LMFDB - Embedded newform 160.2.ba.a.107.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(3,160)] 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("160.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.ba (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	160.107
Dual form			160.2.ba.a.3.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.178125 + 1.40295i) q^{2} +(2.54622 + 1.05468i) q^{3} +(-1.93654 - 0.499802i) q^{4} +(2.21873 + 0.277906i) q^{5} +(-1.93321 + 3.38436i) q^{6} -3.70855 q^{7} +(1.04614 - 2.62785i) q^{8} +(3.24959 + 3.24959i) q^{9} +(-0.785101 + 3.06327i) q^{10} +(1.62306 - 3.91841i) q^{11} +(-4.40374 - 3.31504i) q^{12} +(-2.41888 - 1.00193i) q^{13} +(0.660586 - 5.20291i) q^{14} +(5.35629 + 3.04767i) q^{15} +(3.50040 + 1.93578i) q^{16} +(-2.57998 + 2.57998i) q^{17} +(-5.13785 + 3.98018i) q^{18} +(-0.820706 - 1.98136i) q^{19} +(-4.15777 - 1.64710i) q^{20} +(-9.44280 - 3.91133i) q^{21} +(5.20824 + 2.97504i) q^{22} -5.30550 q^{23} +(5.43526 - 5.58774i) q^{24} +(4.84554 + 1.23320i) q^{25} +(1.83653 - 3.21510i) q^{26} +(1.68286 + 4.06279i) q^{27} +(7.18176 + 1.85354i) q^{28} +(2.00240 + 4.83422i) q^{29} +(-5.22981 + 6.97174i) q^{30} -1.44002i q^{31} +(-3.33931 + 4.56607i) q^{32} +(8.26535 - 8.26535i) q^{33} +(-3.16003 - 4.07914i) q^{34} +(-8.22827 - 1.03063i) q^{35} +(-4.66882 - 7.91712i) q^{36} +(8.58562 - 3.55628i) q^{37} +(2.92594 - 0.798480i) q^{38} +(-5.10230 - 5.10230i) q^{39} +(3.05141 - 5.53976i) q^{40} +(1.63341 - 1.63341i) q^{41} +(7.16941 - 12.5511i) q^{42} +(2.43161 + 5.87042i) q^{43} +(-5.10156 + 6.77697i) q^{44} +(6.30688 + 8.11304i) q^{45} +(0.945044 - 7.44336i) q^{46} +(-2.96683 - 2.96683i) q^{47} +(6.87117 + 8.62072i) q^{48} +6.75333 q^{49} +(-2.59323 + 6.57839i) q^{50} +(-9.29026 + 3.84815i) q^{51} +(4.18350 + 3.14925i) q^{52} +(2.41336 - 0.999648i) q^{53} +(-5.99965 + 1.63729i) q^{54} +(4.69009 - 8.24285i) q^{55} +(-3.87968 + 9.74550i) q^{56} -5.91057i q^{57} +(-7.13886 + 1.94817i) q^{58} +(2.10156 - 5.07362i) q^{59} +(-8.84945 - 8.57902i) q^{60} +(-6.83341 + 2.83049i) q^{61} +(2.02027 + 0.256503i) q^{62} +(-12.0513 - 12.0513i) q^{63} +(-5.81116 - 5.49822i) q^{64} +(-5.08841 - 2.89524i) q^{65} +(10.1236 + 13.0682i) q^{66} +(-3.49753 + 8.44379i) q^{67} +(6.28572 - 3.70676i) q^{68} +(-13.5090 - 5.59561i) q^{69} +(2.91159 - 11.3603i) q^{70} +(-2.44190 + 2.44190i) q^{71} +(11.9390 - 5.13988i) q^{72} +7.04282i q^{73} +(3.45997 + 12.6787i) q^{74} +(11.0372 + 8.25050i) q^{75} +(0.599045 + 4.24718i) q^{76} +(-6.01920 + 14.5316i) q^{77} +(8.06712 - 6.24942i) q^{78} +0.203871i q^{79} +(7.22847 + 5.26775i) q^{80} -1.66719i q^{81} +(2.00064 + 2.58255i) q^{82} +(-2.40680 + 5.81053i) q^{83} +(16.3315 + 12.2940i) q^{84} +(-6.44127 + 5.00729i) q^{85} +(-8.66905 + 2.36576i) q^{86} +14.4209i q^{87} +(-8.59904 - 8.36438i) q^{88} +(-1.94360 + 1.94360i) q^{89} +(-12.5056 + 7.40311i) q^{90} +(8.97054 + 3.71572i) q^{91} +(10.2743 + 2.65170i) q^{92} +(1.51876 - 3.66661i) q^{93} +(4.69079 - 3.63385i) q^{94} +(-1.27029 - 4.62419i) q^{95} +(-13.3184 + 8.10434i) q^{96} +(3.62241 + 3.62241i) q^{97} +(-1.20294 + 9.47459i) q^{98} +(18.0075 - 7.45896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 20 q^{22}+ \cdots + 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 16 * q^19 - 32 * q^20 - 8 * q^21 - 20 * q^22 - 8 * q^23 + 32 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 20 * q^28 + 64 * q^30 + 16 * q^32 - 8 * q^33 - 8 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 4 * q^38 + 16 * q^40 - 8 * q^41 - 68 * q^42 + 28 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 88 * q^48 + 40 * q^49 + 4 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^53 + 56 * q^54 + 28 * q^55 + 40 * q^56 - 36 * q^58 + 12 * q^60 - 40 * q^61 - 32 * q^62 - 56 * q^63 - 48 * q^64 - 8 * q^65 + 72 * q^66 - 28 * q^67 + 8 * q^68 - 24 * q^69 + 4 * q^70 + 24 * q^71 + 88 * q^72 - 16 * q^75 + 56 * q^76 - 32 * q^77 + 112 * q^78 + 80 * q^80 + 68 * q^82 + 36 * q^83 - 56 * q^84 - 4 * q^85 + 24 * q^86 - 24 * q^88 - 84 * q^90 - 8 * q^91 + 92 * q^92 + 8 * q^93 + 32 * q^94 + 24 * q^96 - 8 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−0.178125	+	1.40295i	−0.125954	+	0.992036i
$2$	−0.178125	+	1.40295i	−0.125954	+	0.992036i
$3$	2.54622	+	1.05468i	1.47006	+	0.608920i	0.966874	−	0.255256i	$-0.0821596\pi$
$3$	2.54622	+	1.05468i	1.47006	+	0.608920i	0.503190	+	0.864176i	$0.332160\pi$
$4$	−1.93654	−	0.499802i	−0.968271	−	0.249901i
$5$	2.21873	+	0.277906i	0.992247	+	0.124284i
$5$	2.21873	+	0.277906i	0.992247	+	0.124284i
$6$	−1.93321	+	3.38436i	−0.789231	+	1.38166i
$7$	−3.70855			−1.40170			−0.700850	−	0.713309i	$-0.747196\pi$
$7$	−3.70855			−1.40170			−0.700850	+	0.713309i	$0.747196\pi$
$8$	1.04614	−	2.62785i	0.369868	−	0.929084i
$9$	3.24959	+	3.24959i	1.08320	+	1.08320i
$10$	−0.785101	+	3.06327i	−0.248271	+	0.968691i
$11$	1.62306	−	3.91841i	0.489371	−	1.18145i	−0.465666	−	0.884961i	$-0.654185\pi$
$11$	1.62306	−	3.91841i	0.489371	−	1.18145i	0.955037	−	0.296486i	$-0.0958148\pi$
$12$	−4.40374	−	3.31504i	−1.27125	−	0.956970i
$13$	−2.41888	−	1.00193i	−0.670877	−	0.277886i	0.0211303	−	0.999777i	$-0.493274\pi$
$13$	−2.41888	−	1.00193i	−0.670877	−	0.277886i	−0.692008	+	0.721890i	$0.743274\pi$
$14$	0.660586	−	5.20291i	0.176549	−	1.39054i
$15$	5.35629	+	3.04767i	1.38299	+	0.786904i
$16$	3.50040	+	1.93578i	0.875099	+	0.483944i
$17$	−2.57998	+	2.57998i	−0.625737	+	0.625737i	−0.946993	−	0.321256i	$-0.895895\pi$
$17$	−2.57998	+	2.57998i	−0.625737	+	0.625737i	0.321256	+	0.946993i	$0.395895\pi$
$18$	−5.13785	+	3.98018i	−1.21100	+	0.938137i
$19$	−0.820706	−	1.98136i	−0.188283	−	0.454555i	0.801346	−	0.598201i	$-0.204117\pi$
$19$	−0.820706	−	1.98136i	−0.188283	−	0.454555i	−0.989629	+	0.143646i	$0.954117\pi$
$20$	−4.15777	−	1.64710i	−0.929706	−	0.368304i
$21$	−9.44280	−	3.91133i	−2.06059	−	0.853523i
$22$	5.20824	+	2.97504i	1.11040	+	0.634281i
$23$	−5.30550			−1.10627			−0.553137	−	0.833091i	$-0.686569\pi$
$23$	−5.30550			−1.10627			−0.553137	+	0.833091i	$0.686569\pi$
$24$	5.43526	−	5.58774i	1.10947	−	1.14059i
$25$	4.84554	+	1.23320i	0.969107	+	0.246640i
$26$	1.83653	−	3.21510i	0.360173	−	0.630534i
$27$	1.68286	+	4.06279i	0.323867	+	0.781883i
$28$	7.18176	+	1.85354i	1.35723	+	0.350286i
$29$	2.00240	+	4.83422i	0.371837	+	0.897693i	0.993439	+	0.114360i	$0.0364818\pi$
$29$	2.00240	+	4.83422i	0.371837	+	0.897693i	−0.621603	+	0.783333i	$0.713518\pi$
$30$	−5.22981	+	6.97174i	−0.954829	+	1.27286i
$31$		−	1.44002i		−	0.258635i	−0.991603	−	0.129317i	$-0.958721\pi$
$31$		−	1.44002i		−	0.258635i	0.991603	−	0.129317i	$-0.0412786\pi$
$32$	−3.33931	+	4.56607i	−0.590312	+	0.807175i
$33$	8.26535	−	8.26535i	1.43881	−	1.43881i
$34$	−3.16003	−	4.07914i	−0.541940	−	0.699568i
$35$	−8.22827	−	1.03063i	−1.39083	−	0.174208i
$36$	−4.66882	−	7.91712i	−0.778136	−	1.31952i
$37$	8.58562	−	3.55628i	1.41147	−	0.584649i	0.458766	−	0.888557i	$-0.348292\pi$
$37$	8.58562	−	3.55628i	1.41147	−	0.584649i	0.952701	+	0.303908i	$0.0982915\pi$
$38$	2.92594	−	0.798480i	0.474650	−	0.129531i
$39$	−5.10230	−	5.10230i	−0.817021	−	0.817021i
$40$	3.05141	−	5.53976i	0.482470	−	0.875912i
$41$	1.63341	−	1.63341i	0.255096	−	0.255096i	−0.567960	−	0.823056i	$-0.692267\pi$
$41$	1.63341	−	1.63341i	0.255096	−	0.255096i	0.823056	+	0.567960i	$0.192267\pi$
$42$	7.16941	−	12.5511i	1.10626	−	1.93667i
$43$	2.43161	+	5.87042i	0.370817	+	0.895231i	0.993612	+	0.112847i	$0.0359969\pi$
$43$	2.43161	+	5.87042i	0.370817	+	0.895231i	−0.622796	+	0.782385i	$0.714003\pi$
$44$	−5.10156	+	6.77697i	−0.769089	+	1.02167i
$45$	6.30688	+	8.11304i	0.940174	+	1.20942i
$46$	0.945044	−	7.44336i	0.139339	−	1.09746i
$47$	−2.96683	−	2.96683i	−0.432757	−	0.432757i	0.456808	−	0.889565i	$-0.348993\pi$
$47$	−2.96683	−	2.96683i	−0.432757	−	0.432757i	−0.889565	+	0.456808i	$0.848993\pi$
$48$	6.87117	+	8.62072i	0.991768	+	1.24429i
$49$	6.75333			0.964762
$50$	−2.59323	+	6.57839i	−0.366738	+	0.930324i
$51$	−9.29026	+	3.84815i	−1.30090	+	0.538849i
$52$	4.18350	+	3.14925i	0.580147	+	0.436722i
$53$	2.41336	−	0.999648i	0.331501	−	0.137312i	−0.210724	−	0.977546i	$-0.567582\pi$
$53$	2.41336	−	0.999648i	0.331501	−	0.137312i	0.542225	+	0.840233i	$0.317582\pi$
$54$	−5.99965	+	1.63729i	−0.816449	+	0.222806i
$55$	4.69009	−	8.24285i	0.632411	−	1.11147i
$56$	−3.87968	+	9.74550i	−0.518444	+	1.30230i
$57$		−	5.91057i		−	0.782874i
$58$	−7.13886	+	1.94817i	−0.937378	+	0.255808i
$59$	2.10156	−	5.07362i	0.273600	−	0.660529i	−0.726032	−	0.687661i	$-0.758637\pi$
$59$	2.10156	−	5.07362i	0.273600	−	0.660529i	0.999632	+	0.0271319i	$0.00863741\pi$
$60$	−8.84945	−	8.57902i	−1.14246	−	1.10755i
$61$	−6.83341	+	2.83049i	−0.874928	+	0.362407i	−0.774528	−	0.632540i	$-0.782012\pi$
$61$	−6.83341	+	2.83049i	−0.874928	+	0.362407i	−0.100401	+	0.994947i	$0.532012\pi$
$62$	2.02027	+	0.256503i	0.256575	+	0.0325760i
$63$	−12.0513	−	12.0513i	−1.51832	−	1.51832i
$64$	−5.81116	−	5.49822i	−0.726395	−	0.687277i
$65$	−5.08841	−	2.89524i	−0.631139	−	0.359111i
$66$	10.1236	+	13.0682i	1.24613	+	1.60858i
$67$	−3.49753	+	8.44379i	−0.427291	+	1.03157i	0.552852	+	0.833280i	$0.313540\pi$
$67$	−3.49753	+	8.44379i	−0.427291	+	1.03157i	−0.980143	+	0.198293i	$0.936460\pi$
$68$	6.28572	−	3.70676i	0.762256	−	0.449511i
