6672			0.507269
$530$	−5.73016	−	10.5889i	−0.248902	−	0.459952i
$531$	−12.1010	−	37.2431i	−0.525140	−	1.61621i
$532$	6.30817	+	2.04965i	0.273494	+	0.0888636i
$533$	15.3885	−	21.1805i	0.666552	−	0.917430i
$534$	−52.3279	−	38.0184i	−2.26445	−	1.64522i
$535$	−7.37793	+	15.4127i	−0.318976	+	0.666349i
$536$	0.572121	+	1.76081i	0.0247119	+	0.0760553i
$537$	−25.1016	−	34.5494i	−1.08321	−	1.49092i
$538$		−	4.65046i		−	0.200496i
$539$	16.9300	+	10.8763i	0.729227	+	0.468473i
$540$	−10.5583	−	1.40504i	−0.454359	−	0.0604635i
$541$	6.91720	−	5.02564i	0.297394	−	0.216069i	−0.429075	−	0.903269i	$-0.641160\pi$
$541$	6.91720	−	5.02564i	0.297394	−	0.216069i	0.726468	+	0.687200i	$0.241160\pi$
$542$	1.55066	−	0.503839i	0.0666064	−	0.0216417i
$543$	−13.8247	−	4.49192i	−0.593275	−	0.192767i
$544$	−21.8016	−	15.8398i	−0.934737	−	0.679126i
$545$	15.1924	−	15.9647i	0.650770	−	0.683852i
$546$	−7.16226	+	22.0432i	−0.306516	+	0.943360i
$547$	32.2693	−	10.4849i	1.37974	−	0.448304i	0.477154	−	0.878820i	$-0.341668\pi$
$547$	32.2693	−	10.4849i	1.37974	−	0.448304i	0.902583	+	0.430516i	$0.141668\pi$
$548$	10.4571	+	14.3930i	0.446706	+	0.614838i
$549$	9.55608			0.407844
$550$	−24.8912	+	22.5085i	−1.06137	+	0.959765i
$551$	16.1028			0.686002
$552$	0.999990	+	1.37637i	0.0425624	+	0.0585821i
$553$	0.922187	−	0.299637i	0.0392154	−	0.0127418i
$554$	−7.39974	+	22.7740i	−0.314385	+	0.967577i
$555$	−25.6010	+	26.9025i	−1.08670	+	1.14195i
$556$	−13.1206	−	9.53265i	−0.556436	−	0.404274i
$557$	−21.8178	−	7.08904i	−0.924451	−	0.300372i	−0.192160	−	0.981364i	$-0.561549\pi$
$557$	−21.8178	−	7.08904i	−0.924451	−	0.300372i	−0.732291	+	0.680991i	$0.761549\pi$
$558$	3.11413	−	1.01184i	0.131832	−	0.0428347i
$559$	8.28110	−	6.01657i	0.350253	−	0.254474i
$560$	8.13565	+	1.08265i	0.343794	+	0.0457501i
$561$	−7.36788	+	28.0494i	−0.311072	+	1.18425i
$562$		−	12.6061i		−	0.531757i
$563$	5.45619	+	7.50980i	0.229951	+	0.316500i	0.908364	−	0.418180i	$-0.137332\pi$
$563$	5.45619	+	7.50980i	0.229951	+	0.316500i	−0.678413	+	0.734681i	$0.737332\pi$
$564$	7.33731	+	22.5819i	0.308957	+	0.950871i
$565$	4.84532	−	10.1220i	0.203844	−	0.425836i
$566$	−14.1546	−	10.2839i	−0.594962	−	0.432266i
$567$	−3.20457	+	4.41071i	−0.134579	+	0.185232i
$568$	−1.00013	−	0.324963i	−0.0419647	−	0.0136352i
$569$	−9.55701	−	29.4135i	−0.400651	−	1.23308i	−0.924473	−	0.381248i	$-0.875494\pi$
$569$	−9.55701	−	29.4135i	−0.400651	−	1.23308i	0.523822	−	0.851828i	$-0.324506\pi$
$570$	18.4980	+	34.1830i	0.774797	+	1.43177i
$571$	−2.63736			−0.110370			−0.0551851	−	0.998476i	$-0.517575\pi$
$571$	−2.63736			−0.110370			−0.0551851	+	0.998476i	$0.517575\pi$
$572$	−29.3017	+	11.4138i	−1.22517	+	0.477237i
$573$			57.1712i			2.38836i
$574$	−9.14848	+	6.64676i	−0.381850	+	0.277430i
$575$	16.8115	−	0.833947i	0.701086	−	0.0347780i
$576$	−10.4494	+	32.1599i	−0.435391	+	1.34000i
$577$	−21.5309	+	29.6347i	−0.896342	+	1.23371i	0.0752785	+	0.997163i	$0.476015\pi$
$577$	−21.5309	+	29.6347i	−0.896342	+	1.23371i	−0.971620	+	0.236546i	$0.923985\pi$
$578$	−6.97814	+	9.60459i	−0.290252	+	0.399498i
$579$	18.2036	−	56.0249i	0.756516	−	2.32832i
$580$	−22.6389	+	4.16315i	−0.940028	+	0.172866i
$581$	−5.77854	+	4.19835i	−0.239734	+	0.174177i
$582$		−	16.0118i		−	0.663710i
$583$	5.58719	+	6.83051i	0.231398	+	0.282891i
$584$	0.276837			0.0114556
$585$	−34.4169	+	18.6247i	−1.42297	+	0.770035i
$586$	−3.63360	−	11.1831i	−0.150103	−	0.461968i
$587$	13.0793	+	4.24973i	0.539842	+	0.175405i	0.566231	−	0.824246i	$-0.308401\pi$
$587$	13.0793	+	4.24973i	0.539842	+	0.175405i	−0.0263892	+	0.999652i	$0.508401\pi$
$588$	−19.5817	+	26.9519i	−0.807536	+	1.11148i
$589$	−1.10935	−	0.805989i	−0.0457099	−	0.0332102i
$590$	19.7829	−	41.3269i	0.814448	−	1.70140i
$591$	20.8508	+	64.1723i	0.857689	+	2.63970i
$592$	14.1567	+	19.4850i	0.581837	+	0.800829i
$593$		−	20.1550i		−	0.827668i	−0.910352	−	0.413834i	$-0.864189\pi$
$593$		−	20.1550i		−	0.827668i	0.910352	−	0.413834i	$-0.135811\pi$
$594$	15.2336	−	0.873649i	0.625044	−	0.0358463i
$595$	−0.950563	+	7.14310i	−0.0389693	+	0.292839i
$596$	28.6194	−	20.7932i	1.17230	−	0.851722i
$597$	42.2878	−	13.7401i	1.73072	−	0.562346i
$598$	29.3187	+	9.52624i	1.19893	+	0.389557i
$599$	3.49753	+	2.54110i	0.142905	+	0.103827i	0.656941	−	0.753942i	$-0.271850\pi$
$599$	3.49753	+	2.54110i	0.142905	+	0.103827i	−0.514036	+	0.857769i	$0.671850\pi$
