LMFDB - Embedded newform 322.2.g.b.229.2

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} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 $ x^16 + 12x^14 + 73x^12 + 312x^10 + 1045x^8 + 2808x^6 + 5913x^4 + 8748*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.2
Root			$-0.105715 + 1.72882i$ of defining polynomial
Character	$\chi$	$=$	322.229
Dual form			322.2.g.b.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-2.64992 + 1.52993i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.920495 - 1.59434i) q^{5} +3.05986i q^{6} +(0.254505 + 2.63348i) q^{7} -1.00000 q^{8} +(3.18138 - 5.51031i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-2.64992 + 1.52993i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.920495 - 1.59434i) q^{5} +3.05986i q^{6} +(0.254505 + 2.63348i) q^{7} -1.00000 q^{8} +(3.18138 - 5.51031i) q^{9} +(-0.920495 - 1.59434i) q^{10} +(-3.87183 + 2.23540i) q^{11} +(2.64992 + 1.52993i) q^{12} +2.97881i q^{13} +(2.40791 + 1.09633i) q^{14} +5.63317i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.17962 + 5.50726i) q^{17} +(-3.18138 - 5.51031i) q^{18} +(-3.80919 + 6.59770i) q^{19} -1.84099 q^{20} +(-4.70346 - 6.58914i) q^{21} +4.47080i q^{22} +(2.93627 - 3.79187i) q^{23} +(2.64992 - 1.52993i) q^{24} +(0.805379 + 1.39496i) q^{25} +(2.57973 + 1.48941i) q^{26} +10.2896i q^{27} +(2.15341 - 1.53715i) q^{28} -3.95530 q^{29} +(4.87847 + 2.81659i) q^{30} +(0.468541 - 0.270512i) q^{31} +(0.500000 + 0.866025i) q^{32} +(6.84002 - 11.8473i) q^{33} +6.35924 q^{34} +(4.43295 + 2.01834i) q^{35} -6.36275 q^{36} +(0.545433 + 0.314906i) q^{37} +(3.80919 + 6.59770i) q^{38} +(-4.55737 - 7.89360i) q^{39} +(-0.920495 + 1.59434i) q^{40} +1.40524i q^{41} +(-8.05809 + 0.778751i) q^{42} -5.38135i q^{43} +(3.87183 + 2.23540i) q^{44} +(-5.85688 - 10.1444i) q^{45} +(-1.81572 - 4.43882i) q^{46} +(-7.64578 - 4.41429i) q^{47} -3.05986i q^{48} +(-6.87045 + 1.34047i) q^{49} +1.61076 q^{50} +(-16.8515 - 9.72920i) q^{51} +(2.57973 - 1.48941i) q^{52} +(0.00463568 - 0.00267641i) q^{53} +(8.91102 + 5.14478i) q^{54} +8.23070i q^{55} +(-0.254505 - 2.63348i) q^{56} -23.3112i q^{57} +(-1.97765 + 3.42539i) q^{58} +(12.1940 - 7.04024i) q^{59} +(4.87847 - 2.81659i) q^{60} +(-5.31819 + 9.21137i) q^{61} -0.541025i q^{62} +(15.3210 + 6.97570i) q^{63} +1.00000 q^{64} +(4.74925 + 2.74198i) q^{65} +(-6.84002 - 11.8473i) q^{66} +(1.39781 - 0.807025i) q^{67} +(3.17962 - 5.50726i) q^{68} +(-1.97957 + 14.5404i) q^{69} +(3.96440 - 2.82987i) q^{70} -1.65546 q^{71} +(-3.18138 + 5.51031i) q^{72} +(7.69091 - 4.44035i) q^{73} +(0.545433 - 0.314906i) q^{74} +(-4.26838 - 2.46435i) q^{75} +7.61837 q^{76} +(-6.87229 - 9.62747i) q^{77} -9.11475 q^{78} +(4.47247 + 2.58218i) q^{79} +(0.920495 + 1.59434i) q^{80} +(-6.19818 - 10.7356i) q^{81} +(1.21697 + 0.702619i) q^{82} +10.5071 q^{83} +(-3.35463 + 7.36789i) q^{84} +11.7073 q^{85} +(-4.66039 - 2.69068i) q^{86} +(10.4812 - 6.05133i) q^{87} +(3.87183 - 2.23540i) q^{88} +(2.12719 - 3.68440i) q^{89} -11.7138 q^{90} +(-7.84464 + 0.758123i) q^{91} +(-4.75200 - 0.646949i) q^{92} +(-0.827731 + 1.43367i) q^{93} +(-7.64578 + 4.41429i) q^{94} +(7.01267 + 12.1463i) q^{95} +(-2.64992 - 1.52993i) q^{96} -16.2156 q^{97} +(-2.27435 + 6.62022i) q^{98} +28.4466i 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} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+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 + 8 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^29 + 12 * q^31 + 8 * q^32 - 20 * q^36 - 2 * q^39 - 8 * q^46 - 6 * q^47 - 18 * q^49 + 4 * q^50 - 6 * q^52 + 18 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 12 * q^70 - 52 * q^71 - 10 * q^72 + 24 * q^73 + 30 * q^77 - 4 * q^78 - 20 * q^81 + 54 * q^82 + 80 * q^85 + 54 * q^87 - 16 * q^92 - 26 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−2.64992	+	1.52993i	−1.52993	+	0.883306i	−0.530567	+	0.847643i	$0.678021\pi$
$3$	−2.64992	+	1.52993i	−1.52993	+	0.883306i	−0.999364	+	0.0356629i	$0.988646\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.920495	−	1.59434i	0.411658	−	0.713012i	−0.583413	−	0.812175i	$-0.698283\pi$
$5$	0.920495	−	1.59434i	0.411658	−	0.713012i	0.995071	+	0.0991632i	$0.0316166\pi$
$6$			3.05986i			1.24918i
$7$	0.254505	+	2.63348i	0.0961939	+	0.995363i
$7$	0.254505	+	2.63348i	0.0961939	+	0.995363i
$8$	−1.00000			−0.353553
$9$	3.18138	−	5.51031i	1.06046	−	1.83677i
$10$	−0.920495	−	1.59434i	−0.291086	−	0.504176i
$11$	−3.87183	+	2.23540i	−1.16740	+	0.673999i	−0.953066	−	0.302762i	$-0.902091\pi$
$11$	−3.87183	+	2.23540i	−1.16740	+	0.673999i	−0.214334	+	0.976761i	$0.568758\pi$
$12$	2.64992	+	1.52993i	0.764965	+	0.441653i
$13$			2.97881i			0.826173i	0.910692	+	0.413087i	$0.135549\pi$
$13$			2.97881i			0.826173i	−0.910692	+	0.413087i	$0.864451\pi$
$14$	2.40791	+	1.09633i	0.643542	+	0.293007i
$15$			5.63317i			1.45448i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.17962	+	5.50726i	0.771171	+	1.33571i	0.936922	+	0.349540i	$0.113662\pi$
$17$	3.17962	+	5.50726i	0.771171	+	1.33571i	−0.165750	+	0.986168i	$0.553005\pi$
$18$	−3.18138	−	5.51031i	−0.749858	−	1.29879i
$19$	−3.80919	+	6.59770i	−0.873887	+	1.51362i	−0.0159439	+	0.999873i	$0.505075\pi$
$19$	−3.80919	+	6.59770i	−0.873887	+	1.51362i	−0.857943	+	0.513744i	$0.828258\pi$
$20$	−1.84099			−0.411658
$21$	−4.70346	−	6.58914i	−1.02638	−	1.43787i
$22$			4.47080i			0.953178i
$23$	2.93627	−	3.79187i	0.612255	−	0.790660i
$23$	2.93627	−	3.79187i	0.612255	−	0.790660i
$24$	2.64992	−	1.52993i	0.540912	−	0.312296i
$25$	0.805379	+	1.39496i	0.161076	+	0.278992i
$26$	2.57973	+	1.48941i	0.505926	+	0.292096i
$27$			10.2896i			1.98023i
$28$	2.15341	−	1.53715i	0.406956	−	0.290494i
$29$	−3.95530			−0.734480			−0.367240	−	0.930126i	$-0.619697\pi$
$29$	−3.95530			−0.734480			−0.367240	+	0.930126i	$0.619697\pi$
$30$	4.87847	+	2.81659i	0.890683	+	0.514236i
$31$	0.468541	−	0.270512i	0.0841525	−	0.0485855i	−0.457333	−	0.889295i	$-0.651195\pi$
$31$	0.468541	−	0.270512i	0.0841525	−	0.0485855i	0.541486	+	0.840710i	$0.317862\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	6.84002	−	11.8473i	1.19069	−	2.06234i
$34$	6.35924			1.09060
$35$	4.43295	+	2.01834i	0.749305	+	0.341161i
$36$	−6.36275			−1.06046
$37$	0.545433	+	0.314906i	0.0896687	+	0.0517702i	0.544164	−	0.838979i	$-0.316847\pi$
$37$	0.545433	+	0.314906i	0.0896687	+	0.0517702i	−0.454495	+	0.890749i	$0.650180\pi$
$38$	3.80919	+	6.59770i	0.617932	+	1.07029i
$39$	−4.55737	−	7.89360i	−0.729764	−	1.26399i
$40$	−0.920495	+	1.59434i	−0.145543	+	0.252088i
$41$			1.40524i			0.219461i	0.993961	+	0.109731i	$0.0349988\pi$
$41$			1.40524i			0.219461i	−0.993961	+	0.109731i	$0.965001\pi$
$42$	−8.05809	+	0.778751i	−1.24339	+	0.120164i
$43$		−	5.38135i		−	0.820649i	−0.911940	−	0.410324i	$-0.865415\pi$
$43$		−	5.38135i		−	0.820649i	0.911940	−	0.410324i	$-0.134585\pi$
$44$	3.87183	+	2.23540i	0.583700	+	0.336999i
$45$	−5.85688	−	10.1444i	−0.873092	−	1.51224i
$46$	−1.81572	−	4.43882i	−0.267714	−	0.654469i
$47$	−7.64578	−	4.41429i	−1.11525	−	0.643891i	−0.175067	−	0.984556i	$-0.556014\pi$
$47$	−7.64578	−	4.41429i	−1.11525	−	0.643891i	−0.940185	+	0.340666i	$0.889348\pi$
$48$		−	3.05986i		−	0.441653i
$49$	−6.87045	+	1.34047i	−0.981493	+	0.191496i
$50$	1.61076			0.227796
$51$	−16.8515	−	9.72920i	−2.35968	−	1.36236i
$52$	2.57973	−	1.48941i	0.357744	−	0.206543i
$53$	0.00463568	−	0.00267641i	0.000636760	−	0.000367634i	−0.499682	−	0.866209i	$-0.666550\pi$
$53$	0.00463568	−	0.00267641i	0.000636760	−	0.000367634i	0.500318	+	0.865842i	$0.333216\pi$
$54$	8.91102	+	5.14478i	1.21264	+	0.700116i
$55$			8.23070i			1.10983i
$56$	−0.254505	−	2.63348i	−0.0340097	−	0.351914i
$57$		−	23.3112i		−	3.08764i
$58$	−1.97765	+	3.42539i	−0.259678	+	0.449775i
$59$	12.1940	−	7.04024i	1.58753	−	0.916561i	0.593817	−	0.804600i	$-0.297620\pi$
$59$	12.1940	−	7.04024i	1.58753	−	0.916561i	0.993713	−	0.111961i	$-0.0357131\pi$
$60$	4.87847	−	2.81659i	0.629808	−	0.363620i
$61$	−5.31819	+	9.21137i	−0.680924	+	1.17940i	0.293775	+	0.955875i	$0.405088\pi$
$61$	−5.31819	+	9.21137i	−0.680924	+	1.17940i	−0.974699	+	0.223521i	$0.928245\pi$
$62$		−	0.541025i		−	0.0687102i
$63$	15.3210	+	6.97570i	1.93026	+	0.878855i
$64$	1.00000			0.125000
$65$	4.74925	+	2.74198i	0.589072	+	0.340101i
$66$	−6.84002	−	11.8473i	−0.841948	−	1.45830i
$67$	1.39781	−	0.807025i	0.170769	−	0.0985938i	−0.412179	−	0.911103i	$-0.635232\pi$
$67$	1.39781	−	0.807025i	0.170769	−	0.0985938i	0.582949	+	0.812509i	$0.301899\pi$
$68$	3.17962	−	5.50726i	0.385586	−	0.667854i
$69$	−1.97957	+	14.5404i	−0.238313	+	1.75046i
$70$	3.96440	−	2.82987i	0.473837	−	0.338235i
$71$	−1.65546			−0.196467			−0.0982335	−	0.995163i	$-0.531319\pi$
