LMFDB - Embedded newform 680.2.co.a.99.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (of order $16$, degree $8$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			99.12
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32441 + 0.495923i) q^{2} +(1.03954 + 0.206777i) q^{3} +(1.50812 - 1.31361i) q^{4} +(-2.15293 - 0.604079i) q^{5} +(-1.47932 + 0.241673i) q^{6} +(0.290647 + 0.194204i) q^{7} +(-1.34592 + 2.48767i) q^{8} +(-1.73376 - 0.718147i) q^{9} +(3.15093 - 0.267637i) q^{10} +(-1.13528 + 0.225821i) q^{11} +(1.83937 - 1.05370i) q^{12} +(1.45311 + 1.45311i) q^{13} +(-0.481246 - 0.113067i) q^{14} +(-2.11313 - 1.07314i) q^{15} +(0.548854 - 3.96217i) q^{16} +(3.88693 - 1.37541i) q^{17} +(2.65235 + 0.0913087i) q^{18} +(3.93722 - 1.63085i) q^{19} +(-4.04040 + 1.91708i) q^{20} +(0.261981 + 0.261981i) q^{21} +(1.39158 - 0.862090i) q^{22} +(-1.11058 - 5.58325i) q^{23} +(-1.91352 + 2.30772i) q^{24} +(4.27018 + 2.60108i) q^{25} +(-2.64514 - 1.20388i) q^{26} +(-4.29764 - 2.87159i) q^{27} +(0.693440 - 0.0889139i) q^{28} +(4.03508 - 2.69616i) q^{29} +(3.33085 + 0.373320i) q^{30} +(1.84475 - 9.27417i) q^{31} +(1.23802 + 5.51972i) q^{32} -1.22686 q^{33} +(-4.46579 + 3.74923i) q^{34} +(-0.508427 - 0.593681i) q^{35} +(-3.55808 + 1.19443i) q^{36} +(1.69824 - 8.53762i) q^{37} +(-4.40571 + 4.11247i) q^{38} +(1.21009 + 1.81103i) q^{39} +(4.40041 - 4.54273i) q^{40} +(-6.46731 - 4.32132i) q^{41} +(-0.476893 - 0.217048i) q^{42} +(-2.93144 + 7.07713i) q^{43} +(-1.41550 + 1.83188i) q^{44} +(3.29884 + 2.59345i) q^{45} +(4.23972 + 6.84375i) q^{46} +(-3.81771 - 3.81771i) q^{47} +(1.38984 - 4.00532i) q^{48} +(-2.63202 - 6.35427i) q^{49} +(-6.94540 - 1.32721i) q^{50} +(4.32501 - 0.626065i) q^{51} +(4.10028 + 0.282644i) q^{52} +(-7.79451 + 3.22859i) q^{53} +(7.11592 + 1.67186i) q^{54} +(2.58058 + 0.199623i) q^{55} +(-0.874304 + 0.461651i) q^{56} +(4.43010 - 0.881202i) q^{57} +(-4.00702 + 5.57191i) q^{58} +(1.00326 - 2.42208i) q^{59} +(-4.59654 + 1.15742i) q^{60} +(3.98410 + 2.66209i) q^{61} +(2.15608 + 13.1977i) q^{62} +(-0.364445 - 0.545431i) q^{63} +(-4.37700 - 6.69640i) q^{64} +(-2.25064 - 4.00623i) q^{65} +(1.62486 - 0.608427i) q^{66} +9.04379 q^{67} +(4.05520 - 7.18020i) q^{68} -6.03363i q^{69} +(0.967786 + 0.534136i) q^{70} +(10.2573 + 2.04030i) q^{71} +(4.12001 - 3.34646i) q^{72} +(-2.12827 - 3.18517i) q^{73} +(1.98484 + 12.1495i) q^{74} +(3.90116 + 3.58688i) q^{75} +(3.79550 - 7.63149i) q^{76} +(-0.373821 - 0.154842i) q^{77} +(-2.50078 - 1.79843i) q^{78} +(2.18012 + 10.9602i) q^{79} +(-3.57510 + 8.19870i) q^{80} +(0.107115 + 0.107115i) q^{81} +(10.7084 + 2.51591i) q^{82} +(-15.5635 + 6.44659i) q^{83} +(0.739241 + 0.0509579i) q^{84} +(-9.19913 + 0.613146i) q^{85} +(0.372718 - 10.8268i) q^{86} +(4.75212 - 1.96839i) q^{87} +(0.966224 - 3.12813i) q^{88} +(5.85808 - 5.85808i) q^{89} +(-5.65516 - 1.79881i) q^{90} +(0.140142 + 0.704542i) q^{91} +(-9.00910 - 6.96135i) q^{92} +(3.83536 - 9.25938i) q^{93} +(6.94951 + 3.16292i) q^{94} +(-9.46170 + 1.13270i) q^{95} +(0.145620 + 5.99394i) q^{96} +(6.58914 - 4.40272i) q^{97} +(6.63710 + 7.11037i) q^{98} +(2.13047 + 0.423777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.32441	+	0.495923i	−0.936499	+	0.350671i
$2$	−1.32441	+	0.495923i	−0.936499	+	0.350671i
$3$	1.03954	+	0.206777i	0.600176	+	0.119383i	0.485822	−	0.874058i	$-0.338520\pi$
$3$	1.03954	+	0.206777i	0.600176	+	0.119383i	0.114354	+	0.993440i	$0.463520\pi$
$4$	1.50812	−	1.31361i	0.754060	−	0.656805i
$5$	−2.15293	−	0.604079i	−0.962818	−	0.270152i
$5$	−2.15293	−	0.604079i	−0.962818	−	0.270152i
$6$	−1.47932	+	0.241673i	−0.603928	+	0.0986627i
$7$	0.290647	+	0.194204i	0.109854	+	0.0734023i	0.609284	−	0.792952i	$-0.291457\pi$
$7$	0.290647	+	0.194204i	0.109854	+	0.0734023i	−0.499429	+	0.866355i	$0.666457\pi$
$8$	−1.34592	+	2.48767i	−0.475854	+	0.879524i
$9$	−1.73376	−	0.718147i	−0.577920	−	0.239382i
$10$	3.15093	−	0.267637i	0.996412	−	0.0846343i
$11$	−1.13528	+	0.225821i	−0.342299	+	0.0680875i	−0.363247	−	0.931693i	$-0.618332\pi$
$11$	−1.13528	+	0.225821i	−0.342299	+	0.0680875i	0.0209474	+	0.999781i	$0.493332\pi$
$12$	1.83937	−	1.05370i	0.530980	−	0.304177i
$13$	1.45311	+	1.45311i	0.403020	+	0.403020i	0.879296	−	0.476276i	$-0.158014\pi$
$13$	1.45311	+	1.45311i	0.403020	+	0.403020i	−0.476276	+	0.879296i	$0.658014\pi$
$14$	−0.481246	−	0.113067i	−0.128619	−	0.0302185i
$15$	−2.11313	−	1.07314i	−0.545609	−	0.277083i
$16$	0.548854	−	3.96217i	0.137214	−	0.990541i
$17$	3.88693	−	1.37541i	0.942719	−	0.333587i
$17$	3.88693	−	1.37541i	0.942719	−	0.333587i
$18$	2.65235	+	0.0913087i	0.625166	+	0.0215217i
$19$	3.93722	−	1.63085i	0.903260	−	0.374142i	0.117787	−	0.993039i	$-0.462420\pi$
$19$	3.93722	−	1.63085i	0.903260	−	0.374142i	0.785473	+	0.618896i	$0.212420\pi$
$20$	−4.04040	+	1.91708i	−0.903460	+	0.428672i
$21$	0.261981	+	0.261981i	0.0571690	+	0.0571690i
$22$	1.39158	−	0.862090i	0.296687	−	0.183798i
$23$	−1.11058	−	5.58325i	−0.231571	−	1.16419i	−0.905156	−	0.425079i	$-0.860246\pi$
$23$	−1.11058	−	5.58325i	−0.231571	−	1.16419i	0.673585	−	0.739110i	$-0.264754\pi$
$24$	−1.91352	+	2.30772i	−0.390596	+	0.471061i
$25$	4.27018	+	2.60108i	0.854035	+	0.520215i
$26$	−2.64514	−	1.20388i	−0.518755	−	0.236100i
$27$	−4.29764	−	2.87159i	−0.827081	−	0.552638i
$28$	0.693440	−	0.0889139i	0.131048	−	0.0168031i
$29$	4.03508	−	2.69616i	0.749296	−	0.500664i	−0.121328	−	0.992612i	$-0.538715\pi$
$29$	4.03508	−	2.69616i	0.749296	−	0.500664i	0.870624	+	0.491949i	$0.163715\pi$
$30$	3.33085	+	0.373320i	0.608127	+	0.0681586i
$31$	1.84475	−	9.27417i	0.331326	−	1.66569i	−0.352322	−	0.935879i	$-0.614608\pi$
$31$	1.84475	−	9.27417i	0.331326	−	1.66569i	0.683648	−	0.729812i	$-0.260392\pi$
$32$	1.23802	+	5.51972i	0.218853	+	0.975758i
$33$	−1.22686			−0.213568
$34$	−4.46579	+	3.74923i	−0.765877	+	0.642988i
$35$	−0.508427	−	0.593681i	−0.0859399	−	0.100350i
$36$	−3.55808	+	1.19443i	−0.593014	+	0.199072i
$37$	1.69824	−	8.53762i	0.279189	−	1.40358i	−0.545558	−	0.838073i	$-0.683682\pi$
$37$	1.69824	−	8.53762i	0.279189	−	1.40358i	0.824747	−	0.565503i	$-0.191318\pi$
$38$	−4.40571	+	4.11247i	−0.714701	+	0.667131i
$39$	1.21009	+	1.81103i	0.193769	+	0.289996i
$40$	4.40041	−	4.54273i	0.695766	−	0.718268i
$41$	−6.46731	−	4.32132i	−1.01002	−	0.674876i	−0.0636576	−	0.997972i	$-0.520277\pi$
$41$	−6.46731	−	4.32132i	−1.01002	−	0.674876i	−0.946366	+	0.323095i	$0.895277\pi$
$42$	−0.476893	−	0.217048i	−0.0735862	−	0.0334912i
$43$	−2.93144	+	7.07713i	−0.447041	+	1.07925i	0.526384	+	0.850247i	$0.323547\pi$
$43$	−2.93144	+	7.07713i	−0.447041	+	1.07925i	−0.973425	+	0.229005i	$0.926453\pi$
$44$	−1.41550	+	1.83188i	−0.213394	+	0.276166i
$45$	3.29884	+	2.59345i	0.491762	+	0.386608i
$46$	4.23972	+	6.84375i	0.625113	+	1.00906i
$47$	−3.81771	−	3.81771i	−0.556871	−	0.556871i	0.371545	−	0.928415i	$-0.378828\pi$
$47$	−3.81771	−	3.81771i	−0.556871	−	0.556871i	−0.928415	+	0.371545i	$0.878828\pi$
$48$	1.38984	−	4.00532i	0.200606	−	0.578119i
$49$	−2.63202	−	6.35427i	−0.376003	−	0.907752i
$50$	−6.94540	−	1.32721i	−0.982227	−	0.187696i
$51$	4.32501	−	0.626065i	0.605622	−	0.0876666i
$52$	4.10028	+	0.282644i	0.568607	+	0.0391956i
$53$	−7.79451	+	3.22859i	−1.07066	+	0.443481i	−0.847223	−	0.531238i	$-0.821727\pi$
$53$	−7.79451	+	3.22859i	−1.07066	+	0.443481i	−0.223435	+	0.974719i	$0.571727\pi$
$54$	7.11592	+	1.67186i	0.968354	+	0.227512i
$55$	2.58058	+	0.199623i	0.347966	+	0.0269171i
$56$	−0.874304	+	0.461651i	−0.116834	+	0.0616908i
$57$	4.43010	−	0.881202i	0.586781	−	0.116718i
$58$	−4.00702	+	5.57191i	−0.526147	+	0.731627i
$59$	1.00326	−	2.42208i	0.130613	−	0.315327i	−0.845021	−	0.534734i	$-0.820412\pi$
$59$	1.00326	−	2.42208i	0.130613	−	0.315327i	0.975634	+	0.219406i	$0.0704120\pi$
$60$	−4.59654	+	1.15742i	−0.593411	+	0.149422i
$61$	3.98410	+	2.66209i	0.510111	+	0.340845i	0.783841	−	0.620961i	$-0.213257\pi$
$61$	3.98410	+	2.66209i	0.510111	+	0.340845i	−0.273730	+	0.961807i	$0.588257\pi$
$62$	2.15608	+	13.1977i	0.273822	+	1.67610i
$63$	−0.364445	−	0.545431i	−0.0459158	−	0.0687179i
$64$	−4.37700	−	6.69640i	−0.547126	−	0.837051i
$65$	−2.25064	−	4.00623i	−0.279158	−	0.496911i
$66$	1.62486	−	0.608427i	0.200007	−	0.0748922i
$67$	9.04379			1.10487			0.552437	−	0.833554i	$-0.313698\pi$
$67$	9.04379			1.10487			0.552437	+	0.833554i	$0.313698\pi$
$68$	4.05520	−	7.18020i	0.491766	−	0.870728i
$69$		−	6.03363i		−	0.726364i
$70$	0.967786	+	0.534136i	0.115673	+	0.0638415i
$71$	10.2573	+	2.04030i	1.21731	+	0.242139i	0.761636	−	0.648005i	$-0.224397\pi$
$71$	10.2573	+	2.04030i	1.21731	+	0.242139i	0.455679	+	0.890144i	$0.349397\pi$
$72$	4.12001	−	3.34646i	0.485548	−	0.394384i
$73$	−2.12827	−	3.18517i	−0.249095	−	0.372796i	0.685760	−	0.727828i	$-0.259470\pi$
$73$	−2.12827	−	3.18517i	−0.249095	−	0.372796i	−0.934854	+	0.355032i	$0.884470\pi$
$74$	1.98484	+	12.1495i	0.230733	+	1.41235i
$75$	3.90116	+	3.58688i	0.450467	+	0.414178i
$76$	3.79550	−	7.63149i	0.435374	−	0.875392i
$77$	−0.373821	−	0.154842i	−0.0426008	−	0.0176458i
$78$	−2.50078	−	1.79843i	−0.283158	−	0.203632i
$79$	2.18012	+	10.9602i	0.245283	+	1.23312i	0.885395	+	0.464839i	$0.153888\pi$
$79$	2.18012	+	10.9602i	0.245283	+	1.23312i	−0.640112	+	0.768282i	$0.721112\pi$
$80$	−3.57510	+	8.19870i	−0.399709	+	0.916642i
