LMFDB - Embedded newform 680.2.co.a.419.93

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			419.93
Character	$\chi$	$=$	680.419
Dual form			680.2.co.a.99.93

$q$-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} +(0.265792 + 2.22021i) 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} +(-0.749038 + 3.07229i) 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} +(-0.735389 - 2.25303i) 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} +(-2.51565 + 3.69750i) 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} +(-4.85871 + 1.18023i) 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} +(0.143375 - 3.34864i) 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} +(-5.16543 + 3.64943i) 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} +(-2.05526 - 3.65844i) 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} +(-7.02022 - 0.846435i) 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} +(0.199623 - 2.58058i) 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} +(1.85055 - 4.36386i) 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} +(-3.61244 - 2.83999i) q^{65} +(1.62486 + 0.608427i) q^{66} -9.04379 q^{67} +(-4.05520 - 7.18020i) q^{68} +6.03363i q^{69} +(-0.378945 - 1.03842i) 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} +(4.80676 - 2.23156i) 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} +(-8.65098 + 2.27169i) 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} +(2.02060 - 8.99540i) 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} +(-0.907700 - 5.86453i) 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} +(-2.57435 + 9.17494i) 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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$	$-1$	$-1$

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	$-0.661480\pi$
$3$	−1.03954	+	0.206777i	−0.600176	+	0.119383i	−0.114354	+	0.993440i	$0.536480\pi$
$4$	1.50812	+	1.31361i	0.754060	+	0.656805i
$5$	0.265792	+	2.22021i	0.118866	+	0.992910i
$5$	0.265792	+	2.22021i	0.118866	+	0.992910i
$6$	−1.47932	−	0.241673i	−0.603928	−	0.0986627i
$7$	−0.290647	+	0.194204i	−0.109854	+	0.0734023i	−0.609284	−	0.792952i	$-0.708543\pi$
$7$	−0.290647	+	0.194204i	−0.109854	+	0.0734023i	0.499429	+	0.866355i	$0.333543\pi$
$8$	1.34592	+	2.48767i	0.475854	+	0.879524i
$9$	−1.73376	+	0.718147i	−0.577920	+	0.239382i
$10$	−0.749038	+	3.07229i	−0.236867	+	0.971542i
$11$	−1.13528	−	0.225821i	−0.342299	−	0.0680875i	0.0209474	−	0.999781i	$-0.493332\pi$
$11$	−1.13528	−	0.225821i	−0.342299	−	0.0680875i	−0.363247	+	0.931693i	$0.618332\pi$
$12$	−1.83937	−	1.05370i	−0.530980	−	0.304177i
$13$	−1.45311	+	1.45311i	−0.403020	+	0.403020i	−0.879296	−	0.476276i	$-0.841986\pi$
$13$	−1.45311	+	1.45311i	−0.403020	+	0.403020i	0.476276	+	0.879296i	$0.341986\pi$
$14$	−0.481246	+	0.113067i	−0.128619	+	0.0302185i
$15$	−0.735389	−	2.25303i	−0.189877	−	0.581731i
$16$	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	0.785473	−	0.618896i	$-0.212420\pi$
$19$	3.93722	+	1.63085i	0.903260	+	0.374142i	0.117787	+	0.993039i	$0.462420\pi$
$20$	−2.51565	+	3.69750i	−0.562517	+	0.826786i
$21$	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	−0.673585	−	0.739110i	$-0.735246\pi$
$23$	1.11058	−	5.58325i	0.231571	−	1.16419i	0.905156	−	0.425079i	$-0.139754\pi$
$24$	−1.91352	−	2.30772i	−0.390596	−	0.471061i
$25$	−4.85871	+	1.18023i	−0.971742	+	0.236046i
$26$	−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	0.870624	−	0.491949i	$-0.163715\pi$
$29$	4.03508	+	2.69616i	0.749296	+	0.500664i	−0.121328	+	0.992612i	$0.538715\pi$
$30$	0.143375	−	3.34864i	0.0261766	−	0.611374i
$31$	1.84475	+	9.27417i	0.331326	+	1.66569i	0.683648	+	0.729812i	$0.260392\pi$
$31$	1.84475	+	9.27417i	0.331326	+	1.66569i	−0.352322	+	0.935879i	$0.614608\pi$
$32$	−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	−0.824747	−	0.565503i	$-0.808682\pi$
$37$	−1.69824	−	8.53762i	−0.279189	−	1.40358i	0.545558	−	0.838073i	$-0.316318\pi$
$38$	4.40571	+	4.11247i	0.714701	+	0.667131i
$39$	1.21009	−	1.81103i	0.193769	−	0.289996i
$40$	−5.16543	+	3.64943i	−0.816726	+	0.577026i
$41$	−6.46731	+	4.32132i	−1.01002	+	0.674876i	−0.946366	−	0.323095i	$-0.895277\pi$
$41$	−6.46731	+	4.32132i	−1.01002	+	0.674876i	−0.0636576	+	0.997972i	$0.520277\pi$
$42$	0.476893	−	0.217048i	0.0735862	−	0.0334912i
$43$	2.93144	+	7.07713i	0.447041	+	1.07925i	0.973425	+	0.229005i	$0.0735473\pi$
$43$	2.93144	+	7.07713i	0.447041	+	1.07925i	−0.526384	+	0.850247i	$0.676453\pi$
$44$	−1.41550	−	1.83188i	−0.213394	−	0.276166i
$45$	−2.05526	−	3.65844i	−0.306380	−	0.545368i
$46$	4.23972	−	6.84375i	0.625113	−	1.00906i
$47$	3.81771	−	3.81771i	0.556871	−	0.556871i	−0.371545	−	0.928415i	$-0.621172\pi$
$47$	3.81771	−	3.81771i	0.556871	−	0.556871i	0.928415	+	0.371545i	$0.121172\pi$
$48$	−1.38984	−	4.00532i	−0.200606	−	0.578119i
$49$	−2.63202	+	6.35427i	−0.376003	+	0.907752i
$50$	−7.02022	−	0.846435i	−0.992810	−	0.119704i
$51$	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	$-0.178273\pi$
$53$	7.79451	+	3.22859i	1.07066	+	0.443481i	0.223435	+	0.974719i	$0.428273\pi$
$54$	7.11592	−	1.67186i	0.968354	−	0.227512i
$55$	0.199623	−	2.58058i	0.0269171	−	0.347966i
