LMFDB - Embedded newform 800.2.bb.b.643.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(107,800)] 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("800.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bb (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [88] 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			643.12
Character	$\chi$	$=$	800.643
Dual form			800.2.bb.b.107.12

$q$-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} +(-1.93321 - 3.38436i) q^{6} +3.70855 q^{7} +(-1.04614 - 2.62785i) q^{8} +(3.24959 - 3.24959i) q^{9} +(1.62306 + 3.91841i) q^{11} +(4.40374 - 3.31504i) q^{12} +(2.41888 - 1.00193i) q^{13} +(0.660586 + 5.20291i) q^{14} +(3.50040 - 1.93578i) q^{16} +(2.57998 + 2.57998i) q^{17} +(5.13785 + 3.98018i) q^{18} +(-0.820706 + 1.98136i) q^{19} +(-9.44280 + 3.91133i) q^{21} +(-5.20824 + 2.97504i) q^{22} +5.30550 q^{23} +(5.43526 + 5.58774i) q^{24} +(1.83653 + 3.21510i) q^{26} +(-1.68286 + 4.06279i) q^{27} +(-7.18176 + 1.85354i) q^{28} +(2.00240 - 4.83422i) q^{29} +1.44002i q^{31} +(3.33931 + 4.56607i) q^{32} +(-8.26535 - 8.26535i) q^{33} +(-3.16003 + 4.07914i) q^{34} +(-4.66882 + 7.91712i) q^{36} +(-8.58562 - 3.55628i) q^{37} +(-2.92594 - 0.798480i) q^{38} +(-5.10230 + 5.10230i) q^{39} +(1.63341 + 1.63341i) q^{41} +(-7.16941 - 12.5511i) q^{42} +(-2.43161 + 5.87042i) q^{43} +(-5.10156 - 6.77697i) q^{44} +(0.945044 + 7.44336i) q^{46} +(2.96683 - 2.96683i) q^{47} +(-6.87117 + 8.62072i) q^{48} +6.75333 q^{49} +(-9.29026 - 3.84815i) q^{51} +(-4.18350 + 3.14925i) q^{52} +(-2.41336 - 0.999648i) q^{53} +(-5.99965 - 1.63729i) q^{54} +(-3.87968 - 9.74550i) q^{56} -5.91057i q^{57} +(7.13886 + 1.94817i) q^{58} +(2.10156 + 5.07362i) q^{59} +(-6.83341 - 2.83049i) q^{61} +(-2.02027 + 0.256503i) q^{62} +(12.0513 - 12.0513i) q^{63} +(-5.81116 + 5.49822i) q^{64} +(10.1236 - 13.0682i) q^{66} +(3.49753 + 8.44379i) q^{67} +(-6.28572 - 3.70676i) q^{68} +(-13.5090 + 5.59561i) q^{69} +(-2.44190 - 2.44190i) q^{71} +(-11.9390 - 5.13988i) q^{72} +7.04282i q^{73} +(3.45997 - 12.6787i) q^{74} +(0.599045 - 4.24718i) q^{76} +(6.01920 + 14.5316i) q^{77} +(-8.06712 - 6.24942i) q^{78} -0.203871i q^{79} +1.66719i q^{81} +(-2.00064 + 2.58255i) q^{82} +(2.40680 + 5.81053i) q^{83} +(16.3315 - 12.2940i) q^{84} +(-8.66905 - 2.36576i) q^{86} +14.4209i q^{87} +(8.59904 - 8.36438i) q^{88} +(-1.94360 - 1.94360i) q^{89} +(8.97054 - 3.71572i) q^{91} +(-10.2743 + 2.65170i) q^{92} +(-1.51876 - 3.66661i) q^{93} +(4.69079 + 3.63385i) q^{94} +(-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} - 8 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{19} - 8 q^{21} + 20 q^{22} + 8 q^{23} + 32 q^{24} - 8 q^{26} - 8 q^{27}+ \cdots - 16 q^{98}+O(q^{100}) $ 88 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 + 4 * q^13 - 16 * q^14 - 8 * q^16 + 12 * q^18 - 16 * q^19 - 8 * q^21 + 20 * q^22 + 8 * q^23 + 32 * q^24 - 8 * q^26 - 8 * q^27 + 20 * q^28 - 16 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 4 * q^37 + 4 * q^38 - 8 * q^41 + 68 * q^42 - 28 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^47 + 88 * q^48 + 40 * q^49 + 8 * q^51 - 48 * q^52 + 4 * q^53 + 56 * q^54 + 40 * q^56 + 36 * q^58 - 40 * q^61 + 32 * q^62 + 56 * q^63 - 48 * q^64 + 72 * q^66 + 28 * q^67 - 8 * q^68 - 24 * q^69 + 24 * q^71 - 88 * q^72 + 56 * q^76 + 32 * q^77 - 112 * q^78 - 68 * q^82 - 36 * q^83 - 56 * q^84 + 24 * q^86 + 24 * q^88 - 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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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	$-0.917840\pi$
$3$	−2.54622	+	1.05468i	−1.47006	+	0.608920i	−0.503190	+	0.864176i	$0.667840\pi$
$4$	−1.93654	+	0.499802i	−0.968271	+	0.249901i
$5$		0			0
$5$		0			0
$6$	−1.93321	−	3.38436i	−0.789231	−	1.38166i
$7$	3.70855			1.40170			0.700850	−	0.713309i	$-0.252804\pi$
$7$	3.70855			1.40170			0.700850	+	0.713309i	$0.252804\pi$
$8$	−1.04614	−	2.62785i	−0.369868	−	0.929084i
$9$	3.24959	−	3.24959i	1.08320	−	1.08320i
$10$		0			0
$11$	1.62306	+	3.91841i	0.489371	+	1.18145i	0.955037	+	0.296486i	$0.0958148\pi$
$11$	1.62306	+	3.91841i	0.489371	+	1.18145i	−0.465666	+	0.884961i	$0.654185\pi$
$12$	4.40374	−	3.31504i	1.27125	−	0.956970i
$13$	2.41888	−	1.00193i	0.670877	−	0.277886i	−0.0211303	−	0.999777i	$-0.506726\pi$
$13$	2.41888	−	1.00193i	0.670877	−	0.277886i	0.692008	+	0.721890i	$0.256726\pi$
$14$	0.660586	+	5.20291i	0.176549	+	1.39054i
$15$		0			0
$16$	3.50040	−	1.93578i	0.875099	−	0.483944i
$17$	2.57998	+	2.57998i	0.625737	+	0.625737i	0.946993	−	0.321256i	$-0.104105\pi$
$17$	2.57998	+	2.57998i	0.625737	+	0.625737i	−0.321256	+	0.946993i	$0.604105\pi$
$18$	5.13785	+	3.98018i	1.21100	+	0.938137i
$19$	−0.820706	+	1.98136i	−0.188283	+	0.454555i	−0.989629	−	0.143646i	$-0.954117\pi$
$19$	−0.820706	+	1.98136i	−0.188283	+	0.454555i	0.801346	+	0.598201i	$0.204117\pi$
$20$		0			0
$21$	−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	$-0.313431\pi$
$23$	5.30550			1.10627			0.553137	+	0.833091i	$0.313431\pi$
$24$	5.43526	+	5.58774i	1.10947	+	1.14059i
$25$		0			0
$26$	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	−0.621603	−	0.783333i	$-0.713518\pi$
$29$	2.00240	−	4.83422i	0.371837	−	0.897693i	0.993439	−	0.114360i	$-0.0364818\pi$
$30$		0			0
$31$			1.44002i			0.258635i	0.991603	+	0.129317i	$0.0412786\pi$
$31$			1.44002i			0.258635i	−0.991603	+	0.129317i	$0.958721\pi$
$32$	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
$35$		0			0
$36$	−4.66882	+	7.91712i	−0.778136	+	1.31952i
$37$	−8.58562	−	3.55628i	−1.41147	−	0.584649i	−0.458766	−	0.888557i	$-0.651708\pi$
$37$	−8.58562	−	3.55628i	−1.41147	−	0.584649i	−0.952701	+	0.303908i	$0.901708\pi$
$38$	−2.92594	−	0.798480i	−0.474650	−	0.129531i
$39$	−5.10230	+	5.10230i	−0.817021	+	0.817021i
$40$		0			0
$41$	1.63341	+	1.63341i	0.255096	+	0.255096i	0.823056	−	0.567960i	$-0.192267\pi$
$41$	1.63341	+	1.63341i	0.255096	+	0.255096i	−0.567960	+	0.823056i	$0.692267\pi$
$42$	−7.16941	−	12.5511i	−1.10626	−	1.93667i