$69$	−13.5090	−	5.59561i	−1.62629	−	0.673632i
$70$	2.91159	−	11.3603i	0.348001	−	1.35781i
$71$	−2.44190	+	2.44190i	−0.289800	+	0.289800i	−0.837001	−	0.547201i	$-0.815693\pi$
$71$	−2.44190	+	2.44190i	−0.289800	+	0.289800i	0.547201	+	0.837001i	$0.315693\pi$
$72$	11.9390	−	5.13988i	1.40702	−	0.605741i
$73$			7.04282i			0.824300i	0.911116	+	0.412150i	$0.135222\pi$
$73$			7.04282i			0.824300i	−0.911116	+	0.412150i	$0.864778\pi$
$74$	3.45997	+	12.6787i	0.402214	+	1.47387i
$75$	11.0372	+	8.25050i	1.27447	+	0.952685i
$76$	0.599045	+	4.24718i	0.0687152	+	0.487185i
$77$	−6.01920	+	14.5316i	−0.685951	+	1.65603i
$78$	8.06712	−	6.24942i	0.913422	−	0.707608i
$79$			0.203871i			0.0229372i	0.999934	+	0.0114686i	$0.00365066\pi$
$79$			0.203871i			0.0229372i	−0.999934	+	0.0114686i	$0.996349\pi$
$80$	7.22847	+	5.26775i	0.808168	+	0.588952i
$81$		−	1.66719i		−	0.185243i
$82$	2.00064	+	2.58255i	0.220934	+	0.285195i
$83$	−2.40680	+	5.81053i	−0.264181	+	0.637789i	−0.999189	−	0.0402696i	$-0.987178\pi$
$83$	−2.40680	+	5.81053i	−0.264181	+	0.637789i	0.735008	+	0.678058i	$0.237178\pi$
$84$	16.3315	+	12.2940i	1.78191	+	1.34138i
$85$	−6.44127	+	5.00729i	−0.698654	+	0.543117i
$86$	−8.66905	+	2.36576i	−0.934807	+	0.255106i
$87$			14.4209i			1.54608i
$88$	−8.59904	−	8.36438i	−0.916661	−	0.891646i
$89$	−1.94360	+	1.94360i	−0.206021	+	0.206021i	−0.802574	−	0.596553i	$-0.796537\pi$
$89$	−1.94360	+	1.94360i	−0.206021	+	0.206021i	0.596553	+	0.802574i	$0.296537\pi$
$90$	−12.5056	+	7.40311i	−1.31821	+	0.780356i
$91$	8.97054	+	3.71572i	0.940368	+	0.389513i
$92$	10.2743	+	2.65170i	1.07117	+	0.276459i
$93$	1.51876	−	3.66661i	0.157488	−	0.380209i
$94$	4.69079	−	3.63385i	0.483818	−	0.374803i
$95$	−1.27029	−	4.62419i	−0.130329	−	0.474431i
$96$	−13.3184	+	8.10434i	−1.35930	+	0.827146i
$97$	3.62241	+	3.62241i	0.367800	+	0.367800i	0.866674	−	0.498874i	$-0.166253\pi$
$97$	3.62241	+	3.62241i	0.367800	+	0.367800i	−0.498874	+	0.866674i	$0.666253\pi$
$98$	−1.20294	+	9.47459i	−0.121515	+	0.957079i
$99$	18.0075	−	7.45896i	1.80982	−	0.749653i
$100$	−8.76723	−	4.80995i	−0.876723	−	0.480995i
$101$	0.775088	−	1.87123i	0.0771241	−	0.186194i	−0.880615	−	0.473833i	$-0.842870\pi$
$101$	0.775088	−	1.87123i	0.0771241	−	0.186194i	0.957739	+	0.287639i	$0.0928702\pi$
$102$	−3.74394	−	13.7192i	−0.370705	−	1.35841i
$103$			3.85297i			0.379645i	0.981818	+	0.189822i	$0.0607912\pi$
$103$			3.85297i			0.379645i	−0.981818	+	0.189822i	$0.939209\pi$
$104$	−5.16343	+	5.30829i	−0.506316	+	0.520520i
$105$	−19.8640	−	11.3024i	−1.93853	−	1.10300i
$106$	0.972577	+	3.56390i	0.0944650	+	0.346156i
$107$	−17.3854	+	7.20128i	−1.68071	+	0.696174i	−0.999360	−	0.0357808i	$-0.988608\pi$
$107$	−17.3854	+	7.20128i	−1.68071	+	0.696174i	−0.681353	+	0.731955i	$0.738608\pi$
$108$	−1.22834	−	8.70885i	−0.118197	−	0.838010i
$109$	0.773533	−	0.320408i	0.0740910	−	0.0306895i	−0.345330	−	0.938481i	$-0.612233\pi$
$109$	0.773533	−	0.320408i	0.0740910	−	0.0306895i	0.419421	+	0.907792i	$0.362233\pi$
$110$	10.7289	+	8.04822i	1.02296	+	0.767368i
$111$	25.6117			2.43095
$112$	−12.9814	−	7.17892i	−1.22663	−	0.678344i
$113$	−10.6418	−	10.6418i	−1.00110	−	1.00110i	−0.999999	−	0.00110032i	$-0.999650\pi$
$113$	−10.6418	−	10.6418i	−1.00110	−	1.00110i	−0.00110032	−	0.999999i	$-0.500350\pi$
$114$	8.29224	+	1.05282i	0.776640	+	0.0986058i
$115$	−11.7715	−	1.47443i	−1.09770	−	0.137492i
$116$	−1.46158	−	10.3625i	−0.135704	−	0.962133i
$117$	−4.60450	−	11.1162i	−0.425686	−	1.02770i
$118$	6.74370	+	3.85213i	0.620808	+	0.354617i
$119$	9.56798	−	9.56798i	0.877095	−	0.877095i
$120$	13.6122	−	10.8872i	1.24262	−	0.993861i
$121$	−4.94147	−	4.94147i	−0.449225	−	0.449225i
$122$	−2.75384	−	10.0911i	−0.249321	−	0.913607i
$123$	5.88176	−	2.43631i	0.530341	−	0.219674i
$124$	−0.719724	+	2.78865i	−0.0646331	+	0.250429i
$125$	10.4082	+	4.08274i	0.930940	+	0.365172i
$126$	19.0540	−	14.7607i	1.69746	−	1.31499i
$127$	12.9680	−	12.9680i	1.15073	−	1.15073i	0.164320	−	0.986407i	$-0.447457\pi$
$127$	12.9680	−	12.9680i	1.15073	−	1.15073i	0.986407	−	0.164320i	$-0.0525431\pi$
$128$	8.74884	−	7.17340i	0.773296	−	0.634045i
$129$			17.5120i			1.54184i
$130$	4.96826	−	6.62307i	0.435745	−	0.580881i
$131$	−8.35611	−	20.1734i	−0.730076	−	1.76256i	−0.642344	−	0.766416i	$-0.722038\pi$
$131$	−8.35611	−	20.1734i	−0.730076	−	1.76256i	−0.0877325	−	0.996144i	$-0.527962\pi$
$132$	−20.1372	+	11.8752i	−1.75272	+	1.03360i
$133$	3.04363	+	7.34797i	0.263916	+	0.637150i
$134$	−11.2232	−	6.41091i	−0.969538	−	0.553819i
$135$	2.60474	+	9.48191i	0.224180	+	0.816073i
$136$	4.08076	+	9.47883i	0.349922	+	0.812803i
$137$	−1.88186			−0.160778			−0.0803892	−	0.996764i	$-0.525616\pi$
$137$	−1.88186			−0.160778			−0.0803892	+	0.996764i	$0.525616\pi$
$138$	10.2567	−	17.9557i	0.873105	−	1.52849i
$139$	−0.549075	−	0.227434i	−0.0465719	−	0.0192907i	0.359276	−	0.933231i	$-0.383024\pi$
$139$	−0.549075	−	0.227434i	−0.0465719	−	0.0192907i	−0.405848	+	0.913941i	$0.633024\pi$
$140$	15.4193	+	6.10837i	1.30317	+	0.516251i
$141$	−4.42516	−	10.6833i	−0.372666	−	0.899695i
$142$	−2.99090	−	3.86083i	−0.250991	−	0.323994i
$143$	−7.85198	+	7.85198i	−0.656616	+	0.656616i
$144$	5.08437	+	17.6653i	0.423698	+	1.47211i
$145$	3.09933	+	11.2823i	0.257385	+	0.936946i
$146$	−9.88074	−	1.25450i	−0.817736	−	0.103824i
$147$	17.1955	+	7.12261i	1.41826	+	0.587463i
$148$	−18.4039	+	2.59578i	−1.51279	+	0.213372i
$149$	−3.54082	+	8.54830i	−0.290076	+	0.700304i	−0.999992	−	0.00398147i	$-0.998733\pi$
$149$	−3.54082	+	8.54830i	−0.290076	+	0.700304i	0.709917	+	0.704286i	$0.248733\pi$
$150$	−13.5410	+	14.0150i	−1.10562	+	1.14432i
$151$	7.95693	+	7.95693i	0.647526	+	0.647526i	0.952394	−	0.304869i	$-0.0986126\pi$
$151$	7.95693	+	7.95693i	0.647526	+	0.647526i	−0.304869	+	0.952394i	$0.598613\pi$
$152$	−6.06529	+	0.0839008i	−0.491960	+	0.00680525i
$153$	−16.7677			−1.35559
$154$	−19.3150	−	11.0331i	−1.55645	−	0.889072i
$155$	0.400190	−	3.19501i	0.0321440	−	0.256629i
$156$	7.33068	+	12.4310i	0.586924	+	0.995273i
$157$	−11.4649	−	4.74892i	−0.914999	−	0.379005i	−0.125031	−	0.992153i	$-0.539903\pi$
$157$	−11.4649	−	4.74892i	−0.914999	−	0.379005i	−0.789968	+	0.613148i	$0.789903\pi$
$158$	−0.286021	−	0.0363145i	−0.0227546	−	0.00288903i
$159$	7.19928			0.570940
$160$	−8.67797	+	9.20287i	−0.686054	+	0.727551i
$161$	19.6757			1.55066
$162$	2.33899	+	0.296969i	0.183768	+	0.0233321i
$163$	11.2235	+	4.64892i	0.879091	+	0.364131i	0.776144	−	0.630555i	$-0.217173\pi$
$163$	11.2235	+	4.64892i	0.879091	+	0.364131i	0.102947	+	0.994687i	$0.467173\pi$
$164$	−3.97955	+	2.34679i	−0.310751	+	0.183253i
$165$	20.6356	−	16.0416i	1.60648	−	1.24884i
$166$	−7.72318	−	4.41163i	−0.599435	−	0.342409i
$167$	17.1661			1.32835			0.664175	−	0.747578i	$-0.268783\pi$
$167$	17.1661			1.32835			0.664175	+	0.747578i	$0.268783\pi$
$168$	−20.1569	+	20.7224i	−1.55514	+	1.59877i
$169$	−4.34527	−	4.34527i	−0.334251	−	0.334251i
$170$	−5.87763	−	9.92872i	−0.450793	−	0.761498i
$171$	3.77165	−	9.10556i	0.288425	−	0.696320i
$172$	−1.77487	−	12.5836i	−0.135332	−	0.959494i
$173$	5.63214	+	2.33291i	0.428204	+	0.177368i	0.586368	−	0.810045i	$-0.300557\pi$
$173$	5.63214	+	2.33291i	0.428204	+	0.177368i	−0.158164	+	0.987413i	$0.550557\pi$
$174$	−20.2318	−	2.56873i	−1.53377	−	0.194735i
$175$	−17.9699	−	4.57338i	−1.35840	−	0.345715i
$176$	13.2665	−	10.5741i	1.00000	−	0.797054i
$177$	10.7021	−	10.7021i	0.804419	−	0.804419i
$178$	−2.38057	−	3.07298i	−0.178432	−	0.230330i
$179$	3.97779	+	9.60324i	0.297314	+	0.717780i	0.999980	+	0.00626044i	$0.00199277\pi$
$179$	3.97779	+	9.60324i	0.297314	+	0.717780i	−0.702666	+	0.711520i	$0.748007\pi$
$180$	−8.15863	−	18.8634i	−0.608108	−	1.40600i
$181$	22.2181	+	9.20303i	1.65146	+	0.684056i	0.997378	−	0.0723710i	$-0.0230566\pi$
$181$	22.2181	+	9.20303i	1.65146	+	0.684056i	0.654079	+	0.756427i	$0.273057\pi$
$182$	−6.81085	+	11.9234i	−0.504854	+	0.883819i
$183$	−20.3847			−1.50688
$184$	−5.55032	+	13.9420i	−0.409175	+	1.02782i
$185$	20.0375	−	5.50443i	1.47319	−	0.404694i
$186$	4.87354	+	2.78386i	0.357345	+	0.204122i
$187$	5.92197	+	14.2969i	0.433057	+	1.04549i
$188$	4.26257	+	7.22823i	0.310880	+	0.527173i
$189$	−6.24097	−	15.0670i	−0.453964	−	1.09597i
$190$	6.71378	−	0.958476i	0.487069	−	0.0695351i
$191$			8.62257i			0.623907i	0.950097	+	0.311954i	$0.100983\pi$
$191$			8.62257i			0.623907i	−0.950097	+	0.311954i	$0.899017\pi$
$192$	−8.99766	−	20.1286i	−0.649350	−	1.45266i
$193$	13.1126	−	13.1126i	0.943862	−	0.943862i	−0.0546439	−	0.998506i	$-0.517402\pi$
$193$	13.1126	−	13.1126i	0.943862	−	0.943862i	0.998506	+	0.0546439i	$0.0174024\pi$
$194$	−5.72731	+	4.43683i	−0.411197	+	0.318546i
$195$	−9.90266	−	12.7386i	−0.709145	−	0.912229i
$196$	−13.0781	−	3.37533i	−0.934151	−	0.241095i
$197$	−10.3876	+	4.30267i	−0.740083	+	0.306552i	−0.720688	−	0.693260i	$-0.756174\pi$
$197$	−10.3876	+	4.30267i	−0.740083	+	0.306552i	−0.0193947	+	0.999812i	$0.506174\pi$
$198$	7.25696	+	26.5923i	0.515729	+	1.88983i
$199$	1.56365	+	1.56365i	0.110844	+	0.110844i	0.760353	−	0.649510i	$-0.225026\pi$
$199$	1.56365	+	1.56365i	0.110844	+	0.110844i	−0.649510	+	0.760353i	$0.725026\pi$
$200$	8.30979	−	11.4432i	0.587591	−	0.809158i
$201$	−17.8110	+	17.8110i	−1.25629	+	1.25629i
$202$	2.48718	+	1.42072i	0.174997	+	0.0999617i