$56$	−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	0.975634	−	0.219406i	$-0.0704120\pi$
$59$	1.00326	+	2.42208i	0.130613	+	0.315327i	−0.845021	+	0.534734i	$0.820412\pi$
$60$	1.85055	−	4.36386i	0.238905	−	0.563372i
$61$	3.98410	−	2.66209i	0.510111	−	0.340845i	−0.273730	−	0.961807i	$-0.588257\pi$
$61$	3.98410	−	2.66209i	0.510111	−	0.340845i	0.783841	+	0.620961i	$0.213257\pi$
$62$	−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
$65$	−3.61244	−	2.83999i	−0.448068	−	0.352257i
$66$	1.62486	+	0.608427i	0.200007	+	0.0748922i
$67$	−9.04379			−1.10487			−0.552437	−	0.833554i	$-0.686302\pi$
$67$	−9.04379			−1.10487			−0.552437	+	0.833554i	$0.686302\pi$
$68$	−4.05520	−	7.18020i	−0.491766	−	0.870728i
$69$			6.03363i			0.726364i
$70$	−0.378945	−	1.03842i	−0.0452926	−	0.124115i
$71$	10.2573	−	2.04030i	1.21731	−	0.242139i	0.455679	−	0.890144i	$-0.349397\pi$
$71$	10.2573	−	2.04030i	1.21731	−	0.242139i	0.761636	+	0.648005i	$0.224397\pi$
$72$	−4.12001	−	3.34646i	−0.485548	−	0.394384i
$73$	2.12827	−	3.18517i	0.249095	−	0.372796i	−0.685760	−	0.727828i	$-0.740530\pi$
$73$	2.12827	−	3.18517i	0.249095	−	0.372796i	0.934854	+	0.355032i	$0.115530\pi$
$74$	1.98484	−	12.1495i	0.230733	−	1.41235i
$75$	4.80676	−	2.23156i	0.555037	−	0.257678i
$76$	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	−0.640112	−	0.768282i	$-0.721112\pi$
$79$	2.18012	−	10.9602i	0.245283	−	1.23312i	0.885395	−	0.464839i	$-0.153888\pi$
$80$	−8.65098	+	2.27169i	−0.967209	+	0.253982i
$81$	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	0.999999	+	0.00170618i	$0.000543093\pi$
$83$	15.5635	+	6.44659i	1.70831	+	0.707605i	0.708312	+	0.705899i	$0.249457\pi$
$84$	0.739241	−	0.0509579i	0.0806578	−	0.00555997i
$85$	2.02060	−	8.99540i	0.219164	−	0.975688i
$86$	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	0.945776	−	0.324820i	$-0.105304\pi$
$89$	5.85808	+	5.85808i	0.620955	+	0.620955i	−0.324820	+	0.945776i	$0.605304\pi$
$90$	−0.907700	−	5.86453i	−0.0956800	−	0.618175i
$91$	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
$95$	−2.57435	+	9.17494i	−0.264123	+	0.941329i
$96$	0.145620	−	5.99394i	0.0148623	−	0.611754i
$97$	−6.58914	−	4.40272i	−0.669025	−	0.447029i	0.174113	−	0.984726i	$-0.444294\pi$
$97$	−6.58914	−	4.40272i	−0.669025	−	0.447029i	−0.843138	+	0.537697i	$0.819294\pi$
$98$	−6.63710	+	7.11037i	−0.670449	+	0.718256i
$99$	2.13047	−	0.423777i	0.214121	−	0.0425912i
$100$	−8.87788	−	4.60252i	−0.887788	−	0.460252i
$101$	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	$-0.533186\pi$
$103$	−2.11236			−0.208137			−0.104068	+	0.994570i	$0.533186\pi$
$104$	−5.57062	−	1.65909i	−0.546244	−	0.162687i
$105$	0.651288	+	0.512022i	0.0635592	+	0.0499683i
$106$	8.72198	+	8.14145i	0.847154	+	0.790768i
$107$	−0.293443	+	0.439169i	−0.0283682	+	0.0424561i	−0.845383	−	0.534161i	$-0.820628\pi$
$107$	−0.293443	+	0.439169i	−0.0283682	+	0.0424561i	0.817014	+	0.576617i	$0.195628\pi$
$108$	10.2535	+	1.31472i	0.986644	+	0.126509i
$109$	4.01369	+	6.00691i	0.384442	+	0.575357i	0.972338	−	0.233579i	$-0.0750437\pi$
$109$	4.01369	+	6.00691i	0.384442	+	0.575357i	−0.587896	+	0.808936i	$0.700044\pi$
$110$	1.54415	−	3.31875i	0.147229	−	0.316430i
$111$	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	$-0.995409\pi$
$113$	−0.750418	+	3.77261i	−0.0705934	+	0.354897i	0.929303	+	0.369319i	$0.120409\pi$
$114$	−5.43026	−	3.36406i	−0.508590	−	0.315073i
$115$	12.6912	+	0.981736i	1.18346	+	0.0915473i
$116$	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
$120$	4.61503	−	4.86181i	0.421293	−	0.443820i
$121$	−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
$125$	−3.91178	−	10.4737i	−0.349880	−	0.936795i
$126$	0.753167	−	0.541637i	0.0670974	−	0.0482529i
$127$	1.45525	+	3.51327i	0.129132	+	0.311753i	0.975201	−	0.221321i	$-0.0710369\pi$
$127$	1.45525	+	3.51327i	0.129132	+	0.311753i	−0.846069	+	0.533074i	$0.821037\pi$
$128$	−9.11785	+	6.69812i	−0.805912	+	0.592036i
$129$	−4.51072	−	6.75078i	−0.397147	−	0.594373i
$130$	−3.37593	−	5.55280i	−0.296089	−	0.487013i
$131$	11.5248	−	17.2481i	1.00693	−	1.50698i	0.151900	−	0.988396i	$-0.451461\pi$
$131$	11.5248	−	17.2481i	1.00693	−	1.50698i	0.855029	−	0.518580i	$-0.173539\pi$
$132$	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	−0.874536	−	0.484960i	$-0.838834\pi$
$139$	−2.97288	−	14.9457i	−0.252156	−	1.26768i	0.622380	−	0.782715i	$-0.286166\pi$
$140$	0.0130969	−	1.56322i	0.00110689	−	0.132116i
$141$	−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
$145$	−4.91355	+	9.67537i	−0.408048	+	0.803496i
$146$	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	0.0339466	−	0.999424i	$-0.489192\pi$
$149$	−11.7851	−	11.7851i	−0.965477	−	0.965477i	−0.999424	+	0.0339466i	$0.989192\pi$
$150$	7.47280	−	0.571718i	0.610151	−	0.0466806i
$151$	−0.409485	−	0.169614i	−0.0333234	−	0.0138030i	0.365960	−	0.930631i	$-0.380741\pi$
$151$	−0.409485	−	0.169614i	−0.0333234	−	0.0138030i	−0.399283	+	0.916828i	$0.630741\pi$
$152$	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
$155$	−20.1003	+	6.56074i	−1.61450	+	0.526971i
$156$	4.20395	−	1.14166i	0.336585	−	0.0914060i
$157$	7.46237	+	7.46237i	0.595562	+	0.595562i	0.939128	−	0.343566i	$-0.111635\pi$
$157$	7.46237	+	7.46237i	0.595562	+	0.595562i	−0.343566	+	0.939128i	$0.611635\pi$
