LMFDB - Embedded newform 798.2.cj.b.409.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			409.6
Character	$\chi$	$=$	798.409
Dual form			798.2.cj.b.439.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(3.04553 - 0.537009i) q^{5} +(-0.642788 + 0.766044i) q^{6} +(-2.64029 - 0.169924i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-2.36900 - 1.98783i) q^{10} +4.55626 q^{11} +1.00000 q^{12} +(2.20148 + 1.84727i) q^{13} +(1.56698 + 2.13180i) q^{14} +(-1.05770 - 2.90601i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.0766548 - 0.210607i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.53071 - 4.08129i) q^{19} +3.09251i q^{20} +(0.291139 + 2.62968i) q^{21} +(-2.92871 - 3.49030i) q^{22} +(-1.84953 - 1.55194i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(4.28841 - 1.56085i) q^{25} -2.87383i q^{26} +(0.500000 + 0.866025i) q^{27} +(0.625824 - 2.57067i) q^{28} +(4.41301 + 0.778133i) q^{29} +(-1.54626 + 2.67819i) q^{30} +(0.0496058 + 0.0859197i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-0.791187 - 4.48704i) q^{33} +(-0.210607 + 0.0766548i) q^{34} +(-8.13233 + 0.900351i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(6.04945 - 3.49265i) q^{37} +(-4.11037 + 1.45081i) q^{38} +(1.43692 - 2.48881i) q^{39} +(2.36900 - 1.98783i) q^{40} +(3.92354 - 3.29224i) q^{41} +(1.82731 - 1.91335i) q^{42} +(-2.06485 - 0.751543i) q^{43} +(-0.791187 + 4.48704i) q^{44} +(-2.67819 + 1.54626i) q^{45} +2.41439i q^{46} +(1.62405 + 4.46204i) q^{47} +(-0.173648 + 0.984808i) q^{48} +(6.94225 + 0.897297i) q^{49} +(-3.95222 - 2.28182i) q^{50} +(-0.220719 - 0.0389187i) q^{51} +(-2.20148 + 1.84727i) q^{52} +(-8.20943 - 1.44754i) q^{53} +(0.342020 - 0.939693i) q^{54} +(13.8762 - 2.44676i) q^{55} +(-2.37152 + 1.17299i) q^{56} +(-4.28509 - 0.798745i) q^{57} +(-2.24054 - 3.88074i) q^{58} +(-11.5923 - 4.21927i) q^{59} +(3.04553 - 0.537009i) q^{60} +(-3.87374 + 4.61654i) q^{61} +(0.0339324 - 0.0932284i) q^{62} +(2.53918 - 0.743356i) q^{63} +(0.500000 - 0.866025i) q^{64} +(7.69669 + 4.44368i) q^{65} +(-2.92871 + 3.49030i) q^{66} +(4.53921 - 5.40961i) q^{67} +(0.194097 + 0.112062i) q^{68} +(-1.20720 + 2.09093i) q^{69} +(5.91707 + 5.65099i) q^{70} +(-0.460094 + 1.26410i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(-2.13529 + 0.376509i) q^{73} +(-6.56404 - 2.38911i) q^{74} +(-2.28182 - 3.95222i) q^{75} +(3.75348 + 2.21616i) q^{76} +(-12.0299 - 0.774218i) q^{77} +(-2.83017 + 0.499036i) q^{78} +(5.47822 - 15.0513i) q^{79} +(-3.04553 - 0.537009i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-5.04400 - 0.889393i) q^{82} +(-13.9931 - 8.07893i) q^{83} +(-2.64029 - 0.169924i) q^{84} +(0.120356 - 0.682575i) q^{85} +(0.751543 + 2.06485i) q^{86} -4.48109i q^{87} +(3.94584 - 2.27813i) q^{88} +(1.93181 - 10.9558i) q^{89} +(2.90601 + 1.05770i) q^{90} +(-5.49866 - 5.25140i) q^{91} +(1.84953 - 1.55194i) q^{92} +(0.0760005 - 0.0637720i) q^{93} +(2.37420 - 4.11224i) q^{94} +(2.47013 - 13.2517i) q^{95} +(0.866025 - 0.500000i) q^{96} +(1.27220 + 7.21503i) q^{97} +(-3.77502 - 5.89484i) q^{98} +(-4.28149 + 1.55833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$1$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	3.04553	−	0.537009i	1.36200	−	0.240158i	0.555563	−	0.831474i	$-0.312503\pi$
$5$	3.04553	−	0.537009i	1.36200	−	0.240158i	0.806439	+	0.591317i	$0.201392\pi$
$6$	−0.642788	+	0.766044i	−0.262417	+	0.312736i
$7$	−2.64029	−	0.169924i	−0.997935	−	0.0642252i
$7$	−2.64029	−	0.169924i	−0.997935	−	0.0642252i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−2.36900	−	1.98783i	−0.749144	−	0.628607i
$11$	4.55626			1.37377			0.686883	−	0.726768i	$-0.258979\pi$
$11$	4.55626			1.37377			0.686883	+	0.726768i	$0.258979\pi$
$12$	1.00000			0.288675
$13$	2.20148	+	1.84727i	0.610582	+	0.512339i	0.894827	−	0.446412i	$-0.147299\pi$
$13$	2.20148	+	1.84727i	0.610582	+	0.512339i	−0.284245	+	0.958752i	$0.591743\pi$
$14$	1.56698	+	2.13180i	0.418792	+	0.569749i
$15$	−1.05770	−	2.90601i	−0.273097	−	0.750329i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.0766548	−	0.210607i	0.0185915	−	0.0510798i	−0.930050	−	0.367434i	$-0.880236\pi$
$17$	0.0766548	−	0.210607i	0.0185915	−	0.0510798i	0.948641	+	0.316354i	$0.102459\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	1.53071	−	4.08129i	0.351169	−	0.936312i
$19$	1.53071	−	4.08129i	0.351169	−	0.936312i
$20$			3.09251i			0.691507i
$21$	0.291139	+	2.62968i	0.0635317	+	0.573844i
$22$	−2.92871	−	3.49030i	−0.624403	−	0.744135i
$23$	−1.84953	−	1.55194i	−0.385654	−	0.323602i	0.429263	−	0.903179i	$-0.358773\pi$
$23$	−1.84953	−	1.55194i	−0.385654	−	0.323602i	−0.814917	+	0.579577i	$0.803218\pi$
$24$	−0.642788	−	0.766044i	−0.131208	−	0.156368i
$25$	4.28841	−	1.56085i	0.857682	−	0.312171i
$26$		−	2.87383i		−	0.563605i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	0.625824	−	2.57067i	0.118270	−	0.485811i
$29$	4.41301	+	0.778133i	0.819475	+	0.144496i	0.567643	−	0.823275i	$-0.307856\pi$
$29$	4.41301	+	0.778133i	0.819475	+	0.144496i	0.251833	+	0.967771i	$0.418967\pi$
$30$	−1.54626	+	2.67819i	−0.282306	+	0.488969i
$31$	0.0496058	+	0.0859197i	0.00890946	+	0.0154316i	0.870446	−	0.492264i	$-0.163831\pi$
$31$	0.0496058	+	0.0859197i	0.00890946	+	0.0154316i	−0.861536	+	0.507696i	$0.830497\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	−0.791187	−	4.48704i	−0.137728	−	0.781094i
$34$	−0.210607	+	0.0766548i	−0.0361189	+	0.0131462i
$35$	−8.13233	+	0.900351i	−1.37461	+	0.152187i
$36$	−0.173648	−	0.984808i	−0.0289414	−	0.164135i
$37$	6.04945	−	3.49265i	0.994523	−	0.574188i	0.0878998	−	0.996129i	$-0.471984\pi$
$37$	6.04945	−	3.49265i	0.994523	−	0.574188i	0.906623	+	0.421941i	$0.138651\pi$
$38$	−4.11037	+	1.45081i	−0.666790	+	0.235353i
$39$	1.43692	−	2.48881i	0.230091	−	0.398529i
$40$	2.36900	−	1.98783i	0.374572	−	0.314303i
$41$	3.92354	−	3.29224i	0.612753	−	0.514161i	−0.282763	−	0.959190i	$-0.591251\pi$
$41$	3.92354	−	3.29224i	0.612753	−	0.514161i	0.895516	+	0.445029i	$0.146807\pi$
$42$	1.82731	−	1.91335i	0.281961	−	0.295237i
$43$	−2.06485	−	0.751543i	−0.314886	−	0.114609i	0.179742	−	0.983714i	$-0.442474\pi$
$43$	−2.06485	−	0.751543i	−0.314886	−	0.114609i	−0.494628	+	0.869105i	$0.664696\pi$
$44$	−0.791187	+	4.48704i	−0.119276	+	0.676447i
$45$	−2.67819	+	1.54626i	−0.399242	+	0.230502i
$46$			2.41439i			0.355983i
$47$	1.62405	+	4.46204i	0.236892	+	0.650855i	0.999990	+	0.00457208i	$0.00145534\pi$
$47$	1.62405	+	4.46204i	0.236892	+	0.650855i	−0.763098	+	0.646283i	$0.776322\pi$
$48$	−0.173648	+	0.984808i	−0.0250640	+	0.142145i
$49$	6.94225	+	0.897297i	0.991750	+	0.128185i
$50$	−3.95222	−	2.28182i	−0.558928	−	0.322697i
$51$	−0.220719	−	0.0389187i	−0.0309068	−	0.00544970i
$52$	−2.20148	+	1.84727i	−0.305291	+	0.256170i
$53$	−8.20943	−	1.44754i	−1.12765	−	0.198835i	−0.421454	−	0.906850i	$-0.638480\pi$
$53$	−8.20943	−	1.44754i	−1.12765	−	0.198835i	−0.706198	+	0.708015i	$0.749591\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	13.8762	−	2.44676i	1.87107	−	0.329920i
$56$	−2.37152	+	1.17299i	−0.316908	+	0.156747i
$57$	−4.28509	−	0.798745i	−0.567574	−	0.105796i
$58$	−2.24054	−	3.88074i	−0.294198	−	0.509566i
$59$	−11.5923	−	4.21927i	−1.50919	−	0.549302i	−0.550772	−	0.834656i	$-0.685667\pi$
$59$	−11.5923	−	4.21927i	−1.50919	−	0.549302i	−0.958422	+	0.285354i	$0.907889\pi$
$60$	3.04553	−	0.537009i	0.393176	−	0.0693276i
$61$	−3.87374	+	4.61654i	−0.495981	+	0.591087i	−0.954728	−	0.297480i	$-0.903854\pi$
$61$	−3.87374	+	4.61654i	−0.495981	+	0.591087i	0.458747	+	0.888567i	$0.348298\pi$
$62$	0.0339324	−	0.0932284i	0.00430941	−	0.0118400i
$63$	2.53918	−	0.743356i	0.319906	−	0.0936540i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	7.69669	+	4.44368i	0.954656	+	0.551171i
$66$	−2.92871	+	3.49030i	−0.360499	+	0.429626i
$67$	4.53921	−	5.40961i	0.554552	−	0.660890i	−0.413832	−	0.910353i	$-0.635810\pi$
$67$	4.53921	−	5.40961i	0.554552	−	0.660890i	0.968384	+	0.249464i	$0.0802543\pi$
$68$	0.194097	+	0.112062i	0.0235377	+	0.0135895i
$69$	−1.20720	+	2.09093i	−0.145329	+	0.251718i
$70$	5.91707	+	5.65099i	0.707225	+	0.675423i
$71$	−0.460094	+	1.26410i	−0.0546031	+	0.150021i	−0.963996	−	0.265918i	$-0.914325\pi$
$71$	−0.460094	+	1.26410i	−0.0546031	+	0.150021i	0.909392	+	0.415939i	$0.136547\pi$
$72$	−0.642788	+	0.766044i	−0.0757532	+	0.0902792i
$73$	−2.13529	+	0.376509i	−0.249917	+	0.0440671i	−0.297203	−	0.954814i	$-0.596054\pi$
$73$	−2.13529	+	0.376509i	−0.249917	+	0.0440671i	0.0472862	+	0.998881i	$0.484943\pi$
$74$	−6.56404	−	2.38911i	−0.763054	−	0.277729i
$75$	−2.28182	−	3.95222i	−0.263481	−	0.456363i
$76$	3.75348	+	2.21616i	0.430554	+	0.254211i
$77$	−12.0299	−	0.774218i	−1.37093	−	0.0882304i
$78$	−2.83017	+	0.499036i	−0.320454	+	0.0565047i
$79$	5.47822	−	15.0513i	0.616348	−	1.69340i	−0.0994040	−	0.995047i	$-0.531694\pi$
$79$	5.47822	−	15.0513i	0.616348	−	1.69340i	0.715752	−	0.698355i	$-0.246084\pi$
$80$	−3.04553	−	0.537009i	−0.340501	−	0.0600394i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−5.04400	−	0.889393i	−0.557017	−	0.0982171i
$83$	−13.9931	−	8.07893i	−1.53594	−	0.886777i	−0.999070	−	0.0431147i	$-0.986272\pi$
