LMFDB - Embedded newform 605.2.j.d.444.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not 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:	$4.83094932229$
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:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			444.4
Root			$-1.92464 - 0.625353i$ of defining polynomial
Character	$\chi$	$=$	605.444
Dual form			605.2.j.d.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18949 - 1.63719i) q^{2} +(2.49233 + 0.809808i) q^{3} +(-0.647481 - 1.99274i) q^{4} +(-1.06421 - 1.96658i) q^{5} +(4.29042 - 3.11717i) q^{6} +(0.918552 - 0.298456i) q^{7} +(-0.183406 - 0.0595923i) q^{8} +(3.12889 + 2.27327i) q^{9} +O(q^{10})$	\(q+(1.18949 - 1.63719i) q^{2} +(2.49233 + 0.809808i) q^{3} +(-0.647481 - 1.99274i) q^{4} +(-1.06421 - 1.96658i) 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} -5.49092i q^{12} +(-2.65978 + 3.66088i) q^{13} +(0.603980 - 1.85886i) q^{14} +(-1.05982 - 5.76319i) 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} +(-3.22984 + 3.39403i) q^{20} +2.53103 q^{21} +3.36643i q^{23} +(-0.408851 - 0.297048i) q^{24} +(-2.73490 + 4.18573i) 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} +(-10.6961 - 5.12014i) q^{30} +(0.338464 + 0.245909i) q^{31} -8.07636i q^{32} -6.75241 q^{34} +(-1.56447 - 1.48879i) 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} +(0.0779900 + 0.424103i) q^{40} +(-1.78786 + 5.50247i) q^{41} +(3.01064 - 4.14379i) q^{42} -2.26205i q^{43} +(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} +(3.59970 + 9.45645i) q^{50} +(-2.70208 - 8.31615i) q^{51} +(9.01735 + 2.92991i) q^{52} +(1.56392 - 2.15255i) q^{53} +4.60066 q^{54} -0.186254 q^{56} +(5.04863 - 6.94884i) q^{57} +(9.45574 + 3.07235i) q^{58} +(3.12889 + 9.62972i) q^{59} +(-10.7983 + 5.84350i) 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} -9.60059i q^{67} +(-4.10941 + 5.65612i) q^{68} +(-2.72616 + 8.39026i) q^{69} +(-4.29836 + 0.790444i) 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} +(-10.2059 + 8.21748i) q^{75} -6.86752 q^{76} +23.9977i q^{78} +(-0.812218 - 0.590111i) q^{79} +(-7.66487 - 3.66911i) 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} +(-3.22148 + 6.72976i) q^{85} +(-3.70342 - 2.69069i) q^{86} +12.8750i q^{87} +12.1964 q^{89} +(-12.6778 - 12.0645i) 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} +(-7.20805 + 1.32552i) q^{95} +(6.54030 - 20.1290i) q^{96} +(-1.77467 + 2.44262i) q^{97} +12.2781i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^9	$ 16 q - 4 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{9} - 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} + 12 q^{45} + 62 q^{46} - 10 q^{49} - 28 q^{50} + 42 q^{51} + 40 q^{54} - 20 q^{56} + 2 q^{59} - 32 q^{60} + 40 q^{61} - 8 q^{64} + 40 q^{65} + 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}+O(q^{100}) $ 16 * q - 4 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^9 - 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 + 12 * q^45 + 62 * q^46 - 10 * q^49 - 28 * q^50 + 42 * q^51 + 40 * q^54 - 20 * q^56 + 2 * q^59 - 32 * q^60 + 40 * q^61 - 8 * q^64 + 40 * q^65 + 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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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	−0.144657	−	0.989482i	$-0.546208\pi$
$2$	1.18949	−	1.63719i	0.841097	−	1.15767i	0.985755	−	0.168189i	$-0.0537920\pi$
$3$	2.49233	+	0.809808i	1.43895	+	0.467543i	0.921570	−	0.388213i	$-0.126907\pi$
$3$	2.49233	+	0.809808i	1.43895	+	0.467543i	0.517380	+	0.855756i	$0.326907\pi$
$4$	−0.647481	−	1.99274i	−0.323741	−	0.996371i
$5$	−1.06421	−	1.96658i	−0.475930	−	0.879483i
$5$	−1.06421	−	1.96658i	−0.475930	−	0.879483i
$6$	4.29042	−	3.11717i	1.75156	−	1.27258i
$7$	0.918552	−	0.298456i	0.347180	−	0.112806i	−0.130236	−	0.991483i	$-0.541573\pi$
$7$	0.918552	−	0.298456i	0.347180	−	0.112806i	0.477416	+	0.878677i	$0.341573\pi$
$8$	−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
$11$		0			0
$11$		0			0
$12$		−	5.49092i		−	1.58509i
$13$	−2.65978	+	3.66088i	−0.737691	+	1.01534i	0.261057	+	0.965323i	$0.415929\pi$
$13$	−2.65978	+	3.66088i	−0.737691	+	1.01534i	−0.998748	+	0.0500213i	$0.984071\pi$
$14$	0.603980	−	1.85886i	0.161420	−	0.496801i
$15$	−1.05982	−	5.76319i	−0.273644	−	1.48805i
$16$	3.07453	−	2.23378i	0.768633	−	0.558445i
$17$	−1.96126	−	2.69944i	−0.475675	−	0.654710i	0.501992	−	0.864872i	$-0.332601\pi$
$17$	−1.96126	−	2.69944i	−0.475675	−	0.654710i	−0.977667	+	0.210162i	$0.932601\pi$
$18$	7.44357	−	2.41856i	1.75447	−	0.570060i
$19$	1.01283	−	3.11717i	0.232359	−	0.715129i	−0.765101	−	0.643910i	$-0.777311\pi$
$19$	1.01283	−	3.11717i	0.232359	−	0.715129i	0.997461	−	0.0712189i	$-0.0226889\pi$
$20$	−3.22984	+	3.39403i	−0.722214	+	0.758928i
$21$	2.53103			0.552316
$22$		0			0
$23$			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
$25$	−2.73490	+	4.18573i	−0.546981	+	0.837145i
$26$	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	0.987304	+	0.158841i	$0.0507756\pi$
$29$	1.51820	+	4.67254i	0.281923	+	0.867668i	−0.705382	+	0.708828i	$0.749224\pi$
$30$	−10.6961	−	5.12014i	−1.95283	−	0.934805i
$31$	0.338464	+	0.245909i	0.0607900	+	0.0441665i	0.617765	−	0.786363i	$-0.288038\pi$
$31$	0.338464	+	0.245909i	0.0607900	+	0.0441665i	−0.556975	+	0.830529i	$0.688038\pi$
$32$		−	8.07636i		−	1.42771i
$33$		0			0
$34$	−6.75241			−1.15803
$35$	−1.56447	−	1.48879i	−0.264444	−	0.251651i
$36$	2.50415	−	7.70697i	0.417358	−	1.28449i
$37$	−6.02737	+	1.95841i	−0.990894	+	0.321961i	−0.759221	−	0.650833i	$-0.774420\pi$
$37$	−6.02737	+	1.95841i	−0.990894	+	0.321961i	−0.231673	+	0.972794i	$0.574420\pi$
$38$	−3.89867	−	5.36605i	−0.632447	−	0.870489i
$39$	−9.59368	+	6.97021i	−1.53622	+	1.11613i
$40$	0.0779900	+	0.424103i	0.0123313	+	0.0670565i
$41$	−1.78786	+	5.50247i	−0.279217	+	0.859341i	0.708856	+	0.705353i	$0.249212\pi$
$41$	−1.78786	+	5.50247i	−0.279217	+	0.859341i	−0.988073	+	0.153988i	$0.950788\pi$
$42$	3.01064	−	4.14379i	0.464552	−	0.639401i
$43$		−	2.26205i		−	0.344960i	−0.985013	−	0.172480i	$-0.944822\pi$
$43$		−	2.26205i		−	0.344960i	0.985013	−	0.172480i	$-0.0551780\pi$
$44$		0			0
$45$	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	$-0.297869\pi$
$47$	4.11260	+	1.33626i	0.599884	+	0.194914i	0.00669531	+	0.999978i	$0.497869\pi$
$48$	9.47169	−	3.07754i	1.36712	−	0.444205i
$49$	−4.90846	+	3.56620i	−0.701208	+	0.509457i
$50$	3.59970	+	9.45645i	0.509075	+	1.33734i
$51$	−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	$-0.741504\pi$
$53$	1.56392	−	2.15255i	0.214821	−	0.295676i	0.902805	+	0.430050i	$0.141504\pi$
$54$	4.60066			0.626071
$55$		0			0
$56$	−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	0.918920	+	0.394444i	$0.129063\pi$
$59$	3.12889	+	9.62972i	0.407346	+	1.25368i	−0.511574	+	0.859239i	$0.670937\pi$
$60$	−10.7983	+	5.84350i	−1.39406	+	0.754393i
$61$	−1.99897	+	1.45233i	−0.255941	+	0.185952i	−0.708356	−	0.705856i	$-0.750563\pi$
$61$	−1.99897	+	1.45233i	−0.255941	+	0.185952i	0.452414	+	0.891808i	$0.350563\pi$
$62$	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
$66$		0			0
$67$		−	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