$71$	−1.65546			−0.196467			−0.0982335	+	0.995163i	$0.531319\pi$
$72$	−3.18138	+	5.51031i	−0.374929	+	0.649396i
$73$	7.69091	−	4.44035i	0.900153	−	0.519704i	0.0229031	−	0.999738i	$-0.492709\pi$
$73$	7.69091	−	4.44035i	0.900153	−	0.519704i	0.877250	+	0.480034i	$0.159376\pi$
$74$	0.545433	−	0.314906i	0.0634053	−	0.0366071i
$75$	−4.26838	−	2.46435i	−0.492870	−	0.284558i
$76$	7.61837			0.873887
$77$	−6.87229	−	9.62747i	−0.783170	−	1.09715i
$78$	−9.11475			−1.03204
$79$	4.47247	+	2.58218i	0.503192	+	0.290518i	0.730031	−	0.683414i	$-0.239506\pi$
$79$	4.47247	+	2.58218i	0.503192	+	0.290518i	−0.226839	+	0.973932i	$0.572839\pi$
$80$	0.920495	+	1.59434i	0.102914	+	0.178253i
$81$	−6.19818	−	10.7356i	−0.688687	−	1.19284i
$82$	1.21697	+	0.702619i	0.134392	+	0.0775913i
$83$	10.5071			1.15330			0.576650	−	0.816991i	$-0.304360\pi$
$83$	10.5071			1.15330			0.576650	+	0.816991i	$0.304360\pi$
$84$	−3.35463	+	7.36789i	−0.366020	+	0.803902i
$85$	11.7073			1.26983
$86$	−4.66039	−	2.69068i	−0.502543	−	0.290143i
$87$	10.4812	−	6.05133i	1.12370	−	0.648771i
$88$	3.87183	−	2.23540i	0.412738	−	0.238294i
$89$	2.12719	−	3.68440i	0.225482	−	0.390546i	−0.730982	−	0.682397i	$-0.760938\pi$
$89$	2.12719	−	3.68440i	0.225482	−	0.390546i	0.956464	+	0.291851i	$0.0942710\pi$
$90$	−11.7138			−1.23474
$91$	−7.84464	+	0.758123i	−0.822342	+	0.0794728i
$92$	−4.75200	−	0.646949i	−0.495430	−	0.0674491i
$93$	−0.827731	+	1.43367i	−0.0858317	+	0.148665i
$94$	−7.64578	+	4.41429i	−0.788602	+	0.455300i
$95$	7.01267	+	12.1463i	0.719485	+	1.24618i
$96$	−2.64992	−	1.52993i	−0.270456	−	0.156148i
$97$	−16.2156			−1.64645			−0.823224	−	0.567717i	$-0.807827\pi$
$97$	−16.2156			−1.64645			−0.823224	+	0.567717i	$0.807827\pi$
$98$	−2.27435	+	6.62022i	−0.229744	+	0.668743i
$99$			28.4466i			2.85899i
$100$	0.805379	−	1.39496i	0.0805379	−	0.139496i
$101$	−14.2789	+	8.24392i	−1.42080	+	0.820301i	−0.996368	−	0.0851575i	$-0.972861\pi$
$101$	−14.2789	+	8.24392i	−1.42080	+	0.820301i	−0.424435	+	0.905458i	$0.639527\pi$
$102$	−16.8515	+	9.72920i	−1.66854	+	0.963334i
$103$	−1.82413	+	3.15949i	−0.179737	+	0.311314i	−0.941790	−	0.336200i	$-0.890858\pi$
$103$	−1.82413	+	3.15949i	−0.179737	+	0.311314i	0.762053	+	0.647514i	$0.224191\pi$
$104$		−	2.97881i		−	0.292096i
$105$	−14.8349	+	1.43367i	−1.44773	+	0.139912i
$106$		−	0.00535283i		−	0.000519913i
$107$	3.58484	+	2.06971i	0.346560	+	0.200086i	0.663169	−	0.748470i	$-0.269211\pi$
$107$	3.58484	+	2.06971i	0.346560	+	0.200086i	−0.316609	+	0.948556i	$0.602544\pi$
$108$	8.91102	−	5.14478i	0.857463	−	0.495057i
$109$	−0.818243	+	0.472413i	−0.0783735	+	0.0452489i	−0.538675	−	0.842514i	$-0.681075\pi$
$109$	−0.818243	+	0.472413i	−0.0783735	+	0.0452489i	0.460301	+	0.887763i	$0.347741\pi$
$110$	7.12799	+	4.11535i	0.679627	+	0.392383i
$111$	−1.92714			−0.182916
$112$	−2.40791	−	1.09633i	−0.227527	−	0.103594i
$113$			9.06778i			0.853025i	0.904482	+	0.426512i	$0.140258\pi$
$113$			9.06778i			0.853025i	−0.904482	+	0.426512i	$0.859742\pi$
$114$	−20.1881	−	11.6556i	−1.89079	−	1.09165i
$115$	−3.34273	−	8.17183i	−0.311711	−	0.762027i
$116$	1.97765	+	3.42539i	0.183620	+	0.318039i
$117$	16.4142	+	9.47672i	1.51749	+	0.876123i
$118$		−	14.0805i		−	1.29621i
$119$	−13.6940	+	9.77510i	−1.25533	+	0.896082i
$120$		−	5.63317i		−	0.514236i
$121$	4.49403	−	7.78389i	0.408548	−	0.707626i
$122$	5.31819	+	9.21137i	0.481486	+	0.833959i
$123$	−2.14992	−	3.72377i	−0.193852	−	0.335761i
$124$	−0.468541	−	0.270512i	−0.0420762	−	0.0242927i
$125$	12.1703			1.08855
$126$	13.7016	−	9.78050i	1.22064	−	0.871316i
$127$	1.85962			0.165014			0.0825071	−	0.996590i	$-0.473707\pi$
$127$	1.85962			0.165014			0.0825071	+	0.996590i	$0.473707\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	8.23310	+	14.2601i	0.724884	+	1.25554i
$130$	4.74925	−	2.74198i	0.416537	−	0.240487i
$131$	6.31251	+	3.64453i	0.551526	+	0.318424i	0.749737	−	0.661736i	$-0.230180\pi$
$131$	6.31251	+	3.64453i	0.551526	+	0.318424i	−0.198211	+	0.980159i	$0.563513\pi$
$132$	−13.6800			−1.19069
$133$	−18.3444	−	8.35227i	−1.59066	−	0.724234i
$134$		−	1.61405i		−	0.139433i
$135$	16.4051	+	9.47149i	1.41193	+	0.815176i
$136$	−3.17962	−	5.50726i	−0.272650	−	0.472244i
$137$	12.3351	−	7.12170i	1.05386	−	0.608447i	0.130134	−	0.991496i	$-0.458459\pi$
$137$	12.3351	−	7.12170i	1.05386	−	0.608447i	0.923728	+	0.383049i	$0.125126\pi$
$138$	11.6026	+	8.98459i	0.987680	+	0.764819i
$139$		−	2.19316i		−	0.186021i	−0.995665	−	0.0930105i	$-0.970351\pi$
$139$		−	2.19316i		−	0.186021i	0.995665	−	0.0930105i	$-0.0296490\pi$
$140$	−0.468541	−	4.84821i	−0.0395990	−	0.409749i
$141$	27.0143			2.27501
$142$	−0.827731	+	1.43367i	−0.0694616	+	0.120311i
$143$	−6.65883	−	11.5334i	−0.556840	−	0.964475i
$144$	3.18138	+	5.51031i	0.265115	+	0.459192i
$145$	−3.64083	+	6.30610i	−0.302354	+	0.523693i
$146$		−	8.88070i		−	0.734972i
$147$	16.1553	−	14.0635i	1.33247	−	1.15993i
$148$		−	0.629812i		−	0.0517702i
$149$	−8.65680	−	4.99801i	−0.709193	−	0.409453i	0.101569	−	0.994828i	$-0.467614\pi$
$149$	−8.65680	−	4.99801i	−0.709193	−	0.409453i	−0.810762	+	0.585376i	$0.800947\pi$
$150$	−4.26838	+	2.46435i	−0.348512	+	0.201213i
$151$	−1.97037	−	3.41279i	−0.160347	−	0.277729i	0.774646	−	0.632395i	$-0.217928\pi$
$151$	−1.97037	−	3.41279i	−0.160347	−	0.277729i	−0.934993	+	0.354666i	$0.884595\pi$
$152$	3.80919	−	6.59770i	0.308966	−	0.535144i
$153$	40.4623			3.27118
$154$	−11.7738	+	1.13784i	−0.948758	+	0.0916899i
$155$		−	0.996021i		−	0.0800023i
$156$	−4.55737	+	7.89360i	−0.364882	+	0.631994i
$157$	−4.68661	−	8.11744i	−0.374032	−	0.647842i	0.616150	−	0.787629i	$-0.288692\pi$
$157$	−4.68661	−	8.11744i	−0.374032	−	0.647842i	−0.990182	+	0.139787i	$0.955358\pi$
$158$	4.47247	−	2.58218i	0.355810	−	0.205427i
$159$	−0.00818946	+	0.0141846i	−0.000649466	+	0.00112491i
$160$	1.84099			0.145543
$161$	10.7331	+	6.76757i	0.845889	+	0.533359i
$162$	−12.3964			−0.973951
$163$	−2.05554	+	3.56030i	−0.161002	+	0.278864i	−0.935228	−	0.354045i	$-0.884806\pi$
$163$	−2.05554	+	3.56030i	−0.161002	+	0.278864i	0.774226	+	0.632909i	$0.218139\pi$
$164$	1.21697	−	0.702619i	0.0950296	−	0.0548654i
$165$	−12.5924	−	21.8107i	−0.980317	−	1.69796i
$166$	5.25353	−	9.09938i	0.407753	−	0.706249i
$167$			2.81772i			0.218042i	0.994039	+	0.109021i	$0.0347716\pi$
$167$			2.81772i			0.218042i	−0.994039	+	0.109021i	$0.965228\pi$
$168$	4.70346	+	6.58914i	0.362880	+	0.508363i
$169$	4.12669			0.317437
$170$	5.85365	−	10.1388i	0.448954	−	0.777611i
$171$	24.2369	+	41.9796i	1.85344	+	3.21026i
$172$	−4.66039	+	2.69068i	−0.355351	+	0.205162i
$173$	3.35224	+	1.93542i	0.254866	+	0.147147i	0.621990	−	0.783025i	$-0.286324\pi$
$173$	3.35224	+	1.93542i	0.254866	+	0.147147i	−0.367124	+	0.930172i	$0.619658\pi$
$174$		−	12.1027i		−	0.917500i
$175$	−3.46862	+	2.47598i	−0.262203	+	0.187166i
$176$		−	4.47080i		−	0.336999i
$177$	−21.5422	+	37.3121i	−1.61921	+	2.80455i
$178$	−2.12719	−	3.68440i	−0.159440	−	0.276158i
$179$	2.98121	+	5.16361i	0.222826	+	0.385946i	0.955665	−	0.294456i	$-0.0951384\pi$
$179$	2.98121	+	5.16361i	0.222826	+	0.385946i	−0.732839	+	0.680402i	$0.761805\pi$
$180$	−5.85688	+	10.1444i	−0.436546	+	0.756120i
$181$	−19.8169			−1.47298			−0.736489	−	0.676450i	$-0.763518\pi$
$181$	−19.8169			−1.47298			−0.736489	+	0.676450i	$0.763518\pi$
$182$	−3.26577	+	7.17272i	−0.242075	+	0.531678i
$183$		−	32.5458i		−	2.40586i
$184$	−2.93627	+	3.79187i	−0.216465	+	0.279541i
$185$	1.00414	−	0.579739i	0.0738256	−	0.0426232i
$186$	0.827731	+	1.43367i	0.0606922	+	0.105122i
$187$	−24.6219	−	14.2154i	−1.80053	−	1.03954i
$188$			8.82859i			0.643891i
$189$	−27.0974	+	2.61875i	−1.97104	+	0.190486i
$190$	14.0253			1.01751
$191$	16.7923	+	9.69503i	1.21505	+	0.701508i	0.963854	−	0.266429i	$-0.0858439\pi$
$191$	16.7923	+	9.69503i	1.21505	+	0.701508i	0.251193	+	0.967937i	$0.419177\pi$
$192$	−2.64992	+	1.52993i	−0.191241	+	0.110413i
$193$	11.4197	+	19.7795i	0.822008	+	1.42376i	0.904185	+	0.427142i	$0.140480\pi$
$193$	11.4197	+	19.7795i	0.822008	+	1.42376i	−0.0821765	+	0.996618i	$0.526187\pi$
$194$	−8.10782	+	14.0431i	−0.582107	+	1.00824i
$195$	−16.7802			−1.20165
$196$	4.59611	+	5.27975i	0.328293	+	0.377125i
$197$	17.6879			1.26021			0.630106	−	0.776509i	$-0.283011\pi$
$197$	17.6879			1.26021			0.630106	+	0.776509i	$0.283011\pi$
$198$	24.6355	+	14.2233i	1.75077	+	1.01081i
$199$	−7.00172	−	12.1273i	−0.496339	−	0.859684i	0.503652	−	0.863906i	$-0.331989\pi$
$199$	−7.00172	−	12.1273i	−0.496339	−	0.859684i	−0.999991	+	0.00422238i	$0.998656\pi$
$200$	−0.805379	−	1.39496i	−0.0569489	−	0.0986384i
$201$	−2.46938	+	4.27710i	−0.174177	+	0.301683i
$202$			16.4878i			1.16008i
$203$	−1.00664	−	10.4162i	−0.0706525	−	0.731074i
$204$			19.4584i			1.36236i