$158$	8.32280	−	13.4346i	0.662126	−	1.06880i
$159$	−8.77027	−	1.74451i	−0.695527	−	0.138349i
$160$	−12.5840	−	1.28158i	−0.994854	−	0.101317i
$161$	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	$-0.689976\pi$
$163$	−0.165134	+	0.110339i	−0.0129343	+	0.00864242i	0.549086	+	0.835766i	$0.314976\pi$
$164$	−15.4300	−	1.97846i	−1.20488	−	0.154492i
$165$	0.326089	+	2.72389i	0.0253860	+	0.212054i
$166$	17.4154	+	16.2562i	1.35169	+	1.26173i
$167$	2.28977	−	0.455464i	0.177188	−	0.0352449i	−0.105699	−	0.994398i	$-0.533708\pi$
$167$	2.28977	−	0.455464i	0.177188	−	0.0352449i	0.282887	+	0.959153i	$0.408708\pi$
$168$	1.00433	+	0.299118i	0.0774857	+	0.0230774i
$169$			8.77695i			0.675150i
$170$	7.13712	−	10.9115i	0.547392	−	0.836876i
$171$	−7.99738			−0.611575
$172$	−4.87562	+	14.5239i	−0.371763	+	1.10744i
$173$	3.31329	+	16.6570i	0.251905	+	1.26641i	0.874946	+	0.484221i	$0.160897\pi$
$173$	3.31329	+	16.6570i	0.251905	+	1.26641i	−0.623041	+	0.782189i	$0.714103\pi$
$174$	−5.31758	−	4.96364i	−0.403125	−	0.376293i
$175$	1.18296	−	1.28661i	0.0894237	−	0.0972588i
$176$	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	0.0314672	−	0.999505i	$-0.489982\pi$
$179$	10.1745	−	4.21440i	0.760475	−	0.314999i	0.729007	+	0.684506i	$0.239982\pi$
$180$	1.70619	−	8.21718i	0.127172	−	0.612473i
$181$	−1.50907	+	7.58659i	−0.112168	+	0.563906i	0.883300	+	0.468808i	$0.155316\pi$
$181$	−1.50907	+	7.58659i	−0.112168	+	0.563906i	−0.995468	+	0.0950981i	$0.969684\pi$
$182$	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
$185$	18.5040	−	6.03969i	1.36044	−	0.444047i
$186$	−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
$190$	−7.95956	+	10.8747i	−0.577447	+	0.788933i
$191$	−3.76809	+	3.76809i	−0.272649	+	0.272649i	−0.830166	−	0.557517i	$-0.811754\pi$
$191$	−3.76809	+	3.76809i	−0.272649	+	0.272649i	0.557517	+	0.830166i	$0.311754\pi$
$192$	3.16539	−	7.86622i	0.228443	−	0.567695i
$193$	−13.1399	−	2.61369i	−0.945830	−	0.188137i	−0.302002	−	0.953307i	$-0.597655\pi$
$193$	−13.1399	−	2.61369i	−0.945830	−	0.188137i	−0.643828	+	0.765170i	$0.722655\pi$
$194$	−6.54330	−	9.09871i	−0.469782	−	0.653249i
$195$	4.34250	+	2.20530i	0.310973	+	0.157925i
$196$	−12.3164	+	6.12555i	−0.879746	+	0.437539i
$197$	−0.154712	−	0.231542i	−0.0110228	−	0.0164967i	0.825917	−	0.563791i	$-0.190658\pi$
$197$	−0.154712	−	0.231542i	−0.0110228	−	0.0164967i	−0.836940	+	0.547295i	$0.815658\pi$
$198$	3.03178	+	0.495296i	0.215459	+	0.0351992i
$199$	−16.3037	−	10.8938i	−1.15574	−	0.772240i	−0.178408	−	0.983957i	$-0.557095\pi$
$199$	−16.3037	−	10.8938i	−1.15574	−	0.772240i	−0.977331	+	0.211717i	$0.932095\pi$
$200$	−9.47546	−	10.4984i	−0.670016	−	0.742347i
$201$	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
$210$	0.608648	+	1.00112i	0.0420007	+	0.0690836i
$211$	0.168064	−	0.112297i	0.0115700	−	0.00773083i	−0.549772	−	0.835315i	$-0.685285\pi$
$211$	0.168064	−	0.112297i	0.0115700	−	0.00773083i	0.561342	+	0.827584i	$0.310285\pi$
$212$	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
$215$	−14.9336	+	8.38948i	−1.01846	+	0.572158i
$216$	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
$220$	3.69094	−	3.62960i	0.248843	−	0.244708i
$221$	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	$-0.198463\pi$
$223$	14.5307	+	6.01880i	0.973045	+	0.403049i	0.161200	+	0.986922i	$0.448463\pi$
$224$	−0.712125	−	1.84472i	−0.0475809	−	0.123256i
$225$	7.57625	−	5.53551i	0.505084	−	0.369034i
$226$	−2.86478	+	4.62433i	−0.190563	+	0.307606i
$227$	−3.31294	−	0.658984i	−0.219887	−	0.0437383i	0.0839171	−	0.996473i	$-0.473257\pi$
$227$	−3.31294	−	0.658984i	−0.219887	−	0.0437383i	−0.303804	+	0.952734i	$0.598257\pi$
$228$	−5.52357	−	7.14839i	−0.365807	−	0.473414i
$229$	−16.2420	+	6.72767i	−1.07330	+	0.444577i	−0.848155	−	0.529747i	$-0.822287\pi$
$229$	−16.2420	+	6.72767i	−1.07330	+	0.444577i	−0.225148	+	0.974324i	$0.572287\pi$
$230$	16.3215	+	7.59408i	1.07621	+	0.500739i
$231$	−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	$-0.297055\pi$
$233$	1.23121	+	0.822670i	0.0806594	+	0.0538949i	−0.514587	+	0.857438i	$0.672055\pi$
$234$	3.72148	−	3.98684i	0.243280	−	0.260628i
$235$	9.49086	+	7.46142i	0.619115	+	0.486730i
$236$	−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	$0.0975543\pi$
$239$			9.32836i			0.603401i	−0.953403	+	0.301701i	$0.902446\pi$
$240$	8.52327	−	4.15032i	0.550175	−	0.267902i
$241$	4.33642	+	21.8006i	0.279333	+	1.40430i	0.824446	+	0.565940i	$0.191487\pi$
$241$	4.33642	+	21.8006i	0.279333	+	1.40430i	−0.545113	+	0.838363i	$0.683513\pi$
$242$	−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
$245$	−14.8074	−	4.15474i	−0.946011	−	0.265437i
$246$	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
$250$	0.0133467	−	15.8114i	0.000844122	−	1.00000i
$251$	−9.96167	+	9.96167i	−0.628775	+	0.628775i	−0.947760	−	0.318985i	$-0.896658\pi$
$251$	−9.96167	+	9.96167i	−0.628775	+	0.628775i	0.318985	+	0.947760i	$0.396658\pi$
$252$	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
$255$	−0.240444	+	9.76885i	−0.0150572	+	0.611749i
$256$	−15.3975	+	4.34930i	−0.962345	+	0.271831i
$257$	0.732414	−	1.76820i	0.0456867	−	0.110298i	−0.899389	−	0.437150i	$-0.855988\pi$