$70$	−4.29836	+	0.790444i	−0.513753	+	0.0944761i
$71$	4.41166	−	3.20526i	0.523567	−	0.380394i	−0.294379	−	0.955689i	$-0.595113\pi$
$71$	4.41166	−	3.20526i	0.523567	−	0.380394i	0.817946	+	0.575295i	$0.195113\pi$
$72$	−0.438388	−	0.603390i	−0.0516646	−	0.0711102i
$73$	−1.36528	+	0.443607i	−0.159794	+	0.0519203i	−0.387822	−	0.921734i	$-0.626772\pi$
$73$	−1.36528	+	0.443607i	−0.159794	+	0.0519203i	0.228028	+	0.973655i	$0.426772\pi$
$74$	−3.96321	+	12.1975i	−0.460713	+	1.41793i
$75$	−10.2059	+	8.21748i	−1.17848	+	0.948873i
$76$	−6.86752			−0.787758
$77$		0			0
$78$			23.9977i			2.71721i
$79$	−0.812218	−	0.590111i	−0.0913817	−	0.0663927i	0.541156	−	0.840922i	$-0.317987\pi$
$79$	−0.812218	−	0.590111i	−0.0913817	−	0.0663927i	−0.632538	+	0.774529i	$0.717987\pi$
$80$	−7.66487	−	3.66911i	−0.856958	−	0.410219i
$81$	−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	0.500815	−	0.865554i	$-0.333034\pi$
$83$	−4.34692	−	5.98302i	−0.477136	−	0.656721i	−0.977951	+	0.208833i	$0.933034\pi$
$84$	−1.63880	−	5.04369i	−0.178807	−	0.550312i
$85$	−3.22148	+	6.72976i	−0.349418	+	0.729944i
$86$	−3.70342	−	2.69069i	−0.399350	−	0.290145i
$87$			12.8750i			1.38034i
$88$		0			0
$89$	12.1964			1.29282			0.646410	−	0.762991i	$-0.276270\pi$
$89$	12.1964			1.29282			0.646410	+	0.762991i	$0.276270\pi$
$90$	−12.6778	−	12.0645i	−1.33636	−	1.27171i
$91$	−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
$95$	−7.20805	+	1.32552i	−0.739531	+	0.135995i
$96$	6.54030	−	20.1290i	0.667517	−	2.05440i
$97$	−1.77467	+	2.44262i	−0.180190	+	0.248010i	−0.889552	−	0.456834i	$-0.848983\pi$
$97$	−1.77467	+	2.44262i	−0.180190	+	0.248010i	0.709362	+	0.704844i	$0.248983\pi$
$98$			12.2781i			1.24027i
$99$		0			0
$100$	10.1119	+	2.73978i	1.01119	+	0.273978i
$101$	12.2940	+	8.93210i	1.22330	+	0.888777i	0.996369	−	0.0851342i	$-0.0271319\pi$
$101$	12.2940	+	8.93210i	1.22330	+	0.888777i	0.226928	+	0.973912i	$0.427132\pi$
$102$	−16.8292	−	5.46815i	−1.66634	−	0.541428i
$103$	−9.26987	+	3.01196i	−0.913387	+	0.296778i	−0.727751	−	0.685841i	$-0.759435\pi$
$103$	−9.26987	+	3.01196i	−0.913387	+	0.296778i	−0.185636	+	0.982619i	$0.559435\pi$
$104$	0.705981	−	0.512925i	0.0692272	−	0.0502965i
$105$	−2.69355	−	4.97748i	−0.262864	−	0.485753i
$106$	−1.66387	−	5.12088i	−0.161610	−	0.497384i
$107$	−7.26778	−	2.36144i	−0.702602	−	0.228289i	−0.0641384	−	0.997941i	$-0.520430\pi$
$107$	−7.26778	−	2.36144i	−0.702602	−	0.228289i	−0.638464	+	0.769652i	$0.720430\pi$
$108$	2.79989	−	3.85372i	0.269420	−	0.370825i
$109$	−9.85576			−0.944010			−0.472005	−	0.881596i	$-0.656470\pi$
$109$	−9.85576			−0.944010			−0.472005	+	0.881596i	$0.656470\pi$
$110$		0			0
$111$	−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	$-0.475855\pi$
$113$	−4.77298	−	1.55084i	−0.449004	−	0.145890i	−0.524786	+	0.851234i	$0.675855\pi$
$114$	−5.37130	−	16.5312i	−0.503068	−	1.54829i
$115$	6.62036	−	3.58259i	0.617352	−	0.334078i
$116$	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
$121$		0			0
$122$			5.00023i			0.452700i
$123$	−8.91189	+	12.2662i	−0.803558	+	1.10600i
$124$	0.270884	−	0.833694i	0.0243261	−	0.0748679i
$125$	11.1421	+	0.923914i	0.996580	+	0.0826374i
$126$	6.11547	−	4.44315i	0.544810	−	0.395827i
$127$	4.16764	+	5.73626i	0.369818	+	0.509011i	0.952851	−	0.303438i	$-0.0981344\pi$
$127$	4.16764	+	5.73626i	0.369818	+	0.509011i	−0.583033	+	0.812448i	$0.698134\pi$
$128$	−1.46559	+	0.476198i	−0.129541	+	0.0420903i
$129$	1.83183	−	5.63779i	0.161284	−	0.496380i
$130$	14.1158	−	14.8334i	1.23804	−	1.30097i
$131$	−7.21704			−0.630556			−0.315278	−	0.948999i	$-0.602098\pi$
$131$	−7.21704			−0.630556			−0.315278	+	0.948999i	$0.602098\pi$
$132$		0			0
$133$		−	3.16557i		−	0.274490i
$134$	−15.7180	−	11.4198i	−1.35783	−	0.986521i
$135$	2.19491	−	4.58523i	0.188908	−	0.394634i
$136$	0.198841	+	0.611970i	0.0170505	+	0.0524760i
$137$	−4.99076	−	6.86920i	−0.426390	−	0.586875i	0.540730	−	0.841196i	$-0.318148\pi$
$137$	−4.99076	−	6.86920i	−0.426390	−	0.586875i	−0.967120	+	0.254321i	$0.918148\pi$
$138$	10.4937	+	14.4434i	0.893286	+	1.22950i
$139$	2.39184	+	7.36133i	0.202873	+	0.624380i	0.999794	+	0.0202958i	$0.00646080\pi$
$139$	2.39184	+	7.36133i	0.202873	+	0.624380i	−0.796921	+	0.604084i	$0.793539\pi$
$140$	−1.95381	+	4.08156i	−0.165127	+	0.344954i
$141$	9.16785	+	6.66083i	0.772072	+	0.560943i
$142$		−	11.0354i		−	0.926067i
$143$		0			0
$144$	14.6978			1.22482
$145$	7.57325	−	7.95824i	0.628924	−	0.660896i
$146$	−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	$-0.456921\pi$
$149$	13.6589	−	9.92376i	1.11898	−	0.812986i	0.984054	+	0.177870i	$0.0569206\pi$
$150$	1.31375	+	26.4837i	0.107267	+	2.16239i
$151$	3.79555	−	11.6815i	0.308877	−	0.950626i	−0.669325	−	0.742970i	$-0.733416\pi$
$151$	3.79555	−	11.6815i	0.308877	−	0.950626i	0.978202	−	0.207656i	$-0.0665835\pi$
$152$	−0.371519	+	0.511353i	−0.0301342	+	0.0414762i
$153$		−	12.9047i		−	1.04328i
$154$		0			0
$155$	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	$-0.346274\pi$
$157$	4.00368	+	1.30087i	0.319528	+	0.103821i	−0.144862	+	0.989452i	$0.546274\pi$
$158$	−1.93225	+	0.627827i	−0.153722	+	0.0499472i
$159$	5.64096	−	4.09840i	0.447357	−	0.325024i
$160$	−15.8828	+	8.59496i	−1.25565	+	0.679491i
$161$	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	−0.233928	−	0.972254i	$-0.575158\pi$
$163$	9.74169	−	13.4083i	0.763028	−	1.05022i	0.996956	−	0.0779643i	$-0.0248420\pi$
$164$	12.1226			0.946617
$165$		0			0
$166$	−14.9660			−1.16159
$167$	−5.38810	+	7.41608i	−0.416944	+	0.573874i	−0.964895	−	0.262637i	$-0.915408\pi$
$167$	−5.38810	+	7.41608i	−0.416944	+	0.573874i	0.547951	+	0.836510i	$0.315408\pi$
$168$	−0.464207	−	0.150830i	−0.0358144	−	0.0116368i
$169$	−2.31036	−	7.11055i	−0.177720	−	0.546965i
$170$	7.18599	+	13.2792i	0.551141	+	1.01847i
$171$	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	0.156643	−	0.987655i	$-0.449933\pi$
$173$	−3.90853	−	1.26996i	−0.297160	−	0.0965531i	−0.453803	+	0.891102i	$0.649933\pi$
$174$	21.0788	+	15.3147i	1.59798	+	1.16100i
$175$	−1.26290	+	4.66106i	−0.0954661	+	0.352343i
$176$		0			0
$177$			26.5343i			1.99444i
$178$	14.5075	−	19.9679i	1.08739	−	1.49666i
$179$	5.03576	−	15.4985i	0.376390	−	1.15841i	−0.566145	−	0.824305i	$-0.691566\pi$
$179$	5.03576	−	15.4985i	0.376390	−	1.15841i	0.942536	−	0.334105i	$-0.108434\pi$
$180$	−17.8213	+	3.27724i	−1.32832	+	0.244271i
$181$	4.48753	−	3.26038i	0.333555	−	0.242342i	−0.408382	−	0.912811i	$-0.633907\pi$
$181$	4.48753	−	3.26038i	0.333555	−	0.242342i	0.741938	+	0.670469i	$0.233907\pi$
$182$	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
$185$	10.2658	+	9.76917i	0.754756	+	0.718243i
$186$	2.21870			0.162683
$187$		0			0
$188$		−	9.06056i		−	0.660809i
$189$	1.77637	+	1.29061i	0.129212	+	0.0938779i
$190$	−6.40378	+	13.3777i	−0.464579	+	0.970518i
$191$	6.74155	+	20.7484i	0.487802	+	1.50130i	0.827882	+	0.560903i	$0.189546\pi$
$191$	6.74155	+	20.7484i	0.487802	+	1.50130i	−0.340080	+	0.940396i	$0.610454\pi$
$192$	−13.4678	−	18.5368i	−0.971951	−	1.33778i
$193$	−13.2128	−	18.1858i	−0.951076	−	1.30904i	−0.951048	−	0.309044i	$-0.899991\pi$
$193$	−13.2128	−	18.1858i	−0.951076	−	1.30904i	−2.83481e−5	−	1.00000i	$-0.500009\pi$