$205$	2.24043	+	1.29351i	0.156479	+	0.0903430i
$206$	1.82413	+	3.15949i	0.127093	+	0.220132i
$207$	−11.5530	−	28.2431i	−0.802989	−	1.96303i
$208$	−2.57973	−	1.48941i	−0.178872	−	0.103272i
$209$		−	34.0602i		−	2.35600i
$210$	−6.17583	+	13.5642i	−0.426173	+	0.936019i
$211$	5.21870			0.359270			0.179635	−	0.983733i	$-0.442508\pi$
$211$	5.21870			0.359270			0.179635	+	0.983733i	$0.442508\pi$
$212$	−0.00463568	−	0.00267641i	−0.000318380	−	0.000183817i
$213$	4.38684	−	2.53274i	0.300581	−	0.173541i
$214$	3.58484	−	2.06971i	0.245055	−	0.141482i
$215$	−8.57973	−	4.95351i	−0.585132	−	0.337826i
$216$		−	10.2896i		−	0.700116i
$217$	0.831636	+	1.16505i	0.0564551	+	0.0790886i
$218$			0.944826i			0.0639917i
$219$	−13.5869	+	23.5331i	−0.918114	+	1.59022i
$220$	7.12799	−	4.11535i	0.480569	−	0.277457i
$221$	−16.4051	+	9.47149i	−1.10353	+	0.637121i
$222$	−0.963569	+	1.66895i	−0.0646705	+	0.112013i
$223$		−	0.298887i		−	0.0200149i	−0.999950	−	0.0100075i	$-0.996814\pi$
$223$		−	0.298887i		−	0.0200149i	0.999950	−	0.0100075i	$-0.00318553\pi$
$224$	−2.15341	+	1.53715i	−0.143881	+	0.102705i
$225$	10.2489			0.683257
$226$	7.85292	+	4.53389i	0.522369	+	0.301590i
$227$	−3.68661	−	6.38540i	−0.244689	−	0.423814i	0.717355	−	0.696708i	$-0.245353\pi$
$227$	−3.68661	−	6.38540i	−0.244689	−	0.423814i	−0.962044	+	0.272894i	$0.912019\pi$
$228$	−20.1881	+	11.6556i	−1.33699	+	0.771910i
$229$	9.71859	−	16.8331i	0.642223	−	1.11236i	−0.342713	−	0.939440i	$-0.611346\pi$
$229$	9.71859	−	16.8331i	0.642223	−	1.11236i	0.984936	−	0.172922i	$-0.0553209\pi$
$230$	−8.74837	−	1.19103i	−0.576851	−	0.0785339i
$231$	32.9404	+	14.9979i	2.16732	+	0.986788i
$232$	3.95530			0.259678
$233$	8.90505	−	15.4240i	0.583389	−	1.01046i	−0.411685	−	0.911326i	$-0.635060\pi$
$233$	8.90505	−	15.4240i	0.583389	−	1.01046i	0.995074	−	0.0991336i	$-0.0316071\pi$
$234$	16.4142	−	9.47672i	1.07303	−	0.619512i
$235$	−14.0758	+	8.12667i	−0.918204	+	0.530125i
$236$	−12.1940	−	7.04024i	−0.793765	−	0.458280i
$237$	−15.8022			−1.02646
$238$	1.61846	+	16.7469i	0.104909	+	1.08554i
$239$	10.8924			0.704569			0.352285	−	0.935893i	$-0.385405\pi$
$239$	10.8924			0.704569			0.352285	+	0.935893i	$0.385405\pi$
$240$	−4.87847	−	2.81659i	−0.314904	−	0.181810i
$241$	−0.469400	−	0.813024i	−0.0302367	−	0.0523715i	0.850511	−	0.525957i	$-0.176293\pi$
$241$	−0.469400	−	0.813024i	−0.0302367	−	0.0523715i	−0.880748	+	0.473586i	$0.842959\pi$
$242$	−4.49403	−	7.78389i	−0.288887	−	0.500367i
$243$	6.11630	+	3.53125i	0.392361	+	0.226530i
$244$	10.6364			0.680924
$245$	−4.18705	+	12.1878i	−0.267501	+	0.778647i
$246$	−4.29984			−0.274148
$247$	−19.6533	−	11.3468i	−1.25051	−	0.721982i
$248$	−0.468541	+	0.270512i	−0.0297524	+	0.0171776i
$249$	−27.8429	+	16.0751i	−1.76447	+	1.01872i
$250$	6.08517	−	10.5398i	0.384860	−	0.666597i
$251$	6.67957			0.421611			0.210805	−	0.977528i	$-0.432391\pi$
$251$	6.67957			0.421611			0.210805	+	0.977528i	$0.432391\pi$
$252$	−1.61935	−	16.7562i	−0.102010	−	1.05554i
$253$	−2.89238	+	21.2452i	−0.181842	+	1.33568i
$254$	0.929808	−	1.61047i	0.0583413	−	0.101050i
$255$	−31.0234	+	17.9113i	−1.94276	+	1.12165i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.44032	+	3.14097i	0.339358	+	0.195928i	0.659988	−	0.751276i	$-0.270561\pi$
$257$	5.44032	+	3.14097i	0.339358	+	0.195928i	−0.320630	+	0.947204i	$0.603895\pi$
$258$	16.4662			1.02514
$259$	−0.690484	+	1.51653i	−0.0429046	+	0.0942328i
$260$		−	5.48396i		−	0.340101i
$261$	−12.5833	+	21.7949i	−0.778886	+	1.34907i
$262$	6.31251	−	3.64453i	0.389988	−	0.225160i
$263$	12.4685	−	7.19870i	0.768842	−	0.443891i	−0.0636195	−	0.997974i	$-0.520264\pi$
$263$	12.4685	−	7.19870i	0.768842	−	0.443891i	0.832461	+	0.554083i	$0.186931\pi$
$264$	−6.84002	+	11.8473i	−0.420974	+	0.729148i
$265$		−	0.00985450i		−	0.000605357i
$266$	−16.4055	+	11.7106i	−1.00588	+	0.718021i
$267$			13.0178i			0.796678i
$268$	−1.39781	−	0.807025i	−0.0853847	−	0.0492969i
$269$	7.88280	−	4.55114i	0.480623	−	0.277488i	−0.240053	−	0.970760i	$-0.577165\pi$
$269$	7.88280	−	4.55114i	0.480623	−	0.277488i	0.720676	+	0.693272i	$0.243832\pi$
$270$	16.4051	−	9.47149i	0.998382	−	0.576416i
$271$	−5.60067	−	3.23355i	−0.340217	−	0.196424i	0.320151	−	0.947366i	$-0.396266\pi$
$271$	−5.60067	−	3.23355i	−0.340217	−	0.196424i	−0.660368	+	0.750942i	$0.729600\pi$
$272$	−6.35924			−0.385586
$273$	19.6278	−	14.0107i	1.18793	−	0.847968i
$274$		−	14.2434i		−	0.860475i
$275$	−6.23658	−	3.60069i	−0.376080	−	0.217130i
$276$	13.5822	−	5.55586i	0.817551	−	0.334424i
$277$	1.15132	+	1.99415i	0.0691764	+	0.119817i	0.898539	−	0.438894i	$-0.144630\pi$
$277$	1.15132	+	1.99415i	0.0691764	+	0.119817i	−0.829363	+	0.558711i	$0.811296\pi$
$278$	−1.89933	−	1.09658i	−0.113914	−	0.0657684i
$279$		−	3.44241i		−	0.206092i
$280$	−4.43295	−	2.01834i	−0.264919	−	0.120619i
$281$			13.8075i			0.823688i	0.911254	+	0.411844i	$0.135115\pi$
$281$			13.8075i			0.823688i	−0.911254	+	0.411844i	$0.864885\pi$
$282$	13.5071	−	23.3950i	0.804338	−	1.39315i
$283$	7.16737	+	12.4142i	0.426056	+	0.737950i	0.996518	−	0.0833733i	$-0.0265694\pi$
$283$	7.16737	+	12.4142i	0.426056	+	0.737950i	−0.570463	+	0.821324i	$0.693236\pi$
$284$	0.827731	+	1.43367i	0.0491168	+	0.0850727i
$285$	−37.1660	−	21.4578i	−2.20152	−	1.27105i
$286$	−13.3177			−0.787490
$287$	−3.70067	+	0.357640i	−0.218444	+	0.0211108i
$288$	6.36275			0.374929
$289$	−11.7200	+	20.2996i	−0.689410	+	1.19409i
$290$	3.64083	+	6.30610i	0.213797	+	0.370307i
$291$	42.9701	−	24.8088i	2.51895	−	1.45432i
$292$	−7.69091	−	4.44035i	−0.450076	−	0.259852i
$293$	8.20565			0.479379			0.239690	−	0.970850i	$-0.422954\pi$
$293$	8.20565			0.479379			0.239690	+	0.970850i	$0.422954\pi$
$294$	−4.10165	−	21.0226i	−0.239213	−	1.22607i
$295$		−	25.9220i		−	1.50924i
$296$	−0.545433	−	0.314906i	−0.0317027	−	0.0183035i
$297$	−23.0013	−	39.8394i	−1.33467	−	2.31172i
$298$	−8.65680	+	4.99801i	−0.501475	+	0.289527i
$299$	11.2953	+	8.74660i	0.653223	+	0.505829i
$300$			4.92870i			0.284558i
$301$	14.1717	−	1.36958i	0.816843	−	0.0789414i
$302$	−3.94075			−0.226765
$303$	25.2253	−	43.6914i	1.44915	−	2.51001i
$304$	−3.80919	−	6.59770i	−0.218472	−	0.378404i
$305$	9.79073	+	16.9580i	0.560615	+	0.971015i
$306$	20.2311	−	35.0414i	1.15654	−	2.00318i
$307$			27.7350i			1.58292i	0.611220	+	0.791460i	$0.290679\pi$
$307$			27.7350i			1.58292i	−0.611220	+	0.791460i	$0.709321\pi$
$308$	−4.90149	+	10.7653i	−0.279288	+	0.613410i
$309$		−	11.1632i		−	0.635052i
$310$	−0.862579	−	0.498010i	−0.0489912	−	0.0282851i
$311$	−12.9425	+	7.47234i	−0.733901	+	0.423718i	−0.819847	−	0.572582i	$-0.805942\pi$
$311$	−12.9425	+	7.47234i	−0.733901	+	0.423718i	0.0859468	+	0.996300i	$0.472608\pi$
$312$	4.55737	+	7.89360i	0.258011	+	0.446887i
$313$	8.00364	−	13.8627i	0.452392	−	0.783567i	−0.546142	−	0.837693i	$-0.683904\pi$
$313$	8.00364	−	13.8627i	0.452392	−	0.783567i	0.998534	+	0.0541262i	$0.0172373\pi$
$314$	−9.37321			−0.528961
$315$	25.2245	−	18.0058i	1.42124	−	1.01451i
$316$		−	5.16436i		−	0.290518i
$317$	−5.71100	+	9.89175i	−0.320762	+	0.555576i	−0.980645	−	0.195792i	$-0.937272\pi$
$317$	−5.71100	+	9.89175i	−0.320762	+	0.555576i	0.659884	+	0.751368i	$0.270606\pi$
$318$	0.00818946	+	0.0141846i	0.000459242	+	0.000795430i
$319$	15.3142	−	8.84167i	0.857432	−	0.495039i
$320$	0.920495	−	1.59434i	0.0514572	−	0.0891265i
$321$	−12.6660			−0.706950
$322$	11.2274	−	5.91138i	0.625681	−	0.329428i
$323$	−48.4471			−2.69567
$324$	−6.19818	+	10.7356i	−0.344344	+	0.596421i
$325$	−4.15531	+	2.39907i	−0.230495	+	0.133077i
$326$	2.05554	+	3.56030i	0.113846	+	0.197187i
$327$	1.44552	−	2.50371i	0.0799373	−	0.138455i
$328$		−	1.40524i		−	0.0775913i
$329$	9.67907	−	21.2585i	0.533625	−	1.17202i
$330$	−25.1848			−1.38638
$331$	7.97211	−	13.8081i	0.438187	−	0.758961i	−0.559363	−	0.828923i	$-0.688954\pi$
$331$	7.97211	−	13.8081i	0.438187	−	0.758961i	0.997550	+	0.0699614i	$0.0222876\pi$
$332$	−5.25353	−	9.09938i	−0.288325	−	0.499394i
$333$	3.47046	−	2.00367i	0.190180	−	0.109800i
$334$	2.44022	+	1.40886i	0.133523	+	0.0770895i
$335$		−	2.97145i		−	0.162348i
$336$	8.05809	−	0.778751i	0.439605	−	0.0424843i
$337$			14.1400i			0.770256i	0.922863	+	0.385128i	$0.125843\pi$
$337$			14.1400i			0.770256i	−0.922863	+	0.385128i	$0.874157\pi$
$338$	2.06334	−	3.57382i	0.112231	−	0.194390i
$339$	−13.8731	−	24.0289i	−0.753482	−	1.30507i
$340$	−5.85365	−	10.1388i	−0.317459	−	0.549854i
$341$	−1.20941	+	2.09475i	−0.0654931	+	0.113437i
$342$	48.4738			2.62116
$343$	−5.27867	−	17.7521i	−0.285021	−	0.958521i
$344$			5.38135i			0.290143i
$345$	21.3603	+	16.5405i	1.15000	+	0.890512i
$346$	3.35224	−	1.93542i	0.180218	−	0.104049i
$347$	8.99315	+	15.5766i	0.482778	+	0.836195i	0.999804	−	0.0197738i	$-0.00629459\pi$