$81$	0.107115	+	0.107115i	0.0119017	+	0.0119017i
$82$	10.7084	+	2.51591i	1.18255	+	0.277835i
$83$	−15.5635	+	6.44659i	−1.70831	+	0.707605i	−0.708312	+	0.705899i	$0.750543\pi$
$83$	−15.5635	+	6.44659i	−1.70831	+	0.707605i	−0.999999	+	0.00170618i	$0.999457\pi$
$84$	0.739241	+	0.0509579i	0.0806578	+	0.00555997i
$85$	−9.19913	+	0.613146i	−0.997786	+	0.0665050i
$86$	0.372718	−	10.8268i	0.0401912	−	1.16748i
$87$	4.75212	−	1.96839i	0.509480	−	0.211034i
$88$	0.966224	−	3.12813i	0.103000	−	0.333460i
$89$	5.85808	−	5.85808i	0.620955	−	0.620955i	−0.324820	−	0.945776i	$-0.605304\pi$
$89$	5.85808	−	5.85808i	0.620955	−	0.620955i	0.945776	+	0.324820i	$0.105304\pi$
$90$	−5.65516	−	1.79881i	−0.596106	−	0.189612i
$91$	0.140142	+	0.704542i	0.0146909	+	0.0738561i
$92$	−9.00910	−	6.96135i	−0.939264	−	0.725771i
$93$	3.83536	−	9.25938i	0.397709	−	0.960153i
$94$	6.94951	+	3.16292i	0.716787	+	0.326230i
$95$	−9.46170	+	1.13270i	−0.970750	+	0.116213i
$96$	0.145620	+	5.99394i	0.0148623	+	0.611754i
$97$	6.58914	−	4.40272i	0.669025	−	0.447029i	−0.174113	−	0.984726i	$-0.555706\pi$
$97$	6.58914	−	4.40272i	0.669025	−	0.447029i	0.843138	+	0.537697i	$0.180706\pi$
$98$	6.63710	+	7.11037i	0.670449	+	0.718256i
$99$	2.13047	+	0.423777i	0.214121	+	0.0425912i
$100$	9.85674	−	1.68661i	0.985674	−	0.168661i
$101$	14.0350			1.39654			0.698268	−	0.715837i	$-0.253955\pi$
$101$	14.0350			1.39654			0.698268	+	0.715837i	$0.253955\pi$
$102$	−5.41760	+	2.97404i	−0.536423	+	0.294474i
$103$	2.11236			0.208137			0.104068	−	0.994570i	$-0.466814\pi$
$103$	2.11236			0.208137			0.104068	+	0.994570i	$0.466814\pi$
$104$	−5.57062	+	1.65909i	−0.546244	+	0.162687i
$105$	−0.405769	−	0.722284i	−0.0395990	−	0.0704877i
$106$	8.72198	−	8.14145i	0.847154	−	0.790768i
$107$	0.293443	+	0.439169i	0.0283682	+	0.0424561i	0.845383	−	0.534161i	$-0.179372\pi$
$107$	0.293443	+	0.439169i	0.0283682	+	0.0424561i	−0.817014	+	0.576617i	$0.804372\pi$
$108$	−10.2535	+	1.31472i	−0.986644	+	0.126509i
$109$	4.01369	−	6.00691i	0.384442	−	0.575357i	−0.587896	−	0.808936i	$-0.700044\pi$
$109$	4.01369	−	6.00691i	0.384442	−	0.575357i	0.972338	+	0.233579i	$0.0750437\pi$
$110$	−3.51675	+	1.01539i	−0.335309	+	0.0968135i
$111$	3.53076	−	8.52400i	0.335125	−	0.809063i
$112$	0.928993	−	1.04500i	0.0877816	−	0.0987435i
$113$	0.750418	+	3.77261i	0.0705934	+	0.354897i	0.999896	−	0.0144223i	$-0.00459090\pi$
$113$	0.750418	+	3.77261i	0.0705934	+	0.354897i	−0.929303	+	0.369319i	$0.879591\pi$
$114$	−5.43026	+	3.36406i	−0.508590	+	0.315073i
$115$	−0.981736	+	12.6912i	−0.0915473	+	1.18346i
$116$	2.54369	−	9.36666i	0.236176	−	0.869672i
$117$	−1.47580	−	3.56289i	−0.136437	−	0.329389i
$118$	−0.127559	+	3.70536i	−0.0117428	+	0.341106i
$119$	1.39684	+	0.355099i	0.128048	+	0.0325519i
$120$	5.51372	−	3.81243i	0.503331	−	0.348025i
$121$	−8.92481	+	3.69678i	−0.811347	+	0.336071i
$122$	−6.59677	−	1.54989i	−0.597243	−	0.140320i
$123$	−5.82945	−	5.82945i	−0.525624	−	0.525624i
$124$	−9.40055	−	16.4098i	−0.844194	−	1.47365i
$125$	−7.62212	−	8.17945i	−0.681743	−	0.731592i
$126$	0.753167	+	0.541637i	0.0670974	+	0.0482529i
$127$	−1.45525	+	3.51327i	−0.129132	+	0.311753i	−0.975201	−	0.221321i	$-0.928963\pi$
$127$	−1.45525	+	3.51327i	−0.129132	+	0.311753i	0.846069	+	0.533074i	$0.178963\pi$
$128$	9.11785	+	6.69812i	0.805912	+	0.592036i
$129$	−4.51072	+	6.75078i	−0.397147	+	0.594373i
$130$	4.96755	+	4.18974i	0.435683	+	0.367464i
$131$	11.5248	+	17.2481i	1.00693	+	1.50698i	0.855029	+	0.518580i	$0.173539\pi$
$131$	11.5248	+	17.2481i	1.00693	+	1.50698i	0.151900	+	0.988396i	$0.451461\pi$
$132$	−1.85025	+	1.61161i	−0.161043	+	0.140273i
$133$	1.46106	+	0.290623i	0.126690	+	0.0252002i
$134$	−11.9777	+	4.48502i	−1.03471	+	0.387447i
$135$	7.51783	+	8.77843i	0.647032	+	0.755527i
$136$	−1.80992	+	11.5206i	−0.155199	+	0.987883i
$137$		−	18.6247i		−	1.59121i	−0.605815	−	0.795606i	$-0.707153\pi$
$137$		−	18.6247i		−	1.59121i	0.605815	−	0.795606i	$-0.292847\pi$
$138$	2.99222	+	7.99100i	0.254715	+	0.680239i
$139$	−2.97288	+	14.9457i	−0.252156	+	1.26768i	0.622380	+	0.782715i	$0.286166\pi$
$139$	−2.97288	+	14.9457i	−0.252156	+	1.26768i	−0.874536	+	0.484960i	$0.838834\pi$
$140$	−1.54664	−	0.227468i	−0.130715	−	0.0192245i
$141$	−3.17924	−	4.75806i	−0.267740	−	0.400701i
$142$	−14.5967	+	2.38463i	−1.22493	+	0.200114i
$143$	−1.97782	−	1.32154i	−0.165394	−	0.110513i
$144$	−3.79700	+	6.47529i	−0.316417	+	0.539607i
$145$	−10.3159	+	3.36711i	−0.856691	+	0.279624i
$146$	4.39830	+	3.16302i	0.364006	+	0.261773i
$147$	−1.42217	−	7.14973i	−0.117299	−	0.589700i
$148$	−8.65396	−	15.1066i	−0.711351	−	1.24175i
$149$	−11.7851	+	11.7851i	−0.965477	+	0.965477i	−0.999424	−	0.0339466i	$-0.989192\pi$
$149$	−11.7851	+	11.7851i	−0.965477	+	0.965477i	0.0339466	+	0.999424i	$0.489192\pi$
$150$	−6.94555	−	2.81583i	−0.567102	−	0.229911i
$151$	−0.409485	+	0.169614i	−0.0333234	+	0.0138030i	−0.399283	−	0.916828i	$-0.630741\pi$
$151$	−0.409485	+	0.169614i	−0.0333234	+	0.0138030i	0.365960	+	0.930631i	$0.380741\pi$
$152$	−1.24216	+	11.9895i	−0.100753	+	0.972476i
$153$	−7.72676	−	0.406752i	−0.624671	−	0.0328840i
$154$	0.571881	+	0.0196873i	0.0460835	+	0.00158645i
$155$	−9.57394	+	18.8522i	−0.768997	+	1.51425i
$156$	4.20395	+	1.14166i	0.336585	+	0.0914060i
$157$	−7.46237	+	7.46237i	−0.595562	+	0.595562i	−0.939128	−	0.343566i	$-0.888365\pi$
$157$	−7.46237	+	7.46237i	−0.595562	+	0.595562i	0.343566	+	0.939128i	$0.388365\pi$
$158$	−8.32280	−	13.4346i	−0.662126	−	1.06880i
$159$	−8.77027	+	1.74451i	−0.695527	+	0.138349i
$160$	0.668979	−	12.6314i	0.0528874	−	0.998600i
$161$	0.761505	−	1.83844i	0.0600150	−	0.144889i
$162$	−0.194985	−	0.0887434i	−0.0153195	−	0.00697234i
$163$	0.165134	+	0.110339i	0.0129343	+	0.00864242i	0.562021	−	0.827123i	$-0.310024\pi$
$163$	0.165134	+	0.110339i	0.0129343	+	0.00864242i	−0.549086	+	0.835766i	$0.685024\pi$
$164$	−15.4300	+	1.97846i	−1.20488	+	0.154492i
$165$	2.64133	+	0.741119i	0.205627	+	0.0576960i
$166$	17.4154	−	16.2562i	1.35169	−	1.26173i
$167$	−2.28977	−	0.455464i	−0.177188	−	0.0352449i	0.105699	−	0.994398i	$-0.466292\pi$
$167$	−2.28977	−	0.455464i	−0.177188	−	0.0352449i	−0.282887	+	0.959153i	$0.591292\pi$
$168$	−1.00433	+	0.299118i	−0.0774857	+	0.0230774i
$169$		−	8.77695i		−	0.675150i
$170$	11.8793	−	5.37412i	0.911104	−	0.412176i
$171$	−7.99738			−0.611575
$172$	4.87562	+	14.5239i	0.371763	+	1.10744i
$173$	−3.31329	+	16.6570i	−0.251905	+	1.26641i	0.623041	+	0.782189i	$0.285897\pi$
$173$	−3.31329	+	16.6570i	−0.251905	+	1.26641i	−0.874946	+	0.484221i	$0.839103\pi$
$174$	−5.31758	+	4.96364i	−0.403125	+	0.376293i
$175$	0.735975	+	1.58528i	0.0556345	+	0.119836i
$176$	0.271637	+	4.62210i	0.0204754	+	0.348404i
$177$	1.54375	−	2.31039i	0.116035	−	0.173659i
$178$	−4.85334	+	10.6637i	−0.363773	+	0.799275i
$179$	10.1745	+	4.21440i	0.760475	+	0.314999i	0.729007	−	0.684506i	$-0.239982\pi$
$179$	10.1745	+	4.21440i	0.760475	+	0.314999i	0.0314672	+	0.999505i	$0.489982\pi$
$180$	8.38182	−	0.422161i	0.624744	−	0.0314660i
$181$	−1.50907	−	7.58659i	−0.112168	−	0.563906i	−0.995468	−	0.0950981i	$-0.969684\pi$
$181$	−1.50907	−	7.58659i	−0.112168	−	0.563906i	0.883300	−	0.468808i	$-0.155316\pi$
$182$	−0.535004	−	0.863602i	−0.0396571	−	0.0640145i
$183$	3.59115	+	3.59115i	0.265466	+	0.265466i
$184$	15.3840	+	4.75185i	1.13413	+	0.350311i
$185$	−8.81358	+	17.3550i	−0.647987	+	1.27596i
$186$	−0.487647	+	14.1653i	−0.0357560	+	1.03865i
$187$	−4.10215	+	2.43923i	−0.299979	+	0.178374i
$188$	−10.7726	−	0.742582i	−0.785669	−	0.0541584i
$189$	−0.691422	−	1.66924i	−0.0502935	−	0.121419i
$190$	11.9694	−	6.19244i	0.868354	−	0.449247i
$191$	−3.76809	−	3.76809i	−0.272649	−	0.272649i	0.557517	−	0.830166i	$-0.311754\pi$
$191$	−3.76809	−	3.76809i	−0.272649	−	0.272649i	−0.830166	+	0.557517i	$0.811754\pi$
$192$	−3.16539	−	7.86622i	−0.228443	−	0.567695i
$193$	13.1399	−	2.61369i	0.945830	−	0.188137i	0.302002	−	0.953307i	$-0.402345\pi$
$193$	13.1399	−	2.61369i	0.945830	−	0.188137i	0.643828	+	0.765170i	$0.277345\pi$
$194$	−6.54330	+	9.09871i	−0.469782	+	0.653249i
$195$	−1.51123	−	4.63000i	−0.108221	−	0.331561i
$196$	−12.3164	−	6.12555i	−0.879746	−	0.437539i
$197$	0.154712	−	0.231542i	0.0110228	−	0.0164967i	−0.825917	−	0.563791i	$-0.809342\pi$
$197$	0.154712	−	0.231542i	0.0110228	−	0.0164967i	0.836940	+	0.547295i	$0.184342\pi$
$198$	−3.03178	+	0.495296i	−0.215459	+	0.0351992i
$199$	−16.3037	+	10.8938i	−1.15574	+	0.772240i	−0.977331	−	0.211717i	$-0.932095\pi$
$199$	−16.3037	+	10.8938i	−1.15574	+	0.772240i	−0.178408	+	0.983957i	$0.557095\pi$
$200$	−12.2179	+	7.12195i	−0.863938	+	0.503598i
$201$	9.40134	+	1.87004i	0.663120	+	0.131903i
$202$	−18.5881	+	6.96029i	−1.30785	+	0.489724i
$203$	1.69639			0.119063
$204$	5.70023	−	6.62556i	0.399096	−	0.463882i
$205$	11.3132	+	13.2102i	0.790149	+	0.922643i
$206$	−2.79762	+	1.04757i	−0.194920	+	0.0729874i
$207$	−2.08412	+	10.4776i	−0.144856	+	0.728242i
$208$	6.55500	−	4.95991i	0.454508	−	0.343908i
$209$	−4.10156	+	2.74057i	−0.283711	+	0.189569i
$210$	0.895602	+	0.755370i	0.0618024	+	0.0521255i
$211$	0.168064	+	0.112297i	0.0115700	+	0.00773083i	0.561342	−	0.827584i	$-0.310285\pi$
$211$	0.168064	+	0.112297i	0.0115700	+	0.00773083i	−0.549772	+	0.835315i	$0.685285\pi$
$212$	−7.51394	+	15.1080i	−0.516060	+	1.03763i