$43$	−2.43161	+	5.87042i	−0.370817	+	0.895231i	0.622796	+	0.782385i	$0.285997\pi$
$43$	−2.43161	+	5.87042i	−0.370817	+	0.895231i	−0.993612	+	0.112847i	$0.964003\pi$
$44$	−5.10156	−	6.77697i	−0.769089	−	1.02167i
$45$		0			0
$46$	0.945044	+	7.44336i	0.139339	+	1.09746i
$47$	2.96683	−	2.96683i	0.432757	−	0.432757i	−0.456808	−	0.889565i	$-0.651007\pi$
$47$	2.96683	−	2.96683i	0.432757	−	0.432757i	0.889565	+	0.456808i	$0.151007\pi$
$48$	−6.87117	+	8.62072i	−0.991768	+	1.24429i
$49$	6.75333			0.964762
$50$		0			0
$51$	−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	$-0.432418\pi$
$53$	−2.41336	−	0.999648i	−0.331501	−	0.137312i	−0.542225	+	0.840233i	$0.682418\pi$
$54$	−5.99965	−	1.63729i	−0.816449	−	0.222806i
$55$		0			0
$56$	−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	0.999632	−	0.0271319i	$-0.00863741\pi$
$59$	2.10156	+	5.07362i	0.273600	+	0.660529i	−0.726032	+	0.687661i	$0.758637\pi$
$60$		0			0
$61$	−6.83341	−	2.83049i	−0.874928	−	0.362407i	−0.100401	−	0.994947i	$-0.532012\pi$
$61$	−6.83341	−	2.83049i	−0.874928	−	0.362407i	−0.774528	+	0.632540i	$0.782012\pi$
$62$	−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
$65$		0			0
$66$	10.1236	−	13.0682i	1.24613	−	1.60858i
$67$	3.49753	+	8.44379i	0.427291	+	1.03157i	0.980143	+	0.198293i	$0.0635397\pi$
$67$	3.49753	+	8.44379i	0.427291	+	1.03157i	−0.552852	+	0.833280i	$0.686460\pi$
$68$	−6.28572	−	3.70676i	−0.762256	−	0.449511i
$69$	−13.5090	+	5.59561i	−1.62629	+	0.673632i
$70$		0			0
$71$	−2.44190	−	2.44190i	−0.289800	−	0.289800i	0.547201	−	0.837001i	$-0.315693\pi$
$71$	−2.44190	−	2.44190i	−0.289800	−	0.289800i	−0.837001	+	0.547201i	$0.815693\pi$
$72$	−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
$75$		0			0
$76$	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	$-0.996349\pi$
$79$		−	0.203871i		−	0.0229372i	0.999934	−	0.0114686i	$-0.00365066\pi$
$80$		0			0
$81$			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	$-0.0128217\pi$
$83$	2.40680	+	5.81053i	0.264181	+	0.637789i	−0.735008	+	0.678058i	$0.762822\pi$
$84$	16.3315	−	12.2940i	1.78191	−	1.34138i
$85$		0			0
$86$	−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	0.596553	−	0.802574i	$-0.296537\pi$
$89$	−1.94360	−	1.94360i	−0.206021	−	0.206021i	−0.802574	+	0.596553i	$0.796537\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	−13.3184	−	8.10434i	−1.35930	−	0.827146i
$97$	−3.62241	+	3.62241i	−0.367800	+	0.367800i	−0.866674	−	0.498874i	$-0.833747\pi$
$97$	−3.62241	+	3.62241i	−0.367800	+	0.367800i	0.498874	+	0.866674i	$0.333747\pi$
$98$	1.20294	+	9.47459i	0.121515	+	0.957079i
$99$	18.0075	+	7.45896i	1.80982	+	0.749653i
$100$		0			0
$101$	0.775088	+	1.87123i	0.0771241	+	0.186194i	0.957739	−	0.287639i	$-0.0928702\pi$
$101$	0.775088	+	1.87123i	0.0771241	+	0.186194i	−0.880615	+	0.473833i	$0.842870\pi$
$102$	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
$105$		0			0
$106$	0.972577	−	3.56390i	0.0944650	−	0.346156i
$107$	17.3854	+	7.20128i	1.68071	+	0.696174i	0.999360	−	0.0357808i	$-0.0113918\pi$
$107$	17.3854	+	7.20128i	1.68071	+	0.696174i	0.681353	+	0.731955i	$0.261392\pi$
$108$	1.22834	−	8.70885i	0.118197	−	0.838010i
$109$	0.773533	+	0.320408i	0.0740910	+	0.0306895i	0.419421	−	0.907792i	$-0.362233\pi$
$109$	0.773533	+	0.320408i	0.0740910	+	0.0306895i	−0.345330	+	0.938481i	$0.612233\pi$
$110$		0			0
$111$	25.6117			2.43095
$112$	12.9814	−	7.17892i	1.22663	−	0.678344i
$113$	10.6418	−	10.6418i	1.00110	−	1.00110i	0.00110032	−	0.999999i	$-0.499650\pi$
$113$	10.6418	−	10.6418i	1.00110	−	1.00110i	0.999999	−	0.00110032i	$-0.000350244\pi$
$114$	8.29224	−	1.05282i	0.776640	−	0.0986058i
$115$		0			0
$116$	−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
$120$		0			0
$121$	−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
$125$		0			0
$126$	19.0540	+	14.7607i	1.69746	+	1.31499i
$127$	−12.9680	−	12.9680i	−1.15073	−	1.15073i	−0.986407	−	0.164320i	$-0.947457\pi$
$127$	−12.9680	−	12.9680i	−1.15073	−	1.15073i	−0.164320	−	0.986407i	$-0.552543\pi$
$128$	−8.74884	−	7.17340i	−0.773296	−	0.634045i
$129$		−	17.5120i		−	1.54184i
$130$		0			0
$131$	−8.35611	+	20.1734i	−0.730076	+	1.76256i	−0.0877325	+	0.996144i	$0.527962\pi$
$131$	−8.35611	+	20.1734i	−0.730076	+	1.76256i	−0.642344	+	0.766416i	$0.722038\pi$
$132$	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
$135$		0			0
$136$	4.08076	−	9.47883i	0.349922	−	0.812803i
$137$	1.88186			0.160778			0.0803892	−	0.996764i	$-0.474384\pi$
$137$	1.88186			0.160778			0.0803892	+	0.996764i	$0.474384\pi$
$138$	−10.2567	−	17.9557i	−0.873105	−	1.52849i
$139$	−0.549075	+	0.227434i	−0.0465719	+	0.0192907i	−0.405848	−	0.913941i	$-0.633024\pi$
$139$	−0.549075	+	0.227434i	−0.0465719	+	0.0192907i	0.359276	+	0.933231i	$0.383024\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	0.709917	−	0.704286i	$-0.248733\pi$
$149$	−3.54082	−	8.54830i	−0.290076	−	0.700304i	−0.999992	+	0.00398147i	$0.998733\pi$
$150$		0			0
$151$	7.95693	−	7.95693i	0.647526	−	0.647526i	−0.304869	−	0.952394i	$-0.598613\pi$
$151$	7.95693	−	7.95693i	0.647526	−	0.647526i	0.952394	+	0.304869i	$0.0986126\pi$
$152$	6.06529	+	0.0839008i	0.491960	+	0.00680525i
$153$	16.7677			1.35559
$154$	−19.3150	+	11.0331i	−1.55645	+	0.889072i
$155$		0			0
$156$	7.33068	−	12.4310i	0.586924	−	0.995273i
$157$	11.4649	−	4.74892i	0.914999	−	0.379005i	0.125031	−	0.992153i	$-0.460097\pi$
$157$	11.4649	−	4.74892i	0.914999	−	0.379005i	0.789968	+	0.613148i	$0.210097\pi$
$158$	0.286021	−	0.0363145i	0.0227546	−	0.00288903i
$159$	7.19928			0.570940
$160$		0			0
$161$	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	$-0.782827\pi$
$163$	−11.2235	+	4.64892i	−0.879091	+	0.364131i	−0.102947	+	0.994687i	$0.532827\pi$
$164$	−3.97955	−	2.34679i	−0.310751	−	0.183253i
$165$		0			0
$166$	−7.72318	+	4.41163i	−0.599435	+	0.342409i
$167$	−17.1661			−1.32835			−0.664175	−	0.747578i	$-0.731217\pi$
$167$	−17.1661			−1.32835			−0.664175	+	0.747578i	$0.731217\pi$
$168$	20.1569	+	20.7224i	1.55514	+	1.59877i
$169$	−4.34527	+	4.34527i	−0.334251	+	0.334251i
