LMFDB - Embedded newform 322.2.g.a.45.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(45,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("322.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.g (of order $6$, degree $2$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 $ x^16 + 18x^14 + 226x^12 + 1434x^10 + 6585x^8 + 14406x^6 + 22423x^4 + 8085*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.8
Root			$-1.21724 - 2.10833i$ of defining polynomial
Character	$\chi$	$=$	322.45
Dual form			322.2.g.a.229.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(2.81338 + 1.62431i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55135 + 2.68702i) q^{5} -3.24861i q^{6} +(-0.334108 - 2.62457i) q^{7} +1.00000 q^{8} +(3.77674 + 6.54151i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(2.81338 + 1.62431i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55135 + 2.68702i) q^{5} -3.24861i q^{6} +(-0.334108 - 2.62457i) q^{7} +1.00000 q^{8} +(3.77674 + 6.54151i) q^{9} +(1.55135 - 2.68702i) q^{10} +(-4.07503 - 2.35272i) q^{11} +(-2.81338 + 1.62431i) q^{12} -3.22606i q^{13} +(-2.10589 + 1.60163i) q^{14} +10.0795i q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.465345 - 0.806002i) q^{17} +(3.77674 - 6.54151i) q^{18} +(1.55135 + 2.68702i) q^{19} -3.10270 q^{20} +(3.32313 - 7.92661i) q^{21} +4.70544i q^{22} +(-3.61167 + 3.15529i) q^{23} +(2.81338 + 1.62431i) q^{24} +(-2.31338 + 4.00689i) q^{25} +(-2.79385 + 1.61303i) q^{26} +14.7925i q^{27} +(2.44000 + 1.02294i) q^{28} +1.03907 q^{29} +(8.72909 - 5.03974i) q^{30} +(-8.51685 - 4.91721i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-7.64308 - 13.2382i) q^{33} -0.930691 q^{34} +(6.53395 - 4.96939i) q^{35} -7.55349 q^{36} +(9.60671 - 5.54644i) q^{37} +(1.55135 - 2.68702i) q^{38} +(5.24011 - 9.07613i) q^{39} +(1.55135 + 2.68702i) q^{40} -3.22606i q^{41} +(-8.52622 + 1.08539i) q^{42} +0.943407i q^{43} +(4.07503 - 2.35272i) q^{44} +(-11.7181 + 20.2964i) q^{45} +(4.53839 + 1.55015i) q^{46} +(4.29385 - 2.47905i) q^{47} -3.24861i q^{48} +(-6.77674 + 1.75378i) q^{49} +4.62676 q^{50} +(2.61839 - 1.51173i) q^{51} +(2.79385 + 1.61303i) q^{52} +(6.11070 + 3.52801i) q^{53} +(12.8107 - 7.39626i) q^{54} -14.5996i q^{55} +(-0.334108 - 2.62457i) q^{56} +10.0795i q^{57} +(-0.519534 - 0.899859i) q^{58} +(0.109914 + 0.0634586i) q^{59} +(-8.72909 - 5.03974i) q^{60} +(-2.63736 - 4.56804i) q^{61} +9.83441i q^{62} +(15.9068 - 12.0979i) q^{63} +1.00000 q^{64} +(8.66848 - 5.00475i) q^{65} +(-7.64308 + 13.2382i) q^{66} +(-0.0606084 - 0.0349923i) q^{67} +(0.465345 + 0.806002i) q^{68} +(-15.2862 + 3.01057i) q^{69} +(-7.57059 - 3.17388i) q^{70} -5.66583 q^{71} +(3.77674 + 6.54151i) q^{72} +(-8.51685 - 4.91721i) q^{73} +(-9.60671 - 5.54644i) q^{74} +(-13.0168 + 7.51528i) q^{75} -3.10270 q^{76} +(-4.81338 + 11.4813i) q^{77} -10.4802 q^{78} +(-1.39604 + 0.806002i) q^{79} +(1.55135 - 2.68702i) q^{80} +(-12.6974 + 21.9925i) q^{81} +(-2.79385 + 1.61303i) q^{82} -1.34746 q^{83} +(5.20308 + 6.84123i) q^{84} +2.88766 q^{85} +(0.817014 - 0.471703i) q^{86} +(2.92330 + 1.68777i) q^{87} +(-4.07503 - 2.35272i) q^{88} +(6.59871 + 11.4293i) q^{89} +23.4362 q^{90} +(-8.46702 + 1.07785i) q^{91} +(-0.926724 - 4.70544i) q^{92} +(-15.9741 - 27.6679i) q^{93} +(-4.29385 - 2.47905i) q^{94} +(-4.81338 + 8.33702i) q^{95} +(-2.81338 + 1.62431i) q^{96} -7.02996 q^{97} +(4.90719 + 4.99194i) q^{98} -35.5425i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	2.81338	+	1.62431i	1.62431	+	0.937794i	0.985750	+	0.168219i	$0.0538017\pi$
$3$	2.81338	+	1.62431i	1.62431	+	0.937794i	0.638557	+	0.769575i	$0.279532\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.55135	+	2.68702i	0.693785	+	1.20167i	0.970588	+	0.240745i	$0.0773917\pi$
$5$	1.55135	+	2.68702i	0.693785	+	1.20167i	−0.276803	+	0.960927i	$0.589275\pi$
$6$		−	3.24861i		−	1.32624i
$7$	−0.334108	−	2.62457i	−0.126281	−	0.991995i
$7$	−0.334108	−	2.62457i	−0.126281	−	0.991995i
$8$	1.00000			0.353553
$9$	3.77674	+	6.54151i	1.25891	+	2.18050i
$10$	1.55135	−	2.68702i	0.490580	−	0.849710i
$11$	−4.07503	−	2.35272i	−1.22867	−	0.709372i	−0.261917	−	0.965090i	$-0.584355\pi$
$11$	−4.07503	−	2.35272i	−1.22867	−	0.709372i	−0.966751	+	0.255718i	$0.917688\pi$
$12$	−2.81338	+	1.62431i	−0.812153	+	0.468897i
$13$		−	3.22606i		−	0.894747i	−0.894347	−	0.447374i	$-0.852359\pi$
$13$		−	3.22606i		−	0.894747i	0.894347	−	0.447374i	$-0.147641\pi$
$14$	−2.10589	+	1.60163i	−0.562823	+	0.428054i
$15$			10.0795i			2.60251i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.465345	−	0.806002i	0.112863	−	0.195484i	−0.804061	−	0.594547i	$-0.797331\pi$
$17$	0.465345	−	0.806002i	0.112863	−	0.195484i	0.916923	+	0.399063i	$0.130665\pi$
$18$	3.77674	−	6.54151i	0.890187	−	1.54185i
$19$	1.55135	+	2.68702i	0.355904	+	0.616444i	0.987272	−	0.159039i	$-0.0508395\pi$
$19$	1.55135	+	2.68702i	0.355904	+	0.616444i	−0.631368	+	0.775483i	$0.717506\pi$
$20$	−3.10270			−0.693785
$21$	3.32313	−	7.92661i	0.725167	−	1.72973i
$22$			4.70544i			1.00320i
$23$	−3.61167	+	3.15529i	−0.753085	+	0.657923i
$23$	−3.61167	+	3.15529i	−0.753085	+	0.657923i
$24$	2.81338	+	1.62431i	0.574279	+	0.331560i
$25$	−2.31338	+	4.00689i	−0.462676	+	0.801379i
$26$	−2.79385	+	1.61303i	−0.547919	+	0.316341i
$27$			14.7925i			2.84682i
$28$	2.44000	+	1.02294i	0.461116	+	0.193317i
$29$	1.03907			0.192950			0.0964751	−	0.995335i	$-0.469243\pi$
$29$	1.03907			0.192950			0.0964751	+	0.995335i	$0.469243\pi$
$30$	8.72909	−	5.03974i	1.59371	−	0.920126i
$31$	−8.51685	−	4.91721i	−1.52967	−	0.883156i	−0.999375	−	0.0353436i	$-0.988747\pi$
$31$	−8.51685	−	4.91721i	−1.52967	−	0.883156i	−0.530296	−	0.847813i	$-0.677919\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−7.64308	−	13.2382i	−1.33049	−	2.30448i
$34$	−0.930691			−0.159612
$35$	6.53395	−	4.96939i	1.10444	−	0.839980i
$36$	−7.55349			−1.25891
$37$	9.60671	−	5.54644i	1.57933	−	0.911828i	0.584381	−	0.811480i	$-0.301337\pi$
$37$	9.60671	−	5.54644i	1.57933	−	0.911828i	0.994952	−	0.100349i	$-0.0319959\pi$
$38$	1.55135	−	2.68702i	0.251662	−	0.435892i
$39$	5.24011	−	9.07613i	0.839088	−	1.45334i
$40$	1.55135	+	2.68702i	0.245290	+	0.424855i
$41$		−	3.22606i		−	0.503825i	−0.967750	−	0.251913i	$-0.918940\pi$
$41$		−	3.22606i		−	0.503825i	0.967750	−	0.251913i	$-0.0810596\pi$
$42$	−8.52622	+	1.08539i	−1.31562	+	0.167479i
$43$			0.943407i			0.143868i	0.997409	+	0.0719341i	$0.0229171\pi$
$43$			0.943407i			0.143868i	−0.997409	+	0.0719341i	$0.977083\pi$
$44$	4.07503	−	2.35272i	0.614334	−	0.354686i
$45$	−11.7181	+	20.2964i	−1.74683	+	3.02560i
$46$	4.53839	+	1.55015i	0.669150	+	0.228558i
$47$	4.29385	−	2.47905i	0.626322	−	0.361607i	−0.153004	−	0.988226i	$-0.548895\pi$
$47$	4.29385	−	2.47905i	0.626322	−	0.361607i	0.779326	+	0.626618i	$0.215561\pi$
$48$		−	3.24861i		−	0.468897i
$49$	−6.77674	+	1.75378i	−0.968106	+	0.250540i
$50$	4.62676			0.654323
$51$	2.61839	−	1.51173i	0.366648	−	0.211684i
$52$	2.79385	+	1.61303i	0.387437	+	0.223687i
$53$	6.11070	+	3.52801i	0.839369	+	0.484610i	0.857050	−	0.515234i	$-0.172295\pi$
$53$	6.11070	+	3.52801i	0.839369	+	0.484610i	−0.0176807	+	0.999844i	$0.505628\pi$
$54$	12.8107	−	7.39626i	1.74332	−	1.00650i
$55$		−	14.5996i		−	1.96861i
$56$	−0.334108	−	2.62457i	−0.0446471	−	0.350723i
$57$			10.0795i			1.33506i
$58$	−0.519534	−	0.899859i	−0.0682182	−	0.118157i
$59$	0.109914	+	0.0634586i	0.0143095	+	0.00826161i	0.507138	−	0.861865i	$-0.330704\pi$
$59$	0.109914	+	0.0634586i	0.0143095	+	0.00826161i	−0.492828	+	0.870127i	$0.664037\pi$
$60$	−8.72909	−	5.03974i	−1.12692	−	0.650628i
$61$	−2.63736	−	4.56804i	−0.337679	−	0.584877i	0.646317	−	0.763069i	$-0.276308\pi$
$61$	−2.63736	−	4.56804i	−0.337679	−	0.584877i	−0.983996	+	0.178192i	$0.942975\pi$
$62$			9.83441i			1.24897i
$63$	15.9068	−	12.0979i	2.00407	−	1.52419i
$64$	1.00000			0.125000
$65$	8.66848	−	5.00475i	1.07519	−	0.620763i
$66$	−7.64308	+	13.2382i	−0.940798	+	1.62951i
$67$	−0.0606084	−	0.0349923i	−0.00740450	−	0.00427499i	0.496293	−	0.868155i	$-0.334694\pi$
$67$	−0.0606084	−	0.0349923i	−0.00740450	−	0.00427499i	−0.503698	+	0.863880i	$0.668027\pi$
$68$	0.465345	+	0.806002i	0.0564314	+	0.0977421i
$69$	−15.2862	+	3.01057i	−1.84024	+	0.362430i
$70$	−7.57059	−	3.17388i	−0.904859	−	0.379351i
$71$	−5.66583			−0.672410			−0.336205	−	0.941789i	$-0.609144\pi$
$71$	−5.66583			−0.672410			−0.336205	+	0.941789i	$0.609144\pi$
$72$	3.77674	+	6.54151i	0.445094	+	0.770925i
$73$	−8.51685	−	4.91721i	−0.996822	−	0.575515i	−0.0895154	−	0.995985i	$-0.528532\pi$
$73$	−8.51685	−	4.91721i	−0.996822	−	0.575515i	−0.907306	+	0.420470i	$0.861865\pi$