$347$	8.99315	+	15.5766i	0.482778	+	0.836195i	−0.517027	+	0.855969i	$0.672961\pi$
$348$	−10.4812	−	6.05133i	−0.561852	−	0.324385i
$349$			25.6410i			1.37253i	0.727352	+	0.686265i	$0.240751\pi$
$349$			25.6410i			1.37253i	−0.727352	+	0.686265i	$0.759249\pi$
$350$	0.409946	+	4.24190i	0.0219125	+	0.226739i
$351$	−30.6507			−1.63601
$352$	−3.87183	−	2.23540i	−0.206369	−	0.119147i
$353$	22.1123	−	12.7666i	1.17692	−	0.679496i	0.221621	−	0.975133i	$-0.428865\pi$
$353$	22.1123	−	12.7666i	1.17692	−	0.679496i	0.955300	+	0.295637i	$0.0955319\pi$
$354$	21.5422	+	37.3121i	1.14495	+	1.98312i
$355$	−1.52384	+	2.63937i	−0.0808772	+	0.140083i
$356$	−4.25438			−0.225482
$357$	21.3329	−	46.8542i	1.12906	−	2.47978i
$358$	5.96242			0.315124
$359$	−14.2927	−	8.25192i	−0.754342	−	0.435520i	0.0729186	−	0.997338i	$-0.476769\pi$
$359$	−14.2927	−	8.25192i	−0.754342	−	0.435520i	−0.827261	+	0.561818i	$0.810102\pi$
$360$	5.85688	+	10.1444i	0.308685	+	0.534658i
$361$	−19.5198	−	33.8093i	−1.02736	−	1.77944i
$362$	−9.90844	+	17.1619i	−0.520776	+	0.902011i
$363$			27.5022i			1.44349i
$364$	4.57888	+	6.41460i	0.239998	+	0.336216i
$365$		−	16.3493i		−	0.855760i
$366$	−28.1855	−	16.2729i	−1.47328	−	0.850599i
$367$	17.8726	+	30.9562i	0.932940	+	1.61590i	0.778267	+	0.627934i	$0.216099\pi$
$367$	17.8726	+	30.9562i	0.932940	+	1.61590i	0.154673	+	0.987966i	$0.450568\pi$
$368$	1.81572	+	4.43882i	0.0946511	+	0.231390i
$369$	7.74329	+	4.47059i	0.403100	+	0.232730i
$370$		−	1.15948i		−	0.0602784i
$371$	0.00822809	+	0.0115268i	0.000427181	+	0.000598443i
$372$	1.65546			0.0858317
$373$	−8.31461	−	4.80044i	−0.430514	−	0.248558i	0.269051	−	0.963126i	$-0.413290\pi$
$373$	−8.31461	−	4.80044i	−0.430514	−	0.248558i	−0.699566	+	0.714568i	$0.746623\pi$
$374$	−24.6219	+	14.2154i	−1.27317	+	0.735063i
$375$	−32.2504	+	18.6198i	−1.66540	+	0.961521i
$376$	7.64578	+	4.41429i	0.394301	+	0.227650i
$377$		−	11.7821i		−	0.606808i
$378$	−11.2808	+	24.7764i	−0.580221	+	1.27436i
$379$			28.4573i			1.46175i	0.682509	+	0.730877i	$0.260889\pi$
$379$			28.4573i			1.46175i	−0.682509	+	0.730877i	$0.739111\pi$
$380$	7.01267	−	12.1463i	0.359742	−	0.623092i
$381$	−4.92783	+	2.84508i	−0.252460	+	0.145758i
$382$	16.7923	−	9.69503i	0.859168	−	0.496041i
$383$	2.57501	−	4.46005i	0.131577	−	0.227898i	−0.792708	−	0.609602i	$-0.791329\pi$
$383$	2.57501	−	4.46005i	0.131577	−	0.227898i	0.924285	+	0.381704i	$0.124663\pi$
$384$			3.05986i			0.156148i
$385$	−21.6754	+	2.09475i	−1.10468	+	0.106759i
$386$	22.8394			1.16249
$387$	−29.6529	−	17.1201i	−1.50734	−	0.870264i
$388$	8.10782	+	14.0431i	0.411612	+	0.712933i
$389$	26.8861	−	15.5227i	1.36318	−	0.787033i	0.373134	−	0.927777i	$-0.378283\pi$
$389$	26.8861	−	15.5227i	1.36318	−	0.787033i	0.990046	+	0.140745i	$0.0449497\pi$
$390$	−8.39008	+	14.5320i	−0.424848	+	0.735858i
$391$	30.2191	+	4.11410i	1.52824	+	0.208059i
$392$	6.87045	−	1.34047i	0.347010	−	0.0677039i
$393$	−22.3035			−1.12506
$394$	8.84397	−	15.3182i	0.445553	−	0.771720i
$395$	8.23376	−	4.75376i	0.414286	−	0.239188i
$396$	24.6355	−	14.2233i	1.23798	−	0.714748i
$397$	−4.78832	−	2.76454i	−0.240319	−	0.138748i	0.375004	−	0.927023i	$-0.377641\pi$
$397$	−4.78832	−	2.76454i	−0.240319	−	0.138748i	−0.615323	+	0.788275i	$0.710975\pi$
$398$	−14.0034			−0.701929
$399$	61.3895	−	5.93281i	3.07332	−	0.297012i
$400$	−1.61076			−0.0805379
$401$	−6.14194	−	3.54605i	−0.306714	−	0.177081i	0.338741	−	0.940880i	$-0.389999\pi$
$401$	−6.14194	−	3.54605i	−0.306714	−	0.177081i	−0.645455	+	0.763798i	$0.723332\pi$
$402$	2.46938	+	4.27710i	0.123162	+	0.213322i
$403$	0.805805	+	1.39570i	0.0401400	+	0.0695246i
$404$	14.2789	+	8.24392i	0.710401	+	0.410150i
$405$	−22.8216			−1.13401
$406$	−9.52402	−	4.33632i	−0.472669	−	0.215208i
$407$	−2.81576			−0.139572
$408$	16.8515	+	9.72920i	0.834272	+	0.481667i
$409$	14.5127	−	8.37889i	0.717605	−	0.414310i	−0.0962653	−	0.995356i	$-0.530690\pi$
$409$	14.5127	−	8.37889i	0.717605	−	0.414310i	0.813871	+	0.581046i	$0.197356\pi$
$410$	2.24043	−	1.29351i	0.110647	−	0.0638821i
$411$	−21.7914	+	37.7438i	−1.07489	+	1.86177i
$412$	3.64827			0.179737
$413$	21.6438	+	30.3210i	1.06502	+	1.49200i
$414$	−30.2358	−	4.11638i	−1.48601	−	0.202309i
$415$	9.67170	−	16.7519i	0.474765	−	0.822317i
$416$	−2.57973	+	1.48941i	−0.126481	+	0.0730241i
$417$	3.35538	+	5.81168i	0.164314	+	0.284599i
$418$	−29.4970	−	17.0301i	−1.44275	−	0.832970i
$419$	−35.9118			−1.75441			−0.877204	−	0.480119i	$-0.840594\pi$
$419$	−35.9118			−1.75441			−0.877204	+	0.480119i	$0.840594\pi$
$420$	8.65903	+	12.1305i	0.422517	+	0.591909i
$421$		−	36.1809i		−	1.76335i	−0.471860	−	0.881673i	$-0.656417\pi$
$421$		−	36.1809i		−	1.76335i	0.471860	−	0.881673i	$-0.343583\pi$
$422$	2.60935	−	4.51953i	0.127021	−	0.220007i
$423$	−48.6482	+	28.0871i	−2.36536	+	1.36564i
$424$	−0.00463568	+	0.00267641i	−0.000225129	+	0.000129978i
$425$	−5.12160	+	8.87087i	−0.248434	+	0.430300i
$426$		−	5.06548i		−	0.245423i
$427$	−25.6115	−	11.6610i	−1.23943	−	0.564316i
$428$		−	4.13942i		−	0.200086i
$429$	35.2907	+	20.3751i	1.70385	+	0.983720i
$430$	−8.57973	+	4.95351i	−0.413751	+	0.238879i
$431$	−33.7667	+	19.4952i	−1.62649	+	0.939052i	−0.641356	+	0.767243i	$0.721628\pi$
$431$	−33.7667	+	19.4952i	−1.62649	+	0.939052i	−0.985130	+	0.171809i	$0.945039\pi$
$432$	−8.91102	−	5.14478i	−0.428732	−	0.247528i
$433$	9.77042			0.469537			0.234768	−	0.972051i	$-0.424567\pi$
$433$	9.77042			0.469537			0.234768	+	0.972051i	$0.424567\pi$
$434$	1.42478	−	0.137694i	0.0683916	−	0.00660950i
$435$		−	22.2809i		−	1.06829i
$436$	0.818243	+	0.472413i	0.0391867	+	0.0226245i
$437$	13.8329	+	33.8166i	0.661715	+	1.61767i
$438$	13.5869	+	23.5331i	0.649205	+	1.12446i
$439$	22.6269	+	13.0636i	1.07992	+	0.623494i	0.930876	−	0.365336i	$-0.119046\pi$
$439$	22.6269	+	13.0636i	1.07992	+	0.623494i	0.149047	+	0.988830i	$0.452379\pi$
$440$		−	8.23070i		−	0.392383i
$441$	−14.4711	+	42.1228i	−0.689100	+	2.00585i
$442$			18.9430i			0.901025i
$443$	15.4187	−	26.7060i	0.732566	−	1.26884i	−0.223218	−	0.974769i	$-0.571656\pi$
$443$	15.4187	−	26.7060i	0.732566	−	1.26884i	0.955783	−	0.294072i	$-0.0950106\pi$
$444$	0.963569	+	1.66895i	0.0457290	+	0.0792049i
$445$	−3.91614	−	6.78295i	−0.185643	−	0.321543i
$446$	−0.258844	−	0.149443i	−0.0122566	−	0.00707635i
$447$	30.5864			1.44669
$448$	0.254505	+	2.63348i	0.0120242	+	0.124420i
$449$	−20.7845			−0.980880			−0.490440	−	0.871475i	$-0.663164\pi$
$449$	−20.7845			−0.980880			−0.490440	+	0.871475i	$0.663164\pi$
$450$	5.12443	−	8.87577i	0.241568	−	0.418408i
$451$	−3.14127	−	5.44084i	−0.147917	−	0.256199i
$452$	7.85292	−	4.53389i	0.369370	−	0.213256i
$453$	10.4427	+	6.02907i	0.490639	+	0.283270i
$454$	−7.37323			−0.346043
$455$	−6.01225	+	13.2049i	−0.281858	+	0.619056i
$456$			23.3112i			1.09165i
$457$	15.7019	+	9.06549i	0.734504	+	0.424066i	0.820068	−	0.572267i	$-0.193936\pi$
$457$	15.7019	+	9.06549i	0.734504	+	0.424066i	−0.0855638	+	0.996333i	$0.527269\pi$
$458$	−9.71859	−	16.8331i	−0.454120	−	0.786559i
$459$	−56.6673	+	32.7169i	−2.64500	+	1.52709i
$460$	−5.40564	+	6.98080i	−0.252039	+	0.325481i
$461$		−	3.64937i		−	0.169968i	−0.996382	−	0.0849841i	$-0.972916\pi$
$461$		−	3.64937i		−	0.169968i	0.996382	−	0.0849841i	$-0.0270840\pi$
$462$	29.4587	−	21.0282i	1.37054	−	0.978323i
$463$	25.2623			1.17404			0.587018	−	0.809574i	$-0.300302\pi$
$463$	25.2623			1.17404			0.587018	+	0.809574i	$0.300302\pi$
$464$	1.97765	−	3.42539i	0.0918100	−	0.159020i
$465$	1.52384	+	2.63937i	0.0706665	+	0.122398i
$466$	−8.90505	−	15.4240i	−0.412519	−	0.714503i
$467$	−6.07496	+	10.5221i	−0.281116	+	0.486907i	−0.971660	−	0.236384i	$-0.924038\pi$
$467$	−6.07496	+	10.5221i	−0.281116	+	0.486907i	0.690544	+	0.723290i	$0.257371\pi$
$468$		−	18.9534i		−	0.876123i
$469$	2.48103	+	3.47571i	0.114564	+	0.160493i
$470$			16.2533i			0.749710i
$471$	24.8382	+	14.3404i	1.14449	+	0.660769i
$472$	−12.1940	+	7.04024i	−0.561277	+	0.324053i
$473$	12.0295	+	20.8357i	0.553116	+	0.958025i
$474$	−7.90111	+	13.6851i	−0.362910	+	0.628579i
$475$	−12.2714			−0.563048
$476$	15.3125	+	6.97184i	0.701848	+	0.319554i
$477$		−	0.0340587i		−	0.00155944i
$478$	5.44619	−	9.43308i	0.249103	−	0.431459i
$479$	−7.26682	−	12.5865i	−0.332029	−	0.575092i	0.650880	−	0.759180i	$-0.274400\pi$
$479$	−7.26682	−	12.5865i	−0.332029	−	0.575092i	−0.982910	+	0.184089i	$0.941067\pi$
$480$	−4.87847	+	2.81659i	−0.222671	+	0.128559i
$481$	−0.938046	+	1.62474i	−0.0427712	+	0.0740819i
$482$	−0.938799			−0.0427611
$483$	−38.7958	−	1.51255i	−1.76527	−	0.0688236i
$484$	−8.98806			−0.408548
$485$	−14.9264	+	25.8533i	−0.677773	+	1.17394i
$486$	6.11630	−	3.53125i	0.277441	−	0.160181i
$487$	15.5777	+	26.9814i	0.705895	+	1.22265i	0.966368	+	0.257165i	$0.0827883\pi$