$170$		0			0
$171$	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	$-0.699443\pi$
$173$	−5.63214	+	2.33291i	−0.428204	+	0.177368i	0.158164	+	0.987413i	$0.449443\pi$
$174$	−20.2318	+	2.56873i	−1.53377	+	0.194735i
$175$		0			0
$176$	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	−0.702666	−	0.711520i	$-0.748007\pi$
$179$	3.97779	−	9.60324i	0.297314	−	0.717780i	0.999980	−	0.00626044i	$-0.00199277\pi$
$180$		0			0
$181$	22.2181	−	9.20303i	1.65146	−	0.684056i	0.654079	−	0.756427i	$-0.273057\pi$
$181$	22.2181	−	9.20303i	1.65146	−	0.684056i	0.997378	+	0.0723710i	$0.0230566\pi$
$182$	6.81085	+	11.9234i	0.504854	+	0.883819i
$183$	20.3847			1.50688
$184$	−5.55032	−	13.9420i	−0.409175	−	1.02782i
$185$		0			0
$186$	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
$190$		0			0
$191$		−	8.62257i		−	0.623907i	−0.950097	−	0.311954i	$-0.899017\pi$
$191$		−	8.62257i		−	0.623907i	0.950097	−	0.311954i	$-0.100983\pi$
$192$	8.99766	−	20.1286i	0.649350	−	1.45266i
$193$	−13.1126	−	13.1126i	−0.943862	−	0.943862i	0.0546439	−	0.998506i	$-0.482598\pi$
$193$	−13.1126	−	13.1126i	−0.943862	−	0.943862i	−0.998506	+	0.0546439i	$0.982598\pi$
$194$	−5.72731	−	4.43683i	−0.411197	−	0.318546i
$195$		0			0
$196$	−13.0781	+	3.37533i	−0.934151	+	0.241095i
$197$	10.3876	+	4.30267i	0.740083	+	0.306552i	0.720688	−	0.693260i	$-0.243826\pi$
$197$	10.3876	+	4.30267i	0.740083	+	0.306552i	0.0193947	+	0.999812i	$0.493826\pi$
$198$	−7.25696	+	26.5923i	−0.515729	+	1.88983i
$199$	1.56365	−	1.56365i	0.110844	−	0.110844i	−0.649510	−	0.760353i	$-0.725026\pi$
$199$	1.56365	−	1.56365i	0.110844	−	0.110844i	0.760353	+	0.649510i	$0.225026\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	−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
$210$		0			0
$211$	−4.96614	−	2.05704i	−0.341883	−	0.141613i	0.205134	−	0.978734i	$-0.434237\pi$
$211$	−4.96614	−	2.05704i	−0.341883	−	0.141613i	−0.547017	+	0.837121i	$0.684237\pi$
$212$	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
$215$		0			0
$216$	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
$220$		0			0
$221$	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	−0.153181	+	0.988198i	$0.548952\pi$
$223$	−17.0444	+	17.0444i	−1.14138	+	1.14138i	−0.988198	+	0.153181i	$0.951048\pi$
$224$	12.3840	+	16.9335i	0.827440	+	1.13142i
$225$		0			0
$226$	16.8256	+	13.0344i	1.11922	+	0.867035i
$227$	−9.95905	−	24.0433i	−0.661005	−	1.59581i	−0.796231	−	0.604993i	$-0.793176\pi$
$227$	−9.95905	−	24.0433i	−0.661005	−	1.59581i	0.135225	−	0.990815i	$-0.456824\pi$
$228$	2.95412	+	11.4461i	0.195641	+	0.758035i
$229$	−15.6688	+	6.49021i	−1.03542	+	0.428885i	−0.834666	−	0.550756i	$-0.814339\pi$
$229$	−15.6688	+	6.49021i	−1.03542	+	0.428885i	−0.200755	+	0.979642i	$0.564339\pi$
$230$		0			0
$231$	−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
$235$		0			0
$236$	−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	$0.0565130\pi$
$239$			5.46064i			0.353219i	−0.984281	+	0.176610i	$0.943487\pi$
$240$		0			0
$241$			25.7625i			1.65951i	0.558127	+	0.829755i	$0.311520\pi$
$241$			25.7625i			1.65951i	−0.558127	+	0.829755i	$0.688480\pi$
$242$	−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
$245$		0			0
$246$	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
$250$		0			0
$251$	7.97245	−	3.30230i	0.503217	−	0.208439i	−0.116610	−	0.993178i	$-0.537203\pi$
$251$	7.97245	−	3.30230i	0.503217	−	0.208439i	0.619827	+	0.784739i	$0.287203\pi$
$252$	−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
$255$		0			0
$256$	8.50554	−	13.5520i	0.531596	−	0.846998i
$257$	15.1455	−	15.1455i	0.944747	−	0.944747i	−0.0538042	−	0.998552i	$-0.517135\pi$
$257$	15.1455	−	15.1455i	0.944747	−	0.944747i	0.998552	+	0.0538042i	$0.0171347\pi$
$258$	24.5685	−	3.11933i	1.52957	−	0.194201i
$259$	−31.8402	−	13.1886i	−1.97845	−	0.819502i
$260$		0			0
$261$	−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
$265$		0			0
$266$	−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	0.903480	−	0.428631i	$-0.141004\pi$
$269$	20.3252	+	8.41897i	1.23925	+	0.513314i	0.335769	+	0.941944i	$0.391004\pi$
$270$		0			0
$271$	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
$275$		0			0
$276$	23.3641	−	17.5880i	1.40635	−	1.05867i
$277$	8.98606	−	21.6943i	0.539920	−	1.30348i	−0.384858	−	0.922976i	$-0.625750\pi$
$277$	8.98606	−	21.6943i	0.539920	−	1.30348i	0.924778	−	0.380507i	$-0.124250\pi$
$278$	−0.416883	−	0.729813i	−0.0250030	−	0.0437713i
$279$	4.67946	+	4.67946i	0.280152	+	0.280152i
$280$		0			0
$281$	5.32879	−	5.32879i	0.317889	−	0.317889i	−0.530067	−	0.847956i	$-0.677833\pi$
$281$	5.32879	−	5.32879i	0.317889	−	0.317889i	0.847956	+	0.530067i	$0.177833\pi$
$282$	−15.7764	−	4.30532i	−0.939469	−	0.256378i
$283$	−10.2587	−	4.24930i	−0.609818	−	0.252595i	0.0563329	−	0.998412i	$-0.482059\pi$
$283$	−10.2587	−	4.24930i	−0.609818	−	0.252595i	−0.666151	+	0.745817i	$0.732059\pi$
$284$	5.94931	+	3.50838i	0.353026	+	0.208184i
$285$		0			0
$286$	−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
$290$		0			0
$291$	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	$-0.769804\pi$
$293$	4.25127	−	10.2635i	0.248362	−	0.599598i	0.998065	+	0.0621758i	$0.0198040\pi$
$294$	−13.0556	−	22.8557i	−0.761420	−	1.33297i
$295$		0			0
$296$	−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
$300$		0			0
$301$	−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
$305$		0			0
$306$	2.98676	+	23.5243i	0.170742	+	1.34480i
$307$	0.897767	−	0.371867i	0.0512383	−	0.0212236i	−0.356917	−	0.934136i	$-0.616172\pi$
$307$	0.897767	−	0.371867i	0.0512383	−	0.0212236i	0.408155	+	0.912912i	$0.366172\pi$
$308$	−18.9194	−	25.1327i	−1.07803	−	1.43207i
$309$	−4.06366	−	9.81054i	−0.231173	−	0.558102i
$310$		0			0
$311$	−6.73409	+	6.73409i	−0.381855	+	0.381855i	−0.871770	−	0.489915i	$-0.837028\pi$
$311$	−6.73409	+	6.73409i	−0.381855	+	0.381855i	0.489915	+	0.871770i	$0.337028\pi$
$312$	18.7458	+	8.07032i	1.06127	+	0.456892i
$313$	7.44365			0.420740			0.210370	−	0.977622i	$-0.432533\pi$