$83$	−13.9931	−	8.07893i	−1.53594	−	0.886777i	−0.536874	−	0.843663i	$-0.680395\pi$
$84$	−2.64029	−	0.169924i	−0.288079	−	0.0185402i
$85$	0.120356	−	0.682575i	0.0130545	−	0.0740357i
$86$	0.751543	+	2.06485i	0.0810409	+	0.222658i
$87$		−	4.48109i		−	0.480423i
$88$	3.94584	−	2.27813i	0.420628	−	0.242850i
$89$	1.93181	−	10.9558i	0.204771	−	1.16132i	−0.693028	−	0.720911i	$-0.743724\pi$
$89$	1.93181	−	10.9558i	0.204771	−	1.16132i	0.897799	−	0.440405i	$-0.145165\pi$
$90$	2.90601	+	1.05770i	0.306320	+	0.111492i
$91$	−5.49866	−	5.25140i	−0.576416	−	0.550496i
$92$	1.84953	−	1.55194i	0.192827	−	0.161801i
$93$	0.0760005	−	0.0637720i	0.00788088	−	0.00661285i
$94$	2.37420	−	4.11224i	0.244880	−	0.424145i
$95$	2.47013	−	13.2517i	0.253430	−	1.35960i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	1.27220	+	7.21503i	0.129173	+	0.732575i	0.978742	+	0.205098i	$0.0657512\pi$
$97$	1.27220	+	7.21503i	0.129173	+	0.732575i	−0.849569	+	0.527478i	$0.823138\pi$
$98$	−3.77502	−	5.89484i	−0.381335	−	0.595469i
$99$	−4.28149	+	1.55833i	−0.430306	+	0.156618i
$100$	0.792466	+	4.49430i	0.0792466	+	0.449430i
$101$	5.93513	+	16.3066i	0.590568	+	1.62257i	0.769455	+	0.638702i	$0.220528\pi$
$101$	5.93513	+	16.3066i	0.590568	+	1.62257i	−0.178887	+	0.983870i	$0.557250\pi$
$102$	0.112062	+	0.194097i	0.0110958	+	0.0192184i
$103$	8.28947	−	14.3578i	0.816786	−	1.41471i	−0.0912528	−	0.995828i	$-0.529087\pi$
$103$	8.28947	−	14.3578i	0.816786	−	1.41471i	0.908039	−	0.418887i	$-0.137580\pi$
$104$	2.83017	+	0.499036i	0.277521	+	0.0489345i
$105$	2.29884	+	7.85244i	0.224343	+	0.766319i
$106$	4.16803	+	7.21925i	0.404835	+	0.701195i
$107$			12.0068i			1.16075i	0.814351	+	0.580373i	$0.197093\pi$
$107$			12.0068i			1.16075i	−0.814351	+	0.580373i	$0.802907\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	−0.386528	−	0.460646i	−0.0370227	−	0.0441219i	0.747215	−	0.664582i	$-0.231390\pi$
$109$	−0.386528	−	0.460646i	−0.0370227	−	0.0441219i	−0.784238	+	0.620460i	$0.786946\pi$
$110$	−10.7938	−	9.05707i	−1.02915	−	0.863558i
$111$	−4.49006	−	5.35105i	−0.426178	−	0.507899i
$112$	2.42294	+	1.06271i	0.228947	+	0.100416i
$113$		−	1.33108i		−	0.125217i	−0.998038	−	0.0626087i	$-0.980058\pi$
$113$		−	1.33108i		−	0.125217i	0.998038	−	0.0626087i	$-0.0199420\pi$
$114$	2.14253	+	3.79599i	0.200666	+	0.355527i
$115$	−6.46621	−	3.73327i	−0.602978	−	0.348129i
$116$	−1.53262	+	4.21085i	−0.142300	+	0.390967i
$117$	−2.70052	−	0.982909i	−0.249663	−	0.0908700i
$118$	4.21927	+	11.5923i	0.388415	+	1.06716i
$119$	−0.238178	+	0.543039i	−0.0218338	+	0.0497803i
$120$	−2.36900	−	1.98783i	−0.216259	−	0.181463i
$121$	9.75954			0.887231
$122$	6.02647			0.545611
$123$	−3.92354	−	3.29224i	−0.353773	−	0.296851i
$124$	−0.0932284	+	0.0339324i	−0.00837216	+	0.00304722i
$125$	−1.16868	+	0.674738i	−0.104530	+	0.0603504i
$126$	−2.20160	−	1.46730i	−0.196134	−	0.130718i
$127$	−7.34336	+	8.75147i	−0.651617	+	0.776567i	−0.986157	−	0.165814i	$-0.946975\pi$
$127$	−7.34336	+	8.75147i	−0.651617	+	0.776567i	0.334540	+	0.942382i	$0.391419\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−0.381568	+	2.16398i	−0.0335952	+	0.190528i
$130$	−1.54328	−	8.75235i	−0.135354	−	0.767632i
$131$	9.65154	+	11.5023i	0.843259	+	1.00496i	0.999850	+	0.0172930i	$0.00550481\pi$
$131$	9.65154	+	11.5023i	0.843259	+	1.00496i	−0.156592	+	0.987663i	$0.550051\pi$
$132$	4.55626			0.396572
$133$	−4.73502	+	10.5157i	−0.410578	+	0.911825i
$134$	−7.06175			−0.610042
$135$	1.98783	+	2.36900i	0.171085	+	0.203891i
$136$	−0.0389187	−	0.220719i	−0.00333725	−	0.0189265i
$137$	−3.55421	+	20.1570i	−0.303657	+	1.72212i	0.326102	+	0.945334i	$0.394265\pi$
$137$	−3.55421	+	20.1570i	−0.303657	+	1.72212i	−0.629760	+	0.776790i	$0.716847\pi$
$138$	2.37771	−	0.419255i	0.202404	−	0.0356894i
$139$	−9.36364	+	11.1591i	−0.794213	+	0.946506i	−0.999481	−	0.0321993i	$-0.989749\pi$
$139$	−9.36364	+	11.1591i	−0.794213	+	0.946506i	0.205268	+	0.978706i	$0.434193\pi$
$140$	0.525492	−	8.16513i	0.0444122	−	0.690079i
$141$	4.11224	−	2.37420i	0.346313	−	0.199944i
$142$	1.26410	−	0.460094i	0.106081	−	0.0386103i
$143$	10.0305	+	8.41663i	0.838796	+	0.703834i
$144$	1.00000			0.0833333
$145$	13.8578			1.15083
$146$	1.66096	+	1.39371i	0.137462	+	0.115344i
$147$	−0.321845	−	6.99260i	−0.0265453	−	0.576740i
$148$	2.38911	+	6.56404i	0.196384	+	0.539560i
$149$	9.87842	+	3.59545i	0.809271	+	0.294551i	0.713323	−	0.700836i	$-0.247189\pi$
$149$	9.87842	+	3.59545i	0.809271	+	0.294551i	0.0959485	+	0.995386i	$0.469412\pi$
$150$	−1.56085	+	4.28841i	−0.127443	+	0.350147i
$151$	10.3465	+	5.97353i	0.841983	+	0.486119i	0.857938	−	0.513753i	$-0.171745\pi$
$151$	10.3465	+	5.97353i	0.841983	+	0.486119i	−0.0159546	+	0.999873i	$0.505079\pi$
$152$	−0.715013	−	4.29986i	−0.0579952	−	0.348764i
$153$			0.224124i			0.0181193i
$154$	7.13956	+	9.71306i	0.575322	+	0.782701i
$155$	0.197216	+	0.235032i	0.0158407	+	0.0188783i
$156$	2.20148	+	1.84727i	0.176260	+	0.147900i
$157$	1.14354	+	1.36282i	0.0912648	+	0.108765i	0.809744	−	0.586783i	$-0.199606\pi$
$157$	1.14354	+	1.36282i	0.0912648	+	0.108765i	−0.718479	+	0.695548i	$0.755161\pi$
$158$	−15.0513	+	5.47822i	−1.19742	+	0.435824i
$159$			8.33607i			0.661093i
$160$	1.54626	+	2.67819i	0.122242	+	0.211730i
$161$	4.61959	+	4.41186i	0.364075	+	0.347703i
$162$	−0.984808	−	0.173648i	−0.0773738	−	0.0136431i
$163$	−5.01320	+	8.68311i	−0.392664	+	0.680114i	−0.992800	−	0.119784i	$-0.961780\pi$
$163$	−5.01320	+	8.68311i	−0.392664	+	0.680114i	0.600136	+	0.799898i	$0.295113\pi$
$164$	2.56091	+	4.43562i	0.199973	+	0.346364i
$165$	−4.81917	−	13.2406i	−0.375172	−	1.03078i
$166$	2.80578	+	15.9124i	0.217771	+	1.23504i
$167$	−6.38148	+	2.32267i	−0.493813	+	0.179733i	−0.576909	−	0.816808i	$-0.695741\pi$
$167$	−6.38148	+	2.32267i	−0.493813	+	0.179733i	0.0830960	+	0.996542i	$0.473519\pi$
$168$	1.56698	+	2.13180i	0.120895	+	0.164472i
$169$	−0.823279	−	4.66905i	−0.0633292	−	0.359158i
$170$	−0.600247	+	0.346553i	−0.0460368	+	0.0265794i
$171$	−0.0425118	+	4.35869i	−0.00325096	+	0.333317i
$172$	1.09868	−	1.90297i	0.0837737	−	0.145100i
$173$	10.8163	−	9.07597i	0.822350	−	0.690034i	−0.131171	−	0.991360i	$-0.541874\pi$
$173$	10.8163	−	9.07597i	0.822350	−	0.690034i	0.953521	+	0.301326i	$0.0974293\pi$
$174$	−3.43271	+	2.88039i	−0.260233	+	0.218362i
$175$	−11.5879	+	3.39240i	−0.875961	+	0.256441i
$176$	−4.28149	−	1.55833i	−0.322729	−	0.117464i
$177$	−2.14218	+	12.1489i	−0.161016	+	0.913167i
$178$	−9.63440	+	5.56242i	−0.722129	+	0.416921i
$179$			4.44777i			0.332442i	0.986089	+	0.166221i	$0.0531565\pi$
$179$			4.44777i			0.332442i	−0.986089	+	0.166221i	$0.946844\pi$
$180$	−1.05770	−	2.90601i	−0.0788364	−	0.216601i
$181$	−2.73823	+	15.5293i	−0.203531	+	1.15428i	0.696203	+	0.717845i	$0.254871\pi$
$181$	−2.73823	+	15.5293i	−0.203531	+	1.15428i	−0.899734	+	0.436438i	$0.856240\pi$
$182$	−0.488333	+	7.58775i	−0.0361977	+	0.562442i
$183$	5.21907	+	3.01323i	0.385805	+	0.222745i
$184$	−2.37771	−	0.419255i	−0.175287	−	0.0309079i
$185$	16.5482	−	13.8856i	1.21665	−	1.02089i
$186$	−0.0977043	−	0.0172279i	−0.00716403	−	0.00126321i
$187$	0.349260	−	0.959583i	0.0255404	−	0.0701716i
$188$	−4.67626	+	0.824552i	−0.341052	+	0.0601366i
$189$	−1.17299	−	2.37152i	−0.0853222	−	0.172503i
$190$	−11.7392	+	6.62580i	−0.851648	+	0.480686i
$191$	5.20598	+	9.01702i	0.376691	+	0.652448i	0.990579	−	0.136945i	$-0.0437284\pi$
$191$	5.20598	+	9.01702i	0.376691	+	0.652448i	−0.613887	+	0.789394i	$0.710395\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	−4.00821	+	0.706755i	−0.288517	+	0.0508734i	−0.316034	−	0.948748i	$-0.602351\pi$
$193$	−4.00821	+	0.706755i	−0.288517	+	0.0508734i	0.0275164	+	0.999621i	$0.491240\pi$
$194$	4.70928	−	5.61230i	0.338106	−	0.402940i
$195$	3.03966	−	8.35139i	0.217674	−	0.598056i
$196$	−2.08917	+	6.68097i	−0.149227	+	0.477212i
$197$	−8.94653	+	15.4958i	−0.637414	+	1.10403i	0.348584	+	0.937278i	$0.386663\pi$
$197$	−8.94653	+	15.4958i	−0.637414	+	1.10403i	−0.985998	+	0.166756i	$0.946671\pi$
$198$	3.94584	+	2.27813i	0.280419	+	0.161900i
$199$	4.57937	−	5.45748i	0.324623	−	0.386870i	−0.578909	−	0.815392i	$-0.696521\pi$
$199$	4.57937	−	5.45748i	0.324623	−	0.386870i	0.903531	+	0.428522i	$0.140966\pi$
$200$	2.93345	−	3.49594i	0.207426	−	0.247201i
$201$	−6.11565	−	3.53087i	−0.431365	−	0.249049i
$202$	8.67658	−	15.0283i	0.610482	−	1.05739i
$203$	−11.5194	−	2.80437i	−0.808503	−	0.196828i
$204$	0.0766548	−	0.210607i	0.00536691	−	0.0147455i
$205$	10.1813	−	12.1336i	0.711092	−	0.847446i
$206$	−16.3271	+	2.87890i	−1.13756	+	0.200583i
$207$	2.26879	+	0.825771i	0.157692	+	0.0573951i
$208$	−1.43692	−	2.48881i	−0.0996323	−	0.172568i
$209$	6.97431	−	18.5954i	0.482423	−	1.28627i
$210$	4.53765	−	6.80846i	0.313128	−	0.469828i
$211$	13.2702	−	2.33989i	0.913556	−	0.161084i	0.302938	−	0.953010i	$-0.402032\pi$
$211$	13.2702	−	2.33989i	0.913556	−	0.161084i	0.610617	+	0.791926i	$0.290921\pi$
$212$	2.85110	−	7.83334i	0.195815	−	0.537996i
$213$	1.32479	+	0.233596i	0.0907730	+	0.0160057i
$214$	9.19778	−	7.71785i	0.628747	−	0.527581i
$215$	−6.69214	−	1.18000i	−0.456400	−	0.0804756i