$74$	−9.60671	−	5.54644i	−1.11676	−	0.644760i
$75$	−13.0168	+	7.51528i	−1.50306	+	0.867790i
$76$	−3.10270			−0.355904
$77$	−4.81338	+	11.4813i	−0.548536	+	1.30841i
$78$	−10.4802			−1.18665
$79$	−1.39604	+	0.806002i	−0.157066	+	0.0906823i	−0.576473	−	0.817116i	$-0.695571\pi$
$79$	−1.39604	+	0.806002i	−0.157066	+	0.0906823i	0.419407	+	0.907798i	$0.362238\pi$
$80$	1.55135	−	2.68702i	0.173446	−	0.300418i
$81$	−12.6974	+	21.9925i	−1.41082	+	2.44361i
$82$	−2.79385	+	1.61303i	−0.308529	+	0.178129i
$83$	−1.34746			−0.147903			−0.0739513	−	0.997262i	$-0.523561\pi$
$83$	−1.34746			−0.147903			−0.0739513	+	0.997262i	$0.523561\pi$
$84$	5.20308	+	6.84123i	0.567703	+	0.746439i
$85$	2.88766			0.313210
$86$	0.817014	−	0.471703i	0.0881009	−	0.0508651i
$87$	2.92330	+	1.68777i	0.313410	+	0.180947i
$88$	−4.07503	−	2.35272i	−0.434400	−	0.250801i
$89$	6.59871	+	11.4293i	0.699462	+	1.21150i	0.968653	+	0.248417i	$0.0799104\pi$
$89$	6.59871	+	11.4293i	0.699462	+	1.21150i	−0.269191	+	0.963087i	$0.586756\pi$
$90$	23.4362			2.47039
$91$	−8.46702	+	1.07785i	−0.887584	+	0.112990i
$92$	−0.926724	−	4.70544i	−0.0966177	−	0.490576i
$93$	−15.9741	−	27.6679i	−1.65644	−	2.86903i
$94$	−4.29385	−	2.47905i	−0.442877	−	0.255695i
$95$	−4.81338	+	8.33702i	−0.493843	+	0.855360i
$96$	−2.81338	+	1.62431i	−0.287140	+	0.165780i
$97$	−7.02996			−0.713784			−0.356892	−	0.934146i	$-0.616164\pi$
$97$	−7.02996			−0.713784			−0.356892	+	0.934146i	$0.616164\pi$
$98$	4.90719	+	4.99194i	0.495701	+	0.504262i
$99$		−	35.5425i		−	3.57216i
$100$	−2.31338	−	4.00689i	−0.231338	−	0.400689i
$101$	11.4401	+	6.60497i	1.13834	+	0.657219i	0.946018	−	0.324113i	$-0.105066\pi$
$101$	11.4401	+	6.60497i	1.13834	+	0.657219i	0.192319	+	0.981333i	$0.438399\pi$
$102$	−2.61839	−	1.51173i	−0.259259	−	0.149683i
$103$	−0.113676	−	0.196893i	−0.0112009	−	0.0194005i	0.860371	−	0.509669i	$-0.170232\pi$
$103$	−0.113676	−	0.196893i	−0.0112009	−	0.0194005i	−0.871572	+	0.490268i	$0.836899\pi$
$104$		−	3.22606i		−	0.316341i
$105$	26.4543	−	3.36764i	2.58168	−	0.328648i
$106$		−	7.05603i		−	0.685342i
$107$	−3.77643	+	2.18032i	−0.365081	+	0.210780i	−0.671307	−	0.741179i	$-0.734267\pi$
$107$	−3.77643	+	2.18032i	−0.365081	+	0.210780i	0.306226	+	0.951959i	$0.400934\pi$
$108$	−12.8107	−	7.39626i	−1.23271	−	0.711705i
$109$	−4.89205	−	2.82442i	−0.468573	−	0.270531i	0.247069	−	0.968998i	$-0.420533\pi$
$109$	−4.89205	−	2.82442i	−0.468573	−	0.270531i	−0.715642	+	0.698467i	$0.753866\pi$
$110$	−12.6436	+	7.29979i	−1.20552	+	0.696008i
$111$	36.0364			3.42043
$112$	−2.10589	+	1.60163i	−0.198988	+	0.151340i
$113$			10.4033i			0.978658i	0.872099	+	0.489329i	$0.162758\pi$
$113$			10.4033i			0.978658i	−0.872099	+	0.489329i	$0.837242\pi$
$114$	8.72909	−	5.03974i	0.817554	−	0.472015i
$115$	−14.0813	−	4.80967i	−1.31309	−	0.448504i
$116$	−0.519534	+	0.899859i	−0.0482375	+	0.0835498i
$117$	21.1033	−	12.1840i	1.95100	−	1.12641i
$118$		−	0.126917i		−	0.0116837i
$119$	−2.27088	−	0.952040i	−0.208172	−	0.0872734i
$120$			10.0795i			0.920126i
$121$	5.57059	+	9.64855i	0.506417	+	0.877141i
$122$	−2.63736	+	4.56804i	−0.238775	+	0.413571i
$123$	5.24011	−	9.07613i	0.472484	−	0.818367i
$124$	8.51685	−	4.91721i	0.764836	−	0.441578i
$125$	1.15804			0.103579
$126$	−18.4305	−	7.72676i	−1.64192	−	0.688354i
$127$	−5.96093			−0.528947			−0.264474	−	0.964393i	$-0.585198\pi$
$127$	−5.96093			−0.528947			−0.264474	+	0.964393i	$0.585198\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.53238	+	2.65416i	−0.134919	+	0.233686i
$130$	−8.66848	−	5.00475i	−0.760276	−	0.438945i
$131$	−8.59355	+	4.96149i	−0.750822	+	0.433487i	−0.825991	−	0.563683i	$-0.809384\pi$
$131$	−8.59355	+	4.96149i	−0.750822	+	0.433487i	0.0751686	+	0.997171i	$0.476050\pi$
$132$	15.2862			1.33049
$133$	6.53395	−	4.96939i	0.566566	−	0.430900i
$134$			0.0699846i			0.00604575i
$135$	−39.7478	+	22.9484i	−3.42094	+	1.97508i
$136$	0.465345	−	0.806002i	0.0399030	−	0.0691141i
$137$	−0.877623	−	0.506696i	−0.0749804	−	0.0432899i	0.462041	−	0.886859i	$-0.347117\pi$
$137$	−0.877623	−	0.506696i	−0.0749804	−	0.0432899i	−0.537021	+	0.843569i	$0.680451\pi$
$138$	10.2503	+	11.7329i	0.872564	+	0.998772i
$139$			7.73063i			0.655704i	0.944729	+	0.327852i	$0.106325\pi$
$139$			7.73063i			0.655704i	−0.944729	+	0.327852i	$0.893675\pi$
$140$	1.03664	+	8.14326i	0.0876119	+	0.688231i
$141$	16.1070			1.35645
$142$	2.83292	+	4.90675i	0.237733	+	0.411766i
$143$	−7.59001	+	13.1463i	−0.634709	+	1.09935i
$144$	3.77674	−	6.54151i	0.314729	−	0.545126i
$145$	1.61196	+	2.79200i	0.133866	+	0.231863i
$146$			9.83441i			0.813902i
$147$	−21.9142	−	6.07346i	−1.80746	−	0.500930i
$148$			11.0929i			0.911828i
$149$	−8.15006	+	4.70544i	−0.667679	+	0.385485i	−0.795197	−	0.606352i	$-0.792632\pi$
$149$	−8.15006	+	4.70544i	−0.667679	+	0.385485i	0.127517	+	0.991836i	$0.459299\pi$
$150$	13.0168	+	7.51528i	1.06282	+	0.613620i
$151$	5.05349	−	8.75290i	0.411247	−	0.712301i	−0.583779	−	0.811912i	$-0.698427\pi$
$151$	5.05349	−	8.75290i	0.411247	−	0.712301i	0.995026	+	0.0996117i	$0.0317600\pi$
$152$	1.55135	+	2.68702i	0.125831	+	0.217946i
$153$	7.02996			0.568339
$154$	12.3498	−	1.57213i	0.995172	−	0.126686i
$155$		−	30.5133i		−	2.45088i
$156$	5.24011	+	9.07613i	0.419544	+	0.726672i
$157$	11.1922	−	19.3854i	0.893231	−	1.54712i	0.0572532	−	0.998360i	$-0.481766\pi$
$157$	11.1922	−	19.3854i	0.893231	−	1.54712i	0.835978	−	0.548763i	$-0.184901\pi$
$158$	1.39604	+	0.806002i	0.111063	+	0.0641221i
$159$	11.4612	+	19.8513i	0.908928	+	1.57431i
$160$	−3.10270			−0.245290
$161$	9.48796	+	8.42488i	0.747756	+	0.663973i
$162$	25.3947			1.99520
$163$	5.77674	+	10.0056i	0.452469	+	0.783700i	0.998539	−	0.0540399i	$-0.0172098\pi$
$163$	5.77674	+	10.0056i	0.452469	+	0.783700i	−0.546069	+	0.837740i	$0.683876\pi$
$164$	2.79385	+	1.61303i	0.218163	+	0.125956i
$165$	23.7142	−	41.0742i	1.84615	−	3.19762i
$166$	0.673729	+	1.16693i	0.0522915	+	0.0905715i
$167$			3.07824i			0.238201i	0.992882	+	0.119101i	$0.0380011\pi$
$167$			3.07824i			0.238201i	−0.992882	+	0.119101i	$0.961999\pi$
$168$	3.32313	−	7.92661i	0.256385	−	0.611551i
$169$	2.59256			0.199427
$170$	−1.44383	−	2.50078i	−0.110737	−	0.191801i
$171$	−11.7181	+	20.2964i	−0.896106	+	1.55210i
$172$	−0.817014	−	0.471703i	−0.0622968	−	0.0359670i
$173$	15.6768	−	9.05102i	1.19189	−	0.688136i	0.233152	−	0.972440i	$-0.425096\pi$
$173$	15.6768	−	9.05102i	1.19189	−	0.688136i	0.958734	+	0.284304i	$0.0917625\pi$
$174$		−	3.37553i		−	0.255898i
$175$	11.2893	+	4.73290i	0.853391	+	0.357773i
$176$			4.70544i			0.354686i
$177$	0.206153	+	0.357067i	0.0154954	+	0.0268388i
$178$	6.59871	−	11.4293i	0.494594	−	0.856663i
$179$	1.27674	−	2.21138i	0.0954283	−	0.165287i	−0.814359	−	0.580361i	$-0.802911\pi$
$179$	1.27674	−	2.21138i	0.0954283	−	0.165287i	0.909787	+	0.415075i	$0.136245\pi$
$180$	−11.7181	−	20.2964i	−0.873417	−	1.51280i
$181$	−16.4063			−1.21947			−0.609734	−	0.792606i	$-0.708724\pi$
$181$	−16.4063			−1.21947			−0.609734	+	0.792606i	$0.708724\pi$
$182$	5.16695	+	6.79372i	0.383000	+	0.503584i
$183$		−	17.1355i		−	1.26669i
$184$	−3.61167	+	3.15529i	−0.266256	+	0.232611i
$185$	29.8068	+	17.2089i	2.19144	+	1.26523i
$186$	−15.9741	+	27.6679i	−1.17128	+	2.02871i
$187$	−3.79259	+	2.18966i	−0.277342	+	0.160123i
$188$			4.95811i			0.361607i
$189$	38.8240	−	4.94230i	2.82403	−	0.359499i
$190$	9.62676			0.698399
$191$	5.23308	−	3.02132i	0.378652	−	0.218615i	−0.298580	−	0.954385i	$-0.596513\pi$
$191$	5.23308	−	3.02132i	0.378652	−	0.218615i	0.677232	+	0.735770i	$0.263179\pi$
$192$	2.81338	+	1.62431i	0.203038	+	0.117224i
$193$	−0.409620	+	0.709483i	−0.0294851	+	0.0510697i	−0.880391	−	0.474248i	$-0.842720\pi$
$193$	−0.409620	+	0.709483i	−0.0294851	+	0.0510697i	0.850906	+	0.525317i	$0.176053\pi$
$194$	3.51498	+	6.08812i	0.252361	+	0.437102i
$195$	32.5170			2.32859
$196$	1.86955	−	6.74572i	0.133540	−	0.481837i
$197$	−10.9536			−0.780409			−0.390205	−	0.920728i	$-0.627596\pi$
$197$	−10.9536			−0.780409			−0.390205	+	0.920728i	$0.627596\pi$
$198$	−30.7807	+	17.7712i	−2.18749	+	1.26295i
$199$	3.12167	−	5.40689i	0.221289	−	0.383285i	−0.733910	−	0.679246i	$-0.762307\pi$
$199$	3.12167	−	5.40689i	0.221289	−	0.383285i	0.955200	+	0.295962i	$0.0956401\pi$
$200$	−2.31338	+	4.00689i	−0.163581	+	0.283330i
$201$	−0.113676	−	0.196893i	−0.00801811	−	0.0138878i
$202$		−	13.2099i		−	0.929448i
$203$	−0.347161	−	2.72711i	−0.0243659	−	0.191405i
$204$			3.02345i			0.211684i
$205$	8.66848	−	5.00475i	0.605433	−	0.349547i
$206$	−0.113676	+	0.196893i	−0.00792021	+	0.0137182i
$207$	−34.2807	−	11.7091i	−2.38267	−	0.813837i