$600$	−1.58470	−	1.96816i	−0.0646950	−	0.0803498i
$601$	11.1214	−	34.2281i	0.453650	−	1.39619i	−0.419063	−	0.907957i	$-0.637641\pi$
$601$	11.1214	−	34.2281i	0.453650	−	1.39619i	0.872713	−	0.488234i	$-0.162359\pi$
$602$	−4.20484	+	1.36623i	−0.171376	+	0.0556836i
$603$	−21.8247	−	30.0391i	−0.888771	−	1.22329i
$604$	25.7358			1.04717
$605$	14.8080	−	19.6399i	0.602030	−	0.798473i
$606$	80.5893			3.27372
$607$	−23.3056	−	32.0774i	−0.945945	−	1.30198i	−0.953305	−	0.302009i	$-0.902343\pi$
$607$	−23.3056	−	32.0774i	−0.945945	−	1.30198i	0.00736018	−	0.999973i	$-0.497657\pi$
$608$	25.1754	−	8.17999i	1.02100	−	0.331742i
$609$	3.84261	−	11.8263i	0.155710	−	0.479227i
$610$	8.09955	+	7.70772i	0.327941	+	0.312077i
$611$	15.8305	+	11.5015i	0.640434	+	0.465303i
$612$	−25.7158	−	8.35556i	−1.03950	−	0.337753i
$613$	−3.62818	+	1.17887i	−0.146541	+	0.0476139i	−0.381369	−	0.924423i	$-0.624547\pi$
$613$	−3.62818	+	1.17887i	−0.146541	+	0.0476139i	0.234828	+	0.972037i	$0.424547\pi$
$614$	−30.2424	+	21.9724i	−1.22049	+	0.886735i
$615$	−33.6066	−	4.47217i	−1.35515	−	0.180335i
$616$	0.616721	−	0.0353690i	0.0248484	−	0.00142506i
$617$			28.4055i			1.14356i	0.820407	+	0.571781i	$0.193747\pi$
$617$			28.4055i			1.14356i	−0.820407	+	0.571781i	$0.806253\pi$
$618$	−30.3828	−	41.8184i	−1.22218	−	1.68218i
$619$	−7.43830	−	22.8927i	−0.298971	−	0.920137i	−0.981859	−	0.189614i	$-0.939276\pi$
$619$	−7.43830	−	22.8927i	−0.298971	−	0.920137i	0.682888	−	0.730523i	$-0.260724\pi$
$620$	1.76801	+	0.846330i	0.0710048	+	0.0339894i
$621$	−6.19162	−	4.49848i	−0.248461	−	0.180518i
$622$	13.4786	−	18.5516i	0.540441	−	0.743853i
$623$	11.2031	+	3.64010i	0.448841	+	0.145837i
$624$	13.9262	+	42.8603i	0.557492	+	1.71579i
$625$	−24.8773	+	2.47421i	−0.995091	+	0.0989682i
$626$	10.3511			0.413714
$627$	−18.0365	−	22.0502i	−0.720308	−	0.880599i
$628$		−	8.82059i		−	0.351980i
$629$	−17.1078	+	12.4296i	−0.682135	+	0.495600i
$630$	16.6240	−	3.05706i	0.662316	−	0.121796i
$631$	5.90889	−	18.1857i	0.235229	−	0.723961i	−0.761862	−	0.647740i	$-0.775714\pi$
$631$	5.90889	−	18.1857i	0.235229	−	0.723961i	0.997091	−	0.0762213i	$-0.0242855\pi$
$632$	−0.113800	+	0.156632i	−0.00452672	+	0.00623049i
$633$	−8.97463	+	12.3525i	−0.356710	+	0.490969i
$634$	7.38747	−	22.7363i	0.293394	−	0.902974i
$635$	−2.86749	−	15.5932i	−0.113793	−	0.618796i
$636$	−11.8195	+	8.58735i	−0.468673	+	0.340511i
$637$			27.4546i			1.08779i
$638$	30.7263	−	11.9687i	1.21646	−	0.473847i
$639$	21.0900			0.834307
$640$	−3.03052	+	1.63996i	−0.119792	+	0.0648251i
$641$	3.70172	+	11.3927i	0.146209	+	0.449985i	0.997165	−	0.0752526i	$-0.0239763\pi$
$641$	3.70172	+	11.3927i	0.146209	+	0.449985i	−0.850955	+	0.525238i	$0.823976\pi$
$642$	38.5429	+	12.5233i	1.52117	+	0.494257i
$643$	−15.1301	+	20.8248i	−0.596672	+	0.821248i	−0.995399	−	0.0958216i	$-0.969452\pi$
$643$	−15.1301	+	20.8248i	−0.596672	+	0.821248i	0.398727	+	0.917070i	$0.369452\pi$
$644$	−5.51149	−	4.00433i	−0.217183	−	0.157793i
$645$	−11.9560	−	5.72324i	−0.470767	−	0.225352i
$646$	6.83905	+	21.0484i	0.269079	+	0.828139i
$647$	5.46774	+	7.52570i	0.214959	+	0.295866i	0.902856	−	0.429942i	$-0.141466\pi$
$647$	5.46774	+	7.52570i	0.214959	+	0.295866i	−0.687897	+	0.725808i	$0.741466\pi$
$648$		−	1.08858i		−	0.0427636i
$649$	−8.53167	+	32.4800i	−0.334897	+	1.27495i
$650$	−44.1933	−	11.9740i	−1.73341	−	0.469661i
$651$	−0.856664	+	0.622403i	−0.0335753	+	0.0243939i
$652$	33.0268	−	10.7311i	1.29343	−	0.420261i
$653$	−35.6177	−	11.5729i	−1.39383	−	0.452882i	−0.486637	−	0.873604i	$-0.661777\pi$
$653$	−35.6177	−	11.5729i	−1.39383	−	0.452882i	−0.907189	+	0.420723i	$0.861777\pi$
$654$	−42.2854	−	30.7221i	−1.65349	−	1.20133i
$655$	11.1249	−	11.6904i	0.434685	−	0.456782i
$656$	−6.79446	+	20.9112i	−0.265279	+	0.816445i
$657$	−5.28025	+	1.71566i	−0.206002	+	0.0669342i
$658$	−4.96785	−	6.83766i	−0.193667	−	0.266560i
$659$	4.93753			0.192339			0.0961693	−	0.995365i	$-0.469341\pi$
$659$	4.93753			0.192339			0.0961693	+	0.995365i	$0.469341\pi$
$660$	31.0582	+	26.3372i	1.20894	+	1.02517i
$661$	−4.82155			−0.187537			−0.0937683	−	0.995594i	$-0.529891\pi$
$661$	−4.82155			−0.187537			−0.0937683	+	0.995594i	$0.529891\pi$
$662$	34.8155	+	47.9194i	1.35314	+	1.86244i
$663$	−37.6313	+	12.2272i	−1.46148	+	0.474864i
$664$	0.440710	−	1.35637i	0.0171029	−	0.0526372i