$487$	15.5777	+	26.9814i	0.705895	+	1.22265i	−0.260472	+	0.965481i	$0.583878\pi$
$488$	5.31819	−	9.21137i	0.240743	−	0.416979i
$489$		−	12.5793i		−	0.568858i
$490$	8.46139	+	9.71997i	0.382246	+	0.439103i
$491$	−32.5336			−1.46822			−0.734111	−	0.679029i	$-0.762401\pi$
$491$	−32.5336			−1.46822			−0.734111	+	0.679029i	$0.762401\pi$
$492$	−2.14992	+	3.72377i	−0.0969258	+	0.167880i
$493$	−12.5763	−	21.7829i	−0.566410	−	0.981051i
$494$	−19.6533	+	11.3468i	−0.884244	+	0.510519i
$495$	45.3537	+	26.1849i	2.03850	+	1.17693i
$496$			0.541025i			0.0242927i
$497$	−0.421323	−	4.35963i	−0.0188989	−	0.195556i
$498$			32.1502i			1.44068i
$499$	6.96483	−	12.0634i	0.311789	−	0.540034i	−0.666961	−	0.745093i	$-0.732405\pi$
$499$	6.96483	−	12.0634i	0.311789	−	0.540034i	0.978750	+	0.205059i	$0.0657386\pi$
$500$	−6.08517	−	10.5398i	−0.272137	−	0.471355i
$501$	−4.31092	−	7.46674i	−0.192598	−	0.333589i
$502$	3.33979	−	5.78468i	0.149062	−	0.258183i
$503$	4.12741			0.184032			0.0920162	−	0.995758i	$-0.470669\pi$
$503$	4.12741			0.184032			0.0920162	+	0.995758i	$0.470669\pi$
$504$	−15.3210	−	6.97570i	−0.682450	−	0.310722i
$505$			30.3539i			1.35073i
$506$	16.9527	+	13.1275i	0.753640	+	0.583588i
$507$	−10.9354	+	6.31355i	−0.485657	+	0.280394i
$508$	−0.929808	−	1.61047i	−0.0412535	−	0.0714532i
$509$	−25.7056	−	14.8411i	−1.13938	−	0.657822i	−0.193104	−	0.981178i	$-0.561856\pi$
$509$	−25.7056	−	14.8411i	−1.13938	−	0.657822i	−0.946277	+	0.323356i	$0.895189\pi$
$510$			35.8227i			1.58626i
$511$	13.6510	+	19.1238i	0.603883	+	0.845986i
$512$	−1.00000			−0.0441942
$513$	−67.8875	−	39.1948i	−2.99731	−	1.73049i
$514$	5.44032	−	3.14097i	0.239962	−	0.138542i
$515$	3.35821	+	5.81659i	0.147980	+	0.256310i
$516$	8.23310	−	14.2601i	0.362442	−	0.627768i
$517$	39.4709			1.73593
$518$	0.968115	+	1.35624i	0.0425365	+	0.0595899i
$519$	−11.8442			−0.519903
$520$	−4.74925	−	2.74198i	−0.208268	−	0.120244i
$521$	13.2603	+	22.9675i	0.580943	+	1.00622i	0.995368	+	0.0961392i	$0.0306494\pi$
$521$	13.2603	+	22.9675i	0.580943	+	1.00622i	−0.414425	+	0.910083i	$0.636017\pi$
$522$	12.5833	+	21.7949i	0.550756	+	0.953937i
$523$	7.66702	−	13.2797i	0.335255	−	0.580679i	−0.648279	−	0.761403i	$-0.724511\pi$
$523$	7.66702	−	13.2797i	0.335255	−	0.580679i	0.983534	+	0.180724i	$0.0578441\pi$
$524$		−	7.28906i		−	0.318424i
$525$	5.40349	−	11.8679i	0.235828	−	0.517957i
$526$		−	14.3974i		−	0.627757i
$527$	2.97957	+	1.72025i	0.129792	+	0.0749354i
$528$	6.84002	+	11.8473i	0.297673	+	0.515586i
$529$	−5.75662	−	22.2679i	−0.250288	−	0.968172i
$530$	−0.00853425	−	0.00492725i	−0.000370704	−	0.000214026i
$531$		−	89.5906i		−	3.88790i
$532$	1.93892	+	20.0628i	0.0840626	+	0.869835i
$533$	−4.18594			−0.181313
$534$	11.2738	+	6.50891i	0.487864	+	0.281668i
$535$	6.59965	−	3.81031i	0.285328	−	0.164734i
$536$	−1.39781	+	0.807025i	−0.0603761	+	0.0348582i
$537$	−15.7999	−	9.12210i	−0.681818	−	0.393648i
$538$		−	9.10227i		−	0.392427i
$539$	23.6047	−	20.5483i	1.01673	−	0.885077i
$540$		−	18.9430i		−	0.815176i
$541$	−0.205460	+	0.355867i	−0.00883340	+	0.0152999i	−0.870408	−	0.492331i	$-0.836145\pi$
$541$	−0.205460	+	0.355867i	−0.00883340	+	0.0152999i	0.861575	+	0.507630i	$0.169478\pi$
$542$	−5.60067	+	3.23355i	−0.240569	+	0.138893i
$543$	52.5131	−	30.3185i	2.25355	−	1.30109i
$544$	−3.17962	+	5.50726i	−0.136325	+	0.236122i
$545$			1.73941i			0.0745083i
$546$	−2.31975	−	24.0035i	−0.0992762	−	1.02726i
$547$	4.16687			0.178163			0.0890813	−	0.996024i	$-0.471607\pi$
$547$	4.16687			0.178163			0.0890813	+	0.996024i	$0.471607\pi$
$548$	−12.3351	−	7.12170i	−0.526931	−	0.304224i
$549$	33.8383	+	58.6097i	1.44418	+	2.50140i
$550$	−6.23658	+	3.60069i	−0.265929	+	0.153534i
$551$	15.0665	−	26.0959i	0.641853	−	1.11172i
$552$	1.97957	−	14.5404i	0.0842563	−	0.618883i
$553$	−5.66186	+	12.4353i	−0.240767	+	0.528804i
$554$	2.30265			0.0978302
$555$	−1.77392	+	3.07252i	−0.0752987	+	0.130421i
$556$	−1.89933	+	1.09658i	−0.0805495	+	0.0465053i
$557$	20.1227	−	11.6178i	0.852624	−	0.492263i	−0.00891128	−	0.999960i	$-0.502837\pi$
$557$	20.1227	−	11.6178i	0.852624	−	0.492263i	0.861535	+	0.507698i	$0.169503\pi$
$558$	−2.98121	−	1.72120i	−0.126205	−	0.0728644i
$559$	16.0300			0.677998
$560$	−3.96440	+	2.82987i	−0.167527	+	0.119584i
$561$	86.9946			3.67291
$562$	11.9577	+	6.90377i	0.504404	+	0.291218i
$563$	−9.11708	−	15.7912i	−0.384239	−	0.665522i	0.607424	−	0.794378i	$-0.292203\pi$
$563$	−9.11708	−	15.7912i	−0.384239	−	0.665522i	−0.991663	+	0.128856i	$0.958870\pi$
$564$	−13.5071	−	23.3950i	−0.568753	−	0.985109i
$565$	14.4571	+	8.34684i	0.608217	+	0.351154i
$566$	14.3347			0.602534
$567$	26.6945	−	19.0551i	1.12106	−	0.800238i
$568$	1.65546			0.0694616
$569$	−19.2559	−	11.1174i	−0.807250	−	0.466066i	0.0387500	−	0.999249i	$-0.487662\pi$
$569$	−19.2559	−	11.1174i	−0.807250	−	0.466066i	−0.846000	+	0.533183i	$0.820996\pi$
$570$	−37.1660	+	21.4578i	−1.55671	+	0.898768i
$571$	17.7300	−	10.2364i	0.741978	−	0.428381i	−0.0808098	−	0.996730i	$-0.525751\pi$
$571$	17.7300	−	10.2364i	0.741978	−	0.428381i	0.822788	+	0.568348i	$0.192417\pi$
$572$	−6.65883	+	11.5334i	−0.278420	+	0.482237i
$573$	−59.3309			−2.47858
$574$	−1.54061	+	3.38369i	−0.0643038	+	0.141233i
$575$	7.65432	+	1.04208i	0.319207	+	0.0434577i
$576$	3.18138	−	5.51031i	0.132557	−	0.229596i
$577$	17.1680	−	9.91194i	0.714713	−	0.412640i	−0.0980909	−	0.995177i	$-0.531274\pi$
$577$	17.1680	−	9.91194i	0.714713	−	0.412640i	0.812804	+	0.582538i	$0.197940\pi$
$578$	11.7200	+	20.2996i	0.487486	+	0.844351i
$579$	−60.5225	−	34.9427i	−2.51523	−	1.45217i
$580$	7.28166			0.302354
$581$	2.67410	+	27.6702i	0.110940	+	1.14795i
$582$		−	49.6176i		−	2.05672i
$583$	−0.0119657	+	0.0207252i	−0.000495569	+	0.000858351i
$584$	−7.69091	+	4.44035i	−0.318252	+	0.183743i
$585$	30.2183	−	17.4465i	1.24937	−	0.721326i
$586$	4.10282	−	7.10630i	0.169486	−	0.293559i
$587$		−	1.92967i		−	0.0796460i	−0.999207	−	0.0398230i	$-0.987321\pi$
$587$		−	1.92967i		−	0.0796460i	0.999207	−	0.0398230i	$-0.0126794\pi$
$588$	−20.2570	−	6.95919i	−0.835383	−	0.286992i
$589$			4.12173i			0.169833i
$590$	−22.4491	−	12.9610i	−0.924215	−	0.533596i
$591$	−46.8716	+	27.0613i	−1.92804	+	1.11315i
$592$	−0.545433	+	0.314906i	−0.0224172	+	0.0129426i
$593$	6.42783	+	3.71111i	0.263959	+	0.152397i	0.626139	−	0.779711i	$-0.284634\pi$
$593$	6.42783	+	3.71111i	0.263959	+	0.152397i	−0.362180	+	0.932108i	$0.617967\pi$
$594$	−46.0026			−1.88751
$595$	2.97957	+	30.8309i	0.122150	+	1.26395i
$596$			9.99602i			0.409453i
$597$	37.1080	+	21.4243i	1.51873	+	0.876838i
$598$	13.2224	−	5.40870i	0.540705	−	0.221178i
$599$	−17.3544	−	30.0587i	−0.709081	−	1.22816i	−0.965199	−	0.261518i	$-0.915777\pi$
$599$	−17.3544	−	30.0587i	−0.709081	−	1.22816i	0.256118	−	0.966646i	$-0.417556\pi$
$600$	4.26838	+	2.46435i	0.174256	+	0.100607i
$601$			37.6637i			1.53634i	0.640249	+	0.768168i	$0.278831\pi$
$601$			37.6637i			1.53634i	−0.640249	+	0.768168i	$0.721169\pi$
$602$	5.89976	−	12.9578i	0.240456	−	0.528122i
$603$		−	10.2698i		−	0.418218i
$604$	−1.97037	+	3.41279i	−0.0801734	+	0.138864i
$605$	−8.27346	−	14.3301i	−0.336364	−	0.582600i
$606$	−25.2253	−	43.6914i	−1.02471	−	1.77484i
$607$	−32.7045	−	18.8819i	−1.32743	−	0.766394i	−0.342531	−	0.939507i	$-0.611284\pi$
$607$	−32.7045	−	18.8819i	−1.32743	−	0.766394i	−0.984902	+	0.173113i	$0.944618\pi$
$608$	−7.61837			−0.308966
$609$	18.6036	+	26.0620i	0.753856	+	1.05609i
$610$	19.5815			0.792830
$611$	13.1493	−	22.7753i	0.531966	−	0.921391i
$612$	−20.2311	−	35.0414i	−0.817795	−	1.41646i
$613$	−29.8306	+	17.2227i	−1.20485	+	0.695619i	−0.961629	−	0.274353i	$-0.911536\pi$
$613$	−29.8306	+	17.2227i	−1.20485	+	0.695619i	−0.243218	+	0.969972i	$0.578203\pi$
$614$	24.0192	+	13.8675i	0.969337	+	0.559647i
$615$	−7.91595			−0.319202
$616$	6.87229	+	9.62747i	0.276892	+	0.387902i
$617$			21.6733i			0.872535i	0.899817	+	0.436267i	$0.143700\pi$
$617$			21.6733i			0.872535i	−0.899817	+	0.436267i	$0.856300\pi$
$618$	−9.66760	−	5.58159i	−0.388888	−	0.224525i
$619$	15.2301	+	26.3793i	0.612149	+	1.06027i	0.990878	+	0.134766i	$0.0430281\pi$
$619$	15.2301	+	26.3793i	0.612149	+	1.06027i	−0.378728	+	0.925508i	$0.623639\pi$
$620$	−0.862579	+	0.498010i	−0.0346420	+	0.0200006i
$621$	39.0167	+	30.2129i	1.56569	+	1.21240i
$622$			14.9447i			0.599227i
$623$	10.2442	+	4.66422i	0.410425	+	0.186868i
$624$	9.11475			0.364882
$625$	7.17583	−	12.4289i	0.287033	−	0.497156i
$626$	−8.00364	−	13.8627i	−0.319890	−	0.554065i
$627$	52.1098	+	90.2568i	2.08106	+	3.60451i
$628$	−4.68661	+	8.11744i	−0.187016	+	0.323921i
$629$			4.00513i			0.159695i
$630$	−2.98121	−	30.8480i	−0.118774	−	1.22901i
$631$			19.9508i			0.794228i	0.917769	+	0.397114i	$0.129988\pi$