$194$	1.88809	+	5.81094i	0.135557	+	0.417201i
$195$	23.9172	+	11.4490i	1.71275	+	0.819878i
$196$	10.2847	+	7.47224i	0.734619	+	0.533732i
$197$			25.7479i			1.83446i	0.398358	+	0.917230i	$0.369580\pi$
$197$			25.7479i			1.83446i	−0.398358	+	0.917230i	$0.630420\pi$
$198$		0			0
$199$	−16.9671			−1.20277			−0.601385	−	0.798960i	$-0.705384\pi$
$199$	−16.9671			−1.20277			−0.601385	+	0.798960i	$0.705384\pi$
$200$	0.751036	−	0.604709i	0.0531063	−	0.0427594i
$201$	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
$205$	12.7237	−	2.33982i	0.888664	−	0.163420i
$206$	−6.09526	+	18.7593i	−0.424677	+	1.30702i
$207$	−7.65279	+	10.5332i	−0.531906	+	0.732106i
$208$			17.1969i			1.19239i
$209$		0			0
$210$	−11.3531	−	1.51080i	−0.783436	−	0.104255i
$211$	−4.71363	−	3.42465i	−0.324500	−	0.235763i	0.413593	−	0.910462i	$-0.364274\pi$
$211$	−4.71363	−	3.42465i	−0.324500	−	0.235763i	−0.738093	+	0.674699i	$0.764274\pi$
$212$	−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
$215$	−4.44852	+	2.40730i	−0.303386	+	0.164177i
$216$	−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
$220$		0			0
$221$	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	$-0.619789\pi$
$223$	−18.0913	−	5.87820i	−1.21148	−	0.393634i	−0.843972	+	0.536387i	$0.819789\pi$
$224$	−2.41043	−	7.41856i	−0.161054	−	0.495673i
$225$	−18.0725	+	6.87949i	−1.20483	+	0.458633i
$226$	−8.21644	+	5.96959i	−0.546549	+	0.397091i
$227$	27.0727	−	8.79646i	1.79688	−	0.583841i	0.797079	−	0.603874i	$-0.206377\pi$
$227$	27.0727	−	8.79646i	1.79688	−	0.583841i	0.999799	+	0.0200332i	$0.00637719\pi$
$228$	−17.1161	−	5.56137i	−1.13354	−	0.368311i
$229$	−20.5420	−	14.9247i	−1.35746	−	0.986250i	−0.998602	−	0.0528558i	$-0.983168\pi$
$229$	−20.5420	−	14.9247i	−1.35746	−	0.986250i	−0.358854	−	0.933394i	$-0.616832\pi$
$230$	2.00946	−	15.1003i	0.132500	−	0.995682i
$231$		0			0
$232$		−	0.947446i		−	0.0622029i
$233$	7.35755	−	10.1268i	0.482009	−	0.663429i	−0.496880	−	0.867819i	$-0.665521\pi$
$233$	7.35755	−	10.1268i	0.482009	−	0.663429i	0.978890	+	0.204390i	$0.0655211\pi$
$234$	−10.9442	+	33.6828i	−0.715446	+	2.20192i
$235$	−1.74880	−	9.50984i	−0.114079	−	0.620353i
$236$	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	−0.511252	−	0.859431i	$-0.670818\pi$
$239$	6.30011	−	19.3897i	0.407520	−	1.25422i	0.918773	−	0.394787i	$-0.129182\pi$
$240$	−16.1321	−	15.3517i	−1.04132	−	0.990949i
$241$	22.7935			1.46826			0.734129	−	0.679010i	$-0.237591\pi$
$241$	22.7935			1.46826			0.734129	+	0.679010i	$0.237591\pi$
$242$		0			0
$243$		−	21.6131i		−	1.38648i
$244$	4.18842	+	3.04307i	0.268136	+	0.194812i
$245$	12.2369	+	5.85769i	0.781785	+	0.374234i
$246$	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
$250$	14.7661	−	17.1428i	0.933887	−	1.08421i
$251$	−13.7151	−	9.96460i	−0.865689	−	0.628960i	0.0637374	−	0.997967i	$-0.479698\pi$
$251$	−13.7151	−	9.96460i	−0.865689	−	0.628960i	−0.929427	+	0.369007i	$0.879698\pi$
$252$		−	7.82663i		−	0.493031i
$253$		0			0
$254$	14.3487			0.900320
$255$	−13.4788	+	14.1640i	−0.844076	+	0.886985i
$256$	4.44000	−	13.6649i	0.277500	−	0.854057i
$257$	−4.50405	+	1.46346i	−0.280955	+	0.0912879i	−0.446105	−	0.894981i	$-0.647189\pi$
$257$	−4.50405	+	1.46346i	−0.280955	+	0.0912879i	0.165150	+	0.986268i	$0.447189\pi$
$258$	−7.05121	−	9.70516i	−0.438989	−	0.604217i
$259$	−4.95196	+	3.59781i	−0.307700	+	0.223557i
$260$	−3.83445	−	20.8514i	−0.237803	−	1.29315i
$261$	−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	$-0.811507\pi$
$263$		−	18.1037i		−	1.11632i	0.829732	−	0.558162i	$-0.188493\pi$
$264$		0			0
$265$	−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	−0.643018	−	0.765851i	$-0.722318\pi$
$269$	−1.85914	+	1.35074i	−0.113354	+	0.0823562i	0.529664	+	0.848207i	$0.322318\pi$
$270$	−4.89608	−	9.04759i	−0.297966	−	0.550619i
$271$	−0.248971	−	0.766255i	−0.0151239	−	0.0465467i	0.943210	−	0.332198i	$-0.107790\pi$
$271$	−0.248971	−	0.766255i	−0.0151239	−	0.0465467i	−0.958334	+	0.285651i	$0.907790\pi$
$272$	−12.0599	−	3.91850i	−0.731239	−	0.237594i
$273$	−6.73199	+	9.26579i	−0.407439	+	0.560791i
$274$	−17.1827			−1.03804
$275$		0			0
$276$	18.4848			1.11265
$277$	6.95521	−	9.57302i	0.417898	−	0.575187i	−0.547225	−	0.836986i	$-0.684316\pi$
$277$	6.95521	−	9.57302i	0.417898	−	0.575187i	0.965122	+	0.261799i	$0.0843157\pi$
$278$	14.8970	+	4.84033i	0.893462	+	0.290304i
$279$	0.500000	+	1.53884i	0.0299342	+	0.0921280i
$280$	0.198214	+	0.366284i	0.0118455	+	0.0218897i
$281$	5.03960	−	3.66148i	0.300637	−	0.218426i	−0.427231	−	0.904142i	$-0.640511\pi$
$281$	5.03960	−	3.66148i	0.300637	−	0.218426i	0.727869	+	0.685717i	$0.240511\pi$
$282$	21.8101	−	7.08655i	1.29878	−	0.421998i
$283$	−8.22250	−	2.67165i	−0.488777	−	0.158813i	0.0542519	−	0.998527i	$-0.482723\pi$
$283$	−8.22250	−	2.67165i	−0.488777	−	0.158813i	−0.543029	+	0.839714i	$0.682723\pi$
$284$	−9.24372	−	6.71596i	−0.548514	−	0.398519i
$285$	−19.0383	−	2.53351i	−1.12773	−	0.150072i
$286$		0			0
$287$			5.58790i			0.329843i
$288$	18.3597	−	25.2700i	1.08186	−	1.48905i
$289$	1.81285	−	5.57937i	0.106638	−	0.328198i
$290$	−4.02087	−	21.8651i	−0.236114	−	1.28397i
$291$	−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	−0.465953	−	0.884810i	$-0.654288\pi$
$293$	−5.52610	+	1.79554i	−0.322838	+	0.104896i	0.143115	+	0.989706i	$0.454288\pi$
$294$	−9.94288	+	30.6010i	−0.579880	+	1.78469i
$295$	15.6079	−	16.4013i	0.908725	−	0.954920i
$296$	1.22216			0.0710369
$297$		0			0
$298$		−	34.1665i		−	1.97921i
$299$	−12.3241	−	8.95396i	−0.712719	−	0.517821i
$300$	22.9835	+	15.0171i	1.32695	+	0.867014i
$301$	−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
$305$	4.98346	+	2.38554i	0.285352	+	0.136596i
$306$	−21.1275	−	15.3500i	−1.20778	−	0.877503i
$307$		−	18.4721i		−	1.05426i	−0.849785	−	0.527130i	$-0.823268\pi$
$307$		−	18.4721i		−	1.05426i	0.849785	−	0.527130i	$-0.176732\pi$
$308$		0			0
$309$	−25.5427			−1.45307
$310$	−1.37141	−	1.30507i	−0.0778911	−	0.0741230i
$311$	−3.50158	+	10.7768i	−0.198557	+	0.611094i	0.801360	+	0.598182i	$0.204110\pi$
$311$	−3.50158	+	10.7768i	−0.198557	+	0.611094i	−0.999917	+	0.0129120i	$0.995890\pi$
$312$	2.17491	−	0.706672i	0.123130	−	0.0400074i
$313$	−3.00651	−	4.13811i	−0.169938	−	0.233900i	0.715550	−	0.698561i	$-0.246176\pi$
$313$	−3.00651	−	4.13811i	−0.169938	−	0.233900i	−0.885488	+	0.464661i	$0.846176\pi$
$314$	6.89212	−	5.00742i	0.388945	−	0.282585i
$315$	−1.51064	−	8.21472i	−0.0851149	−	0.462847i
$316$	−0.650043	+	2.00063i	−0.0365678	+	0.112544i
$317$	6.94368	−	9.55715i	0.389996	−	0.536783i	−0.568202	−	0.822889i	$-0.692361\pi$
$317$	6.94368	−	9.55715i	0.389996	−	0.536783i	0.958198	+	0.286106i	$0.0923609\pi$
$318$		−	14.1104i		−	0.791270i
$319$		0			0
$320$	−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
$325$	−8.04918	−	21.1453i	−0.446488	−	1.17293i
$326$	−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
$330$		0			0
$331$	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
$335$	−18.8804	+	10.2171i	−1.03154	+	0.558218i
$336$	7.78174	−	5.65376i	0.424529	−	0.308438i
$337$	−25.3400	+	8.23348i	−1.38036	+	0.448506i	−0.902788	−	0.430087i	$-0.858483\pi$
$337$	−25.3400	+	8.23348i	−1.38036	+	0.448506i	−0.477572	+	0.878593i	$0.658483\pi$