$208$	−2.79385	+	1.61303i	−0.193718	+	0.111843i
$209$		−	14.5996i		−	1.00987i
$210$	−16.1436	−	21.2263i	−1.11402	−	1.46475i
$211$	−7.26575			−0.500195			−0.250098	−	0.968221i	$-0.580463\pi$
$211$	−7.26575			−0.500195			−0.250098	+	0.968221i	$0.580463\pi$
$212$	−6.11070	+	3.52801i	−0.419684	+	0.242305i
$213$	−15.9401	−	9.20305i	−1.09220	−	0.630582i
$214$	3.77643	+	2.18032i	0.258152	+	0.149044i
$215$	−2.53495	+	1.46356i	−0.172882	+	0.0998136i
$216$			14.7925i			1.00650i
$217$	−10.0600	+	23.9960i	−0.682918	+	1.62895i
$218$			5.64885i			0.382588i
$219$	−15.9741	−	27.6679i	−1.07943	−	1.86963i
$220$	12.6436	+	7.29979i	0.852432	+	0.492152i
$221$	−2.60021	−	1.50123i	−0.174909	−	0.100984i
$222$	−18.0182	−	31.2085i	−1.20930	−	2.09458i
$223$			16.5020i			1.10506i	0.833494	+	0.552528i	$0.186337\pi$
$223$			16.5020i			1.10506i	−0.833494	+	0.552528i	$0.813663\pi$
$224$	2.44000	+	1.02294i	0.163029	+	0.0683480i
$225$	−34.9482			−2.32988
$226$	9.00951	−	5.20164i	0.599303	−	0.346008i
$227$	−1.02540	+	1.77604i	−0.0680580	+	0.117880i	−0.898046	−	0.439901i	$-0.855014\pi$
$227$	−1.02540	+	1.77604i	−0.0680580	+	0.117880i	0.829988	+	0.557781i	$0.188347\pi$
$228$	−8.72909	−	5.03974i	−0.578098	−	0.333765i
$229$	7.23080	+	12.5241i	0.477825	+	0.827617i	0.999677	−	0.0254191i	$-0.00809201\pi$
$229$	7.23080	+	12.5241i	0.477825	+	0.827617i	−0.521852	+	0.853036i	$0.674759\pi$
$230$	2.87535	+	14.5996i	0.189595	+	0.962668i
$231$	−32.1910	+	24.4828i	−2.11801	+	1.61085i
$232$	1.03907			0.0682182
$233$	6.58670	+	11.4085i	0.431509	+	0.747395i	0.997003	−	0.0773568i	$-0.0246481\pi$
$233$	6.58670	+	11.4085i	0.431509	+	0.747395i	−0.565495	+	0.824752i	$0.691315\pi$
$234$	−21.1033	−	12.1840i	−1.37957	−	0.796492i
$235$	13.3225	+	7.69177i	0.869066	+	0.501756i
$236$	−0.109914	+	0.0634586i	−0.00715477	+	0.00413081i
$237$	−5.23678			−0.340165
$238$	0.310951	+	2.44266i	0.0201560	+	0.158334i
$239$	25.1016			1.62369			0.811844	−	0.583874i	$-0.198464\pi$
$239$	25.1016			1.62369			0.811844	+	0.583874i	$0.198464\pi$
$240$	8.72909	−	5.03974i	0.563460	−	0.325314i
$241$	−10.3525	+	17.9310i	−0.666862	+	1.15504i	0.311916	+	0.950110i	$0.399029\pi$
$241$	−10.3525	+	17.9310i	−0.666862	+	1.15504i	−0.978777	+	0.204928i	$0.934304\pi$
$242$	5.57059	−	9.64855i	0.358091	−	0.620232i
$243$	−33.0129	+	19.0600i	−2.11778	+	1.22270i
$244$	5.27471			0.337679
$245$	−15.2256	−	15.4885i	−0.972725	−	0.989525i
$246$	−10.4802			−0.668194
$247$	8.66848	−	5.00475i	0.551562	−	0.318444i
$248$	−8.51685	−	4.91721i	−0.540820	−	0.312243i
$249$	−3.79091	−	2.18868i	−0.240239	−	0.138702i
$250$	−0.579022	−	1.00290i	−0.0366205	−	0.0634286i
$251$	−17.3900			−1.09765			−0.548823	−	0.835939i	$-0.684924\pi$
$251$	−17.3900			−1.09765			−0.548823	+	0.835939i	$0.684924\pi$
$252$	2.52368	+	19.8247i	0.158977	+	1.24884i
$253$	22.1412	−	4.36065i	1.39200	−	0.274152i
$254$	2.98047	+	5.16232i	0.187011	+	0.323913i
$255$	8.12408	+	4.69044i	0.508750	+	0.293727i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.2301	+	9.37043i	−1.01240	+	0.584511i	−0.911894	−	0.410425i	$-0.865380\pi$
$257$	−16.2301	+	9.37043i	−1.01240	+	0.584511i	−0.100509	+	0.994936i	$0.532047\pi$
$258$	3.06476			0.190804
$259$	−17.7667	−	23.3604i	−1.10397	−	1.45154i
$260$			10.0095i			0.620763i
$261$	3.92429	+	6.79708i	0.242908	+	0.420728i
$262$	8.59355	+	4.96149i	0.530912	+	0.306522i
$263$	−14.2608	−	8.23345i	−0.879356	−	0.507697i	−0.00891017	−	0.999960i	$-0.502836\pi$
$263$	−14.2608	−	8.23345i	−0.879356	−	0.507697i	−0.870446	+	0.492264i	$0.836170\pi$
$264$	−7.64308	−	13.2382i	−0.470399	−	0.814755i
$265$			21.8928i			1.34486i
$266$	−7.57059	−	3.17388i	−0.464183	−	0.194603i
$267$			42.8733i			2.62381i
$268$	0.0606084	−	0.0349923i	0.00370225	−	0.00213749i
$269$	−19.0168	−	10.9794i	−1.15948	−	0.669425i	−0.208299	−	0.978065i	$-0.566793\pi$
$269$	−19.0168	−	10.9794i	−1.15948	−	0.669425i	−0.951179	+	0.308640i	$0.900126\pi$
$270$	39.7478	+	22.9484i	2.41897	+	1.39659i
$271$	20.0532	−	11.5777i	1.21815	−	0.703298i	0.253626	−	0.967302i	$-0.418377\pi$
$271$	20.0532	−	11.5777i	1.21815	−	0.703298i	0.964521	+	0.264005i	$0.0850435\pi$
$272$	−0.930691			−0.0564314
$273$	−25.5717	−	10.7206i	−1.54767	−	0.648841i
$274$			1.01339i			0.0612212i
$275$	18.8542	−	10.8855i	1.13695	−	0.656419i
$276$	5.03585	−	14.7435i	0.303123	−	0.887454i
$277$	−15.3874	+	26.6518i	−0.924539	+	1.60135i	−0.132239	+	0.991218i	$0.542217\pi$
$277$	−15.3874	+	26.6518i	−0.924539	+	1.60135i	−0.792300	+	0.610131i	$0.791117\pi$
$278$	6.69492	−	3.86532i	0.401535	−	0.231826i
$279$		−	74.2841i		−	4.44727i
$280$	6.53395	−	4.96939i	0.390478	−	0.296978i
$281$		−	17.0698i		−	1.01830i	−0.860678	−	0.509149i	$-0.829960\pi$
$281$		−	17.0698i		−	1.01830i	0.860678	−	0.509149i	$-0.170040\pi$
$282$	−8.05349	−	13.9490i	−0.479578	−	0.830654i
$283$	−0.484315	+	0.838858i	−0.0287895	+	0.0498649i	−0.880061	−	0.474860i	$-0.842499\pi$
$283$	−0.484315	+	0.838858i	−0.0287895	+	0.0498649i	0.851272	+	0.524725i	$0.175832\pi$
$284$	2.83292	−	4.90675i	0.168103	−	0.291162i
$285$	−27.0838	+	15.6368i	−1.60430	+	0.926245i
$286$	15.1800			0.897614
$287$	−8.46702	+	1.07785i	−0.499792	+	0.0636236i
$288$	−7.55349			−0.445094
$289$	8.06691	+	13.9723i	0.474524	+	0.821900i
$290$	1.61196	−	2.79200i	0.0946575	−	0.163952i
$291$	−19.7780	−	11.4188i	−1.15940	−	0.669382i
$292$	8.51685	−	4.91721i	0.498411	−	0.287758i
$293$	−17.0414			−0.995570			−0.497785	−	0.867301i	$-0.665853\pi$
$293$	−17.0414			−0.995570			−0.497785	+	0.867301i	$0.665853\pi$
$294$	5.69735	+	22.0150i	0.332276	+	1.28394i
$295$			0.393787i			0.0229271i
$296$	9.60671	−	5.54644i	0.558379	−	0.322380i
$297$	34.8027	−	60.2800i	2.01946	−	3.49780i
$298$	8.15006	+	4.70544i	0.472121	+	0.272579i
$299$	10.1791	+	11.6515i	0.588675	+	0.673821i
$300$		−	15.0306i		−	0.867790i
$301$	2.47604	−	0.315200i	0.142716	−	0.0181678i
$302$	−10.1070			−0.581591
$303$	21.4570	+	37.1646i	1.23267	+	2.13505i
$304$	1.55135	−	2.68702i	0.0889761	−	0.154111i
$305$	8.18293	−	14.1733i	0.468553	−	0.811558i
$306$	−3.51498	−	6.08812i	−0.200938	−	0.348035i
$307$			1.94919i			0.111246i	0.998452	+	0.0556231i	$0.0177145\pi$
$307$			1.94919i			0.111246i	−0.998452	+	0.0556231i	$0.982285\pi$
$308$	−7.53638	−	9.90915i	−0.429425	−	0.564626i
$309$		−	0.738581i		−	0.0420164i
$310$	−26.4253	+	15.2566i	−1.50085	+	0.866518i
$311$	3.54032	+	2.04401i	0.200753	+	0.115905i	0.597007	−	0.802236i	$-0.296357\pi$
$311$	3.54032	+	2.04401i	0.200753	+	0.115905i	−0.396254	+	0.918141i	$0.629690\pi$
$312$	5.24011	−	9.07613i	0.296663	−	0.513835i
$313$	3.35966	+	5.81911i	0.189899	+	0.328916i	0.945217	−	0.326444i	$-0.105850\pi$
$313$	3.35966	+	5.81911i	0.189899	+	0.328916i	−0.755317	+	0.655360i	$0.772517\pi$
$314$	−22.3843			−1.26322
$315$	57.1844	+	23.9738i	3.22197	+	1.35077i
$316$		−	1.61200i		−	0.0906823i
$317$	9.99120	+	17.3053i	0.561162	+	0.971961i	0.997395	+	0.0721273i	$0.0229788\pi$
$317$	9.99120	+	17.3053i	0.561162	+	0.971961i	−0.436234	+	0.899833i	$0.643688\pi$
$318$	11.4612	−	19.8513i	0.642709	−	1.11321i
$319$	−4.23424	−	2.44464i	−0.237072	−	0.136873i
$320$	1.55135	+	2.68702i	0.0867232	+	0.150209i
$321$	−14.1661			−0.790672
$322$	2.55218	−	12.4293i	0.142227	−	0.692655i
$323$	2.88766			0.160673
$324$	−12.6974	−	21.9925i	−0.705409	−	1.22180i
$325$	12.9265	+	7.46310i	0.717032	+	0.413978i
$326$	5.77674	−	10.0056i	0.319944	−	0.554160i
$327$	−9.17546	−	15.8924i	−0.507404	−	0.878850i
$328$		−	3.22606i		−	0.178129i
$329$	−7.94106	−	10.4412i	−0.437805	−	0.575644i
$330$	−47.4284			−2.61085
$331$	−10.1864	−	17.6433i	−0.559893	−	0.969763i	−0.997505	−	0.0705994i	$-0.977509\pi$
$331$	−10.1864	−	17.6433i	−0.559893	−	0.969763i	0.437612	−	0.899164i	$-0.355825\pi$
$332$	0.673729	−	1.16693i	0.0369757	−	0.0640437i
$333$	72.5642	+	41.8949i	3.97649	+	2.29583i
$334$	2.66583	−	1.53912i	0.145868	−	0.0842168i
$335$		−	0.217141i		−	0.0118637i
$336$	−8.52622	+	1.08539i	−0.465143	+	0.0592128i
$337$			20.0890i			1.09432i	0.837029	+	0.547158i	$0.184290\pi$
$337$			20.0890i			1.09432i	−0.837029	+	0.547158i	$0.815710\pi$
$338$	−1.29628	−	2.24522i	−0.0705082	−	0.122124i
$339$	−16.8981	+	29.2684i	−0.917780	+	1.58964i
$340$	−1.44383	+	2.50078i	−0.0783026	+	0.135624i
$341$	23.1376	+	40.0755i	1.25297	+	2.17021i
$342$	23.4362			1.26729
$343$	6.86709	+	17.2001i	0.370788	+	0.928718i
$344$			0.943407i			0.0508651i
$345$	−31.8037	−	36.4038i	−1.71225	−	1.95991i
$346$	−15.6768	−	9.05102i	−0.842791	−	0.486586i
$347$	−6.94257	+	12.0249i	−0.372697	+	0.645530i	−0.989979	−	0.141212i	$-0.954900\pi$
$347$	−6.94257	+	12.0249i	−0.372697	+	0.645530i	0.617283	+	0.786742i	$0.288234\pi$