$203$	−7.42600	−	17.9280i	−0.521203	−	1.25830i
$204$	19.9143	−	2.80882i	1.39428	−	0.196657i
$205$	4.07804	−	3.17017i	0.284822	−	0.221414i
$206$	−5.40553	−	0.686312i	−0.376621	−	0.0478176i
$207$	−17.2407	−	17.2407i	−1.19831	−	1.19831i
$208$	−6.52753	−	8.18958i	−0.452603	−	0.567845i
$209$	−9.09585			−0.629173
$210$	19.3950	−	25.8550i	1.33838	−	1.78417i
$211$	−4.96614	+	2.05704i	−0.341883	+	0.141613i	−0.547017	−	0.837121i	$-0.684237\pi$
$211$	−4.96614	+	2.05704i	−0.341883	+	0.141613i	0.205134	+	0.978734i	$0.434237\pi$
$212$	−5.17321	+	0.729657i	−0.355298	+	0.0501131i
$213$	−8.79305	+	3.64220i	−0.602490	+	0.249559i
$214$	−7.00626	−	25.6736i	−0.478938	−	1.75501i
$215$	3.76366	+	13.7007i	0.256679	+	0.934377i
$216$	12.4369	−	0.172039i	0.846223	−	0.0117058i
$217$			5.34037i			0.362528i
$218$	0.311731	+	1.14230i	0.0211131	+	0.0773664i
$219$	−7.42793	+	17.9326i	−0.501933	+	1.21177i
$220$	−13.2023	+	13.6185i	−0.890102	+	0.918160i
$221$	8.82564	−	3.65570i	0.593677	−	0.245909i
$222$	−4.56208	+	35.9319i	−0.306187	+	2.41159i
$223$	17.0444	+	17.0444i	1.14138	+	1.14138i	0.988198	+	0.153181i	$0.0489516\pi$
$223$	17.0444	+	17.0444i	1.14138	+	1.14138i	0.153181	+	0.988198i	$0.451048\pi$
$224$	12.3840	−	16.9335i	0.827440	−	1.13142i
$225$	11.7386	+	19.7534i	0.782574	+	1.31689i
$226$	16.8256	−	13.0344i	1.11922	−	0.867035i
$227$	9.95905	−	24.0433i	0.661005	−	1.59581i	−0.135225	−	0.990815i	$-0.543176\pi$
$227$	9.95905	−	24.0433i	0.661005	−	1.59581i	0.796231	−	0.604993i	$-0.206824\pi$
$228$	−2.95412	+	11.4461i	−0.195641	+	0.758035i
$229$	−15.6688	−	6.49021i	−1.03542	−	0.428885i	−0.200755	−	0.979642i	$-0.564339\pi$
$229$	−15.6688	−	6.49021i	−1.03542	−	0.428885i	−0.834666	+	0.550756i	$0.814339\pi$
$230$	4.16535	−	16.2522i	0.274655	−	1.07164i
$231$	−30.6525	+	30.6525i	−2.01678	+	2.01678i
$232$	14.7984	−	0.204706i	0.971563	−	0.0134396i
$233$			22.4264i			1.46920i	0.678500	+	0.734600i	$0.262630\pi$
$233$			22.4264i			1.46920i	−0.678500	+	0.734600i	$0.737370\pi$
$234$	16.4157	−	4.47980i	1.07313	−	0.292854i
$235$	−5.75810	−	7.40711i	−0.375617	−	0.483186i
$236$	−6.60557	+	8.77492i	−0.429986	+	0.571199i
$237$	−0.215019	+	0.519101i	−0.0139670	+	0.0337192i
$238$	11.7191	+	15.1277i	0.759637	+	0.980584i
$239$		−	5.46064i		−	0.353219i	−0.984281	−	0.176610i	$-0.943487\pi$
$239$		−	5.46064i		−	0.353219i	0.984281	−	0.176610i	$-0.0565130\pi$
$240$	12.8495	+	21.0366i	0.829433	+	1.35791i
$241$		−	25.7625i		−	1.65951i	−0.558127	−	0.829755i	$-0.688480\pi$
$241$		−	25.7625i		−	1.65951i	0.558127	−	0.829755i	$-0.311520\pi$
$242$	7.81284	−	6.05244i	0.502229	−	0.389066i
$243$	6.80694	−	16.4334i	0.436665	−	1.05420i
$244$	14.6479	−	2.06601i	0.937734	−	0.132263i
$245$	14.9838	+	1.87679i	0.957282	+	0.119904i
$246$	2.37033	+	8.68579i	0.151127	+	0.553786i
$247$			5.61497i			0.357272i
$248$	−3.78415	−	1.50647i	−0.240293	−	0.0956607i
$249$	−12.2565	+	12.2565i	−0.776725	+	0.776725i
$250$	−7.58186	+	13.8750i	−0.479519	+	0.877532i
$251$	7.97245	+	3.30230i	0.503217	+	0.208439i	0.619827	−	0.784739i	$-0.287203\pi$
$251$	7.97245	+	3.30230i	0.503217	+	0.208439i	−0.116610	+	0.993178i	$0.537203\pi$
$252$	17.3145	+	29.3610i	1.09071	+	1.84957i
$253$	−8.61115	+	20.7891i	−0.541378	+	1.30700i
$254$	15.8836	+	20.5035i	0.996625	+	1.28650i
$255$	−21.6820	+	5.95619i	−1.35778	+	0.372991i
$256$	8.50554	+	13.5520i	0.531596	+	0.846998i
$257$	−15.1455	−	15.1455i	−0.944747	−	0.944747i	0.0538042	−	0.998552i	$-0.482865\pi$
$257$	−15.1455	−	15.1455i	−0.944747	−	0.944747i	−0.998552	+	0.0538042i	$0.982865\pi$
$258$	−24.5685	−	3.11933i	−1.52957	−	0.194201i
$259$	−31.8402	+	13.1886i	−1.97845	+	0.819502i
$260$	8.40687	+	8.14996i	0.521372	+	0.505439i
$261$	−9.20226	+	22.2162i	−0.569606	+	1.37515i
$262$	29.7908	−	8.12981i	1.84048	−	0.502261i
$263$		−	6.87330i		−	0.423826i	−0.977289	−	0.211913i	$-0.932031\pi$
$263$		−	6.87330i		−	0.423826i	0.977289	−	0.211913i	$-0.0679693\pi$
$264$	−13.0733	−	30.3668i	−0.804608	−	1.86895i
$265$	5.63242	−	1.54726i	0.345997	−	0.0950475i
$266$	−10.8510	+	2.96120i	−0.665317	+	0.181563i
$267$	−6.99873	+	2.89897i	−0.428315	+	0.177414i
$268$	10.9933	−	14.6037i	0.671525	−	0.892062i
$269$	20.3252	−	8.41897i	1.23925	−	0.513314i	0.335769	−	0.941944i	$-0.391004\pi$
$269$	20.3252	−	8.41897i	1.23925	−	0.513314i	0.903480	+	0.428631i	$0.141004\pi$
$270$	−13.7666	+	1.96536i	−0.837810	+	0.119608i
$271$	12.4734			0.757703			0.378851	−	0.925457i	$-0.376319\pi$
$271$	12.4734			0.757703			0.378851	+	0.925457i	$0.376319\pi$
$272$	−14.0252	+	4.03669i	−0.850403	+	0.244760i
$273$	18.9221	+	18.9221i	1.14522	+	1.14522i
$274$	0.335207	−	2.64016i	0.0202506	−	0.159498i
$275$	12.6968	−	16.9853i	0.765645	−	1.02425i
$276$	23.3641	+	17.5880i	1.40635	+	1.05867i
$277$	−8.98606	−	21.6943i	−0.539920	−	1.30348i	−0.924778	−	0.380507i	$-0.875750\pi$
$277$	−8.98606	−	21.6943i	−0.539920	−	1.30348i	0.384858	−	0.922976i	$-0.374250\pi$
$278$	0.416883	−	0.729813i	0.0250030	−	0.0437713i
$279$	4.67946	−	4.67946i	0.280152	−	0.280152i
$280$	−11.3163	+	20.5445i	−0.676278	+	1.22777i
$281$	5.32879	+	5.32879i	0.317889	+	0.317889i	0.847956	−	0.530067i	$-0.177833\pi$
$281$	5.32879	+	5.32879i	0.317889	+	0.317889i	−0.530067	+	0.847956i	$0.677833\pi$
$282$	15.7764	−	4.30532i	0.939469	−	0.256378i
$283$	10.2587	−	4.24930i	0.609818	−	0.252595i	−0.0563329	−	0.998412i	$-0.517941\pi$
$283$	10.2587	−	4.24930i	0.609818	−	0.252595i	0.666151	+	0.745817i	$0.267941\pi$
$284$	5.94931	−	3.50838i	0.353026	−	0.208184i
$285$	1.64259	−	13.1140i	0.0972984	−	0.776804i
$286$	−9.61731	−	12.4146i	−0.568684	−	0.734090i
$287$	−6.05759	+	6.05759i	−0.357568	+	0.357568i
$288$	−25.6892	+	3.98648i	−1.51375	+	0.234906i
$289$			3.68741i			0.216906i
$290$	−16.3806	+	2.33854i	−0.961903	+	0.137324i
$291$	5.40299	+	13.0440i	0.316729	+	0.764651i
$292$	3.52002	−	13.6387i	0.205993	−	0.798146i
$293$	−4.25127	−	10.2635i	−0.248362	−	0.599598i	0.749704	−	0.661774i	$-0.230196\pi$
$293$	−4.25127	−	10.2635i	−0.248362	−	0.599598i	−0.998065	+	0.0621758i	$0.980196\pi$
$294$	−13.0556	+	22.8557i	−0.761420	+	1.33297i
$295$	6.07280	−	10.6730i	0.353572	−	0.621404i
$296$	−0.363559	−	26.2821i	−0.0211314	−	1.52762i
$297$	18.6511			1.08224
$298$	−11.3621	−	6.49027i	−0.658191	−	0.375971i
$299$	12.8334	+	5.31576i	0.742174	+	0.307418i
$300$	−17.2504	−	21.4938i	−0.995951	−	1.24095i
$301$	−9.01774	−	21.7708i	−0.519774	−	1.25485i
$302$	−12.5805	+	9.74585i	−0.723927	+	0.560811i
$303$	3.94710	−	3.94710i	0.226755	−	0.226755i
$304$	0.962673	−	8.52425i	0.0552131	−	0.488899i
$305$	−15.9481	+	4.38105i	−0.913186	+	0.250858i
$306$	2.98676	−	23.5243i	0.170742	−	1.34480i
$307$	−0.897767	−	0.371867i	−0.0512383	−	0.0212236i	0.356917	−	0.934136i	$-0.383828\pi$
$307$	−0.897767	−	0.371867i	−0.0512383	−	0.0212236i	−0.408155	+	0.912912i	$0.633828\pi$
$308$	18.9194	−	25.1327i	1.07803	−	1.43207i
$309$	−4.06366	+	9.81054i	−0.231173	+	0.558102i
$310$	4.41116	+	1.13056i	0.250537	+	0.0642114i
$311$	−6.73409	−	6.73409i	−0.381855	−	0.381855i	0.489915	−	0.871770i	$-0.337028\pi$
$311$	−6.73409	−	6.73409i	−0.381855	−	0.381855i	−0.871770	+	0.489915i	$0.837028\pi$
$312$	−18.7458	+	8.07032i	−1.06127	+	0.456892i
$313$	−7.44365			−0.420740			−0.210370	−	0.977622i	$-0.567467\pi$
$313$	−7.44365			−0.420740			−0.210370	+	0.977622i	$0.567467\pi$
$314$	8.70469	−	15.2388i	0.491234	−	0.859975i
$315$	−23.3894	−	30.0876i	−1.31784	−	1.69525i
$316$	0.101895	−	0.394804i	0.00573204	−	0.0222095i
$317$	−5.47419	−	2.26749i	−0.307461	−	0.127355i	0.223618	−	0.974677i	$-0.428213\pi$
$317$	−5.47419	−	2.26749i	−0.307461	−	0.127355i	−0.531079	+	0.847322i	$0.678213\pi$
$318$	−1.28237	+	10.1002i	−0.0719119	+	0.566393i
$319$	22.1925			1.24254
$320$	−11.3654	−	13.8140i	−0.635346	−	0.772228i
$321$	−51.8623			−2.89467
$322$	−3.50474	+	27.6040i	−0.195312	+	1.53831i
$323$	7.22927	+	2.99446i	0.402248	+	0.166616i
$324$	−0.833265	+	3.22858i	−0.0462925	+	0.179366i
$325$	−10.4852	−	7.83787i	−0.581614	−	0.434767i
$326$	−8.52139	+	14.9179i	−0.471956	+	0.826226i
$327$	2.30752			0.127606
$328$	−2.58357	−	6.00114i	−0.142654	−	0.331358i
$329$	11.0026	+	11.0026i	0.606596	+	0.606596i
$330$	18.8299	+	31.8081i	1.03655	+	1.75098i
$331$	−6.91960	+	16.7054i	−0.380336	+	0.918212i	0.611565	+	0.791195i	$0.290540\pi$
$331$	−6.91960	+	16.7054i	−0.380336	+	0.918212i	−0.991900	+	0.127018i	$0.959460\pi$
$332$	7.56499	−	10.0494i	0.415183	−	0.551533i
$333$	39.4562	+	16.3433i	2.16219	+	0.895607i
$334$	−3.05771	+	24.0831i	−0.167310	+	1.31777i
$335$	−10.1067	+	17.7625i	−0.552186	+	0.970469i
$336$	−25.4821	−	31.9704i	−1.39016	−	1.74413i
$337$	−5.47917	+	5.47917i	−0.298470	+	0.298470i	−0.840414	−	0.541945i	$-0.817688\pi$
$337$	−5.47917	+	5.47917i	−0.298470	+	0.298470i	0.541945	+	0.840414i	$0.317688\pi$
$338$	6.87020	−	5.32220i	0.373690	−	0.289489i
$339$	−15.8728	−	38.3202i	−0.862090	−	2.08127i
$340$	14.9765	−	6.47747i	0.812212	−	0.351290i
$341$	−5.64258	−	2.33724i	−0.305563	−	0.126568i
$342$	12.1028	+	6.91337i	0.654446	+	0.373832i
$343$	0.914780			0.0493935
$344$	17.9704	−	0.248583i	0.968899	−	0.0134027i
$345$	−28.4178	−	16.1694i	−1.52996	−	0.870531i
$346$	−4.27619	+	7.48607i	−0.229889	+	0.402454i
$347$	−6.97500	−	16.8391i	−0.374438	−	0.903973i	−0.992987	−	0.118226i	$-0.962279\pi$