$313$	7.44365			0.420740			0.210370	+	0.977622i	$0.432533\pi$
$314$	8.70469	+	15.2388i	0.491234	+	0.859975i
$315$		0			0
$316$	0.101895	+	0.394804i	0.00573204	+	0.0222095i
$317$	5.47419	−	2.26749i	0.307461	−	0.127355i	−0.223618	−	0.974677i	$-0.571787\pi$
$317$	5.47419	−	2.26749i	0.307461	−	0.127355i	0.531079	+	0.847322i	$0.321787\pi$
$318$	1.28237	+	10.1002i	0.0719119	+	0.566393i
$319$	22.1925			1.24254
$320$		0			0
$321$	−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
$325$		0			0
$326$	−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
$330$		0			0
$331$	−6.91960	−	16.7054i	−0.380336	−	0.918212i	−0.991900	−	0.127018i	$-0.959460\pi$
$331$	−6.91960	−	16.7054i	−0.380336	−	0.918212i	0.611565	−	0.791195i	$-0.290540\pi$
$332$	−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
$335$		0			0
$336$	−25.4821	+	31.9704i	−1.39016	+	1.74413i
$337$	5.47917	+	5.47917i	0.298470	+	0.298470i	0.840414	−	0.541945i	$-0.182312\pi$
$337$	5.47917	+	5.47917i	0.298470	+	0.298470i	−0.541945	+	0.840414i	$0.682312\pi$
$338$	−6.87020	−	5.32220i	−0.373690	−	0.289489i
$339$	−15.8728	+	38.3202i	−0.862090	+	2.08127i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−4.27619	−	7.48607i	−0.229889	−	0.402454i
$347$	6.97500	−	16.8391i	0.374438	−	0.903973i	−0.618549	−	0.785746i	$-0.712279\pi$
$347$	6.97500	−	16.8391i	0.374438	−	0.903973i	0.992987	−	0.118226i	$-0.0377209\pi$
$348$	−7.20760	−	27.9267i	−0.386368	−	1.49703i
$349$	1.95879	−	4.72895i	0.104852	−	0.253135i	−0.862743	−	0.505643i	$-0.831255\pi$
$349$	1.95879	−	4.72895i	0.104852	−	0.253135i	0.967595	+	0.252508i	$0.0812554\pi$
$350$		0			0
$351$			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	$-0.259146\pi$
$353$	−0.763353	−	0.763353i	−0.0406292	−	0.0406292i	−0.727130	+	0.686500i	$0.759146\pi$
$354$	13.1082	−	16.9208i	0.696694	−	0.899333i
$355$		0			0
$356$	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	−0.964862	−	0.262756i	$-0.915369\pi$
$359$	−13.3030	+	13.3030i	−0.702107	+	0.702107i	0.262756	+	0.964862i	$0.415369\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	3.63102	+	28.5987i	0.189797	+	1.49488i
$367$	−8.06357	+	8.06357i	−0.420915	+	0.420915i	−0.885519	−	0.464604i	$-0.846197\pi$
$367$	−8.06357	+	8.06357i	−0.420915	+	0.420915i	0.464604	+	0.885519i	$0.346197\pi$
$368$	18.5714	−	10.2703i	0.968099	−	0.535374i
$369$	10.6158			0.552638
$370$		0			0
$371$	−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	$-0.523116\pi$
$373$	−16.0127	−	6.63267i	−0.829105	−	0.343427i	−0.756549	+	0.653938i	$0.773116\pi$
$374$	−21.1127	−	5.76159i	−1.09171	−	0.297925i
$375$		0			0
$376$	−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	−0.952867	−	0.303388i	$-0.901882\pi$
$379$	−9.60968	−	23.1998i	−0.493616	−	1.19170i	0.459251	−	0.888307i	$-0.348118\pi$
$380$		0			0
$381$	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	$-0.674968\pi$
$383$	6.46368	−	6.46368i	0.330278	−	0.330278i	0.852692	+	0.522414i	$0.174968\pi$
$384$	29.8422	+	9.03786i	1.52288	+	0.461211i
$385$		0			0
$386$	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	0.325153	−	0.945661i	$-0.394584\pi$
$389$	24.1362	−	9.99755i	1.22375	−	0.506896i	0.898602	+	0.438766i	$0.144584\pi$
$390$		0			0
$391$	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			0
$396$	−38.6003	−	5.44440i	−1.93974	−	0.273591i
$397$	10.7897	+	26.0485i	0.541517	+	1.30734i	0.923652	+	0.383232i	$0.125189\pi$
$397$	10.7897	+	26.0485i	0.541517	+	1.30734i	−0.382135	+	0.924106i	$0.624811\pi$
$398$	2.47224	+	1.91519i	0.123922	+	0.0960000i
$399$		−	21.9196i		−	1.09735i
$400$		0			0
$401$		−	34.5054i		−	1.72312i	−0.507659	−	0.861558i	$-0.669489\pi$
$401$		−	34.5054i		−	1.72312i	0.507659	−	0.861558i	$-0.330511\pi$
$402$	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			0
$406$	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	0.954025	−	0.299728i	$-0.0968959\pi$
$409$	13.2323	+	13.2323i	0.654297	+	0.654297i	−0.299728	+	0.954025i	$0.596896\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	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	−0.266765	−	0.963761i	$-0.585955\pi$
$419$	−23.2713	−	9.63930i	−1.13688	−	0.470911i	−0.870114	+	0.492851i	$0.835955\pi$
$420$		0			0
$421$	−9.47180	−	22.8669i	−0.461627	−	1.11447i	−0.967729	−	0.251993i	$-0.918914\pi$
$421$	−9.47180	−	22.8669i	−0.461627	−	1.11447i	0.506102	−	0.862474i	$-0.331086\pi$
$422$	2.00133	−	7.33366i	0.0974234	−	0.356997i
$423$		−	19.2820i		−	0.937522i
$424$	−0.102194	+	7.38773i	−0.00496298	+	0.358780i
$425$		0			0
$426$	−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
$430$		0			0
$431$	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	0.182486	−	0.983208i	$-0.441586\pi$
$433$	24.2565	−	24.2565i	1.16569	−	1.16569i	0.983208	−	0.182486i	$-0.0584144\pi$
$434$	−7.49228	+	0.951255i	−0.359641	+	0.0456617i
$435$		0			0
$436$	−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	0.930086	−	0.367341i	$-0.119732\pi$
$439$	11.7908	+	11.7908i	0.562745	+	0.562745i	−0.367341	+	0.930086i	$0.619732\pi$
$440$		0			0
$441$	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	$-0.228126\pi$
$443$	17.3149	+	7.17207i	0.822656	+	0.340755i	0.0686646	+	0.997640i	$0.478126\pi$
$444$	−49.5981	+	12.8008i	−2.35382	+	0.607497i
$445$		0			0
$446$	−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	$0.303563\pi$
$449$			34.5622i			1.63109i	−0.578693	+	0.815546i	$0.696437\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	−15.5321	+	6.18331i	−0.727356	+	0.289560i
$457$	−39.6621			−1.85532			−0.927658	−	0.373430i	$-0.878182\pi$
$457$	−39.6621			−1.85532			−0.927658	+	0.373430i	$0.878182\pi$
$458$	−11.8965	−	20.8264i	−0.555885	−	0.973155i
$459$	−14.8236	+	6.14016i	−0.691909	+	0.286598i
$460$		0			0
$461$	−5.87134	+	14.1747i	−0.273456	+	0.660180i	−0.999626	−	0.0273342i	$-0.991298\pi$
$461$	−5.87134	+	14.1747i	−0.273456	+	0.660180i	0.726171	+	0.687514i	$0.241298\pi$
$462$	37.5439	−	48.4639i	1.74670	−	2.25474i
$463$	19.2066	+	19.2066i	0.892605	+	0.892605i	0.994768	−	0.102163i	$-0.0325764\pi$