$631$			19.9508i			0.794228i	−0.917769	+	0.397114i	$0.870012\pi$
$632$	−4.47247	−	2.58218i	−0.177905	−	0.102714i
$633$	−13.8291	+	7.98426i	−0.549659	+	0.317346i
$634$	5.71100	+	9.89175i	0.226813	+	0.392851i
$635$	1.71177	−	2.96487i	0.0679294	−	0.117657i
$636$	0.0163789			0.000649466
$637$	−3.99300	−	20.4658i	−0.158209	−	0.810884i
$638$		−	17.6833i		−	0.700090i
$639$	−5.26665	+	9.12210i	−0.208345	+	0.360865i
$640$	−0.920495	−	1.59434i	−0.0363857	−	0.0630220i
$641$	−32.4982	+	18.7628i	−1.28360	+	0.741087i	−0.977505	−	0.210914i	$-0.932356\pi$
$641$	−32.4982	+	18.7628i	−1.28360	+	0.741087i	−0.306095	+	0.952001i	$0.599023\pi$
$642$	−6.33302	+	10.9691i	−0.249944	+	0.432916i
$643$	−5.69930			−0.224758			−0.112379	−	0.993665i	$-0.535847\pi$
$643$	−5.69930			−0.224758			−0.112379	+	0.993665i	$0.535847\pi$
$644$	0.494321	−	12.6789i	0.0194790	−	0.499620i
$645$	30.3141			1.19362
$646$	−24.2235	+	41.9564i	−0.953062	+	1.65075i
$647$	−2.00126	+	1.15543i	−0.0786776	+	0.0454245i	−0.538823	−	0.842419i	$-0.681131\pi$
$647$	−2.00126	+	1.15543i	−0.0786776	+	0.0454245i	0.460145	+	0.887844i	$0.347797\pi$
$648$	6.19818	+	10.7356i	0.243488	+	0.421733i
$649$	−31.4755	+	54.5172i	−1.23552	+	2.13999i
$650$			4.79814i			0.188199i
$651$	−3.98621	−	1.81494i	−0.156232	−	0.0711330i
$652$	4.11108			0.161002
$653$	20.0312	−	34.6951i	0.783882	−	1.35772i	−0.145783	−	0.989317i	$-0.546570\pi$
$653$	20.0312	−	34.6951i	0.783882	−	1.35772i	0.929665	−	0.368407i	$-0.120097\pi$
$654$	−1.44552	−	2.50371i	−0.0565242	−	0.0979028i
$655$	11.6213	−	6.70954i	0.454080	−	0.262163i
$656$	−1.21697	−	0.702619i	−0.0475148	−	0.0274327i
$657$		−	56.5057i		−	2.20450i
$658$	−13.5709	−	19.0116i	−0.529047	−	0.741148i
$659$		−	30.5586i		−	1.19039i	−0.803580	−	0.595197i	$-0.797074\pi$
$659$		−	30.5586i		−	1.19039i	0.803580	−	0.595197i	$-0.202926\pi$
$660$	−12.5924	+	21.8107i	−0.490158	+	0.848979i
$661$	0.250564	+	0.433989i	0.00974581	+	0.0168802i	0.870857	−	0.491536i	$-0.163564\pi$
$661$	0.250564	+	0.433989i	0.00974581	+	0.0168802i	−0.861111	+	0.508416i	$0.830231\pi$
$662$	−7.97211	−	13.8081i	−0.309845	−	0.536667i
$663$	28.9814	−	50.1973i	1.12555	−	1.94950i
$664$	−10.5071			−0.407753
$665$	−30.2023	+	21.5590i	−1.17120	+	0.836024i
$666$		−	4.00734i		−	0.155281i
$667$	−11.6138	+	14.9980i	−0.449689	+	0.580724i
$668$	2.44022	−	1.40886i	0.0944150	−	0.0545105i
$669$	0.457276	+	0.792026i	0.0176793	+	0.0306215i
$670$	−2.57335	−	1.48572i	−0.0994171	−	0.0573985i
$671$		−	47.5531i		−	1.83577i
$672$	3.35463	−	7.36789i	0.129408	−	0.284222i
$673$	−44.4337			−1.71279			−0.856396	−	0.516320i	$-0.827301\pi$
$673$	−44.4337			−1.71279			−0.856396	+	0.516320i	$0.827301\pi$
$674$	12.2456	+	7.07001i	0.471683	+	0.272327i
$675$	−14.3535	+	8.28700i	−0.552466	+	0.318967i
$676$	−2.06334	−	3.57382i	−0.0793594	−	0.137454i
$677$	5.86630	−	10.1607i	0.225460	−	0.390509i	−0.730997	−	0.682380i	$-0.760945\pi$
$677$	5.86630	−	10.1607i	0.225460	−	0.390509i	0.956457	+	0.291872i	$0.0942781\pi$
$678$	−27.7461			−1.06558
$679$	−4.12696	−	42.7036i	−0.158378	−	1.63881i
$680$	−11.7073			−0.448954
$681$	19.5385	+	11.2805i	0.748715	+	0.432271i
$682$	1.20941	+	2.09475i	0.0463106	+	0.0802123i
$683$	10.3596	+	17.9434i	0.396400	+	0.686584i	0.993279	−	0.115747i	$-0.0369261\pi$
$683$	10.3596	+	17.9434i	0.396400	+	0.686584i	−0.596879	+	0.802331i	$0.703593\pi$
$684$	24.2369	−	41.9796i	0.926721	−	1.60513i
$685$		−	26.2219i		−	1.00189i
$686$	−18.0131	−	4.30457i	−0.687742	−	0.164349i
$687$			59.4751i			2.26912i
$688$	4.66039	+	2.69068i	0.177676	+	0.102581i
$689$	0.00797253	+	0.0138088i	0.000303729	+	0.000526074i
$690$	25.0047	−	10.2283i	0.951911	−	0.389384i
$691$	30.3661	+	17.5319i	1.15518	+	0.666943i	0.950144	−	0.311811i	$-0.100936\pi$
$691$	30.3661	+	17.5319i	1.15518	+	0.666943i	0.205036	+	0.978755i	$0.434269\pi$
$692$		−	3.87083i		−	0.147147i
$693$	−74.9136	+	7.23981i	−2.84573	+	0.275018i
$694$	17.9863			0.682751
$695$	−3.49664	−	2.01879i	−0.132635	−	0.0765770i
$696$	−10.4812	+	6.05133i	−0.397289	+	0.229375i
$697$	−7.73902	+	4.46812i	−0.293136	+	0.169242i
$698$	22.2057	+	12.8205i	0.840500	+	0.485263i
$699$			54.4964i			2.06124i
$700$	3.87857	+	1.76593i	0.146596	+	0.0667458i
$701$		−	9.80074i		−	0.370169i	−0.982723	−	0.185084i	$-0.940744\pi$
$701$		−	9.80074i		−	0.370169i	0.982723	−	0.185084i	$-0.0592559\pi$
$702$	−15.3253	+	26.5442i	−0.578417	+	1.00185i
$703$	−4.15531	+	2.39907i	−0.156721	+	0.0904827i
$704$	−3.87183	+	2.23540i	−0.145925	+	0.0842498i
$705$	24.8665	−	43.0700i	0.936526	−	1.62211i
$706$		−	25.5331i		−	0.960952i
$707$	−25.3443	−	35.5051i	−0.953169	−	1.33531i
$708$	43.0843			1.61921
$709$	33.8219	+	19.5271i	1.27021	+	0.733356i	0.975027	−	0.222085i	$-0.0712862\pi$
$709$	33.8219	+	19.5271i	1.27021	+	0.733356i	0.295182	+	0.955441i	$0.404620\pi$
$710$	1.52384	+	2.63937i	0.0571888	+	0.0990539i
$711$	28.4572	−	16.4298i	1.06723	−	0.616164i
$712$	−2.12719	+	3.68440i	−0.0797199	+	0.138079i
$713$	0.350015	−	2.57095i	0.0131082	−	0.0962827i
$714$	−29.9104	−	41.9019i	−1.11937	−	1.56814i
$715$	−24.5177			−0.916910
$716$	2.98121	−	5.16361i	0.111413	−	0.192973i
$717$	−28.8639	+	16.6646i	−1.07794	+	0.622350i
$718$	−14.2927	+	8.25192i	−0.533400	+	0.307959i
$719$	−9.40678	−	5.43101i	−0.350814	−	0.202542i	0.314230	−	0.949347i	$-0.398254\pi$
$719$	−9.40678	−	5.43101i	−0.350814	−	0.202542i	−0.665044	+	0.746805i	$0.731587\pi$
$720$	11.7138			0.436546
$721$	−8.78471	−	3.99971i	−0.327160	−	0.148957i
$722$	−39.0396			−1.45290
$723$	2.48774	+	1.43630i	0.0925201	+	0.0534165i
$724$	9.90844	+	17.1619i	0.368244	+	0.637818i
$725$	−3.18551	−	5.51747i	−0.118307	−	0.204914i
$726$	23.8176	+	13.7511i	0.883955	+	0.510352i
$727$	9.04746			0.335552			0.167776	−	0.985825i	$-0.446342\pi$
$727$	9.04746			0.335552			0.167776	+	0.985825i	$0.446342\pi$
$728$	7.84464	−	0.758123i	0.290742	−	0.0280979i
$729$	15.5788			0.576994
$730$	−14.1589	−	8.17464i	−0.524044	−	0.302557i
$731$	29.6365	−	17.1107i	1.09615	−	0.632861i
$732$	−28.1855	+	16.2729i	−1.04177	+	0.601464i
$733$	4.80870	−	8.32891i	0.177613	−	0.307635i	−0.763449	−	0.645868i	$-0.776496\pi$
$733$	4.80870	−	8.32891i	0.177613	−	0.307635i	0.941063	+	0.338232i	$0.109829\pi$
$734$	35.7451			1.31938
$735$	−7.55110	−	38.7025i	−0.278526	−	1.42756i
$736$	4.75200	+	0.646949i	0.175161	+	0.0238469i
$737$	−3.60805	+	6.24932i	−0.132904	+	0.230197i
$738$	7.74329	−	4.47059i	0.285035	−	0.164565i
$739$	26.1195	+	45.2403i	0.960820	+	1.66419i	0.720448	+	0.693509i	$0.243936\pi$
$739$	26.1195	+	45.2403i	0.960820	+	1.66419i	0.240372	+	0.970681i	$0.422731\pi$
$740$	−1.00414	−	0.579739i	−0.0369128	−	0.0213116i
$741$	69.4395			2.55093
$742$	0.0140966	−	0.00136232i	0.000517502	−	5.00124e-5i
$743$		−	0.812773i		−	0.0298177i	−0.999889	−	0.0149089i	$-0.995254\pi$
$743$		−	0.812773i		−	0.0298177i	0.999889	−	0.0149089i	$-0.00474582\pi$
$744$	0.827731	−	1.43367i	0.0303461	−	0.0525609i
$745$	−15.9371	+	9.20128i	−0.583890	+	0.337109i
$746$	−8.31461	+	4.80044i	−0.304420	+	0.175757i
$747$	33.4269	−	57.8971i	1.22303	−	2.11835i
$748$			28.4309i			1.03954i
$749$	−4.53818	+	9.96736i	−0.165821	+	0.364200i
$750$			37.2395i			1.35980i
$751$	−0.626162	−	0.361515i	−0.0228490	−	0.0131919i	0.488532	−	0.872546i	$-0.337533\pi$
$751$	−0.626162	−	0.361515i	−0.0228490	−	0.0131919i	−0.511381	+	0.859354i	$0.670866\pi$
$752$	7.64578	−	4.41429i	0.278813	−	0.160973i
$753$	−17.7003	+	10.2193i	−0.645036	+	0.372411i
$754$	−10.2036	−	5.89104i	−0.371593	−	0.214539i
$755$	−7.25487			−0.264032
$756$	15.8166	+	22.1576i	0.575244	+	0.805865i
$757$		−	6.02295i		−	0.218908i	−0.993992	−	0.109454i	$-0.965090\pi$
$757$		−	6.02295i		−	0.218908i	0.993992	−	0.109454i	$-0.0349102\pi$
$758$	24.6448	+	14.2287i	0.895138	+	0.516808i
$759$	−24.8392	−	60.7232i	−0.901604	−	2.20411i
$760$	−7.01267	−	12.1463i	−0.254376	−	0.440593i
$761$	10.6425	+	6.14447i	0.385792	+	0.222737i	0.680335	−	0.732901i	$-0.261834\pi$
$761$	10.6425	+	6.14447i	0.385792	+	0.222737i	−0.294543	+	0.955638i	$0.595168\pi$
$762$			5.69017i			0.206133i
$763$	−1.45234	−	2.03460i	−0.0525782	−	0.0736573i
$764$		−	19.3901i		−	0.701508i
$765$	37.2453	−	64.5108i	1.34661	−	2.33239i
$766$	−2.57501	−	4.46005i	−0.0930389	−	0.161148i
$767$	20.9715	+	36.3238i	0.757238	+	1.31157i
$768$	2.64992	+	1.52993i	0.0956207	+	0.0552066i
$769$	−14.9885			−0.540500			−0.270250	−	0.962790i	$-0.587106\pi$
$769$	−14.9885			−0.540500			−0.270250	+	0.962790i	$0.587106\pi$
$770$	−9.02359	+	19.8188i	−0.325187	+	0.714221i
$771$	−19.2219			−0.692259
$772$	11.4197	−	19.7795i	0.411004	−	0.711880i
$773$	−14.3108	−	24.7870i	−0.514723	−	0.891526i	−0.999854	−	0.0170845i	$-0.994562\pi$
$773$	−14.3108	−	24.7870i	−0.514723	−	0.891526i	0.485131	−	0.874441i	$-0.338772\pi$