$347$	−6.97500	−	16.8391i	−0.374438	−	0.903973i	0.618549	−	0.785746i	$-0.287721\pi$
$348$	7.20760	−	27.9267i	0.386368	−	1.49703i
$349$	1.95879	+	4.72895i	0.104852	+	0.253135i	0.967595	−	0.252508i	$-0.0812554\pi$
$349$	1.95879	+	4.72895i	0.104852	+	0.253135i	−0.862743	+	0.505643i	$0.831255\pi$
$350$	9.61712	−	24.3963i	0.514057	−	1.30404i
$351$		−	11.5135i		−	0.614546i
$352$	12.4719	+	20.4958i	0.664753	+	1.09243i
$353$	0.763353	−	0.763353i	0.0406292	−	0.0406292i	−0.686500	−	0.727130i	$-0.740854\pi$
$353$	0.763353	−	0.763353i	0.0406292	−	0.0406292i	0.727130	+	0.686500i	$0.240854\pi$
$354$	13.1082	+	16.9208i	0.696694	+	0.899333i
$355$	−6.09654	+	4.73930i	−0.323571	+	0.251536i
$356$	4.73529	−	2.79245i	0.250970	−	0.148000i
$357$	34.4534	−	14.2711i	1.82347	−	0.755305i
$358$	−14.1814	+	3.87007i	−0.749512	+	0.204540i
$359$	−13.3030	−	13.3030i	−0.702107	−	0.702107i	0.262756	−	0.964862i	$-0.415369\pi$
$359$	−13.3030	−	13.3030i	−0.702107	−	0.702107i	−0.964862	+	0.262756i	$0.915369\pi$
$360$	27.9177	−	8.08610i	1.47139	−	0.426175i
$361$	10.1828	−	10.1828i	0.535937	−	0.535937i
$362$	−16.8690	+	29.5316i	−0.886615	+	1.55215i
$363$	−7.37042	−	17.7938i	−0.386847	−	0.933931i
$364$	−15.5147	−	11.6791i	−0.813192	−	0.612154i
$365$	−1.95725	+	15.6261i	−0.102447	+	0.817909i
$366$	3.63102	−	28.5987i	0.189797	−	1.49488i
$367$	8.06357	+	8.06357i	0.420915	+	0.420915i	0.885519	−	0.464604i	$-0.153803\pi$
$367$	8.06357	+	8.06357i	0.420915	+	0.420915i	−0.464604	+	0.885519i	$0.653803\pi$
$368$	−18.5714	−	10.2703i	−0.968099	−	0.535374i
$369$	10.6158			0.552638
$370$	4.15326	+	29.0921i	0.215918	+	1.51243i
$371$	−8.95008	+	3.70724i	−0.464665	+	0.192471i
$372$	−4.77372	+	6.34146i	−0.247506	+	0.328790i
$373$	16.0127	−	6.63267i	0.829105	−	0.343427i	0.0725569	−	0.997364i	$-0.476884\pi$
$373$	16.0127	−	6.63267i	0.829105	−	0.343427i	0.756549	+	0.653938i	$0.226884\pi$
$374$	−21.1127	+	5.76159i	−1.09171	+	0.297925i
$375$	22.1957	+	21.3729i	1.14618	+	1.10369i
$376$	−10.9001	+	4.69265i	−0.562131	+	0.242005i
$377$		−	13.6997i		−	0.705570i
$378$	22.2500	−	6.07196i	1.14442	−	0.312308i
$379$	−9.60968	+	23.1998i	−0.493616	+	1.19170i	0.459251	+	0.888307i	$0.348118\pi$
$379$	−9.60968	+	23.1998i	−0.493616	+	1.19170i	−0.952867	+	0.303388i	$0.901882\pi$
$380$	0.148801	+	9.58983i	0.00763335	+	0.491948i
$381$	46.6967	−	19.3424i	2.39234	−	0.990941i
$382$	−12.0970	−	1.53590i	−0.618938	−	0.0785833i
$383$	−6.46368	−	6.46368i	−0.330278	−	0.330278i	0.522414	−	0.852692i	$-0.325032\pi$
$383$	−6.46368	−	6.46368i	−0.330278	−	0.330278i	−0.852692	+	0.522414i	$0.825032\pi$
$384$	29.8422	−	9.03786i	1.52288	−	0.461211i
$385$	−17.3934	+	30.5690i	−0.886451	+	1.55794i
$386$	16.0606	+	20.7319i	0.817462	+	1.05523i
$387$	−11.1747	+	26.9782i	−0.568043	+	1.37138i
$388$	−5.20447	−	8.82545i	−0.264217	−	0.448044i
$389$	24.1362	+	9.99755i	1.22375	+	0.506896i	0.898602	−	0.438766i	$-0.144584\pi$
$389$	24.1362	+	9.99755i	1.22375	+	0.506896i	0.325153	+	0.945661i	$0.394584\pi$
$390$	19.6355	−	11.6239i	0.994284	−	0.588598i
$391$	13.6881	−	13.6881i	0.692236	−	0.692236i
$392$	7.06496	−	17.7467i	0.356835	−	0.896345i
$393$		−	60.1791i		−	3.03563i
$394$	−4.18614	−	15.3396i	−0.210895	−	0.772800i
$395$	−0.0566570	+	0.452334i	−0.00285072	+	0.0227594i
$396$	−38.6003	+	5.44440i	−1.93974	+	0.273591i
$397$	−10.7897	+	26.0485i	−0.541517	+	1.30734i	0.382135	+	0.924106i	$0.375189\pi$
$397$	−10.7897	+	26.0485i	−0.541517	+	1.30734i	−0.923652	+	0.383232i	$0.874811\pi$
$398$	−2.47224	+	1.91519i	−0.123922	+	0.0960000i
$399$			21.9196i			1.09735i
$400$	14.5741	+	13.6966i	0.728705	+	0.684828i
$401$			34.5054i			1.72312i	0.507659	+	0.861558i	$0.330511\pi$
$401$			34.5054i			1.72312i	−0.507659	+	0.861558i	$0.669489\pi$
$402$	−21.8154	−	28.1605i	−1.08805	−	1.40452i
$403$	−1.44280	+	3.48323i	−0.0718711	+	0.173512i
$404$	−2.43623	+	3.23632i	−0.121207	+	0.161013i
$405$	0.463323	−	3.69905i	0.0230227	−	0.183807i
$406$	26.4748	−	7.22490i	1.31392	−	0.358566i
$407$		−	39.4141i		−	1.95368i
$408$	0.393397	+	28.4391i	0.0194760	+	1.40795i
$409$	13.2323	−	13.2323i	0.654297	−	0.654297i	−0.299728	−	0.954025i	$-0.596896\pi$
$409$	13.2323	−	13.2323i	0.654297	−	0.654297i	0.954025	+	0.299728i	$0.0968959\pi$
$410$	3.72119	+	6.28597i	0.183776	+	0.310442i
$411$	−4.79164	−	1.98476i	−0.236354	−	0.0979012i
$412$	1.92572	−	7.46145i	0.0948736	−	0.367599i
$413$	−7.79375	+	18.8158i	−0.383505	+	0.925864i
$414$	27.2588	−	21.1168i	1.33970	−	1.03784i
$415$	−6.95483	+	12.2231i	−0.341399	+	0.600010i
$416$	12.6523	−	7.69903i	0.620330	−	0.377476i
$417$	−1.15820	−	1.15820i	−0.0567172	−	0.0567172i
$418$	1.62020	−	12.7610i	0.0792466	−	0.624162i
$419$	−23.2713	+	9.63930i	−1.13688	+	0.470911i	−0.870114	−	0.492851i	$-0.835955\pi$
$419$	−23.2713	+	9.63930i	−1.13688	+	0.470911i	−0.266765	+	0.963761i	$0.585955\pi$
$420$	32.8186	+	31.8157i	1.60138	+	1.55245i
$421$	−9.47180	+	22.8669i	−0.461627	+	1.11447i	0.506102	+	0.862474i	$0.331086\pi$
$421$	−9.47180	+	22.8669i	−0.461627	+	1.11447i	−0.967729	+	0.251993i	$0.918914\pi$
$422$	−2.00133	−	7.33366i	−0.0974234	−	0.356997i
$423$		−	19.2820i		−	0.937522i
$424$	−0.102194	−	7.38773i	−0.00496298	−	0.358780i
$425$	−15.6830	+	9.31976i	−0.760738	+	0.452075i
$426$	−3.54356	−	12.9850i	−0.171686	−	0.629124i
$427$	25.3420	−	10.4970i	1.22639	−	0.507986i
$428$	37.2668	−	5.25632i	1.80136	−	0.254074i
$429$	−28.2743	+	11.7116i	−1.36509	+	0.565440i
$430$	−19.8917	+	2.83980i	−0.959265	+	0.136947i
$431$	6.73695			0.324508			0.162254	−	0.986749i	$-0.448124\pi$
$431$	6.73695			0.324508			0.162254	+	0.986749i	$0.448124\pi$
$432$	−1.97396	+	17.4790i	−0.0949723	+	0.840959i
$433$	−24.2565	−	24.2565i	−1.16569	−	1.16569i	−0.983208	−	0.182486i	$-0.941586\pi$
$433$	−24.2565	−	24.2565i	−1.16569	−	1.16569i	−0.182486	−	0.983208i	$-0.558414\pi$
$434$	−7.49228	−	0.951255i	−0.359641	−	0.0456617i
$435$	−4.00767	+	31.9961i	−0.192153	+	1.53410i
$436$	−1.65812	+	0.233870i	−0.0794096	+	0.0112004i
$437$	4.35426	+	10.5121i	0.208292	+	0.502862i
$438$	−23.8355	−	13.6153i	−1.13890	−	0.650563i
$439$	11.7908	−	11.7908i	0.562745	−	0.562745i	−0.367341	−	0.930086i	$-0.619732\pi$
$439$	11.7908	−	11.7908i	0.562745	−	0.562745i	0.930086	+	0.367341i	$0.119732\pi$
$440$	−16.7544	−	20.9480i	−0.798736	−	0.998659i
$441$	21.9455	+	21.9455i	1.04503	+	1.04503i
$442$	3.55670	+	13.0331i	0.169175	+	0.619922i
$443$	−17.3149	+	7.17207i	−0.822656	+	0.340755i	−0.753991	−	0.656885i	$-0.771874\pi$
$443$	−17.3149	+	7.17207i	−0.822656	+	0.340755i	−0.0686646	+	0.997640i	$0.521874\pi$
$444$	−49.5981	−	12.8008i	−2.35382	−	0.607497i
$445$	−4.85247	+	3.77219i	−0.230029	+	0.178819i
$446$	−26.9485	+	20.8764i	−1.27605	+	0.988528i
$447$	−18.0315	+	18.0315i	−0.852859	+	0.852859i
$448$	21.5510	+	20.3904i	1.01819	+	0.963356i
$449$		−	34.5622i		−	1.63109i	−0.578693	−	0.815546i	$-0.696437\pi$
$449$		−	34.5622i		−	1.63109i	0.578693	−	0.815546i	$-0.303563\pi$
$450$	−29.8040	+	12.9501i	−1.40497	+	0.610474i
$451$	−3.74926	−	9.05151i	−0.176546	−	0.426219i
$452$	15.2896	+	25.9272i	0.719160	+	1.21951i
$453$	11.8681	+	28.6522i	0.557612	+	1.34620i
$454$	31.9576	+	18.2548i	1.49984	+	0.856739i
$455$	18.8706	+	10.7372i	0.884667	+	0.503366i
$456$	−15.5321	−	6.18331i	−0.727356	−	0.289560i
$457$	39.6621			1.85532			0.927658	−	0.373430i	$-0.121818\pi$
$457$	39.6621			1.85532			0.927658	+	0.373430i	$0.121818\pi$
$458$	11.8965	−	20.8264i	0.555885	−	0.973155i
$459$	−14.8236	−	6.14016i	−0.691909	−	0.286598i
$460$	22.0590	+	8.73871i	1.02851	+	0.407444i
$461$	−5.87134	−	14.1747i	−0.273456	−	0.660180i	0.726171	−	0.687514i	$-0.241298\pi$
$461$	−5.87134	−	14.1747i	−0.273456	−	0.660180i	−0.999626	+	0.0273342i	$0.991298\pi$
$462$	−37.5439	−	48.4639i	−1.74670	−	2.25474i
$463$	−19.2066	+	19.2066i	−0.892605	+	0.892605i	−0.994768	−	0.102163i	$-0.967424\pi$
$463$	−19.2066	+	19.2066i	−0.892605	+	0.892605i	0.102163	+	0.994768i	$0.467424\pi$
$464$	−2.34878	+	20.7979i	−0.109039	+	0.965518i
$465$	4.38869	−	7.71314i	0.203521	−	0.357688i
$466$	−31.4631	−	3.99470i	−1.45750	−	0.185051i
$467$	13.7733	+	5.70508i	0.637352	+	0.264000i	0.677873	−	0.735179i	$-0.262902\pi$
$467$	13.7733	+	5.70508i	0.637352	+	0.264000i	−0.0405215	+	0.999179i	$0.512902\pi$
$468$	3.36089	+	23.8284i	0.155357	+	1.10147i
$469$	12.9708	−	31.3142i	0.598934	−	1.44595i
$470$	11.4175	−	6.75894i	0.526649	−	0.311767i
$471$	−24.1836	−	24.1836i	−1.11432	−	1.11432i
$472$	−11.1342	−	10.8303i	−0.512492	−	0.498506i
$473$	26.9494			1.23913
$474$	−0.689973	−	0.394125i	−0.0316915	−	0.0181028i
$475$	−1.53335	−	10.6128i	−0.0703549	−	0.486951i
$476$	−23.3109	+	13.7467i	−1.06845	+	0.630079i
$477$	11.0909	+	4.59400i	0.507817	+	0.210345i
$478$	7.66100	+	0.972677i	0.350406	+	0.0444892i
$479$	−9.35639			−0.427504			−0.213752	−	0.976888i	$-0.568568\pi$
$479$	−9.35639			−0.427504			−0.213752	+	0.976888i	$0.568568\pi$
$480$	−31.8021	+	14.2801i	−1.45156	+	0.651794i
$481$	−24.3308			−1.10939
$482$	36.1436	+	4.58896i	1.64629	+	0.209021i
$483$	50.0988	+	20.7516i	2.27957	+	0.944230i
$484$	7.09962	+	12.0391i	0.322710	+	0.547233i
$485$	7.03047	+	9.04385i	0.319237	+	0.410660i
$486$	21.8428	+	12.4770i	0.990808	+	0.565968i
$487$	−5.49190			−0.248862			−0.124431	−	0.992228i	$-0.539711\pi$
$487$	−5.49190			−0.248862			−0.124431	+	0.992228i	$0.539711\pi$
$488$	0.289361	+	20.9183i	0.0130988	+	0.946925i