$216$	0.866025	+	0.500000i	0.0589256	+	0.0340207i
$217$	−0.116374	−	0.235282i	−0.00789997	−	0.0159720i
$218$	−0.104420	+	0.592195i	−0.00707221	+	0.0401085i
$219$	0.741579	+	2.03747i	0.0501112	+	0.137680i
$220$			14.0903i			0.949968i
$221$	0.557802	−	0.322047i	0.0375218	−	0.0216632i
$222$	−1.21298	+	6.87918i	−0.0814102	+	0.461700i
$223$	−17.9307	−	6.52624i	−1.20073	−	0.437030i	−0.337250	−	0.941415i	$-0.609497\pi$
$223$	−17.9307	−	6.52624i	−1.20073	−	0.437030i	−0.863479	+	0.504386i	$0.831719\pi$
$224$	−0.743356	−	2.53918i	−0.0496675	−	0.169656i
$225$	−3.49594	+	2.93345i	−0.233063	+	0.195563i
$226$	−1.01967	+	0.855601i	−0.0678271	+	0.0569137i
$227$	7.94146	−	13.7550i	0.527093	−	0.912952i	−0.472408	−	0.881380i	$-0.656615\pi$
$227$	7.94146	−	13.7550i	0.527093	−	0.912952i	0.999501	−	0.0315725i	$-0.0100515\pi$
$228$	1.53071	−	4.08129i	0.101374	−	0.270290i
$229$	23.4932	−	13.5638i	1.55248	−	0.896322i	0.554536	−	0.832159i	$-0.312896\pi$
$229$	23.4932	−	13.5638i	1.55248	−	0.896322i	0.997939	−	0.0641629i	$-0.0204377\pi$
$230$	1.29655	+	7.35311i	0.0854921	+	0.484850i
$231$	1.32651	+	11.9815i	0.0872777	+	0.788327i
$232$	4.21085	−	1.53262i	0.276456	−	0.100622i
$233$	4.13979	+	23.4779i	0.271207	+	1.53809i	0.750759	+	0.660577i	$0.229688\pi$
$233$	4.13979	+	23.4779i	0.271207	+	1.53809i	−0.479552	+	0.877514i	$0.659201\pi$
$234$	0.982909	+	2.70052i	0.0642548	+	0.176539i
$235$	7.34225	+	12.7171i	0.478955	+	0.829575i
$236$	6.16816	−	10.6836i	0.401513	−	0.695441i
$237$	−15.7739	−	2.78136i	−1.02463	−	0.180669i
$238$	0.569090	−	0.166604i	0.0368886	−	0.0107993i
$239$	10.4381	+	18.0792i	0.675182	+	1.16945i	0.976416	+	0.215899i	$0.0692681\pi$
$239$	10.4381	+	18.0792i	0.675182	+	1.16945i	−0.301234	+	0.953550i	$0.597399\pi$
$240$			3.09251i			0.199621i
$241$	−19.5354	+	7.11031i	−1.25839	+	0.458015i	−0.883228	−	0.468945i	$-0.844634\pi$
$241$	−19.5354	+	7.11031i	−1.25839	+	0.458015i	−0.375160	+	0.926960i	$0.622412\pi$
$242$	−6.27331	−	7.47624i	−0.403264	−	0.480591i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−3.87374	−	4.61654i	−0.247991	−	0.295544i
$245$	21.6247	−	0.995309i	1.38155	−	0.0635880i
$246$			5.12181i			0.326555i
$247$	10.9091	−	6.15728i	0.694127	−	0.391778i
$248$	0.0859197	+	0.0496058i	0.00545591	+	0.00314997i
$249$	−5.52631	+	15.1834i	−0.350216	+	0.962210i
$250$	1.26809	+	0.461548i	0.0802012	+	0.0291908i
$251$	−7.25867	−	19.9430i	−0.458163	−	1.25879i	−0.926851	−	0.375429i	$-0.877495\pi$
$251$	−7.25867	−	19.9430i	−0.458163	−	1.25879i	0.468688	−	0.883364i	$-0.344727\pi$
$252$	0.291139	+	2.62968i	0.0183400	+	0.165655i
$253$	−8.42696	−	7.07106i	−0.529798	−	0.444554i
$254$	11.4242			0.716820
$255$	−0.693105			−0.0434039
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	10.3143	−	3.75410i	0.643389	−	0.234174i	0.000340600	−	1.00000i	$-0.499892\pi$
$257$	10.3143	−	3.75410i	0.643389	−	0.234174i	0.643048	+	0.765825i	$0.277669\pi$
$258$	1.90297	−	1.09868i	0.118474	−	0.0684009i
$259$	−16.5658	+	8.19366i	−1.02935	+	0.509129i
$260$	−5.71269	+	6.80812i	−0.354286	+	0.422222i
$261$	−4.41301	+	0.778133i	−0.273158	+	0.0481652i
$262$	2.60735	−	14.7870i	0.161083	−	0.913545i
$263$	3.64955	+	20.6976i	0.225041	+	1.27627i	0.862607	+	0.505875i	$0.168830\pi$
$263$	3.64955	+	20.6976i	0.225041	+	1.27627i	−0.637566	+	0.770396i	$0.720059\pi$
$264$	−2.92871	−	3.49030i	−0.180250	−	0.214813i
$265$	−25.7794			−1.58362
$266$	11.0991	−	3.13211i	0.680529	−	0.192042i
$267$	−11.1248			−0.680829
$268$	4.53921	+	5.40961i	0.277276	+	0.330445i
$269$	0.181526	+	1.02949i	0.0110679	+	0.0627689i	0.989841	−	0.142176i	$-0.0454097\pi$
$269$	0.181526	+	1.02949i	0.0110679	+	0.0627689i	−0.978774	+	0.204944i	$0.934299\pi$
$270$	0.537009	−	3.04553i	0.0326813	−	0.185345i
$271$	−7.16586	+	1.26354i	−0.435295	+	0.0767543i	−0.387002	−	0.922079i	$-0.626489\pi$
$271$	−7.16586	+	1.26354i	−0.435295	+	0.0767543i	−0.0482933	+	0.998833i	$0.515378\pi$
$272$	−0.144064	+	0.171689i	−0.00873516	+	0.0104102i
$273$	−4.21679	+	6.32702i	−0.255211	+	0.382929i
$274$	17.7257	−	10.2340i	1.07085	−	0.618256i
$275$	19.5391	−	7.11166i	1.17825	−	0.428849i
$276$	−1.84953	−	1.55194i	−0.111329	−	0.0934159i
$277$	−10.2121			−0.613586			−0.306793	−	0.951776i	$-0.599256\pi$
$277$	−10.2121			−0.613586			−0.306793	+	0.951776i	$0.599256\pi$
$278$	14.5672			0.873684
$279$	−0.0760005	−	0.0637720i	−0.00455003	−	0.00381793i
$280$	−6.59263	+	4.84589i	−0.393985	+	0.289597i
$281$	−0.293708	−	0.806955i	−0.0175211	−	0.0481389i	0.930624	−	0.365977i	$-0.119265\pi$
$281$	−0.293708	−	0.806955i	−0.0175211	−	0.0481389i	−0.948145	+	0.317838i	$0.897043\pi$
$282$	−4.46204	−	1.62405i	−0.265711	−	0.0967107i
$283$	6.00676	−	16.5034i	0.357065	−	0.981028i	−0.622977	−	0.782240i	$-0.714077\pi$
$283$	6.00676	−	16.5034i	0.357065	−	0.981028i	0.980042	−	0.198788i	$-0.0637006\pi$
$284$	−1.16500	−	0.672613i	−0.0691300	−	0.0399122i
$285$	−13.4793	−	0.131468i	−0.798445	−	0.00778751i
$286$		−	13.0939i		−	0.774261i
$287$	−10.9187	+	8.02575i	−0.644510	+	0.473745i
$288$	−0.642788	−	0.766044i	−0.0378766	−	0.0451396i
$289$	12.9843	+	10.8951i	0.763781	+	0.640888i
$290$	−8.90763	−	10.6157i	−0.523074	−	0.623376i
$291$	6.88450	−	2.50575i	0.403577	−	0.146890i
$292$		−	2.16823i		−	0.126886i
$293$	−1.78851	−	3.09780i	−0.104486	−	0.180975i	0.809042	−	0.587751i	$-0.199986\pi$
$293$	−1.78851	−	3.09780i	−0.104486	−	0.180975i	−0.913528	+	0.406776i	$0.866653\pi$
$294$	−5.14976	+	4.74130i	−0.300340	+	0.276518i
$295$	−37.5706	−	6.62471i	−2.18745	−	0.385706i
$296$	3.49265	−	6.04945i	0.203006	−	0.351617i
$297$	2.27813	+	3.94584i	0.132191	+	0.228961i
$298$	−3.59545	−	9.87842i	−0.208279	−	0.572241i
$299$	−1.20487	−	6.83315i	−0.0696794	−	0.395172i
$300$	4.28841	−	1.56085i	0.247592	−	0.0901159i
$301$	5.32409	+	2.33516i	0.306875	+	0.134596i
$302$	−2.07459	−	11.7656i	−0.119379	−	0.677032i
$303$	15.0283	−	8.67658i	0.863352	−	0.498457i
$304$	−2.83428	+	3.31163i	−0.162557	+	0.189935i
$305$	−9.31846	+	16.1400i	−0.533573	+	0.924176i
$306$	0.171689	−	0.144064i	0.00981479	−	0.00823559i
$307$	−24.7945	+	20.8051i	−1.41510	+	1.18741i	−0.461195	+	0.887299i	$0.652579\pi$
$307$	−24.7945	+	20.8051i	−1.41510	+	1.18741i	−0.953905	+	0.300110i	$0.902977\pi$
$308$	2.85142	−	11.7127i	0.162475	−	0.667390i
$309$	−15.5791	−	5.67033i	−0.886264	−	0.322574i
$310$	0.0532775	−	0.302152i	0.00302596	−	0.0171611i
$311$	−28.4714	+	16.4380i	−1.61447	+	0.932112i	−0.626147	+	0.779705i	$0.715369\pi$
$311$	−28.4714	+	16.4380i	−1.61447	+	0.932112i	−0.988318	+	0.152407i	$0.951298\pi$
$312$		−	2.87383i		−	0.162699i
$313$	−4.31223	−	11.8477i	−0.243741	−	0.669674i	−0.999883	−	0.0152665i	$-0.995140\pi$
$313$	−4.31223	−	11.8477i	−0.243741	−	0.669674i	0.756142	−	0.654408i	$-0.227082\pi$
$314$	0.308927	−	1.75201i	0.0174338	−	0.0988718i
$315$	7.33395	−	3.62747i	0.413221	−	0.204385i
$316$	13.8713	+	8.00862i	0.780324	+	0.450520i
$317$	−32.7073	−	5.76718i	−1.83703	−	0.323917i	−0.855878	−	0.517178i	$-0.826982\pi$
$317$	−32.7073	−	5.76718i	−1.83703	−	0.323917i	−0.981147	+	0.193261i	$0.938094\pi$
$318$	6.38580	−	5.35832i	0.358098	−	0.300480i
$319$	20.1068	+	3.54538i	1.12577	+	0.198503i
$320$	1.05770	−	2.90601i	0.0591273	−	0.162451i
$321$	11.8244	−	2.08497i	0.659976	−	0.116371i
$322$	0.410263	−	6.37470i	0.0228631	−	0.355248i
$323$	−0.742214	−	0.635229i	−0.0412979	−	0.0353451i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	12.3242	+	4.48564i	0.683623	+	0.248818i
$326$	9.87407	−	1.74106i	0.546874	−	0.0964287i
$327$	−0.386528	+	0.460646i	−0.0213750	+	0.0254738i
$328$	1.75176	−	4.81293i	0.0967249	−	0.265750i
$329$	−3.52975	−	12.0570i	−0.194602	−	0.664726i
$330$	−7.04515	+	12.2026i	−0.387823	+	0.671729i
$331$	15.6375	+	9.02829i	0.859513	+	0.496240i	0.863849	−	0.503751i	$-0.168047\pi$
$331$	15.6375	+	9.02829i	0.859513	+	0.496240i	−0.00433630	+	0.999991i	$0.501380\pi$
$332$	10.3861	−	12.3776i	0.570010	−	0.679311i
$333$	−4.49006	+	5.35105i	−0.246054	+	0.293236i
$334$	5.88120	+	3.39551i	0.321805	+	0.185794i
$335$	10.9193	−	18.9127i	0.596584	−	1.03331i
$336$	0.625824	−	2.57067i	0.0341415	−	0.140242i
$337$	4.24155	−	11.6536i	0.231052	−	0.634810i	−0.768938	−	0.639324i	$-0.779214\pi$
$337$	4.24155	−	11.6536i	0.231052	−	0.634810i	0.999990	+	0.00451331i	$0.00143664\pi$
$338$	−3.04750	+	3.63187i	−0.165762	+	0.197548i
$339$	−1.31086	+	0.231139i	−0.0711959	+	0.0125538i
$340$	0.651306	+	0.237056i	0.0353220	+	0.0128562i
$341$	0.226017	+	0.391473i	0.0122395	+	0.0211995i
$342$	3.36628	−	2.76915i	0.182027	−	0.149738i
$343$	−18.1771	−	3.54878i	−0.981470	−	0.191616i
$344$	−2.16398	+	0.381568i	−0.116674	+	0.0205728i
$345$	−2.55371	+	7.01625i	−0.137487	+	0.377742i
$346$	−13.9052	−	2.45186i	−0.747548	−	0.131813i
$347$	−14.1224	+	11.8501i	−0.758130	+	0.636147i	−0.937639	−	0.347609i	$-0.886994\pi$
$347$	−14.1224	+	11.8501i	−0.758130	+	0.636147i	0.179509	+	0.983756i	$0.442549\pi$
$348$	4.41301	+	0.778133i	0.236562	+	0.0417123i
$349$	−5.73159	−	3.30914i	−0.306805	−	0.177134i	0.338691	−	0.940898i	$-0.390016\pi$
$349$	−5.73159	−	3.30914i	−0.306805	−	0.177134i	−0.645496	+	0.763764i	$0.723349\pi$