$774$	−29.6529	+	17.1201i	−1.06585	+	0.615370i
$775$	0.754707	+	0.435730i	0.0271099	+	0.0156519i
$776$	16.2156			0.582107
$777$	−0.490467	−	5.07508i	−0.0175954	−	0.182068i
$778$		−	31.0454i		−	1.11303i
$779$	−9.27135	−	5.35282i	−0.332181	−	0.191785i
$780$	8.39008	+	14.5320i	0.300413	+	0.520331i
$781$	6.40966	−	3.70062i	0.229356	−	0.132419i
$782$	18.6725	−	24.1134i	0.667726	−	0.862295i
$783$		−	40.6983i		−	1.45444i
$784$	2.27435	−	6.62022i	0.0812267	−	0.236437i
$785$	−17.2560			−0.615893
$786$	−11.1518	+	19.3154i	−0.397770	+	0.688957i
$787$	3.34199	+	5.78849i	0.119129	+	0.206338i	0.919423	−	0.393271i	$-0.128656\pi$
$787$	3.34199	+	5.78849i	0.119129	+	0.206338i	−0.800294	+	0.599608i	$0.795323\pi$
$788$	−8.84397	−	15.3182i	−0.315053	−	0.545688i
$789$	−22.0270	+	38.1519i	−0.784183	+	1.35825i
$790$		−	9.50753i		−	0.338263i
$791$	−23.8798	+	2.30780i	−0.849069	+	0.0820558i
$792$		−	28.4466i		−	1.01081i
$793$	−27.4389	−	15.8419i	−0.974385	−	0.562562i
$794$	−4.78832	+	2.76454i	−0.169931	+	0.0981098i
$795$	0.0150767	+	0.0261136i	0.000534715	+	0.000926154i
$796$	−7.00172	+	12.1273i	−0.248169	+	0.429842i
$797$	−26.7030			−0.945869			−0.472935	−	0.881097i	$-0.656805\pi$
$797$	−26.7030			−0.945869			−0.472935	+	0.881097i	$0.656805\pi$
$798$	25.5568	−	56.1313i	0.904701	−	1.98703i
$799$		−	56.1431i		−	1.98620i
$800$	−0.805379	+	1.39496i	−0.0284745	+	0.0493192i
$801$	−13.5348	−	23.4430i	−0.478229	−	0.828316i
$802$	−6.14194	+	3.54605i	−0.216880	+	0.125215i
$803$	−19.8519	+	34.3845i	−0.700559	+	1.21340i
$804$	4.93877			0.174177
$805$	20.6696	−	10.8828i	0.728508	−	0.383568i
$806$	1.61161			0.0567666
$807$	−13.9258	+	24.1203i	−0.490213	+	0.849074i
$808$	14.2789	−	8.24392i	0.502330	−	0.290020i
$809$	16.0121	+	27.7338i	0.562955	+	0.975067i	0.997237	+	0.0742900i	$0.0236691\pi$
$809$	16.0121	+	27.7338i	0.562955	+	0.975067i	−0.434281	+	0.900777i	$0.642998\pi$
$810$	−11.4108	+	19.7641i	−0.400934	+	0.694439i
$811$			1.69852i			0.0596430i	0.999555	+	0.0298215i	$0.00949389\pi$
$811$			1.69852i			0.0596430i	−0.999555	+	0.0298215i	$0.990506\pi$
$812$	−8.51737	+	6.07988i	−0.298901	+	0.213362i
$813$	19.7884			0.694010
$814$	−1.40788	+	2.43852i	−0.0493463	+	0.0854702i
$815$	3.78423	+	6.55448i	0.132556	+	0.229593i
$816$	16.8515	−	9.72920i	0.589919	−	0.340590i
$817$	35.5046	+	20.4986i	1.24215	+	0.717154i
$818$		−	16.7578i		−	0.585922i
$819$	−20.7793	+	45.6383i	−0.726087	+	1.59473i
$820$		−	2.58703i		−	0.0903430i
$821$	−16.0148	+	27.7385i	−0.558921	+	0.968080i	0.438665	+	0.898650i	$0.355451\pi$
$821$	−16.0148	+	27.7385i	−0.558921	+	0.968080i	−0.997587	+	0.0694298i	$0.977882\pi$
$822$	21.7914	+	37.7438i	0.760062	+	1.31647i
$823$	−8.78303	−	15.2127i	−0.306157	−	0.530280i	0.671361	−	0.741130i	$-0.265710\pi$
$823$	−8.78303	−	15.2127i	−0.306157	−	0.530280i	−0.977518	+	0.210851i	$0.932377\pi$
$824$	1.82413	−	3.15949i	0.0635467	−	0.110066i
$825$	22.0352			0.767168
$826$	37.0807	−	3.58355i	1.29020	−	0.124688i
$827$		−	21.1467i		−	0.735341i	−0.929956	−	0.367671i	$-0.880155\pi$
$827$		−	21.1467i		−	0.735341i	0.929956	−	0.367671i	$-0.119845\pi$
$828$	−18.6828	+	24.1268i	−0.649271	+	0.838463i
$829$	8.96964	−	5.17862i	0.311529	−	0.179861i	−0.336082	−	0.941833i	$-0.609102\pi$
$829$	8.96964	−	5.17862i	0.311529	−	0.179861i	0.647610	+	0.761972i	$0.275769\pi$
$830$	−9.67170	−	16.7519i	−0.335709	−	0.581466i
$831$	−6.10183	−	3.52289i	−0.211670	−	0.122208i
$832$			2.97881i			0.103272i
$833$	−29.2277	−	33.5752i	−1.01268	−	1.16331i
$834$	6.71076			0.232374
$835$	4.49242	+	2.59370i	0.155467	+	0.0897587i
$836$	−29.4970	+	17.0301i	−1.02018	+	0.588999i
$837$	2.78345	+	4.82108i	0.0962102	+	0.166641i
$838$	−17.9559	+	31.1005i	−0.620277	+	1.07435i
$839$	−46.8984			−1.61911			−0.809556	−	0.587043i	$-0.800292\pi$
$839$	−46.8984			−1.61911			−0.809556	+	0.587043i	$0.800292\pi$
$840$	14.8349	−	1.43367i	0.511851	−	0.0494664i
$841$	−13.3556			−0.460539
$842$	−31.3335	−	18.0904i	−1.07983	−	0.623437i
$843$	−21.1246	−	36.5888i	−0.727569	−	1.26019i
$844$	−2.60935	−	4.51953i	−0.0898176	−	0.155569i
$845$	3.79859	−	6.57936i	0.130676	−	0.226337i
$846$			56.1741i			1.93131i
$847$	21.6425	+	9.85391i	0.743645	+	0.338584i
$848$			0.00535283i			0.000183817i
$849$	−37.9859	−	21.9312i	−1.30367	−	0.752675i
$850$	5.12160	+	8.87087i	0.175669	+	0.304268i
$851$	2.79562	−	1.14356i	0.0958328	−	0.0392009i
$852$	−4.38684	−	2.53274i	−0.150291	−	0.0867703i
$853$			18.3922i			0.629737i	0.949135	+	0.314868i	$0.101960\pi$
$853$			18.3922i			0.629737i	−0.949135	+	0.314868i	$0.898040\pi$
$854$	−22.9045	+	16.3497i	−0.783775	+	0.559475i
$855$	89.2398			3.05194
$856$	−3.58484	−	2.06971i	−0.122527	−	0.0707412i
$857$	40.2901	−	23.2615i	1.37628	−	0.794597i	0.384572	−	0.923095i	$-0.374349\pi$
$857$	40.2901	−	23.2615i	1.37628	−	0.794597i	0.991710	+	0.128498i	$0.0410156\pi$
$858$	35.2907	−	20.3751i	1.20481	−	0.695595i
$859$	−37.7477	−	21.7937i	−1.28794	−	0.743590i	−0.309650	−	0.950851i	$-0.600212\pi$
$859$	−37.7477	−	21.7937i	−1.28794	−	0.743590i	−0.978286	+	0.207261i	$0.933545\pi$
$860$			9.90701i			0.337826i
$861$	9.25931	−	6.60949i	0.315556	−	0.225251i
$862$			38.9905i			1.32802i
$863$	−15.2915	+	26.4856i	−0.520527	+	0.901580i	0.479188	+	0.877712i	$0.340931\pi$
$863$	−15.2915	+	26.4856i	−0.520527	+	0.901580i	−0.999715	+	0.0238674i	$0.992402\pi$
$864$	−8.91102	+	5.14478i	−0.303159	+	0.175029i
$865$	6.17144	−	3.56308i	0.209835	−	0.121148i
$866$	4.88521	−	8.46144i	0.166006	−	0.287531i
$867$		−	71.7229i		−	2.43584i
$868$	0.593143	−	1.30274i	0.0201326	−	0.0442179i
$869$	−23.0888			−0.783235
$870$	−19.2958	−	11.1404i	−0.654189	−	0.377696i
$871$	2.40397	+	4.16380i	0.0814555	+	0.141085i
$872$	0.818243	−	0.472413i	0.0277092	−	0.0159979i
$873$	−51.5880	+	89.3531i	−1.74599	+	3.02414i
$874$	36.2025	+	4.92870i	1.22457	+	0.166716i
$875$	3.09741	+	32.0504i	0.104712	+	1.08350i
$876$	27.1737			0.918114
$877$	12.6689	−	21.9432i	0.427798	−	0.740968i	−0.568879	−	0.822421i	$-0.692623\pi$
$877$	12.6689	−	21.9432i	0.427798	−	0.740968i	0.996677	+	0.0814535i	$0.0259562\pi$
$878$	22.6269	−	13.0636i	0.763621	−	0.440877i
$879$	−21.7443	+	12.5541i	−0.733417	+	0.423438i
$880$	−7.12799	−	4.11535i	−0.240285	−	0.138728i
$881$	−8.10042			−0.272910			−0.136455	−	0.990646i	$-0.543571\pi$
$881$	−8.10042			−0.272910			−0.136455	+	0.990646i	$0.543571\pi$
$882$	29.2439	+	33.5938i	0.984693	+	1.13116i
$883$	19.8733			0.668790			0.334395	−	0.942433i	$-0.391468\pi$
$883$	19.8733			0.668790			0.334395	+	0.942433i	$0.391468\pi$
$884$	16.4051	+	9.47149i	0.551763	+	0.318561i
$885$	39.6589	+	68.6912i	1.33312	+	2.30903i
$886$	−15.4187	−	26.7060i	−0.518002	−	0.897206i
$887$	−15.3662	−	8.87166i	−0.515946	−	0.297881i	0.219329	−	0.975651i	$-0.429613\pi$
$887$	−15.3662	−	8.87166i	−0.515946	−	0.297881i	−0.735274	+	0.677770i	$0.762947\pi$
$888$	1.92714			0.0646705
$889$	0.473282	+	4.89726i	0.0158734	+	0.164249i
$890$	−7.83227			−0.262538
$891$	47.9966	+	27.7109i	1.60795	+	0.928348i
$892$	−0.258844	+	0.149443i	−0.00866673	+	0.00500374i
$893$	58.2484	−	33.6297i	1.94921	−	1.12538i
$894$	15.2932	−	26.4886i	0.511482	−	0.885912i
$895$	10.9768			0.366913
$896$	2.40791	+	1.09633i	0.0804428	+	0.0366259i
$897$	−43.3132	−	5.89678i	−1.44619	−	0.196888i
$898$	−10.3922	+	17.9999i	−0.346793	+	0.600664i
$899$	−1.85322	+	1.06996i	−0.0618083	+	0.0356851i
$900$	−5.12443	−	8.87577i	−0.170814	−	0.295859i
$901$	0.0294794	+	0.0170200i	0.000982102	+	0.000567017i
$902$	−6.28254			−0.209186
$903$	−35.4585	+	25.3110i	−1.17998	+	0.842297i
$904$		−	9.06778i		−	0.301590i
$905$	−18.2413	+	31.5949i	−0.606362	+	1.05025i
$906$	10.4427	−	6.02907i	0.346934	−	0.200302i
$907$	−25.5078	+	14.7269i	−0.846972	+	0.489000i	−0.859628	−	0.510920i	$-0.829305\pi$
$907$	−25.5078	+	14.7269i	−0.846972	+	0.489000i	0.0126559	+	0.999920i	$0.495971\pi$
$908$	−3.68661	+	6.38540i	−0.122345	+	0.211907i
$909$			104.908i			3.47958i
$910$	8.42966	+	11.8092i	0.279441	+	0.391471i
$911$			5.77190i			0.191231i	0.995418	+	0.0956157i	$0.0304820\pi$
$911$			5.77190i			0.191231i	−0.995418	+	0.0956157i	$0.969518\pi$
$912$	20.1881	+	11.6556i	0.668494	+	0.385955i
$913$	−40.6815	+	23.4875i	−1.34636	+	0.777323i
$914$	15.7019	−	9.06549i	0.519373	−	0.299860i
$915$	−51.8893	−	29.9583i	−1.71541	−	0.990390i
$916$	−19.4372			−0.642223
$917$	−7.99123	+	17.5514i	−0.263894	+	0.579599i
$918$			65.4338i			2.15964i
$919$	−31.4219	−	18.1415i	−1.03651	−	0.598432i	−0.117670	−	0.993053i	$-0.537543\pi$
$919$	−31.4219	−	18.1415i	−1.03651	−	0.598432i	−0.918844	+	0.394621i	$0.870876\pi$
$920$	3.34273	+	8.17183i	0.110206	+	0.269417i
$921$	−42.4327	−	73.4955i	−1.39820	−	2.42176i
$922$	−3.16045	−	1.82469i	−0.104084	−	0.0600929i
$923$		−	4.93131i		−	0.162316i
$924$	−3.48164	−	36.0261i	−0.114538	−	1.18517i