$463$	19.2066	+	19.2066i	0.892605	+	0.892605i	−0.102163	+	0.994768i	$0.532576\pi$
$464$	−2.34878	−	20.7979i	−0.109039	−	0.965518i
$465$		0			0
$466$	−31.4631	+	3.99470i	−1.45750	+	0.185051i
$467$	−13.7733	+	5.70508i	−0.637352	+	0.264000i	−0.677873	−	0.735179i	$-0.737098\pi$
$467$	−13.7733	+	5.70508i	−0.637352	+	0.264000i	0.0405215	+	0.999179i	$0.487098\pi$
$468$	−3.36089	+	23.8284i	−0.155357	+	1.10147i
$469$	12.9708	+	31.3142i	0.598934	+	1.44595i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−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	$0.568568\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	21.8428	−	12.4770i	0.990808	−	0.565968i
$487$	5.49190			0.248862			0.124431	−	0.992228i	$-0.460289\pi$
$487$	5.49190			0.248862			0.124431	+	0.992228i	$0.460289\pi$
$488$	−0.289361	+	20.9183i	−0.0130988	+	0.946925i
$489$	23.6744	−	23.6744i	1.07059	−	1.07059i
$490$		0			0
$491$	−3.70433	−	8.94304i	−0.167174	−	0.403594i	0.817985	−	0.575240i	$-0.195091\pi$
$491$	−3.70433	−	8.94304i	−0.167174	−	0.403594i	−0.985159	+	0.171646i	$0.945091\pi$
$492$	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
$495$		0			0
$496$	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	−0.822986	−	0.568062i	$-0.807693\pi$
$499$	3.58828	−	8.66289i	0.160634	−	0.387804i	0.983619	+	0.180258i	$0.0576933\pi$
$500$		0			0
$501$	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	$-0.495504\pi$
$503$	0.633548			0.0282485			0.0141243	+	0.999900i	$0.495504\pi$
$504$	−44.2762	−	19.0615i	−1.97222	−	0.849067i
$505$		0			0
$506$	−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	0.656644	+	0.754201i	$0.271975\pi$
$509$	−7.69272	+	18.5719i	−0.340974	+	0.823183i	−0.997618	+	0.0689828i	$0.978025\pi$
$510$		0			0
$511$			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
$515$		0			0
$516$	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
$520$		0			0
$521$	−1.28598	−	1.28598i	−0.0563400	−	0.0563400i	0.678375	−	0.734715i	$-0.262684\pi$
$521$	−1.28598	−	1.28598i	−0.0563400	−	0.0563400i	−0.734715	+	0.678375i	$0.762684\pi$
$522$	29.5291	−	16.8676i	1.29245	−	0.738274i
$523$	−1.71691	+	4.14499i	−0.0750754	+	0.181248i	−0.956962	−	0.290214i	$-0.906274\pi$
$523$	−1.71691	+	4.14499i	−0.0750754	+	0.181248i	0.881886	+	0.471462i	$0.156274\pi$
$524$	6.09924	−	43.2431i	0.266447	−	1.88908i
$525$		0			0
$526$	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
$530$		0			0
$531$	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
$535$		0			0
$536$	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			0
$541$	−19.1096	−	7.91546i	−0.821587	−	0.340312i	−0.0680201	−	0.997684i	$-0.521668\pi$
$541$	−19.1096	−	7.91546i	−0.821587	−	0.340312i	−0.753567	+	0.657372i	$0.771668\pi$
$542$	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
$545$		0			0
$546$	−29.9173	−	23.1763i	−1.28034	−	0.991854i
$547$	7.69432	+	18.5757i	0.328985	+	0.794241i	0.998668	+	0.0515935i	$0.0164300\pi$
$547$	7.69432	+	18.5757i	0.328985	+	0.794241i	−0.669683	+	0.742647i	$0.733570\pi$
$548$	−3.64431	+	0.940558i	−0.155677	+	0.0401787i
$549$	−31.4037	+	13.0078i	−1.34028	+	0.555161i
$550$		0			0
$551$	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
$555$		0			0
$556$	0.949635	−	0.714865i	0.0402735	−	0.0303170i
$557$	−8.02477	−	19.3735i	−0.340021	−	0.820882i	−0.997713	−	0.0675954i	$-0.978467\pi$
$557$	−8.02477	−	19.3735i	−0.340021	−	0.820882i	0.657692	−	0.753287i	$-0.271533\pi$
$558$	−5.73153	+	7.39859i	−0.242635	+	0.313207i
$559$			16.6362i			0.703635i
$560$		0			0
$561$		−	42.6489i		−	1.80064i
$562$	8.42522	+	6.52683i	0.355396	+	0.275318i
$563$	15.8057	+	38.1583i	0.666129	+	1.60818i	0.788030	+	0.615636i	$0.211101\pi$
$563$	15.8057	+	38.1583i	0.666129	+	1.60818i	−0.121901	+	0.992542i	$0.538899\pi$
$564$	3.22999	−	22.9003i	0.136007	−	0.964279i
$565$		0			0
$566$	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	0.297813	−	0.954624i	$-0.403743\pi$
$569$	−15.6674	−	15.6674i	−0.656811	−	0.656811i	−0.954624	+	0.297813i	$0.903743\pi$
$570$		0			0
$571$	23.0913	−	9.56473i	0.966340	−	0.400271i	0.156992	−	0.987600i	$-0.449820\pi$
$571$	23.0913	−	9.56473i	0.966340	−	0.400271i	0.809349	+	0.587329i	$0.199820\pi$
$572$	−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
$575$		0			0
$576$	−1.01694	+	36.7508i	−0.0423724	+	1.53128i
$577$	−27.8886	+	27.8886i	−1.16102	+	1.16102i	−0.176762	+	0.984254i	$0.556562\pi$
$577$	−27.8886	+	27.8886i	−1.16102	+	1.16102i	−0.984254	+	0.176762i	$0.943438\pi$
$578$	5.17325	−	0.656821i	0.215179	−	0.0273201i
$579$	47.2171	+	19.5579i	1.96227	+	0.812800i
$580$		0			0
$581$	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
$585$		0			0
$586$	15.1564	+	4.13613i	0.626105	+	0.170862i
$587$	−33.2273	−	13.7632i	−1.37144	−	0.568067i	−0.429258	−	0.903182i	$-0.641225\pi$
$587$	−33.2273	−	13.7632i	−1.37144	−	0.568067i	−0.942177	+	0.335114i	$0.891225\pi$
$588$	29.7399	−	22.3876i	1.22645	−	0.923248i
$589$	−2.85319	−	1.18183i	−0.117564	−	0.0486965i
$590$		0			0
$591$	−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	$-0.603757\pi$
$593$	15.2714	−	15.2714i	0.627123	−	0.627123i	0.947343	+	0.320220i	$0.103757\pi$
$594$	−3.32223	−	26.1665i	−0.136313	−	1.07363i
$595$		0			0
$596$	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	0.813669	−	0.581328i	$-0.197467\pi$
$599$	5.68644	+	5.68644i	0.232342	+	0.232342i	−0.581328	+	0.813669i	$0.697467\pi$
$600$		0			0
$601$	0.490584	−	0.490584i	0.0200113	−	0.0200113i	−0.697030	−	0.717042i	$-0.745496\pi$
$601$	0.490584	−	0.490584i	0.0200113	−	0.0200113i	0.717042	+	0.697030i	$0.245496\pi$
$602$	−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
$605$		0			0
$606$	4.83450	−	6.24066i	0.196388	−	0.253509i
$607$	−5.39237	−	5.39237i	−0.218870	−	0.218870i	0.589152	−	0.808022i	$-0.299462\pi$
$607$	−5.39237	−	5.39237i	−0.218870	−	0.218870i	−0.808022	+	0.589152i	$0.799462\pi$
$608$	−11.7876	+	2.86897i	−0.478051	+	0.116352i
$609$			53.4807i			2.16715i
$610$		0			0