$665$	−5.12770	−	4.87964i	−0.198844	−	0.189224i
$666$	40.1286	+	29.1551i	1.55495	+	1.12974i
$667$	−15.7297	−	5.11091i	−0.609058	−	0.197895i
$668$	18.2670	−	5.93532i	0.706773	−	0.229645i
$669$	−40.3292	+	29.3009i	−1.55922	+	1.13284i
$670$	5.73070	−	43.0639i	0.221396	−	1.66370i
$671$	−6.89474	−	4.42935i	−0.266168	−	0.170993i
$672$		−	20.4415i		−	0.788548i
$673$	−19.3464	−	26.6280i	−0.745749	−	1.02644i	−0.998267	−	0.0588431i	$-0.981259\pi$
$673$	−19.3464	−	26.6280i	−0.745749	−	1.02644i	0.252518	−	0.967592i	$-0.418741\pi$
$674$	−16.6619	−	51.2802i	−0.641794	−	1.97524i
$675$	9.51587	+	6.21756i	0.366266	+	0.239314i
$676$	−12.6736	−	9.20789i	−0.487445	−	0.354150i
$677$	−10.0761	+	13.8686i	−0.387258	+	0.533014i	−0.957489	−	0.288470i	$-0.906854\pi$
$677$	−10.0761	+	13.8686i	−0.387258	+	0.533014i	0.570231	+	0.821484i	$0.306854\pi$
$678$	−25.3123	−	8.22448i	−0.972114	−	0.315859i
$679$	0.901110	+	2.77333i	0.0345814	+	0.106431i
$680$	−0.684782	−	1.26543i	−0.0262602	−	0.0485268i
$681$	−74.5977			−2.85859
$682$	−2.71585	−	0.713386i	−0.103995	−	0.0273170i
$683$			19.3586i			0.740737i	0.928885	+	0.370368i	$0.120769\pi$
$683$			19.3586i			0.740737i	−0.928885	+	0.370368i	$0.879231\pi$
$684$	21.4877	−	15.6117i	0.821602	−	0.596929i
$685$	−3.43383	−	18.6729i	−0.131200	−	0.713454i
$686$	7.89232	−	24.2901i	0.301330	−	0.927399i
$687$	39.1115	−	53.8324i	1.49220	−	2.05383i
$688$	−5.05292	+	6.95475i	−0.192641	+	0.265148i
$689$	−3.72054	+	11.4506i	−0.141741	+	0.436234i
$690$	−7.22009	−	39.2622i	−0.274864	−	1.49469i
$691$	7.39559	−	5.37321i	0.281342	−	0.204407i	−0.438161	−	0.898897i	$-0.644370\pi$
$691$	7.39559	−	5.37321i	0.281342	−	0.204407i	0.719502	+	0.694490i	$0.244370\pi$
$692$		−	8.61097i		−	0.327340i
$693$	−11.5438	+	4.49665i	−0.438514	+	0.170814i
$694$	8.72467			0.331184
$695$	8.23717	+	15.2217i	0.312454	+	0.577391i
$696$	0.767250	+	2.36135i	0.0290825	+	0.0895068i
$697$	−18.3600	−	5.96554i	−0.695436	−	0.225961i
$698$	−15.6650	+	21.5610i	−0.592929	+	0.816096i
$699$	−26.5383	−	19.2812i	−1.00377	−	0.729281i
$700$	8.47058	+	5.53458i	0.320158	+	0.209187i
$701$	−4.72594	−	14.5450i	−0.178496	−	0.549355i	0.821279	−	0.570526i	$-0.193261\pi$
$701$	−4.72594	−	14.5450i	−0.178496	−	0.549355i	−0.999776	+	0.0211707i	$0.993261\pi$
$702$	12.2368	+	16.8425i	0.461847	+	0.635678i
$703$		−	20.7719i		−	0.783428i
$704$	22.4457	−	18.3601i	0.845956	−	0.691971i
$705$	3.34254	−	25.1179i	0.125887	−	0.945994i
$706$	41.7327	−	30.3206i	1.57063	−	1.14113i
$707$	−13.9585	+	4.53539i	−0.524964	+	0.170571i
$708$	−52.8760	−	17.1805i	−1.98720	−	0.645681i
$709$	34.7172	+	25.2235i	1.30383	+	0.947290i	0.999985	−	0.00543044i	$-0.00172857\pi$
$709$	34.7172	+	25.2235i	1.30383	+	0.947290i	0.303848	+	0.952721i	$0.401729\pi$
$710$	17.8755	+	17.0107i	0.670854	+	0.638401i
$711$	1.19986	−	3.69278i	0.0449982	−	0.138490i
$712$	−2.23690	+	0.726814i	−0.0838315	+	0.0272385i
$713$	0.827834	+	1.13942i	0.0310026	+	0.0426714i
$714$	17.0905			0.639598
$715$	33.4646	+	2.51489i	1.25151	+	0.0940516i
$716$	−34.1450			−1.27606
$717$	31.4039	+	43.2238i	1.17280	+	1.61422i
$718$	−50.5682	+	16.4306i	−1.88719	+	0.613184i
$719$	−1.48738	+	4.57768i	−0.0554699	+	0.170719i	−0.974953	−	0.222411i	$-0.928607\pi$
$719$	−1.48738	+	4.57768i	−0.0554699	+	0.170719i	0.919483	+	0.393129i	$0.128607\pi$
$720$	22.6563	−	23.8081i	0.844351	−	0.887274i
$721$	7.61592	+	5.53329i	0.283632	+	0.206071i
$722$	15.8925	+	5.16378i	0.591457	+	0.192176i
$723$	56.8090	−	18.4584i	2.11275	−	0.686473i
$724$	−9.40269	+	6.83146i	−0.349448	+	0.253889i
$725$	23.7101	+	6.42417i	0.880571	+	0.238588i
$726$	−50.8053	−	28.6686i	−1.88556	−	1.06399i
$727$		−	21.8922i		−	0.811937i	−0.913887	−	0.405969i	$-0.866934\pi$
$727$		−	21.8922i		−	0.811937i	0.913887	−	0.405969i	$-0.133066\pi$
$728$	0.495395	+	0.681853i	0.0183606	+	0.0252712i
$729$	12.2694	+	37.7614i	0.454423	+	1.39857i
$730$	−5.85925	−	2.80477i	−0.216860	−	0.103809i
$731$	−6.10627	−	4.43647i	−0.225849	−	0.164089i
$732$	7.97464	−	10.9762i	0.294751	−	0.405690i
$733$	45.6788	+	14.8419i	1.68718	+	0.548199i	0.986284	−	0.165060i	$-0.0527817\pi$
$733$	45.6788	+	14.8419i	1.68718	+	0.548199i	0.700901	+	0.713259i	$0.252782\pi$
$734$	1.26242	+	3.88533i	0.0465968	+	0.143410i
$735$	31.2680	−	16.9206i	1.15334	−	0.624125i
$736$	−27.1885			−1.00218
$737$	1.82312	+	31.7893i	0.0671554	+	1.17097i