$350$	10.0473	+	6.69623i	0.537049	+	0.357929i
$351$	−0.499036	+	2.83017i	−0.0266366	+	0.151064i
$352$	1.55833	+	4.28149i	0.0830595	+	0.228204i
$353$			3.92156i			0.208724i	0.994539	+	0.104362i	$0.0332800\pi$
$353$			3.92156i			0.208724i	−0.994539	+	0.104362i	$0.966720\pi$
$354$	10.6836	−	6.16816i	0.567825	−	0.327834i
$355$	−0.722398	+	4.09692i	−0.0383409	+	0.217442i
$356$	10.4539	+	3.80492i	0.554057	+	0.201660i
$357$	0.576148	+	0.140262i	0.0304930	+	0.00742345i
$358$	3.40719	−	2.85897i	0.180076	−	0.151101i
$359$	5.12396	−	4.29951i	0.270432	−	0.226920i	−0.497479	−	0.867476i	$-0.665741\pi$
$359$	5.12396	−	4.29951i	0.270432	−	0.226920i	0.767911	+	0.640557i	$0.221296\pi$
$360$	−1.54626	+	2.67819i	−0.0814949	+	0.141153i
$361$	−14.3139	−	12.4945i	−0.753361	−	0.657607i
$362$	13.6562	−	7.88443i	0.717756	−	0.414396i
$363$	−1.69473	−	9.61127i	−0.0889501	−	0.504461i
$364$	6.12645	−	4.50323i	0.321113	−	0.236033i
$365$	−6.30090	+	2.29334i	−0.329804	+	0.120039i
$366$	−1.04648	−	5.93491i	−0.0547006	−	0.310223i
$367$	1.09458	+	3.00734i	0.0571367	+	0.156982i	0.964977	−	0.262334i	$-0.0844922\pi$
$367$	1.09458	+	3.00734i	0.0571367	+	0.156982i	−0.907840	+	0.419316i	$0.862270\pi$
$368$	1.20720	+	2.09093i	0.0629295	+	0.108997i
$369$	−2.56091	+	4.43562i	−0.133315	+	0.230909i
$370$	−21.2739	−	3.75117i	−1.10598	−	0.195014i
$371$	21.4293	+	5.21691i	1.11255	+	0.270849i
$372$	0.0496058	+	0.0859197i	0.00257194	+	0.00445473i
$373$			20.0600i			1.03867i	0.854572	+	0.519334i	$0.173820\pi$
$373$			20.0600i			1.03867i	−0.854572	+	0.519334i	$0.826180\pi$
$374$	−0.959583	+	0.349260i	−0.0496188	+	0.0180598i
$375$	0.867426	+	1.03376i	0.0447937	+	0.0533830i
$376$	3.63749	+	3.05221i	0.187589	+	0.157406i
$377$	8.27776	+	9.86505i	0.426326	+	0.508076i
$378$	−1.06271	+	2.42294i	−0.0546598	+	0.124623i
$379$			27.6816i			1.42191i	0.703238	+	0.710955i	$0.251737\pi$
$379$			27.6816i			1.42191i	−0.703238	+	0.710955i	$0.748263\pi$
$380$	12.6214	+	4.73373i	0.647466	+	0.242835i
$381$	9.89368	+	5.71212i	0.506868	+	0.292641i
$382$	3.56110	−	9.78404i	0.182202	−	0.500595i
$383$	−18.9670	−	6.90343i	−0.969169	−	0.352749i	−0.191549	−	0.981483i	$-0.561351\pi$
$383$	−18.9670	−	6.90343i	−0.969169	−	0.352749i	−0.777620	+	0.628734i	$0.783573\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	−37.0530	+	4.10224i	−1.88840	+	0.209069i
$386$	3.11783	+	2.61617i	0.158694	+	0.133160i
$387$	2.19736			0.111698
$388$	−7.32633			−0.371938
$389$	0.775787	+	0.650963i	0.0393340	+	0.0330051i	0.662243	−	0.749289i	$-0.269605\pi$
$389$	0.775787	+	0.650963i	0.0393340	+	0.0330051i	−0.622909	+	0.782295i	$0.714049\pi$
$390$	−8.35139	+	3.03966i	−0.422889	+	0.153919i
$391$	−0.468626	+	0.270561i	−0.0236994	+	0.0136829i
$392$	6.46081	−	2.69404i	0.326320	−	0.136070i
$393$	9.65154	−	11.5023i	0.486856	−	0.580212i
$394$	17.6212	−	3.10710i	0.887745	−	0.156533i
$395$	8.60140	−	48.7810i	0.432784	−	2.45444i
$396$	−0.791187	−	4.48704i	−0.0397586	−	0.225482i
$397$	−5.01871	−	5.98106i	−0.251882	−	0.300181i	0.625256	−	0.780420i	$-0.284994\pi$
$397$	−5.01871	−	5.98106i	−0.251882	−	0.300181i	−0.877138	+	0.480239i	$0.840550\pi$
$398$	−7.12423			−0.357105
$399$	11.1782	+	2.83706i	0.559608	+	0.142030i
$400$	−4.56363			−0.228182
$401$	−11.1367	−	13.2723i	−0.556142	−	0.662785i	0.412583	−	0.910920i	$-0.364627\pi$
$401$	−11.1367	−	13.2723i	−0.556142	−	0.662785i	−0.968725	+	0.248135i	$0.920182\pi$
$402$	1.22626	+	6.95447i	0.0611603	+	0.346857i
$403$	−0.0495102	+	0.280786i	−0.00246628	+	0.0139870i
$404$	−17.0895	+	3.01335i	−0.850236	+	0.149920i
$405$	1.98783	−	2.36900i	0.0987760	−	0.117717i
$406$	5.25625	+	10.6270i	0.260863	+	0.527408i
$407$	27.5629	−	15.9134i	1.36624	−	0.788800i
$408$	−0.210607	+	0.0766548i	−0.0104266	+	0.00379498i
$409$	−10.8345	−	9.09121i	−0.535731	−	0.449531i	0.334344	−	0.942451i	$-0.391485\pi$
$409$	−10.8345	−	9.09121i	−0.535731	−	0.449531i	−0.870075	+	0.492920i	$0.835930\pi$
$410$	−15.8393			−0.782246
$411$	20.4679			1.00961
$412$	12.7002	+	10.6567i	0.625694	+	0.525020i
$413$	29.8902	+	13.1099i	1.47080	+	0.645096i
$414$	−0.825771	−	2.26879i	−0.0405844	−	0.111505i
$415$	−46.9549	−	17.0902i	−2.30493	−	0.838924i
$416$	−0.982909	+	2.70052i	−0.0481911	+	0.132404i
$417$	12.6156	+	7.28362i	0.617788	+	0.356680i
$418$	−18.7279	+	6.61028i	−0.916013	+	0.323320i
$419$			2.06472i			0.100868i	0.998727	+	0.0504341i	$0.0160605\pi$
$419$			2.06472i			0.100868i	−0.998727	+	0.0504341i	$0.983940\pi$
$420$	−8.13233	+	0.900351i	−0.396817	+	0.0439326i
$421$	8.88264	+	10.5859i	0.432913	+	0.515926i	0.937760	−	0.347283i	$-0.112896\pi$
$421$	8.88264	+	10.5859i	0.432913	+	0.515926i	−0.504847	+	0.863209i	$0.668451\pi$
$422$	−10.3224	−	8.66148i	−0.502484	−	0.421634i
$423$	−3.05221	−	3.63749i	−0.148404	−	0.176861i
$424$	−7.83334	+	2.85110i	−0.380421	+	0.138462i
$425$		−	1.02282i		−	0.0496140i
$426$	−0.672613	−	1.16500i	−0.0325882	−	0.0564444i
$427$	11.0122	−	11.5308i	0.532920	−	0.558013i
$428$	−11.8244	−	2.08497i	−0.571556	−	0.100781i
$429$	6.54697	−	11.3397i	0.316091	−	0.547485i
$430$	3.39769	+	5.88497i	0.163851	+	0.283798i
$431$	5.47026	+	15.0294i	0.263493	+	0.723942i	0.998926	+	0.0463435i	$0.0147569\pi$
$431$	5.47026	+	15.0294i	0.263493	+	0.723942i	−0.735432	+	0.677598i	$0.763021\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	32.5478	−	11.8464i	1.56415	−	0.569303i	0.592466	−	0.805596i	$-0.298155\pi$
$433$	32.5478	−	11.8464i	1.56415	−	0.569303i	0.971682	+	0.236293i	$0.0759324\pi$
$434$	−0.105433	+	0.240384i	−0.00506094	+	0.0115388i
$435$	−2.40638	−	13.6473i	−0.115377	−	0.654337i
$436$	0.520768	−	0.300665i	0.0249403	−	0.0143993i
$437$	−9.16502	+	5.17291i	−0.438422	+	0.247454i
$438$	1.08412	−	1.87774i	0.0518010	−	0.0897220i
$439$	26.4632	−	22.2052i	1.26302	−	1.05980i	0.267664	−	0.963512i	$-0.413748\pi$
$439$	26.4632	−	22.2052i	1.26302	−	1.05980i	0.995354	−	0.0962850i	$-0.0306960\pi$
$440$	10.7938	−	9.05707i	0.514574	−	0.431779i
$441$	−6.83048	+	1.53121i	−0.325261	+	0.0729146i
$442$	−0.605251	−	0.220293i	−0.0287888	−	0.0104783i
$443$	−1.69577	+	9.61718i	−0.0805684	+	0.456926i	0.917657	+	0.397374i	$0.130078\pi$
$443$	−1.69577	+	9.61718i	−0.0805684	+	0.456926i	−0.998225	+	0.0595522i	$0.981033\pi$
$444$	6.04945	−	3.49265i	0.287094	−	0.165754i
$445$		−	34.4037i		−	1.63089i
$446$	6.52624	+	17.9307i	0.309027	+	0.849043i
$447$	1.82546	−	10.3527i	0.0863412	−	0.489665i
$448$	−1.46730	+	2.20160i	−0.0693235	+	0.104016i
$449$	1.81759	+	1.04939i	0.0857773	+	0.0495236i	0.542275	−	0.840201i	$-0.317563\pi$
$449$	1.81759	+	1.04939i	0.0857773	+	0.0495236i	−0.456498	+	0.889725i	$0.650896\pi$
$450$	4.49430	+	0.792466i	0.211863	+	0.0373572i
$451$	17.8767	−	15.0003i	0.841779	−	0.706337i
$452$	1.31086	+	0.231139i	0.0616575	+	0.0108719i
$453$	4.08614	−	11.2266i	0.191984	−	0.527470i
$454$	−15.6416	+	2.75804i	−0.734098	+	0.129441i
$455$	−19.5664	−	13.0405i	−0.917286	−	0.611346i
$456$	−4.11037	+	1.45081i	−0.192486	+	0.0679405i
$457$	−6.23123	−	10.7928i	−0.291485	−	0.504866i	0.682676	−	0.730721i	$-0.260816\pi$
$457$	−6.23123	−	10.7928i	−0.291485	−	0.504866i	−0.974161	+	0.225855i	$0.927483\pi$
$458$	−25.4916	−	9.27820i	−1.19115	−	0.433542i
$459$	0.220719	−	0.0389187i	0.0103023	−	0.00181657i
$460$	4.79940	−	5.71970i	0.223773	−	0.266682i
$461$	12.2062	−	33.5363i	0.568500	−	1.56194i	−0.238346	−	0.971180i	$-0.576605\pi$
$461$	12.2062	−	33.5363i	0.568500	−	1.56194i	0.806846	−	0.590762i	$-0.201173\pi$
$462$	8.32573	−	8.71774i	0.387348	−	0.405586i
$463$	2.24904	−	3.89546i	0.104522	−	0.181037i	−0.809021	−	0.587780i	$-0.800002\pi$
$463$	2.24904	−	3.89546i	0.104522	−	0.181037i	0.913543	+	0.406743i	$0.133335\pi$
$464$	−3.88074	−	2.24054i	−0.180159	−	0.104015i
$465$	0.197216	−	0.235032i	0.00914565	−	0.0108994i
$466$	15.3241	−	18.2626i	0.709877	−	0.845998i
$467$	−25.9120	−	14.9603i	−1.19907	−	0.692281i	−0.238719	−	0.971089i	$-0.576728\pi$
$467$	−25.9120	−	14.9603i	−1.19907	−	0.692281i	−0.960347	+	0.278808i	$0.910061\pi$
$468$	1.43692	−	2.48881i	0.0664215	−	0.115045i
$469$	−12.9040	+	13.5116i	−0.595853	+	0.623909i
$470$	5.02239	−	13.7989i	0.231666	−	0.636496i
$471$	1.14354	−	1.36282i	0.0526918	−	0.0627956i
$472$	−12.1489	+	2.14218i	−0.559198	+	0.0986017i
$473$	−9.40798	−	3.42423i	−0.432580	−	0.157446i
$474$	8.00862	+	13.8713i	0.367848	+	0.637132i
$475$	0.194008	−	19.8915i	0.00890170	−	0.912683i
$476$	−0.493430	−	0.328857i	−0.0226163	−	0.0150732i
$477$	8.20943	−	1.44754i	0.375884	−	0.0662785i
$478$	7.14005	−	19.6171i	0.326578	−	0.897267i
$479$	−0.586318	−	0.103384i	−0.0267896	−	0.00472372i	0.160237	−	0.987079i	$-0.448774\pi$
$479$	−0.586318	−	0.103384i	−0.0267896	−	0.00472372i	−0.187027	+	0.982355i	$0.559885\pi$
$480$	2.36900	−	1.98783i	0.108130	−	0.0907315i
$481$	19.7696	+	3.48592i	0.901417	+	0.158944i
$482$	18.0039	+	10.3946i	0.820057	+	0.473460i
$483$	3.54265	−	5.31552i	0.161196	−	0.241864i
$484$	−1.69473	+	9.61127i	−0.0770330	+	0.436876i
$485$	7.74908	+	21.2904i	0.351867	+	0.966748i
$486$			1.00000i			0.0453609i
$487$	−16.7178	+	9.65204i	−0.757557	+	0.437376i	−0.828418	−	0.560111i	$-0.810759\pi$