$611$	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	−0.346244	−	0.938145i	$-0.612543\pi$
$613$	13.9134	−	33.5899i	0.561956	−	1.35668i	0.908200	−	0.418537i	$-0.137457\pi$
$614$	0.681627	+	1.19328i	0.0275082	+	0.0481570i
$615$		0			0
$616$	31.8900	−	31.0197i	1.28488	−	1.24982i
$617$	9.87023			0.397360			0.198680	−	0.980064i	$-0.436334\pi$
$617$	9.87023			0.397360			0.198680	+	0.980064i	$0.436334\pi$
$618$	13.0399	−	7.44862i	0.524540	−	0.299627i
$619$	−28.4293	+	11.7758i	−1.14267	+	0.473309i	−0.872069	−	0.489383i	$-0.837222\pi$
$619$	−28.4293	+	11.7758i	−1.14267	+	0.473309i	−0.270599	+	0.962692i	$0.587222\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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
$630$		0			0
$631$	3.97486	−	3.97486i	0.158236	−	0.158236i	−0.623548	−	0.781785i	$-0.714310\pi$
$631$	3.97486	−	3.97486i	0.158236	−	0.158236i	0.781785	+	0.623548i	$0.214310\pi$
$632$	−0.535741	+	0.213278i	−0.0213106	+	0.00848376i
$633$	14.8144			0.588821
$634$	4.15626	+	7.27613i	0.165066	+	0.288972i
$635$		0			0
$636$	−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
$640$		0			0
$641$	−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	$-0.458688\pi$
$643$	23.3820	−	9.68514i	0.922096	−	0.381945i	0.792675	+	0.609645i	$0.208688\pi$
$644$	−38.1028	+	9.83396i	−1.50146	+	0.387512i
$645$		0			0
$646$	−5.48880	−	9.60893i	−0.215954	−	0.378058i
$647$	3.30587			0.129967			0.0649836	−	0.997886i	$-0.479300\pi$
$647$	3.30587			0.129967			0.0649836	+	0.997886i	$0.479300\pi$
$648$	4.38112	−	1.74412i	0.172107	−	0.0685156i
$649$	−16.4696	+	16.4696i	−0.646488	+	0.646488i
$650$		0			0
$651$	−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	$-0.381282\pi$
$653$	32.7223	−	13.5540i	1.28052	−	0.530410i	0.916147	+	0.400842i	$0.131282\pi$
$654$	−0.411027	−	3.23733i	−0.0160724	−	0.126590i
$655$		0			0
$656$	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	−0.593147	−	0.805094i	$-0.702115\pi$
$659$	10.1544	−	24.5149i	0.395559	−	0.954964i	0.988706	−	0.149870i	$-0.0478854\pi$
$660$		0			0
$661$	−29.1101	+	12.0578i	−1.13225	+	0.468994i	−0.868545	−	0.495610i	$-0.834945\pi$
$661$	−29.1101	+	12.0578i	−1.13225	+	0.468994i	−0.263705	+	0.964603i	$0.584945\pi$
$662$	22.2043	−	12.6835i	0.862995	−	0.492959i
$663$	−26.3276			−1.02248
$664$	12.7513	−	12.4034i	0.494847	−	0.481344i
$665$		0			0
$666$	−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
$670$		0			0
$671$		−	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	$-0.357517\pi$
$673$	−12.1579	−	12.1579i	−0.468654	−	0.468654i	−0.901478	+	0.432824i	$0.857517\pi$
$674$	−6.71103	+	8.66299i	−0.258499	+	0.333686i
$675$		0			0
$676$	6.24302	−	10.5866i	0.240116	−	0.407176i
$677$	38.8974	+	16.1118i	1.49495	+	0.619228i	0.972387	−	0.233375i	$-0.0749768\pi$
$677$	38.8974	+	16.1118i	1.49495	+	0.619228i	0.522561	+	0.852602i	$0.324977\pi$
$678$	−56.5888	−	15.4429i	−2.17328	−	0.593081i
$679$	−13.4339	+	13.4339i	−0.515546	+	0.515546i
$680$		0			0
$681$	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	0.565955	+	0.824436i	$0.308508\pi$
$683$	−10.9032	+	26.3227i	−0.417200	+	1.00721i	−0.983155	+	0.182774i	$0.941492\pi$
$684$	−11.8549	−	15.7482i	−0.453285	−	0.602149i
$685$		0			0
$686$	−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
$690$		0			0
$691$	19.5933	+	8.11580i	0.745363	+	0.308740i	0.722848	−	0.691007i	$-0.242833\pi$
$691$	19.5933	+	8.11580i	0.745363	+	0.308740i	0.0225151	+	0.999747i	$0.492833\pi$
$692$	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
$695$		0			0
$696$	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
$700$		0			0
$701$	17.3571	+	7.18953i	0.655567	+	0.271545i	0.685572	−	0.728005i	$-0.259552\pi$
$701$	17.3571	+	7.18953i	0.655567	+	0.271545i	−0.0300049	+	0.999550i	$0.509552\pi$
$702$	−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
$705$		0			0
$706$	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	−0.370428	−	0.928861i	$-0.620789\pi$
$709$	0.650888	−	0.269607i	0.0244446	−	0.0101253i	0.394872	+	0.918736i	$0.370789\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	−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	$-0.719408\pi$
$719$		−	41.3849i		−	1.54340i	0.635989	−	0.771698i	$-0.280592\pi$
$720$		0			0
$721$			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
$725$		0			0
$726$	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
$730$		0			0
$731$	−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	−0.803476	−	0.595337i	$-0.797019\pi$
$733$	−17.7686	−	42.8973i	−0.656299	−	1.58445i	0.147177	−	0.989110i	$-0.452981\pi$
$734$	−12.7491	−	9.87647i	−0.470579	−	0.364547i
$735$		0			0
$736$	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	0.808705	−	0.588214i	$-0.200169\pi$
$739$	26.2226	+	10.8618i	0.964616	+	0.399557i	0.155911	+	0.987771i	$0.450169\pi$
$740$		0			0
$741$	−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
$745$		0			0
$746$	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
$750$		0			0
$751$	−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
$755$		0			0
$756$	4.55537	−	32.2972i	0.165677	−	1.17464i
$757$	−14.0127	+	33.8297i	−0.509302	+	1.22956i	0.434985	+	0.900438i	$0.356754\pi$
$757$	−14.0127	+	33.8297i	−0.509302	+	1.22956i	−0.944286	+	0.329125i	$0.893246\pi$
$758$	30.8365	−	17.6144i	1.12003	−	0.639783i
$759$	−43.8518	−	43.8518i	−1.59172	−	1.59172i
$760$		0			0
$761$	21.9685	−	21.9685i	0.796356	−	0.796356i	−0.186163	−	0.982519i	$-0.559605\pi$
$761$	21.9685	−	21.9685i	0.796356	−	0.796356i	0.982519	+	0.186163i	$0.0596051\pi$
$762$	−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
$765$		0			0
$766$	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	$-0.898634\pi$
$769$		−	17.3648i		−	0.626192i	0.949721	−	0.313096i	$-0.101366\pi$
$770$		0			0
$771$	−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	$-0.819960\pi$
$773$	3.66118	−	8.83886i	0.131683	−	0.317912i	0.975944	+	0.218021i	$0.0699601\pi$
$774$	−35.8586	+	20.4831i	−1.28891	+	0.736250i
$775$		0			0
$776$	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