$489$	23.6744	+	23.6744i	1.07059	+	1.07059i
$490$	−5.30205	+	20.6873i	−0.239522	+	0.934556i
$491$	−3.70433	+	8.94304i	−0.167174	+	0.403594i	−0.985159	−	0.171646i	$-0.945091\pi$
$491$	−3.70433	+	8.94304i	−0.167174	+	0.403594i	0.817985	+	0.575240i	$0.195091\pi$
$492$	−12.6080	+	1.77829i	−0.568410	+	0.0801717i
$493$	−17.6384	−	7.30605i	−0.794392	−	0.329048i
$494$	−7.87753	−	1.00017i	−0.354427	−	0.0449997i
$495$	42.0267	−	11.5450i	1.88896	−	0.518910i
$496$	2.78755	−	5.04063i	0.125165	−	0.226331i
$497$	9.05590	−	9.05590i	0.406213	−	0.406213i
$498$	−15.0121	−	19.3785i	−0.672708	−	0.868370i
$499$	3.58828	+	8.66289i	0.160634	+	0.387804i	0.983619	−	0.180258i	$-0.0576933\pi$
$499$	3.58828	+	8.66289i	0.160634	+	0.387804i	−0.822986	+	0.568062i	$0.807693\pi$
$500$	−18.1154	−	13.1085i	−0.810146	−	0.586228i
$501$	43.7086	+	18.1047i	1.95276	+	0.808859i
$502$	−6.05305	+	10.5967i	−0.270161	+	0.472955i
$503$	−0.633548			−0.0282485			−0.0141243	−	0.999900i	$-0.504496\pi$
$503$	−0.633548			−0.0282485			−0.0141243	+	0.999900i	$0.504496\pi$
$504$	−44.2762	+	19.0615i	−1.97222	+	0.849067i
$505$	2.23974	−	3.93635i	0.0996670	−	0.175165i
$506$	−27.6323	−	15.7841i	−1.22841	−	0.701688i
$507$	−6.48116	−	15.6469i	−0.287838	−	0.694903i
$508$	−31.5946	+	18.6317i	−1.40178	+	0.826648i
$509$	−7.69272	−	18.5719i	−0.340974	−	0.823183i	−0.997618	−	0.0689828i	$-0.978025\pi$
$509$	−7.69272	−	18.5719i	−0.340974	−	0.823183i	0.656644	−	0.754201i	$-0.271975\pi$
$510$	−4.49413	−	31.4798i	−0.199003	−	1.39395i
$511$		−	26.1187i		−	1.15542i
$512$	−20.5278	+	9.51891i	−0.907209	+	0.420680i
$513$	6.66871	−	6.66871i	0.294431	−	0.294431i
$514$	23.9461	−	18.5505i	1.05622	−	0.818229i
$515$	−1.07077	+	8.54872i	−0.0471836	+	0.376701i
$516$	8.75253	−	33.9127i	0.385309	−	1.49292i
$517$	−16.4406	+	6.80993i	−0.723058	+	0.299501i
$518$	−12.8315	−	47.0195i	−0.563783	−	2.06592i
$519$	11.8802	+	11.8802i	0.521484	+	0.521484i
$520$	−12.9315	+	10.3427i	−0.567083	+	0.453558i
$521$	−1.28598	+	1.28598i	−0.0563400	+	0.0563400i	−0.734715	−	0.678375i	$-0.762684\pi$
$521$	−1.28598	+	1.28598i	−0.0563400	+	0.0563400i	0.678375	+	0.734715i	$0.262684\pi$
$522$	−29.5291	−	16.8676i	−1.29245	−	0.738274i
$523$	1.71691	+	4.14499i	0.0750754	+	0.181248i	0.956962	−	0.290214i	$-0.0937265\pi$
$523$	1.71691	+	4.14499i	0.0750754	+	0.181248i	−0.881886	+	0.471462i	$0.843726\pi$
$524$	6.09924	+	43.2431i	0.266447	+	1.88908i
$525$	−40.9320	−	30.5974i	−1.78642	−	1.33538i
$526$	9.64290	+	1.22431i	0.420450	+	0.0533823i
$527$	3.71522	+	3.71522i	0.161837	+	0.161837i
$528$	44.9319	−	12.9321i	1.95541	−	0.562799i
$529$	5.14833			0.223841
$530$	1.16746	+	8.17761i	0.0507111	+	0.355213i
$531$	23.3164	−	9.65797i	1.01185	−	0.419120i
$532$	−2.22159	−	15.7509i	−0.0963180	−	0.682887i
$533$	−5.58760	+	2.31446i	−0.242026	+	0.100250i
$534$	−2.82046	−	10.3353i	−0.122053	−	0.447250i
$535$	−40.5749	+	11.1462i	−1.75420	+	0.481891i
$536$	18.5301	+	18.0244i	0.800376	+	0.778535i
$537$			28.6473i			1.23622i
$538$	8.19097	+	30.0149i	0.353138	+	1.29403i
$539$	10.9611	−	26.4624i	0.472127	−	1.13981i
$540$	−0.305117	−	19.6640i	−0.0131302	−	0.846203i
$541$	−19.1096	+	7.91546i	−0.821587	+	0.340312i	−0.753567	−	0.657372i	$-0.771668\pi$
$541$	−19.1096	+	7.91546i	−0.821587	+	0.340312i	−0.0680201	+	0.997684i	$0.521668\pi$
$542$	−2.22182	+	17.4995i	−0.0954354	+	0.751669i
$543$	46.8659	+	46.8659i	2.01121	+	2.01121i
$544$	−3.16503	−	20.3957i	−0.135700	−	0.874459i
$545$	1.80531	−	0.495929i	0.0773308	−	0.0212433i
$546$	−29.9173	+	23.1763i	−1.28034	+	0.991854i
$547$	−7.69432	+	18.5757i	−0.328985	+	0.794241i	0.669683	+	0.742647i	$0.266430\pi$
$547$	−7.69432	+	18.5757i	−0.328985	+	0.794241i	−0.998668	+	0.0515935i	$0.983570\pi$
$548$	3.64431	+	0.940558i	0.155677	+	0.0401787i
$549$	−31.4037	−	13.0078i	−1.34028	−	0.555161i
$550$	21.5679	+	20.8385i	0.919657	+	0.888555i
$551$	7.93496	−	7.93496i	0.338041	−	0.338041i
$552$	−28.8368	+	29.6458i	−1.22737	+	1.26181i
$553$		−	0.756064i		−	0.0321511i
$554$	32.0366	−	8.74270i	1.36111	−	0.371442i
$555$	56.8254	+	7.11765i	2.41210	+	0.302127i
$556$	0.949635	+	0.714865i	0.0402735	+	0.0303170i
$557$	8.02477	−	19.3735i	0.340021	−	0.820882i	−0.657692	−	0.753287i	$-0.728467\pi$
$557$	8.02477	−	19.3735i	0.340021	−	0.820882i	0.997713	−	0.0675954i	$-0.0215327\pi$
$558$	5.73153	+	7.39859i	0.242635	+	0.313207i
$559$		−	16.6362i		−	0.703635i
$560$	−26.8071	−	19.5357i	−1.13281	−	0.825534i
$561$			42.6489i			1.80064i
$562$	−8.42522	+	6.52683i	−0.355396	+	0.275318i
$563$	−15.8057	+	38.1583i	−0.666129	+	1.60818i	0.121901	+	0.992542i	$0.461101\pi$
$563$	−15.8057	+	38.1583i	−0.666129	+	1.60818i	−0.788030	+	0.615636i	$0.788899\pi$
$564$	3.22999	+	22.9003i	0.136007	+	0.964279i
$565$	−20.6539	−	26.5688i	−0.868918	−	1.11776i
$566$	4.13422	+	15.1494i	0.173774	+	0.636776i
$567$			6.18286i			0.259656i
$568$	3.86236	+	8.97152i	0.162061	+	0.376436i
$569$	−15.6674	+	15.6674i	−0.656811	+	0.656811i	−0.954624	−	0.297813i	$-0.903743\pi$
$569$	−15.6674	+	15.6674i	−0.656811	+	0.656811i	0.297813	+	0.954624i	$0.403743\pi$
$570$	18.1057	+	4.64040i	0.758363	+	0.194365i
$571$	23.0913	+	9.56473i	0.966340	+	0.400271i	0.809349	−	0.587329i	$-0.199820\pi$
$571$	23.0913	+	9.56473i	0.966340	+	0.400271i	0.156992	+	0.987600i	$0.449820\pi$
$572$	19.1301	−	11.2813i	0.799871	−	0.471693i
$573$	−9.09406	+	21.9550i	−0.379910	+	0.917183i
$574$	−7.41949	−	9.57751i	−0.309683	−	0.399757i
$575$	−25.7080	−	6.54274i	−1.07210	−	0.272851i
$576$	−1.01694	−	36.7508i	−0.0423724	−	1.53128i
$577$	27.8886	+	27.8886i	1.16102	+	1.16102i	0.984254	+	0.176762i	$0.0565624\pi$
$577$	27.8886	+	27.8886i	1.16102	+	1.16102i	0.176762	+	0.984254i	$0.443438\pi$
$578$	−5.17325	−	0.656821i	−0.215179	−	0.0273201i
$579$	47.2171	−	19.5579i	1.96227	−	0.812800i
$580$	−0.363053	−	23.3978i	−0.0150750	−	0.971539i
$581$	8.92574	−	21.5486i	0.370302	−	0.893988i
$582$	−19.2625	+	5.25667i	−0.798455	+	0.217896i
$583$		−	11.0791i		−	0.458848i
$584$	18.5075	+	7.36781i	0.765844	+	0.304882i
$585$	−7.12687	−	25.9436i	−0.294660	−	1.07263i
$586$	15.1564	−	4.13613i	0.626105	−	0.170862i
$587$	33.2273	−	13.7632i	1.37144	−	0.568067i	0.429258	−	0.903182i	$-0.358775\pi$
$587$	33.2273	−	13.7632i	1.37144	−	0.568067i	0.942177	+	0.335114i	$0.108775\pi$
$588$	−29.7399	−	22.3876i	−1.22645	−	0.923248i
$589$	−2.85319	+	1.18183i	−0.117564	+	0.0486965i
$590$	13.8919	+	10.4210i	0.571922	+	0.429024i
$591$	−30.9870			−1.27463
$592$	36.9372	+	4.17145i	1.51811	+	0.171446i
$593$	−15.2714	−	15.2714i	−0.627123	−	0.627123i	0.320220	−	0.947343i	$-0.396243\pi$
$593$	−15.2714	−	15.2714i	−0.627123	−	0.627123i	−0.947343	+	0.320220i	$0.896243\pi$
$594$	−3.32223	+	26.1665i	−0.136313	+	1.07363i
$595$	23.8878	−	18.5698i	0.979303	−	0.761286i
$596$	11.1294	−	14.7844i	0.455879	−	0.605595i
$597$	2.33225	+	5.63054i	0.0954525	+	0.230443i
$598$	−9.74370	+	17.0577i	−0.398450	+	0.697543i
$599$	5.68644	−	5.68644i	0.232342	−	0.232342i	−0.581328	−	0.813669i	$-0.697467\pi$
$599$	5.68644	−	5.68644i	0.232342	−	0.232342i	0.813669	+	0.581328i	$0.197467\pi$
$600$	33.2275	−	20.3728i	1.35651	−	0.831718i
$601$	0.490584	+	0.490584i	0.0200113	+	0.0200113i	0.717042	−	0.697030i	$-0.245496\pi$
$601$	0.490584	+	0.490584i	0.0200113	+	0.0200113i	−0.697030	+	0.717042i	$0.745496\pi$
$602$	32.1496	−	8.77353i	1.31032	−	0.357582i
$603$	−38.8044	+	16.0733i	−1.58024	+	0.654555i
$604$	−11.4320	−	19.3858i	−0.465163	−	0.788798i
$605$	−9.59053	−	12.3371i	−0.389911	−	0.501573i
$606$	4.83450	+	6.24066i	0.196388	+	0.253509i
$607$	5.39237	−	5.39237i	0.218870	−	0.218870i	−0.589152	−	0.808022i	$-0.700538\pi$
$607$	5.39237	−	5.39237i	0.218870	−	0.218870i	0.808022	+	0.589152i	$0.200538\pi$
$608$	11.7876	+	2.86897i	0.478051	+	0.116352i
$609$		−	53.4807i		−	2.16715i
$610$	−3.30564	−	23.1548i	−0.133841	−	0.937510i
$611$	4.20385	+	10.1490i	0.170070	+	0.410584i
$612$	32.4715	+	8.38055i	1.31258	+	0.338764i
$613$	−13.9134	−	33.5899i	−0.561956	−	1.35668i	−0.908200	−	0.418537i	$-0.862543\pi$
$613$	−13.9134	−	33.5899i	−0.561956	−	1.35668i	0.346244	−	0.938145i	$-0.387457\pi$
$614$	0.681627	−	1.19328i	0.0275082	−	0.0481570i
$615$	13.7271	−	3.77093i	0.553531	−	0.152058i
$616$	31.8900	+	31.0197i	1.28488	+	1.24982i
$617$	−9.87023			−0.397360			−0.198680	−	0.980064i	$-0.563666\pi$
$617$	−9.87023			−0.397360			−0.198680	+	0.980064i	$0.563666\pi$
$618$	−13.0399	−	7.44862i	−0.524540	−	0.299627i
$619$	−28.4293	−	11.7758i	−1.14267	−	0.473309i	−0.270599	−	0.962692i	$-0.587222\pi$
$619$	−28.4293	−	11.7758i	−1.14267	−	0.473309i	−0.872069	+	0.489383i	$0.837222\pi$
$620$	−2.37186	+	5.98726i	−0.0952561	+	0.240454i
$621$	−8.92842	−	21.5551i	−0.358285	−	0.864977i
$622$	10.6471	−	8.24809i	0.426910	−	0.330718i
$623$	7.20795	−	7.20795i	0.288780	−	0.288780i
$624$	−7.98316	−	27.7370i	−0.319582	−	1.11037i
$625$	21.9584	+	11.9510i	0.878338	+	0.478041i
$626$	1.32590	−	10.4431i	0.0529937	−	0.417389i
$627$	−23.1601	−	9.59321i	−0.924924	−	0.383116i
$628$	19.8288	+	14.9267i	0.791254	+	0.595639i
$629$	−12.9756	+	31.3259i	−0.517371	+	1.24904i
$630$	46.3777	−	27.4548i	1.84773	−	1.09382i
$631$	3.97486	+	3.97486i	0.158236	+	0.158236i	0.781785	−	0.623548i	$-0.214310\pi$
$631$	3.97486	+	3.97486i	0.158236	+	0.158236i	−0.623548	+	0.781785i	$0.714310\pi$