$487$	−16.7178	+	9.65204i	−0.757557	+	0.437376i	0.0708611	+	0.997486i	$0.477425\pi$
$488$	−1.04648	+	5.93491i	−0.0473721	+	0.268661i
$489$	9.42173	+	3.42923i	0.426065	+	0.155075i
$490$	−14.6625	−	15.9257i	−0.662386	−	0.719450i
$491$	−27.6723	+	23.2198i	−1.24883	+	1.04790i	−0.252053	+	0.967713i	$0.581106\pi$
$491$	−27.6723	+	23.2198i	−1.24883	+	1.04790i	−0.996780	+	0.0801818i	$0.974450\pi$
$492$	3.92354	−	3.29224i	0.176887	−	0.148426i
$493$	0.502159	−	0.869765i	0.0226161	−	0.0391722i
$494$	−11.7290	−	4.39900i	−0.527711	−	0.197920i
$495$	−12.2026	+	7.04515i	−0.548464	+	0.316656i
$496$	−0.0172279	−	0.0977043i	−0.000773556	−	0.00438705i
$497$	1.42958	−	3.25940i	0.0641255	−	0.146204i
$498$	15.1834	−	5.52631i	0.680385	−	0.247640i
$499$	−6.74997	−	38.2810i	−0.302170	−	1.71369i	−0.636535	−	0.771248i	$-0.719633\pi$
$499$	−6.74997	−	38.2810i	−0.302170	−	1.71369i	0.334365	−	0.942444i	$-0.391478\pi$
$500$	−0.461548	−	1.26809i	−0.0206410	−	0.0567108i
$501$	3.39551	+	5.88120i	0.151700	+	0.262753i
$502$	−10.6115	+	18.3796i	−0.473613	+	0.820322i
$503$	2.08375	+	0.367421i	0.0929097	+	0.0163825i	0.219910	−	0.975520i	$-0.429424\pi$
$503$	2.08375	+	0.367421i	0.0929097	+	0.0163825i	−0.127000	+	0.991903i	$0.540535\pi$
$504$	1.82731	−	1.91335i	0.0813950	−	0.0852275i
$505$	26.8324	+	46.4751i	1.19403	+	2.06812i
$506$			11.0006i			0.489037i
$507$	−4.45515	+	1.62154i	−0.197860	+	0.0720153i
$508$	−7.34336	−	8.75147i	−0.325809	−	0.388284i
$509$	−10.3246	−	8.66334i	−0.457629	−	0.383996i	0.384629	−	0.923071i	$-0.374329\pi$
$509$	−10.3246	−	8.66334i	−0.457629	−	0.383996i	−0.842258	+	0.539075i	$0.818774\pi$
$510$	0.445519	+	0.530949i	0.0197279	+	0.0235108i
$511$	5.70176	−	0.631257i	0.252231	−	0.0279251i
$512$		−	1.00000i		−	0.0441942i
$513$	4.29986	−	0.715013i	0.189843	−	0.0315686i
$514$	−9.50572	−	5.48813i	−0.419279	−	0.242071i
$515$	17.5356	−	48.1786i	0.772709	−	2.12300i
$516$	−2.06485	−	0.751543i	−0.0908998	−	0.0330848i
$517$	7.39960	+	20.3302i	0.325434	+	0.894123i
$518$	16.9250	+	7.42334i	0.743641	+	0.326163i
$519$	−10.8163	−	9.07597i	−0.474784	−	0.398391i
$520$	8.88737			0.389737
$521$	−33.7917			−1.48044			−0.740220	−	0.672365i	$-0.765279\pi$
$521$	−33.7917			−1.48044			−0.740220	+	0.672365i	$0.765279\pi$
$522$	3.43271	+	2.88039i	0.150246	+	0.126071i
$523$	7.83639	−	2.85221i	0.342662	−	0.124719i	−0.164956	−	0.986301i	$-0.552748\pi$
$523$	7.83639	−	2.85221i	0.342662	−	0.124719i	0.507618	+	0.861582i	$0.330526\pi$
$524$	−13.0035	+	7.50756i	−0.568060	+	0.327969i
$525$	5.35308	+	10.8227i	0.233627	+	0.472343i
$526$	13.5094	−	16.0999i	0.589039	−	0.701989i
$527$	0.0218979	−	0.00386118i	0.000953886	−	0.000168196i
$528$	−0.791187	+	4.48704i	−0.0344320	+	0.195274i
$529$	−2.98166	−	16.9098i	−0.129637	−	0.735211i
$530$	16.5707	+	19.7482i	0.719784	+	0.857805i
$531$	12.3363			0.535350
$532$	−9.53370	−	6.48911i	−0.413338	−	0.281339i
$533$	14.7192			0.637561
$534$	7.15091	+	8.52213i	0.309450	+	0.368788i
$535$	6.44778	+	36.5672i	0.278762	+	1.58094i
$536$	1.22626	−	6.95447i	0.0529664	−	0.300387i
$537$	4.38020	−	0.772347i	0.189019	−	0.0333292i
$538$	0.671950	−	0.800799i	0.0289698	−	0.0345249i
$539$	31.6307	+	4.08832i	1.36243	+	0.176096i
$540$	−2.67819	+	1.54626i	−0.115251	+	0.0665403i
$541$	−10.5096	+	3.82518i	−0.451843	+	0.164457i	−0.557910	−	0.829902i	$-0.688396\pi$
$541$	−10.5096	+	3.82518i	−0.451843	+	0.164457i	0.106067	+	0.994359i	$0.466174\pi$
$542$	5.57405	+	4.67719i	0.239426	+	0.200902i
$543$	15.7689			0.676706
$544$	0.224124			0.00960922
$545$	−1.42455	−	1.19534i	−0.0610212	−	0.0512028i
$546$	7.55728	−	0.836685i	0.323422	−	0.0358068i
$547$	−6.99508	−	19.2188i	−0.299088	−	0.821738i	−0.994653	−	0.103274i	$-0.967068\pi$
$547$	−6.99508	−	19.2188i	−0.299088	−	0.821738i	0.695565	−	0.718463i	$-0.255154\pi$
$548$	−19.2335	−	7.00044i	−0.821616	−	0.299044i
$549$	2.06117	−	5.66302i	0.0879687	−	0.241692i
$550$	−18.0074	−	10.3966i	−0.767836	−	0.443311i
$551$	9.93082	−	16.8197i	0.423067	−	0.716543i
$552$			2.41439i			0.102763i
$553$	−17.0217	+	38.8089i	−0.723834	+	1.65032i
$554$	6.56421	+	7.82292i	0.278887	+	0.332364i
$555$	−16.5482	−	13.8856i	−0.702431	−	0.589410i
$556$	−9.36364	−	11.1591i	−0.397107	−	0.473253i
$557$	5.52761	−	2.01189i	0.234212	−	0.0852463i	−0.222248	−	0.974990i	$-0.571339\pi$
$557$	5.52761	−	2.01189i	0.234212	−	0.0852463i	0.456460	+	0.889744i	$0.349117\pi$
$558$			0.0992116i			0.00419996i
$559$	−3.15743	−	5.46883i	−0.133545	−	0.231307i
$560$	7.94983	+	1.93537i	0.335942	+	0.0817842i
$561$	−1.00565	−	0.177324i	−0.0424587	−	0.00748661i
$562$	−0.429372	+	0.743694i	−0.0181120	+	0.0313708i
$563$	3.10669	+	5.38094i	0.130931	+	0.226780i	0.924036	−	0.382306i	$-0.124870\pi$
$563$	3.10669	+	5.38094i	0.130931	+	0.226780i	−0.793105	+	0.609086i	$0.791537\pi$
$564$	1.62405	+	4.46204i	0.0683848	+	0.187886i
$565$	−0.714801	−	4.05384i	−0.0300719	−	0.170546i
$566$	−16.5034	+	6.00676i	−0.693692	+	0.252483i
$567$	−2.13180	+	1.56698i	−0.0895273	+	0.0658068i
$568$	0.233596	+	1.32479i	0.00980147	+	0.0555869i
$569$	−18.0309	+	10.4101i	−0.755893	+	0.436415i	−0.827819	−	0.560995i	$-0.810419\pi$
$569$	−18.0309	+	10.4101i	−0.755893	+	0.436415i	0.0719264	+	0.997410i	$0.477085\pi$
$570$	8.56362	+	10.4103i	0.358691	+	0.436038i
$571$	−6.20322	+	10.7443i	−0.259597	+	0.449635i	−0.966134	−	0.258041i	$-0.916923\pi$
$571$	−6.20322	+	10.7443i	−0.259597	+	0.449635i	0.706537	+	0.707676i	$0.250256\pi$
$572$	−10.0305	+	8.41663i	−0.419398	+	0.351917i
$573$	7.97602	−	6.69267i	0.333203	−	0.279590i
$574$	13.1665	+	3.20535i	0.549559	+	0.133789i
$575$	−10.3539	−	3.76852i	−0.431788	−	0.157158i
$576$	−0.173648	+	0.984808i	−0.00723534	+	0.0410337i
$577$	−5.39880	+	3.11700i	−0.224755	+	0.129762i	−0.608150	−	0.793822i	$-0.708088\pi$
$577$	−5.39880	+	3.11700i	−0.224755	+	0.129762i	0.383395	+	0.923584i	$0.374755\pi$
$578$		−	16.9498i		−	0.705017i
$579$	1.39204	+	3.82459i	0.0578511	+	0.158944i
$580$	−2.40638	+	13.6473i	−0.0999197	+	0.566673i
$581$	35.5731	+	23.7085i	1.47582	+	0.983593i
$582$	−6.34479	−	3.66317i	−0.263000	−	0.151843i
$583$	−37.4043	−	6.59539i	−1.54913	−	0.273153i
$584$	−1.66096	+	1.39371i	−0.0687311	+	0.0576722i
$585$	−8.75235	−	1.54328i	−0.361865	−	0.0638066i
$586$	−1.22342	+	3.36131i	−0.0505388	+	0.138854i
$587$	1.61400	−	0.284592i	0.0666170	−	0.0117464i	−0.140240	−	0.990117i	$-0.544788\pi$
$587$	1.61400	−	0.284592i	0.0666170	−	0.0117464i	0.206857	+	0.978371i	$0.433676\pi$
$588$	6.94225	+	0.897297i	0.286294	+	0.0370039i
$589$	0.426595	−	0.0709376i	0.0175776	−	0.00292293i
$590$	19.0751	+	33.0390i	0.785309	+	1.36020i
$591$	16.8140	+	6.11979i	0.691635	+	0.251734i
$592$	−6.87918	+	1.21298i	−0.282732	+	0.0498534i
$593$	−14.1666	+	16.8831i	−0.581754	+	0.693308i	−0.973999	−	0.226553i	$-0.927254\pi$
$593$	−14.1666	+	16.8831i	−0.581754	+	0.693308i	0.392245	+	0.919861i	$0.371699\pi$
$594$	1.55833	−	4.28149i	0.0639392	−	0.175672i
$595$	−0.433762	+	1.78174i	−0.0177825	+	0.0730444i
$596$	−5.25620	+	9.10400i	−0.215302	+	0.372914i
$597$	−6.16976	−	3.56211i	−0.252512	−	0.145788i
$598$	−4.46002	+	5.31525i	−0.182384	+	0.217357i
$599$	−11.9541	+	14.2464i	−0.488433	+	0.582091i	−0.952818	−	0.303542i	$-0.901831\pi$
$599$	−11.9541	+	14.2464i	−0.488433	+	0.582091i	0.464385	+	0.885633i	$0.346275\pi$
$600$	−3.95222	−	2.28182i	−0.161349	−	0.0931547i
$601$	−15.4067	+	26.6852i	−0.628453	+	1.08851i	0.359410	+	0.933180i	$0.382978\pi$
$601$	−15.4067	+	26.6852i	−0.628453	+	1.08851i	−0.987862	+	0.155332i	$0.950355\pi$
$602$	−1.63342	−	5.57950i	−0.0665733	−	0.227403i
$603$	−2.41526	+	6.63587i	−0.0983570	+	0.270234i
$604$	−7.67943	+	9.15198i	−0.312471	+	0.372389i
$605$	29.7230	−	5.24096i	1.20841	−	0.213075i
$606$	−16.3066	−	5.93513i	−0.662412	−	0.241098i
$607$	6.00320	+	10.3979i	0.243663	+	0.422036i	0.961755	−	0.273912i	$-0.0883177\pi$
$607$	6.00320	+	10.3979i	0.243663	+	0.422036i	−0.718092	+	0.695948i	$0.754984\pi$
$608$	4.35869	+	0.0425118i	0.176768	+	0.00172408i
$609$	−0.761444	+	11.8314i	−0.0308553	+	0.479431i
$610$	18.3538	−	3.23627i	0.743123	−	0.131033i
$611$	−4.66725	+	12.8232i	−0.188817	+	0.518770i
$612$	−0.220719	−	0.0389187i	−0.00892203	−	0.00157319i
$613$	−23.8802	+	20.0379i	−0.964512	+	0.809322i	−0.981681	−	0.190531i	$-0.938979\pi$
$613$	−23.8802	+	20.0379i	−0.964512	+	0.809322i	0.0171693	+	0.999853i	$0.494535\pi$
$614$	31.8752	+	5.62047i	1.28638	+	0.226824i
$615$	−13.7172	−	7.91963i	−0.553131	−	0.319350i
$616$	−10.8053	+	5.34443i	−0.435357	+	0.215333i
$617$	4.28012	−	24.2738i	0.172311	−	0.977226i	−0.768890	−	0.639381i	$-0.779191\pi$
$617$	4.28012	−	24.2738i	0.172311	−	0.977226i	0.941202	−	0.337845i	$-0.109698\pi$
$618$	5.67033	+	15.5791i	0.228094	+	0.626684i
$619$			32.3829i			1.30158i	0.759259	+	0.650788i	$0.225561\pi$
$619$			32.3829i			1.30158i	−0.759259	+	0.650788i	$0.774439\pi$
$620$	−0.265708	+	0.153407i	−0.0106711	+	0.00616095i
$621$	0.419255	−	2.37771i	0.0168241	−	0.0954143i
$622$	30.8933	+	11.2442i	1.23871	+	0.450853i
$623$	−6.96219	+	28.5983i	−0.278934	+	1.14577i
$624$	−2.20148	+	1.84727i	−0.0881299	+	0.0739498i
$625$	−20.6766	+	17.3498i	−0.827065	+	0.693990i
$626$	−6.30405	+	10.9189i	−0.251961	+	0.436409i