$338$	−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
$341$		0			0
$342$		−	25.6525i		−	1.38713i
$343$	−7.41820	+	10.2103i	−0.400545	+	0.551303i
$344$	−0.134801	+	0.414875i	−0.00726798	+	0.0223686i
$345$	19.4014	−	3.56779i	1.04453	−	0.192084i
$346$	−6.72833	+	4.88842i	−0.361717	+	0.262803i
$347$	2.53411	+	3.48790i	0.136038	+	0.187240i	0.871601	−	0.490216i	$-0.163082\pi$
$347$	2.53411	+	3.48790i	0.136038	+	0.187240i	−0.735563	+	0.677457i	$0.763082\pi$
$348$	25.6565	−	8.33631i	1.37533	−	0.446873i
$349$	−4.06960	+	12.5249i	−0.217841	+	0.670444i	0.781099	+	0.624407i	$0.214659\pi$
$349$	−4.06960	+	12.5249i	−0.217841	+	0.670444i	−0.998940	+	0.0460373i	$0.985341\pi$
$350$	6.12885	+	7.61189i	0.327601	+	0.406873i
$351$	−10.2874			−0.549100
$352$		0			0
$353$		−	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
$355$	−10.9983	−	5.26482i	−0.583732	−	0.279428i
$356$	−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	0.899591	+	0.436734i	$0.143865\pi$
$359$	8.11915	+	24.9882i	0.428512	+	1.31883i	−0.471078	+	0.882091i	$0.656135\pi$
$360$	−0.720078	+	1.50426i	−0.0379514	+	0.0792816i
$361$	6.68037	+	4.85358i	0.351599	+	0.255451i
$362$		−	11.2252i		−	0.589981i
$363$		0			0
$364$	9.15736			0.479976
$365$	2.32534	+	2.21285i	0.121714	+	0.115826i
$366$	−4.04923	+	12.4622i	−0.211657	+	0.651412i
$367$	−1.91993	+	0.623823i	−0.100220	+	0.0325633i	−0.358698	−	0.933454i	$-0.616779\pi$
$367$	−1.91993	+	0.623823i	−0.100220	+	0.0325633i	0.258478	+	0.966017i	$0.416779\pi$
$368$	7.51985	+	10.3502i	0.391999	+	0.539541i
$369$	−18.1026	+	13.1523i	−0.942384	+	0.684682i
$370$	28.2051	−	5.18675i	1.46631	−	0.269646i
$371$	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	$-0.926234\pi$
$373$		−	8.87153i		−	0.459351i	0.973267	−	0.229675i	$-0.0737664\pi$
$374$		0			0
$375$	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	−0.0566685	−	0.998393i	$-0.518048\pi$
$379$	17.0412	−	12.3812i	0.875348	−	0.635978i	0.932017	+	0.362415i	$0.118048\pi$
$380$	7.30850	+	13.5055i	0.374918	+	0.692820i
$381$	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	0.214970	+	0.976621i	$0.431035\pi$
$383$	−15.2704	+	21.0179i	−0.780281	+	1.07396i	−0.995251	+	0.0973436i	$0.968965\pi$
$384$	−4.03836			−0.206082
$385$		0			0
$386$	−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	0.963108	−	0.269116i	$-0.0867315\pi$
$389$	0.507965	+	1.56335i	0.0257548	+	0.0792652i	−0.937353	+	0.348381i	$0.886731\pi$
$390$	47.1935	−	25.5387i	2.38974	−	1.29320i
$391$	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
$396$		0			0
$397$			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
$400$	0.941436	+	18.9783i	0.0470718	+	0.948916i
$401$	−22.4842	+	16.3357i	−1.12281	+	0.815766i	−0.984632	−	0.174641i	$-0.944123\pi$
$401$	−22.4842	+	16.3357i	−1.12281	+	0.815766i	−0.138174	+	0.990408i	$0.544123\pi$
$402$	−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
$405$	−8.70140	+	9.14374i	−0.432376	+	0.454356i
$406$	9.60255			0.476567
$407$		0			0
$408$			1.68626i			0.0834822i
$409$	−31.9019	−	23.1781i	−1.57745	−	1.14608i	−0.919547	−	0.392980i	$-0.871444\pi$
$409$	−31.9019	−	23.1781i	−1.57745	−	1.14608i	−0.657902	−	0.753104i	$-0.728556\pi$
$410$	11.3040	−	23.6144i	0.558266	−	1.16623i
$411$	−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
$415$	−7.14006	+	14.9158i	−0.350492	+	0.732187i
$416$	29.5665	+	21.4814i	1.44962	+	1.05321i
$417$			20.2838i			0.993303i
$418$		0			0
$419$	−14.7812			−0.722111			−0.361055	−	0.932544i	$-0.617583\pi$
$419$	−14.7812			−0.722111			−0.361055	+	0.932544i	$0.617583\pi$
$420$	−8.17482	+	8.59039i	−0.398890	+	0.419168i
$421$	−3.33036	+	10.2498i	−0.162312	+	0.499545i	−0.998828	−	0.0483974i	$-0.984589\pi$
$421$	−3.33036	+	10.2498i	−0.162312	+	0.499545i	0.836516	+	0.547942i	$0.184589\pi$
$422$	−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
$425$	16.6630	−	0.826581i	0.808273	−	0.0400951i
$426$	8.93653	−	27.5038i	0.432976	−	1.33256i
$427$	−1.40270	+	1.93065i	−0.0678813	+	0.0934306i
$428$			16.0118i			0.773960i
$429$		0			0
$430$	−1.35025	+	10.1466i	−0.0651146	+	0.489310i
$431$	26.0435	+	18.9217i	1.25447	+	0.911428i	0.998473	−	0.0552489i	$-0.0175952\pi$
$431$	26.0435	+	18.9217i	1.25447	+	0.911428i	0.256000	+	0.966677i	$0.417595\pi$
$432$	8.21685	+	2.66982i	0.395334	+	0.128452i
$433$	0.363904	−	0.118240i	0.0174881	−	0.00568223i	−0.300260	−	0.953857i	$-0.597073\pi$
$433$	0.363904	−	0.118240i	0.0174881	−	0.00568223i	0.317748	+	0.948175i	$0.397073\pi$
$434$	0.661536	−	0.480634i	0.0317547	−	0.0230712i
$435$	25.3197	−	13.7017i	1.21399	−	0.656947i
$436$	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	$-0.281751\pi$
$439$	26.5331			1.26635			0.633177	+	0.774007i	$0.281751\pi$
$440$		0			0
$441$	−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	$-0.288055\pi$
$443$	13.7913	+	4.48106i	0.655243	+	0.212901i	0.0375185	+	0.999296i	$0.488055\pi$
$444$	10.7535	+	33.0958i	0.510337	+	1.57066i
$445$	−12.9796	−	23.9853i	−0.615292	−	1.13701i
$446$	−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	0.763876	−	0.645362i	$-0.223294\pi$
$449$	8.18240	+	5.94486i	0.386151	+	0.280555i	−0.377725	+	0.925918i	$0.623294\pi$
$450$	−10.2340	+	37.7713i	−0.482435	+	1.78055i
$451$		0			0
$452$			10.5155i			0.494606i
$453$	18.9195	−	26.0405i	0.888917	−	1.22349i
$454$	17.8012	−	54.7866i	0.835454	−	2.57126i
$455$	9.61144	−	1.76749i	0.450591	−	0.0828610i
$456$	−1.34005	+	0.973602i	−0.0627535	+	0.0455931i
$457$	22.9758	+	31.6235i	1.07476	+	1.47928i	0.865160	+	0.501496i	$0.167217\pi$
$457$	22.9758	+	31.6235i	1.07476	+	1.47928i	0.209602	+	0.977787i	$0.432783\pi$
$458$	−48.8691	+	15.8785i	−2.28351	+	0.741956i
$459$	2.34410	−	7.21440i	0.109413	−	0.336739i
$460$	−11.4257	−	10.8730i	−0.532728	−	0.506957i
$461$	−39.1322			−1.82257			−0.911285	−	0.411776i	$-0.864908\pi$
$461$	−39.1322			−1.82257			−0.911285	+	0.411776i	$0.864908\pi$
$462$		0			0
$463$			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
$465$	1.05851	−	2.21125i	0.0490872	−	0.102544i
$466$	−7.82780	−	24.0915i	−0.362616	−	1.11602i
$467$	6.61206	+	9.10071i	0.305969	+	0.421131i	0.934119	−	0.356962i	$-0.116187\pi$
$467$	6.61206	+	9.10071i	0.305969	+	0.421131i	−0.628150	+	0.778093i	$0.716187\pi$
$468$	21.5538	+	29.6662i	0.996324	+	1.37132i
$469$	−2.86535	−	8.81864i	−0.132310	−	0.407207i
$470$	−17.6496	−	8.44874i	−0.814117	−	0.389711i
$471$	8.92504	+	6.48442i	0.411244	+	0.298786i
$472$		−	1.95261i		−	0.0898762i
$473$		0			0
$474$	−5.32424			−0.244550
$475$	10.2776	+	12.7646i	0.471571	+	0.585680i
$476$	−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	$-0.858996\pi$
$479$	−16.9621	+	12.3237i	−0.775017	+	0.563083i	0.128462	+	0.991714i	$0.458996\pi$
$480$	−46.5456	+	8.55946i	−2.12451	+	0.390684i
$481$	8.86200	−	27.2744i	0.404072	−	1.24361i
$482$	27.1126	−	37.3174i	1.23495	−	1.69976i
$483$			8.52053i			0.387697i
$484$		0			0
$485$	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	$-0.229145\pi$
$487$	21.4645	+	6.97424i	0.972649	+	0.316033i	0.220764	+	0.975327i	$0.429145\pi$
$488$	0.453171	−	0.147244i	0.0205141	−	0.00666543i
$489$	35.1377	−	25.5290i	1.58898	−	1.15446i
$490$	24.1458	−	13.0665i	1.09080	−	0.590283i