$632$	0.535741	+	0.213278i	0.0213106	+	0.00848376i
$633$	−14.8144			−0.588821
$634$	4.15626	−	7.27613i	0.165066	−	0.288972i
$635$	32.3765	−	25.1687i	1.28482	−	0.998789i
$636$	−13.9417	−	3.59821i	−0.552825	−	0.142678i
$637$	−16.3355	−	6.76639i	−0.647237	−	0.268094i
$638$	−3.95305	+	31.1350i	−0.156503	+	1.23265i
$639$	−15.8703			−0.627821
$640$	21.4049	−	13.4845i	0.846102	−	0.533021i
$641$	−22.0503			−0.870935			−0.435468	−	0.900204i	$-0.643417\pi$
$641$	−22.0503			−0.870935			−0.435468	+	0.900204i	$0.643417\pi$
$642$	9.23798	−	72.7602i	0.364594	−	2.87162i
$643$	−23.3820	−	9.68514i	−0.922096	−	0.381945i	−0.129422	−	0.991590i	$-0.541312\pi$
$643$	−23.3820	−	9.68514i	−0.922096	−	0.381945i	−0.792675	+	0.609645i	$0.791312\pi$
$644$	−38.1028	−	9.83396i	−1.50146	−	0.387512i
$645$	−4.86669	+	38.8544i	−0.191626	+	1.52989i
$646$	−5.48880	+	9.60893i	−0.215954	+	0.378058i
$647$	−3.30587			−0.129967			−0.0649836	−	0.997886i	$-0.520700\pi$
$647$	−3.30587			−0.129967			−0.0649836	+	0.997886i	$0.520700\pi$
$648$	−4.38112	−	1.74412i	−0.172107	−	0.0685156i
$649$	−16.4696	−	16.4696i	−0.646488	−	0.646488i
$650$	12.8638	−	13.3141i	0.504561	−	0.522222i
$651$	−5.63239	+	13.5978i	−0.220751	+	0.532939i
$652$	−19.4112	−	14.6124i	−0.760202	−	0.572264i
$653$	−32.7223	−	13.5540i	−1.28052	−	0.530410i	−0.364376	−	0.931252i	$-0.618718\pi$
$653$	−32.7223	−	13.5540i	−1.28052	−	0.530410i	−0.916147	+	0.400842i	$0.868718\pi$
$654$	−0.411027	+	3.23733i	−0.0160724	+	0.126590i
$655$	−12.9336	−	47.0816i	−0.505359	−	1.83963i
$656$	8.87951	−	2.55567i	0.346687	−	0.0997821i
$657$	−22.8863	+	22.8863i	−0.892879	+	0.892879i
$658$	−17.3960	+	13.4763i	−0.678168	+	0.525362i
$659$	10.1544	+	24.5149i	0.395559	+	0.954964i	0.988706	+	0.149870i	$0.0478854\pi$
$659$	10.1544	+	24.5149i	0.395559	+	0.954964i	−0.593147	+	0.805094i	$0.702115\pi$
$660$	−47.9793	+	20.7515i	−1.86759	+	0.807753i
$661$	−29.1101	−	12.0578i	−1.13225	−	0.468994i	−0.263705	−	0.964603i	$-0.584945\pi$
$661$	−29.1101	−	12.0578i	−1.13225	−	0.468994i	−0.868545	+	0.495610i	$0.834945\pi$
$662$	−22.2043	−	12.6835i	−0.862995	−	0.492959i
$663$	26.3276			1.02248
$664$	12.7513	+	12.4034i	0.494847	+	0.481344i
$665$	4.71095	+	17.1490i	0.182683	+	0.665010i
$666$	−29.9570	+	52.4439i	−1.16081	+	2.03216i
$667$	−10.6237	−	25.6480i	−0.411353	−	0.993094i
$668$	−33.2428	−	8.57963i	−1.28620	−	0.331956i
$669$	25.4225	+	61.3753i	0.982891	+	2.37291i
$670$	−23.1197	−	17.3431i	−0.893191	−	0.670022i
$671$			31.3702i			1.21103i
$672$	49.3918	−	30.0554i	1.90533	−	1.15941i
$673$	12.1579	−	12.1579i	0.468654	−	0.468654i	−0.432824	−	0.901478i	$-0.642483\pi$
$673$	12.1579	−	12.1579i	0.468654	−	0.468654i	0.901478	+	0.432824i	$0.142483\pi$
$674$	−6.71103	−	8.66299i	−0.258499	−	0.333686i
$675$	3.14414	+	21.7617i	0.121018	+	0.837607i
$676$	6.24302	+	10.5866i	0.240116	+	0.407176i
$677$	−38.8974	+	16.1118i	−1.49495	+	0.619228i	−0.972387	−	0.233375i	$-0.925023\pi$
$677$	−38.8974	+	16.1118i	−1.49495	+	0.619228i	−0.522561	+	0.852602i	$0.675023\pi$
$678$	56.5888	−	15.4429i	2.17328	−	0.593081i
$679$	−13.4339	−	13.4339i	−0.515546	−	0.515546i
$680$	6.41988	+	22.1650i	0.246191	+	0.849990i
$681$	50.7160	−	50.7160i	1.94344	−	1.94344i
$682$	4.28411	−	7.49995i	0.164047	−	0.287188i
$683$	10.9032	+	26.3227i	0.417200	+	1.00721i	0.983155	+	0.182774i	$0.0585077\pi$
$683$	10.9032	+	26.3227i	0.417200	+	1.00721i	−0.565955	+	0.824436i	$0.691492\pi$
$684$	−11.8549	+	15.7482i	−0.453285	+	0.602149i
$685$	−4.17535	−	0.522982i	−0.159532	−	0.0199821i
$686$	−0.162945	+	1.28339i	−0.00622128	+	0.0490001i
$687$	−33.0511	−	33.0511i	−1.26098	−	1.26098i
$688$	−2.85223	+	25.2559i	−0.108740	+	0.962871i
$689$	−6.83923			−0.260554
$690$	27.7468	−	36.9886i	1.05630	−	1.40813i
$691$	19.5933	−	8.11580i	0.745363	−	0.308740i	0.0225151	−	0.999747i	$-0.492833\pi$
$691$	19.5933	−	8.11580i	0.745363	−	0.308740i	0.722848	+	0.691007i	$0.242833\pi$
$692$	−9.74090	−	7.33274i	−0.370293	−	0.278749i
$693$	−66.7817	+	27.6619i	−2.53683	+	1.05079i
$694$	24.8669	−	6.78611i	0.943935	−	0.257597i
$695$	−1.15504	−	0.657207i	−0.0438133	−	0.0249293i
$696$	37.8960	+	15.0864i	1.43644	+	0.571847i
$697$			8.42834i			0.319246i
$698$	−6.98339	+	1.90575i	−0.264325	+	0.0721336i
$699$	−23.6527	+	57.1026i	−0.894626	+	2.15982i
$700$	32.5137	+	17.8379i	1.22890	+	0.674211i
$701$	17.3571	−	7.18953i	0.655567	−	0.271545i	−0.0300049	−	0.999550i	$-0.509552\pi$
$701$	17.3571	−	7.18953i	0.655567	−	0.271545i	0.685572	+	0.728005i	$0.259552\pi$
$702$	16.1529	+	2.05085i	0.609652	+	0.0774043i
$703$	−14.0925	−	14.0925i	−0.531511	−	0.531511i
$704$	−30.9762	+	13.8466i	−1.16746	+	0.521863i
$705$	−6.84929	−	24.9331i	−0.257959	−	0.939036i
$706$	0.934975	+	1.20692i	0.0351882	+	0.0454230i
$707$	−2.87445	+	6.93954i	−0.108105	+	0.260988i
$708$	−26.0740	+	15.3762i	−0.979922	+	0.577871i
$709$	0.650888	+	0.269607i	0.0244446	+	0.0101253i	0.394872	−	0.918736i	$-0.370789\pi$
$709$	0.650888	+	0.269607i	0.0244446	+	0.0101253i	−0.370428	+	0.928861i	$0.620789\pi$
$710$	−5.56306	−	9.39733i	−0.208778	−	0.352676i
$711$	−0.662496	+	0.662496i	−0.0248455	+	0.0248455i
$712$	3.07420	+	7.14078i	0.115211	+	0.267612i
$713$			7.64001i			0.286121i
$714$	13.8846	+	50.8785i	0.519617	+	1.90408i
$715$	−19.6036	+	15.2393i	−0.733132	+	0.569918i
$716$	−2.90345	−	20.5852i	−0.108507	−	0.769305i
$717$	5.75923	−	13.9040i	0.215082	−	0.519255i
$718$	21.0331	−	16.2939i	0.784948	−	0.608083i
$719$			41.3849i			1.54340i	0.635989	+	0.771698i	$0.280592\pi$
$719$			41.3849i			1.54340i	−0.635989	+	0.771698i	$0.719408\pi$
$720$	6.37154	+	40.6076i	0.237453	+	1.51335i
$721$		−	14.2889i		−	0.532148i
$722$	12.4722	+	16.0998i	0.464166	+	0.599172i
$723$	27.1713	−	65.5972i	1.01051	−	2.43959i
$724$	−38.4266	−	28.9267i	−1.42811	−	1.07505i
$725$	3.74115	+	25.8938i	0.138943	+	0.961670i
$726$	26.2767	−	7.17082i	0.975218	−	0.266134i
$727$		−	31.9347i		−	1.18439i	−0.805794	−	0.592196i	$-0.798261\pi$
$727$		−	31.9347i		−	1.18439i	0.805794	−	0.592196i	$-0.201739\pi$
$728$	19.1488	−	19.6860i	0.709703	−	0.729613i
$729$	31.1273	−	31.1273i	1.15286	−	1.15286i
$730$	−21.5741	−	5.52933i	−0.798492	−	0.204650i
$731$	−21.4191	−	8.87207i	−0.792213	−	0.328145i
$732$	39.4758	+	10.1883i	1.45907	+	0.376570i
$733$	17.7686	−	42.8973i	0.656299	−	1.58445i	−0.147177	−	0.989110i	$-0.547019\pi$
$733$	17.7686	−	42.8973i	0.656299	−	1.58445i	0.803476	−	0.595337i	$-0.202981\pi$
$734$	−12.7491	+	9.87647i	−0.470579	+	0.364547i
$735$	36.1728	+	20.5819i	1.33425	+	0.759175i
$736$	17.7167	−	24.2253i	0.653046	−	0.892956i
$737$	27.4095	+	27.4095i	1.00964	+	1.00964i
$738$	−1.89095	+	14.8935i	−0.0696067	+	0.548237i
$739$	26.2226	−	10.8618i	0.964616	−	0.399557i	0.155911	−	0.987771i	$-0.450169\pi$
$739$	26.2226	−	10.8618i	0.964616	−	0.399557i	0.808705	+	0.588214i	$0.200169\pi$
$740$	−41.5546	+	0.644785i	−1.52758	+	0.0237028i
$741$	−5.92200	+	14.2970i	−0.217550	+	0.525213i
$742$	−3.60685	−	13.2169i	−0.132412	−	0.485207i
$743$			4.46895i			0.163950i	0.996634	+	0.0819749i	$0.0261227\pi$
$743$			4.46895i			0.163950i	−0.996634	+	0.0819749i	$0.973877\pi$
$744$	−8.04644	−	7.82687i	−0.294997	−	0.286947i
$745$	−10.2318	+	17.9824i	−0.374863	+	0.658823i
$746$	6.45305	+	23.6465i	0.236263	+	0.865758i
$747$	−26.7029	+	11.0607i	−0.977010	+	0.404691i
$748$	−4.32253	−	30.6464i	−0.158047	−	1.12054i
$749$	64.4747	−	26.7063i	2.35585	−	0.975827i
$750$	−33.9388	+	27.3324i	−1.23927	+	0.998039i
$751$	−16.8523			−0.614949			−0.307474	−	0.951556i	$-0.599484\pi$
$751$	−16.8523			−0.614949			−0.307474	+	0.951556i	$0.599484\pi$
$752$	−4.64197	−	16.1282i	−0.169275	−	0.588136i
$753$	16.8168	+	16.8168i	0.612837	+	0.612837i
$754$	19.2200	+	2.44026i	0.699951	+	0.0888691i
$755$	15.4430	+	19.8656i	0.562029	+	0.722982i
$756$	4.55537	+	32.2972i	0.165677	+	1.17464i
$757$	14.0127	+	33.8297i	0.509302	+	1.22956i	0.944286	+	0.329125i	$0.106754\pi$
$757$	14.0127	+	33.8297i	0.509302	+	1.22956i	−0.434985	+	0.900438i	$0.643246\pi$
$758$	−30.8365	−	17.6144i	−1.12003	−	0.639783i
$759$	−43.8518	+	43.8518i	−1.59172	+	1.59172i
$760$	−13.4806	−	1.49943i	−0.488991	−	0.0543900i
$761$	21.9685	+	21.9685i	0.796356	+	0.796356i	0.982519	−	0.186163i	$-0.0596051\pi$
$761$	21.9685	+	21.9685i	0.796356	+	0.796356i	−0.186163	+	0.982519i	$0.559605\pi$
$762$	18.8186	+	68.9585i	0.681725	+	2.49810i
$763$	−2.86869	+	1.18825i	−0.103853	+	0.0430175i
$764$	4.30958	−	16.6980i	0.155915	−	0.604111i
$765$	−37.2031	−	4.65986i	−1.34508	−	0.168478i
$766$	10.2196	−	7.91688i	0.369248	−	0.286048i
$767$	−10.1669	+	10.1669i	−0.367104	+	0.367104i
$768$	7.36403	+	43.4770i	0.265726	+	1.56884i
$769$			17.3648i			0.626192i	0.949721	+	0.313096i	$0.101366\pi$
$769$			17.3648i			0.626192i	−0.949721	+	0.313096i	$0.898634\pi$
$770$	−39.7886	−	29.8472i	−1.43388	−	1.07562i
$771$	−22.5901	−	54.5373i	−0.813563	−	1.96411i
$772$	−31.9467	+	18.8393i	−1.14979	+	0.678043i
$773$	−3.66118	−	8.83886i	−0.131683	−	0.317912i	0.844261	−	0.535933i	$-0.180040\pi$
$773$	−3.66118	−	8.83886i	−0.131683	−	0.317912i	−0.975944	+	0.218021i	$0.930040\pi$
$774$	−35.8586	−	20.4831i	−1.28891	−	0.736250i
$775$	1.77583	−	6.97766i	0.0637896	−	0.250645i
$776$	13.3087	−	5.72958i	0.477755	−	0.205680i
$777$	−94.9821			−3.40746
$778$	−18.3253	+	32.0811i	−0.656995	+	1.15016i
$779$	−4.57693	−	1.89583i	−0.163985	−	0.0679250i