$627$	−19.5240	−	3.63929i	−0.779714	−	0.145339i
$628$	−1.54069	+	0.889520i	−0.0614804	+	0.0354957i
$629$	−0.271859	−	1.54179i	−0.0108397	−	0.0614751i
$630$	−7.49298	−	3.28644i	−0.298527	−	0.130935i
$631$	44.0823	−	16.0447i	1.75489	−	0.638728i	0.755034	−	0.655686i	$-0.227620\pi$
$631$	44.0823	−	16.0447i	1.75489	−	0.638728i	0.999856	+	0.0169579i	$0.00539811\pi$
$632$	−2.78136	−	15.7739i	−0.110637	−	0.627452i
$633$	−4.60868	−	12.6622i	−0.183179	−	0.503279i
$634$	16.6059	+	28.7623i	0.659506	+	1.14230i
$635$	−17.6648	+	30.5963i	−0.701006	+	1.21418i
$636$	−8.20943	−	1.44754i	−0.325525	−	0.0573988i
$637$	13.6257	+	14.7996i	0.539871	+	0.586380i
$638$	−10.2085	−	17.6817i	−0.404159	−	0.700024i
$639$		−	1.34523i		−	0.0532163i
$640$	−2.90601	+	1.05770i	−0.114870	+	0.0418093i
$641$	18.9597	+	22.5953i	0.748863	+	0.892460i	0.997089	−	0.0762422i	$-0.0242922\pi$
$641$	18.9597	+	22.5953i	0.748863	+	0.892460i	−0.248227	+	0.968702i	$0.579848\pi$
$642$	−9.19778	−	7.71785i	−0.363007	−	0.304599i
$643$	−20.4930	−	24.4226i	−0.808166	−	0.963135i	0.191666	−	0.981460i	$-0.438611\pi$
$643$	−20.4930	−	24.4226i	−0.808166	−	0.963135i	−0.999832	+	0.0183254i	$0.994167\pi$
$644$	−5.14701	+	3.78330i	−0.202821	+	0.149083i
$645$			6.79537i			0.267568i
$646$	−0.00952790	+	0.976886i	−0.000374870	+	0.0384351i
$647$	7.22934	+	4.17386i	0.284215	+	0.164091i	0.635330	−	0.772241i	$-0.280864\pi$
$647$	7.22934	+	4.17386i	0.284215	+	0.164091i	−0.351115	+	0.936332i	$0.614197\pi$
$648$	0.342020	−	0.939693i	0.0134358	−	0.0369146i
$649$	−52.8178	−	19.2241i	−2.07328	−	0.754612i
$650$	−4.48564	−	12.3242i	−0.175941	−	0.483394i
$651$	−0.211500	+	0.155462i	−0.00828932	+	0.00609304i
$652$	−7.68066	−	6.44484i	−0.300798	−	0.252399i
$653$	34.4050			1.34637			0.673186	−	0.739473i	$-0.264925\pi$
$653$	34.4050			1.34637			0.673186	+	0.739473i	$0.264925\pi$
$654$	0.601331			0.0235139
$655$	35.5709	+	29.8475i	1.38987	+	1.16624i
$656$	−4.81293	+	1.75176i	−0.187913	+	0.0683948i
$657$	1.87774	−	1.08412i	0.0732577	−	0.0422954i
$658$	−6.96735	+	10.4541i	−0.271615	+	0.407542i
$659$	8.69169	−	10.3584i	0.338580	−	0.403504i	−0.569709	−	0.821846i	$-0.692944\pi$
$659$	8.69169	−	10.3584i	0.338580	−	0.403504i	0.908290	+	0.418342i	$0.137389\pi$
$660$	13.8762	−	2.44676i	0.540132	−	0.0952398i
$661$	1.44806	−	8.21234i	0.0563229	−	0.319423i	−0.943609	−	0.331061i	$-0.892593\pi$
$661$	1.44806	−	8.21234i	0.0563229	−	0.319423i	0.999932	+	0.0116379i	$0.00370454\pi$
$662$	−3.13549	−	17.7823i	−0.121864	−	0.691128i
$663$	−0.414016	−	0.493405i	−0.0160790	−	0.0191623i
$664$	−16.1579			−0.627046
$665$	−8.77363	+	34.5686i	−0.340227	+	1.34051i
$666$	6.98530			0.270675
$667$	−6.95439	−	8.28792i	−0.269275	−	0.320909i
$668$	−1.17925	−	6.68785i	−0.0456265	−	0.258761i
$669$	−3.31346	+	18.7916i	−0.128106	+	0.726524i
$670$	−21.5068	+	3.79222i	−0.830879	+	0.146506i
$671$	−17.6498	+	21.0342i	−0.681362	+	0.812015i
$672$	−2.37152	+	1.17299i	−0.0914833	+	0.0452489i
$673$	2.10179	−	1.21347i	0.0810181	−	0.0467758i	−0.458944	−	0.888465i	$-0.651772\pi$
$673$	2.10179	−	1.21347i	0.0810181	−	0.0467758i	0.539962	+	0.841690i	$0.318439\pi$
$674$	−11.6536	+	4.24155i	−0.448879	+	0.163378i
$675$	3.49594	+	2.93345i	0.134559	+	0.112908i
$676$	4.74108			0.182349
$677$	18.5958			0.714695			0.357347	−	0.933972i	$-0.383681\pi$
$677$	18.5958			0.714695			0.357347	+	0.933972i	$0.383681\pi$
$678$	1.01967	+	0.855601i	0.0391600	+	0.0328591i
$679$	−2.13298	−	19.2659i	−0.0818563	−	0.739359i
$680$	−0.237056	−	0.651306i	−0.00909068	−	0.0249764i
$681$	−14.9251	−	5.43228i	−0.571930	−	0.208165i
$682$	0.154605	−	0.424773i	0.00592012	−	0.0162654i
$683$	0.618435	+	0.357054i	0.0236638	+	0.0136623i	0.511785	−	0.859113i	$-0.328984\pi$
$683$	0.618435	+	0.357054i	0.0236638	+	0.0136623i	−0.488121	+	0.872776i	$0.662318\pi$
$684$	−4.28509	−	0.798745i	−0.163845	−	0.0305408i
$685$			63.2972i			2.41846i
$686$	8.96548	+	16.2056i	0.342304	+	0.618731i
$687$	−17.4373	−	20.7810i	−0.665275	−	0.792844i
$688$	1.68328	+	1.41244i	0.0641744	+	0.0538487i
$689$	−15.3989	−	18.3517i	−0.586653	−	0.699145i
$690$	7.01625	−	2.55371i	0.267104	−	0.0972180i
$691$		−	19.2181i		−	0.731090i	−0.930794	−	0.365545i	$-0.880883\pi$
$691$		−	19.2181i		−	0.731090i	0.930794	−	0.365545i	$-0.119117\pi$
$692$	7.05985	+	12.2280i	0.268375	+	0.464840i
$693$	11.5692	−	3.38692i	0.439476	−	0.128659i
$694$	18.1554	+	3.20129i	0.689170	+	0.121519i
$695$	−22.5247	+	39.0139i	−0.854409	+	1.47988i
$696$	−2.24054	−	3.88074i	−0.0849276	−	0.147099i
$697$	−0.392612	−	1.07869i	−0.0148712	−	0.0408583i
$698$	1.14925	+	6.51773i	0.0434998	+	0.246700i
$699$	22.4024	−	8.15380i	0.847336	−	0.308405i
$700$	−1.32865	−	12.0009i	−0.0502183	−	0.453592i
$701$	1.07438	+	6.09313i	0.0405789	+	0.230134i	0.998352	−	0.0573916i	$-0.0182783\pi$
$701$	1.07438	+	6.09313i	0.0405789	+	0.230134i	−0.957773	+	0.287526i	$0.907167\pi$
$702$	2.48881	−	1.43692i	0.0939342	−	0.0542329i
$703$	−4.99458	−	30.0358i	−0.188374	−	1.13282i
$704$	2.27813	−	3.94584i	0.0858603	−	0.148714i
$705$	11.2490	−	9.43901i	0.423661	−	0.355494i
$706$	3.00409	−	2.52073i	0.113061	−	0.0948690i
$707$	−12.8996	−	44.0628i	−0.485138	−	1.65715i
$708$	−11.5923	−	4.21927i	−0.435667	−	0.158570i
$709$	1.53641	−	8.71343i	0.0577012	−	0.327240i	−0.942270	−	0.334855i	$-0.891313\pi$
$709$	1.53641	−	8.71343i	0.0577012	−	0.327240i	0.999971	+	0.00761485i	$0.00242391\pi$
$710$	3.60278	−	2.08006i	0.135210	−	0.0780634i
$711$			16.0172i			0.600694i
$712$	−3.80492	−	10.4539i	−0.142595	−	0.391778i
$713$	0.0415950	−	0.235897i	0.00155774	−	0.00883440i
$714$	−0.262894	−	0.531514i	−0.00983856	−	0.0198914i
$715$	35.0681	+	20.2466i	1.31147	+	0.757180i
$716$	−4.38020	−	0.772347i	−0.163696	−	0.0288640i
$717$	15.9920	−	13.4189i	0.597233	−	0.501138i
$718$	−6.58723	−	1.16151i	−0.245833	−	0.0433471i
$719$	−9.23149	+	25.3633i	−0.344277	+	0.945892i	0.639862	+	0.768490i	$0.278992\pi$
$719$	−9.23149	+	25.3633i	−0.344277	+	0.945892i	−0.984138	+	0.177402i	$0.943231\pi$
$720$	3.04553	−	0.537009i	0.113500	−	0.0200131i
$721$	−24.3263	+	36.5001i	−0.905960	+	1.35934i
$722$	−0.370592	+	18.9964i	−0.0137920	+	0.706972i
$723$	10.3946	+	18.0039i	0.386579	+	0.669574i
$724$	−14.8179	−	5.39327i	−0.550702	−	0.200439i
$725$	20.1394	−	3.55111i	0.747957	−	0.131885i
$726$	−6.27331	+	7.47624i	−0.232824	+	0.277469i
$727$	5.72240	−	15.7222i	0.212232	−	0.583103i	−0.787204	−	0.616693i	$-0.788472\pi$
$727$	5.72240	−	15.7222i	0.212232	−	0.583103i	0.999436	+	0.0335902i	$0.0106941\pi$
$728$	−7.38768	−	1.79851i	−0.273806	−	0.0666574i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	5.80694	+	3.35264i	0.214925	+	0.124087i
$731$	−0.316561	+	0.377263i	−0.0117084	+	0.0139536i
$732$	−3.87374	+	4.61654i	−0.143177	+	0.170632i
$733$	0.250025	+	0.144352i	0.00923489	+	0.00533177i	0.504610	−	0.863347i	$-0.331636\pi$
$733$	0.250025	+	0.144352i	0.00923489	+	0.00533177i	−0.495375	+	0.868679i	$0.664970\pi$
$734$	1.60017	−	2.77158i	0.0590634	−	0.102301i
$735$	−4.73528	−	21.1233i	−0.174663	−	0.779146i
$736$	0.825771	−	2.26879i	0.0304383	−	0.0836286i
$737$	20.6818	−	24.6476i	0.761825	−	0.907907i
$738$	5.04400	−	0.889393i	0.185672	−	0.0327390i
$739$	−13.8262	−	5.03232i	−0.508604	−	0.185117i	0.0749556	−	0.997187i	$-0.476118\pi$
$739$	−13.8262	−	5.03232i	−0.508604	−	0.185117i	−0.583560	+	0.812070i	$0.698341\pi$
$740$	10.8011	+	18.7080i	0.397055	+	0.687719i
$741$	−7.95807	−	9.67412i	−0.292347	−	0.355388i
$742$	−9.77809	−	19.7692i	−0.358965	−	0.725748i
$743$	29.0204	−	5.11708i	1.06466	−	0.187728i	0.386234	−	0.922401i	$-0.373776\pi$
$743$	29.0204	−	5.11708i	1.06466	−	0.187728i	0.678421	+	0.734673i	$0.262664\pi$
$744$	0.0339324	−	0.0932284i	0.00124402	−	0.00341792i
$745$	32.0158	+	5.64525i	1.17297	+	0.206826i
$746$	15.3668	−	12.8943i	0.562620	−	0.472094i
$747$	15.9124	+	2.80578i	0.582204	+	0.102658i
$748$	0.884356	+	0.510583i	0.0323353	+	0.0186688i
$749$	2.04025	−	31.7015i	0.0745491	−	1.15835i
$750$	0.234334	−	1.32897i	0.00855667	−	0.0485273i
$751$	−13.8500	−	38.0527i	−0.505395	−	1.38856i	−0.885941	−	0.463799i	$-0.846486\pi$
$751$	−13.8500	−	38.0527i	−0.505395	−	1.38856i	0.380546	−	0.924762i	$-0.375736\pi$
$752$		−	4.74840i		−	0.173156i
$753$	−18.3796	+	10.6115i	−0.669790	+	0.386703i
$754$	2.23622	−	12.6823i	0.0814385	−	0.461861i
$755$	34.7183	+	12.6364i	1.26353	+	0.459887i
$756$	2.53918	−	0.743356i	0.0923490	−	0.0270356i
$757$	37.7946	−	31.7134i	1.37367	−	1.15264i	0.402179	−	0.915561i	$-0.368253\pi$
$757$	37.7946	−	31.7134i	1.37367	−	1.15264i	0.971489	−	0.237083i	$-0.0761915\pi$
$758$	21.2054	−	17.7934i	0.770213	−	0.646285i
$759$	−5.50031	+	9.52681i	−0.199648	+	0.345801i
$760$	−4.48665	−	12.7114i	−0.162748	−	0.461090i
$761$	−7.90559	+	4.56430i	−0.286577	+	0.165456i	−0.636397	−	0.771361i	$-0.719576\pi$
$761$	−7.90559	+	4.56430i	−0.286577	+	0.165456i	0.349820	+	0.936817i	$0.386243\pi$
$762$	−1.98380	−	11.2507i	−0.0718654	−	0.407569i
$763$	0.942271	+	1.28192i	0.0341125	+	0.0464086i
$764$	−9.78404	+	3.56110i	−0.353974	+	0.128836i
$765$	0.120356	+	0.682575i	0.00435150	+	0.0246786i
$766$	6.90343	+	18.9670i	0.249431	+	0.685306i