$925$			1.01448i			0.0333557i
$926$	12.6311	−	21.8778i	0.415085	−	0.718948i
$927$	11.6065	+	20.1031i	0.381208	+	0.660271i
$928$	−1.97765	−	3.42539i	−0.0649195	−	0.112444i
$929$	−27.1962	−	15.7017i	−0.892279	−	0.515157i	−0.0175914	−	0.999845i	$-0.505600\pi$
$929$	−27.1962	−	15.7017i	−0.892279	−	0.515157i	−0.874687	+	0.484688i	$0.838933\pi$
$930$	3.04769			0.0999376
$931$	17.3268	−	50.4353i	0.567864	−	1.65295i
$932$	−17.8101			−0.583389
$933$	22.8643	−	39.6022i	0.748545	−	1.29652i
$934$	6.07496	+	10.5221i	0.198779	+	0.344295i
$935$	−45.3286	+	26.1705i	−1.48240	+	0.855866i
$936$	−16.4142	−	9.47672i	−0.536514	−	0.309756i
$937$	−48.0322			−1.56914			−0.784572	−	0.620037i	$-0.787118\pi$
$937$	−48.0322			−1.56914			−0.784572	+	0.620037i	$0.787118\pi$
$938$	4.25057	−	0.410784i	0.138786	−	0.0134126i
$939$			48.9801i			1.59840i
$940$	14.0758	+	8.12667i	0.459102	+	0.265063i
$941$	−9.33369	−	16.1664i	−0.304270	−	0.527011i	0.672829	−	0.739798i	$-0.265079\pi$
$941$	−9.33369	−	16.1664i	−0.304270	−	0.527011i	−0.977098	+	0.212788i	$0.931746\pi$
$942$	24.8382	−	14.3404i	0.809274	−	0.467234i
$943$	5.32849	+	4.12616i	0.173519	+	0.134366i
$944$			14.0805i			0.458280i
$945$	−20.7678	+	45.6131i	−0.675577	+	1.48379i
$946$	24.0590			0.782224
$947$	0.280769	−	0.486306i	0.00912377	−	0.0158028i	−0.861427	−	0.507881i	$-0.830429\pi$
$947$	0.280769	−	0.486306i	0.00912377	−	0.0158028i	0.870551	+	0.492078i	$0.163762\pi$
$948$	7.90111	+	13.6851i	0.256616	+	0.444472i
$949$	13.2270	+	22.9098i	0.429365	+	0.743682i
$950$	−6.13568	+	10.6273i	−0.199068	+	0.344795i
$951$		−	34.9498i		−	1.13332i
$952$	13.6940	−	9.77510i	0.443827	−	0.316813i
$953$			9.07184i			0.293866i	0.989146	+	0.146933i	$0.0469401\pi$
$953$			9.07184i			0.293866i	−0.989146	+	0.146933i	$0.953060\pi$
$954$	−0.0294957	−	0.0170294i	−0.000954959	−	0.000551346i
$955$	30.9144	−	17.8484i	1.00037	−	0.577562i
$956$	−5.44619	−	9.43308i	−0.176142	−	0.305088i
$957$	−27.0543	+	46.8594i	−0.874541	+	1.51475i
$958$	−14.5336			−0.469561
$959$	21.8942	+	30.6719i	0.707001	+	0.990446i
$960$			5.63317i			0.181810i
$961$	−15.3536	+	26.5933i	−0.495279	+	0.857848i
$962$	0.938046	+	1.62474i	0.0302438	+	0.0523838i
$963$	22.8095	−	13.1690i	0.735024	−	0.424367i
$964$	−0.469400	+	0.813024i	−0.0151183	+	0.0261857i
$965$	42.0471			1.35354
$966$	−20.7078	+	32.8419i	−0.666263	+	1.05667i
$967$	35.8545			1.15300			0.576502	−	0.817096i	$-0.304417\pi$
$967$	35.8545			1.15300			0.576502	+	0.817096i	$0.304417\pi$
$968$	−4.49403	+	7.78389i	−0.144444	+	0.250184i
$969$	128.381	−	74.1206i	4.12418	−	2.38110i
$970$	14.9264	+	25.8533i	0.479258	+	0.830099i
$971$	−8.36455	+	14.4878i	−0.268431	+	0.464937i	−0.968457	−	0.249181i	$-0.919839\pi$
$971$	−8.36455	+	14.4878i	−0.268431	+	0.464937i	0.700026	+	0.714118i	$0.253172\pi$
$972$		−	7.06250i		−	0.226530i
$973$	5.77564	−	0.558170i	0.185158	−	0.0178941i
$974$	31.1555			0.998286
$975$	7.34083	−	12.7147i	0.235095	−	0.407196i
$976$	−5.31819	−	9.21137i	−0.170231	−	0.294849i
$977$	−10.7826	+	6.22533i	−0.344965	+	0.199166i	−0.662466	−	0.749092i	$-0.730490\pi$
$977$	−10.7826	+	6.22533i	−0.344965	+	0.199166i	0.317500	+	0.948258i	$0.397157\pi$
$978$	−10.8940	−	6.28967i	−0.348353	−	0.201122i
$979$			19.0205i			0.607898i
$980$	12.6484	−	2.46779i	0.404039	−	0.0788307i
$981$			6.01169i			0.191939i
$982$	−16.2668	+	28.1750i	−0.519095	+	0.899099i
$983$	9.31761	+	16.1386i	0.297186	+	0.514741i	0.975491	−	0.220040i	$-0.0706186\pi$
$983$	9.31761	+	16.1386i	0.297186	+	0.514741i	−0.678305	+	0.734780i	$0.737285\pi$
$984$	2.14992	+	3.72377i	0.0685369	+	0.118709i
$985$	16.2816	−	28.2006i	0.518776	−	0.898547i
$986$	−25.1527			−0.801025
$987$	6.87527	+	71.1416i	0.218842	+	2.26446i
$988$			22.6937i			0.721982i
$989$	−20.4054	−	15.8011i	−0.648854	−	0.502446i
$990$	45.3537	−	26.1849i	1.44143	−	0.832212i
$991$	−15.1438	−	26.2298i	−0.481059	−	0.833218i	0.518705	−	0.854953i	$-0.326414\pi$
$991$	−15.1438	−	26.2298i	−0.481059	−	0.833218i	−0.999764	+	0.0217351i	$0.993081\pi$
$992$	0.468541	+	0.270512i	0.0148762	+	0.00858878i
$993$			48.7871i			1.54821i
$994$	−3.98621	−	1.81494i	−0.126435	−	0.0575663i
$995$	−25.7802			−0.817287
$996$	27.8429	+	16.0751i	0.882235	+	0.509358i
$997$	53.1326	−	30.6761i	1.68273	−	0.971522i	0.722888	−	0.690965i	$-0.242814\pi$
$997$	53.1326	−	30.6761i	1.68273	−	0.971522i	0.959838	−	0.280556i	$-0.0905190\pi$
$998$	−6.96483	−	12.0634i	−0.220468	−	0.381862i
$999$	−3.24025	+	5.61227i	−0.102517	+	0.177564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.b.229.2	yes	16
7.2	even	3		2254.2.c.b.2253.1		16
7.3	odd	6	inner	322.2.g.b.45.1	✓	16
7.5	odd	6		2254.2.c.b.2253.16		16
23.22	odd	2	inner	322.2.g.b.229.1	yes	16
161.45	even	6	inner	322.2.g.b.45.2	yes	16
161.68	even	6		2254.2.c.b.2253.15		16
161.114	odd	6		2254.2.c.b.2253.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.b.45.1	✓	16	7.3	odd	6	inner
322.2.g.b.45.2	yes	16	161.45	even	6	inner
322.2.g.b.229.1	yes	16	23.22	odd	2	inner
322.2.g.b.229.2	yes	16	1.1	even	1	trivial
2254.2.c.b.2253.1		16	7.2	even	3
2254.2.c.b.2253.2		16	161.114	odd	6
2254.2.c.b.2253.15		16	161.68	even	6
2254.2.c.b.2253.16		16	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-2.64992 + 1.52993i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.920495 - 1.59434i) q^{5} +3.05986i q^{6} +(0.254505 + 2.63348i) q^{7} -1.00000 q^{8} +(3.18138 - 5.51031i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-2.64992 + 1.52993i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.920495 - 1.59434i) q^{5} +3.05986i q^{6} +(0.254505 + 2.63348i) q^{7} -1.00000 q^{8} +(3.18138 - 5.51031i) q^{9} +(-0.920495 - 1.59434i) q^{10} +(-3.87183 + 2.23540i) q^{11} +(2.64992 + 1.52993i) q^{12} +2.97881i q^{13} +(2.40791 + 1.09633i) q^{14} +5.63317i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.17962 + 5.50726i) q^{17} +(-3.18138 - 5.51031i) q^{18} +(-3.80919 + 6.59770i) q^{19} -1.84099 q^{20} +(-4.70346 - 6.58914i) q^{21} +4.47080i q^{22} +(2.93627 - 3.79187i) q^{23} +(2.64992 - 1.52993i) q^{24} +(0.805379 + 1.39496i) q^{25} +(2.57973 + 1.48941i) q^{26} +10.2896i q^{27} +(2.15341 - 1.53715i) q^{28} -3.95530 q^{29} +(4.87847 + 2.81659i) q^{30} +(0.468541 - 0.270512i) q^{31} +(0.500000 + 0.866025i) q^{32} +(6.84002 - 11.8473i) q^{33} +6.35924 q^{34} +(4.43295 + 2.01834i) q^{35} -6.36275 q^{36} +(0.545433 + 0.314906i) q^{37} +(3.80919 + 6.59770i) q^{38} +(-4.55737 - 7.89360i) q^{39} +(-0.920495 + 1.59434i) q^{40} +1.40524i q^{41} +(-8.05809 + 0.778751i) q^{42} -5.38135i q^{43} +(3.87183 + 2.23540i) q^{44} +(-5.85688 - 10.1444i) q^{45} +(-1.81572 - 4.43882i) q^{46} +(-7.64578 - 4.41429i) q^{47} -3.05986i q^{48} +(-6.87045 + 1.34047i) q^{49} +1.61076 q^{50} +(-16.8515 - 9.72920i) q^{51} +(2.57973 - 1.48941i) q^{52} +(0.00463568 - 0.00267641i) q^{53} +(8.91102 + 5.14478i) q^{54} +8.23070i q^{55} +(-0.254505 - 2.63348i) q^{56} -23.3112i q^{57} +(-1.97765 + 3.42539i) q^{58} +(12.1940 - 7.04024i) q^{59} +(4.87847 - 2.81659i) q^{60} +(-5.31819 + 9.21137i) q^{61} -0.541025i q^{62} +(15.3210 + 6.97570i) q^{63} +1.00000 q^{64} +(4.74925 + 2.74198i) q^{65} +(-6.84002 - 11.8473i) q^{66} +(1.39781 - 0.807025i) q^{67} +(3.17962 - 5.50726i) q^{68} +(-1.97957 + 14.5404i) q^{69} +(3.96440 - 2.82987i) q^{70} -1.65546 q^{71} +(-3.18138 + 5.51031i) q^{72} +(7.69091 - 4.44035i) q^{73} +(0.545433 - 0.314906i) q^{74} +(-4.26838 - 2.46435i) q^{75} +7.61837 q^{76} +(-6.87229 - 9.62747i) q^{77} -9.11475 q^{78} +(4.47247 + 2.58218i) q^{79} +(0.920495 + 1.59434i) q^{80} +(-6.19818 - 10.7356i) q^{81} +(1.21697 + 0.702619i) q^{82} +10.5071 q^{83} +(-3.35463 + 7.36789i) q^{84} +11.7073 q^{85} +(-4.66039 - 2.69068i) q^{86} +(10.4812 - 6.05133i) q^{87} +(3.87183 - 2.23540i) q^{88} +(2.12719 - 3.68440i) q^{89} -11.7138 q^{90} +(-7.84464 + 0.758123i) q^{91} +(-4.75200 - 0.646949i) q^{92} +(-0.827731 + 1.43367i) q^{93} +(-7.64578 + 4.41429i) q^{94} +(7.01267 + 12.1463i) q^{95} +(-2.64992 - 1.52993i) q^{96} -16.2156 q^{97} +(-2.27435 + 6.62022i) q^{98} +28.4466i 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	\( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+O(q^{100}) \) 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 + 8 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^29 + 12 * q^31 + 8 * q^32 - 20 * q^36 - 2 * q^39 - 8 * q^46 - 6 * q^47 - 18 * q^49 + 4 * q^50 - 6 * q^52 + 18 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 12 * q^70 - 52 * q^71 - 10 * q^72 + 24 * q^73 + 30 * q^77 - 4 * q^78 - 20 * q^81 + 54 * q^82 + 80 * q^85 + 54 * q^87 - 16 * q^92 - 26 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96

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