$780$	12.8102	+	29.6182i	0.458677	+	1.06050i
$781$	5.60502	+	13.5317i	0.200563	+	0.484203i
$782$	16.7655	+	21.6419i	0.599534	+	0.773913i
$783$	−16.2707	+	16.2707i	−0.581466	+	0.581466i
$784$	23.6393	+	13.0729i	0.844262	+	0.466891i
$785$	−24.1178	−	13.7227i	−0.860801	−	0.489786i
$786$	84.4283	+	10.7194i	3.01146	+	0.382349i
$787$	−32.0088	−	13.2585i	−1.14099	−	0.472614i	−0.269488	−	0.963004i	$-0.586854\pi$
$787$	−32.0088	−	13.2585i	−1.14099	−	0.472614i	−0.871503	+	0.490390i	$0.836854\pi$
$788$	22.2664	−	3.14058i	0.793208	−	0.111878i
$789$	7.24913	−	17.5010i	0.258076	−	0.623050i
$790$	−0.624511	−	0.160059i	−0.0222191	−	0.00569465i
$791$	39.4658	+	39.4658i	1.40324	+	1.40324i
$792$	−0.762529	−	55.1241i	−0.0270953	−	1.95875i
$793$	19.3652			0.687677
$794$	−34.6229	−	19.7773i	−1.22872	−	0.701868i
$795$	15.9733	+	2.00073i	0.566513	+	0.0709584i
$796$	−2.24655	−	3.80958i	−0.0796270	−	0.135027i
$797$	−37.8964	−	15.6972i	−1.34236	−	0.556023i	−0.408203	−	0.912891i	$-0.633844\pi$
$797$	−37.8964	−	15.6972i	−1.34236	−	0.556023i	−0.934155	+	0.356868i	$0.883844\pi$
$798$	−30.7522	−	3.90444i	−1.08862	−	0.138216i
$799$	15.3087			0.541584
$800$	−21.8116	+	18.0070i	−0.771157	+	0.636645i
$801$	−12.6318			−0.446323
$802$	−48.4094	−	6.14628i	−1.70939	−	0.217033i
$803$	27.5967	+	11.4309i	0.973867	+	0.403389i
$804$	43.3937	−	25.5898i	1.53038	−	0.902482i
$805$	43.6551	+	5.46801i	1.53864	+	0.192722i
$806$	−4.62980	−	2.64463i	−0.163078	−	0.0931532i
$807$	60.6318			2.13434
$808$	−4.10645	−	3.99439i	−0.144464	−	0.140522i
$809$	−4.54672	−	4.54672i	−0.159854	−	0.159854i	0.622648	−	0.782502i	$-0.286057\pi$
$809$	−4.54672	−	4.54672i	−0.159854	−	0.159854i	−0.782502	+	0.622648i	$0.786057\pi$
$810$	5.10705	+	1.30891i	0.179443	+	0.0459905i
$811$	−8.69312	+	20.9871i	−0.305257	+	0.736955i	0.694589	+	0.719407i	$0.255586\pi$
$811$	−8.69312	+	20.9871i	−0.305257	+	0.736955i	−0.999846	+	0.0175486i	$0.994414\pi$
$812$	5.42034	+	38.4298i	0.190217	+	1.34862i
$813$	31.7600	+	13.1554i	1.11387	+	0.461381i
$814$	55.2960	+	7.02064i	1.93812	+	0.246073i
$815$	23.6099	+	13.4338i	0.827020	+	0.470565i
$816$	−39.9688	−	4.51381i	−1.39919	−	0.158015i
$817$	9.63579	−	9.63579i	0.337114	−	0.337114i
$818$	16.2073	+	20.9213i	0.566675	+	0.731497i
$819$	17.0760	+	41.2251i	0.596684	+	1.44052i
$820$	−9.48175	+	4.10095i	−0.331117	+	0.143211i
$821$	9.76690	+	4.04558i	0.340867	+	0.141192i	0.546549	−	0.837427i	$-0.315941\pi$
$821$	9.76690	+	4.04558i	0.340867	+	0.141192i	−0.205682	+	0.978619i	$0.565941\pi$
$822$	3.63804	−	6.36890i	0.126891	−	0.222141i
$823$	−32.4078			−1.12966			−0.564832	−	0.825206i	$-0.691059\pi$
$823$	−32.4078			−1.12966			−0.564832	+	0.825206i	$0.691059\pi$
$824$	10.1250	+	4.03077i	0.352722	+	0.140419i
$825$	50.2429	−	29.8572i	1.74923	−	1.03950i
$826$	−25.0093	−	14.2858i	−0.870187	−	0.497067i
$827$	−6.17678	−	14.9121i	−0.214788	−	0.518543i	0.779360	−	0.626577i	$-0.215545\pi$
$827$	−6.17678	−	14.9121i	−0.214788	−	0.518543i	−0.994147	+	0.108034i	$0.965545\pi$
$828$	24.7704	+	42.0043i	0.860831	+	1.45975i
$829$	2.07649	+	5.01309i	0.0721194	+	0.174112i	0.955829	−	0.293925i	$-0.0949616\pi$
$829$	2.07649	+	5.01309i	0.0721194	+	0.174112i	−0.883709	+	0.468037i	$0.844962\pi$
$830$	−15.9096	−	11.9345i	−0.552232	−	0.414254i
$831$		−	64.7159i		−	2.24497i
$832$	8.54767	+	19.1219i	0.296337	+	0.662934i
$833$	−17.4235	+	17.4235i	−0.603687	+	0.603687i
$834$	1.83120	−	1.41859i	0.0634092	−	0.0491218i
$835$	38.0869	+	4.77056i	1.31805	+	0.165092i
$836$	17.6145	+	4.54612i	0.609210	+	0.157231i
$837$	5.85048	−	2.42335i	0.202222	−	0.0837632i
$838$	−9.37826	−	34.3656i	−0.323967	−	1.18714i
$839$	−31.8237	−	31.8237i	−1.09868	−	1.09868i	−0.994566	−	0.104110i	$-0.966801\pi$
$839$	−31.8237	−	31.8237i	−1.09868	−	1.09868i	−0.104110	−	0.994566i	$-0.533199\pi$
$840$	−50.4817	+	40.3757i	−1.74178	+	1.39309i
$841$	1.14598	−	1.14598i	0.0395166	−	0.0395166i
$842$	−30.3940	−	17.3616i	−1.04745	−	0.598322i
$843$	7.94812	+	19.1885i	0.273748	+	0.660885i
$844$	10.6453	−	1.50146i	0.366425	−	0.0516825i
$845$	−8.43340	−	10.8486i	−0.290118	−	0.373202i
$846$	27.0517	+	3.43461i	0.930055	+	0.118084i
$847$	18.3257	+	18.3257i	0.629678	+	0.629678i
$848$	10.3828	+	1.17257i	0.356548	+	0.0402662i
$849$	30.6027			1.05028
$850$	−10.2816	−	23.6626i	−0.352657	−	0.811620i
$851$	−45.5510	+	18.8679i	−1.56147	+	0.646782i
$852$	18.8485	−	2.65849i	0.645739	−	0.0910784i
$853$	42.6825	−	17.6797i	1.46142	−	0.605341i	0.496537	−	0.868015i	$-0.334605\pi$
$853$	42.6825	−	17.6797i	1.46142	−	0.605341i	0.964884	+	0.262675i	$0.0846046\pi$
$854$	10.2127	+	37.4234i	0.349473	+	1.28060i
$855$	10.8988	−	19.1546i	0.372730	−	0.655074i
$856$	0.736187	+	53.2198i	0.0251624	+	1.81902i
$857$		−	44.9421i		−	1.53519i	−0.640934	−	0.767596i	$-0.721453\pi$
$857$		−	44.9421i		−	1.53519i	0.640934	−	0.767596i	$-0.278547\pi$
$858$	−11.3944	−	41.7535i	−0.388999	−	1.42544i
$859$	−15.0404	+	36.3106i	−0.513170	+	1.23890i	0.428859	+	0.903372i	$0.358916\pi$
$859$	−15.0404	+	36.3106i	−0.513170	+	1.23890i	−0.942029	+	0.335531i	$0.891084\pi$
$860$	−0.440872	−	28.4130i	−0.0150336	−	0.968875i
$861$	−21.8128	+	9.03516i	−0.743378	+	0.307917i
$862$	−1.20002	+	9.45161i	−0.0408729	+	0.321923i
$863$	−38.7485	−	38.7485i	−1.31901	−	1.31901i	−0.914558	−	0.404455i	$-0.867461\pi$
$863$	−38.7485	−	38.7485i	−1.31901	−	1.31901i	−0.404455	−	0.914558i	$-0.632539\pi$
$864$	−24.1706	−	5.88282i	−0.822299	−	0.200138i
$865$	11.8479	+	6.74131i	0.402840	+	0.229211i
$866$	38.3514	−	29.7100i	1.30323	−	1.00959i
$867$	−3.88904	+	9.38897i	−0.132079	+	0.318866i
$868$	2.66913	−	10.3419i	0.0905962	−	0.351026i
$869$	0.798850	+	0.330894i	0.0270991	+	0.0112248i
$870$	−44.1751	−	11.3219i	−1.49768	−	0.383848i
$871$	16.9202	−	16.9202i	0.573320	−	0.573320i
$872$	−0.0327553	−	2.36792i	−0.00110923	−	0.0801879i
$873$			23.5427i			0.796800i
$874$	−15.5236	+	4.23634i	−0.525093	+	0.143296i
$875$	−38.5994	−	15.1411i	−1.30490	−	0.511861i
$876$	23.3473	−	31.0148i	0.788831	−	1.04789i
$877$	6.21828	−	15.0122i	0.209976	−	0.506928i	−0.783443	−	0.621464i	$-0.786538\pi$
$877$	6.21828	−	15.0122i	0.209976	−	0.506928i	0.993419	+	0.114536i	$0.0365382\pi$
$878$	14.4417	+	18.6422i	0.487384	+	0.629143i
$879$		−	30.6168i		−	1.03268i
$880$	32.3735	−	19.7743i	1.09131	−	0.666591i
$881$		−	29.0942i		−	0.980208i	−0.871664	−	0.490104i	$-0.836959\pi$
$881$		−	29.0942i		−	0.980208i	0.871664	−	0.490104i	$-0.163041\pi$
$882$	−34.6976	+	26.8795i	−1.16833	+	0.905079i
$883$	13.2835	−	32.0692i	0.447025	−	1.07921i	−0.526406	−	0.850233i	$-0.676461\pi$
$883$	13.2835	−	32.0692i	0.447025	−	1.07921i	0.973431	−	0.228980i	$-0.0735390\pi$
$884$	−18.9183	+	2.66835i	−0.636293	+	0.0897462i
$885$	26.7193	−	20.7709i	0.898159	−	0.698207i
$886$	−6.97784	−	25.5695i	−0.234425	−	0.859023i
$887$			33.3087i			1.11840i	0.829034	+	0.559199i	$0.188891\pi$
$887$			33.3087i			1.11840i	−0.829034	+	0.559199i	$0.811109\pi$
$888$	26.7935	−	67.3035i	0.899131	−	2.25856i
$889$	−48.0926	+	48.0926i	−1.61297	+	1.61297i
$890$	−4.42785	−	7.47970i	−0.148422	−	0.250720i
$891$	−6.53274	−	2.70595i	−0.218855	−	0.0906527i
$892$	−24.4884	−	41.5261i	−0.819933	−	1.39040i
$893$	−3.44347	+	8.31327i	−0.115231	+	0.278193i
$894$	−22.0854	−	28.5091i	−0.738646	−	0.953488i
$895$	6.15685	+	22.4125i	0.205801	+	0.749166i
$896$	−32.4455	+	26.6029i	−1.08393	+	0.888741i
$897$	27.0702	+	27.0702i	0.903849	+	0.903849i
$898$	48.4891	+	6.15640i	1.61810	+	0.205442i
$899$	6.96137	−	2.88349i	0.232175	−	0.0961699i
$900$	−12.8595	−	44.1203i	−0.428651	−	1.47068i
$901$	−3.64736	+	8.80551i	−0.121511	+	0.293354i
$902$	13.3667	−	3.64772i	0.445061	−	0.121456i
$903$		−	64.9441i		−	2.16120i
$904$	−39.0980	+	16.8322i	−1.30038	+	0.559831i
$905$	46.7384	+	26.5936i	1.55364	+	0.884001i
$906$	−42.3116	+	11.5467i	−1.40571	+	0.383614i
$907$	−0.145961	+	0.0604591i	−0.00484656	+	0.00200751i	−0.385105	−	0.922873i	$-0.625835\pi$
$907$	−0.145961	+	0.0604591i	−0.00484656	+	0.00200751i	0.380259	+	0.924880i	$0.375835\pi$
$908$	−31.3030	+	41.5833i	−1.03883	+	1.37999i
$909$	8.59943	−	3.56200i	0.285225	−	0.118144i
$910$	−18.4250	+	24.5620i	−0.610784	+	0.814221i
$911$	−7.19740			−0.238461			−0.119230	−	0.992867i	$-0.538043\pi$
$911$	−7.19740			−0.238461			−0.119230	+	0.992867i	$0.538043\pi$
$912$	11.4415	−	20.6893i	0.378867	−	0.685092i
$913$	18.8617	+	18.8617i	0.624231	+	0.624231i
$914$	−7.06483	+	55.6440i	−0.233684	+	1.84054i
$915$	−45.2281	−	5.66503i	−1.49519	−	0.187280i
$916$	27.0994	+	20.3999i	0.895390	+	0.674030i
$917$	30.9890	+	74.8141i	1.02335	+	2.47058i
$918$	11.2548	−	19.7031i	0.371464	−	0.650300i
$919$	−18.9346	+	18.9346i	−0.624593	+	0.624593i	−0.946703	−	0.322109i	$-0.895608\pi$
$919$	−18.9346	+	18.9346i	−0.624593	+	0.624593i	0.322109	+	0.946703i	$0.395608\pi$
$920$	−16.1893	+	29.3912i	−0.533744	+	0.968998i
$921$	−1.89372	−	1.89372i	−0.0624000	−	0.0624000i
$922$	20.9322	−	5.71234i	0.689365	−	0.188126i
$923$	8.35329	−	3.46004i	0.274952	−	0.113889i
$924$	74.6800	−	44.0396i	2.45679	−	1.44880i
$925$	45.9875	−	6.64431i	1.51206	−	0.218463i
$926$	−23.5247	−	30.3670i	−0.773069	−	0.997923i
$927$	−12.5206	+	12.5206i	−0.411230	+	0.411230i
$928$	−28.7601	−	6.99985i	−0.944095	−	0.229781i
$929$			1.41239i			0.0463390i	0.999732	+	0.0231695i	$0.00737573\pi$