$767$	−17.7263	−	30.7028i	−0.640058	−	1.10861i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	2.81577	+	0.496496i	0.101539	+	0.0179041i	0.224187	−	0.974546i	$-0.428027\pi$
$769$	2.81577	+	0.496496i	0.101539	+	0.0179041i	−0.122648	+	0.992450i	$0.539139\pi$
$770$	26.9597	+	25.7474i	0.971561	+	0.927872i
$771$	−5.48813	−	9.50572i	−0.197650	−	0.342340i
$772$		−	4.07004i		−	0.146484i
$773$	−21.4185	+	7.79570i	−0.770370	+	0.280392i	−0.697151	−	0.716924i	$-0.745549\pi$
$773$	−21.4185	+	7.79570i	−0.770370	+	0.280392i	−0.0732191	+	0.997316i	$0.523327\pi$
$774$	−1.41244	−	1.68328i	−0.0507690	−	0.0605042i
$775$	0.346838	+	0.291032i	0.0124588	+	0.0104542i
$776$	4.70928	+	5.61230i	0.169053	+	0.201470i
$777$	10.9458	+	14.8913i	0.392678	+	0.534222i
$778$		−	1.01272i		−	0.0363077i
$779$	−7.43079	−	21.0525i	−0.266236	−	0.754286i
$780$	7.69669	+	4.44368i	0.275586	+	0.159109i
$781$	−2.09631	+	5.75957i	−0.0750119	+	0.206093i
$782$	0.508489	+	0.185075i	0.0181835	+	0.00661826i
$783$	1.53262	+	4.21085i	0.0547715	+	0.150483i
$784$	−6.21669	−	3.21757i	−0.222025	−	0.114913i
$785$	4.21455	+	3.53643i	0.150424	+	0.126220i
$786$	−15.0151			−0.535572
$787$	45.3973			1.61824			0.809120	−	0.587644i	$-0.199944\pi$
$787$	45.3973			1.61824			0.809120	+	0.587644i	$0.199944\pi$
$788$	−13.7069	−	11.5014i	−0.488288	−	0.409722i
$789$	19.7494	−	7.18821i	0.703099	−	0.255907i
$790$	−42.8973	+	24.7668i	−1.52622	+	0.881162i
$791$	−0.226182	+	3.51443i	−0.00804211	+	0.124959i
$792$	−2.92871	+	3.49030i	−0.104067	+	0.124022i
$793$	−17.0559	+	3.00742i	−0.605674	+	0.106797i
$794$	−1.35580	+	7.68911i	−0.0481154	+	0.272876i
$795$	4.47655	+	25.3878i	0.158767	+	0.900411i
$796$	4.57937	+	5.45748i	0.162311	+	0.193435i
$797$	13.0762			0.463182			0.231591	−	0.972813i	$-0.425607\pi$
$797$	13.0762			0.463182			0.231591	+	0.972813i	$0.425607\pi$
$798$	−5.01187	−	10.3866i	−0.177418	−	0.367681i
$799$	1.06423			0.0376497
$800$	2.93345	+	3.49594i	0.103713	+	0.123600i
$801$	1.93181	+	10.9558i	0.0682571	+	0.387105i
$802$	−3.00858	+	17.0625i	−0.106236	+	0.602497i
$803$	−9.72895	+	1.71548i	−0.343327	+	0.0605378i
$804$	4.53921	−	5.40961i	0.160085	−	0.190782i
$805$	16.4383	+	10.9557i	0.579374	+	0.386137i
$806$	0.246919	−	0.142559i	0.00869736	−	0.00502142i
$807$	0.982325	−	0.357537i	0.0345795	−	0.0125859i
$808$	13.2933	+	11.1544i	0.467656	+	0.392410i
$809$	19.0132			0.668470			0.334235	−	0.942490i	$-0.391522\pi$
$809$	19.0132			0.668470			0.334235	+	0.942490i	$0.391522\pi$
$810$	−3.09251			−0.108660
$811$	23.0996	+	19.3829i	0.811138	+	0.680626i	0.950879	−	0.309562i	$-0.100183\pi$
$811$	23.0996	+	19.3829i	0.811138	+	0.680626i	−0.139741	+	0.990188i	$0.544627\pi$
$812$	4.76209	−	10.8574i	0.167117	−	0.381021i
$813$	2.48868	+	6.83759i	0.0872818	+	0.239805i
$814$	−29.9075	−	10.8854i	−1.04826	−	0.381534i
$815$	−10.6049	+	29.1368i	−0.371475	+	1.02062i
$816$	0.194097	+	0.112062i	0.00679475	+	0.00392295i
$817$	−6.22794	+	7.27685i	−0.217888	+	0.254585i
$818$			14.1434i			0.494513i
$819$	6.96314	+	3.05405i	0.243312	+	0.106717i
$820$	10.1813	+	12.1336i	0.355546	+	0.423723i
$821$	19.8503	+	16.6564i	0.692780	+	0.581311i	0.919709	−	0.392600i	$-0.128424\pi$
$821$	19.8503	+	16.6564i	0.692780	+	0.581311i	−0.226930	+	0.973911i	$0.572869\pi$
$822$	−13.1565	−	15.6793i	−0.458886	−	0.546879i
$823$	28.6199	−	10.4168i	0.997626	−	0.363106i	0.208957	−	0.977925i	$-0.432993\pi$
$823$	28.6199	−	10.4168i	0.997626	−	0.363106i	0.788668	+	0.614819i	$0.210771\pi$
$824$		−	16.5789i		−	0.577555i
$825$	−10.3966	−	18.0074i	−0.361962	−	0.626936i
$826$	−9.17027	−	31.3241i	−0.319074	−	1.08990i
$827$	−6.16094	−	1.08634i	−0.214237	−	0.0377757i	0.0654995	−	0.997853i	$-0.479136\pi$
$827$	−6.16094	−	1.08634i	−0.214237	−	0.0377757i	−0.279736	+	0.960077i	$0.590247\pi$
$828$	−1.20720	+	2.09093i	−0.0419530	+	0.0726647i
$829$	−13.7203	−	23.7643i	−0.476526	−	0.825367i	0.523112	−	0.852264i	$-0.324771\pi$
$829$	−13.7203	−	23.7643i	−0.476526	−	0.825367i	−0.999638	+	0.0268968i	$0.991437\pi$
$830$	17.0902	+	46.9549i	0.593209	+	1.62983i
$831$	1.77331	+	10.0570i	0.0615155	+	0.348872i
$832$	2.70052	−	0.982909i	0.0936237	−	0.0340762i
$833$	0.721134	−	1.39331i	0.0249858	−	0.0482752i
$834$	−2.52957	−	14.3459i	−0.0875919	−	0.496759i
$835$	−18.1877	+	10.5007i	−0.629411	+	0.363390i
$836$	17.1019	+	10.0974i	0.591480	+	0.349227i
$837$	−0.0496058	+	0.0859197i	−0.00171463	+	0.00296982i
$838$	1.58167	−	1.32718i	0.0546378	−	0.0458466i
$839$	−18.2951	+	15.3514i	−0.631615	+	0.529988i	−0.901430	−	0.432924i	$-0.857482\pi$
$839$	−18.2951	+	15.3514i	−0.631615	+	0.529988i	0.269815	+	0.962912i	$0.413037\pi$
$840$	5.91707	+	5.65099i	0.204158	+	0.194978i
$841$	−8.38192	−	3.05077i	−0.289032	−	0.105199i
$842$	2.39963	−	13.6090i	0.0826968	−	0.468997i
$843$	−0.743694	+	0.429372i	−0.0256142	+	0.0147883i
$844$			13.4749i			0.463824i
$845$	−5.01464	−	13.7776i	−0.172509	−	0.473964i
$846$	−0.824552	+	4.67626i	−0.0283487	+	0.160773i
$847$	−25.7680	−	1.65838i	−0.885399	−	0.0569826i
$848$	7.21925	+	4.16803i	0.247910	+	0.143131i
$849$	−17.2958	−	3.04971i	−0.593590	−	0.104666i
$850$	−0.783524	+	0.657455i	−0.0268747	+	0.0225505i
$851$	−16.6090	−	2.92862i	−0.569351	−	0.100392i
$852$	−0.460094	+	1.26410i	−0.0157626	+	0.0433073i
$853$	−36.7051	+	6.47210i	−1.25676	+	0.221601i	−0.762084	−	0.647478i	$-0.775824\pi$
$853$	−36.7051	+	6.47210i	−1.25676	+	0.221601i	−0.494675	+	0.869078i	$0.664713\pi$
$854$	−15.9116	−	1.02404i	−0.544484	−	0.0350419i
$855$	2.21119	+	13.2974i	0.0756210	+	0.454760i
$856$	6.00342	+	10.3982i	0.205193	+	0.355404i
$857$	−26.2657	−	9.55995i	−0.897221	−	0.326562i	−0.148082	−	0.988975i	$-0.547310\pi$
$857$	−26.2657	−	9.55995i	−0.897221	−	0.326562i	−0.749138	+	0.662414i	$0.769532\pi$
$858$	−12.8950	+	2.27374i	−0.440229	+	0.0776242i
$859$	−10.0376	+	11.9624i	−0.342479	+	0.408150i	−0.909601	−	0.415484i	$-0.863612\pi$
$859$	−10.0376	+	11.9624i	−0.342479	+	0.408150i	0.567122	+	0.823634i	$0.308057\pi$
$860$	2.32415	−	6.38556i	0.0792530	−	0.217746i
$861$	9.79984	+	9.35916i	0.333978	+	0.318959i
$862$	7.99699	−	13.8512i	0.272378	−	0.471773i
$863$	28.0514	+	16.1955i	0.954881	+	0.551301i	0.894594	−	0.446880i	$-0.147465\pi$
$863$	28.0514	+	16.1955i	0.954881	+	0.551301i	0.0602872	+	0.998181i	$0.480798\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	28.0676	−	33.4496i	0.954326	−	1.13732i
$866$	−29.9962	−	17.3183i	−1.01931	−	0.588501i
$867$	8.47488	−	14.6789i	0.287822	−	0.498523i
$868$	0.251916	−	0.0737495i	0.00855058	−	0.00250322i
$869$	24.9602	−	68.5776i	0.846717	−	2.32634i
$870$	−8.90763	+	10.6157i	−0.301997	+	0.359906i
$871$	19.9860	−	3.52407i	0.677199	−	0.119408i
$872$	−0.565066	−	0.205667i	−0.0191356	−	0.00696477i
$873$	−3.66317	−	6.34479i	−0.123979	−	0.214739i
$874$	9.85384	+	3.69573i	0.333311	+	0.125010i
$875$	3.20031	−	1.58292i	0.108190	−	0.0535123i
$876$	−2.13529	+	0.376509i	−0.0721448	+	0.0127211i
$877$	3.41986	−	9.39598i	0.115480	−	0.317280i	−0.868465	−	0.495751i	$-0.834893\pi$
$877$	3.41986	−	9.39598i	0.115480	−	0.317280i	0.983945	+	0.178471i	$0.0571151\pi$
$878$	−34.0204	−	5.99871i	−1.14813	−	0.202447i
$879$	−2.74016	+	2.29927i	−0.0924234	+	0.0775524i
$880$	−13.8762	−	2.44676i	−0.467768	−	0.0824801i
$881$	−40.9366	−	23.6347i	−1.37919	−	0.796275i	−0.387126	−	0.922027i	$-0.626532\pi$
$881$	−40.9366	−	23.6347i	−1.37919	−	0.796275i	−0.992062	+	0.125752i	$0.959866\pi$
$882$	5.56352	+	4.24821i	0.187333	+	0.143045i
$883$	−8.71731	+	49.4383i	−0.293361	+	1.66373i	0.380430	+	0.924810i	$0.375776\pi$
$883$	−8.71731	+	49.4383i	−0.293361	+	1.66373i	−0.673790	+	0.738923i	$0.735335\pi$
$884$	0.220293	+	0.605251i	0.00740926	+	0.0203568i
$885$			38.1502i			1.28240i
$886$	8.45721	−	4.88277i	0.284125	−	0.164040i
$887$	−10.0101	+	56.7701i	−0.336106	+	1.90615i	0.0799202	+	0.996801i	$0.474533\pi$
$887$	−10.0101	+	56.7701i	−0.336106	+	1.90615i	−0.416026	+	0.909352i	$0.636578\pi$
$888$	−6.56404	−	2.38911i	−0.220275	−	0.0801734i
$889$	20.8757	−	21.8586i	0.700147	−	0.733114i
$890$	−26.3548	+	22.1143i	−0.883414	+	0.741273i
$891$	3.49030	−	2.92871i	0.116929	−	0.0981155i
$892$	9.54073	−	16.5250i	0.319447	−	0.553299i
$893$	20.6968	+	0.201863i	0.692593	+	0.00675509i
$894$	−9.10400	+	5.25620i	−0.304483	+	0.175793i
$895$	2.38849	+	13.5458i	0.0798385	+	0.452787i
$896$	2.62968	−	0.291139i	0.0878516	−	0.00972627i
$897$	−6.52012	+	2.37313i	−0.217700	+	0.0792365i
$898$	−0.364448	−	2.06689i	−0.0121618	−	0.0689729i
$899$	0.152054	+	0.417765i	0.00507128	+	0.0139332i
$900$	−2.28182	−	3.95222i	−0.0760605	−	0.131741i
$901$	−0.934155	+	1.61800i	−0.0311212	+	0.0539035i
$902$	−22.9818	−	4.05231i	−0.765210	−	0.134927i
$903$	1.37516	−	5.64870i	0.0457625	−	0.187977i
$904$	−0.665539	−	1.15275i	−0.0221355	−	0.0383398i
$905$			48.7654i			1.62102i
$906$	−11.2266	+	4.08614i	−0.372978	+	0.135753i
$907$	35.9834	+	42.8834i	1.19481	+	1.42392i	0.880138	+	0.474718i	$0.157450\pi$
$907$	35.9834	+	42.8834i	1.19481	+	1.42392i	0.314672	+	0.949201i	$0.398106\pi$
$908$	12.1670	+	10.2093i	0.403777	+	0.338809i
$909$	−11.1544	−	13.2933i	−0.369968	−	0.440911i
$910$	2.58746	+	23.3710i	0.0857734	+	0.774740i