$738$			45.2820i			1.66685i
$739$	−27.5934	+	20.0478i	−1.01504	+	0.737470i	−0.965260	−	0.261290i	$-0.915852\pi$
$739$	−27.5934	+	20.0478i	−1.01504	+	0.737470i	−0.0497805	+	0.998760i	$0.515852\pi$
$740$	5.37029	+	29.2032i	0.197416	+	1.07353i
$741$	12.0106	−	36.9648i	0.441220	−	1.35794i
$742$	3.05671	−	4.20720i	0.112215	−	0.154451i
$743$	15.5411	−	21.3906i	0.570149	−	0.784743i	−0.422423	−	0.906399i	$-0.638820\pi$
$743$	15.5411	−	21.3906i	0.570149	−	0.784743i	0.992572	+	0.121656i	$0.0388203\pi$
$744$	0.0653350	−	0.201080i	0.00239530	−	0.00737196i
$745$	−37.1296	+	6.82792i	−1.36032	+	0.250156i
$746$	−14.5244	+	10.5526i	−0.531777	+	0.386359i
$747$			28.6019i			1.04649i
$748$	14.6811	+	17.9481i	0.536794	+	0.656247i
$749$	−7.38062			−0.269682
$750$	13.5997	+	57.7114i	0.496590	+	2.10732i
$751$	14.1963	+	43.6918i	0.518032	+	1.59434i	0.777697	+	0.628639i	$0.216388\pi$
$751$	14.1963	+	43.6918i	0.518032	+	1.59434i	−0.259666	+	0.965699i	$0.583612\pi$
$752$	−15.6292	−	5.07825i	−0.569939	−	0.185185i
$753$	26.1132	−	35.9417i	0.951617	−	1.30979i
$754$	36.3977	+	26.4445i	1.32553	+	0.963052i
$755$	−24.7728	−	11.8585i	−0.901575	−	0.431577i
$756$	−1.42168	−	4.37549i	−0.0517061	−	0.159135i
$757$	18.1365	+	24.9628i	0.659183	+	0.907288i	0.999454	−	0.0330398i	$-0.0105188\pi$
$757$	18.1365	+	24.9628i	0.659183	+	0.907288i	−0.340271	+	0.940327i	$0.610519\pi$
$758$			42.6271i			1.54828i
$759$	10.6201	+	27.2640i	0.385485	+	0.989620i
$760$	1.40099	+	0.186436i	0.0508194	+	0.00676275i
$761$	11.4860	−	8.34507i	0.416367	−	0.302508i	−0.359807	−	0.933027i	$-0.617158\pi$
$761$	11.4860	−	8.34507i	0.416367	−	0.302508i	0.776175	+	0.630518i	$0.217158\pi$
$762$	−35.7618	+	11.6197i	−1.29551	+	0.420938i
$763$	9.05303	+	2.94151i	0.327742	+	0.106490i
$764$	36.9811	+	26.8684i	1.33793	+	0.972063i
$765$	20.9035	+	19.8923i	0.755767	+	0.719206i
$766$	−16.2464	+	50.0012i	−0.587005	+	1.80662i
$767$	−43.5754	+	14.1585i	−1.57342	+	0.511234i
$768$	−22.1319	−	30.4620i	−0.798617	−	1.09920i
$769$	30.0208			1.08258			0.541290	−	0.840836i	$-0.317936\pi$
$769$	30.0208			1.08258			0.541290	+	0.840836i	$0.317936\pi$
$770$	−13.4112	−	5.49973i	−0.483307	−	0.198196i
$771$	−12.4107			−0.446961
$772$	−27.6846	−	38.1046i	−0.996392	−	1.37142i
$773$	−28.9401	+	9.40320i	−1.04090	+	0.338209i	−0.779092	−	0.626910i	$-0.784319\pi$
$773$	−28.9401	+	9.40320i	−1.04090	+	0.338209i	−0.261810	+	0.965119i	$0.584319\pi$
$774$	−5.47091	+	16.8377i	−0.196648	+	0.605220i
$775$	−1.31188	−	1.62933i	−0.0471241	−	0.0585271i
$776$	−0.471046	−	0.342235i	−0.0169096	−	0.0122855i
$777$	−15.2555	−	4.95680i	−0.547287	−	0.177824i
$778$	3.16373	−	1.02796i	0.113425	−	0.0368541i
$779$	15.3414	−	11.1461i	0.549661	−	0.399352i
$780$	−7.32892	+	55.0739i	−0.262417	+	1.97196i
$781$	−15.2165	−	9.77544i	−0.544488	−	0.349793i
$782$		−	22.7315i		−	0.812876i
$783$	−6.56512	−	9.03612i	−0.234618	−	0.322925i
$784$	−7.12510	−	21.9288i	−0.254468	−	0.783172i
$785$	−4.06436	+	8.49055i	−0.145063	+	0.303041i
$786$	−30.9642	−	22.4968i	−1.10445	−	0.802433i
$787$	17.9067	−	24.6465i	0.638306	−	0.878553i	−0.360218	−	0.932868i	$-0.617298\pi$
$787$	17.9067	−	24.6465i	0.638306	−	0.878553i	0.998524	+	0.0543151i	$0.0172976\pi$
$788$	51.3089	+	16.6713i	1.82780	+	0.593890i
$789$	−14.6605	−	45.1205i	−0.521929	−	1.60633i
$790$	3.99549	−	2.16215i	0.142153	−	0.0769259i
$791$	4.84709			0.172343
$792$	1.33700	−	2.08118i	0.0475083	−	0.0739516i
$793$		−	11.1809i		−	0.397044i
$794$	−27.3555	+	19.8749i	−0.970810	+	0.705334i
$795$	15.3341	−	2.81985i	0.543845	−	0.100010i
$796$	10.9859	−	33.8112i	0.389385	−	1.19840i
$797$	−19.4235	+	26.7341i	−0.688014	+	0.946970i	−0.999995	−	0.00311796i	$-0.999008\pi$
$797$	−19.4235	+	26.7341i	−0.688014	+	0.946970i	0.311981	+	0.950088i	$0.399008\pi$
$798$	−9.86764	+	13.5816i	−0.349311	+	0.480785i
$799$	4.45870	−	13.7225i	0.157737	−	0.485466i
$800$	40.3322	−	2.00071i	1.42596	−	0.0707359i
$801$	38.1613	−	27.7258i	1.34836	−	0.979642i
$802$		−	56.2421i		−	1.98598i
$803$	4.60494	+	1.20960i	0.162505	+	0.0426859i
$804$	−52.7160			−1.85915
$805$	3.46015	+	6.39409i	0.121954	+	0.225362i
$806$	−1.18388	−	3.64361i	−0.0417004	−	0.128341i
$807$	5.72743	+	1.86095i	0.201615	+	0.0655087i
$808$	1.72251	−	2.37083i	0.0605977	−	0.0834056i
$809$	8.89072	+	6.45948i	0.312581	+	0.227103i	0.733003	−	0.680225i	$-0.238118\pi$