$348$	−2.92330	+	1.68777i	−0.156705	+	0.0904737i
$349$			20.1833i			1.08038i	0.841542	+	0.540192i	$0.181649\pi$
$349$			20.1833i			1.08038i	−0.841542	+	0.540192i	$0.818351\pi$
$350$	−1.54584	−	12.1433i	−0.0826286	−	0.649085i
$351$	47.7215			2.54719
$352$	4.07503	−	2.35272i	0.217200	−	0.125400i
$353$	−4.57228	−	2.63981i	−0.243358	−	0.140503i	0.373361	−	0.927686i	$-0.378205\pi$
$353$	−4.57228	−	2.63981i	−0.243358	−	0.140503i	−0.616719	+	0.787183i	$0.711539\pi$
$354$	0.206153	−	0.357067i	0.0109569	−	0.0189779i
$355$	−8.78969	−	15.2242i	−0.466509	−	0.808016i
$356$	−13.1974			−0.699462
$357$	−4.84246	−	6.36706i	−0.256290	−	0.336981i
$358$	−2.55349			−0.134956
$359$	−2.79577	+	1.61414i	−0.147555	+	0.0851910i	−0.571960	−	0.820282i	$-0.693817\pi$
$359$	−2.79577	+	1.61414i	−0.147555	+	0.0851910i	0.424405	+	0.905473i	$0.360483\pi$
$360$	−11.7181	+	20.2964i	−0.617599	+	1.06971i
$361$	4.68662	−	8.11746i	0.246664	−	0.427235i
$362$	8.20313	+	14.2082i	0.431147	+	0.746769i
$363$			36.1934i			1.89966i
$364$	3.30006	−	7.87158i	0.172970	−	0.412583i
$365$		−	30.5133i		−	1.59714i
$366$	−14.8398	+	8.56775i	−0.775688	+	0.447844i
$367$	11.5097	−	19.9354i	0.600803	−	1.04062i	−0.391897	−	0.920009i	$-0.628181\pi$
$367$	11.5097	−	19.9354i	0.600803	−	1.04062i	0.992700	−	0.120612i	$-0.0384857\pi$
$368$	4.53839	+	1.55015i	0.236580	+	0.0808074i
$369$	21.1033	−	12.1840i	1.09859	−	0.634273i
$370$		−	34.4179i		−	1.78930i
$371$	7.21789	−	17.2167i	0.374734	−	0.893846i
$372$	31.9482			1.65644
$373$	21.6500	−	12.4996i	1.12099	−	0.647206i	0.179339	−	0.983787i	$-0.442604\pi$
$373$	21.6500	−	12.4996i	1.12099	−	0.647206i	0.941654	+	0.336581i	$0.109271\pi$
$374$	3.79259	+	2.18966i	0.196110	+	0.113224i
$375$	3.25802	+	1.88102i	0.168243	+	0.0971353i
$376$	4.29385	−	2.47905i	0.221438	−	0.127847i
$377$		−	3.35209i		−	0.172642i
$378$	−23.6922	−	31.1514i	−1.21859	−	1.60226i
$379$		−	28.1584i		−	1.44640i	−0.690639	−	0.723200i	$-0.742671\pi$
$379$		−	28.1584i		−	1.44640i	0.690639	−	0.723200i	$-0.257329\pi$
$380$	−4.81338	−	8.33702i	−0.246921	−	0.427680i
$381$	−16.7704	−	9.68238i	−0.859172	−	0.496043i
$382$	−5.23308	−	3.02132i	−0.267747	−	0.154584i
$383$	10.7874	+	18.6844i	0.551211	+	0.954726i	0.998188	+	0.0601804i	$0.0191676\pi$
$383$	10.7874	+	18.6844i	0.551211	+	0.954726i	−0.446976	+	0.894546i	$0.647499\pi$
$384$		−	3.24861i		−	0.165780i
$385$	−38.3176	+	4.87784i	−1.95285	+	0.248598i
$386$	0.819241			0.0416983
$387$	−6.17131	+	3.56301i	−0.313705	+	0.181118i
$388$	3.51498	−	6.08812i	0.178446	−	0.309078i
$389$	17.4619	+	10.0816i	0.885352	+	0.511158i	0.872419	−	0.488758i	$-0.162550\pi$
$389$	17.4619	+	10.0816i	0.885352	+	0.511158i	0.0129327	+	0.999916i	$0.495883\pi$
$390$	−16.2585	−	28.1605i	−0.823281	−	1.42596i
$391$	0.862494	+	4.37931i	0.0436182	+	0.221471i
$392$	−6.77674	+	1.75378i	−0.342277	+	0.0885793i
$393$	−32.2359			−1.62609
$394$	5.47678	+	9.48607i	0.275916	+	0.477901i
$395$	−4.33148	−	2.50078i	−0.217941	−	0.125828i
$396$	30.7807	+	17.7712i	1.54679	+	0.893039i
$397$	−11.7504	+	6.78407i	−0.589733	+	0.340483i	−0.764992	−	0.644040i	$-0.777257\pi$
$397$	−11.7504	+	6.78407i	−0.589733	+	0.340483i	0.175259	+	0.984522i	$0.443924\pi$
$398$	−6.24334			−0.312951
$399$	26.4543	−	3.36764i	1.32437	−	0.168593i
$400$	4.62676			0.231338
$401$	23.8069	−	13.7449i	1.18886	−	0.686387i	0.230811	−	0.972999i	$-0.425862\pi$
$401$	23.8069	−	13.7449i	1.18886	−	0.686387i	0.958047	+	0.286611i	$0.0925288\pi$
$402$	−0.113676	+	0.196893i	−0.00566966	+	0.00982014i
$403$	−15.8632	+	27.4758i	−0.790202	+	1.36867i
$404$	−11.4401	+	6.60497i	−0.569168	+	0.328610i
$405$	−78.7922			−3.91522
$406$	−2.18816	+	1.66420i	−0.108597	+	0.0825931i
$407$	−52.1969			−2.58730
$408$	2.61839	−	1.51173i	0.129630	−	0.0748416i
$409$	16.4277	+	9.48455i	0.812299	+	0.468981i	0.847753	−	0.530390i	$-0.177955\pi$
$409$	16.4277	+	9.48455i	0.812299	+	0.468981i	−0.0354549	+	0.999371i	$0.511288\pi$
$410$	−8.66848	−	5.00475i	−0.428106	−	0.247167i
$411$	−1.64606	−	2.85106i	−0.0811941	−	0.140632i
$412$	0.227353			0.0112009
$413$	0.129829	−	0.309678i	0.00638845	−	0.0152383i
$414$	7.00000	+	35.5425i	0.344031	+	1.74682i
$415$	−2.09038	−	3.62064i	−0.102613	−	0.177730i
$416$	2.79385	+	1.61303i	0.136980	+	0.0790852i
$417$	−12.5569	+	21.7492i	−0.614915	+	1.06506i
$418$	−12.6436	+	7.29979i	−0.618419	+	0.357045i
$419$	18.6542			0.911315			0.455658	−	0.890155i	$-0.349404\pi$
$419$	18.6542			0.911315			0.455658	+	0.890155i	$0.349404\pi$
$420$	−10.3107	+	24.5939i	−0.503110	+	1.20006i
$421$		−	9.45988i		−	0.461046i	−0.973067	−	0.230523i	$-0.925956\pi$
$421$		−	9.45988i		−	0.461046i	0.973067	−	0.230523i	$-0.0740437\pi$
$422$	3.63288	+	6.29233i	0.176846	+	0.306306i
$423$	32.4335	+	18.7255i	1.57697	+	0.910465i
$424$	6.11070	+	3.52801i	0.296762	+	0.171335i
$425$	2.15304	+	3.72918i	0.104438	+	0.180892i
$426$			18.4061i			0.891778i
$427$	−11.1080	+	8.44815i	−0.537553	+	0.408835i
$428$		−	4.36065i		−	0.210780i
$429$	−42.7072	+	24.6570i	−2.06192	+	1.19045i
$430$	2.53495	+	1.46356i	0.122246	+	0.0705789i
$431$	21.5150	+	12.4217i	1.03634	+	0.598332i	0.918795	−	0.394735i	$-0.129164\pi$
$431$	21.5150	+	12.4217i	1.03634	+	0.598332i	0.117547	+	0.993067i	$0.462497\pi$
$432$	12.8107	−	7.39626i	0.616355	−	0.355853i
$433$	−10.4433			−0.501873			−0.250936	−	0.968004i	$-0.580738\pi$
$433$	−10.4433			−0.501873			−0.250936	+	0.968004i	$0.580738\pi$
$434$	25.8111	−	3.28576i	1.23897	−	0.157721i
$435$			10.4733i			0.502155i
$436$	4.89205	−	2.82442i	0.234287	−	0.135265i
$437$	−14.0813	−	4.80967i	−0.673599	−	0.230078i
$438$	−15.9741	+	27.6679i	−0.763272	+	1.32203i
$439$	−5.77431	+	3.33380i	−0.275593	+	0.159114i	−0.631427	−	0.775436i	$-0.717530\pi$
$439$	−5.77431	+	3.33380i	−0.275593	+	0.159114i	0.355834	+	0.934549i	$0.384197\pi$
$440$		−	14.5996i		−	0.696008i
$441$	−37.0664	−	37.7066i	−1.76507	−	1.79555i
$442$			3.00246i			0.142813i
$443$	4.21957	+	7.30851i	0.200478	+	0.347238i	0.948683	−	0.316230i	$-0.102417\pi$
$443$	4.21957	+	7.30851i	0.200478	+	0.347238i	−0.748205	+	0.663468i	$0.769084\pi$
$444$	−18.0182	+	31.2085i	−0.855107	+	1.48109i
$445$	−20.4738	+	35.4617i	−0.970553	+	1.68105i
$446$	14.2912	−	8.25101i	0.676706	−	0.390696i
$447$	−30.5723			−1.44602
$448$	−0.334108	−	2.62457i	−0.0157851	−	0.123999i
$449$	−1.33217			−0.0628690			−0.0314345	−	0.999506i	$-0.510008\pi$
$449$	−1.33217			−0.0628690			−0.0314345	+	0.999506i	$0.510008\pi$
$450$	17.4741	+	30.2660i	0.823737	+	1.42675i
$451$	−7.59001	+	13.1463i	−0.357400	+	0.619034i
$452$	−9.00951	−	5.20164i	−0.423772	−	0.244665i
$453$	28.4348	−	16.4168i	1.33598	−	0.771330i
$454$	2.05080			0.0962486
$455$	−16.0315	−	21.0789i	−0.751569	−	0.988194i
$456$			10.0795i			0.472015i
$457$	26.4216	−	15.2545i	1.23595	−	0.713575i	0.267685	−	0.963507i	$-0.413742\pi$
$457$	26.4216	−	15.2545i	1.23595	−	0.713575i	0.968263	+	0.249932i	$0.0804082\pi$
$458$	7.23080	−	12.5241i	0.337873	−	0.585214i
$459$	11.9228	+	6.88363i	0.556508	+	0.321300i
$460$	11.2059	−	9.78992i	0.522480	−	0.456457i
$461$		−	33.1586i		−	1.54435i	−0.635410	−	0.772175i	$-0.719169\pi$
$461$		−	33.1586i		−	1.54435i	0.635410	−	0.772175i	$-0.280831\pi$
$462$	37.2982	+	15.6368i	1.73527	+	0.727490i
$463$	−13.9556			−0.648570			−0.324285	−	0.945959i	$-0.605124\pi$
$463$	−13.9556			−0.648570			−0.324285	+	0.945959i	$0.605124\pi$
$464$	−0.519534	−	0.899859i	−0.0241188	−	0.0417749i
$465$	49.5629	−	85.8454i	2.29842	−	3.98099i
$466$	6.58670	−	11.4085i	0.305123	−	0.528488i
$467$	0.703338	+	1.21822i	0.0325466	+	0.0563724i	0.881840	−	0.471549i	$-0.156305\pi$
$467$	0.703338	+	1.21822i	0.0325466	+	0.0563724i	−0.849293	+	0.527921i	$0.822972\pi$
$468$			24.3680i			1.12641i
$469$	−0.0715900	+	0.170762i	−0.00330572	+	0.00788507i
$470$		−	15.3835i		−	0.709590i
$471$	62.9756	−	36.3590i	2.90176	−	1.67533i
$472$	0.109914	+	0.0634586i	0.00505918	+	0.00292092i
$473$	2.21957	−	3.84441i	0.102056	−	0.176766i
$474$	2.61839	+	4.53518i	0.120267	+	0.208308i
$475$	−14.3555			−0.658674
$476$	1.95993	−	1.49062i	0.0898334	−	0.0683226i
$477$			53.2976i			2.44033i
$478$	−12.5508	−	21.7386i	−0.574060	−	0.994302i
$479$	6.46237	−	11.1931i	0.295273	−	0.511428i	−0.679775	−	0.733420i	$-0.737923\pi$
$479$	6.46237	−	11.1931i	0.295273	−	0.511428i	0.975048	+	0.221992i	$0.0712560\pi$
$480$	−8.72909	−	5.03974i	−0.398426	−	0.230032i
$481$	−17.8931	−	30.9918i	−0.815856	−	1.41310i
$482$	20.7049			0.943085
$483$	13.0087	+	39.1138i	0.591915	+	1.77974i
$484$	−11.1412			−0.506417
$485$	−10.9059	−	18.8896i	−0.495213	−	0.857734i
$486$	33.0129	+	19.0600i	1.49750	+	0.864580i