$257$	0.732414	−	1.76820i	0.0456867	−	0.110298i	0.945075	+	0.326852i	$0.105988\pi$
$258$	−2.62618	−	11.1778i	−0.163499	−	0.695897i
$259$	2.15163	+	2.15163i	0.133696	+	0.133696i
$260$	−1.71735	−	9.02838i	−0.106506	−	0.559916i
$261$	−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	−0.586165	−	0.810192i	$-0.699363\pi$
$263$	−12.0750	−	29.1516i	−0.744576	−	1.79757i	−0.158411	−	0.987373i	$-0.550637\pi$
$264$	1.65125	+	3.05202i	0.101627	+	0.187839i
$265$	−5.09644	+	18.1636i	−0.313072	+	1.11578i
$266$	−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	0.573925	+	0.818908i	$0.305420\pi$
$269$	5.85638	+	29.4420i	0.357070	+	1.79511i	−0.216855	+	0.976204i	$0.569580\pi$
$270$	5.60325	+	15.3545i	0.341003	+	0.934445i
$271$	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
$275$	5.78251	−	0.242694i	0.348698	−	0.0146350i
$276$	−7.92584	+	9.09945i	−0.477080	+	0.547722i
$277$	0.571726	+	0.382015i	0.0343517	+	0.0229531i	0.572628	−	0.819816i	$-0.305924\pi$
$277$	0.571726	+	0.382015i	0.0343517	+	0.0229531i	−0.538276	+	0.842769i	$0.680924\pi$
$278$	3.47460	−	21.2685i	0.208392	−	1.27560i
$279$	−9.85857	−	14.7544i	−0.590217	−	0.883322i
$280$	0.792582	−	2.06385i	0.0473658	−	0.123338i
$281$	−4.71661	+	1.95368i	−0.281369	+	0.116547i	−0.518905	−	0.854832i	$-0.673660\pi$
$281$	−4.71661	+	1.95368i	−0.281369	+	0.116547i	0.237536	+	0.971379i	$0.423660\pi$
$282$	−6.57024	+	4.72497i	−0.391252	+	0.281368i
$283$	−1.27833	+	6.42658i	−0.0759886	+	0.382020i	−1.00000		0.000344581i	$-0.999890\pi$
$283$	−1.27833	+	6.42658i	−0.0759886	+	0.382020i	0.924011	+	0.382365i	$0.124890\pi$
$284$	18.1494	+	10.3971i	1.07697	+	0.616951i
$285$	0.778971	−	10.0700i	0.0461422	−	0.596495i
$286$	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
$290$	−11.3058	+	10.3774i	−0.663899	+	0.609382i
$291$	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	$-0.284634\pi$
$293$	−2.62876	−	2.62876i	−0.153574	−	0.153574i	−0.779712	+	0.626138i	$0.784634\pi$
$294$	5.42925	−	8.76388i	0.316640	−	0.511120i
$295$	−5.11087	+	2.87121i	−0.297566	+	0.167169i
$296$	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
$300$	10.1806	+	2.94875i	0.587776	+	0.170246i
$301$	−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
$310$	−29.8747	−	1.27912i	−1.69677	−	0.0726489i
$311$	11.5632	−	17.3056i	0.655690	−	0.981310i	−0.343422	−	0.939181i	$-0.611586\pi$
$311$	11.5632	−	17.3056i	0.655690	−	0.981310i	0.999112	−	0.0421284i	$-0.0134138\pi$
$312$	6.13392	+	0.572808i	0.347265	+	0.0324289i
$313$	−8.96622	−	13.4189i	−0.506801	−	0.758481i	0.486545	−	0.873656i	$-0.338257\pi$
$313$	−8.96622	−	13.4189i	−0.506801	−	0.758481i	−0.993345	+	0.115175i	$0.963257\pi$
$314$	6.18247	+	13.5840i	0.348897	+	0.766589i
$315$	1.30784	+	0.664176i	0.0736885	+	0.0374221i
$316$	17.6853	−	13.6655i	0.994878	−	0.768744i
$317$	−10.8427	−	2.15675i	−0.608987	−	0.121135i	−0.119043	−	0.992889i	$-0.537983\pi$
$317$	−10.8427	−	2.15675i	−0.608987	−	0.121135i	−0.489944	+	0.871754i	$0.662983\pi$
$318$	−10.7503	−	6.65983i	−0.602846	−	0.373465i
$319$	−3.97209	−	3.97209i	−0.222395	−	0.222395i
$320$	−16.0308	−	7.93804i	−0.896151	−	0.443750i
$321$	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
$325$	5.34522	−	8.77524i	0.296500	−	0.486762i
$326$	−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
$330$	−0.918963	+	3.76926i	−0.0505872	+	0.207491i
$331$	−4.09213	−	9.87927i	−0.224924	−	0.543014i	0.770622	−	0.637292i	$-0.219946\pi$
$331$	−4.09213	−	9.87927i	−0.224924	−	0.543014i	−0.995546	+	0.0942786i	$0.969946\pi$
$332$	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
$335$	−2.40377	−	20.0792i	−0.131332	−	1.09704i
$336$	1.18180	+	0.894224i	0.0644727	+	0.0487839i
$337$	−6.23650	−	31.3530i	−0.339724	−	1.70791i	−0.652256	−	0.757999i	$-0.726177\pi$
$337$	−6.23650	−	31.3530i	−0.339724	−	1.70791i	0.312532	−	0.949907i	$-0.398823\pi$
$338$	−4.35269	+	11.6243i	−0.236755	+	0.632277i
$339$		−	4.07693i		−	0.221428i
$340$	14.8638	−	10.9119i	0.806100	−	0.591779i
$341$		−	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
$345$	−13.3960	+	1.60369i	−0.721214	+	0.0863400i
$346$	−3.87245	+	23.7039i	−0.208184	+	1.27433i
$347$	−12.4213	−	18.5897i	−0.666808	−	0.997949i	−0.998510	−	0.0545650i	$-0.982623\pi$
$347$	−12.4213	−	18.5897i	−0.666808	−	0.997949i	0.331702	−	0.943384i	$-0.392377\pi$
$348$	−4.58107	−	9.21100i	−0.245571	−	0.493762i
$349$	1.07004	+	2.58329i	0.0572777	+	0.138281i	0.949928	−	0.312470i	$-0.101156\pi$
$349$	1.07004	+	2.58329i	0.0572777	+	0.138281i	−0.892650	+	0.450751i	$0.851156\pi$
$350$	2.20479	−	1.11734i	0.117851	−	0.0597245i
$351$	−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	0.993156	+	0.116799i	$0.0372634\pi$
$353$	20.8542	+	20.8542i	1.10995	+	1.10995i	0.116799	+	0.993156i	$0.462737\pi$
$354$	−0.898783	−	3.82548i	−0.0477698	−	0.203322i
$355$	7.25621	+	22.2311i	0.385120	+	1.17990i
$356$	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	−0.290678	−	0.956821i	$-0.593881\pi$
$359$	11.2061	−	27.0540i	0.591437	−	1.42785i	0.882115	−	0.471034i	$-0.156119\pi$
$360$	6.33478	−	10.0368i	0.333872	−	0.528985i
$361$	−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
$365$	7.63745	+	3.87861i	0.399762	+	0.203016i
$366$	−6.53710	+	2.97522i	−0.341699	+	0.155517i