$929$			1.41239i			0.0463390i	−0.999732	+	0.0231695i	$0.992624\pi$
$930$	10.0394	+	7.53102i	0.329206	+	0.246952i
$931$	−5.54250	−	13.3808i	−0.181648	−	0.438537i
$932$	11.2087	−	43.4296i	0.367155	−	1.42258i
$933$	−10.0442	−	24.2488i	−0.328832	−	0.793871i
$934$	−10.4573	+	18.3070i	−0.342174	+	0.599024i
$935$	9.16605	+	33.3667i	0.299762	+	1.09121i
$936$	−34.0288	+	0.470718i	−1.11226	+	0.0153859i
$937$	−12.6258			−0.412468			−0.206234	−	0.978503i	$-0.566121\pi$
$937$	−12.6258			−0.412468			−0.206234	+	0.978503i	$0.566121\pi$
$938$	41.6218	+	23.7752i	1.35900	+	0.776287i
$939$	−18.9532	−	7.85068i	−0.618515	−	0.256197i
$940$	7.44873	+	17.2221i	0.242951	+	0.561723i
$941$	11.3405	+	27.3783i	0.369688	+	0.892507i	0.993801	+	0.111172i	$0.0354606\pi$
$941$	11.3405	+	27.3783i	0.369688	+	0.892507i	−0.624113	+	0.781334i	$0.714539\pi$
$942$	38.2362	−	29.6207i	1.24580	−	0.965096i
$943$	−8.66607	+	8.66607i	−0.282206	+	0.282206i
$944$	17.1777	−	13.6915i	0.559087	−	0.445621i
$945$	−9.65981	−	35.1641i	−0.314234	−	1.14389i
$946$	−4.80037	+	37.8087i	−0.156073	+	1.22927i
$947$	29.7484	+	12.3222i	0.966694	+	0.400418i	0.809480	−	0.587147i	$-0.199749\pi$
$947$	29.7484	+	12.3222i	0.966694	+	0.400418i	0.157213	+	0.987565i	$0.449749\pi$
$948$	0.675840	−	0.897794i	0.0219503	−	0.0291590i
$949$	7.05644	−	17.0358i	0.229062	−	0.553004i
$950$	15.1624	−	0.260798i	0.491934	−	0.00846141i
$951$	−11.5471	−	11.5471i	−0.374439	−	0.374439i
$952$	−15.1337	−	35.1527i	−0.490486	−	1.13931i
$953$	−60.5106			−1.96013			−0.980066	−	0.198673i	$-0.936337\pi$
$953$	−60.5106			−1.96013			−0.980066	+	0.198673i	$0.936337\pi$
$954$	−8.42072	+	14.7417i	−0.272631	+	0.477279i
$955$	−2.39627	+	19.1312i	−0.0775414	+	0.619070i
$956$	−2.72924	+	10.5748i	−0.0882698	+	0.342012i
$957$	56.5071	+	23.4060i	1.82662	+	0.756609i
$958$	1.66661	−	13.1266i	0.0538457	−	0.424100i
$959$	6.97898			0.225363
$960$	−14.3695	−	47.1605i	−0.463774	−	1.52210i
$961$	28.9264			0.933108
$962$	4.33392	−	34.1349i	0.139731	−	1.10055i
$963$	−79.8967	−	33.0943i	−2.57463	−	1.06645i
$964$	−12.8762	+	49.8903i	−0.414713	+	1.60686i
$965$	32.7373	−	25.4492i	1.05385	−	0.819237i
$966$	−38.0373	+	66.5897i	−1.22383	+	2.14249i
$967$	−18.3324			−0.589531			−0.294766	−	0.955570i	$-0.595242\pi$
$967$	−18.3324			−0.589531			−0.294766	+	0.955570i	$0.595242\pi$
$968$	−18.1549	+	7.81594i	−0.583522	+	0.251214i
$969$	15.2492	+	15.2492i	0.489873	+	0.489873i
$970$	−13.9404	+	8.25247i	−0.447599	+	0.264971i
$971$	0.992401	−	2.39587i	0.0318477	−	0.0768870i	−0.907156	−	0.420796i	$-0.861751\pi$
$971$	0.992401	−	2.39587i	0.0318477	−	0.0768870i	0.939003	+	0.343908i	$0.111751\pi$
$972$	−21.3954	+	28.4219i	−0.686257	+	0.911631i
$973$	2.03627	+	0.843451i	0.0652798	+	0.0270398i
$974$	0.978247	−	7.70487i	0.0313451	−	0.246880i
$975$	−18.4312	−	31.0155i	−0.590271	−	0.993291i
$976$	−29.3988	−	3.32011i	−0.941034	−	0.106274i
$977$	21.9823	−	21.9823i	0.703276	−	0.703276i	−0.261836	−	0.965112i	$-0.584328\pi$
$977$	21.9823	−	21.9823i	0.703276	−	0.703276i	0.965112	+	0.261836i	$0.0843280\pi$
$978$	−37.4310	+	28.9970i	−1.19691	+	0.927222i
$979$	4.46126	+	10.7704i	0.142582	+	0.344224i
$980$	−28.0788	−	11.1234i	−0.896944	−	0.355325i
$981$	3.55486	+	1.47247i	0.113498	+	0.0470124i
$982$	−11.8868	−	6.78997i	−0.379323	−	0.216677i
$983$	33.0141			1.05299			0.526493	−	0.850180i	$-0.323507\pi$
$983$	33.0141			1.05299			0.526493	+	0.850180i	$0.323507\pi$
$984$	−0.249064	−	18.0051i	−0.00793985	−	0.573982i
$985$	−24.2429	+	6.65969i	−0.772444	+	0.212195i
$986$	13.3919	−	23.4444i	0.426484	−	0.746620i
$987$	16.4109	+	39.6195i	0.522366	+	1.26110i
$988$	2.80637	−	10.8736i	0.0892826	−	0.345936i
$989$	−12.9009	−	31.1455i	−0.410225	−	0.990370i
$990$	8.71107	+	61.0179i	0.276856	+	1.93928i
$991$		−	1.26612i		−	0.0402198i	−0.999798	−	0.0201099i	$-0.993598\pi$
$991$		−	1.26612i		−	0.0402198i	0.999798	−	0.0201099i	$-0.00640161\pi$
$992$	6.57522	+	4.80866i	0.208764	+	0.152675i
$993$	−35.2377	+	35.2377i	−1.11824	+	1.11824i
$994$	11.0919	+	14.3181i	0.351814	+	0.454142i
$995$	3.03476	+	3.90386i	0.0962084	+	0.123761i
$996$	29.8611	−	17.6094i	0.946185	−	0.557976i
$997$	−9.06030	+	3.75290i	−0.286943	+	0.118856i	−0.521512	−	0.853244i	$-0.674632\pi$
$997$	−9.06030	+	3.75290i	−0.286943	+	0.118856i	0.234570	+	0.972099i	$0.424632\pi$
$998$	−12.7928	+	3.49111i	−0.404948	+	0.110509i
$999$	28.8968	+	28.8968i	0.914255	+	0.914255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.ba.a.107.11	yes	88
4.3	odd	2		640.2.ba.a.207.2		88
5.2	odd	4		800.2.v.b.43.1		88
5.3	odd	4		160.2.u.a.43.22	✓	88
5.4	even	2		800.2.bb.b.107.12		88
20.3	even	4		640.2.u.a.463.21		88
32.3	odd	8		160.2.u.a.67.22	yes	88
32.29	even	8		640.2.u.a.47.21		88
160.3	even	8	inner	160.2.ba.a.3.11	yes	88
160.67	even	8		800.2.bb.b.643.12		88
160.93	odd	8		640.2.ba.a.303.2		88
160.99	odd	8		800.2.v.b.707.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.22	✓	88	5.3	odd	4
160.2.u.a.67.22	yes	88	32.3	odd	8
160.2.ba.a.3.11	yes	88	160.3	even	8	inner
160.2.ba.a.107.11	yes	88	1.1	even	1	trivial
640.2.u.a.47.21		88	32.29	even	8
640.2.u.a.463.21		88	20.3	even	4
640.2.ba.a.207.2		88	4.3	odd	2
640.2.ba.a.303.2		88	160.93	odd	8
800.2.v.b.43.1		88	5.2	odd	4
800.2.v.b.707.1		88	160.99	odd	8
800.2.bb.b.107.12		88	5.4	even	2
800.2.bb.b.643.12		88	160.67	even	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.ba (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.178125 + 1.40295i) q^{2} +(2.54622 + 1.05468i) q^{3} +(-1.93654 - 0.499802i) q^{4} +(2.21873 + 0.277906i) q^{5} +(-1.93321 + 3.38436i) q^{6} -3.70855 q^{7} +(1.04614 - 2.62785i) q^{8} +(3.24959 + 3.24959i) q^{9} +(-0.785101 + 3.06327i) q^{10} +(1.62306 - 3.91841i) q^{11} +(-4.40374 - 3.31504i) q^{12} +(-2.41888 - 1.00193i) q^{13} +(0.660586 - 5.20291i) q^{14} +(5.35629 + 3.04767i) q^{15} +(3.50040 + 1.93578i) q^{16} +(-2.57998 + 2.57998i) q^{17} +(-5.13785 + 3.98018i) q^{18} +(-0.820706 - 1.98136i) q^{19} +(-4.15777 - 1.64710i) q^{20} +(-9.44280 - 3.91133i) q^{21} +(5.20824 + 2.97504i) q^{22} -5.30550 q^{23} +(5.43526 - 5.58774i) q^{24} +(4.84554 + 1.23320i) q^{25} +(1.83653 - 3.21510i) q^{26} +(1.68286 + 4.06279i) q^{27} +(7.18176 + 1.85354i) q^{28} +(2.00240 + 4.83422i) q^{29} +(-5.22981 + 6.97174i) q^{30} -1.44002i q^{31} +(-3.33931 + 4.56607i) q^{32} +(8.26535 - 8.26535i) q^{33} +(-3.16003 - 4.07914i) q^{34} +(-8.22827 - 1.03063i) q^{35} +(-4.66882 - 7.91712i) q^{36} +(8.58562 - 3.55628i) q^{37} +(2.92594 - 0.798480i) q^{38} +(-5.10230 - 5.10230i) q^{39} +(3.05141 - 5.53976i) q^{40} +(1.63341 - 1.63341i) q^{41} +(7.16941 - 12.5511i) q^{42} +(2.43161 + 5.87042i) q^{43} +(-5.10156 + 6.77697i) q^{44} +(6.30688 + 8.11304i) q^{45} +(0.945044 - 7.44336i) q^{46} +(-2.96683 - 2.96683i) q^{47} +(6.87117 + 8.62072i) q^{48} +6.75333 q^{49} +(-2.59323 + 6.57839i) q^{50} +(-9.29026 + 3.84815i) q^{51} +(4.18350 + 3.14925i) q^{52} +(2.41336 - 0.999648i) q^{53} +(-5.99965 + 1.63729i) q^{54} +(4.69009 - 8.24285i) q^{55} +(-3.87968 + 9.74550i) q^{56} -5.91057i q^{57} +(-7.13886 + 1.94817i) q^{58} +(2.10156 - 5.07362i) q^{59} +(-8.84945 - 8.57902i) q^{60} +(-6.83341 + 2.83049i) q^{61} +(2.02027 + 0.256503i) q^{62} +(-12.0513 - 12.0513i) q^{63} +(-5.81116 - 5.49822i) q^{64} +(-5.08841 - 2.89524i) q^{65} +(10.1236 + 13.0682i) q^{66} +(-3.49753 + 8.44379i) q^{67} +(6.28572 - 3.70676i) q^{68} +(-13.5090 - 5.59561i) q^{69} +(2.91159 - 11.3603i) q^{70} +(-2.44190 + 2.44190i) q^{71} +(11.9390 - 5.13988i) q^{72} +7.04282i q^{73} +(3.45997 + 12.6787i) q^{74} +(11.0372 + 8.25050i) q^{75} +(0.599045 + 4.24718i) q^{76} +(-6.01920 + 14.5316i) q^{77} +(8.06712 - 6.24942i) q^{78} +0.203871i q^{79} +(7.22847 + 5.26775i) q^{80} -1.66719i q^{81} +(2.00064 + 2.58255i) q^{82} +(-2.40680 + 5.81053i) q^{83} +(16.3315 + 12.2940i) q^{84} +(-6.44127 + 5.00729i) q^{85} +(-8.66905 + 2.36576i) q^{86} +14.4209i q^{87} +(-8.59904 - 8.36438i) q^{88} +(-1.94360 + 1.94360i) q^{89} +(-12.5056 + 7.40311i) q^{90} +(8.97054 + 3.71572i) q^{91} +(10.2743 + 2.65170i) q^{92} +(1.51876 - 3.66661i) q^{93} +(4.69079 - 3.63385i) q^{94} +(-1.27029 - 4.62419i) q^{95} +(-13.3184 + 8.10434i) q^{96} +(3.62241 + 3.62241i) q^{97} +(-1.20294 + 9.47459i) q^{98} +(18.0075 - 7.45896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 20 q^{22}+ \cdots + 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 16 * q^19 - 32 * q^20 - 8 * q^21 - 20 * q^22 - 8 * q^23 + 32 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 20 * q^28 + 64 * q^30 + 16 * q^32 - 8 * q^33 - 8 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 4 * q^38 + 16 * q^40 - 8 * q^41 - 68 * q^42 + 28 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 88 * q^48 + 40 * q^49 + 4 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^53 + 56 * q^54 + 28 * q^55 + 40 * q^56 - 36 * q^58 + 12 * q^60 - 40 * q^61 - 32 * q^62 - 56 * q^63 - 48 * q^64 - 8 * q^65 + 72 * q^66 - 28 * q^67 + 8 * q^68 - 24 * q^69 + 4 * q^70 + 24 * q^71 + 88 * q^72 - 16 * q^75 + 56 * q^76 - 32 * q^77 + 112 * q^78 + 80 * q^80 + 68 * q^82 + 36 * q^83 - 56 * q^84 - 4 * q^85 + 24 * q^86 - 24 * q^88 - 84 * q^90 - 8 * q^91 + 92 * q^92 + 8 * q^93 + 32 * q^94 + 24 * q^96 - 8 * q^97 + 16 * q^98

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