$487$	16.7694	−	29.0454i	0.759893	−	1.31617i	−0.183012	−	0.983111i	$-0.558585\pi$
$487$	16.7694	−	29.0454i	0.759893	−	1.31617i	0.942905	−	0.333063i	$-0.108082\pi$
$488$	−2.63736	−	4.56804i	−0.119388	−	0.206785i
$489$			37.5328i			1.69729i
$490$	−5.80067	+	20.9300i	−0.262047	+	0.945520i
$491$	29.8359			1.34647			0.673237	−	0.739427i	$-0.264904\pi$
$491$	29.8359			1.34647			0.673237	+	0.739427i	$0.264904\pi$
$492$	5.24011	+	9.07613i	0.236242	+	0.409184i
$493$	0.483525	−	0.837491i	0.0217769	−	0.0377187i
$494$	−8.66848	−	5.00475i	−0.390013	−	0.225174i
$495$	95.5034	−	55.1389i	4.29256	−	2.47831i
$496$			9.83441i			0.441578i
$497$	1.89300	+	14.8704i	0.0849126	+	0.667027i
$498$			4.37737i			0.196155i
$499$	−6.64018	−	11.5011i	−0.297255	−	0.514861i	0.678252	−	0.734830i	$-0.262738\pi$
$499$	−6.64018	−	11.5011i	−0.297255	−	0.514861i	−0.975507	+	0.219968i	$0.929405\pi$
$500$	−0.579022	+	1.00290i	−0.0258946	+	0.0448508i
$501$	−5.00000	+	8.66025i	−0.223384	+	0.386912i
$502$	8.69499	+	15.0602i	0.388076	+	0.672168i
$503$	−29.8310			−1.33010			−0.665050	−	0.746799i	$-0.731590\pi$
$503$	−29.8310			−1.33010			−0.665050	+	0.746799i	$0.731590\pi$
$504$	15.9068	−	12.0979i	0.708546	−	0.538883i
$505$			40.9865i			1.82388i
$506$	−14.8470	−	16.9945i	−0.660031	−	0.755498i
$507$	7.29385	+	4.21110i	0.323931	+	0.187022i
$508$	2.98047	−	5.16232i	0.132237	−	0.229041i
$509$	−14.9680	+	8.64177i	−0.663444	+	0.383040i	−0.793588	−	0.608455i	$-0.791789\pi$
$509$	−14.9680	+	8.64177i	−0.663444	+	0.383040i	0.130144	+	0.991495i	$0.458456\pi$
$510$		−	9.38088i		−	0.415392i
$511$	−10.0600	+	23.9960i	−0.445028	+	1.06152i
$512$	1.00000			0.0441942
$513$	−39.7478	+	22.9484i	−1.75491	+	1.01320i
$514$	16.2301	+	9.37043i	0.715877	+	0.413312i
$515$	0.352704	−	0.610901i	0.0155420	−	0.0269195i
$516$	−1.53238	−	2.65416i	−0.0674593	−	0.116843i
$517$	−23.3301			−1.02606
$518$	−11.3473	+	27.0666i	−0.498573	+	1.18924i
$519$	58.8065			2.58132
$520$	8.66848	−	5.00475i	0.380138	−	0.219473i
$521$	−10.3631	+	17.9494i	−0.454016	+	0.786379i	−0.998631	−	0.0523071i	$-0.983343\pi$
$521$	−10.3631	+	17.9494i	−0.454016	+	0.786379i	0.544615	+	0.838686i	$0.316676\pi$
$522$	3.92429	−	6.79708i	0.171762	−	0.297500i
$523$	−22.7019	−	39.3208i	−0.992684	−	1.71938i	−0.600906	−	0.799320i	$-0.705193\pi$
$523$	−22.7019	−	39.3208i	−0.992684	−	1.71938i	−0.391779	−	0.920060i	$-0.628140\pi$
$524$		−	9.92298i		−	0.433487i
$525$	24.0734	+	31.6527i	1.05065	+	1.38144i
$526$			16.4669i			0.717991i
$527$	−7.92655	+	4.57640i	−0.345286	+	0.199351i
$528$	−7.64308	+	13.2382i	−0.332622	+	0.576119i
$529$	3.08832	−	22.7917i	0.134275	−	0.990944i
$530$	18.9597	−	10.9464i	0.823556	−	0.475480i
$531$			0.958668i			0.0416027i
$532$	1.03664	+	8.14326i	0.0449440	+	0.353055i
$533$	−10.4074			−0.450796
$534$	37.1294	−	21.4367i	1.60675	−	0.927655i
$535$	−11.7171	−	6.76490i	−0.506576	−	0.292472i
$536$	−0.0606084	−	0.0349923i	−0.00261788	−	0.00151144i
$537$	7.18393	−	4.14765i	0.310010	−	0.178984i
$538$			21.9588i			0.946710i
$539$	31.7416	+	8.79707i	1.36721	+	0.378917i
$540$		−	45.8968i		−	1.97508i
$541$	−9.86344	−	17.0840i	−0.424062	−	0.734498i	0.572270	−	0.820065i	$-0.306063\pi$
$541$	−9.86344	−	17.0840i	−0.424062	−	0.734498i	−0.996332	+	0.0855677i	$0.972730\pi$
$542$	−20.0532	−	11.5777i	−0.861360	−	0.497306i
$543$	−46.1571	−	26.6488i	−1.98079	−	1.14361i
$544$	0.465345	+	0.806002i	0.0199515	+	0.0345570i
$545$		−	17.5267i		−	0.750761i
$546$	3.50152	+	27.5061i	0.149851	+	1.17715i
$547$	19.4631			0.832183			0.416092	−	0.909323i	$-0.363400\pi$
$547$	19.4631			0.832183			0.416092	+	0.909323i	$0.363400\pi$
$548$	0.877623	−	0.506696i	0.0374902	−	0.0216450i
$549$	19.9212	−	34.5046i	0.850218	−	1.47262i
$550$	−18.8542	−	10.8855i	−0.803946	−	0.464159i
$551$	1.61196	+	2.79200i	0.0686718	+	0.118943i
$552$	−15.2862	+	3.01057i	−0.650622	+	0.128138i
$553$	2.58184	+	3.39470i	0.109791	+	0.144357i
$554$	30.7748			1.30750
$555$	55.9052	+	96.8306i	2.37304	+	4.11023i
$556$	−6.69492	−	3.86532i	−0.283928	−	0.163926i
$557$	−34.7308	−	20.0518i	−1.47159	−	0.849624i	−0.472102	−	0.881544i	$-0.656504\pi$
$557$	−34.7308	−	20.0518i	−1.47159	−	0.849624i	−0.999490	+	0.0319201i	$0.989838\pi$
$558$	−64.3319	+	37.1420i	−2.72339	+	1.57235i
$559$	3.04348			0.128726
$560$	−7.57059	−	3.17388i	−0.319916	−	0.134121i
$561$	−14.2267			−0.600651
$562$	−14.7829	+	8.53490i	−0.623578	+	0.360023i
$563$	−11.9265	+	20.6573i	−0.502642	+	0.870601i	0.497353	+	0.867548i	$0.334305\pi$
$563$	−11.9265	+	20.6573i	−0.502642	+	0.870601i	−0.999995	+	0.00305324i	$0.999028\pi$
$564$	−8.05349	+	13.9490i	−0.339113	+	0.587361i
$565$	−27.9538	+	16.1391i	−1.17603	+	0.678979i
$566$	0.968630			0.0407145
$567$	61.9631	+	25.9772i	2.60220	+	1.09094i
$568$	−5.66583			−0.237733
$569$	−30.9726	+	17.8820i	−1.29844	+	0.749653i	−0.980134	−	0.198336i	$-0.936446\pi$
$569$	−30.9726	+	17.8820i	−1.29844	+	0.749653i	−0.318303	+	0.947989i	$0.603113\pi$
$570$	27.0838	+	15.6368i	1.13441	+	0.654954i
$571$	35.9107	+	20.7331i	1.50282	+	0.867652i	0.999995	+	0.00326291i	$0.00103862\pi$
$571$	35.9107	+	20.7331i	1.50282	+	0.867652i	0.502823	+	0.864389i	$0.332295\pi$
$572$	−7.59001	−	13.1463i	−0.317354	−	0.549674i
$573$	19.6302			0.820063
$574$	5.16695	+	6.79372i	0.215665	+	0.283565i
$575$	−4.28773	−	21.7710i	−0.178811	−	0.907912i
$576$	3.77674	+	6.54151i	0.157364	+	0.272563i
$577$	17.3612	+	10.0235i	0.722758	+	0.417285i	0.815767	−	0.578381i	$-0.196315\pi$
$577$	17.3612	+	10.0235i	0.722758	+	0.417285i	−0.0930089	+	0.995665i	$0.529649\pi$
$578$	8.06691	−	13.9723i	0.335539	−	0.581171i
$579$	−2.30484	+	1.33070i	−0.0957858	+	0.0553019i
$580$	−3.22392			−0.133866
$581$	0.450196	+	3.53650i	0.0186773	+	0.146719i
$582$			22.8376i			0.946650i
$583$	−16.6009	−	28.7535i	−0.687537	−	1.19085i
$584$	−8.51685	−	4.91721i	−0.352430	−	0.203475i
$585$	65.4772	+	37.8033i	2.70715	+	1.56297i
$586$	8.52070	+	14.7583i	0.351987	+	0.609659i
$587$		−	8.10913i		−	0.334699i	−0.985898	−	0.167350i	$-0.946479\pi$
$587$		−	8.10913i		−	0.334699i	0.985898	−	0.167350i	$-0.0535209\pi$
$588$	16.2169	−	15.9416i	0.668773	−	0.657419i
$589$		−	30.5133i		−	1.25728i
$590$	0.341029	−	0.196893i	0.0140399	−	0.00810597i
$591$	−30.8166	−	17.7919i	−1.26762	−	0.731863i
$592$	−9.60671	−	5.54644i	−0.394833	−	0.227957i
$593$	−26.6773	+	15.4022i	−1.09551	+	0.632491i	−0.935037	−	0.354550i	$-0.884634\pi$
$593$	−26.6773	+	15.4022i	−1.09551	+	0.632491i	−0.160469	+	0.987041i	$0.551301\pi$
$594$	−69.6053			−2.85594
$595$	−0.964789	−	7.57886i	−0.0395525	−	0.310703i
$596$		−	9.41088i		−	0.385485i
$597$	17.5649	−	10.1411i	0.718884	−	0.415048i
$598$	5.00089	−	14.6411i	0.204501	−	0.598720i
$599$	18.4909	−	32.0273i	0.755520	−	1.30860i	−0.189596	−	0.981862i	$-0.560718\pi$
$599$	18.4909	−	32.0273i	0.755520	−	1.30860i	0.945116	−	0.326736i	$-0.105949\pi$
$600$	−13.0168	+	7.51528i	−0.531411	+	0.306810i
$601$		−	26.9636i		−	1.09987i	−0.835208	−	0.549935i	$-0.814653\pi$
$601$		−	26.9636i		−	1.09987i	0.835208	−	0.549935i	$-0.185347\pi$
$602$	−1.51099	−	1.98671i	−0.0615834	−	0.0809723i
$603$		−	0.528628i		−	0.0215274i
$604$	5.05349	+	8.75290i	0.205623	+	0.356150i
$605$	−17.2839	+	29.9366i	−0.702690	+	1.21709i
$606$	21.4570	−	37.1646i	0.871631	−	1.50971i
$607$	−30.8119	+	17.7893i	−1.25062	+	0.722043i	−0.971232	−	0.238136i	$-0.923464\pi$
$607$	−30.8119	+	17.7893i	−1.25062	+	0.722043i	−0.279384	+	0.960179i	$0.590130\pi$
$608$	−3.10270			−0.125831
$609$	3.45296	−	8.23629i	0.139921	−	0.333751i
$610$	−16.3659			−0.662635
$611$	−7.99757	−	13.8522i	−0.323547	−	0.560400i
$612$	−3.51498	+	6.08812i	−0.142085	+	0.246098i
$613$	−8.48739	−	4.90020i	−0.342803	−	0.197917i	0.318708	−	0.947853i	$-0.396751\pi$
$613$	−8.48739	−	4.90020i	−0.342803	−	0.197917i	−0.661511	+	0.749936i	$0.730084\pi$
$614$	1.68805	−	0.974596i	0.0681241	−	0.0393315i
$615$	32.5170			1.31121
$616$	−4.81338	+	11.4813i	−0.193937	+	0.462594i
$617$		−	29.4350i		−	1.18501i	−0.805567	−	0.592504i	$-0.798139\pi$
$617$		−	29.4350i		−	1.18501i	0.805567	−	0.592504i	$-0.201861\pi$
$618$	−0.639630	+	0.369291i	−0.0257297	+	0.0148550i
$619$	−16.5761	+	28.7106i	−0.666248	+	1.15398i	0.312697	+	0.949853i	$0.398767\pi$
$619$	−16.5761	+	28.7106i	−0.666248	+	1.15398i	−0.978945	+	0.204123i	$0.934566\pi$
$620$	26.4253	+	15.2566i	1.06126	+	0.612721i
$621$	−46.6747	−	53.4257i	−1.87299	−	2.14390i
$622$		−	4.08801i		−	0.163914i
$623$	27.7923	−	21.1374i	1.11348	−	0.846853i
$624$	−10.4802			−0.419544
$625$	13.3634	+	23.1462i	0.534538	+	0.925846i
$626$	3.35966	−	5.81911i	0.134279	−	0.232578i
$627$	23.7142	−	41.0742i	0.947054	−	1.64035i