$809$	8.89072	+	6.45948i	0.312581	+	0.227103i	−0.420422	+	0.907329i	$0.638118\pi$
$810$	−11.0290	+	23.0398i	−0.387519	+	0.809537i
$811$	12.5951	+	38.7638i	0.442275	+	1.36118i	0.885445	+	0.464744i	$0.153854\pi$
$811$	12.5951	+	38.7638i	0.442275	+	1.36118i	−0.443171	+	0.896437i	$0.646146\pi$
$812$	−5.84397	−	8.04353i	−0.205083	−	0.282273i
$813$			2.11138i			0.0740494i
$814$	−15.4392	−	39.6355i	−0.541142	−	1.38923i
$815$	−36.7358	−	4.88858i	−1.28680	−	0.171240i
$816$	26.8841	−	19.5324i	0.941130	−	0.683771i
$817$	7.05121	−	2.29108i	0.246691	−	0.0801547i
$818$	75.8941	+	24.6595i	2.65358	+	0.862199i
$819$	−13.6746	−	9.93519i	−0.477830	−	0.347164i
$820$	−18.6867	+	19.6366i	−0.652567	+	0.685741i
$821$	4.66851	−	14.3682i	0.162932	−	0.501454i	−0.835946	−	0.548812i	$-0.815080\pi$
$821$	4.66851	−	14.3682i	0.162932	−	0.501454i	0.998878	+	0.0473584i	$0.0150803\pi$
$822$	−42.8250	+	13.9147i	−1.49369	+	0.485330i
$823$	21.4138	+	29.4735i	0.746437	+	1.02738i	0.998222	+	0.0595989i	$0.0189822\pi$
$823$	21.4138	+	29.4735i	0.746437	+	1.02738i	−0.251786	+	0.967783i	$0.581018\pi$
$824$	−1.87964			−0.0654805
$825$	−17.7604	−	39.6627i	−0.618339	−	1.38088i
$826$	19.7901			0.688585
$827$	−2.23560	−	3.07703i	−0.0777393	−	0.106999i	0.768376	−	0.639998i	$-0.221065\pi$
$827$	−2.23560	−	3.07703i	−0.0777393	−	0.106999i	−0.846116	+	0.532999i	$0.821065\pi$
$828$	−25.9449	+	8.43002i	−0.901649	+	0.292963i
$829$	8.43810	−	25.9698i	0.293067	−	0.901969i	−0.690796	−	0.723049i	$-0.742740\pi$
$829$	8.43810	−	25.9698i	0.293067	−	0.901969i	0.983864	−	0.178919i	$-0.0572601\pi$
$830$	−23.0696	+	24.2424i	−0.800759	+	0.841466i
$831$	−25.0870	−	18.2268i	−0.870259	−	0.632280i
$832$	37.6279	+	12.2261i	1.30451	+	0.423862i
$833$	19.2535	−	6.25584i	0.667094	−	0.216752i
$834$	33.2085	−	24.1274i	1.14992	−	0.835464i
$835$	−20.3184	−	2.70386i	−0.703148	−	0.0935710i
$836$	−22.7396	+	1.30412i	−0.786466	+	0.0451038i
$837$			0.951115i			0.0328754i
$838$	−17.5821	−	24.1998i	−0.607365	−	0.835967i
$839$	−8.75291	−	26.9387i	−0.302184	−	0.930026i	−0.980713	−	0.195453i	$-0.937382\pi$
$839$	−8.75291	−	26.9387i	−0.302184	−	0.930026i	0.678529	−	0.734573i	$-0.262618\pi$
$840$	0.471243	−	0.984439i	0.0162594	−	0.0339664i
$841$	3.93381	+	2.85808i	0.135649	+	0.0985546i
$842$	12.8195	−	17.6445i	0.441788	−	0.608070i
$843$	15.5255	+	5.04453i	0.534725	+	0.173743i
$844$	3.77247	+	11.6105i	0.129854	+	0.399649i
$845$	7.95655	+	14.7031i	0.273714	+	0.505802i
$846$	−33.8442			−1.16359
$847$	10.4132	+	2.10635i	0.357800	+	0.0723750i
$848$		−	10.1115i		−	0.347232i
$849$	18.3297	−	13.3173i	0.629073	−	0.457048i
$850$	1.67274	+	33.7206i	0.0573745	+	1.15661i
$851$	−6.59285	+	20.2907i	−0.226000	+	0.695556i
$852$	17.5998	−	24.2240i	0.602959	−	0.829902i
$853$	−4.90400	+	6.74977i	−0.167910	+	0.231108i	−0.884677	−	0.466205i	$-0.845621\pi$
$853$	−4.90400	+	6.74977i	−0.167910	+	0.231108i	0.716767	+	0.697313i	$0.245621\pi$
$854$	−1.49235	+	4.59298i	−0.0510671	+	0.157168i
$855$	−27.8773	+	5.12646i	−0.953382	+	0.175321i
$856$	1.19223	−	0.866207i	0.0407497	−	0.0296064i
$857$		−	8.59547i		−	0.293616i	−0.989165	−	0.146808i	$-0.953100\pi$
$857$		−	8.59547i		−	0.293616i	0.989165	−	0.146808i	$-0.0468999\pi$
$858$	−4.55708	−	79.4609i	−0.155576	−	2.71275i
$859$	−9.40807			−0.320999			−0.160500	−	0.987036i	$-0.551311\pi$
$859$	−9.40807			−0.320999			−0.160500	+	0.987036i	$0.551311\pi$
$860$	−9.32095	+	5.04401i	−0.317842	+	0.171999i
$861$	−4.52513	−	13.9269i	−0.154216	−	0.474628i
$862$	−61.9571	−	20.1311i	−2.11027	−	0.685667i
$863$	6.06951	−	8.35396i	0.206608	−	0.284372i	−0.693120	−	0.720822i	$-0.743764\pi$
$863$	6.06951	−	8.35396i	0.206608	−	0.284372i	0.899728	+	0.436450i	$0.143764\pi$
$864$	−14.8543	−	10.7922i	−0.505352	−	0.367160i
$865$	−3.96777	+	8.28877i	−0.134908	+	0.281827i
$866$	−0.239279	−	0.736426i	−0.00813104	−	0.0250248i
$867$	−9.03644	−	12.4376i	−0.306893	−	0.422403i
$868$			0.846638i			0.0287368i
$869$	−2.57734	+	2.10820i	−0.0874304	+	0.0715159i
$870$	7.68522	−	57.7514i	0.260553	−	1.95795i
$871$	−35.1466	+	25.5355i	−1.19090	+	0.865237i
$872$	−1.80761	+	0.587328i	−0.0612133	+	0.0198894i
$873$	11.1055	+	3.60838i	0.375863	+	0.122125i
$874$	18.0644	+	13.1246i	0.611038	+	0.443945i
$875$	−5.60342	−	9.23057i	−0.189430	−	0.312050i
$876$	−2.43581	+	7.49665i	−0.0822984	+	0.253288i