$491$	6.20389	+	19.0936i	0.279977	+	0.861682i	0.987859	+	0.155351i	$0.0496509\pi$
$491$	6.20389	+	19.0936i	0.279977	+	0.861682i	−0.707882	+	0.706331i	$0.750349\pi$
$492$	30.2136	+	9.81699i	1.36213	+	0.442584i
$493$	9.63565	−	13.2623i	0.433968	−	0.597306i
$494$	30.0141			1.35040
$495$		0			0
$496$	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	0.913711	−	0.406364i	$-0.133203\pi$
$499$	−1.43750	−	4.42417i	−0.0643513	−	0.198053i	−0.978063	+	0.208311i	$0.933203\pi$
$500$	−5.37318	−	22.8016i	−0.240296	−	1.01972i
$501$	−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	0.571337	−	0.820716i	$-0.306425\pi$
$503$	12.3611	+	4.01636i	0.551154	+	0.179081i	−0.0201833	+	0.999796i	$0.506425\pi$
$504$	−0.582768	−	0.423406i	−0.0259585	−	0.0188600i
$505$	4.48232	−	33.6828i	0.199460	−	1.49887i
$506$		0			0
$507$		−	19.5928i		−	0.870147i
$508$	8.73242	−	12.0191i	0.387439	−	0.533263i
$509$	−9.12976	+	28.0985i	−0.404669	+	1.24544i	0.516501	+	0.856286i	$0.327234\pi$
$509$	−9.12976	+	28.0985i	−0.404669	+	1.24544i	−0.921171	+	0.389158i	$0.872766\pi$
$510$	7.15631	+	38.9154i	0.316887	+	1.72320i
$511$	−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
$515$	15.7884	+	15.0246i	0.695720	+	0.662063i
$516$	−12.4207			−0.546793
$517$		0			0
$518$			12.3869i			0.544248i
$519$	−8.71293	−	6.33032i	−0.382455	−	0.277870i
$520$	−1.76003	−	0.842510i	−0.0771822	−	0.0369465i
$521$	−9.71896	−	29.9119i	−0.425796	−	1.31046i	−0.902230	−	0.431254i	$-0.858071\pi$
$521$	−9.71896	−	29.9119i	−0.425796	−	1.31046i	0.476435	−	0.879210i	$-0.341929\pi$
$522$	22.6016	+	31.1085i	0.989247	+	1.36158i
$523$	−5.30194	−	7.29750i	−0.231838	−	0.319097i	0.677210	−	0.735790i	$-0.263189\pi$
$523$	−5.30194	−	7.29750i	−0.231838	−	0.319097i	−0.909047	+	0.416693i	$0.863189\pi$
$524$	4.67290	+	14.3817i	0.204137	+	0.628268i
$525$	−6.92212	+	10.5942i	−0.302106	+	0.462369i
$526$	−29.6393	−	21.5342i	−1.29234	−	0.938937i
$527$		−	1.39595i		−	0.0608088i
$528$		0			0
$529$	11.6672			0.507269
$530$	−8.29992	+	8.72185i	−0.360526	+	0.378853i
$531$	−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
$535$	3.09048	+	16.8058i	0.133613	+	0.726577i
$536$	−0.572121	+	1.76081i	−0.0247119	+	0.0760553i
$537$	25.1016	−	34.5494i	1.08321	−	1.49092i
$538$			4.65046i			0.200496i
$539$		0			0
$540$	−10.5583	−	1.40504i	−0.454359	−	0.0604635i
$541$	−6.91720	−	5.02564i	−0.297394	−	0.216069i	0.429075	−	0.903269i	$-0.358840\pi$
$541$	−6.91720	−	5.02564i	−0.297394	−	0.216069i	−0.726468	+	0.687200i	$0.758840\pi$
$542$	−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
$545$	10.4886	+	19.3822i	0.449283	+	0.830241i
$546$	7.16226	+	22.0432i	0.306516	+	0.943360i
$547$	32.2693	+	10.4849i	1.37974	+	0.448304i	0.902583	−	0.430516i	$-0.141668\pi$
$547$	32.2693	+	10.4849i	1.37974	+	0.448304i	0.477154	+	0.878820i	$0.341668\pi$
$548$	−10.4571	+	14.3930i	−0.446706	+	0.614838i
$549$	−9.55608			−0.407844
$550$		0			0
$551$	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
$555$	17.6746	+	32.6613i	0.750246	+	1.38640i
$556$	13.1206	−	9.53265i	0.556436	−	0.404274i
$557$	−21.8178	+	7.08904i	−0.924451	+	0.300372i	−0.732291	−	0.680991i	$-0.761549\pi$
$557$	−21.8178	+	7.08904i	−0.924451	+	0.300372i	−0.192160	+	0.981364i	$0.561549\pi$
$558$	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
$561$		0			0
$562$		−	12.6061i		−	0.531757i
$563$	5.45619	−	7.50980i	0.229951	−	0.316500i	−0.678413	−	0.734681i	$-0.737332\pi$
$563$	5.45619	−	7.50980i	0.229951	−	0.316500i	0.908364	+	0.418180i	$0.137332\pi$
$564$	7.33731	−	22.5819i	0.308957	−	0.950871i
$565$	2.02962	+	11.0369i	0.0853867	+	0.464325i
$566$	−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	−0.523822	−	0.851828i	$-0.675494\pi$
$569$	9.55701	−	29.4135i	0.400651	−	1.23308i	0.924473	−	0.381248i	$-0.124506\pi$
$570$	−26.7937	+	28.1558i	−1.12227	+	1.17932i
$571$	2.63736			0.110370			0.0551851	−	0.998476i	$-0.482425\pi$
$571$	2.63736			0.110370			0.0551851	+	0.998476i	$0.482425\pi$
$572$		0			0
$573$			57.1712i			2.38836i
$574$	9.14848	+	6.64676i	0.381850	+	0.277430i
$575$	−14.0909	−	9.20685i	−0.587633	−	0.383952i
$576$	−10.4494	−	32.1599i	−0.435391	−	1.34000i
$577$	21.5309	+	29.6347i	0.896342	+	1.23371i	0.971620	+	0.236546i	$0.0760154\pi$
$577$	21.5309	+	29.6347i	0.896342	+	1.23371i	−0.0752785	+	0.997163i	$0.523985\pi$
$578$	−6.97814	−	9.60459i	−0.290252	−	0.399498i
$579$	−18.2036	−	56.0249i	−0.756516	−	2.32832i
$580$	−20.7623	−	9.93873i	−0.862106	−	0.412683i
$581$	−5.77854	−	4.19835i	−0.239734	−	0.174177i
$582$			16.0118i			0.663710i
$583$		0			0
$584$	0.276837			0.0114556
$585$	28.3485	+	26.9771i	1.17207	+	1.11537i
$586$	−3.63360	+	11.1831i	−0.150103	+	0.461968i
$587$	−13.0793	+	4.24973i	−0.539842	+	0.175405i	−0.566231	−	0.824246i	$-0.691599\pi$
$587$	−13.0793	+	4.24973i	−0.539842	+	0.175405i	0.0263892	+	0.999652i	$0.491599\pi$
$588$	19.5817	+	26.9519i	0.807536	+	1.11148i
$589$	1.10935	−	0.805989i	0.0457099	−	0.0332102i
$590$	−8.28669	−	45.0623i	−0.341158	−	1.85518i
$591$	−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	$0.135811\pi$
$593$			20.1550i			0.827668i	−0.910352	+	0.413834i	$0.864189\pi$
$594$		0			0
$595$	−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	−0.514036	−	0.857769i	$-0.671850\pi$
$599$	3.49753	−	2.54110i	0.142905	−	0.103827i	0.656941	+	0.753942i	$0.271850\pi$
$600$	2.36153	−	0.898943i	0.0964091	−	0.0366992i
$601$	−11.1214	−	34.2281i	−0.453650	−	1.39619i	−0.872713	−	0.488234i	$-0.837641\pi$
$601$	−11.1214	−	34.2281i	−0.453650	−	1.39619i	0.419063	−	0.907957i	$-0.362359\pi$
$602$	−4.20484	−	1.36623i	−0.171376	−	0.0556836i
$603$	21.8247	−	30.0391i	0.888771	−	1.22329i
$604$	−25.7358			−1.04717
$605$		0			0
$606$	80.5893			3.27372
$607$	−23.3056	+	32.0774i	−0.945945	+	1.30198i	0.00736018	+	0.999973i	$0.497657\pi$
$607$	−23.3056	+	32.0774i	−0.945945	+	1.30198i	−0.953305	+	0.302009i	$0.902343\pi$
$608$	−25.1754	−	8.17999i	−1.02100	−	0.331742i
$609$	3.84261	+	11.8263i	0.155710	+	0.479227i
$610$	9.83338	−	5.32131i	0.398142	−	0.215454i
$611$	−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	0.234828	−	0.972037i	$-0.424547\pi$
$613$	−3.62818	−	1.17887i	−0.146541	−	0.0476139i	−0.381369	+	0.924423i	$0.624547\pi$
$614$	−30.2424	−	21.9724i	−1.22049	−	0.886735i
$615$	33.6066	+	4.47217i	1.35515	+	0.180335i
$616$		0			0
$617$			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	0.682888	+	0.730523i	$0.260724\pi$
$619$	−7.43830	+	22.8927i	−0.298971	+	0.920137i	−0.981859	+	0.189614i	$0.939276\pi$
$620$	−1.92781	+	0.354512i	−0.0774226	+	0.0142376i
$621$	−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
$625$	−10.0406	−	22.8951i	−0.401624	−	0.915805i
$626$	−10.3511			−0.413714
$627$		0			0
$628$		−	8.82059i		−	0.351980i
$629$	17.1078	+	12.4296i	0.682135	+	0.495600i
$630$	−15.2460	−	7.29813i	−0.607415	−	0.290765i
$631$	5.90889	+	18.1857i	0.235229	+	0.723961i	0.997091	+	0.0762213i	$0.0242855\pi$
$631$	5.90889	+	18.1857i	0.235229	+	0.723961i	−0.761862	+	0.647740i	$0.775714\pi$
$632$	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
$635$	6.84558	−	14.3006i	0.271659	−	0.567502i
$636$	−11.8195	−	8.58735i	−0.468673	−	0.340511i
$637$		−	27.4546i		−	1.08779i
$638$		0			0