$213$	10.2409	+	4.24193i	0.701696	+	0.290652i
$214$	−0.606433	−	0.436114i	−0.0414549	−	0.0298122i
$215$	10.5863	−	13.4657i	0.721981	−	0.918354i
$216$	12.9278	−	6.82618i	0.879628	−	0.464463i
$217$	2.33725	−	2.33725i	0.158663	−	0.158663i
$218$	−2.33680	+	9.94609i	−0.158268	+	0.673634i
$219$	−1.55379	−	3.75118i	−0.104995	−	0.253481i
$220$	4.15406	−	3.08883i	0.280066	−	0.208249i
$221$	7.64676	+	3.64951i	0.514377	+	0.245493i
$222$	−0.448918	+	13.0403i	−0.0301294	+	0.875205i
$223$	−14.5307	+	6.01880i	−0.973045	+	0.403049i	−0.811845	−	0.583873i	$-0.801537\pi$
$223$	−14.5307	+	6.01880i	−0.973045	+	0.403049i	−0.161200	+	0.986922i	$0.551537\pi$
$224$	−0.712125	+	1.84472i	−0.0475809	+	0.123256i
$225$	−5.53551	−	7.57625i	−0.369034	−	0.505084i
$226$	−2.86478	−	4.62433i	−0.190563	−	0.307606i
$227$	3.31294	−	0.658984i	0.219887	−	0.0437383i	−0.0839171	−	0.996473i	$-0.526743\pi$
$227$	3.31294	−	0.658984i	0.219887	−	0.0437383i	0.303804	+	0.952734i	$0.401743\pi$
$228$	5.52357	−	7.14839i	0.365807	−	0.473414i
$229$	−16.2420	−	6.72767i	−1.07330	−	0.444577i	−0.225148	−	0.974324i	$-0.572287\pi$
$229$	−16.2420	−	6.72767i	−1.07330	−	0.444577i	−0.848155	+	0.529747i	$0.822287\pi$
$230$	−4.99364	−	17.2952i	−0.329271	−	1.14041i
$231$	−0.356583	−	0.238261i	−0.0234614	−	0.0156764i
$232$	1.27625	+	13.6668i	0.0837901	+	0.897267i
$233$	−1.23121	+	0.822670i	−0.0806594	+	0.0538949i	−0.595246	−	0.803544i	$-0.702945\pi$
$233$	−1.23121	+	0.822670i	−0.0806594	+	0.0538949i	0.514587	+	0.857438i	$0.327945\pi$
$234$	3.72148	+	3.98684i	0.243280	+	0.260628i
$235$	5.91305	+	10.5255i	0.385725	+	0.686605i
$236$	−1.66863	−	4.97067i	−0.108619	−	0.323563i
$237$			11.8443i			0.769373i
$238$	−2.02609	+	0.222428i	−0.131332	+	0.0144178i
$239$		−	9.32836i		−	0.603401i	−0.953403	−	0.301701i	$-0.902446\pi$
$239$		−	9.32836i		−	0.603401i	0.953403	−	0.301701i	$-0.0975543\pi$
$240$	−5.41175	+	7.78359i	−0.349327	+	0.502429i
$241$	4.33642	−	21.8006i	0.279333	−	1.40430i	−0.545113	−	0.838363i	$-0.683513\pi$
$241$	4.33642	−	21.8006i	0.279333	−	1.40430i	0.824446	−	0.565940i	$-0.191487\pi$
$242$	9.98679	−	9.32207i	0.641975	−	0.599245i
$243$	8.70397	+	13.0264i	0.558360	+	0.835645i
$244$	9.50545	−	1.21880i	0.608524	−	0.0780258i
$245$	1.82807	+	15.2702i	0.116791	+	0.975578i
$246$	10.6115	+	4.82962i	0.676567	+	0.307925i
$247$	8.09101	+	3.35140i	0.514818	+	0.213245i
$248$	20.5882	+	17.0714i	1.30735	+	1.08404i
$249$	−17.5118	+	3.48331i	−1.10976	+	0.220746i
$250$	14.1512	+	7.05295i	0.894999	+	0.446068i
$251$	−9.96167	−	9.96167i	−0.628775	−	0.628775i	0.318985	−	0.947760i	$-0.396658\pi$
$251$	−9.96167	−	9.96167i	−0.628775	−	0.628775i	−0.947760	+	0.318985i	$0.896658\pi$
$252$	−1.26611	−	0.343836i	−0.0797575	−	0.0216597i
$253$	2.52163	+	6.08775i	0.158533	+	0.382734i
$254$	0.185027	−	5.37470i	0.0116096	−	0.337239i
$255$	−9.68961	−	1.26478i	−0.606787	−	0.0792035i
$256$	−15.3975	−	4.34930i	−0.962345	−	0.271831i
$257$	−0.732414	−	1.76820i	−0.0456867	−	0.110298i	0.899389	−	0.437150i	$-0.144012\pi$
$257$	−0.732414	−	1.76820i	−0.0456867	−	0.110298i	−0.945075	+	0.326852i	$0.894012\pi$
$258$	2.62618	−	11.1778i	0.163499	−	0.695897i
$259$	2.15163	−	2.15163i	0.133696	−	0.133696i
$260$	−8.65686	−	3.08541i	−0.536876	−	0.191349i
$261$	−8.93210	+	1.77671i	−0.552883	+	0.109975i
$262$	−23.8173	−	17.1281i	−1.47144	−	1.05818i
$263$	12.0750	−	29.1516i	0.744576	−	1.79757i	0.158411	−	0.987373i	$-0.449363\pi$
$263$	12.0750	−	29.1516i	0.744576	−	1.79757i	0.586165	−	0.810192i	$-0.300637\pi$
$264$	1.65125	−	3.05202i	0.101627	−	0.187839i
$265$	18.7313	−	2.24241i	1.15066	−	0.137750i
$266$	−2.07917	+	0.339670i	−0.127482	+	0.0208265i
$267$	7.30100	−	4.87837i	0.446814	−	0.298551i
$268$	13.6391	−	11.8800i	0.833142	−	0.725687i
$269$	5.85638	−	29.4420i	0.357070	−	1.79511i	−0.216855	−	0.976204i	$-0.569580\pi$
$269$	5.85638	−	29.4420i	0.357070	−	1.79511i	0.573925	−	0.818908i	$-0.305420\pi$
$270$	−14.3101	−	7.89798i	−0.870886	−	0.480655i
$271$	6.93392			0.421206			0.210603	−	0.977572i	$-0.432457\pi$
$271$	6.93392			0.421206			0.210603	+	0.977572i	$0.432457\pi$
$272$	−3.31625	−	16.1556i	−0.201077	−	0.979575i
$273$			0.761375i			0.0460805i
$274$	9.23640	+	24.6667i	0.557991	+	1.49017i
$275$	−5.43521	−	1.98865i	−0.327756	−	0.119920i
$276$	−7.92584	−	9.09945i	−0.477080	−	0.547722i
$277$	−0.571726	+	0.382015i	−0.0343517	+	0.0229531i	−0.572628	−	0.819816i	$-0.694076\pi$
$277$	−0.571726	+	0.382015i	−0.0343517	+	0.0229531i	0.538276	+	0.842769i	$0.319076\pi$
$278$	−3.47460	−	21.2685i	−0.208392	−	1.27560i
$279$	−9.85857	+	14.7544i	−0.590217	+	0.883322i
$280$	2.16119	−	0.465752i	0.129156	−	0.0278340i
$281$	−4.71661	−	1.95368i	−0.281369	−	0.116547i	0.237536	−	0.971379i	$-0.423660\pi$
$281$	−4.71661	−	1.95368i	−0.281369	−	0.116547i	−0.518905	+	0.854832i	$0.673660\pi$
$282$	6.57024	+	4.72497i	0.391252	+	0.281368i
$283$	1.27833	+	6.42658i	0.0759886	+	0.382020i	1.00000		0.000344581i	$-0.000109683\pi$
$283$	1.27833	+	6.42658i	0.0759886	+	0.382020i	−0.924011	+	0.382365i	$0.875110\pi$
$284$	18.1494	−	10.3971i	1.07697	−	0.616951i
$285$	−10.0700	−	0.778971i	−0.596495	−	0.0461422i
$286$	3.27483	+	0.769411i	0.193645	+	0.0454962i
$287$	−1.04049	−	2.51196i	−0.0614180	−	0.148276i
$288$	1.81754	−	10.4590i	0.107099	−	0.616300i
$289$	13.2165	−	10.6923i	0.777440	−	0.628957i
$290$	11.9927	−	9.57535i	0.704235	−	0.562284i
$291$	7.76002	−	3.21431i	0.454901	−	0.188426i
$292$	−7.39376	−	2.00791i	−0.432687	−	0.117504i
$293$	2.62876	−	2.62876i	0.153574	−	0.153574i	−0.626138	−	0.779712i	$-0.715366\pi$
$293$	2.62876	−	2.62876i	0.153574	−	0.153574i	0.779712	+	0.626138i	$0.215366\pi$
$294$	5.42925	+	8.76388i	0.316640	+	0.511120i
$295$	−3.62306	+	4.60850i	−0.210943	+	0.268317i
$296$	18.9531	+	15.7156i	1.10163	+	0.913450i
$297$	5.52748	+	2.28956i	0.320737	+	0.132854i
$298$	9.76383	−	21.4529i	0.565604	−	1.24273i
$299$	6.49928	−	9.72686i	0.375863	−	0.562519i
$300$	10.5952	+	0.284847i	0.611714	+	0.0164457i
$301$	−2.22642	+	1.48765i	−0.128329	+	0.0857467i
$302$	0.458210	−	0.427711i	0.0263670	−	0.0246120i
$303$	14.5899	+	2.90211i	0.838168	+	0.166722i
$304$	−4.30074	−	16.4950i	−0.246664	−	0.946054i
$305$	−6.96935	−	8.13799i	−0.399064	−	0.465980i
$306$	10.4351	−	3.29317i	0.596535	−	0.188258i
$307$		−	4.84862i		−	0.276725i	−0.990382	−	0.138363i	$-0.955816\pi$
$307$		−	4.84862i		−	0.276725i	0.990382	−	0.138363i	$-0.0441839\pi$
$308$	−0.767169	+	0.257535i	−0.0437135	+	0.0146744i
$309$	2.19587	+	0.436786i	0.124919	+	0.0248479i
$310$	3.33056	−	29.7160i	0.189163	−	1.68776i
$311$	11.5632	+	17.3056i	0.655690	+	0.981310i	0.999112	+	0.0421284i	$0.0134138\pi$
$311$	11.5632	+	17.3056i	0.655690	+	0.981310i	−0.343422	+	0.939181i	$0.611586\pi$
$312$	−6.13392	+	0.572808i	−0.347265	+	0.0324289i
$313$	8.96622	−	13.4189i	0.506801	−	0.758481i	−0.486545	−	0.873656i	$-0.661743\pi$
$313$	8.96622	−	13.4189i	0.506801	−	0.758481i	0.993345	+	0.115175i	$0.0367429\pi$
$314$	6.18247	−	13.5840i	0.348897	−	0.766589i
$315$	0.455140	+	1.39443i	0.0256442	+	0.0785670i
$316$	17.6853	+	13.6655i	0.994878	+	0.768744i
$317$	10.8427	−	2.15675i	0.608987	−	0.121135i	0.119043	−	0.992889i	$-0.462017\pi$
$317$	10.8427	−	2.15675i	0.608987	−	0.121135i	0.489944	+	0.871754i	$0.337017\pi$
$318$	10.7503	−	6.65983i	0.602846	−	0.373465i
$319$	−3.97209	+	3.97209i	−0.222395	+	0.222395i
$320$	5.37821	+	17.0609i	0.300651	+	0.953734i
$321$	0.214235	+	0.517209i	0.0119574	+	0.0288678i
$322$	−0.0968215	+	2.81249i	−0.00539565	+	0.156734i
$323$	13.0606	−	11.7543i	0.726712	−	0.654027i
$324$	0.302250	+	0.0208349i	0.0167917	+	0.00115750i
$325$	2.42538	+	9.98467i	0.134536	+	0.553850i
$326$	−0.273425	−	0.0642402i	−0.0151436	−	0.00355794i
$327$	5.41446	−	5.41446i	0.299420	−	0.299420i
$328$	19.4545	−	10.2724i	1.07419	−	0.567198i
$329$	−0.368192	−	1.85102i	−0.0202991	−	0.102050i
$330$	−3.86574	+	0.328353i	−0.212802	+	0.0180752i
$331$	−4.09213	+	9.87927i	−0.224924	+	0.543014i	−0.995546	−	0.0942786i	$-0.969946\pi$
$331$	−4.09213	+	9.87927i	−0.224924	+	0.543014i	0.770622	+	0.637292i	$0.219946\pi$
$332$	−15.0032	+	30.1666i	−0.823410	+	1.65560i
$333$	−9.07560	+	13.5826i	−0.497340	+	0.744322i
$334$	3.25847	−	0.532331i	0.178296	−	0.0291278i
$335$	−19.4706	−	5.46317i	−1.06379	−	0.298485i
$336$	1.18180	−	0.894224i	0.0644727	−	0.0487839i
$337$	6.23650	−	31.3530i	0.339724	−	1.70791i	−0.312532	−	0.949907i	$-0.601177\pi$
$337$	6.23650	−	31.3530i	0.339724	−	1.70791i	0.652256	−	0.757999i	$-0.273823\pi$
$338$	4.35269	+	11.6243i	0.236755	+	0.632277i
$339$			4.07693i			0.221428i
$340$	−13.0680	+	13.0088i	−0.708710	+	0.705500i
$341$			10.9453i			0.592724i
$342$	10.5918	−	3.96609i	0.572739	−	0.214461i
$343$	0.946404	−	4.75789i	0.0511010	−	0.256902i
$344$	−13.6601	−	16.8177i	−0.736502	−	0.906750i
$345$	−3.64479	+	12.9900i	−0.196229	+	0.699356i
$346$	−3.87245	−	23.7039i	−0.208184	−	1.27433i
$347$	12.4213	−	18.5897i	0.666808	−	0.997949i	−0.331702	−	0.943384i	$-0.607623\pi$
$347$	12.4213	−	18.5897i	0.666808	−	0.997949i	0.998510	−	0.0545650i	$-0.0173772\pi$
$348$	4.58107	−	9.21100i	0.245571	−	0.493762i
$349$	1.07004	−	2.58329i	0.0572777	−	0.138281i	−0.892650	−	0.450751i	$-0.851156\pi$
$349$	1.07004	−	2.58329i	0.0572777	−	0.138281i	0.949928	+	0.312470i	$0.101156\pi$
$350$	−1.76091	−	1.73458i	−0.0941246	−	0.0927170i