$877$	−28.3445	+	9.20969i	−0.957126	+	0.310989i	−0.745608	−	0.666385i	$-0.767841\pi$
$877$	−28.3445	+	9.20969i	−0.957126	+	0.310989i	−0.211518	+	0.977374i	$0.567841\pi$
$878$	−31.5608	−	43.4398i	−1.06513	−	1.46602i
$879$	15.2269			0.513591
$880$	−27.3819	+	6.67613i	−0.923043	+	0.225052i
$881$	30.1175			1.01469			0.507343	−	0.861744i	$-0.330628\pi$
$881$	30.1175			1.01469			0.507343	+	0.861744i	$0.330628\pi$
$882$	−27.9113	−	38.4167i	−0.939824	−	1.29356i
$883$	47.8970	−	15.5627i	1.61186	−	0.523726i	0.641860	−	0.766822i	$-0.278163\pi$
$883$	47.8970	−	15.5627i	1.61186	−	0.523726i	0.970002	+	0.243096i	$0.0781631\pi$
$884$	−9.77622	+	30.0881i	−0.328810	+	1.01197i
$885$	42.9811	+	40.9019i	1.44480	+	1.37490i
$886$	−23.7410	−	17.2488i	−0.797593	−	0.579485i
$887$	39.3789	+	12.7950i	1.32221	+	0.429613i	0.883255	−	0.468893i	$-0.155347\pi$
$887$	39.3789	+	12.7950i	1.32221	+	0.429613i	0.438959	+	0.898507i	$0.355347\pi$
$888$	3.04604	−	0.989719i	0.102218	−	0.0332128i
$889$	5.54021	−	4.02520i	0.185813	−	0.135001i
$890$	54.7077	+	7.28019i	1.83381	+	0.244033i
$891$	4.75642	−	18.1076i	0.159346	−	0.606628i
$892$			39.8572i			1.33452i
$893$	8.33074	+	11.4663i	0.278777	+	0.383704i
$894$	27.6683	+	85.1542i	0.925366	+	2.84798i
$895$	32.8674	+	15.7334i	1.09864	+	0.525909i
$896$	−1.20409	−	0.874825i	−0.0402259	−	0.0292258i
$897$	−23.4647	+	32.2964i	−0.783464	+	1.07835i
$898$	19.4658	+	6.32481i	0.649581	+	0.211062i
$899$	0.635162	+	1.95483i	0.0211838	+	0.0651971i
$900$	37.8672	−	14.4146i	1.26224	−	0.480485i
$901$	8.87793			0.295767
$902$	20.9887	−	32.6711i	0.698848	−	1.08783i
$903$		−	5.72532i		−	0.190527i
$904$	−0.782977	+	0.568866i	−0.0260414	+	0.0189202i
$905$	12.1987	−	2.24327i	0.405498	−	0.0745687i
$906$	−20.1287	+	61.9499i	−0.668733	+	2.05815i
$907$	−2.72271	+	3.74749i	−0.0904062	+	0.124433i	−0.851824	−	0.523828i	$-0.824504\pi$
$907$	−2.72271	+	3.74749i	−0.0904062	+	0.124433i	0.761418	+	0.648261i	$0.224504\pi$
$908$	−35.0582	+	48.2534i	−1.16345	+	1.60135i
$909$	−18.1614	+	55.8951i	−0.602376	+	1.85392i
$910$	−3.57683	−	19.4505i	−0.118571	−	0.644778i
$911$	−5.64577	+	4.10189i	−0.187053	+	0.135902i	−0.677371	−	0.735642i	$-0.736881\pi$
$911$	−5.64577	+	4.10189i	−0.187053	+	0.135902i	0.490318	+	0.871544i	$0.336881\pi$
$912$			32.6419i			1.08088i
$913$	13.2573	−	20.6363i	0.438752	−	0.682963i
$914$	79.1032			2.61650
$915$	−12.7339	+	6.89090i	−0.420968	+	0.227806i
$916$	−16.4404	−	50.5984i	−0.543207	−	1.67182i
$917$	6.62923	+	2.15397i	0.218916	+	0.0711303i
$918$	9.02308	−	12.4192i	0.297806	−	0.409895i
$919$	−18.9477	−	13.7663i	−0.625027	−	0.454109i	0.229647	−	0.973274i	$-0.426243\pi$
$919$	−18.9477	−	13.7663i	−0.625027	−	0.454109i	−0.854674	+	0.519165i	$0.826243\pi$
$920$	−1.30936	−	0.626782i	−0.0431684	−	0.0206644i
$921$	−14.9589	−	46.0387i	−0.492912	−	1.51703i
$922$	46.5474	+	64.0671i	1.53296	+	2.10994i
$923$		−	24.6758i		−	0.812215i
$924$	−4.46857	+	17.0118i	−0.147005	+	0.559647i
$925$	8.28691	−	30.5850i	0.272472	−	1.00563i
$926$	−21.1507	+	15.3669i	−0.695057	+	0.504988i
$927$	35.8514	−	11.6488i	1.17751	−	0.382597i
$928$	−37.7371	−	12.2615i	−1.23878	−	0.402504i
$929$	−14.6355	−	10.6333i	−0.480175	−	0.348868i	0.321218	−	0.947005i	$-0.395908\pi$
$929$	−14.6355	−	10.6333i	−0.480175	−	0.348868i	−0.801394	+	0.598137i	$0.795908\pi$
$930$	−3.42006	+	3.59392i	−0.112148	+	0.117849i
$931$	−6.14504	+	18.9125i	−0.201395	+	0.619831i
$932$	−24.9440	+	8.10480i	−0.817068	+	0.265481i
$933$	17.4542	+	24.0237i	0.571426	+	0.786500i
$934$	−22.7646			−0.744881
$935$	−5.86164	−	24.0413i	−0.191696	−	0.786235i
$936$	3.37495			0.110314
$937$	−6.47128	−	8.90696i	−0.211408	−	0.290978i	0.690124	−	0.723691i	$-0.257556\pi$
$937$	−6.47128	−	8.90696i	−0.211408	−	0.290978i	−0.901531	+	0.432714i	$0.857556\pi$
$938$	17.8461	−	5.79856i	0.582697	−	0.189330i
$939$	−4.14216	+	12.7483i	−0.135174	+	0.416023i
$940$	−14.6766	−	13.9666i	−0.478698	−	0.455540i
$941$	−27.3293	−	19.8559i	−0.890908	−	0.647283i	0.0452063	−	0.998978i	$-0.485605\pi$
$941$	−27.3293	−	19.8559i	−0.890908	−	0.647283i	−0.936115	+	0.351695i	$0.885605\pi$
$942$	21.2325	+	6.89886i	0.691793	+	0.224777i
$943$	−18.5237	+	6.01870i	−0.603213	+	0.195996i
$944$	31.1305	−	22.6177i	1.01321	−	0.736142i
$945$	−0.647654	+	4.86686i	−0.0210682	+	0.158319i
$946$	11.7517	−	9.61264i	0.382082	−	0.312534i