$639$	21.0900			0.834307
$640$	2.49618	+	2.37542i	0.0986700	+	0.0938968i
$641$	3.70172	−	11.3927i	0.146209	−	0.449985i	−0.850955	−	0.525238i	$-0.823976\pi$
$641$	3.70172	−	11.3927i	0.146209	−	0.449985i	0.997165	+	0.0752526i	$0.0239763\pi$
$642$	−38.5429	+	12.5233i	−1.52117	+	0.494257i
$643$	15.1301	+	20.8248i	0.596672	+	0.821248i	0.995399	−	0.0958216i	$-0.0305478\pi$
$643$	15.1301	+	20.8248i	0.596672	+	0.821248i	−0.398727	+	0.917070i	$0.630548\pi$
$644$	5.51149	−	4.00433i	0.217183	−	0.157793i
$645$	−13.0366	+	2.39736i	−0.513317	+	0.0943960i
$646$	−6.83905	+	21.0484i	−0.269079	+	0.828139i
$647$	−5.46774	+	7.52570i	−0.214959	+	0.295866i	−0.902856	−	0.429942i	$-0.858534\pi$
$647$	−5.46774	+	7.52570i	−0.214959	+	0.295866i	0.687897	+	0.725808i	$0.258534\pi$
$648$			1.08858i			0.0427636i
$649$		0			0
$650$	−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	$-0.338223\pi$
$653$	35.6177	−	11.5729i	1.39383	−	0.452882i	0.907189	+	0.420723i	$0.138223\pi$
$654$	−42.2854	+	30.7221i	−1.65349	+	1.20133i
$655$	7.68047	+	14.1929i	0.300101	+	0.554563i
$656$	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	$-0.530659\pi$
$659$	−4.93753			−0.192339			−0.0961693	+	0.995365i	$0.530659\pi$
$660$		0			0
$661$	−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
$665$	−6.22536	+	3.36884i	−0.241409	+	0.130638i
$666$	−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
$671$		0			0
$672$		−	20.4415i		−	0.788548i
$673$	−19.3464	+	26.6280i	−0.745749	+	1.02644i	0.252518	+	0.967592i	$0.418741\pi$
$673$	−19.3464	+	26.6280i	−0.745749	+	1.02644i	−0.998267	+	0.0588431i	$0.981259\pi$
$674$	−16.6619	+	51.2802i	−0.641794	+	1.97524i
$675$	−11.3531	+	0.563180i	−0.436981	+	0.0216768i
$676$	−12.6736	+	9.20789i	−0.487445	+	0.354150i
$677$	−10.0761	−	13.8686i	−0.387258	−	0.533014i	0.570231	−	0.821484i	$-0.306854\pi$
$677$	−10.0761	−	13.8686i	−0.387258	−	0.533014i	−0.957489	+	0.288470i	$0.906854\pi$
$678$	−25.3123	+	8.22448i	−0.972114	+	0.315859i
$679$	−0.901110	+	2.77333i	−0.0345814	+	0.106431i
$680$	0.991882	−	1.04230i	0.0380369	−	0.0399705i
$681$	74.5977			2.85859
$682$		0			0
$683$			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
$685$	−8.19762	+	17.1250i	−0.313215	+	0.654314i
$686$	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
$690$	17.2366	−	36.0076i	0.656185	−	1.37079i
$691$	7.39559	+	5.37321i	0.281342	+	0.204407i	0.719502	−	0.694490i	$-0.244370\pi$
$691$	7.39559	+	5.37321i	0.281342	+	0.204407i	−0.438161	+	0.898897i	$0.644370\pi$
$692$			8.61097i			0.327340i
$693$		0			0
$694$	8.72467			0.331184
$695$	11.9312	−	12.5378i	0.452578	−	0.475585i
$696$	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
$700$	10.1060	−	0.501317i	0.381971	−	0.0189480i
$701$	4.72594	−	14.5450i	0.178496	−	0.549355i	−0.821279	−	0.570526i	$-0.806739\pi$
$701$	4.72594	−	14.5450i	0.178496	−	0.549355i	0.999776	+	0.0211707i	$0.00673934\pi$
$702$	−12.2368	+	16.8425i	−0.461847	+	0.635678i
$703$			20.7719i			0.783428i
$704$		0			0
$705$	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	0.303848	−	0.952721i	$-0.401729\pi$
$709$	34.7172	−	25.2235i	1.30383	−	0.947290i	0.999985	+	0.00543044i	$0.00172857\pi$
$710$	−21.7020	+	11.7440i	−0.814460	+	0.440743i
$711$	−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
$715$		0			0
$716$	−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	0.919483	−	0.393129i	$-0.128607\pi$
$719$	−1.48738	−	4.57768i	−0.0554699	−	0.170719i	−0.974953	+	0.222411i	$0.928607\pi$
$720$	−15.6416	−	28.9045i	−0.582929	−	1.07721i
$721$	−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
$726$		0			0
$727$		−	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
$730$	6.38884	−	1.17487i	0.236461	−	0.0434839i
$731$	−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	0.700901	−	0.713259i	$-0.252782\pi$
$733$	45.6788	−	14.8419i	1.68718	−	0.548199i	0.986284	+	0.165060i	$0.0527817\pi$
$734$	−1.26242	+	3.88533i	−0.0465968	+	0.143410i
$735$	25.7548	+	24.5089i	0.949979	+	0.904023i
$736$	27.1885			1.00218
$737$		0			0
$738$			45.2820i			1.66685i
$739$	27.5934	+	20.0478i	1.01504	+	0.737470i	0.965260	−	0.261290i	$-0.0841478\pi$
$739$	27.5934	+	20.0478i	1.01504	+	0.737470i	0.0497805	+	0.998760i	$0.484148\pi$
$740$	12.8205	−	26.7824i	0.471292	−	0.984542i
$741$	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	0.992572	−	0.121656i	$-0.0388203\pi$
$743$	15.5411	+	21.3906i	0.570149	+	0.784743i	−0.422423	+	0.906399i	$0.638820\pi$
$744$	−0.0653350	−	0.201080i	−0.00239530	−	0.00737196i
$745$	−34.0519	−	16.3003i	−1.24756	−	0.597199i
$746$	−14.5244	−	10.5526i	−0.531777	−	0.386359i
$747$		−	28.6019i		−	1.04649i
$748$		0			0
$749$	−7.38062			−0.269682
$750$	50.6843	−	30.7679i	1.85073	−	1.12348i
$751$	14.1963	−	43.6918i	0.518032	−	1.59434i	−0.259666	−	0.965699i	$-0.583612\pi$
$751$	14.1963	−	43.6918i	0.518032	−	1.59434i	0.777697	−	0.628639i	$-0.216388\pi$
$752$	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
$755$	−27.0119	+	4.96733i	−0.983064	+	0.180780i
$756$	1.42168	−	4.37549i	0.0517061	−	0.159135i
$757$	−18.1365	+	24.9628i	−0.659183	+	0.907288i	−0.999454	−	0.0330398i	$-0.989481\pi$
$757$	−18.1365	+	24.9628i	−0.659183	+	0.907288i	0.340271	+	0.940327i	$0.389481\pi$
$758$		−	42.6271i		−	1.54828i
$759$		0			0
$760$	1.40099	+	0.186436i	0.0508194	+	0.00676275i
$761$	−11.4860	−	8.34507i	−0.416367	−	0.302508i	0.359807	−	0.933027i	$-0.382842\pi$
$761$	−11.4860	−	8.34507i	−0.416367	−	0.302508i	−0.776175	+	0.630518i	$0.782842\pi$
$762$	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
$765$	−25.3782	+	13.7334i	−0.917550	+	0.496530i
$766$	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	$-0.682064\pi$
$769$	−30.0208			−1.08258			−0.541290	+	0.840836i	$0.682064\pi$
$770$		0			0
$771$	−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	$-0.215681\pi$
$773$	28.9401	+	9.40320i	1.04090	+	0.338209i	0.261810	+	0.965119i	$0.415681\pi$
$774$	−5.47091	−	16.8377i	−0.196648	−	0.605220i
$775$	−1.95497	+	0.744183i	−0.0702248	+	0.0267318i
$776$	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
$781$		0			0
$782$		−	22.7315i		−	0.812876i
$783$	−6.56512	+	9.03612i	−0.234618	+	0.322925i
$784$	−7.12510	+	21.9288i	−0.254468	+	0.783172i
$785$	−1.70249	−	9.25797i	−0.0607643	−	0.330431i
$786$	−30.9642	+	22.4968i	−1.10445	+	0.802433i
$787$	17.9067	+	24.6465i	0.638306	+	0.878553i	0.998524	−	0.0543151i	$-0.0172976\pi$
$787$	17.9067	+	24.6465i	0.638306	+	0.878553i	−0.360218	+	0.932868i	$0.617298\pi$
$788$	51.3089	−	16.6713i	1.82780	−	0.593890i
$789$	14.6605	−	45.1205i	0.521929	−	1.60633i
$790$	3.29100	+	3.13180i	0.117089	+	0.111424i
$791$	−4.84709			−0.172343
$792$		0			0
$793$		−	11.1809i		−	0.397044i
$794$	27.3555	+	19.8749i	0.970810	+	0.705334i
$795$	−14.0630	−	6.73186i	−0.498764	−	0.238754i
$796$	10.9859	+	33.8112i	0.389385	+	1.19840i
$797$	19.4235	+	26.7341i	0.688014	+	0.946970i	0.999995	−	0.00311796i	$-0.000992479\pi$
$797$	19.4235	+	26.7341i	0.688014	+	0.946970i	−0.311981	+	0.950088i	$0.600992\pi$
$798$	−9.86764	−	13.5816i	−0.349311	−	0.480785i
$799$	−4.45870	−	13.7225i	−0.157737	−	0.485466i
$800$	33.8054	+	22.0881i	1.19520	+	0.780931i
$801$	38.1613	+	27.7258i	1.34836	+	0.979642i