$628$	11.1922	+	19.3854i	0.446616	+	0.773561i
$629$		−	10.3240i		−	0.411646i
$630$	−7.83023	−	61.5100i	−0.311964	−	2.45062i
$631$		−	10.1452i		−	0.403874i	−0.979399	−	0.201937i	$-0.935276\pi$
$631$		−	10.1452i		−	0.403874i	0.979399	−	0.201937i	$-0.0647236\pi$
$632$	−1.39604	+	0.806002i	−0.0555313	+	0.0320610i
$633$	−20.4413	−	11.8018i	−0.812470	−	0.469080i
$634$	9.99120	−	17.3053i	0.396801	−	0.687280i
$635$	−9.24750	−	16.0171i	−0.366976	−	0.635621i
$636$	−22.9223			−0.908928
$637$	5.65780	+	21.8622i	0.224170	+	0.866210i
$638$			4.88927i			0.193568i
$639$	−21.3984	−	37.0631i	−0.846507	−	1.46619i
$640$	1.55135	−	2.68702i	0.0613225	−	0.106214i
$641$	30.2623	+	17.4719i	1.19529	+	0.690100i	0.959501	−	0.281704i	$-0.0908998\pi$
$641$	30.2623	+	17.4719i	1.19529	+	0.690100i	0.235787	+	0.971805i	$0.424233\pi$
$642$	7.08303	+	12.2682i	0.279545	+	0.484186i
$643$	42.1949			1.66401			0.832003	−	0.554771i	$-0.187194\pi$
$643$	42.1949			1.66401			0.832003	+	0.554771i	$0.187194\pi$
$644$	−12.0401	+	4.00438i	−0.474448	+	0.157795i
$645$	−9.50905			−0.374418
$646$	−1.44383	−	2.50078i	−0.0568067	−	0.0983920i
$647$	−33.1663	−	19.1486i	−1.30390	−	0.752809i	−0.322832	−	0.946456i	$-0.604635\pi$
$647$	−33.1663	−	19.1486i	−1.30390	−	0.752809i	−0.981071	+	0.193648i	$0.937968\pi$
$648$	−12.6974	+	21.9925i	−0.498799	+	0.863946i
$649$	−0.298601	−	0.517192i	−0.0117211	−	0.0203016i
$650$		−	14.9262i		−	0.585454i
$651$	−67.2794	+	51.1692i	−2.63689	+	2.00548i
$652$	−11.5535			−0.452469
$653$	5.35245	+	9.27071i	0.209458	+	0.362791i	0.951544	−	0.307513i	$-0.0994969\pi$
$653$	5.35245	+	9.27071i	0.209458	+	0.362791i	−0.742086	+	0.670304i	$0.766164\pi$
$654$	−9.17546	+	15.8924i	−0.358789	+	0.621441i
$655$	−26.6632	−	15.3940i	−1.04182	−	0.601495i
$656$	−2.79385	+	1.61303i	−0.109081	+	0.0629782i
$657$		−	74.2841i		−	2.89810i
$658$	−5.07184	+	12.0978i	−0.197721	+	0.471621i
$659$		−	0.414779i		−	0.0161575i	−0.999967	−	0.00807875i	$-0.997428\pi$
$659$		−	0.414779i		−	0.0161575i	0.999967	−	0.00807875i	$-0.00257157\pi$
$660$	23.7142	+	41.0742i	0.923074	+	1.59881i
$661$	10.5494	−	18.2721i	0.410325	−	0.710704i	−0.584600	−	0.811322i	$-0.698749\pi$
$661$	10.5494	−	18.2721i	0.410325	−	0.710704i	0.994925	+	0.100618i	$0.0320819\pi$
$662$	−10.1864	+	17.6433i	−0.395904	+	0.685726i
$663$	−4.87692	−	8.44707i	−0.189404	−	0.328057i
$664$	−1.34746			−0.0522915
$665$	23.4893	+	9.84759i	0.910876	+	0.381873i
$666$		−	83.7899i		−	3.24679i
$667$	−3.75277	+	3.27856i	−0.145308	+	0.126946i
$668$	−2.66583	−	1.53912i	−0.103144	−	0.0595503i
$669$	−26.8043	+	46.4265i	−1.03632	+	1.79495i
$670$	−0.188050	+	0.108571i	−0.00726500	+	0.00419445i
$671$			24.8199i			0.958160i
$672$	5.20308	+	6.84123i	0.200713	+	0.263906i
$673$	45.4558			1.75219			0.876095	−	0.482138i	$-0.160140\pi$
$673$	45.4558			1.75219			0.876095	+	0.482138i	$0.160140\pi$
$674$	17.3976	−	10.0445i	0.670129	−	0.386899i
$675$	−59.2721	−	34.2207i	−2.28138	−	1.31716i
$676$	−1.29628	+	2.24522i	−0.0498568	+	0.0863546i
$677$	−1.96363	−	3.40110i	−0.0754684	−	0.130715i	0.825821	−	0.563932i	$-0.190712\pi$
$677$	−1.96363	−	3.40110i	−0.0754684	−	0.130715i	−0.901290	+	0.433217i	$0.857379\pi$
$678$	33.7962			1.29794
$679$	2.34877	+	18.4506i	0.0901374	+	0.708070i
$680$	2.88766			0.110737
$681$	−5.76967	+	3.33112i	−0.221094	+	0.127649i
$682$	23.1376	−	40.0755i	0.885985	−	1.53457i
$683$	−15.8947	+	27.5304i	−0.608194	+	1.05342i	0.383344	+	0.923606i	$0.374772\pi$
$683$	−15.8947	+	27.5304i	−0.608194	+	1.05342i	−0.991538	+	0.129817i	$0.958561\pi$
$684$	−11.7181	−	20.2964i	−0.448053	−	0.776051i
$685$		−	3.14425i		−	0.120136i
$686$	11.4622	−	14.5471i	0.437628	−	0.555411i
$687$			46.9802i			1.79240i
$688$	0.817014	−	0.471703i	0.0311484	−	0.0179835i
$689$	11.3816	−	19.7135i	0.433603	−	0.751023i
$690$	−15.6247	+	45.7447i	−0.594824	+	1.74147i
$691$	−0.651666	+	0.376240i	−0.0247906	+	0.0143128i	−0.512344	−	0.858780i	$-0.671223\pi$
$691$	−0.651666	+	0.376240i	−0.0247906	+	0.0143128i	0.487554	+	0.873093i	$0.337889\pi$
$692$			18.1020i			0.688136i
$693$	−93.2838	+	11.8750i	−3.54356	+	0.451095i
$694$	13.8851			0.527073
$695$	−20.7724	+	11.9929i	−0.787940	+	0.454918i
$696$	2.92330	+	1.68777i	0.110807	+	0.0639746i
$697$	−2.60021	−	1.50123i	−0.0984899	−	0.0568632i
$698$	17.4792	−	10.0916i	0.661598	−	0.381974i
$699$			42.7953i			1.61867i
$700$	−9.74346	+	7.41037i	−0.368268	+	0.280086i
$701$		−	50.4674i		−	1.90613i	−0.302771	−	0.953063i	$-0.597912\pi$
$701$		−	50.4674i		−	1.90613i	0.302771	−	0.953063i	$-0.402088\pi$
$702$	−23.8608	−	41.3280i	−0.900566	−	1.55983i
$703$	29.8068	+	17.2089i	1.12418	+	0.649047i
$704$	−4.07503	−	2.35272i	−0.153584	−	0.0886715i
$705$	24.9876	+	43.2798i	0.941087	+	1.63001i
$706$			5.27961i			0.198701i
$707$	13.5130	−	32.2322i	0.508207	−	1.21222i
$708$	−0.412305			−0.0154954
$709$	−2.83450	+	1.63650i	−0.106452	+	0.0614600i	−0.552281	−	0.833658i	$-0.686242\pi$
$709$	−2.83450	+	1.63650i	−0.106452	+	0.0614600i	0.445829	+	0.895118i	$0.352909\pi$
$710$	−8.78969	+	15.2242i	−0.329871	+	0.571354i
$711$	−10.5449	−	6.08812i	−0.395466	−	0.228322i
$712$	6.59871	+	11.4293i	0.247297	+	0.428331i
$713$	46.2752	−	9.11379i	1.73302	−	0.341314i
$714$	−3.09281	+	7.37722i	−0.115745	+	0.276086i
$715$	−47.0991			−1.76141
$716$	1.27674	+	2.21138i	0.0477141	+	0.0826433i
$717$	70.6204	+	40.7727i	2.63737	+	1.52268i
$718$	2.79577	+	1.61414i	0.104337	+	0.0602392i
$719$	−13.9709	+	8.06611i	−0.521027	+	0.300815i	−0.737355	−	0.675506i	$-0.763925\pi$
$719$	−13.9709	+	8.06611i	−0.521027	+	0.300815i	0.216328	+	0.976321i	$0.430592\pi$
$720$	23.4362			0.873417
$721$	−0.478780	+	0.364135i	−0.0178307	+	0.0135611i
$722$	−9.37324			−0.348836
$723$	−58.2509	+	33.6312i	−2.16638	+	1.25076i
$724$	8.20313	−	14.2082i	0.304867	−	0.528045i
$725$	−2.40376	+	4.16344i	−0.0892734	+	0.154626i
$726$	31.3444	−	18.0967i	1.16330	−	0.671631i
$727$	46.2373			1.71485			0.857423	−	0.514612i	$-0.172064\pi$
$727$	46.2373			1.71485			0.857423	+	0.514612i	$0.172064\pi$
$728$	−8.46702	+	1.07785i	−0.313808	+	0.0399478i
$729$	−47.6531			−1.76493
$730$	−26.4253	+	15.2566i	−0.978042	+	0.564673i
$731$	0.760387	+	0.439010i	0.0281239	+	0.0162374i
$732$	14.8398	+	8.56775i	0.548494	+	0.316673i
$733$	−19.9439	−	34.5439i	−0.736645	−	1.27591i	−0.953998	−	0.299814i	$-0.903075\pi$
$733$	−19.9439	−	34.5439i	−0.736645	−	1.27591i	0.217352	−	0.976093i	$-0.430258\pi$
$734$	−23.0195			−0.849664
$735$	−17.6772	−	68.3061i	−0.652033	−	2.51951i
$736$	−0.926724	−	4.70544i	−0.0341595	−	0.173445i
$737$	0.164654	+	0.285189i	0.00606511	+	0.0105051i
$738$	−21.1033	−	12.1840i	−0.776823	−	0.448499i
$739$	20.0129	−	34.6634i	0.736187	−	1.27511i	−0.218014	−	0.975946i	$-0.569958\pi$
$739$	20.0129	−	34.6634i	0.736187	−	1.27511i	0.954201	−	0.299167i	$-0.0967089\pi$
$740$	−29.8068	+	17.2089i	−1.09572	+	0.632613i
$741$	32.5170			1.19454
$742$	−18.5190	+	2.35748i	−0.679855	+	0.0865456i
$743$			48.3916i			1.77532i	0.460503	+	0.887658i	$0.347669\pi$
$743$			48.3916i			1.77532i	−0.460503	+	0.887658i	$0.652331\pi$
$744$	−15.9741	−	27.6679i	−0.585639	−	1.01436i
$745$	−25.2872	−	14.5996i	−0.926452	−	0.534887i
$746$	−21.6500	−	12.4996i	−0.792662	−	0.457644i
$747$	−5.08900	−	8.81441i	−0.186197	−	0.322502i
$748$		−	4.37931i		−	0.160123i
$749$	6.98415	+	9.18305i	0.255195	+	0.335541i
$750$		−	3.76203i		−	0.137370i
$751$	−24.0230	+	13.8697i	−0.876611	+	0.506111i	−0.869539	−	0.493864i	$-0.835584\pi$
$751$	−24.0230	+	13.8697i	−0.876611	+	0.506111i	−0.00707137	+	0.999975i	$0.502251\pi$
$752$	−4.29385	−	2.47905i	−0.156581	−	0.0904018i
$753$	−48.9246	−	28.2467i	−1.78291	−	1.02937i
$754$	−2.90300	+	1.67605i	−0.105721	+	0.0610380i
$755$	31.3589			1.14127
$756$	−15.1318	+	36.0937i	−0.550340	+	1.31272i
$757$			19.0317i			0.691720i	0.938286	+	0.345860i	$0.112413\pi$
$757$			19.0317i			0.691720i	−0.938286	+	0.345860i	$0.887587\pi$
$758$	−24.3859	+	14.0792i	−0.885735	+	0.511379i
$759$	69.3746	+	23.6959i	2.51814	+	0.860107i
$760$	−4.81338	+	8.33702i	−0.174600	+	0.302416i
$761$	24.2384	−	13.9940i	0.878640	−	0.507283i	0.00843014	−	0.999964i	$-0.497317\pi$
$761$	24.2384	−	13.9940i	0.878640	−	0.507283i	0.870210	+	0.492682i	$0.163983\pi$
$762$			19.3648i			0.701511i
$763$	−5.77843	+	13.7832i	−0.209193	+	0.498985i
$764$			6.04264i			0.218615i
$765$	10.9059	+	18.8896i	0.394305	+	0.682956i
$766$	10.7874	−	18.6844i	0.389765	−	0.675093i
$767$	0.204721	−	0.354588i	0.00739205	−	0.0128034i
$768$	−2.81338	+	1.62431i	−0.101519	+	0.0586121i
$769$	30.0343			1.08307			0.541533	−	0.840680i	$-0.317844\pi$
$769$	30.0343			1.08307			0.541533	+	0.840680i	$0.317844\pi$