$947$		−	46.9853i		−	1.52682i	−0.645915	−	0.763409i	$-0.723524\pi$
$947$		−	46.9853i		−	1.52682i	0.645915	−	0.763409i	$-0.276476\pi$
$948$	−3.24025	−	4.45982i	−0.105238	−	0.144848i
$949$	2.00736	+	6.17803i	0.0651618	+	0.200547i
$950$	−27.7631	−	18.1401i	−0.900754	−	0.588542i
$951$	25.0454	+	18.1966i	0.812154	+	0.590064i
$952$	0.365292	−	0.502781i	0.0118392	−	0.0162952i
$953$	−40.4110	−	13.1303i	−1.30904	−	0.425333i	−0.430323	−	0.902675i	$-0.641600\pi$
$953$	−40.4110	−	13.1303i	−1.30904	−	0.425333i	−0.878718	+	0.477341i	$0.841600\pi$
$954$	−6.43506	−	19.8051i	−0.208343	−	0.641213i
$955$	−23.2170	−	42.9032i	−0.751284	−	1.38832i
$956$	42.7180			1.38160
$957$	2.44491	+	42.6314i	0.0790328	+	1.37808i
$958$			42.4291i			1.37082i
$959$	6.63443	−	4.82019i	0.214237	−	0.155652i
$960$	−9.26632	−	50.3895i	−0.299069	−	1.62631i
$961$	−9.52544	+	29.3163i	−0.307272	+	0.945687i
$962$	34.1123	−	46.9515i	1.09982	−	1.51378i
$963$	−17.3719	+	23.9103i	−0.559800	+	0.770499i
$964$	14.7584	−	45.4216i	0.475335	−	1.46293i
$965$	9.09089	+	49.4354i	0.292646	+	1.59138i
$966$	13.9498	−	10.1351i	0.448826	−	0.326091i
$967$			54.1642i			1.74180i	0.491458	+	0.870901i	$0.336464\pi$
$967$			54.1642i			1.74180i	−0.491458	+	0.870901i	$0.663536\pi$
$968$	−1.92930	+	0.881863i	−0.0620101	+	0.0283442i
$969$	−28.6596			−0.920680
$970$	6.50233	+	12.0158i	0.208777	+	0.385804i
$971$	1.61878	+	4.98209i	0.0519491	+	0.159883i	0.973665	−	0.227982i	$-0.0732127\pi$
$971$	1.61878	+	4.98209i	0.0519491	+	0.159883i	−0.921716	+	0.387865i	$0.873213\pi$
$972$	43.0694	+	13.9941i	1.38145	+	0.448861i
$973$	−4.39406	+	6.04791i	−0.140867	+	0.193887i
$974$	−36.9500	−	26.8457i	−1.18395	−	0.860193i
$975$	32.4317	−	49.6362i	1.03864	−	1.58963i
$976$	2.90169	+	8.93049i	0.0928809	+	0.285858i
$977$	4.57381	+	6.29530i	0.146329	+	0.201405i	0.875890	−	0.482512i	$-0.160275\pi$
$977$	4.57381	+	6.29530i	0.146329	+	0.201405i	−0.729561	+	0.683916i	$0.760275\pi$
$978$			87.8938i			2.81053i
$979$	−40.3846	+	2.31606i	−1.29070	+	0.0740216i
$980$	3.74973	−	28.1777i	0.119781	−	0.900104i
$981$	30.8376	−	22.4048i	0.984567	−	0.715330i
$982$	−38.6394	+	12.5547i	−1.23303	+	0.400637i
$983$	−48.9924	−	15.9186i	−1.56261	−	0.507724i	−0.605109	−	0.796143i	$-0.706871\pi$
$983$	−48.9924	−	15.9186i	−1.56261	−	0.507724i	−0.957504	+	0.288419i	$0.906871\pi$
$984$	2.36547	+	1.71861i	0.0754083	+	0.0547873i
$985$	−41.7073	−	39.6896i	−1.32890	−	1.26462i
$986$	10.2515	−	31.5509i	0.326474	−	1.00478i
$987$	10.4091	−	3.38213i	0.331326	−	0.107654i
$988$	−18.2661	−	25.1411i	−0.581122	−	0.799846i
$989$	−7.61503			−0.242144
$990$	−49.3831	+	30.5023i	−1.56950	+	0.969428i
$991$	−22.3382			−0.709596			−0.354798	−	0.934943i	$-0.615450\pi$
$991$	−22.3382			−0.709596			−0.354798	+	0.934943i	$0.615450\pi$
$992$	1.98605	+	2.73356i	0.0630571	+	0.0867906i
$993$	−72.9487	+	23.7025i	−2.31496	+	0.752175i
$994$	−3.29357	+	10.1366i	−0.104466	+	0.321512i
$995$	−26.1544	+	27.4840i	−0.829150	+	0.871300i
$996$	32.8522	+	23.8686i	1.04096	+	0.756304i
$997$	0.175514	+	0.0570278i	0.00555857	+	0.00180609i	0.311795	−	0.950149i	$-0.399070\pi$
$997$	0.175514	+	0.0570278i	0.00555857	+	0.00180609i	−0.306236	+	0.951955i	$0.599070\pi$
$998$	−8.95311	+	2.90904i	−0.283406	+	0.0920841i
$999$	−11.6562	+	8.46873i	−0.368786	+	0.267939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.j.a.14.4	yes	16
3.2	odd	2		495.2.ba.a.289.1		16
4.3	odd	2		880.2.cd.c.289.4		16
5.2	odd	4		275.2.h.d.201.1		16
5.3	odd	4		275.2.h.d.201.4		16
5.4	even	2	inner	55.2.j.a.14.1	yes	16
11.2	odd	10		605.2.b.f.364.8		8
11.3	even	5		605.2.j.h.269.4		16
11.4	even	5	inner	55.2.j.a.4.1	✓	16
11.5	even	5		605.2.j.h.9.1		16
11.6	odd	10		605.2.j.g.9.4		16
11.7	odd	10		605.2.j.d.444.4		16
11.8	odd	10		605.2.j.g.269.1		16
11.9	even	5		605.2.b.g.364.1		8
11.10	odd	2		605.2.j.d.124.1		16
15.14	odd	2		495.2.ba.a.289.4		16
20.19	odd	2		880.2.cd.c.289.1		16
33.26	odd	10		495.2.ba.a.334.4		16
44.15	odd	10		880.2.cd.c.609.1		16
55.2	even	20		3025.2.a.bk.1.1		8
55.4	even	10	inner	55.2.j.a.4.4	yes	16
55.9	even	10		605.2.b.g.364.8		8
55.13	even	20		3025.2.a.bk.1.8		8
55.14	even	10		605.2.j.h.269.1		16
55.19	odd	10		605.2.j.g.269.4		16
55.24	odd	10		605.2.b.f.364.1		8
55.29	odd	10		605.2.j.d.444.1		16
55.37	odd	20		275.2.h.d.26.1		16
55.39	odd	10		605.2.j.g.9.1		16
55.42	odd	20		3025.2.a.bl.1.8		8