$911$		−	0.476333i		−	0.0157816i	−0.999969	−	0.00789082i	$-0.997488\pi$
$911$		−	0.476333i		−	0.0157816i	0.999969	−	0.00789082i	$-0.00251175\pi$
$912$	3.75348	+	2.21616i	0.124290	+	0.0733845i
$913$	−63.7563	−	36.8097i	−2.11003	−	1.21822i
$914$	−4.26241	+	11.7109i	−0.140988	+	0.387362i
$915$	17.5130	+	6.37420i	0.578961	+	0.210725i
$916$	9.27820	+	25.4916i	0.306560	+	0.842268i
$917$	−23.5283	−	32.0093i	−0.776974	−	1.05704i
$918$	−0.171689	−	0.144064i	−0.00566657	−	0.00475482i
$919$	56.9746			1.87942			0.939710	−	0.341973i	$-0.111095\pi$
$919$	56.9746			1.87942			0.939710	+	0.341973i	$0.111095\pi$
$920$	−7.46654			−0.246165
$921$	24.7945	+	20.8051i	0.817008	+	0.685551i
$922$	−33.5363	+	12.2062i	−1.10446	+	0.401990i
$923$	−3.34802	+	1.93298i	−0.110201	+	0.0636247i
$924$	−12.0299	−	0.774218i	−0.395753	−	0.0254699i
$925$	20.4910	−	24.4202i	0.673740	−	0.802932i
$926$	−4.42975	+	0.781084i	−0.145571	+	0.0256680i
$927$	−2.87890	+	16.3271i	−0.0945556	+	0.536251i
$928$	0.778133	+	4.41301i	0.0255435	+	0.144864i
$929$	−0.290374	−	0.346054i	−0.00952686	−	0.0113537i	0.761260	−	0.648447i	$-0.224581\pi$
$929$	−0.290374	−	0.346054i	−0.00952686	−	0.0113537i	−0.770787	+	0.637093i	$0.780137\pi$
$930$	−0.306813			−0.0100608
$931$	14.2887	−	26.9598i	0.468293	−	0.883573i
$932$	−23.8401			−0.780909
$933$	21.1322	+	25.1844i	0.691839	+	0.824501i
$934$	5.19567	+	29.4661i	0.170007	+	0.964160i
$935$	0.548376	−	3.10999i	0.0179338	−	0.101708i
$936$	−2.83017	+	0.499036i	−0.0925071	+	0.0163115i
$937$	5.75973	−	6.86418i	0.188162	−	0.224243i	−0.663714	−	0.747987i	$-0.731021\pi$
$937$	5.75973	−	6.86418i	0.188162	−	0.224243i	0.851876	+	0.523744i	$0.175465\pi$
$938$	18.6451	+	1.19996i	0.608783	+	0.0391801i
$939$	−10.9189	+	6.30405i	−0.356326	+	0.205725i
$940$	−13.7989	+	5.02239i	−0.450071	+	0.163812i
$941$	28.9388	+	24.2825i	0.943377	+	0.791587i	0.978170	−	0.207807i	$-0.0666327\pi$
$941$	28.9388	+	24.2825i	0.943377	+	0.791587i	−0.0347930	+	0.999395i	$0.511077\pi$
$942$	−1.77904			−0.0579642
$943$	−12.3661			−0.402695
$944$	9.45016	+	7.92963i	0.307577	+	0.258087i
$945$	−4.84589	−	6.59263i	−0.157637	−	0.214458i
$946$	3.42423	+	9.40798i	0.111331	+	0.305880i
$947$	−30.5908	−	11.1341i	−0.994067	−	0.361811i	−0.206773	−	0.978389i	$-0.566296\pi$
$947$	−30.5908	−	11.1341i	−0.994067	−	0.361811i	−0.787294	+	0.616578i	$0.788518\pi$
$948$	5.47822	−	15.0513i	0.177924	−	0.488843i
$949$	−5.39632	−	3.11557i	−0.175172	−	0.101136i
$950$	−15.3624	+	12.6374i	−0.498424	+	0.410010i
$951$			33.2119i			1.07697i
$952$	0.0652511	+	0.589374i	0.00211480	+	0.0191017i
$953$	−24.5562	−	29.2649i	−0.795452	−	0.947983i	0.204068	−	0.978957i	$-0.434584\pi$
$953$	−24.5562	−	29.2649i	−0.795452	−	0.947983i	−0.999520	+	0.0309740i	$0.990139\pi$
$954$	−6.38580	−	5.35832i	−0.206748	−	0.173482i
$955$	20.6972	+	24.6659i	0.669745	+	0.798171i
$956$	−19.6171	+	7.14005i	−0.634463	+	0.230926i
$957$		−	20.4170i		−	0.659988i
$958$	0.297682	+	0.515600i	0.00961765	+	0.0166583i
$959$	12.8093	−	52.6162i	0.413634	−	1.69907i
$960$	−3.04553	−	0.537009i	−0.0982941	−	0.0173319i
$961$	15.4951	−	26.8383i	0.499841	−	0.865750i
$962$	−10.0373	−	17.3851i	−0.323615	−	0.560518i
$963$	−4.10658	−	11.2827i	−0.132333	−	0.363581i
$964$	−3.61000	−	20.4733i	−0.116270	−	0.659402i
$965$	−11.8276	+	4.30489i	−0.380743	+	0.138579i
$966$	−6.34909	+	0.702924i	−0.204279	+	0.0226162i
$967$	−4.78853	−	27.1571i	−0.153989	−	0.873314i	−0.959704	−	0.281012i	$-0.909330\pi$
$967$	−4.78853	−	27.1571i	−0.153989	−	0.873314i	0.805715	−	0.592303i	$-0.201781\pi$
$968$	8.45201	−	4.87977i	0.271658	−	0.156842i
$969$	−0.496694	+	0.841244i	−0.0159561	+	0.0270247i
$970$	11.3284	−	19.6213i	0.363733	−	0.630003i
$971$	−26.1842	+	21.9711i	−0.840290	+	0.705087i	−0.957629	−	0.288005i	$-0.907008\pi$
$971$	−26.1842	+	21.9711i	−0.840290	+	0.705087i	0.117339	+	0.993092i	$0.462564\pi$
$972$	0.766044	−	0.642788i	0.0245709	−	0.0206174i
$973$	26.6189	−	27.8723i	0.853363	−	0.893544i
$974$	18.1399	+	6.60238i	0.581240	+	0.211554i
$975$	2.27742	−	12.9159i	0.0729357	−	0.413639i
$976$	5.21907	−	3.01323i	0.167058	−	0.0964512i
$977$		−	20.6990i		−	0.662220i	−0.943592	−	0.331110i	$-0.892577\pi$
$977$		−	20.6990i		−	0.662220i	0.943592	−	0.331110i	$-0.107423\pi$
$978$	−3.42923	−	9.42173i	−0.109655	−	0.301274i
$979$	8.80183	−	49.9177i	0.281308	−	1.59538i
$980$	−2.77490	+	21.4690i	−0.0886409	+	0.685802i
$981$	0.520768	+	0.300665i	0.0166268	+	0.00959951i
$982$	35.5748	+	6.27280i	1.13524	+	0.200173i
$983$	20.5525	−	17.2456i	0.655522	−	0.550048i	−0.253219	−	0.967409i	$-0.581489\pi$
$983$	20.5525	−	17.2456i	0.655522	−	0.550048i	0.908741	+	0.417361i	$0.137045\pi$
$984$	−5.04400	−	0.889393i	−0.160797	−	0.0283528i
$985$	−18.9255	+	51.9974i	−0.603017	+	1.65678i
$986$	−0.989060	+	0.174398i	−0.0314981	+	0.00555396i
$987$	−11.2609	+	5.56981i	−0.358439	+	0.177289i
$988$	4.16939	+	11.8125i	0.132646	+	0.375806i
$989$	2.65265	+	4.59452i	0.0843494	+	0.146097i
$990$	13.2406	+	4.81917i	0.420812	+	0.153163i
$991$	0.498522	−	0.0879028i	0.0158361	−	0.00279232i	−0.165725	−	0.986172i	$-0.552996\pi$
$991$	0.498522	−	0.0879028i	0.0158361	−	0.00279232i	0.181561	+	0.983380i	$0.441885\pi$
$992$	−0.0637720	+	0.0760005i	−0.00202476	+	0.00241302i
$993$	6.17572	−	16.9676i	0.195980	−	0.538452i
$994$	−3.41577	+	0.999981i	−0.108342	+	0.0317175i
$995$	11.0159	−	19.0801i	0.349227	−	0.604879i
$996$	−13.9931	−	8.07893i	−0.443389	−	0.255991i
$997$	5.56477	−	6.63184i	0.176238	−	0.210032i	−0.670693	−	0.741735i	$-0.734003\pi$
$997$	5.56477	−	6.63184i	0.176238	−	0.210032i	0.846931	+	0.531703i	$0.178448\pi$
$998$	−24.9861	+	29.7773i	−0.790922	+	0.942584i
$999$	6.04945	+	3.49265i	0.191396	+	0.110503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.b.409.6	yes	84
7.5	odd	6		798.2.ca.b.523.6	yes	84
19.2	odd	18		798.2.ca.b.325.6	✓	84
133.40	even	18	inner	798.2.cj.b.439.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.325.6	✓	84	19.2	odd	18
798.2.ca.b.523.6	yes	84	7.5	odd	6
798.2.cj.b.409.6	yes	84	1.1	even	1	trivial
798.2.cj.b.439.6	yes	84	133.40	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(3.04553 - 0.537009i) q^{5} +(-0.642788 + 0.766044i) q^{6} +(-2.64029 - 0.169924i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-2.36900 - 1.98783i) q^{10} +4.55626 q^{11} +1.00000 q^{12} +(2.20148 + 1.84727i) q^{13} +(1.56698 + 2.13180i) q^{14} +(-1.05770 - 2.90601i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.0766548 - 0.210607i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.53071 - 4.08129i) q^{19} +3.09251i q^{20} +(0.291139 + 2.62968i) q^{21} +(-2.92871 - 3.49030i) q^{22} +(-1.84953 - 1.55194i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(4.28841 - 1.56085i) q^{25} -2.87383i q^{26} +(0.500000 + 0.866025i) q^{27} +(0.625824 - 2.57067i) q^{28} +(4.41301 + 0.778133i) q^{29} +(-1.54626 + 2.67819i) q^{30} +(0.0496058 + 0.0859197i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-0.791187 - 4.48704i) q^{33} +(-0.210607 + 0.0766548i) q^{34} +(-8.13233 + 0.900351i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(6.04945 - 3.49265i) q^{37} +(-4.11037 + 1.45081i) q^{38} +(1.43692 - 2.48881i) q^{39} +(2.36900 - 1.98783i) q^{40} +(3.92354 - 3.29224i) q^{41} +(1.82731 - 1.91335i) q^{42} +(-2.06485 - 0.751543i) q^{43} +(-0.791187 + 4.48704i) q^{44} +(-2.67819 + 1.54626i) q^{45} +2.41439i q^{46} +(1.62405 + 4.46204i) q^{47} +(-0.173648 + 0.984808i) q^{48} +(6.94225 + 0.897297i) q^{49} +(-3.95222 - 2.28182i) q^{50} +(-0.220719 - 0.0389187i) q^{51} +(-2.20148 + 1.84727i) q^{52} +(-8.20943 - 1.44754i) q^{53} +(0.342020 - 0.939693i) q^{54} +(13.8762 - 2.44676i) q^{55} +(-2.37152 + 1.17299i) q^{56} +(-4.28509 - 0.798745i) q^{57} +(-2.24054 - 3.88074i) q^{58} +(-11.5923 - 4.21927i) q^{59} +(3.04553 - 0.537009i) q^{60} +(-3.87374 + 4.61654i) q^{61} +(0.0339324 - 0.0932284i) q^{62} +(2.53918 - 0.743356i) q^{63} +(0.500000 - 0.866025i) q^{64} +(7.69669 + 4.44368i) q^{65} +(-2.92871 + 3.49030i) q^{66} +(4.53921 - 5.40961i) q^{67} +(0.194097 + 0.112062i) q^{68} +(-1.20720 + 2.09093i) q^{69} +(5.91707 + 5.65099i) q^{70} +(-0.460094 + 1.26410i) q^{71} +(-0.642788 + 0.766044i) q^{72} +(-2.13529 + 0.376509i) q^{73} +(-6.56404 - 2.38911i) q^{74} +(-2.28182 - 3.95222i) q^{75} +(3.75348 + 2.21616i) q^{76} +(-12.0299 - 0.774218i) q^{77} +(-2.83017 + 0.499036i) q^{78} +(5.47822 - 15.0513i) q^{79} +(-3.04553 - 0.537009i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-5.04400 - 0.889393i) q^{82} +(-13.9931 - 8.07893i) q^{83} +(-2.64029 - 0.169924i) q^{84} +(0.120356 - 0.682575i) q^{85} +(0.751543 + 2.06485i) q^{86} -4.48109i q^{87} +(3.94584 - 2.27813i) q^{88} +(1.93181 - 10.9558i) q^{89} +(2.90601 + 1.05770i) q^{90} +(-5.49866 - 5.25140i) q^{91} +(1.84953 - 1.55194i) q^{92} +(0.0760005 - 0.0637720i) q^{93} +(2.37420 - 4.11224i) q^{94} +(2.47013 - 13.2517i) q^{95} +(0.866025 - 0.500000i) q^{96} +(1.27220 + 7.21503i) q^{97} +(-3.77502 - 5.89484i) q^{98} +(-4.28149 + 1.55833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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