$351$	−2.07220	−	10.4177i	−0.110606	−	0.556054i
$352$	−2.65197	−	5.98685i	−0.141350	−	0.319100i
$353$	−20.8542	+	20.8542i	−1.10995	+	1.10995i	−0.116799	+	0.993156i	$0.537263\pi$
$353$	−20.8542	+	20.8542i	−1.10995	+	1.10995i	−0.993156	+	0.116799i	$0.962737\pi$
$354$	−0.898783	+	3.82548i	−0.0477698	+	0.203322i
$355$	−20.8507	−	10.5888i	−1.10664	−	0.561996i
$356$	1.13945	−	16.5299i	0.0603909	−	0.876084i
$357$	1.37864	+	0.657971i	0.0729652	+	0.0348235i
$358$	−15.5652	−	0.535839i	−0.822644	−	0.0283200i
$359$	11.2061	+	27.0540i	0.591437	+	1.42785i	0.882115	+	0.471034i	$0.156119\pi$
$359$	11.2061	+	27.0540i	0.591437	+	1.42785i	−0.290678	+	0.956821i	$0.593881\pi$
$360$	−10.8916	+	4.71585i	−0.574038	+	0.248547i
$361$	−0.593011	+	0.593011i	−0.0312111	+	0.0312111i
$362$	5.76098	+	9.29936i	0.302791	+	0.488764i
$363$	−10.0421	+	1.99749i	−0.527072	+	0.104841i
$364$	1.13684	+	0.878442i	0.0595869	+	0.0460429i
$365$	2.65790	+	8.14308i	0.139121	+	0.426229i
$366$	−6.53710	−	2.97522i	−0.341699	−	0.155517i
$367$	−11.1268	+	16.6525i	−0.580816	+	0.869253i	−0.999239	−	0.0389992i	$-0.987583\pi$
$367$	−11.1268	+	16.6525i	−0.580816	+	0.869253i	0.418423	+	0.908252i	$0.362583\pi$
$368$	−22.7313	+	1.33590i	−1.18495	+	0.0696387i
$369$	8.10942	+	12.1366i	0.422160	+	0.631806i
$370$	3.06605	−	27.3560i	0.159396	−	1.42217i
$371$	−2.89246	−	0.575346i	−0.150169	−	0.0298705i
$372$	−6.37904	−	19.0024i	−0.330738	−	0.985231i
$373$			6.48277i			0.335665i	0.985816	+	0.167833i	$0.0536768\pi$
$373$			6.48277i			0.335665i	−0.985816	+	0.167833i	$0.946323\pi$
$374$	4.22326	−	5.26489i	0.218380	−	0.272241i
$375$	−6.23215	−	10.0789i	−0.321827	−	0.520472i
$376$	14.6355	−	4.35888i	0.754770	−	0.224792i
$377$	9.78122	+	1.94561i	0.503759	+	0.100204i
$378$	1.74354	+	1.86786i	0.0896780	+	0.0960726i
$379$	0.793765	−	0.530377i	0.0407730	−	0.0272436i	−0.535017	−	0.844841i	$-0.679695\pi$
$379$	0.793765	−	0.530377i	0.0407730	−	0.0272436i	0.575790	+	0.817598i	$0.304695\pi$
$380$	−12.7814	+	14.1372i	−0.655675	+	0.725225i
$381$	−2.23924	+	3.35126i	−0.114720	+	0.171690i
$382$	6.85917	+	3.12181i	0.350946	+	0.159726i
$383$	−1.27965	−	0.530048i	−0.0653870	−	0.0270842i	0.349750	−	0.936843i	$-0.386266\pi$
$383$	−1.27965	−	0.530048i	−0.0653870	−	0.0270842i	−0.415137	+	0.909759i	$0.636266\pi$
$384$	8.09332	+	8.84830i	0.413010	+	0.451538i
$385$	0.711272	+	0.559180i	0.0362498	+	0.0284985i
$386$	−16.1064	+	9.97797i	−0.819795	+	0.507865i
$387$	10.1648	−	10.1648i	0.516708	−	0.516708i
$388$	4.15375	−	15.2954i	0.210875	−	0.776506i
$389$	16.3015	−	6.75231i	0.826519	−	0.342356i	0.0709955	−	0.997477i	$-0.477382\pi$
$389$	16.3015	−	6.75231i	0.826519	−	0.342356i	0.755524	+	0.655121i	$0.227382\pi$
$390$	4.29761	+	5.38256i	0.217618	+	0.272556i
$391$	−11.9960	−	20.1742i	−0.606665	−	1.02025i
$392$	19.3498	+	2.00472i	0.977313	+	0.101254i
$393$	8.41397	+	20.3131i	0.424428	+	1.02466i
$394$	−0.0900744	+	0.383382i	−0.00453788	+	0.0193145i
$395$	1.92720	−	24.9135i	0.0969679	−	1.25353i
$396$	3.76969	−	2.15950i	0.189434	−	0.108519i
$397$	0.839779	+	4.22185i	0.0421473	+	0.211889i	0.996120	−	0.0880044i	$-0.0280490\pi$
$397$	0.839779	+	4.22185i	0.0421473	+	0.211889i	−0.953973	+	0.299893i	$0.903049\pi$
$398$	16.1903	−	22.5132i	0.811546	−	1.12849i
$399$	1.45873	+	0.604226i	0.0730279	+	0.0302491i
$400$	12.6496	−	15.4915i	0.632480	−	0.774577i
$401$	−21.6182	+	32.3539i	−1.07956	+	1.61568i	−0.342956	+	0.939352i	$0.611428\pi$
$401$	−21.6182	+	32.3539i	−1.07956	+	1.61568i	−0.736604	+	0.676324i	$0.763572\pi$
$402$	−13.3786	+	2.18564i	−0.667265	+	0.109010i
$403$	16.1570	−	10.7958i	0.804837	−	0.537775i
$404$	21.1665	−	18.4365i	1.05307	−	0.917252i
$405$	−0.165905	−	0.295317i	−0.00824388	−	0.0146744i
$406$	−2.24672	+	0.841280i	−0.111503	+	0.0417520i
$407$			10.0761i			0.499452i
$408$	−4.26367	+	11.6018i	−0.211083	+	0.574376i
$409$	0.0529070			0.00261608			0.00130804	−	0.999999i	$-0.499584\pi$
$409$	0.0529070			0.00261608			0.00130804	+	0.999999i	$0.499584\pi$
$410$	−21.5346	−	11.8853i	−1.06352	−	0.586972i
$411$	3.85114	−	19.3610i	0.189963	−	0.955007i
$412$	3.18569	−	2.77481i	0.156948	−	0.136705i
$413$	0.761971	−	0.509133i	0.0374942	−	0.0250528i
$414$	−2.43585	−	14.9102i	−0.119715	−	0.732795i
$415$	37.4012	−	4.47747i	1.83595	−	0.219791i
$416$	−6.22177	+	9.81973i	−0.305047	+	0.481452i
$417$	−6.18083	+	14.9218i	−0.302676	+	0.730726i
$418$	4.07303	−	5.66370i	0.199218	−	0.277021i
$419$	−29.0182	+	5.77208i	−1.41763	+	0.281985i	−0.843654	−	0.536887i	$-0.819600\pi$
$419$	−29.0182	+	5.77208i	−1.41763	+	0.281985i	−0.573978	+	0.818871i	$0.694600\pi$
$420$	−1.56075	−	0.556269i	−0.0761567	−	0.0271431i
$421$	−21.7139	+	21.7139i	−1.05827	+	1.05827i	−0.0600790	+	0.998194i	$0.519135\pi$
$421$	−21.7139	+	21.7139i	−1.05827	+	1.05827i	−0.998194	+	0.0600790i	$0.980865\pi$
$422$	−0.278276	−	0.0653801i	−0.0135463	−	0.00318265i
$423$	3.87732	+	9.36067i	0.188522	+	0.455132i
$424$	2.45911	−	23.7356i	0.119425	−	1.15270i
$425$	20.1754	+	4.23695i	0.978652	+	0.205522i
$426$	−15.6668	−	0.539340i	−0.759061	−	0.0261311i
$427$	0.640978	+	1.54746i	0.0310191	+	0.0748867i
$428$	1.01944	+	0.276849i	0.0492767	+	0.0133820i
$429$	−1.78276	−	1.78276i	−0.0860723	−	0.0860723i
$430$	−7.34267	+	23.0841i	−0.354095	+	1.11321i
$431$	−14.1994	+	2.82444i	−0.683962	+	0.136049i	−0.524828	−	0.851208i	$-0.675870\pi$
$431$	−14.1994	+	2.82444i	−0.683962	+	0.136049i	−0.159134	+	0.987257i	$0.550870\pi$
$432$	−13.7365	+	15.4519i	−0.660897	+	0.743429i
$433$	24.0610	+	9.96637i	1.15630	+	0.478953i	0.876640	−	0.481147i	$-0.159780\pi$
$433$	24.0610	+	9.96637i	1.15630	+	0.478953i	0.279656	+	0.960100i	$0.409780\pi$
$434$	−1.93638	+	4.25458i	−0.0929494	+	0.204226i
$435$	−11.4200	+	1.36714i	−0.547548	+	0.0655496i
$436$	−1.83761	−	14.3316i	−0.0880057	−	0.686357i
$437$	−13.4780	−	20.1713i	−0.644742	−	0.964924i
$438$	3.91815	+	4.19754i	0.187216	+	0.200566i
$439$	−2.39252	+	12.0280i	−0.114189	+	0.574066i	0.880750	+	0.473582i	$0.157039\pi$
$439$	−2.39252	+	12.0280i	−0.114189	+	0.574066i	−0.994939	+	0.100484i	$0.967961\pi$
$440$	−3.96985	+	6.15096i	−0.189255	+	0.293236i
$441$			12.9070i			0.614617i
$442$	−11.9373	−	1.04124i	−0.567800	−	0.0495267i
$443$			15.8964i			0.755263i	0.925956	+	0.377631i	$0.123261\pi$
$443$			15.8964i			0.755263i	−0.925956	+	0.377631i	$0.876739\pi$
$444$	−5.87241	−	17.4933i	−0.278692	−	0.830194i
$445$	−16.1508	+	9.07326i	−0.765619	+	0.430114i
$446$	16.2597	−	15.1774i	0.769919	−	0.718673i
$447$	−14.6880	+	9.81419i	−0.694718	+	0.464195i
$448$	0.0283059	−	2.79632i	0.00133733	−	0.132114i
$449$	22.6605	+	15.1413i	1.06941	+	0.714560i	0.960159	−	0.279454i	$-0.0901533\pi$
$449$	22.6605	+	15.1413i	1.06941	+	0.714560i	0.109256	+	0.994014i	$0.465153\pi$
$450$	11.0885	+	7.28888i	0.522718	+	0.343601i
$451$	8.31804	+	3.44544i	0.391681	+	0.162240i
$452$	6.08746	+	4.70379i	0.286330	+	0.221248i
$453$	−0.460746	+	0.0916481i	−0.0216477	+	0.00430600i
$454$	−4.06088	+	2.51573i	−0.190586	+	0.118069i
$455$	0.123884	−	1.60148i	0.00580776	−	0.0750787i
$456$	−3.77042	+	12.2067i	−0.176566	+	0.571629i
$457$	−9.16487	+	3.79621i	−0.428715	+	0.177579i	−0.586598	−	0.809878i	$-0.699533\pi$
$457$	−9.16487	+	3.79621i	−0.428715	+	0.177579i	0.157883	+	0.987458i	$0.449533\pi$
$458$	24.8475	+	0.855389i	1.16105	+	0.0399697i
$459$	−20.6542	−	5.25065i	−0.964058	−	0.245079i
$460$	15.1907	+	20.4295i	0.708271	+	0.952529i
$461$	−4.20317	−	10.1473i	−0.195761	−	0.472609i	0.795268	−	0.606258i	$-0.207330\pi$
$461$	−4.20317	−	10.1473i	−0.195761	−	0.472609i	−0.991029	+	0.133650i	$0.957330\pi$
$462$	0.590420	+	0.138717i	0.0274688	+	0.00645372i
$463$	−21.1983	+	21.1983i	−0.985168	+	0.985168i	−0.999892	−	0.0147237i	$-0.995313\pi$
$463$	−21.1983	+	21.1983i	−0.985168	+	0.985168i	0.0147237	+	0.999892i	$0.495313\pi$
$464$	−8.46795	−	17.4675i	−0.393115	−	0.810907i
$465$	−13.8507	+	17.6179i	−0.642309	+	0.817011i
$466$	1.22265	−	1.70014i	0.0566381	−	0.0787574i
$467$	19.3956	+	8.03393i	0.897522	+	0.371766i	0.783267	−	0.621685i	$-0.213552\pi$
$467$	19.3956	+	8.03393i	0.897522	+	0.371766i	0.114255	+	0.993451i	$0.463552\pi$
$468$	−6.90592	−	3.43464i	−0.319226	−	0.158766i
$469$	2.62855	+	1.75634i	0.121375	+	0.0811004i
$470$	−13.0511	−	11.0076i	−0.602003	−	0.507742i
$471$	−9.30044	+	6.21436i	−0.428542	+	0.286343i
$472$	4.67502	+	5.75569i	0.215185	+	0.264927i
$473$	1.72984	−	8.69649i	0.0795381	−	0.399865i
$474$	−5.87388	−	15.6868i	−0.269796	−	0.720516i
$475$	21.0546	+	3.27699i	0.966050	+	0.150359i
$476$	2.57306	−	1.29937i	0.117936	−	0.0595565i
$477$	15.8324			0.724916
$478$	4.62615	+	12.3546i	0.211595	+	0.565085i
$479$	24.4332	+	4.86006i	1.11638	+	0.222062i	0.718603	−	0.695421i	$-0.244782\pi$
$479$	24.4332	+	4.86006i	1.11638	+	0.222062i	0.397776	+	0.917482i	$0.369782\pi$
$480$	3.30731	−	12.9925i	0.150957	−	0.593023i
$481$	14.8738	−	9.93836i	0.678187	−	0.453150i
$482$	5.06825	+	31.0235i	0.230853	+	1.41308i
$483$	1.17176	−	1.75366i	0.0533168	−	0.0797943i
$484$	−8.60357	+	17.2989i	−0.391071	+	0.786314i
$485$	−16.8455	+	5.49837i	−0.764915	+	0.249668i
$486$	−17.9877	−	12.9358i	−0.815940	−	0.586780i
$487$	10.2993	−	2.04866i	0.466706	−	0.0928336i	0.0438649	−	0.999037i	$-0.486033\pi$
$487$	10.2993	−	2.04866i	0.466706	−	0.0928336i	0.422841	+	0.906204i	$0.361033\pi$
$488$	−11.9847	+	6.32816i	−0.542520	+	0.286463i