$802$			56.2421i			1.98598i
$803$		0			0
$804$	−52.7160			−1.85915
$805$	5.01190	−	5.26668i	0.176646	−	0.185626i
$806$	−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	$-0.761882\pi$
$809$	−8.89072	+	6.45948i	−0.312581	+	0.227103i	0.420422	+	0.907329i	$0.361882\pi$
$810$	4.61984	+	25.1223i	0.162325	+	0.882707i
$811$	−12.5951	+	38.7638i	−0.442275	+	1.36118i	0.443171	+	0.896437i	$0.353854\pi$
$811$	−12.5951	+	38.7638i	−0.442275	+	1.36118i	−0.885445	+	0.464744i	$0.846146\pi$
$812$	5.84397	−	8.04353i	0.205083	−	0.282273i
$813$		−	2.11138i		−	0.0740494i
$814$		0			0
$815$	−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
$820$	−12.9010	−	23.8401i	−0.450524	−	0.832534i
$821$	−4.66851	−	14.3682i	−0.162932	−	0.501454i	0.835946	−	0.548812i	$-0.184920\pi$
$821$	−4.66851	−	14.3682i	−0.162932	−	0.501454i	−0.998878	+	0.0473584i	$0.984920\pi$
$822$	−42.8250	−	13.9147i	−1.49369	−	0.485330i
$823$	−21.4138	+	29.4735i	−0.746437	+	1.02738i	0.251786	+	0.967783i	$0.418982\pi$
$823$	−21.4138	+	29.4735i	−0.746437	+	1.02738i	−0.998222	+	0.0595989i	$0.981018\pi$
$824$	1.87964			0.0654805
$825$		0			0
$826$	19.7901			0.688585
$827$	−2.23560	+	3.07703i	−0.0777393	+	0.106999i	−0.846116	−	0.532999i	$-0.821065\pi$
$827$	−2.23560	+	3.07703i	−0.0777393	+	0.106999i	0.768376	+	0.639998i	$0.221065\pi$
$828$	25.9449	+	8.43002i	0.901649	+	0.292963i
$829$	8.43810	+	25.9698i	0.293067	+	0.901969i	0.983864	+	0.178919i	$0.0572601\pi$
$829$	8.43810	+	25.9698i	0.293067	+	0.901969i	−0.690796	+	0.723049i	$0.742740\pi$
$830$	15.9270	+	29.4318i	0.552834	+	1.02159i
$831$	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
$836$		0			0
$837$			0.951115i			0.0328754i
$838$	−17.5821	+	24.1998i	−0.607365	+	0.835967i
$839$	−8.75291	+	26.9387i	−0.302184	+	0.930026i	0.678529	+	0.734573i	$0.262618\pi$
$839$	−8.75291	+	26.9387i	−0.302184	+	0.930026i	−0.980713	+	0.195453i	$0.937382\pi$
$840$	0.197395	+	1.07342i	0.00681078	+	0.0370364i
$841$	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
$845$	−11.5248	+	12.1106i	−0.396464	+	0.416619i
$846$	33.8442			1.16359
$847$		0			0
$848$		−	10.1115i		−	0.347232i
$849$	−18.3297	−	13.3173i	−0.629073	−	0.457048i
$850$	18.4672	−	28.2637i	0.633419	−	0.969438i
$851$	−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	0.716767	−	0.697313i	$-0.245621\pi$
$853$	−4.90400	−	6.74977i	−0.167910	−	0.231108i	−0.884677	+	0.466205i	$0.845621\pi$
$854$	1.49235	+	4.59298i	0.0510671	+	0.157168i
$855$	−25.5664	−	12.2384i	−0.874354	−	0.418546i
$856$	1.19223	+	0.866207i	0.0407497	+	0.0296064i
$857$			8.59547i			0.293616i	0.989165	+	0.146808i	$0.0468999\pi$
$857$			8.59547i			0.293616i	−0.989165	+	0.146808i	$0.953100\pi$
$858$		0			0
$859$	−9.40807			−0.320999			−0.160500	−	0.987036i	$-0.551311\pi$
$859$	−9.40807			−0.320999			−0.160500	+	0.987036i	$0.551311\pi$
$860$	7.67747	+	7.30606i	0.261800	+	0.249135i
$861$	−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	$-0.256236\pi$
$863$	−6.06951	−	8.35396i	−0.206608	−	0.284372i	−0.899728	+	0.436450i	$0.856236\pi$
$864$	14.8543	−	10.7922i	0.505352	−	0.367160i
$865$	1.66203	+	9.03795i	0.0565106	+	0.307300i
$866$	0.239279	−	0.736426i	0.00813104	−	0.0250248i
$867$	9.03644	−	12.4376i	0.306893	−	0.422403i
$868$		−	0.846638i		−	0.0287368i
$869$		0			0
$870$	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
$875$	10.5103	−	2.47676i	0.355315	−	0.0837298i
$876$	2.43581	+	7.49665i	0.0822984	+	0.253288i
$877$	−28.3445	−	9.20969i	−0.957126	−	0.310989i	−0.211518	−	0.977374i	$-0.567841\pi$
$877$	−28.3445	−	9.20969i	−0.957126	−	0.310989i	−0.745608	+	0.666385i	$0.767841\pi$
$878$	31.5608	−	43.4398i	1.06513	−	1.46602i
$879$	−15.2269			−0.513591
$880$		0			0
$881$	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	$-0.721837\pi$
$883$	−47.8970	−	15.5627i	−1.61186	−	0.523726i	−0.970002	+	0.243096i	$0.921837\pi$
$884$	−9.77622	−	30.0881i	−0.328810	−	1.01197i
$885$	52.1819	−	28.2381i	1.75408	−	0.949214i
$886$	23.7410	−	17.2488i	0.797593	−	0.579485i
$887$	39.3789	−	12.7950i	1.32221	−	0.429613i	0.438959	−	0.898507i	$-0.355347\pi$
$887$	39.3789	−	12.7950i	1.32221	−	0.429613i	0.883255	+	0.468893i	$0.155347\pi$
$888$	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
$891$		0			0
$892$			39.8572i			1.33452i
$893$	8.33074	−	11.4663i	0.278777	−	0.383704i
$894$	27.6683	−	85.1542i	0.925366	−	2.84798i
$895$	−35.8382	+	6.59043i	−1.19794	+	0.220294i
$896$	−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
$900$	25.4107	+	31.5595i	0.847022	+	1.05198i
$901$	−8.87793			−0.295767
$902$		0			0
$903$		−	5.72532i		−	0.190527i
$904$	0.782977	+	0.568866i	0.0260414	+	0.0189202i
$905$	−11.1875	−	5.35536i	−0.371885	−	0.178018i
$906$	−20.1287	−	61.9499i	−0.668733	−	2.05815i
$907$	2.72271	+	3.74749i	0.0904062	+	0.124433i	0.851824	−	0.523828i	$-0.175496\pi$
$907$	2.72271	+	3.74749i	0.0904062	+	0.124433i	−0.761418	+	0.648261i	$0.775496\pi$
$908$	−35.0582	−	48.2534i	−1.16345	−	1.60135i
$909$	18.1614	+	55.8951i	0.602376	+	1.85392i
$910$	8.53900	−	17.8382i	0.283065	−	0.591330i
$911$	−5.64577	−	4.10189i	−0.187053	−	0.135902i	0.490318	−	0.871544i	$-0.336881\pi$
$911$	−5.64577	−	4.10189i	−0.187053	−	0.135902i	−0.677371	+	0.735642i	$0.736881\pi$
$912$		−	32.6419i		−	1.08088i
$913$		0			0
$914$	79.1032			2.61650
$915$	10.4886	+	9.98121i	0.346743	+	0.329969i
$916$	−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	$-0.573757\pi$
$919$	18.9477	−	13.7663i	0.625027	−	0.454109i	0.854674	+	0.519165i	$0.173757\pi$
$920$	−1.42771	+	0.262548i	−0.0470702	+	0.00865594i
$921$	14.9589	−	46.0387i	0.492912	−	1.51703i
$922$	−46.5474	+	64.0671i	−1.53296	+	2.10994i
$923$			24.6758i			0.812215i
$924$		0			0
$925$	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	−0.801394	−	0.598137i	$-0.795908\pi$
$929$	−14.6355	+	10.6333i	−0.480175	+	0.348868i	0.321218	+	0.947005i	$0.395908\pi$
$930$	−2.36116	−	4.36325i	−0.0774256	−	0.143077i
$931$	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
$935$		0			0
$936$	3.37495			0.110314
$937$	−6.47128	+	8.90696i	−0.211408	+	0.290978i	−0.901531	−	0.432714i	$-0.857556\pi$
$937$	−6.47128	+	8.90696i	−0.211408	+	0.290978i	0.690124	+	0.723691i	$0.257556\pi$
$938$	−17.8461	−	5.79856i	−0.582697	−	0.189330i
$939$	−4.14216	−	12.7483i	−0.135174	−	0.416023i
$940$	−17.8183	+	9.64236i	−0.581170	+	0.314499i
$941$	27.3293	−	19.8559i	0.890908	−	0.647283i	−0.0452063	−	0.998978i	$-0.514395\pi$
$941$	27.3293	−	19.8559i	0.890908	−	0.647283i	0.936115	+	0.351695i	$0.114395\pi$
$942$	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
$946$		0			0
$947$		−	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
$950$	33.1233	−	1.64311i	1.07466	−	0.0533096i
$951$	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	−0.878718	−	0.477341i	$-0.841600\pi$
$953$	−40.4110	+	13.1303i	−1.30904	+	0.425333i	−0.430323	+	0.902675i	$0.641600\pi$
$954$	6.43506	−	19.8051i	0.208343	−	0.641213i
$955$	33.6290	−	35.3385i	1.08821	−	1.14353i
$956$	−42.7180			−1.38160
$957$		0			0
$958$			42.4291i			1.37082i
$959$	−6.63443	−	4.82019i	−0.214237	−	0.155652i
$960$	−22.1216	+	46.2125i	−0.713970	+	1.49150i
$961$	−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