55.48	odd	20		275.2.h.d.26.4		16
55.49	even	10		605.2.j.h.9.4		16
55.53	odd	20		3025.2.a.bl.1.1		8
55.54	odd	2		605.2.j.d.124.4		16
165.59	odd	10		495.2.ba.a.334.1		16
220.59	odd	10		880.2.cd.c.609.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	11.4	even	5	inner
55.2.j.a.4.4	yes	16	55.4	even	10	inner
55.2.j.a.14.1	yes	16	5.4	even	2	inner
55.2.j.a.14.4	yes	16	1.1	even	1	trivial
275.2.h.d.26.1		16	55.37	odd	20
275.2.h.d.26.4		16	55.48	odd	20
275.2.h.d.201.1		16	5.2	odd	4
275.2.h.d.201.4		16	5.3	odd	4
495.2.ba.a.289.1		16	3.2	odd	2
495.2.ba.a.289.4		16	15.14	odd	2
495.2.ba.a.334.1		16	165.59	odd	10
495.2.ba.a.334.4		16	33.26	odd	10
605.2.b.f.364.1		8	55.24	odd	10
605.2.b.f.364.8		8	11.2	odd	10
605.2.b.g.364.1		8	11.9	even	5
605.2.b.g.364.8		8	55.9	even	10
605.2.j.d.124.1		16	11.10	odd	2
605.2.j.d.124.4		16	55.54	odd	2
605.2.j.d.444.1		16	55.29	odd	10
605.2.j.d.444.4		16	11.7	odd	10
605.2.j.g.9.1		16	55.39	odd	10
605.2.j.g.9.4		16	11.6	odd	10
605.2.j.g.269.1		16	11.8	odd	10
605.2.j.g.269.4		16	55.19	odd	10
605.2.j.h.9.1		16	11.5	even	5
605.2.j.h.9.4		16	55.49	even	10
605.2.j.h.269.1		16	55.14	even	10
605.2.j.h.269.4		16	11.3	even	5
880.2.cd.c.289.1		16	20.19	odd	2
880.2.cd.c.289.4		16	4.3	odd	2
880.2.cd.c.609.1		16	44.15	odd	10
880.2.cd.c.609.4		16	220.59	odd	10
3025.2.a.bk.1.1		8	55.2	even	20
3025.2.a.bk.1.8		8	55.13	even	20
3025.2.a.bl.1.1		8	55.53	odd	20
3025.2.a.bl.1.8		8	55.42	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18949 + 1.63719i) q^{2} +(-2.49233 + 0.809808i) q^{3} +(-0.647481 + 1.99274i) q^{4} +(1.54147 - 1.61983i) q^{5} +(-4.29042 - 3.11717i) q^{6} +(0.918552 + 0.298456i) q^{7} +(-0.183406 + 0.0595923i) q^{8} +(3.12889 - 2.27327i) q^{9} +(4.48555 + 0.596911i) q^{10} +(-3.31118 + 0.189896i) q^{11} -5.49092i q^{12} +(-2.65978 - 3.66088i) q^{13} +(0.603980 + 1.85886i) q^{14} +(-2.53011 + 5.28546i) q^{15} +(3.07453 + 2.23378i) q^{16} +(-1.96126 + 2.69944i) q^{17} +(7.44357 + 2.41856i) q^{18} +(-1.01283 - 3.11717i) q^{19} +(2.22984 + 4.12057i) q^{20} -2.53103 q^{21} +(-4.24952 - 5.19517i) q^{22} +3.36643i q^{23} +(0.408851 - 0.297048i) q^{24} +(-0.247725 - 4.99386i) q^{25} +(2.82978 - 8.70916i) q^{26} +(-1.33628 + 1.83923i) q^{27} +(-1.18949 + 1.63719i) q^{28} +(-1.51820 + 4.67254i) q^{29} +(-11.6629 + 2.14473i) q^{30} +(0.338464 - 0.245909i) q^{31} +8.07636i q^{32} +(8.09880 - 3.15471i) q^{33} -6.75241 q^{34} +(1.89937 - 1.02784i) q^{35} +(2.50415 + 7.70697i) q^{36} +(6.02737 + 1.95841i) q^{37} +(3.89867 - 5.36605i) q^{38} +(9.59368 + 6.97021i) q^{39} +(-0.186186 + 0.388948i) q^{40} +(1.78786 + 5.50247i) q^{41} +(-3.01064 - 4.14379i) q^{42} +2.26205i q^{43} +(1.76552 - 6.72129i) q^{44} +(1.14077 - 8.57246i) q^{45} +(-5.51149 + 4.00433i) q^{46} +(-4.11260 + 1.33626i) q^{47} +(-9.47169 - 3.07754i) q^{48} +(-4.90846 - 3.56620i) q^{49} +(7.88125 - 6.34573i) q^{50} +(2.70208 - 8.31615i) q^{51} +(9.01735 - 2.92991i) q^{52} +(-1.56392 - 2.15255i) q^{53} -4.60066 q^{54} +(-4.79650 + 5.65629i) q^{55} -0.186254 q^{56} +(5.04863 + 6.94884i) q^{57} +(-9.45574 + 3.07235i) q^{58} +(3.12889 - 9.62972i) q^{59} +(-8.89437 - 8.46410i) q^{60} +(1.99897 + 1.45233i) q^{61} +(0.805201 + 0.261626i) q^{62} +(3.55252 - 1.15428i) q^{63} +(-7.07350 + 5.13920i) q^{64} +(-10.0300 - 1.33473i) q^{65} +(14.7983 + 9.50680i) q^{66} -9.60059i q^{67} +(-4.10941 - 5.65612i) q^{68} +(-2.72616 - 8.39026i) q^{69} +(3.94206 + 1.88703i) q^{70} +(4.41166 + 3.20526i) q^{71} +(-0.438388 + 0.603390i) q^{72} +(-1.36528 - 0.443607i) q^{73} +(3.96321 + 12.1975i) q^{74} +(4.66148 + 12.2458i) q^{75} +6.86752 q^{76} +(-3.09817 - 0.813812i) q^{77} +23.9977i q^{78} +(0.812218 - 0.590111i) q^{79} +(8.35766 - 1.53692i) q^{80} +(-1.74436 + 5.36858i) q^{81} +(-6.88197 + 9.47221i) q^{82} +(-4.34692 + 5.98302i) q^{83} +(1.63880 - 5.04369i) q^{84} +(1.34942 + 7.33802i) q^{85} +(-3.70342 + 2.69069i) q^{86} -12.8750i q^{87} +(0.595976 - 0.232149i) q^{88} +12.1964 q^{89} +(15.3917 - 8.32920i) q^{90} +(-1.35054 - 4.15654i) q^{91} +(-6.70842 - 2.17970i) q^{92} +(-0.644427 + 0.886978i) q^{93} +(-7.07962 - 5.14365i) q^{94} +(-6.61056 - 3.16442i) q^{95} +(-6.54030 - 20.1290i) q^{96} +(1.77467 + 2.44262i) q^{97} -12.2781i q^{98} +(-9.92863 + 8.12138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

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