$489$	0.148847	+	0.148847i	0.00673110	+	0.00673110i
$490$	−9.99396	−	19.3174i	−0.451481	−	0.872673i
$491$	−12.0483	−	29.0872i	−0.543732	−	1.31269i	−0.922072	−	0.387018i	$-0.873505\pi$
$491$	−12.0483	−	29.0872i	−0.543732	−	1.31269i	0.378340	−	0.925667i	$-0.376495\pi$
$492$	−16.4491	−	1.13389i	−0.741585	−	0.0511195i
$493$	11.9758	−	16.0297i	0.539362	−	0.721941i
$494$	−12.3778	−	0.426114i	−0.556905	−	0.0191718i
$495$	−4.33075	−	2.19934i	−0.194653	−	0.0988528i
$496$	−35.7333	−	12.3994i	−1.60447	−	0.556748i
$497$	2.58501	+	2.58501i	0.115954	+	0.115954i
$498$	21.4653	−	13.2978i	0.961883	−	0.595890i
$499$	−3.94808	−	19.8484i	−0.176741	−	0.888535i	−0.962765	−	0.270339i	$-0.912864\pi$
$499$	−3.94808	−	19.8484i	−0.176741	−	0.888535i	0.786025	−	0.618195i	$-0.212136\pi$
$500$	−22.2397	−	2.32310i	−0.994589	−	0.103892i
$501$	−2.28612	−	0.946943i	−0.102136	−	0.0423063i
$502$	18.1336	+	8.25311i	0.809340	+	0.368354i
$503$	−6.80067	+	10.1779i	−0.303227	+	0.453811i	−0.951523	−	0.307577i	$-0.900482\pi$
$503$	−6.80067	+	10.1779i	−0.303227	+	0.453811i	0.648296	+	0.761388i	$0.275482\pi$
$504$	1.84737	−	0.172514i	0.0822883	−	0.00768438i
$505$	−30.2163	−	8.47826i	−1.34461	−	0.377278i
$506$	−6.35873	−	6.81214i	−0.282680	−	0.302837i
$507$	1.81487	−	9.12396i	0.0806011	−	0.405209i
$508$	2.42039	+	7.21006i	0.107387	+	0.319895i
$509$	41.1246			1.82281			0.911407	−	0.411505i	$-0.134997\pi$
$509$	41.1246			1.82281			0.911407	+	0.411505i	$0.134997\pi$
$510$	13.4602	−	3.13022i	0.596030	−	0.138609i
$511$		−	1.33908i		−	0.0592374i
$512$	22.5495	−	1.87573i	0.996558	−	0.0828962i
$513$	−21.6039	−	4.29728i	−0.953834	−	0.189729i
$514$	1.84691	+	1.97861i	0.0814637	+	0.0872725i
$515$	−4.54774	−	1.27603i	−0.200398	−	0.0562286i
$516$	2.06518	+	16.1063i	0.0909143	+	0.709041i
$517$	5.19628	+	3.47205i	0.228532	+	0.152700i
$518$	−1.78260	+	3.91668i	−0.0783228	+	0.172089i
$519$	−6.88856	+	16.6305i	−0.302374	+	0.729996i
$520$	12.9954	−	0.206797i	0.569884	−	0.00906864i
$521$	39.7388	−	7.90454i	1.74099	−	0.346304i	0.780614	−	0.625014i	$-0.214907\pi$
$521$	39.7388	−	7.90454i	1.74099	−	0.346304i	0.960376	+	0.278709i	$0.0899066\pi$
$522$	10.9487	−	6.78272i	0.479210	−	0.296872i
$523$	12.7943	−	12.7943i	0.559456	−	0.559456i	−0.369697	−	0.929152i	$-0.620538\pi$
$523$	12.7943	−	12.7943i	0.559456	−	0.559456i	0.929152	+	0.369697i	$0.120538\pi$
$524$	40.0382	+	10.8731i	1.74907	+	0.474994i
$525$	0.437273	+	1.80014i	0.0190842	+	0.0785646i
$526$	−1.53527	+	44.5969i	−0.0669411	+	1.94452i
$527$	−5.58541	−	38.5854i	−0.243304	−	1.68080i
$528$	−0.673366	+	4.86101i	−0.0293045	+	0.211548i
$529$	−8.69009	+	3.59955i	−0.377830	+	0.156502i
$530$	−23.6959	+	12.2592i	−1.02928	+	0.532504i
$531$	−3.47881	+	3.47881i	−0.150968	+	0.150968i
$532$	2.58522	−	1.48097i	0.112083	−	0.0642082i
$533$	−3.11836	−	15.6770i	−0.135071	−	0.679048i
$534$	−7.25021	+	10.0817i	−0.313747	+	0.436278i
$535$	−0.366469	−	1.12276i	−0.0158438	−	0.0485412i
$536$	−12.1722	+	22.4980i	−0.525759	+	0.971764i
$537$	9.70527	+	6.48486i	0.418814	+	0.279842i
$538$	6.84473	+	41.8976i	0.295097	+	1.80633i
$539$	4.42300	+	6.61949i	0.190512	+	0.285122i
$540$	22.8692	+	3.36344i	0.984135	+	0.144739i
$541$	1.37135	−	6.89424i	0.0589590	−	0.296407i	−0.940044	−	0.341054i	$-0.889216\pi$
$541$	1.37135	−	6.89424i	0.0589590	−	0.296407i	0.999003	+	0.0446469i	$0.0142163\pi$
$542$	−9.18335	+	3.43869i	−0.394459	+	0.147704i
$543$		−	8.19857i		−	0.351834i
$544$	12.4040	+	19.7520i	0.531817	+	0.846859i
$545$	−12.2698	+	10.5078i	−0.525581	+	0.450106i
$546$	−0.377583	−	1.00837i	−0.0161591	−	0.0431543i
$547$	−33.0094	−	6.56599i	−1.41138	−	0.280741i	−0.570206	−	0.821502i	$-0.693136\pi$
$547$	−33.0094	−	6.56599i	−1.41138	−	0.280741i	−0.841176	+	0.540761i	$0.818136\pi$
$548$	−24.4655	−	28.0882i	−1.04512	−	1.19987i
$549$	−4.99570	−	7.47659i	−0.213211	−	0.319093i
$550$	8.18467	−	0.0616631i	0.348995	−	0.00262933i
$551$	11.4900	−	17.1960i	0.489490	−	0.732573i
$552$	15.0097	+	8.12078i	0.638855	+	0.345643i
$553$	−1.49487	+	3.60895i	−0.0635685	+	0.153468i
$554$	0.567749	−	0.789477i	0.0241214	−	0.0335417i
$555$	−12.7506	+	16.2187i	−0.541234	+	0.688445i
$556$	15.1493	+	26.4451i	0.642475	+	1.12152i
$557$	−9.63731	−	9.63731i	−0.408346	−	0.408346i	0.472815	−	0.881161i	$-0.343238\pi$
$557$	−9.63731	−	9.63731i	−0.408346	−	0.408346i	−0.881161	+	0.472815i	$0.843238\pi$
$558$	5.73974	−	24.4299i	0.242982	−	1.03420i
$559$	−14.5435	+	6.02413i	−0.615126	+	0.254794i
$560$	−2.63132	+	1.68863i	−0.111193	+	0.0713576i
$561$	−4.76871	+	1.68743i	−0.201335	+	0.0712436i
$562$	7.21560	+	0.248401i	0.304372	+	0.0104782i
$563$	−3.31011	−	7.99132i	−0.139505	−	0.336794i	0.838651	−	0.544670i	$-0.183345\pi$
$563$	−3.31011	−	7.99132i	−0.139505	−	0.336794i	−0.978155	+	0.207876i	$0.933345\pi$
$564$	−11.0449	−	2.99945i	−0.465075	−	0.126300i
$565$	0.663359	−	8.57545i	0.0279077	−	0.360772i
$566$	−4.88012	−	7.87747i	−0.205127	−	0.331115i
$567$	0.0103305	+	0.0519350i	0.000433840	+	0.00218106i
$568$	−18.8811	+	22.7706i	−0.792231	+	0.955435i
$569$	−15.9129	+	38.4171i	−0.667102	+	1.61053i	0.119332	+	0.992854i	$0.461925\pi$
$569$	−15.9129	+	38.4171i	−0.667102	+	1.61053i	−0.786435	+	0.617673i	$0.788075\pi$
$570$	13.7231	−	3.96227i	0.574798	−	0.165961i
$571$	1.94059	−	2.90430i	0.0812113	−	0.121541i	−0.788640	−	0.614855i	$-0.789215\pi$
$571$	1.94059	−	2.90430i	0.0812113	−	0.121541i	0.869851	+	0.493314i	$0.164215\pi$
$572$	−4.71879	+	0.605050i	−0.197302	+	0.0252984i
$573$	−3.13791	−	4.69621i	−0.131088	−	0.196187i
$574$	2.62377	+	2.81086i	0.109514	+	0.117323i
$575$	9.78010	−	26.7302i	0.407858	−	1.11473i
$576$	2.77967	+	14.7533i	0.115820	+	0.614720i
$577$	−5.29189			−0.220304			−0.110152	−	0.993915i	$-0.535134\pi$
$577$	−5.29189			−0.220304			−0.110152	+	0.993915i	$0.535134\pi$
$578$	−12.2015	+	20.7153i	−0.507515	+	0.861643i
$579$	14.1998			0.590125
$580$	−11.1346	+	18.6291i	−0.462338	+	0.773532i
$581$	−5.77543	−	1.14880i	−0.239605	−	0.0476604i
$582$	−8.68340	+	8.10543i	−0.359938	+	0.335981i
$583$	8.11985	−	5.42551i	0.336290	−	0.224702i
$584$	10.7881	−	1.00744i	0.446416	−	0.0416880i
$585$	1.02501	+	8.56213i	0.0423790	+	0.354000i
$586$	−2.17789	+	4.78521i	−0.0899677	+	0.197675i
$587$	10.8316	−	26.1498i	0.447067	−	1.07932i	−0.526348	−	0.850269i	$-0.676439\pi$
$587$	10.8316	−	26.1498i	0.447067	−	1.07932i	0.973415	−	0.229047i	$-0.0735608\pi$
$588$	−11.5368	−	8.91448i	−0.475768	−	0.367627i
$589$	−7.86160	−	39.5229i	−0.323932	−	1.62851i
$590$	2.51296	−	7.90030i	0.103457	−	0.325250i
$591$	0.208706	−	0.208706i	0.00858502	−	0.00858502i
$592$	−32.8954	−	11.4146i	−1.35199	−	0.469137i
$593$	−6.43032	+	2.66353i	−0.264062	+	0.109378i	−0.510786	−	0.859708i	$-0.670646\pi$
$593$	−6.43032	+	2.66353i	−0.264062	+	0.109378i	0.246725	+	0.969086i	$0.420646\pi$
$594$	−8.45609	−	0.291106i	−0.346958	−	0.0119442i
$595$	−2.79278	−	1.60830i	−0.114493	−	0.0659340i
$596$	−2.29233	+	33.2545i	−0.0938974	+	1.36216i
$597$	−19.2009	+	7.95326i	−0.785839	+	0.325505i
$598$	−3.78393	+	16.1055i	−0.154736	+	0.658602i
$599$	14.1101	+	14.1101i	0.576522	+	0.576522i	0.933943	−	0.357422i	$-0.116344\pi$
$599$	14.1101	+	14.1101i	0.576522	+	0.576522i	−0.357422	+	0.933943i	$0.616344\pi$
$600$	−14.1736	+	4.87715i	−0.578636	+	0.199109i
$601$	−1.05241	−	5.29084i	−0.0429288	−	0.215818i	0.953367	−	0.301815i	$-0.0975924\pi$
$601$	−1.05241	−	5.29084i	−0.0429288	−	0.215818i	−0.996295	+	0.0859971i	$0.972592\pi$
$602$	2.21094	−	3.07439i	0.0901111	−	0.125303i
$603$	−15.6798	−	6.49477i	−0.638529	−	0.264487i
$604$	−0.394745	+	0.793702i	−0.0160620	+	0.0322953i
$605$	21.4476	−	2.56759i	0.871969	−	0.104388i
$606$	−20.7622	+	3.39188i	−0.843407	+	0.137786i
$607$	6.68178	+	9.99999i	0.271205	+	0.405887i	0.941925	−	0.335824i	$-0.109015\pi$
$607$	6.68178	+	9.99999i	0.271205	+	0.405887i	−0.670720	+	0.741711i	$0.734015\pi$
$608$	13.8762	+	19.7133i	0.562754	+	0.799480i
$609$	1.76346	+	0.350774i	0.0714590	+	0.0142141i
$610$	13.2661	+	7.32177i	0.537128	+	0.296450i
$611$		−	11.0951i		−	0.448860i
$612$	−12.1872	+	9.53652i	−0.492638	+	0.385491i
$613$	−34.3264			−1.38643			−0.693215	−	0.720731i	$-0.743807\pi$
$613$	−34.3264			−1.38643			−0.693215	+	0.720731i	$0.743807\pi$
$614$	2.40454	+	6.42156i	0.0970394	+	0.259153i
$615$	9.02893	+	16.0718i	0.364081	+	0.648079i
$616$	0.888328	−	0.721539i	0.0357917	−	0.0290716i
$617$	−8.09974	−	12.1221i	−0.326083	−	0.488018i	0.631818	−	0.775117i	$-0.282309\pi$
$617$	−8.09974	−	12.1221i	−0.326083	−	0.488018i	−0.957901	+	0.287099i	$0.907309\pi$
$618$	−3.12484	+	0.510500i	−0.125700	+	0.0205353i
$619$	15.5530	+	10.3922i	0.625127	+	0.417697i	0.827385	−	0.561636i	$-0.189828\pi$
$619$	15.5530	+	10.3922i	0.625127	+	0.417697i	−0.202257	+	0.979332i	$0.564828\pi$
$620$	10.3258	+	41.0079i	0.414695	+	1.64692i
$621$	−11.2599	+	27.1839i	−0.451846	+	1.09085i
$622$	−23.8967	−	17.1852i	−0.958169	−	0.689064i
$623$	2.84030	−	0.564971i	0.113794	−	0.0226351i
$624$	7.83975	−	3.80059i	0.313841	−	0.152145i
$625$	11.4688	+	22.2141i	0.458752	+	0.888564i
$626$	−5.22020	+	22.2187i	−0.208641	+	0.888036i
$627$	−4.83040	+	2.00082i	−0.192908	+	0.0799050i
$628$	−1.45150	+	21.0568i	−0.0579213	+	0.840258i
$629$	−5.14181	−	35.5209i	−0.205018	−	1.41631i
$630$	−1.29432	−	1.62108i	−0.0515670	−	0.0645853i