$367$	11.1268	+	16.6525i	0.580816	+	0.869253i	0.999239	−	0.0389992i	$-0.0124170\pi$
$367$	11.1268	+	16.6525i	0.580816	+	0.869253i	−0.418423	+	0.908252i	$0.637417\pi$
$368$	22.7313	+	1.33590i	1.18495	+	0.0696387i
$369$	8.10942	−	12.1366i	0.422160	−	0.631806i
$370$	27.5020	+	1.17753i	1.42976	+	0.0612168i
$371$	−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	0.575790	−	0.817598i	$-0.304695\pi$
$379$	0.793765	+	0.530377i	0.0407730	+	0.0272436i	−0.535017	+	0.844841i	$0.679695\pi$
$380$	−15.9347	+	10.4552i	−0.817434	+	0.536341i
$381$	−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	$-0.613734\pi$
$383$	1.27965	−	0.530048i	0.0653870	−	0.0270842i	0.415137	+	0.909759i	$0.363734\pi$
$384$	8.09332	−	8.84830i	0.413010	−	0.451538i
$385$	0.443141	+	0.788807i	0.0225845	+	0.0402013i
$386$	−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	0.755524	−	0.655121i	$-0.227382\pi$
$389$	16.3015	+	6.75231i	0.826519	+	0.342356i	0.0709955	+	0.997477i	$0.477382\pi$
$390$	4.65759	+	5.07427i	0.235846	+	0.256946i
$391$	−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
$395$	24.9135	+	1.92720i	1.25353	+	0.0969679i
$396$	3.76969	+	2.15950i	0.189434	+	0.108519i
$397$	−0.839779	+	4.22185i	−0.0421473	+	0.211889i	−0.996120	−	0.0880044i	$-0.971951\pi$
$397$	−0.839779	+	4.22185i	−0.0421473	+	0.211889i	0.953973	+	0.299893i	$0.0969510\pi$
$398$	−16.1903	−	22.5132i	−0.811546	−	1.12849i
$399$	1.45873	−	0.604226i	0.0730279	−	0.0302491i
$400$	−7.34300	−	18.6032i	−0.367150	−	0.930162i
$401$	−21.6182	−	32.3539i	−1.07956	−	1.61568i	−0.736604	−	0.676324i	$-0.763572\pi$
$401$	−21.6182	−	32.3539i	−1.07956	−	1.61568i	−0.342956	−	0.939352i	$-0.611428\pi$
$402$	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
$405$	0.266289	+	0.209348i	0.0132320	+	0.0104026i
$406$	−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	$0.499584\pi$
$410$	−8.43206	−	23.1063i	−0.416430	−	1.14114i
$411$	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
$415$	−10.1762	+	36.2677i	−0.499529	+	1.78031i
$416$	−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	−0.573978	−	0.818871i	$-0.694600\pi$
$419$	−29.0182	−	5.77208i	−1.41763	−	0.281985i	−0.843654	+	0.536887i	$0.819600\pi$
$420$	0.309622	+	1.62773i	0.0151080	+	0.0794251i
$421$	−21.7139	−	21.7139i	−1.05827	−	1.05827i	−0.998194	−	0.0600790i	$-0.980865\pi$
$421$	−21.7139	−	21.7139i	−1.05827	−	1.05827i	−0.0600790	−	0.998194i	$-0.519135\pi$
$422$	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
$425$	20.5088	+	2.09525i	0.994822	+	0.101634i
$426$	−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
$430$	−23.9387	+	3.70519i	−1.15443	+	0.178680i
$431$	−14.1994	−	2.82444i	−0.683962	−	0.136049i	−0.159134	−	0.987257i	$-0.550870\pi$
$431$	−14.1994	−	2.82444i	−0.683962	−	0.136049i	−0.524828	+	0.851208i	$0.675870\pi$
$432$	13.7365	+	15.4519i	0.660897	+	0.743429i
$433$	−24.0610	+	9.96637i	−1.15630	+	0.478953i	−0.876640	−	0.481147i	$-0.840220\pi$
$433$	−24.0610	+	9.96637i	−1.15630	+	0.478953i	−0.279656	+	0.960100i	$0.590220\pi$
$434$	−1.93638	−	4.25458i	−0.0929494	−	0.204226i
$435$	3.10718	−	11.0739i	0.148978	−	0.530953i
$436$	−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	−0.994939	−	0.100484i	$-0.967961\pi$
$439$	−2.39252	−	12.0280i	−0.114189	−	0.574066i	0.880750	−	0.473582i	$-0.157039\pi$
$440$	6.68831	−	2.97666i	0.318853	−	0.141907i
$441$		−	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
$445$	−11.4492	+	14.5632i	−0.542742	+	0.690363i
$446$	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	0.109256	−	0.994014i	$-0.465153\pi$
$449$	22.6605	−	15.1413i	1.06941	−	0.714560i	0.960159	+	0.279454i	$0.0901533\pi$
$450$	12.7792	−	3.57404i	0.602420	−	0.168482i
$451$	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
$455$	1.60148	+	0.123884i	0.0750787	+	0.00580776i
$456$	−3.77042	−	12.2067i	−0.176566	−	0.571629i
$457$	9.16487	+	3.79621i	0.428715	+	0.177579i	0.586598	−	0.809878i	$-0.300467\pi$
$457$	9.16487	+	3.79621i	0.428715	+	0.177579i	−0.157883	+	0.987458i	$0.550467\pi$
$458$	−24.8475	+	0.855389i	−1.16105	+	0.0399697i
$459$	−20.6542	+	5.25065i	−0.964058	+	0.245079i
$460$	17.8502	+	18.1519i	0.832272	+	0.846336i
$461$	−4.20317	+	10.1473i	−0.195761	+	0.472609i	−0.991029	−	0.133650i	$-0.957330\pi$
$461$	−4.20317	+	10.1473i	−0.195761	+	0.472609i	0.795268	+	0.606258i	$0.207330\pi$
$462$	−0.590420	+	0.138717i	−0.0274688	+	0.00645372i
$463$	21.1983	+	21.1983i	0.985168	+	0.985168i	0.999892	−	0.0147237i	$-0.00468687\pi$
$463$	21.1983	+	21.1983i	0.985168	+	0.985168i	−0.0147237	+	0.999892i	$0.504687\pi$
$464$	−8.46795	+	17.4675i	−0.393115	+	0.810907i
$465$	19.5384	−	10.9764i	0.906072	−	0.509019i
$466$	1.22265	+	1.70014i	0.0566381	+	0.0787574i
$467$	−19.3956	+	8.03393i	−0.897522	+	0.371766i	−0.783267	−	0.621685i	$-0.786448\pi$
$467$	−19.3956	+	8.03393i	−0.897522	+	0.371766i	−0.114255	+	0.993451i	$0.536448\pi$
$468$	6.90592	−	3.43464i	0.319226	−	0.158766i
$469$	2.62855	−	1.75634i	0.121375	−	0.0811004i
$470$	8.86949	+	14.5887i	0.409119	+	0.672927i
$471$	−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	0.397776	−	0.917482i	$-0.369782\pi$
$479$	24.4332	−	4.86006i	1.11638	−	0.222062i	0.718603	+	0.695421i	$0.244782\pi$
$480$	13.3465	−	1.26984i	0.609184	−	0.0579598i