$780$		0			0
$781$	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
$785$		0			0
$786$	84.4283	−	10.7194i	3.01146	−	0.382349i
$787$	32.0088	−	13.2585i	1.14099	−	0.472614i	0.269488	−	0.963004i	$-0.413146\pi$
$787$	32.0088	−	13.2585i	1.14099	−	0.472614i	0.871503	+	0.490390i	$0.163146\pi$
$788$	−22.2664	−	3.14058i	−0.793208	−	0.111878i
$789$	7.24913	+	17.5010i	0.258076	+	0.623050i
$790$		0			0
$791$	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
$795$		0			0
$796$	−2.24655	+	3.80958i	−0.0796270	+	0.135027i
$797$	37.8964	−	15.6972i	1.34236	−	0.556023i	0.408203	−	0.912891i	$-0.366156\pi$
$797$	37.8964	−	15.6972i	1.34236	−	0.556023i	0.934155	+	0.356868i	$0.116156\pi$
$798$	30.7522	−	3.90444i	1.08862	−	0.138216i
$799$	15.3087			0.541584
$800$		0			0
$801$	−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
$805$		0			0
$806$	−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	−0.782502	−	0.622648i	$-0.786057\pi$
$809$	−4.54672	+	4.54672i	−0.159854	+	0.159854i	0.622648	+	0.782502i	$0.286057\pi$
$810$		0			0
$811$	−8.69312	−	20.9871i	−0.305257	−	0.736955i	−0.999846	−	0.0175486i	$-0.994414\pi$
$811$	−8.69312	−	20.9871i	−0.305257	−	0.736955i	0.694589	−	0.719407i	$-0.255586\pi$
$812$	−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
$815$		0			0
$816$	−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
$820$		0			0
$821$	9.76690	−	4.04558i	0.340867	−	0.141192i	−0.205682	−	0.978619i	$-0.565941\pi$
$821$	9.76690	−	4.04558i	0.340867	−	0.141192i	0.546549	+	0.837427i	$0.315941\pi$
$822$	−3.63804	−	6.36890i	−0.126891	−	0.222141i
$823$	32.4078			1.12966			0.564832	−	0.825206i	$-0.308941\pi$
$823$	32.4078			1.12966			0.564832	+	0.825206i	$0.308941\pi$
$824$	10.1250	−	4.03077i	0.352722	−	0.140419i
$825$		0			0
$826$	−25.0093	+	14.2858i	−0.870187	+	0.497067i
$827$	6.17678	−	14.9121i	0.214788	−	0.518543i	−0.779360	−	0.626577i	$-0.784455\pi$
$827$	6.17678	−	14.9121i	0.214788	−	0.518543i	0.994147	+	0.108034i	$0.0344554\pi$
$828$	−24.7704	+	42.0043i	−0.860831	+	1.45975i
$829$	2.07649	−	5.01309i	0.0721194	−	0.174112i	−0.883709	−	0.468037i	$-0.844962\pi$
$829$	2.07649	−	5.01309i	0.0721194	−	0.174112i	0.955829	+	0.293925i	$0.0949616\pi$
$830$		0			0
$831$			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
$835$		0			0
$836$	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	−0.104110	+	0.994566i	$0.533199\pi$
$839$	−31.8237	+	31.8237i	−1.09868	+	1.09868i	−0.994566	+	0.104110i	$0.966801\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	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
$850$		0			0
$851$	−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	$-0.665395\pi$
$853$	−42.6825	−	17.6797i	−1.46142	−	0.605341i	−0.964884	+	0.262675i	$0.915395\pi$
$854$	10.2127	−	37.4234i	0.349473	−	1.28060i
$855$		0			0
$856$	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	−0.942029	−	0.335531i	$-0.891084\pi$
$859$	−15.0404	−	36.3106i	−0.513170	−	1.23890i	0.428859	−	0.903372i	$-0.358916\pi$
$860$		0			0
$861$	−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	0.404455	−	0.914558i	$-0.367461\pi$
$863$	38.7485	−	38.7485i	1.31901	−	1.31901i	0.914558	−	0.404455i	$-0.132539\pi$
$864$	−24.1706	+	5.88282i	−0.822299	+	0.200138i
$865$		0			0
$866$	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
$870$		0			0
$871$	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
$875$		0			0
$876$	23.3473	+	31.0148i	0.788831	+	1.04789i
$877$	−6.21828	−	15.0122i	−0.209976	−	0.506928i	0.783443	−	0.621464i	$-0.213462\pi$
$877$	−6.21828	−	15.0122i	−0.209976	−	0.506928i	−0.993419	+	0.114536i	$0.963462\pi$
$878$	−14.4417	+	18.6422i	−0.487384	+	0.629143i
$879$			30.6168i			1.03268i
$880$		0			0
$881$			29.0942i			0.980208i	0.871664	+	0.490104i	$0.163041\pi$
$881$			29.0942i			0.980208i	−0.871664	+	0.490104i	$0.836959\pi$
$882$	34.6976	+	26.8795i	1.16833	+	0.905079i
$883$	−13.2835	−	32.0692i	−0.447025	−	1.07921i	−0.973431	−	0.228980i	$-0.926461\pi$
$883$	−13.2835	−	32.0692i	−0.447025	−	1.07921i	0.526406	−	0.850233i	$-0.323539\pi$
$884$	−18.9183	−	2.66835i	−0.636293	−	0.0897462i
$885$		0			0
$886$	−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
$890$		0			0
$891$	−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
$895$		0			0
$896$	−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
$900$		0			0
$901$	−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
$905$		0			0
$906$	−42.3116	−	11.5467i	−1.40571	−	0.383614i
$907$	0.145961	+	0.0604591i	0.00484656	+	0.00200751i	0.385105	−	0.922873i	$-0.374165\pi$
$907$	0.145961	+	0.0604591i	0.00484656	+	0.00200751i	−0.380259	+	0.924880i	$0.624165\pi$
$908$	31.3030	+	41.5833i	1.03883	+	1.37999i
$909$	8.59943	+	3.56200i	0.285225	+	0.118144i
$910$		0			0
$911$	−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
$915$		0			0
$916$	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	0.322109	−	0.946703i	$-0.395608\pi$
$919$	−18.9346	−	18.9346i	−0.624593	−	0.624593i	−0.946703	+	0.322109i	$0.895608\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	$-0.992624\pi$
$929$		−	1.41239i		−	0.0463390i	0.999732	−	0.0231695i	$-0.00737573\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−34.0288	−	0.470718i	−1.11226	−	0.0153859i
$937$	12.6258			0.412468			0.206234	−	0.978503i	$-0.433879\pi$
$937$	12.6258			0.412468			0.206234	+	0.978503i	$0.433879\pi$
$938$	−41.6218	+	23.7752i	−1.35900	+	0.776287i
$939$	−18.9532	+	7.85068i	−0.618515	+	0.256197i
$940$		0			0
$941$	11.3405	−	27.3783i	0.369688	−	0.892507i	−0.624113	−	0.781334i	$-0.714539\pi$
$941$	11.3405	−	27.3783i	0.369688	−	0.892507i	0.993801	−	0.111172i	$-0.0354606\pi$
$942$	−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
$945$		0			0
$946$	−4.80037	−	37.8087i	−0.156073	−	1.22927i
$947$	−29.7484	+	12.3222i	−0.966694	+	0.400418i	−0.809480	−	0.587147i	$-0.800251\pi$
$947$	−29.7484	+	12.3222i	−0.966694	+	0.400418i	−0.157213	+	0.987565i	$0.550251\pi$
$948$	−0.675840	−	0.897794i	−0.0219503	−	0.0291590i
$949$	7.05644	+	17.0358i	0.229062	+	0.553004i