$631$	8.74317	+	21.1079i	0.348060	+	0.840291i	0.996849	+	0.0793229i	$0.0252758\pi$
$631$	8.74317	+	21.1079i	0.348060	+	0.840291i	−0.648789	+	0.760968i	$0.724724\pi$
$632$	−30.1997	−	9.32814i	−1.20128	−	0.371053i
$633$	0.151488	+	0.151488i	0.00602112	+	0.00602112i
$634$	−13.2906	+	8.23356i	−0.527837	+	0.326997i
$635$	5.25533	−	6.68473i	0.208551	−	0.265275i
$636$	−10.9350	+	14.1517i	−0.433601	+	0.561150i
$637$	5.40882	−	13.0581i	0.214305	−	0.517379i
$638$	3.29083	−	7.23053i	0.130285	−	0.286260i
$639$	−16.3184	−	10.9036i	−0.645547	−	0.431341i
$640$	−15.5839	−	19.9285i	−0.616006	−	0.787742i
$641$	12.7532	+	19.0865i	0.503722	+	0.753873i	0.992982	−	0.118265i	$-0.0377331\pi$
$641$	12.7532	+	19.0865i	0.503722	+	0.753873i	−0.489260	+	0.872138i	$0.662733\pi$
$642$	−0.540231	−	0.578753i	−0.0213212	−	0.0228415i
$643$	−4.07841	+	20.5035i	−0.160837	+	0.808581i	0.813164	+	0.582035i	$0.197743\pi$
$643$	−4.07841	+	20.5035i	−0.160837	+	0.808581i	−0.974000	+	0.226546i	$0.927257\pi$
$644$	−1.26655	−	3.77290i	−0.0499090	−	0.148673i
$645$	13.7893	−	11.8091i	0.542952	−	0.464982i
$646$	−11.4684	+	22.0446i	−0.451217	+	0.867332i
$647$	35.5741			1.39856			0.699281	−	0.714847i	$-0.253504\pi$
$647$	35.5741			1.39856			0.699281	+	0.714847i	$0.253504\pi$
$648$	−0.410636	+	0.122299i	−0.0161313	+	0.00480435i
$649$	−0.592020	+	2.97629i	−0.0232388	+	0.116829i
$650$	−8.16383	−	12.0210i	−0.320212	−	0.471502i
$651$	2.91295	−	1.94637i	0.114168	−	0.0762843i
$652$	0.393984	−	0.0505172i	0.0154296	−	0.00197841i
$653$	3.50257	+	2.34035i	0.137066	+	0.0915848i	0.622213	−	0.782848i	$-0.286234\pi$
$653$	3.50257	+	2.34035i	0.137066	+	0.0915848i	−0.485147	+	0.874433i	$0.661234\pi$
$654$	−4.48581	+	9.85612i	−0.175409	+	0.385405i
$655$	−14.3929	−	44.0958i	−0.562376	−	1.72297i
$656$	−20.6714	+	23.2528i	−0.807082	+	0.907868i
$657$	1.40248	+	7.05074i	0.0547159	+	0.275075i
$658$	1.40560	+	2.26892i	0.0547961	+	0.0884517i
$659$	−4.14646	−	4.14646i	−0.161523	−	0.161523i	0.621718	−	0.783241i	$-0.286435\pi$
$659$	−4.14646	−	4.14646i	−0.161523	−	0.161523i	−0.783241	+	0.621718i	$0.786435\pi$
$660$	4.95699	−	2.35198i	0.192950	−	0.0915509i
$661$	8.12424	−	3.36517i	0.315996	−	0.130890i	−0.219048	−	0.975714i	$-0.570295\pi$
$661$	8.12424	−	3.36517i	0.315996	−	0.130890i	0.535044	+	0.844824i	$0.320295\pi$
$662$	0.520293	−	15.1136i	0.0202218	−	0.587406i
$663$	7.19445	+	5.37497i	0.279409	+	0.208746i
$664$	4.91015	−	47.3933i	0.190551	−	1.83922i
$665$	−2.96999	−	1.50829i	−0.115171	−	0.0584888i
$666$	5.28389	−	22.4897i	0.204746	−	0.871459i
$667$	−19.5346	−	19.5346i	−0.756383	−	0.756383i
$668$	−4.05156	+	2.32098i	−0.156759	+	0.0898013i
$669$	−16.3497	+	3.25216i	−0.632116	+	0.125736i
$670$	28.4964	−	2.42046i	1.10091	−	0.0935103i
$671$	−5.12421	−	2.12252i	−0.197818	−	0.0819389i
$672$	−1.12173	+	1.77040i	−0.0432715	+	0.0682948i
$673$	13.3059	+	8.89072i	0.512905	+	0.342712i	0.784936	−	0.619576i	$-0.212696\pi$
$673$	13.3059	+	8.89072i	0.512905	+	0.342712i	−0.272032	+	0.962288i	$0.587696\pi$
$674$	7.28900	+	44.6170i	0.280762	+	1.71858i
$675$	−10.8825	−	23.4407i	−0.418866	−	0.902232i
$676$	−11.5295	−	13.2367i	−0.443442	−	0.509104i
$677$	19.4710	+	3.87301i	0.748330	+	0.148852i	0.554501	−	0.832183i	$-0.312909\pi$
$677$	19.4710	+	3.87301i	0.748330	+	0.148852i	0.193829	+	0.981035i	$0.437909\pi$
$678$	−2.02184	−	5.39952i	−0.0776484	−	0.207367i
$679$	2.77014			0.106308
$680$	10.8560	−	23.7097i	0.416308	−	0.909224i
$681$	3.58018			0.137193
$682$	−5.42805	−	14.4961i	−0.207851	−	0.555085i
$683$	−12.0199	−	2.39090i	−0.459927	−	0.0914852i	−0.0403116	−	0.999187i	$-0.512835\pi$
$683$	−12.0199	−	2.39090i	−0.459927	−	0.0914852i	−0.419615	+	0.907702i	$0.637835\pi$
$684$	−12.0610	+	10.5054i	−0.461164	+	0.401686i
$685$	−11.2508	+	40.0975i	−0.429870	+	1.53205i
$686$	1.10612	+	6.77074i	0.0422320	+	0.258508i
$687$	−15.4931	−	10.3521i	−0.591097	−	0.394958i
$688$	26.4318	+	15.4992i	1.00770	+	0.590900i
$689$	−16.0178	−	6.63477i	−0.610228	−	0.252765i
$690$	−1.61483	−	19.0116i	−0.0614753	−	0.723758i
$691$	−19.1984	+	3.81879i	−0.730340	+	0.145274i	−0.546234	−	0.837633i	$-0.683939\pi$
$691$	−19.1984	+	3.81879i	−0.730340	+	0.145274i	−0.184106	+	0.982906i	$0.558939\pi$
$692$	16.8840	+	29.4732i	0.641834	+	1.12040i
$693$	0.536917	+	0.536917i	0.0203958	+	0.0203958i
$694$	−7.23176	+	30.7804i	−0.274514	+	1.16841i
$695$	15.4288	−	30.3811i	0.585246	−	1.15242i
$696$	−1.49926	+	14.4710i	−0.0568291	+	0.548522i
$697$	−31.0816	−	7.90145i	−1.17730	−	0.299289i
$698$	−0.136050	+	3.95199i	−0.00514955	+	0.149585i
$699$	−1.45000	+	0.600609i	−0.0548440	+	0.0227171i
$700$	3.19238	+	1.42401i	0.120661	+	0.0538226i
$701$	21.4877	+	21.4877i	0.811580	+	0.811580i	0.984871	−	0.173291i	$-0.0554401\pi$
$701$	21.4877	+	21.4877i	0.811580	+	0.811580i	−0.173291	+	0.984871i	$0.555440\pi$
$702$	7.91081	+	12.7696i	0.298574	+	0.481958i
$703$	−7.23723	−	36.3840i	−0.272957	−	1.37225i
$704$	6.48131	+	6.61386i	0.244273	+	0.249269i
$705$	3.97041	+	12.1643i	0.149534	+	0.458133i
$706$	17.2774	−	37.9615i	0.650243	−	1.42870i
$707$	4.07924	+	2.72566i	0.153415	+	0.102509i
$708$	−0.706786	−	5.51223i	−0.0265626	−	0.207162i
$709$	32.0939	−	21.4445i	1.20531	−	0.805364i	0.219896	−	0.975523i	$-0.429428\pi$
$709$	32.0939	−	21.4445i	1.20531	−	0.805364i	0.985417	+	0.170159i	$0.0544282\pi$
$710$	32.8660	+	3.68361i	1.23344	+	0.138244i
$711$	4.09124	−	20.5680i	0.153433	−	0.771362i
$712$	6.68847	+	22.4575i	0.250661	+	0.841629i
$713$	−53.8288			−2.01590
$714$	−2.15218	−	0.187726i	−0.0805434	−	0.00702545i
$715$	3.45979	+	4.03994i	0.129389	+	0.151085i
$716$	20.8804	−	7.00945i	0.780337	−	0.261956i
$717$	1.92889	−	9.69716i	0.0720356	−	0.362147i
$718$	−28.2582	−	30.2732i	−1.05459	−	1.12978i
$719$	15.2915	+	22.8853i	0.570276	+	0.853478i	0.998745	−	0.0500781i	$-0.0159470\pi$
$719$	15.2915	+	22.8853i	0.570276	+	0.853478i	−0.428469	+	0.903556i	$0.640947\pi$
$720$	12.0862	−	11.6471i	0.450428	−	0.434063i
$721$	0.613950	+	0.410229i	0.0228647	+	0.0152777i
$722$	0.491301	−	1.07948i	0.0182843	−	0.0401740i
$723$	9.01572	−	21.7659i	0.335298	−	0.809482i
$724$	−12.2417	−	9.45916i	−0.454958	−	0.351547i
$725$	24.2434	−	1.01751i	0.900378	−	0.0377893i
$726$	12.3092	−	7.62559i	0.456838	−	0.283012i
$727$	−23.7467	−	23.7467i	−0.880717	−	0.880717i	0.112891	−	0.993607i	$-0.463989\pi$
$727$	−23.7467	−	23.7467i	−0.880717	−	0.880717i	−0.993607	+	0.112891i	$0.963989\pi$
$728$	−1.94129	−	0.599629i	−0.0719489	−	0.0222237i
$729$	6.18062	+	14.9213i	0.228912	+	0.552642i
$730$	−7.55849	−	9.46666i	−0.279752	−	0.350377i
$731$	−1.66034	+	31.5403i	−0.0614101	+	1.16656i
$732$	10.1333	+	0.698515i	0.374537	+	0.0258178i
$733$	14.1416	−	5.85764i	0.522332	−	0.216357i	−0.105909	−	0.994376i	$-0.533775\pi$
$733$	14.1416	−	5.85764i	0.522332	−	0.216357i	0.628241	+	0.778019i	$0.283775\pi$
$734$	6.47813	−	27.5728i	0.239112	−	1.01773i
$735$	−1.25718	+	16.2519i	−0.0463717	+	0.599462i
$736$	29.4431	−	13.0423i	1.08529	−	0.480744i
$737$	−10.2672	+	2.04228i	−0.378198	+	0.0752282i
$738$	−16.7590	−	12.0522i	−0.616908	−	0.443647i
$739$	−6.25000	+	15.0888i	−0.229910	+	0.555052i	−0.996166	−	0.0874836i	$-0.972117\pi$
$739$	−6.25000	+	15.0888i	−0.229910	+	0.555052i	0.766256	+	0.642535i	$0.222117\pi$
$740$	9.50575	+	37.7510i	0.349438	+	1.38775i
$741$	7.71790	+	5.15694i	0.283524	+	0.189445i
$742$	4.11613	−	0.672444i	0.151108	−	0.0246862i
$743$	4.81601	+	7.20767i	0.176682	+	0.264424i	0.909232	−	0.416290i	$-0.136670\pi$
$743$	4.81601	+	7.20767i	0.176682	+	0.264424i	−0.732550	+	0.680714i	$0.761670\pi$
$744$	17.8722	+	22.0035i	0.655227	+	0.806687i
$745$	32.4917	−	18.2534i	1.19040	−	0.668752i
$746$	−3.21496	−	8.58585i	−0.117708	−	0.314350i
$747$	31.6129			1.15666
$748$	−2.98234	+	9.06728i	−0.109045	+	0.331532i
$749$			0.184631i			0.00674628i
$750$	13.2523	+	10.2579i	0.483905	+	0.374567i
$751$	−33.7341	−	6.71014i	−1.23098	−	0.244856i	−0.463595	−	0.886047i	$-0.653441\pi$
$751$	−33.7341	−	6.71014i	−1.23098	−	0.244856i	−0.767381	+	0.641191i	$0.778441\pi$
$752$	−17.2218	+	13.0310i	−0.628014	+	0.475193i
$753$	−8.29568	−	12.4154i	−0.302311	−	0.452441i
$754$	−13.9192	+	2.27396i	−0.506908	+	0.0828126i
$755$	0.984050	−	0.117805i	0.0358132	−	0.00428737i
$756$	−3.23548	−	1.60916i	−0.117673	−	0.0585244i
$757$	21.9866	+	9.10715i	0.799117	+	0.331005i	0.744603	−	0.667508i	$-0.232639\pi$
$757$	21.9866	+	9.10715i	0.799117	+	0.331005i	0.0545141	+	0.998513i	$0.482639\pi$
$758$	−0.788244	+	1.09608i	−0.0286303	+	0.0398115i
$759$	1.36252	+	6.84985i	0.0494563	+	0.248634i
$760$	9.91688	−	25.0621i	0.359723	−	0.909098i
$761$	5.98972	+	5.98972i	0.217127	+	0.217127i	0.807287	−	0.590160i	$-0.200935\pi$
$761$	5.98972	+	5.98972i	0.217127	+	0.217127i	−0.590160	+	0.807287i	$0.700935\pi$
$762$	1.30370	−	5.54894i	0.0472282	−	0.201017i
$763$	2.33313	−	0.966416i	0.0844652	−	0.0349866i
$764$	−10.6325	−	0.732929i	−0.384671	−	0.0265165i
$765$	16.3894	+	5.54328i	0.592561	+	0.200418i
$766$	1.95764	+	0.0673929i	0.0707325	+	0.00243500i
$767$	4.97738	−	2.06170i	0.179723	−	0.0744436i
$768$	−15.1069	−	7.70510i	−0.545125	−	0.278034i
$769$	13.9724	−	13.9724i	0.503858	−	0.503858i	−0.408776	−	0.912635i	$-0.634044\pi$
$769$	13.9724	−	13.9724i	0.503858	−	0.503858i	0.912635	+	0.408776i	$0.134044\pi$
$770$	−1.21933	−	0.387847i	−0.0439414	−	0.0139770i
$771$	−0.395748	−	1.98956i	−0.0142525	−	0.0716522i