$481$	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
$485$	8.02364	−	15.7995i	0.364335	−	0.717419i
$486$	−17.9877	+	12.9358i	−0.815940	+	0.586780i
$487$	−10.2993	−	2.04866i	−0.466706	−	0.0928336i	−0.0438649	−	0.999037i	$-0.513967\pi$
$487$	−10.2993	−	2.04866i	−0.466706	−	0.0928336i	−0.422841	+	0.906204i	$0.638967\pi$
$488$	11.9847	+	6.32816i	0.542520	+	0.286463i
$489$	0.148847	−	0.148847i	0.00673110	−	0.00673110i
$490$	−17.5506	−	12.8459i	−0.792857	−	0.580319i
$491$	−12.0483	+	29.0872i	−0.543732	+	1.31269i	0.378340	+	0.925667i	$0.376495\pi$
$491$	−12.0483	+	29.0872i	−0.543732	+	1.31269i	−0.922072	+	0.387018i	$0.873505\pi$
$492$	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
$495$	1.50714	+	4.61747i	0.0677409	+	0.207540i
$496$	−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	0.786025	+	0.618195i	$0.212136\pi$
$499$	−3.94808	+	19.8484i	−0.176741	+	0.888535i	−0.962765	+	0.270339i	$0.912864\pi$
$500$	7.85891	−	20.9341i	0.351461	−	0.936203i
$501$	−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	$-0.0995182\pi$
$503$	6.80067	+	10.1779i	0.303227	+	0.453811i	−0.648296	+	0.761388i	$0.724518\pi$
$504$	1.84737	+	0.172514i	0.0822883	+	0.00768438i
$505$	3.73040	+	31.1607i	0.166001	+	1.38663i
$506$	−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	$0.134997\pi$
$510$	−5.16305	+	12.8187i	−0.228624	+	0.567622i
$511$			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
$515$	−0.561448	−	4.68988i	−0.0247404	−	0.206661i
$516$	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
$520$	2.20290	−	12.8089i	0.0966037	−	0.561709i
$521$	39.7388	+	7.90454i	1.74099	+	0.346304i	0.960376	−	0.278709i	$-0.0899066\pi$
$521$	39.7388	+	7.90454i	1.74099	+	0.346304i	0.780614	+	0.625014i	$0.214907\pi$
$522$	−10.9487	−	6.78272i	−0.479210	−	0.296872i
$523$	−12.7943	−	12.7943i	−0.559456	−	0.559456i	0.369697	−	0.929152i	$-0.379462\pi$
$523$	−12.7943	−	12.7943i	−0.559456	−	0.559456i	−0.929152	+	0.369697i	$0.879462\pi$
$524$	40.0382	−	10.8731i	1.74907	−	0.474994i
$525$	−0.963692	+	1.58209i	−0.0420590	+	0.0690481i
$526$	−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
$530$	−15.7575	+	21.5286i	−0.684464	+	0.935143i
$531$	−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
$535$	−1.05304	−	0.534779i	−0.0455271	−	0.0231205i
$536$	−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
$540$	−0.193656	+	23.1144i	−0.00833364	+	0.994687i
$541$	1.37135	+	6.89424i	0.0589590	+	0.296407i	0.999003	−	0.0446469i	$-0.0142163\pi$
$541$	1.37135	+	6.89424i	0.0589590	+	0.296407i	−0.940044	+	0.341054i	$0.889216\pi$
$542$	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	$-0.306864\pi$
$547$	33.0094	−	6.56599i	1.41138	−	0.280741i	0.841176	+	0.540761i	$0.181864\pi$
$548$	24.4655	−	28.0882i	1.04512	−	1.19987i
$549$	−4.99570	+	7.47659i	−0.213211	+	0.319093i
$550$	7.77876	+	2.54625i	0.331688	+	0.108573i
$551$	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
$555$	−17.9867	+	10.1047i	−0.763492	+	0.428919i
$556$	15.1493	−	26.4451i	0.642475	−	1.12152i
$557$	9.63731	−	9.63731i	0.408346	−	0.408346i	−0.472815	−	0.881161i	$-0.656762\pi$
$557$	9.63731	−	9.63731i	0.408346	−	0.408346i	0.881161	+	0.472815i	$0.156762\pi$
$558$	−5.73974	−	24.4299i	−0.242982	−	1.03420i
$559$	−14.5435	−	6.02413i	−0.615126	−	0.254794i
$560$	2.07321	−	2.34032i	0.0876092	−	0.0988965i
$561$	−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	$-0.816655\pi$
$563$	3.31011	−	7.99132i	0.139505	−	0.336794i	0.978155	+	0.207876i	$0.0666550\pi$
$564$	−11.0449	+	2.99945i	−0.465075	+	0.126300i
$565$	−8.57545	−	0.663359i	−0.360772	−	0.0279077i
$566$	−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	−0.786435	−	0.617673i	$-0.788075\pi$
$569$	−15.9129	−	38.4171i	−0.667102	−	1.61053i	0.119332	−	0.992854i	$-0.461925\pi$
$570$	6.02562	−	12.9505i	0.252385	−	0.542436i
$571$	1.94059	+	2.90430i	0.0812113	+	0.121541i	0.869851	−	0.493314i	$-0.164215\pi$
$571$	1.94059	+	2.90430i	0.0812113	+	0.121541i	−0.788640	+	0.614855i	$0.789215\pi$
$572$	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
$575$	1.19356	+	28.4381i	0.0497749	+	1.18595i
$576$	2.77967	−	14.7533i	0.115820	−	0.614720i
$577$	5.29189			0.220304			0.110152	−	0.993915i	$-0.464866\pi$
$577$	5.29189			0.220304			0.110152	+	0.993915i	$0.464866\pi$
$578$	12.2015	+	20.7153i	0.507515	+	0.861643i
$579$	14.1998			0.590125
$580$	−20.1199	+	8.13713i	−0.835434	+	0.337876i
$581$	−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
$585$	8.30263	+	2.32960i	0.343271	+	0.0963169i
$586$	−2.17789	−	4.78521i	−0.0899677	−	0.197675i
$587$	−10.8316	−	26.1498i	−0.447067	−	1.07932i	−0.973415	−	0.229047i	$-0.926439\pi$
$587$	−10.8316	−	26.1498i	−0.447067	−	1.07932i	0.526348	−	0.850269i	$-0.323561\pi$
$588$	11.5368	−	8.91448i	0.475768	−	0.367627i
$589$	−7.86160	+	39.5229i	−0.323932	+	1.62851i
$590$	−8.19279	+	1.26806i	−0.337292	+	0.0522054i
$591$	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	$-0.329354\pi$
$593$	6.43032	+	2.66353i	0.264062	+	0.109378i	−0.246725	+	0.969086i	$0.579354\pi$
$594$	−8.45609	+	0.291106i	−0.346958	+	0.0119442i
$595$	1.15966	+	3.00690i	0.0475416	+	0.123271i
$596$	−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	−0.357422	−	0.933943i	$-0.616344\pi$