$950$		0			0
$951$	−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	$-0.0636632\pi$
$953$	60.5106			1.96013			0.980066	+	0.198673i	$0.0636632\pi$
$954$	−8.42072	−	14.7417i	−0.272631	−	0.477279i
$955$		0			0
$956$	−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
$960$		0			0
$961$	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
$965$		0			0
$966$	−38.0373	−	66.5897i	−1.22383	−	2.14249i
$967$	18.3324			0.589531			0.294766	−	0.955570i	$-0.404758\pi$
$967$	18.3324			0.589531			0.294766	+	0.955570i	$0.404758\pi$
$968$	18.1549	+	7.81594i	0.583522	+	0.251214i
$969$	15.2492	−	15.2492i	0.489873	−	0.489873i
$970$		0			0
$971$	0.992401	+	2.39587i	0.0318477	+	0.0768870i	0.939003	−	0.343908i	$-0.111751\pi$
$971$	0.992401	+	2.39587i	0.0318477	+	0.0768870i	−0.907156	+	0.420796i	$0.861751\pi$
$972$	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
$975$		0			0
$976$	−29.3988	+	3.32011i	−0.941034	+	0.106274i
$977$	−21.9823	−	21.9823i	−0.703276	−	0.703276i	0.261836	−	0.965112i	$-0.415672\pi$
$977$	−21.9823	−	21.9823i	−0.703276	−	0.703276i	−0.965112	+	0.261836i	$0.915672\pi$
$978$	37.4310	+	28.9970i	1.19691	+	0.927222i
$979$	4.46126	−	10.7704i	0.142582	−	0.344224i
$980$		0			0
$981$	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	$-0.676493\pi$
$983$	−33.0141			−1.05299			−0.526493	+	0.850180i	$0.676493\pi$
$984$	−0.249064	+	18.0051i	−0.00793985	+	0.573982i
$985$		0			0
$986$	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
$990$		0			0
$991$			1.26612i			0.0402198i	0.999798	+	0.0201099i	$0.00640161\pi$
$991$			1.26612i			0.0402198i	−0.999798	+	0.0201099i	$0.993598\pi$
$992$	−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
$995$		0			0
$996$	29.8611	+	17.6094i	0.946185	+	0.557976i
$997$	9.06030	+	3.75290i	0.286943	+	0.118856i	0.521512	−	0.853244i	$-0.325368\pi$
$997$	9.06030	+	3.75290i	0.286943	+	0.118856i	−0.234570	+	0.972099i	$0.575368\pi$
$998$	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	800.2.bb.b.643.12		88
5.2	odd	4		800.2.v.b.707.1		88
5.3	odd	4		160.2.u.a.67.22	yes	88
5.4	even	2		160.2.ba.a.3.11	yes	88
20.3	even	4		640.2.u.a.47.21		88
20.19	odd	2		640.2.ba.a.303.2		88
32.11	odd	8		800.2.v.b.43.1		88
160.43	even	8		160.2.ba.a.107.11	yes	88
160.53	odd	8		640.2.ba.a.207.2		88
160.107	even	8	inner	800.2.bb.b.107.12		88
160.139	odd	8		160.2.u.a.43.22	✓	88
160.149	even	8		640.2.u.a.463.21		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.22	✓	88	160.139	odd	8
160.2.u.a.67.22	yes	88	5.3	odd	4
160.2.ba.a.3.11	yes	88	5.4	even	2
160.2.ba.a.107.11	yes	88	160.43	even	8
640.2.u.a.47.21		88	20.3	even	4
640.2.u.a.463.21		88	160.149	even	8
640.2.ba.a.207.2		88	160.53	odd	8
640.2.ba.a.303.2		88	20.19	odd	2
800.2.v.b.43.1		88	32.11	odd	8
800.2.v.b.707.1		88	5.2	odd	4
800.2.bb.b.107.12		88	160.107	even	8	inner
800.2.bb.b.643.12		88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bb (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} +(-1.93321 - 3.38436i) q^{6} +3.70855 q^{7} +(-1.04614 - 2.62785i) q^{8} +(3.24959 - 3.24959i) q^{9} +(1.62306 + 3.91841i) q^{11} +(4.40374 - 3.31504i) q^{12} +(2.41888 - 1.00193i) q^{13} +(0.660586 + 5.20291i) q^{14} +(3.50040 - 1.93578i) q^{16} +(2.57998 + 2.57998i) q^{17} +(5.13785 + 3.98018i) q^{18} +(-0.820706 + 1.98136i) q^{19} +(-9.44280 + 3.91133i) q^{21} +(-5.20824 + 2.97504i) q^{22} +5.30550 q^{23} +(5.43526 + 5.58774i) q^{24} +(1.83653 + 3.21510i) q^{26} +(-1.68286 + 4.06279i) q^{27} +(-7.18176 + 1.85354i) q^{28} +(2.00240 - 4.83422i) q^{29} +1.44002i q^{31} +(3.33931 + 4.56607i) q^{32} +(-8.26535 - 8.26535i) q^{33} +(-3.16003 + 4.07914i) q^{34} +(-4.66882 + 7.91712i) q^{36} +(-8.58562 - 3.55628i) q^{37} +(-2.92594 - 0.798480i) q^{38} +(-5.10230 + 5.10230i) q^{39} +(1.63341 + 1.63341i) q^{41} +(-7.16941 - 12.5511i) q^{42} +(-2.43161 + 5.87042i) q^{43} +(-5.10156 - 6.77697i) q^{44} +(0.945044 + 7.44336i) q^{46} +(2.96683 - 2.96683i) q^{47} +(-6.87117 + 8.62072i) q^{48} +6.75333 q^{49} +(-9.29026 - 3.84815i) q^{51} +(-4.18350 + 3.14925i) q^{52} +(-2.41336 - 0.999648i) q^{53} +(-5.99965 - 1.63729i) q^{54} +(-3.87968 - 9.74550i) q^{56} -5.91057i q^{57} +(7.13886 + 1.94817i) q^{58} +(2.10156 + 5.07362i) q^{59} +(-6.83341 - 2.83049i) q^{61} +(-2.02027 + 0.256503i) q^{62} +(12.0513 - 12.0513i) q^{63} +(-5.81116 + 5.49822i) q^{64} +(10.1236 - 13.0682i) q^{66} +(3.49753 + 8.44379i) q^{67} +(-6.28572 - 3.70676i) q^{68} +(-13.5090 + 5.59561i) q^{69} +(-2.44190 - 2.44190i) q^{71} +(-11.9390 - 5.13988i) q^{72} +7.04282i q^{73} +(3.45997 - 12.6787i) q^{74} +(0.599045 - 4.24718i) q^{76} +(6.01920 + 14.5316i) q^{77} +(-8.06712 - 6.24942i) q^{78} -0.203871i q^{79} +1.66719i q^{81} +(-2.00064 + 2.58255i) q^{82} +(2.40680 + 5.81053i) q^{83} +(16.3315 - 12.2940i) q^{84} +(-8.66905 - 2.36576i) q^{86} +14.4209i q^{87} +(8.59904 - 8.36438i) q^{88} +(-1.94360 - 1.94360i) q^{89} +(8.97054 - 3.71572i) q^{91} +(-10.2743 + 2.65170i) q^{92} +(-1.51876 - 3.66661i) q^{93} +(4.69079 + 3.63385i) q^{94} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{19} - 8 q^{21} + 20 q^{22} + 8 q^{23} + 32 q^{24} - 8 q^{26} - 8 q^{27}+ \cdots - 16 q^{98}+O(q^{100}) \) 88 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 + 4 * q^13 - 16 * q^14 - 8 * q^16 + 12 * q^18 - 16 * q^19 - 8 * q^21 + 20 * q^22 + 8 * q^23 + 32 * q^24 - 8 * q^26 - 8 * q^27 + 20 * q^28 - 16 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 4 * q^37 + 4 * q^38 - 8 * q^41 + 68 * q^42 - 28 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^47 + 88 * q^48 + 40 * q^49 + 8 * q^51 - 48 * q^52 + 4 * q^53 + 56 * q^54 + 40 * q^56 + 36 * q^58 - 40 * q^61 + 32 * q^62 + 56 * q^63 - 48 * q^64 + 72 * q^66 + 28 * q^67 - 8 * q^68 - 24 * q^69 + 24 * q^71 - 88 * q^72 + 56 * q^76 + 32 * q^77 - 112 * q^78 - 68 * q^82 - 36 * q^83 - 56 * q^84 + 24 * q^86 + 24 * q^88 - 8 * q^91 - 92 * q^92 - 8 * q^93 + 32 * q^94 + 24 * q^96 + 8 * q^97 - 16 * q^98

Introduction

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