$772$	16.3832	−	21.2025i	0.589643	−	0.763093i
$773$	16.0177	−	38.6701i	0.576116	−	1.39087i	−0.320156	−	0.947365i	$-0.603735\pi$
$773$	16.0177	−	38.6701i	0.576116	−	1.39087i	0.896273	−	0.443503i	$-0.146265\pi$
$774$	−8.42143	+	18.5034i	−0.302702	+	0.665090i
$775$	32.0002	−	34.8040i	1.14948	−	1.25020i
$776$	2.08407	+	22.3173i	0.0748138	+	0.801144i
$777$	2.68160	−	1.79179i	0.0962020	−	0.0642801i
$778$	−18.2412	+	17.0271i	−0.653980	+	0.610452i
$779$	−32.5106	−	6.46677i	−1.16481	−	0.231696i
$780$	−8.36113	−	4.99743i	−0.299376	−	0.178937i
$781$	−12.1056			−0.433173
$782$	25.8925	+	20.7698i	0.925914	+	0.742727i
$783$	−25.0836			−0.896414
$784$	−26.6213	+	6.94095i	−0.950759	+	0.247891i
$785$	20.5738	−	11.5581i	0.734310	−	0.412525i
$786$	−21.2173	−	22.7302i	−0.756795	−	0.810759i
$787$	18.1847	+	27.2153i	0.648215	+	0.970122i	0.999428	+	0.0338263i	$0.0107693\pi$
$787$	18.1847	+	27.2153i	0.648215	+	0.970122i	−0.351213	+	0.936296i	$0.614231\pi$
$788$	−0.0708327	−	0.552425i	−0.00252331	−	0.0196793i
$789$	18.5803	−	27.8073i	0.661475	−	0.989967i
$790$	9.80278	+	33.9514i	0.348767	+	1.20794i
$791$	−0.514549	+	1.24223i	−0.0182953	+	0.0441687i
$792$	−3.92166	+	4.72954i	−0.139350	+	0.168057i
$793$	1.92102	+	9.65763i	0.0682175	+	0.342952i
$794$	−3.20593	−	5.17500i	−0.113774	−	0.183654i
$795$	19.9356	+	1.54213i	0.707041	+	0.0546936i
$796$	−10.2778	+	37.8459i	−0.364285	+	1.34141i
$797$	−17.1386	−	41.3763i	−0.607081	−	1.46562i	−0.866160	−	0.499767i	$-0.833419\pi$
$797$	−17.1386	−	41.3763i	−0.607081	−	1.46562i	0.259078	−	0.965856i	$-0.416581\pi$
$798$	−2.23161	−	0.0768242i	−0.0789980	−	0.00271955i
$799$	−20.0901	−	9.58826i	−0.710737	−	0.339208i
$800$	−9.07063	+	26.7904i	−0.320695	+	0.947182i
$801$	−14.3635	+	5.94954i	−0.507508	+	0.210217i
$802$	12.5863	−	53.5707i	0.444437	−	1.89165i
$803$	3.13545	+	3.13545i	0.110648	+	0.110648i
$804$	16.6349	−	9.52945i	0.586667	−	0.336078i
$805$	−2.75003	+	3.49801i	−0.0969256	+	0.123289i
$806$	−16.0446	+	22.3106i	−0.565147	+	0.785858i
$807$	12.1758	−	29.3951i	0.428610	−	1.03476i
$808$	−18.8900	+	34.9145i	−0.664547	+	1.22829i
$809$	8.47819	−	12.6885i	0.298077	−	0.446104i	−0.651954	−	0.758258i	$-0.726051\pi$
$809$	8.47819	−	12.6885i	0.298077	−	0.446104i	0.950031	+	0.312154i	$0.101051\pi$
$810$	0.366181	+	0.308845i	0.0128663	+	0.0108517i
$811$	17.2985	+	25.8890i	0.607432	+	0.909087i	0.999943	−	0.0106608i	$-0.00339349\pi$
$811$	17.2985	+	25.8890i	0.607432	+	0.909087i	−0.392511	+	0.919747i	$0.628393\pi$
$812$	2.55836	−	2.22840i	0.0897809	−	0.0782014i
$813$	7.20806	+	1.43377i	0.252798	+	0.0502846i
$814$	−4.99695	−	13.3448i	−0.175143	−	0.467736i
$815$	−0.288868	−	0.337306i	−0.0101186	−	0.0118153i
$816$	−0.106773	−	17.4800i	−0.00373780	−	0.611923i
$817$			32.6449i			1.14210i
$818$	−0.0700705	+	0.0262378i	−0.00244996	+	0.000917383i
$819$	0.262992	−	1.32215i	0.00918968	−	0.0461996i
$820$	34.4148	+	5.06148i	1.20182	+	0.176754i
$821$	11.7296	+	17.5547i	0.409367	+	0.612662i	0.977667	−	0.210160i	$-0.0673985\pi$
$821$	11.7296	+	17.5547i	0.409367	+	0.612662i	−0.568300	+	0.822822i	$0.692399\pi$
$822$	4.50108	+	27.5518i	0.156993	+	0.960978i
$823$	30.9304	+	20.6670i	1.07817	+	0.720407i	0.962062	−	0.272830i	$-0.0879595\pi$
$823$	30.9304	+	20.6670i	1.07817	+	0.720407i	0.116104	+	0.993237i	$0.462960\pi$
$824$	−2.84306	+	5.25484i	−0.0990427	+	0.183061i
$825$	−5.23890	−	3.19115i	−0.182395	−	0.111101i
$826$	−0.756671	+	1.05218i	−0.0263280	+	0.0366100i
$827$	7.45579	+	37.4828i	0.259263	+	1.30340i	0.862588	+	0.505908i	$0.168842\pi$
$827$	7.45579	+	37.4828i	0.259263	+	1.30340i	−0.603325	+	0.797496i	$0.706158\pi$
$828$	10.6204	+	18.5392i	0.369083	+	0.644281i
$829$	1.42135	−	1.42135i	0.0493656	−	0.0493656i	−0.681993	−	0.731359i	$-0.738887\pi$
$829$	1.42135	−	1.42135i	0.0493656	−	0.0493656i	0.731359	+	0.681993i	$0.238887\pi$
$830$	−47.3140	+	24.4781i	−1.64229	+	0.849648i
$831$	−0.673322	+	0.278899i	−0.0233573	+	0.00967490i
$832$	3.37034	−	16.0909i	0.116845	−	0.557850i
$833$	−18.9702	−	21.0785i	−0.657280	−	0.730326i
$834$	0.785861	−	22.8278i	0.0272121	−	0.790463i
$835$	4.65458	+	2.36379i	0.161078	+	0.0818022i
$836$	−2.58560	+	9.52096i	−0.0894247	+	0.329289i
$837$	−34.5597	+	34.5597i	−1.19456	+	1.19456i
$838$	35.5695	−	22.0354i	1.22873	−	0.761200i
$839$	28.7422	−	5.71717i	0.992290	−	0.197379i	0.327858	−	0.944727i	$-0.393673\pi$
$839$	28.7422	−	5.71717i	0.992290	−	0.197379i	0.664432	+	0.747348i	$0.268673\pi$
$840$	2.34294	−	0.0372835i	0.0808390	−	0.00128640i
$841$	−2.08518	+	5.03406i	−0.0719027	+	0.173588i
$842$	17.9897	−	39.5266i	0.619966	−	1.36218i
$843$	−4.49911	−	3.00621i	−0.154957	−	0.103539i
$844$	0.400975	−	0.0514136i	0.0138021	−	0.00176973i
$845$	−5.30198	+	18.8961i	−0.182394	+	0.650046i
$846$	−9.77733	−	10.4745i	−0.336152	−	0.360121i
$847$	−3.31190	−	0.658779i	−0.113798	−	0.0226359i
$848$	8.51416	+	32.6552i	0.292378	+	1.12138i
$849$			6.94499i			0.238351i
$850$	−28.8217	+	4.39401i	−0.988578	+	0.150713i
$851$	−49.5537			−1.69868
$852$	21.0168	−	7.05525i	0.720023	−	0.241709i
$853$	−1.79203	+	9.00915i	−0.0613580	+	0.308468i	−0.999261	−	0.0384292i	$-0.987765\pi$
$853$	−1.79203	+	9.00915i	−0.0613580	+	0.308468i	0.937903	+	0.346897i	$0.112765\pi$
$854$	−1.61634	−	1.73159i	−0.0553099	−	0.0592538i
$855$	17.2178	+	4.83105i	0.588835	+	0.165219i
$856$	−1.48746	+	0.138904i	−0.0508403	+	0.00474765i
$857$	0.806870	−	1.20757i	0.0275622	−	0.0412497i	−0.817433	−	0.576024i	$-0.804603\pi$
$857$	0.806870	−	1.20757i	0.0275622	−	0.0412497i	0.844995	+	0.534774i	$0.179603\pi$
$858$	3.24521	+	1.47699i	0.110790	+	0.0504236i
$859$	27.4739	+	11.3801i	0.937399	+	0.388283i	0.798481	−	0.602021i	$-0.205637\pi$
$859$	27.4739	+	11.3801i	0.937399	+	0.388283i	0.138918	+	0.990304i	$0.455637\pi$
$860$	−1.72324	−	34.2142i	−0.0587621	−	1.16670i
$861$	−0.562210	−	2.82642i	−0.0191601	−	0.0963241i
$862$	17.4051	−	10.7825i	0.592822	−	0.367255i
$863$	−22.1448	−	22.1448i	−0.753818	−	0.753818i	0.221371	−	0.975190i	$-0.428947\pi$
$863$	−22.1448	−	22.1448i	−0.753818	−	0.753818i	−0.975190	+	0.221371i	$0.928947\pi$
$864$	10.5298	−	27.2768i	0.358231	−	0.927977i
$865$	17.1954	−	33.8598i	0.584662	−	1.15127i
$866$	−36.8091	−	1.26717i	−1.25082	−	0.0430603i
$867$	15.9499	−	8.38214i	0.541688	−	0.284673i
$868$	0.454619	−	6.59510i	0.0154308	−	0.223852i
$869$	−4.95009	−	11.9506i	−0.167920	−	0.405396i
$870$	14.4468	−	7.47411i	0.489792	−	0.253396i
$871$	13.1416	+	13.1416i	0.445286	+	0.445286i
$872$	9.54111	+	18.0695i	0.323103	+	0.611912i
$873$	−14.5858	+	2.90129i	−0.493654	+	0.0981939i
$874$	27.8538	+	20.0310i	0.942170	+	0.677558i
$875$	−0.626863	−	3.85758i	−0.0211918	−	0.130410i
$876$	−7.27089	−	3.61616i	−0.245661	−	0.122179i
$877$	−19.1332	+	28.6349i	−0.646083	+	0.966931i	0.353422	+	0.935464i	$0.385018\pi$
$877$	−19.1332	+	28.6349i	−0.646083	+	0.966931i	−0.999505	+	0.0314670i	$0.989982\pi$
$878$	−2.79630	−	17.1165i	−0.0943705	−	0.577655i
$879$	3.27625	−	2.18912i	0.110505	−	0.0738372i
$880$	2.20730	−	10.1151i	0.0744081	−	0.340981i
$881$	18.7176	+	3.72317i	0.630613	+	0.125437i	0.500041	−	0.866002i	$-0.333318\pi$
$881$	18.7176	+	3.72317i	0.630613	+	0.125437i	0.130573	+	0.991439i	$0.458318\pi$
$882$	−6.40086	−	17.0941i	−0.215528	−	0.575588i
$883$	−2.13355			−0.0717996			−0.0358998	−	0.999355i	$-0.511430\pi$
$883$	−2.13355			−0.0717996			−0.0358998	+	0.999355i	$0.511430\pi$
$884$	16.3263	−	4.54096i	0.549112	−	0.152729i
$885$	−4.71923	+	4.04154i	−0.158635	+	0.135855i
$886$	−7.88342	−	21.0534i	−0.264849	−	0.707303i
$887$	3.28868	−	16.5333i	0.110423	−	0.555134i	−0.885478	−	0.464682i	$-0.846169\pi$
$887$	3.28868	−	16.5333i	0.110423	−	0.555134i	0.995901	−	0.0904522i	$-0.0288312\pi$
$888$	16.4528	+	20.2560i	0.552120	+	0.679746i
$889$	−1.10526	+	0.738508i	−0.0370691	+	0.0247688i
$890$	16.8906	−	20.0262i	0.566173	−	0.671281i
$891$	−0.145794	−	0.0974167i	−0.00488429	−	0.00326358i
$892$	−14.0076	+	28.1647i	−0.469010	+	0.943024i
$893$	−21.2573	−	8.80505i	−0.711348	−	0.294650i
$894$	14.5858	−	20.2821i	0.487823	−	0.678336i
$895$	−19.3590	−	15.2195i	−0.647101	−	0.508731i
$896$	1.34927	+	3.71752i	0.0450761	+	0.124194i
$897$	8.76752	−	8.76752i	0.292739	−	0.292739i
$898$	−37.5207	−	8.81536i	−1.25208	−	0.294172i
$899$	−17.5609	−	42.3958i	−0.585689	−	1.41398i
$900$	−18.3005	−	4.15440i	−0.610015	−	0.138480i
$901$	−25.8561	+	23.2700i	−0.861391	+	0.775235i
$902$	−12.7252	−	0.438071i	−0.423702	−	0.0145862i
$903$	−2.62206	+	1.08609i	−0.0872567	+	0.0361429i
$904$	−10.3950	−	3.21083i	−0.345733	−	0.106791i
$905$	−1.33399	+	17.2449i	−0.0443434	+	0.573241i
$906$	0.564766	−	0.349874i	0.0187631	−	0.0116238i
$907$	−44.1047	+	8.77296i	−1.46447	+	0.291301i	−0.862028	−	0.506860i	$-0.830806\pi$
$907$	−44.1047	+	8.77296i	−1.46447	+	0.291301i	−0.602443	+	0.798162i	$0.705806\pi$
$908$	4.13066	−	5.34573i	0.137081	−	0.177404i
$909$	−24.3333	−	10.0792i	−0.807086	−	0.334306i
$910$	0.630140	+	2.18246i	0.0208889	+	0.0723477i
$911$	−15.4110	−	10.2973i	−0.510589	−	0.341165i	0.273440	−	0.961889i	$-0.411839\pi$
$911$	−15.4110	−	10.2973i	−0.510589	−	0.341165i	−0.784029	+	0.620724i	$0.786839\pi$
$912$	−1.05999	−	18.0364i	−0.0350997	−	0.597247i
$913$	16.2131	−	10.8332i	0.536574	−	0.358527i
$914$	10.2554	−	9.57281i	0.339219	−	0.316641i
$915$	−5.56215	−	9.90083i	−0.183879	−	0.327311i