$965$	−21.7027	+	45.3376i	−0.698636	+	1.45947i
$966$	13.9498	+	10.1351i	0.448826	+	0.326091i
$967$		−	54.1642i		−	1.74180i	−0.491458	−	0.870901i	$-0.663536\pi$
$967$		−	54.1642i		−	1.74180i	0.491458	−	0.870901i	$-0.336464\pi$
$968$		0			0
$969$	−28.6596			−0.920680
$970$	9.41838	−	9.89717i	0.302406	−	0.317779i
$971$	1.61878	−	4.98209i	0.0519491	−	0.159883i	−0.921716	−	0.387865i	$-0.873213\pi$
$971$	1.61878	−	4.98209i	0.0519491	−	0.159883i	0.973665	+	0.227982i	$0.0732127\pi$
$972$	−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
$975$	−2.93763	−	59.2194i	−0.0940794	−	1.89654i
$976$	−2.90169	+	8.93049i	−0.0928809	+	0.285858i
$977$	−4.57381	+	6.29530i	−0.146329	+	0.201405i	−0.875890	−	0.482512i	$-0.839725\pi$
$977$	−4.57381	+	6.29530i	−0.146329	+	0.201405i	0.729561	+	0.683916i	$0.239725\pi$
$978$		−	87.8938i		−	2.81053i
$979$		0			0
$980$	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	$-0.293129\pi$
$983$	48.9924	−	15.9186i	1.56261	−	0.507724i	0.957504	+	0.288419i	$0.0931295\pi$
$984$	2.36547	−	1.71861i	0.0754083	−	0.0547873i
$985$	50.6354	−	27.4012i	1.61338	−	0.873075i
$986$	−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
$990$		0			0
$991$	−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
$995$	18.0566	+	33.3673i	0.572434	+	1.05781i
$996$	−32.8522	+	23.8686i	−1.04096	+	0.756304i
$997$	0.175514	−	0.0570278i	0.00555857	−	0.00180609i	−0.306236	−	0.951955i	$-0.599070\pi$
$997$	0.175514	−	0.0570278i	0.00555857	−	0.00180609i	0.311795	+	0.950149i	$0.399070\pi$
$998$	−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	605.2.j.d.444.4		16
5.4	even	2	inner	605.2.j.d.444.1		16
11.2	odd	10		605.2.j.h.269.4		16
11.3	even	5	inner	605.2.j.d.124.1		16
11.4	even	5		605.2.j.g.9.4		16
11.5	even	5		605.2.b.f.364.8		8
11.6	odd	10		605.2.b.g.364.1		8
11.7	odd	10		605.2.j.h.9.1		16
11.8	odd	10		55.2.j.a.14.4	yes	16
11.9	even	5		605.2.j.g.269.1		16
11.10	odd	2		55.2.j.a.4.1	✓	16
33.8	even	10		495.2.ba.a.289.1		16
33.32	even	2		495.2.ba.a.334.4		16
44.19	even	10		880.2.cd.c.289.4		16
44.43	even	2		880.2.cd.c.609.1		16
55.4	even	10		605.2.j.g.9.1		16
55.8	even	20		275.2.h.d.201.4		16
55.9	even	10		605.2.j.g.269.4		16
55.14	even	10	inner	605.2.j.d.124.4		16
55.17	even	20		3025.2.a.bl.1.8		8
55.19	odd	10		55.2.j.a.14.1	yes	16
55.24	odd	10		605.2.j.h.269.1		16
55.27	odd	20		3025.2.a.bk.1.1		8
55.28	even	20		3025.2.a.bl.1.1		8
55.29	odd	10		605.2.j.h.9.4		16
55.32	even	4		275.2.h.d.26.1		16
55.38	odd	20		3025.2.a.bk.1.8		8
55.39	odd	10		605.2.b.g.364.8		8
55.43	even	4		275.2.h.d.26.4		16
55.49	even	10		605.2.b.f.364.1		8
55.52	even	20		275.2.h.d.201.1		16
55.54	odd	2		55.2.j.a.4.4	yes	16
165.74	even	10		495.2.ba.a.289.4		16
165.164	even	2		495.2.ba.a.334.1		16
220.19	even	10		880.2.cd.c.289.1		16
220.219	even	2		880.2.cd.c.609.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	11.10	odd	2
55.2.j.a.4.4	yes	16	55.54	odd	2
55.2.j.a.14.1	yes	16	55.19	odd	10
55.2.j.a.14.4	yes	16	11.8	odd	10
275.2.h.d.26.1		16	55.32	even	4
275.2.h.d.26.4		16	55.43	even	4
275.2.h.d.201.1		16	55.52	even	20
275.2.h.d.201.4		16	55.8	even	20
495.2.ba.a.289.1		16	33.8	even	10
495.2.ba.a.289.4		16	165.74	even	10
495.2.ba.a.334.1		16	165.164	even	2
495.2.ba.a.334.4		16	33.32	even	2
605.2.b.f.364.1		8	55.49	even	10
605.2.b.f.364.8		8	11.5	even	5
605.2.b.g.364.1		8	11.6	odd	10
605.2.b.g.364.8		8	55.39	odd	10
605.2.j.d.124.1		16	11.3	even	5	inner
605.2.j.d.124.4		16	55.14	even	10	inner
605.2.j.d.444.1		16	5.4	even	2	inner
605.2.j.d.444.4		16	1.1	even	1	trivial
605.2.j.g.9.1		16	55.4	even	10
605.2.j.g.9.4		16	11.4	even	5
605.2.j.g.269.1		16	11.9	even	5
605.2.j.g.269.4		16	55.9	even	10
605.2.j.h.9.1		16	11.7	odd	10
605.2.j.h.9.4		16	55.29	odd	10
605.2.j.h.269.1		16	55.24	odd	10
605.2.j.h.269.4		16	11.2	odd	10
880.2.cd.c.289.1		16	220.19	even	10
880.2.cd.c.289.4		16	44.19	even	10
880.2.cd.c.609.1		16	44.43	even	2
880.2.cd.c.609.4		16	220.219	even	2
3025.2.a.bk.1.1		8	55.27	odd	20
3025.2.a.bk.1.8		8	55.38	odd	20
3025.2.a.bl.1.1		8	55.28	even	20
3025.2.a.bl.1.8		8	55.17	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18949 - 1.63719i) q^{2} +(2.49233 + 0.809808i) q^{3} +(-0.647481 - 1.99274i) q^{4} +(-1.06421 - 1.96658i) q^{5} +(4.29042 - 3.11717i) q^{6} +(0.918552 - 0.298456i) q^{7} +(-0.183406 - 0.0595923i) q^{8} +(3.12889 + 2.27327i) q^{9} +O(q^{10})\)	\(q+(1.18949 - 1.63719i) q^{2} +(2.49233 + 0.809808i) q^{3} +(-0.647481 - 1.99274i) q^{4} +(-1.06421 - 1.96658i) 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} -5.49092i q^{12} +(-2.65978 + 3.66088i) q^{13} +(0.603980 - 1.85886i) q^{14} +(-1.05982 - 5.76319i) 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} +(-3.22984 + 3.39403i) q^{20} +2.53103 q^{21} +3.36643i q^{23} +(-0.408851 - 0.297048i) q^{24} +(-2.73490 + 4.18573i) 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} +(-10.6961 - 5.12014i) q^{30} +(0.338464 + 0.245909i) q^{31} -8.07636i q^{32} -6.75241 q^{34} +(-1.56447 - 1.48879i) 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} +(0.0779900 + 0.424103i) q^{40} +(-1.78786 + 5.50247i) q^{41} +(3.01064 - 4.14379i) q^{42} -2.26205i q^{43} +(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} +(3.59970 + 9.45645i) q^{50} +(-2.70208 - 8.31615i) q^{51} +(9.01735 + 2.92991i) q^{52} +(1.56392 - 2.15255i) q^{53} +4.60066 q^{54} -0.186254 q^{56} +(5.04863 - 6.94884i) q^{57} +(9.45574 + 3.07235i) q^{58} +(3.12889 + 9.62972i) q^{59} +(-10.7983 + 5.84350i) 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} -9.60059i q^{67} +(-4.10941 + 5.65612i) q^{68} +(-2.72616 + 8.39026i) q^{69} +(-4.29836 + 0.790444i) 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} +(-10.2059 + 8.21748i) q^{75} -6.86752 q^{76} +23.9977i q^{78} +(-0.812218 - 0.590111i) q^{79} +(-7.66487 - 3.66911i) 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} +(-3.22148 + 6.72976i) q^{85} +(-3.70342 - 2.69069i) q^{86} +12.8750i q^{87} +12.1964 q^{89} +(-12.6778 - 12.0645i) 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} +(-7.20805 + 1.32552i) q^{95} +(6.54030 - 20.1290i) q^{96} +(-1.77467 + 2.44262i) q^{97} +12.2781i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^9	\( 16 q - 4 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{9} - 12 q^{14} - 16 q^{15} + 16 q^{16} - 6 q^{19} - 8 q^{20} - 8 q^{21} - 6 q^{24} - 16 q^{25} + 40 q^{26} - 2 q^{29} - 26 q^{30} + 8 q^{31} - 16 q^{34} - 22 q^{35} + 10 q^{36} - 30 q^{39} - 12 q^{40} + 52 q^{41} + 12 q^{45} + 62 q^{46} - 10 q^{49} - 28 q^{50} + 42 q^{51} + 40 q^{54} - 20 q^{56} + 2 q^{59} - 32 q^{60} + 40 q^{61} - 8 q^{64} + 40 q^{65} + 26 q^{69} - 34 q^{70} + 36 q^{71} - 48 q^{74} - 20 q^{75} - 56 q^{76} - 38 q^{79} + 34 q^{80} + 68 q^{81} - 12 q^{84} - 58 q^{85} + 22 q^{86} + 24 q^{89} - 78 q^{90} - 20 q^{91} - 14 q^{94} - 48 q^{95} + 86 q^{96}+O(q^{100}) \) 16 * q - 4 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^9 - 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 + 12 * q^45 + 62 * q^46 - 10 * q^49 - 28 * q^50 + 42 * q^51 + 40 * q^54 - 20 * q^56 + 2 * q^59 - 32 * q^60 + 40 * q^61 - 8 * q^64 + 40 * q^65 + 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more