$599$	14.1101	−	14.1101i	0.576522	−	0.576522i	0.933943	+	0.357422i	$0.116344\pi$
$600$	12.0209	+	8.95413i	0.490751	+	0.365551i
$601$	−1.05241	+	5.29084i	−0.0429288	+	0.215818i	−0.996295	−	0.0859971i	$-0.972592\pi$
$601$	−1.05241	+	5.29084i	−0.0429288	+	0.215818i	0.953367	+	0.301815i	$0.0975924\pi$
$602$	−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
$605$	5.83550	−	20.7976i	0.237247	−	0.845542i
$606$	−20.7622	−	3.39188i	−0.843407	−	0.137786i
$607$	−6.68178	+	9.99999i	−0.271205	+	0.405887i	−0.941925	−	0.335824i	$-0.890985\pi$
$607$	−6.68178	+	9.99999i	−0.271205	+	0.405887i	0.670720	+	0.741711i	$0.265985\pi$
$608$	−13.8762	+	19.7133i	−0.562754	+	0.799480i
$609$	1.76346	−	0.350774i	0.0714590	−	0.0142141i
$610$	5.19446	+	14.2343i	0.210317	+	0.576330i
$611$			11.0951i			0.448860i
$612$	12.1872	+	9.53652i	0.492638	+	0.385491i
$613$	34.3264			1.38643			0.693215	−	0.720731i	$-0.256193\pi$
$613$	34.3264			1.38643			0.693215	+	0.720731i	$0.256193\pi$
$614$	2.40454	−	6.42156i	0.0970394	−	0.259153i
$615$	14.4921	+	11.3932i	0.584376	+	0.459419i
$616$	0.888328	+	0.721539i	0.0357917	+	0.0290716i
$617$	8.09974	−	12.1221i	0.326083	−	0.488018i	−0.631818	−	0.775117i	$-0.717691\pi$
$617$	8.09974	−	12.1221i	0.326083	−	0.488018i	0.957901	+	0.287099i	$0.0926908\pi$
$618$	3.12484	+	0.510500i	0.125700	+	0.0205353i
$619$	15.5530	−	10.3922i	0.625127	−	0.417697i	−0.202257	−	0.979332i	$-0.564828\pi$
$619$	15.5530	−	10.3922i	0.625127	−	0.417697i	0.827385	+	0.561636i	$0.189828\pi$
$620$	−38.9320	−	16.5096i	−1.56355	−	0.663043i
$621$	−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
$625$	22.2141	−	11.4688i	0.888564	−	0.458752i
$626$	−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
$630$	1.40274	+	1.52823i	0.0558864	+	0.0608861i
$631$	8.74317	−	21.1079i	0.348060	−	0.840291i	−0.648789	−	0.760968i	$-0.724724\pi$
$631$	8.74317	−	21.1079i	0.348060	−	0.840291i	0.996849	−	0.0793229i	$-0.0252758\pi$
$632$	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
$635$	−7.41343	+	4.16476i	−0.294193	+	0.165273i
$636$	−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
$640$	−17.2947	−	18.4633i	−0.683634	−	0.729825i
$641$	12.7532	−	19.0865i	0.503722	−	0.753873i	−0.489260	−	0.872138i	$-0.662733\pi$
$641$	12.7532	−	19.0865i	0.503722	−	0.753873i	0.992982	+	0.118265i	$0.0377331\pi$
$642$	0.540231	−	0.578753i	0.0213212	−	0.0228415i
$643$	4.07841	+	20.5035i	0.160837	+	0.808581i	0.974000	+	0.226546i	$0.0727433\pi$
$643$	4.07841	+	20.5035i	0.160837	+	0.808581i	−0.813164	+	0.582035i	$0.802257\pi$
$644$	−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	$-0.746496\pi$
$647$	−35.5741			−1.39856			−0.699281	+	0.714847i	$0.746496\pi$
$648$	0.410636	+	0.122299i	0.0161313	+	0.00480435i
$649$	−0.592020	−	2.97629i	−0.0232388	−	0.116829i
$650$	11.4311	−	8.97118i	0.448365	−	0.351879i
$651$	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	$-0.713766\pi$
$653$	−3.50257	+	2.34035i	−0.137066	+	0.0915848i	0.485147	+	0.874433i	$0.338766\pi$
$654$	−4.48581	−	9.85612i	−0.175409	−	0.385405i
$655$	41.3578	+	21.0032i	1.61598	+	0.820662i
$656$	−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	−0.783241	−	0.621718i	$-0.786435\pi$
$659$	−4.14646	+	4.14646i	−0.161523	+	0.161523i	0.621718	+	0.783241i	$0.286435\pi$
$660$	−3.08634	+	4.53630i	−0.120136	+	0.176575i
$661$	8.12424	+	3.36517i	0.315996	+	0.130890i	0.535044	−	0.844824i	$-0.320295\pi$
$661$	8.12424	+	3.36517i	0.315996	+	0.130890i	−0.219048	+	0.975714i	$0.570295\pi$
$662$	−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
$665$	−1.03358	−	3.16662i	−0.0400807	−	0.122796i
$666$	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
$670$	6.77414	−	27.7851i	0.261708	−	1.07343i
$671$	−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	$-0.787304\pi$
$673$	−13.3059	+	8.89072i	−0.512905	+	0.342712i	0.272032	+	0.962288i	$0.412304\pi$
$674$	7.28900	−	44.6170i	0.280762	−	1.71858i
$675$	−17.4918	+	19.0244i	−0.673261	+	0.732251i
$676$	−11.5295	+	13.2367i	−0.443442	+	0.509104i
$677$	−19.4710	+	3.87301i	−0.748330	+	0.148852i	−0.554501	−	0.832183i	$-0.687091\pi$
$677$	−19.4710	+	3.87301i	−0.748330	+	0.148852i	−0.193829	+	0.981035i	$0.562091\pi$
$678$	2.02184	−	5.39952i	0.0776484	−	0.207367i
$679$	2.77014			0.106308
$680$	25.0971	−	7.08050i	0.962431	−	0.271525i
$681$	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	$-0.487165\pi$
$683$	12.0199	−	2.39090i	0.459927	−	0.0914852i	0.419615	+	0.907702i	$0.362165\pi$
$684$	−12.0610	−	10.5054i	−0.461164	−	0.401686i
$685$	41.3507	−	4.95029i	1.57993	−	0.189141i
$686$	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
$690$	−18.5370	−	4.51942i	−0.705693	−	0.172051i
$691$	−19.1984	−	3.81879i	−0.730340	−	0.145274i	−0.184106	−	0.982906i	$-0.558939\pi$
$691$	−19.1984	−	3.81879i	−0.730340	−	0.145274i	−0.546234	+	0.837633i	$0.683939\pi$
$692$	−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
$695$	32.3924	−	10.5729i	1.22871	−	0.401052i
$696$	−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
$700$	3.47416	−	0.386414i	0.131311	−	0.0146051i
$701$	21.4877	−	21.4877i	0.811580	−	0.811580i	−0.173291	−	0.984871i	$-0.555440\pi$
$701$	21.4877	−	21.4877i	0.811580	−	0.811580i	0.984871	+	0.173291i	$0.0554401\pi$