$916$	−33.3325	+	11.1896i	−1.10134	+	0.369714i
$917$			7.25129i			0.239459i
$918$	29.9586	−	3.28891i	0.988781	−	0.108550i
$919$			37.1432i			1.22524i	0.790377	+	0.612621i	$0.209885\pi$
$919$			37.1432i			1.22524i	−0.790377	+	0.612621i	$0.790115\pi$
$920$	−30.2502	−	19.5236i	−0.997319	−	0.643673i
$921$	1.00258	−	5.04031i	0.0330362	−	0.166084i
$922$	10.5990	+	11.3548i	0.349060	+	0.373950i
$923$	11.9402	+	17.8697i	0.393015	+	0.588189i
$924$	−0.850752	+	0.109085i	−0.0279877	+	0.00358862i
$925$	29.4588	−	32.0399i	0.968598	−	1.05346i
$926$	17.5625	−	38.5879i	0.577139	−	1.26808i
$927$	−3.66232	−	1.51698i	−0.120286	−	0.0498242i
$928$	19.8776	+	18.9346i	0.652513	+	0.621560i
$929$	37.0147	−	7.36268i	1.21441	−	0.241562i	0.454000	−	0.891002i	$-0.349997\pi$
$929$	37.0147	−	7.36268i	1.21441	−	0.241562i	0.760413	+	0.649440i	$0.224997\pi$
$930$	9.60681	−	30.2022i	0.315020	−	0.990368i
$931$	−20.7257	−	20.7257i	−0.679257	−	0.679257i
$932$	−0.776149	+	2.85802i	−0.0254236	+	0.0936176i
$933$	8.44199	+	20.3808i	0.276379	+	0.667237i
$934$	−29.6720	−	1.02147i	−0.970896	−	0.0334236i
$935$	10.3051	−	2.77345i	0.337013	−	0.0907014i
$936$	10.8496	+	1.12406i	0.354630	+	0.0367411i
$937$	10.5028	+	25.3560i	0.343112	+	0.828345i	0.997398	+	0.0720975i	$0.0229693\pi$
$937$	10.5028	+	25.3560i	0.343112	+	0.828345i	−0.654286	+	0.756247i	$0.727031\pi$
$938$	−4.35229	−	1.02256i	−0.142107	−	0.0333877i
$939$	12.0954	−	12.0954i	0.394719	−	0.394719i
$940$	22.7439	+	8.10620i	0.741825	+	0.264395i
$941$	−6.81317	+	1.35522i	−0.222103	+	0.0441790i	−0.304887	−	0.952388i	$-0.598619\pi$
$941$	−6.81317	+	1.35522i	−0.222103	+	0.0441790i	0.0827842	+	0.996567i	$0.473619\pi$
$942$	9.23575	−	12.8427i	0.300917	−	0.418436i
$943$	−16.9446	+	40.9078i	−0.551791	+	1.33214i
$944$	−9.04603	−	5.30444i	−0.294423	−	0.172645i
$945$	0.480226	+	4.01142i	0.0156218	+	0.130492i
$946$	2.02178	+	12.3756i	0.0657336	+	0.402365i
$947$	30.7100	−	20.5198i	0.997942	−	0.666804i	0.0545599	−	0.998511i	$-0.482624\pi$
$947$	30.7100	−	20.5198i	0.997942	−	0.666804i	0.943383	+	0.331707i	$0.107624\pi$
$948$	15.5588	+	17.8627i	0.505328	+	0.580153i
$949$	1.53580	−	7.72100i	0.0498543	−	0.250634i
$950$	−29.5100	+	6.10138i	−0.957431	+	0.197955i
$951$	11.7173			0.379961
$952$	−2.76340	+	2.99694i	−0.0895623	+	0.0971313i
$953$			55.1891i			1.78775i	0.448315	+	0.893875i	$0.352024\pi$
$953$			55.1891i			1.78775i	−0.448315	+	0.893875i	$0.647976\pi$
$954$	−20.9686	+	7.85166i	−0.678883	+	0.254207i
$955$	5.83618	+	10.3886i	0.188854	+	0.336168i
$956$	−12.2538	−	14.0683i	−0.396317	−	0.455001i
$957$	−4.95047	+	3.30780i	−0.160026	+	0.106926i
$958$	−34.7697	+	5.68026i	−1.12336	+	0.183521i
$959$	3.61699	−	5.41320i	0.116799	−	0.174801i
$960$	2.06304	+	18.8475i	0.0665844	+	0.608301i
$961$	−53.9669	−	22.3538i	−1.74087	−	0.721091i
$962$	−14.7703	+	20.5387i	−0.476215	+	0.662195i
$963$	−0.193372	−	0.972149i	−0.00623134	−	0.0313271i
$964$	−22.0977	−	38.5744i	−0.711720	−	1.24240i
$965$	−29.8681	−	2.31046i	−0.961488	−	0.0743765i
$966$	−0.682206	+	2.90366i	−0.0219496	+	0.0934239i
$967$	3.75359	+	9.06197i	0.120707	+	0.291413i	0.972671	−	0.232188i	$-0.0745883\pi$
$967$	3.75359	+	9.06197i	0.120707	+	0.291413i	−0.851964	+	0.523601i	$0.824588\pi$
$968$	2.81571	−	27.1776i	0.0905003	−	0.873520i
$969$	16.0075	−	9.51839i	0.514235	−	0.305775i
$970$	19.5836	−	15.6362i	0.628791	−	0.502047i
$971$	22.5048	−	9.32181i	0.722215	−	0.299151i	0.00886622	−	0.999961i	$-0.497178\pi$
$971$	22.5048	−	9.32181i	0.722215	−	0.299151i	0.713348	+	0.700810i	$0.247178\pi$
$972$	30.2383	+	8.21177i	0.969893	+	0.263393i
$973$	−3.76657	+	3.76657i	−0.120751	+	0.120751i
$974$	−12.6245	+	7.82092i	−0.404515	+	0.250599i
$975$	0.456678	+	10.8809i	0.0146254	+	0.348469i
$976$	12.7343	−	14.3246i	0.407616	−	0.458518i
$977$	11.4274	+	4.73338i	0.365595	+	0.151434i	0.557915	−	0.829898i	$-0.311601\pi$
$977$	11.4274	+	4.73338i	0.365595	+	0.151434i	−0.192321	+	0.981332i	$0.561601\pi$
$978$	−0.270951	−	0.123318i	−0.00866407	−	0.00394327i
$979$	−5.32767	+	7.97343i	−0.170273	+	0.254832i
$980$	22.8161	+	20.6280i	0.728832	+	0.658936i
$981$	−11.2726	+	7.53212i	−0.359907	+	0.240482i
$982$	30.3819	+	32.5483i	0.969524	+	1.03866i
$983$	−6.33908	−	1.26092i	−0.202185	−	0.0402171i	0.0929586	−	0.995670i	$-0.470368\pi$
$983$	−6.33908	−	1.26092i	−0.202185	−	0.0402171i	−0.295144	+	0.955453i	$0.595368\pi$
$984$	22.3477	−	6.65579i	0.712420	−	0.212179i
$985$	−0.472953	+	0.405035i	−0.0150695	+	0.0129055i
$986$	−7.91133	+	27.1689i	−0.251948	+	0.865235i
$987$		−	2.00034i		−	0.0636715i
$988$	16.6046	−	5.57411i	0.528264	−	0.177336i
$989$	42.7690	+	8.50728i	1.35997	+	0.270516i
$990$	6.82639	+	0.765099i	0.216957	+	0.0243165i
$991$	−5.89100	−	8.81651i	−0.187134	−	0.280066i	0.726026	−	0.687667i	$-0.241365\pi$
$991$	−5.89100	−	8.81651i	−0.187134	−	0.280066i	−0.913160	+	0.407602i	$0.866365\pi$
$992$	53.4747	−	1.29914i	1.69782	−	0.0412478i
$993$	−6.29671	+	9.42370i	−0.199820	+	0.299052i
$994$	−4.70559	−	2.14165i	−0.149252	−	0.0679290i
$995$	41.6814	−	13.6048i	1.32139	−	0.431301i
$996$	−21.8342	+	28.2569i	−0.691842	+	0.895354i
$997$	12.0547	−	2.39783i	0.381777	−	0.0759402i	−0.000471116	−	1.00000i	$-0.500150\pi$
$997$	12.0547	−	2.39783i	0.381777	−	0.0759402i	0.382248	+	0.924060i	$0.375150\pi$
$998$	15.0721	+	24.3294i	0.477100	+	0.770134i
$999$	−31.8149	+	31.8149i	−1.00658	+	1.00658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.99.12	✓	832
5.4	even	2	inner	680.2.co.a.99.93	yes	832
8.3	odd	2	inner	680.2.co.a.99.90	yes	832
17.11	odd	16	inner	680.2.co.a.419.15	yes	832
40.19	odd	2	inner	680.2.co.a.99.15	yes	832
85.79	odd	16	inner	680.2.co.a.419.90	yes	832
136.11	even	16	inner	680.2.co.a.419.93	yes	832
680.419	even	16	inner	680.2.co.a.419.12	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.12	✓	832	1.1	even	1	trivial
680.2.co.a.99.15	yes	832	40.19	odd	2	inner
680.2.co.a.99.90	yes	832	8.3	odd	2	inner
680.2.co.a.99.93	yes	832	5.4	even	2	inner
680.2.co.a.419.12	yes	832	680.419	even	16	inner
680.2.co.a.419.15	yes	832	17.11	odd	16	inner
680.2.co.a.419.90	yes	832	85.79	odd	16	inner
680.2.co.a.419.93	yes	832	136.11	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32441 + 0.495923i) q^{2} +(1.03954 + 0.206777i) q^{3} +(1.50812 - 1.31361i) q^{4} +(-2.15293 - 0.604079i) q^{5} +(-1.47932 + 0.241673i) q^{6} +(0.290647 + 0.194204i) q^{7} +(-1.34592 + 2.48767i) q^{8} +(-1.73376 - 0.718147i) q^{9} +(3.15093 - 0.267637i) q^{10} +(-1.13528 + 0.225821i) q^{11} +(1.83937 - 1.05370i) q^{12} +(1.45311 + 1.45311i) q^{13} +(-0.481246 - 0.113067i) q^{14} +(-2.11313 - 1.07314i) q^{15} +(0.548854 - 3.96217i) q^{16} +(3.88693 - 1.37541i) q^{17} +(2.65235 + 0.0913087i) q^{18} +(3.93722 - 1.63085i) q^{19} +(-4.04040 + 1.91708i) q^{20} +(0.261981 + 0.261981i) q^{21} +(1.39158 - 0.862090i) q^{22} +(-1.11058 - 5.58325i) q^{23} +(-1.91352 + 2.30772i) q^{24} +(4.27018 + 2.60108i) q^{25} +(-2.64514 - 1.20388i) q^{26} +(-4.29764 - 2.87159i) q^{27} +(0.693440 - 0.0889139i) q^{28} +(4.03508 - 2.69616i) q^{29} +(3.33085 + 0.373320i) q^{30} +(1.84475 - 9.27417i) q^{31} +(1.23802 + 5.51972i) q^{32} -1.22686 q^{33} +(-4.46579 + 3.74923i) q^{34} +(-0.508427 - 0.593681i) q^{35} +(-3.55808 + 1.19443i) q^{36} +(1.69824 - 8.53762i) q^{37} +(-4.40571 + 4.11247i) q^{38} +(1.21009 + 1.81103i) q^{39} +(4.40041 - 4.54273i) q^{40} +(-6.46731 - 4.32132i) q^{41} +(-0.476893 - 0.217048i) q^{42} +(-2.93144 + 7.07713i) q^{43} +(-1.41550 + 1.83188i) q^{44} +(3.29884 + 2.59345i) q^{45} +(4.23972 + 6.84375i) q^{46} +(-3.81771 - 3.81771i) q^{47} +(1.38984 - 4.00532i) q^{48} +(-2.63202 - 6.35427i) q^{49} +(-6.94540 - 1.32721i) q^{50} +(4.32501 - 0.626065i) q^{51} +(4.10028 + 0.282644i) q^{52} +(-7.79451 + 3.22859i) q^{53} +(7.11592 + 1.67186i) q^{54} +(2.58058 + 0.199623i) q^{55} +(-0.874304 + 0.461651i) q^{56} +(4.43010 - 0.881202i) q^{57} +(-4.00702 + 5.57191i) q^{58} +(1.00326 - 2.42208i) q^{59} +(-4.59654 + 1.15742i) q^{60} +(3.98410 + 2.66209i) q^{61} +(2.15608 + 13.1977i) q^{62} +(-0.364445 - 0.545431i) q^{63} +(-4.37700 - 6.69640i) q^{64} +(-2.25064 - 4.00623i) q^{65} +(1.62486 - 0.608427i) q^{66} +9.04379 q^{67} +(4.05520 - 7.18020i) q^{68} -6.03363i q^{69} +(0.967786 + 0.534136i) q^{70} +(10.2573 + 2.04030i) q^{71} +(4.12001 - 3.34646i) q^{72} +(-2.12827 - 3.18517i) q^{73} +(1.98484 + 12.1495i) q^{74} +(3.90116 + 3.58688i) q^{75} +(3.79550 - 7.63149i) q^{76} +(-0.373821 - 0.154842i) q^{77} +(-2.50078 - 1.79843i) q^{78} +(2.18012 + 10.9602i) q^{79} +(-3.57510 + 8.19870i) q^{80} +(0.107115 + 0.107115i) q^{81} +(10.7084 + 2.51591i) q^{82} +(-15.5635 + 6.44659i) q^{83} +(0.739241 + 0.0509579i) q^{84} +(-9.19913 + 0.613146i) q^{85} +(0.372718 - 10.8268i) q^{86} +(4.75212 - 1.96839i) q^{87} +(0.966224 - 3.12813i) q^{88} +(5.85808 - 5.85808i) q^{89} +(-5.65516 - 1.79881i) q^{90} +(0.140142 + 0.704542i) q^{91} +(-9.00910 - 6.96135i) q^{92} +(3.83536 - 9.25938i) q^{93} +(6.94951 + 3.16292i) q^{94} +(-9.46170 + 1.13270i) q^{95} +(0.145620 + 5.99394i) q^{96} +(6.58914 - 4.40272i) q^{97} +(6.63710 + 7.11037i) q^{98} +(2.13047 + 0.423777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

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Database

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