$770$	23.3832	+	30.7451i	0.842670	+	1.10798i
$771$	−60.8818			−2.19260
$772$	−0.409620	−	0.709483i	−0.0147426	−	0.0255349i
$773$	1.35500	−	2.34692i	0.0487359	−	0.0844130i	−0.840628	−	0.541612i	$-0.817814\pi$
$773$	1.35500	−	2.34692i	0.0487359	−	0.0844130i	0.889364	+	0.457199i	$0.151147\pi$
$774$	6.17131	+	3.56301i	0.221823	+	0.128070i
$775$	39.4054	−	22.7507i	1.41549	−	0.817231i
$776$	−7.02996			−0.252361
$777$	−12.0401	−	94.5802i	−0.431935	−	3.39305i
$778$		−	20.1632i		−	0.722887i
$779$	8.66848	−	5.00475i	0.310580	−	0.179314i
$780$	−16.2585	+	28.1605i	−0.582147	+	1.00831i
$781$	23.0884	+	13.3301i	0.826169	+	0.476989i
$782$	3.36135	−	2.93660i	0.120202	−	0.105012i
$783$			15.3704i			0.549295i
$784$	4.90719	+	4.99194i	0.175257	+	0.178284i
$785$	69.4519			2.47884
$786$	16.1180	+	27.9171i	0.574909	+	0.995771i
$787$	−11.7106	+	20.2833i	−0.417437	+	0.723022i	−0.995681	−	0.0928421i	$-0.970405\pi$
$787$	−11.7106	+	20.2833i	−0.417437	+	0.723022i	0.578244	+	0.815864i	$0.303738\pi$
$788$	5.47678	−	9.48607i	0.195102	−	0.337927i
$789$	−26.7473	−	46.3277i	−0.952229	−	1.64931i
$790$			5.00157i			0.177948i
$791$	27.3042	−	3.47582i	0.970824	−	0.123586i
$792$		−	35.5425i		−	1.26295i
$793$	−14.7367	+	8.50827i	−0.523317	+	0.302137i
$794$	11.7504	+	6.78407i	0.417004	+	0.240758i
$795$	−35.5605	+	61.5927i	−1.26120	+	2.18447i
$796$	3.12167	+	5.40689i	0.110645	+	0.191642i
$797$	−28.7489			−1.01834			−0.509169	−	0.860667i	$-0.670047\pi$
$797$	−28.7489			−1.01834			−0.509169	+	0.860667i	$0.670047\pi$
$798$	−16.1436	−	21.2263i	−0.571478	−	0.751402i
$799$		−	4.61446i		−	0.163248i
$800$	−2.31338	−	4.00689i	−0.0817904	−	0.141665i
$801$	−49.8433	+	86.3311i	−1.76113	+	3.05036i
$802$	−23.8069	−	13.7449i	−0.840650	−	0.485349i
$803$	23.1376	+	40.0755i	0.816509	+	1.41424i
$804$	0.227353			0.00801811
$805$	−7.91864	+	38.5643i	−0.279095	+	1.35921i
$806$	31.7264			1.11751
$807$	−35.6678	−	61.7784i	−1.25556	−	2.17470i
$808$	11.4401	+	6.60497i	0.402463	+	0.232362i
$809$	16.6368	−	28.8157i	0.584917	−	1.01311i	−0.409969	−	0.912100i	$-0.634460\pi$
$809$	16.6368	−	28.8157i	0.584917	−	1.01311i	0.994886	−	0.101007i	$-0.0322063\pi$
$810$	39.3961	+	68.2361i	1.38424	+	2.39757i
$811$		−	26.7933i		−	0.940839i	−0.882443	−	0.470419i	$-0.844103\pi$
$811$		−	26.7933i		−	0.940839i	0.882443	−	0.470419i	$-0.155897\pi$
$812$	2.53533	+	1.06290i	0.0889725	+	0.0373006i
$813$	75.2232			2.63819
$814$	26.0984	+	45.2038i	0.914750	+	1.58439i
$815$	−17.9235	+	31.0444i	−0.627833	+	1.08744i
$816$	−2.61839	−	1.51173i	−0.0916619	−	0.0529210i
$817$	−2.53495	+	1.46356i	−0.0886867	+	0.0512033i
$818$		−	18.9691i		−	0.663239i
$819$	−39.0285	−	51.3163i	−1.36377	−	1.79314i
$820$			10.0095i			0.349547i
$821$	0.649981	+	1.12580i	0.0226845	+	0.0392907i	0.877145	−	0.480226i	$-0.159445\pi$
$821$	0.649981	+	1.12580i	0.0226845	+	0.0392907i	−0.854460	+	0.519517i	$0.826112\pi$
$822$	−1.64606	+	2.85106i	−0.0574129	+	0.0994420i
$823$	−4.01854	+	6.96031i	−0.140077	+	0.242621i	−0.927526	−	0.373760i	$-0.878068\pi$
$823$	−4.01854	+	6.96031i	−0.140077	+	0.242621i	0.787448	+	0.616381i	$0.211402\pi$
$824$	−0.113676	−	0.196893i	−0.00396010	−	0.00685910i
$825$	70.7254			2.46234
$826$	−0.333103	+	0.0424041i	−0.0115901	+	0.00147543i
$827$		−	56.3043i		−	1.95789i	−0.204115	−	0.978947i	$-0.565432\pi$
$827$		−	56.3043i		−	1.95789i	0.204115	−	0.978947i	$-0.434568\pi$
$828$	27.2807	−	23.8334i	0.948070	−	0.828269i
$829$	−0.720317	−	0.415875i	−0.0250177	−	0.0144439i	0.487439	−	0.873157i	$-0.337931\pi$
$829$	−0.720317	−	0.415875i	−0.0250177	−	0.0144439i	−0.512457	+	0.858713i	$0.671264\pi$
$830$	−2.09038	+	3.62064i	−0.0725581	+	0.125674i
$831$	−86.5813	+	49.9877i	−3.00347	+	1.73405i
$832$		−	3.22606i		−	0.111843i
$833$	−1.73998	+	6.27818i	−0.0602866	+	0.217526i
$834$	25.1138			0.869621
$835$	−8.27128	+	4.77543i	−0.286239	+	0.165260i
$836$	12.6436	+	7.29979i	0.437288	+	0.252469i
$837$	72.7379	−	125.986i	2.51419	−	4.35470i
$838$	−9.32708	−	16.1550i	−0.322199	−	0.558064i
$839$	−44.8066			−1.54689			−0.773447	−	0.633861i	$-0.781469\pi$
$839$	−44.8066			−1.54689			−0.773447	+	0.633861i	$0.781469\pi$
$840$	26.4543	−	3.36764i	0.912760	−	0.116194i
$841$	−27.9203			−0.962770
$842$	−8.19249	+	4.72994i	−0.282332	+	0.163004i
$843$	27.7266	−	48.0238i	0.954954	−	1.65403i
$844$	3.63288	−	6.29233i	0.125049	−	0.216591i
$845$	4.02196	+	6.96625i	0.138360	+	0.239646i
$846$		−	37.4510i		−	1.28759i
$847$	23.4621	−	17.8441i	0.806168	−	0.613129i
$848$		−	7.05603i		−	0.242305i
$849$	−2.72512	+	1.57335i	−0.0935260	+	0.0539973i
$850$	2.15304	−	3.72918i	0.0738487	−	0.127910i
$851$	−17.1957	+	50.3438i	−0.589460	+	1.72576i
$852$	15.9401	−	9.20305i	0.546100	−	0.315291i
$853$			46.7117i			1.59938i	0.600414	+	0.799690i	$0.295003\pi$
$853$			46.7117i			1.59938i	−0.600414	+	0.799690i	$0.704997\pi$
$854$	12.8703	+	5.39571i	0.440413	+	0.184637i
$855$	−72.7156			−2.48682
$856$	−3.77643	+	2.18032i	−0.129076	+	0.0745219i
$857$	−26.9819	−	15.5780i	−0.921684	−	0.532135i	−0.0375121	−	0.999296i	$-0.511943\pi$
$857$	−26.9819	−	15.5780i	−0.921684	−	0.532135i	−0.884172	+	0.467162i	$0.845277\pi$
$858$	42.7072	+	24.6570i	1.45800	+	0.841777i
$859$	43.3969	−	25.0552i	1.48068	−	0.854873i	0.480923	−	0.876763i	$-0.340302\pi$
$859$	43.3969	−	25.0552i	1.48068	−	0.854873i	0.999760	+	0.0218902i	$0.00696842\pi$
$860$		−	2.92711i		−	0.0998136i
$861$	−25.5717	−	10.7206i	−0.871481	−	0.365358i
$862$		−	24.8434i		−	0.846170i
$863$	7.05717	+	12.2234i	0.240229	+	0.416089i	0.960779	−	0.277314i	$-0.0894442\pi$
$863$	7.05717	+	12.2234i	0.240229	+	0.416089i	−0.720551	+	0.693402i	$0.756111\pi$
$864$	−12.8107	−	7.39626i	−0.435829	−	0.251626i
$865$	48.6405	+	28.0826i	1.65383	+	0.954837i
$866$	5.22165	+	9.04416i	0.177439	+	0.307333i
$867$			52.4125i			1.78002i
$868$	−15.7511	−	20.7102i	−0.534627	−	0.702950i
$869$	7.58519			0.257310
$870$	9.07012	−	5.23663i	0.307506	−	0.177538i
$871$	−0.112887	+	0.195526i	−0.00382503	+	0.00662515i
$872$	−4.89205	−	2.82442i	−0.165666	−	0.0956471i
$873$	−26.5504	−	45.9866i	−0.898593	−	1.55641i
$874$	2.87535	+	14.5996i	0.0972602	+	0.493838i
$875$	−0.386912	−	3.03937i	−0.0130800	−	0.102749i
$876$	31.9482			1.07943
$877$	−10.1192	−	17.5270i	−0.341702	−	0.591845i	0.643047	−	0.765827i	$-0.277670\pi$
$877$	−10.1192	−	17.5270i	−0.341702	−	0.591845i	−0.984749	+	0.173982i	$0.944337\pi$
$878$	5.77431	+	3.33380i	0.194874	+	0.112510i
$879$	−47.9440	−	27.6805i	−1.61711	−	0.933639i
$880$	−12.6436	+	7.29979i	−0.426216	+	0.246076i
$881$	−15.7711			−0.531343			−0.265671	−	0.964064i	$-0.585594\pi$
$881$	−15.7711			−0.531343			−0.265671	+	0.964064i	$0.585594\pi$
$882$	−14.1216	+	50.9537i	−0.475501	+	1.71570i
$883$	−54.7968			−1.84406			−0.922029	−	0.387120i	$-0.873470\pi$
$883$	−54.7968			−1.84406			−0.922029	+	0.387120i	$0.873470\pi$
$884$	2.60021	−	1.50123i	0.0874544	−	0.0504918i
$885$	−0.639630	+	1.10787i	−0.0215009	+	0.0372407i
$886$	4.21957	−	7.30851i	0.141759	−	0.245534i
$887$	4.24959	−	2.45350i	0.142687	−	0.0823805i	−0.426957	−	0.904272i	$-0.640414\pi$
$887$	4.24959	−	2.45350i	0.142687	−	0.0823805i	0.569644	+	0.821891i	$0.307081\pi$
$888$	36.0364			1.20930
$889$	1.99160	+	15.6449i	0.0667960	+	0.524713i
$890$	40.9477			1.37257
$891$	103.484	−	59.7467i	3.46685	−	2.00159i
$892$	−14.2912	−	8.25101i	−0.478504	−	0.276264i
$893$	13.3225	+	7.69177i	0.445822	+	0.257395i
$894$	15.2862	+	26.4764i	0.511246	+	0.885503i
$895$	7.92271			0.264827
$896$	−2.10589	+	1.60163i	−0.0703529	+	0.0535068i
$897$	9.71227	+	49.3140i	0.324283	+	1.64655i
$898$	0.666086	+	1.15369i	0.0222276	+	0.0384993i
$899$	−8.84959	−	5.10931i	−0.295150	−	0.170405i
$900$	17.4741	−	30.2660i	0.582470	−	1.00887i
$901$	5.68717	−	3.28349i	0.189467	−	0.109389i
$902$	15.1800			0.505440
$903$	7.47802	+	3.13507i	0.248853	+	0.104329i
$904$			10.4033i			0.346008i
$905$	−25.4519	−	44.0839i	−0.846049	−	1.46540i
$906$	−28.4348	−	16.4168i	−0.944682	−	0.545412i
$907$	27.2884	+	15.7550i	0.906096	+	0.523135i	0.879173	−	0.476503i	$-0.158096\pi$
$907$	27.2884	+	15.7550i	0.906096	+	0.523135i	0.0269232	+	0.999638i	$0.491429\pi$
$908$	−1.02540	−	1.77604i	−0.0340290	−	0.0589400i
$909$			99.7811i			3.30953i
$910$	−10.2391	+	24.4232i	−0.339423	+	0.809620i
$911$			20.6927i			0.685580i	0.939412	+	0.342790i	$0.111372\pi$
$911$			20.6927i			0.685580i	−0.939412	+	0.342790i	$0.888628\pi$
$912$	8.72909	−	5.03974i	0.289049	−	0.166882i
$913$	5.49093	+	3.17019i	0.181723	+	0.104918i
$914$	−26.4216	−	15.2545i	−0.873947	−	0.504574i
$915$	46.0434	−	26.5832i	1.52215	−	0.878813i
$916$	−14.4616			−0.477825
$917$	15.8930	+	20.8967i	0.524832	+	0.690070i
$918$		−	13.7673i		−	0.454387i
$919$	6.28438	−	3.62829i	0.207303	−	0.119686i	−0.392755	−	0.919643i	$-0.628478\pi$
$919$	6.28438	−	3.62829i	0.207303	−	0.119686i	0.600057	+	0.799957i	$0.295144\pi$
$920$	−14.0813	−	4.80967i	−0.464246	−	0.158570i
$921$	−3.16609	+	5.48382i	−0.104326	+	0.180698i
$922$	−28.7162	+	16.5793i	−0.945718	+	0.546010i
$923$			18.2783i			0.601637i
$924$	−5.10723	−	40.1196i	−0.168015	−	1.31984i
$925$			51.3241i			1.68753i
$926$	6.97778	+	12.0859i	0.229304	+	0.397166i
$927$	0.858653	−	1.48723i	0.0282019	−	0.0488471i
$928$	−0.519534	+	0.899859i	−0.0170545	+	0.0295393i
$929$	2.05400	−	1.18588i	0.0673894	−	0.0389073i	−0.465927	−	0.884823i	$-0.654279\pi$
$929$	2.05400	−	1.18588i	0.0673894	−	0.0389073i	0.533316	+	0.845916i	$0.320946\pi$
$930$	−99.1257			−3.25046
$931$	−15.2256	−	15.4885i	−0.498997	−	0.507615i
$932$	−13.1734			−0.431509
$933$	6.64018	+	11.5011i	0.217390	+	0.376530i
$934$	0.703338	−	1.21822i	0.0230139	−	0.0398613i
$935$	−11.7673	−	6.79385i	−0.384832	−	0.222183i
$936$	21.1033	−	12.1840i	0.689783	−	0.398246i
$937$	19.4559			0.635595			0.317797	−	0.948159i	$-0.397057\pi$
$937$	19.4559			0.635595			0.317797	+	0.948159i	$0.397057\pi$
$938$	0.183679	−	0.0233824i	0.00599735	−	0.000763463i
$939$			21.8285i			0.712346i
$940$	−13.3225	+	7.69177i	−0.434533	+	0.250878i
$941$	0.566992	−	0.982059i	0.0184834	−	0.0320142i	−0.856636	−	0.515922i	$-0.827450\pi$
$941$	0.566992	−	0.982059i	0.0184834	−	0.0320142i	0.875119	+	0.483907i	$0.160783\pi$
$942$	−62.9756	−	36.3590i	−2.05186	−	1.18464i
$943$	10.1791	+	11.6515i	0.331478	+	0.379424i
$944$		−	0.126917i		−	0.00413081i
$945$	73.5097	+	96.6536i	2.39127	+	3.14414i
$946$	−4.43915			−0.144329
$947$	−13.1070	−	22.7019i	−0.425919	−	0.737714i	0.570586	−	0.821238i	$-0.306716\pi$
$947$	−13.1070	−	22.7019i	−0.425919	−	0.737714i	−0.996506	+	0.0835235i	$0.973383\pi$
$948$	2.61839	−	4.53518i	0.0850413	−	0.147296i
$949$	−15.8632	+	27.4758i	−0.514941	+	0.891904i
$950$	7.17773	+	12.4322i	0.232876	+	0.403354i
$951$			64.9151i			2.10502i
$952$	−2.27088	−	0.952040i	−0.0735998	−	0.0308558i
$953$		−	37.8441i		−	1.22589i	−0.790125	−	0.612945i	$-0.789985\pi$
$953$		−	37.8441i		−	1.22589i	0.790125	−	0.612945i	$-0.210015\pi$
$954$	46.1571	−	26.6488i	1.49439	−	0.862787i
$955$	16.2367	+	9.37425i	0.525407	+	0.303344i
$956$	−12.5508	+	21.7386i	−0.405922	+	0.703077i
$957$	−7.94168	−	13.7554i	−0.256718	−	0.444649i
$958$	−12.9247			−0.417579
$959$	−1.03664	+	2.47267i	−0.0334748	+	0.0798468i
$960$			10.0795i			0.325314i
$961$	32.8578	+	56.9114i	1.05993	+	1.83585i
$962$	−17.8931	+	30.9918i	−0.576897	+	0.999215i
$963$	−28.5252	−	16.4690i	−0.919213	−	0.530708i
$964$	−10.3525	−	17.9310i	−0.333431	−	0.577519i
$965$	−2.54186			−0.0818254
$966$	27.3692	−	30.8227i	0.880588	−	0.991705i
$967$	31.3048			1.00670			0.503348	−	0.864084i	$-0.332102\pi$
$967$	31.3048			1.00670			0.503348	+	0.864084i	$0.332102\pi$
$968$	5.57059	+	9.64855i	0.179046	+	0.310116i
$969$	8.12408	+	4.69044i	0.260983	+	0.150679i
$970$	−10.9059	+	18.8896i	−0.350169	+	0.606510i
$971$	−24.9884	−	43.2811i	−0.801915	−	1.38896i	−0.918354	−	0.395759i	$-0.870481\pi$
$971$	−24.9884	−	43.2811i	−0.801915	−	1.38896i	0.116439	−	0.993198i	$-0.462852\pi$
$972$		−	38.1200i		−	1.22270i
$973$	20.2896	−	2.58287i	0.650454	−	0.0828029i
$974$	−33.5388			−1.07465
$975$	24.2447	+	41.9931i	0.776453	+	1.34486i
$976$	−2.63736	+	4.56804i	−0.0844197	+	0.146219i
$977$	−25.2635	−	14.5859i	−0.808251	−	0.466644i	0.0380970	−	0.999274i	$-0.487870\pi$
$977$	−25.2635	−	14.5859i	−0.808251	−	0.466644i	−0.846348	+	0.532630i	$0.821204\pi$
$978$	32.5044	−	18.7664i	1.03938	−	0.600083i
$979$		−	62.0997i		−	1.98472i
$980$	21.0262	−	5.44146i	0.671658	−	0.173821i
$981$		−	42.6685i		−	1.36230i
$982$	−14.9179	−	25.8386i	−0.476050	−	0.824543i
$983$	16.1562	−	27.9834i	0.515304	−	0.892533i	−0.484538	−	0.874770i	$-0.661012\pi$
$983$	16.1562	−	27.9834i	0.515304	−	0.892533i	0.999842	−	0.0177627i	$-0.00565435\pi$
$984$	5.24011	−	9.07613i	0.167048	−	0.289336i
$985$	−16.9928	−	29.4324i	−0.541436	−	0.937795i
$986$	−0.967051			−0.0307972
$987$	−5.38147	−	42.2739i	−0.171294	−	1.34559i
$988$			10.0095i			0.318444i
$989$	−2.97672	−	3.40727i	−0.0946542	−	0.108345i
$990$	−95.5034	−	55.1389i	−3.03530	−	1.75243i
$991$	21.1885	−	36.6996i	0.673076	−	1.16580i	−0.303951	−	0.952688i	$-0.598306\pi$
$991$	21.1885	−	36.6996i	0.673076	−	1.16580i	0.977027	−	0.213114i	$-0.0683607\pi$
$992$	8.51685	−	4.91721i	0.270410	−	0.156121i
$993$		−	66.1831i		−	2.10026i
$994$	11.9316	−	9.07457i	0.378448	−	0.287828i
$995$	19.3712			0.614110
$996$	3.79091	−	2.18868i	0.120120	−	0.0693511i
$997$	−17.4915	−	10.0987i	−0.553960	−	0.319829i	0.196758	−	0.980452i	$-0.436959\pi$
$997$	−17.4915	−	10.0987i	−0.553960	−	0.319829i	−0.750718	+	0.660623i	$0.770292\pi$
$998$	−6.64018	+	11.5011i	−0.210191	+	0.364062i
$999$	82.0458	+	142.107i	2.59581	+	4.49608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.a.45.8	yes	16
7.3	odd	6		2254.2.c.c.2253.16		16
7.4	even	3		2254.2.c.c.2253.1		16
7.5	odd	6	inner	322.2.g.a.229.7	yes	16
23.22	odd	2	inner	322.2.g.a.45.7	✓	16
161.45	even	6		2254.2.c.c.2253.15		16
161.68	even	6	inner	322.2.g.a.229.8	yes	16
161.137	odd	6		2254.2.c.c.2253.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.a.45.7	✓	16	23.22	odd	2	inner
322.2.g.a.45.8	yes	16	1.1	even	1	trivial
322.2.g.a.229.7	yes	16	7.5	odd	6	inner
322.2.g.a.229.8	yes	16	161.68	even	6	inner
2254.2.c.c.2253.1		16	7.4	even	3
2254.2.c.c.2253.2		16	161.137	odd	6
2254.2.c.c.2253.15		16	161.45	even	6
2254.2.c.c.2253.16		16	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(2.81338 + 1.62431i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55135 + 2.68702i) q^{5} -3.24861i q^{6} +(-0.334108 - 2.62457i) q^{7} +1.00000 q^{8} +(3.77674 + 6.54151i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(2.81338 + 1.62431i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55135 + 2.68702i) q^{5} -3.24861i q^{6} +(-0.334108 - 2.62457i) q^{7} +1.00000 q^{8} +(3.77674 + 6.54151i) q^{9} +(1.55135 - 2.68702i) q^{10} +(-4.07503 - 2.35272i) q^{11} +(-2.81338 + 1.62431i) q^{12} -3.22606i q^{13} +(-2.10589 + 1.60163i) q^{14} +10.0795i q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.465345 - 0.806002i) q^{17} +(3.77674 - 6.54151i) q^{18} +(1.55135 + 2.68702i) q^{19} -3.10270 q^{20} +(3.32313 - 7.92661i) q^{21} +4.70544i q^{22} +(-3.61167 + 3.15529i) q^{23} +(2.81338 + 1.62431i) q^{24} +(-2.31338 + 4.00689i) q^{25} +(-2.79385 + 1.61303i) q^{26} +14.7925i q^{27} +(2.44000 + 1.02294i) q^{28} +1.03907 q^{29} +(8.72909 - 5.03974i) q^{30} +(-8.51685 - 4.91721i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-7.64308 - 13.2382i) q^{33} -0.930691 q^{34} +(6.53395 - 4.96939i) q^{35} -7.55349 q^{36} +(9.60671 - 5.54644i) q^{37} +(1.55135 - 2.68702i) q^{38} +(5.24011 - 9.07613i) q^{39} +(1.55135 + 2.68702i) q^{40} -3.22606i q^{41} +(-8.52622 + 1.08539i) q^{42} +0.943407i q^{43} +(4.07503 - 2.35272i) q^{44} +(-11.7181 + 20.2964i) q^{45} +(4.53839 + 1.55015i) q^{46} +(4.29385 - 2.47905i) q^{47} -3.24861i q^{48} +(-6.77674 + 1.75378i) q^{49} +4.62676 q^{50} +(2.61839 - 1.51173i) q^{51} +(2.79385 + 1.61303i) q^{52} +(6.11070 + 3.52801i) q^{53} +(12.8107 - 7.39626i) q^{54} -14.5996i q^{55} +(-0.334108 - 2.62457i) q^{56} +10.0795i q^{57} +(-0.519534 - 0.899859i) q^{58} +(0.109914 + 0.0634586i) q^{59} +(-8.72909 - 5.03974i) q^{60} +(-2.63736 - 4.56804i) q^{61} +9.83441i q^{62} +(15.9068 - 12.0979i) q^{63} +1.00000 q^{64} +(8.66848 - 5.00475i) q^{65} +(-7.64308 + 13.2382i) q^{66} +(-0.0606084 - 0.0349923i) q^{67} +(0.465345 + 0.806002i) q^{68} +(-15.2862 + 3.01057i) q^{69} +(-7.57059 - 3.17388i) q^{70} -5.66583 q^{71} +(3.77674 + 6.54151i) q^{72} +(-8.51685 - 4.91721i) q^{73} +(-9.60671 - 5.54644i) q^{74} +(-13.0168 + 7.51528i) q^{75} -3.10270 q^{76} +(-4.81338 + 11.4813i) q^{77} -10.4802 q^{78} +(-1.39604 + 0.806002i) q^{79} +(1.55135 - 2.68702i) q^{80} +(-12.6974 + 21.9925i) q^{81} +(-2.79385 + 1.61303i) q^{82} -1.34746 q^{83} +(5.20308 + 6.84123i) q^{84} +2.88766 q^{85} +(0.817014 - 0.471703i) q^{86} +(2.92330 + 1.68777i) q^{87} +(-4.07503 - 2.35272i) q^{88} +(6.59871 + 11.4293i) q^{89} +23.4362 q^{90} +(-8.46702 + 1.07785i) q^{91} +(-0.926724 - 4.70544i) q^{92} +(-15.9741 - 27.6679i) q^{93} +(-4.29385 - 2.47905i) q^{94} +(-4.81338 + 8.33702i) q^{95} +(-2.81338 + 1.62431i) q^{96} -7.02996 q^{97} +(4.90719 + 4.99194i) q^{98} -35.5425i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

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