$702$	−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
$705$	−11.4089	−	5.79393i	−0.429685	−	0.218212i
$706$	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	0.985417	−	0.170159i	$-0.0544282\pi$
$709$	32.0939	+	21.4445i	1.20531	+	0.805364i	0.219896	+	0.975523i	$0.429428\pi$
$710$	−1.41471	+	33.0416i	−0.0530931	+	1.24003i
$711$	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	−0.428469	−	0.903556i	$-0.640947\pi$
$719$	15.2915	−	22.8853i	0.570276	−	0.853478i	0.998745	+	0.0500781i	$0.0159470\pi$
$720$	13.3673	−	10.1512i	0.498170	−	0.378314i
$721$	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
$725$	−22.7874	−	8.33751i	−0.846302	−	0.309647i
$726$	12.3092	+	7.62559i	0.456838	+	0.283012i
$727$	23.7467	−	23.7467i	0.880717	−	0.880717i	−0.112891	−	0.993607i	$-0.536011\pi$
$727$	23.7467	−	23.7467i	0.880717	−	0.880717i	0.993607	+	0.112891i	$0.0360110\pi$
$728$	1.94129	−	0.599629i	0.0719489	−	0.0222237i
$729$	6.18062	−	14.9213i	0.228912	−	0.552642i
$730$	8.19162	+	8.92446i	0.303185	+	0.330309i
$731$	−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	$-0.466225\pi$
$733$	−14.1416	−	5.85764i	−0.522332	−	0.216357i	−0.628241	+	0.778019i	$0.716225\pi$
$734$	6.47813	+	27.5728i	0.239112	+	1.01773i
$735$	16.2519	+	1.25718i	0.599462	+	0.0463717i
$736$	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	0.766256	−	0.642535i	$-0.222117\pi$
$739$	−6.25000	−	15.0888i	−0.229910	−	0.555052i	−0.996166	+	0.0874836i	$0.972117\pi$
$740$	35.8400	+	15.1984i	1.31750	+	0.558705i
$741$	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	$-0.863330\pi$
$743$	−4.81601	+	7.20767i	−0.176682	+	0.264424i	0.732550	+	0.680714i	$0.238330\pi$
$744$	17.8722	−	22.0035i	0.655227	−	0.806687i
$745$	23.0332	−	29.2980i	0.843870	−	1.07339i
$746$	−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
$750$	3.25555	+	16.4393i	0.118876	+	0.600277i
$751$	−33.7341	+	6.71014i	−1.23098	+	0.244856i	−0.767381	−	0.641191i	$-0.778441\pi$
$751$	−33.7341	+	6.71014i	−1.23098	+	0.244856i	−0.463595	+	0.886047i	$0.653441\pi$
$752$	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
$755$	0.267742	−	0.954226i	0.00974412	−	0.0347278i
$756$	−3.23548	+	1.60916i	−0.117673	+	0.0585244i
$757$	−21.9866	+	9.10715i	−0.799117	+	0.331005i	−0.744603	−	0.667508i	$-0.767361\pi$
$757$	−21.9866	+	9.10715i	−0.799117	+	0.331005i	−0.0545141	+	0.998513i	$0.517361\pi$
$758$	0.788244	+	1.09608i	0.0286303	+	0.0398115i
$759$	1.36252	−	6.84985i	0.0494563	−	0.248634i
$760$	−26.2891	+	5.94458i	−0.953605	+	0.215633i
$761$	5.98972	−	5.98972i	0.217127	−	0.217127i	−0.590160	−	0.807287i	$-0.700935\pi$
$761$	5.98972	−	5.98972i	0.217127	−	0.217127i	0.807287	+	0.590160i	$0.200935\pi$
$762$	−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
$765$	2.95679	+	17.0469i	0.106903	+	0.616334i
$766$	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	0.912635	−	0.408776i	$-0.134044\pi$
$769$	13.9724	+	13.9724i	0.503858	+	0.503858i	−0.408776	+	0.912635i	$0.634044\pi$
$770$	0.195712	+	1.26447i	0.00705296	+	0.0455682i
$771$	−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	−0.896273	−	0.443503i	$-0.853735\pi$
$773$	−16.0177	−	38.6701i	−0.576116	−	1.39087i	0.320156	−	0.947365i	$-0.396265\pi$
$774$	−8.42143	−	18.5034i	−0.302702	−	0.665090i
$775$	−19.9088	−	42.8833i	−0.715144	−	1.54041i
$776$	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
$780$	3.65211	+	9.03022i	0.130766	+	0.323334i
$781$	−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
$785$	−14.5846	+	18.5515i	−0.520547	+	0.662132i
$786$	−21.2173	+	22.7302i	−0.756795	+	0.810759i
$787$	−18.1847	+	27.2153i	−0.648215	+	0.970122i	0.351213	+	0.936296i	$0.385769\pi$
$787$	−18.1847	+	27.2153i	−0.648215	+	0.970122i	−0.999428	+	0.0338263i	$0.989231\pi$
$788$	0.0708327	−	0.552425i	0.00252331	−	0.0196793i
$789$	18.5803	+	27.8073i	0.661475	+	0.989967i
$790$	32.0399	+	14.9076i	1.13993	+	0.530388i
$791$	−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
$795$	1.54213	−	19.9356i	0.0546936	−	0.707041i
$796$	−10.2778	−	37.8459i	−0.364285	−	1.34141i
$797$	17.1386	−	41.3763i	0.607081	−	1.46562i	−0.259078	−	0.965856i	$-0.583419\pi$
$797$	17.1386	−	41.3763i	0.607081	−	1.46562i	0.866160	−	0.499767i	$-0.166581\pi$
$798$	2.23161	−	0.0768242i	0.0789980	−	0.00271955i
$799$	−20.0901	+	9.58826i	−0.710737	+	0.339208i
$800$	−0.499362	−	28.2799i	−0.0176551	−	0.999844i
$801$	−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
$805$	−3.87932	+	2.17935i	−0.136728	+	0.0768119i
$806$	−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	0.950031	−	0.312154i	$-0.101051\pi$
$809$	8.47819	+	12.6885i	0.298077	+	0.446104i	−0.651954	+	0.758258i	$0.726051\pi$
$810$	0.248855	+	0.409322i	0.00874388	+	0.0143821i
$811$	17.2985	−	25.8890i	0.607432	−	0.909087i	−0.392511	−	0.919747i	$-0.628393\pi$
$811$	17.2985	−	25.8890i	0.607432	−	0.909087i	0.999943	+	0.0106608i	$0.00339349\pi$
$812$	−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
$820$	0.291424	−	34.7838i	0.0101770	−	1.21470i
$821$	11.7296	−	17.5547i	0.409367	−	0.612662i	−0.568300	−	0.822822i	$-0.692399\pi$
$821$	11.7296	−	17.5547i	0.409367	−	0.612662i	0.977667	+	0.210160i	$0.0673985\pi$
$822$	−4.50108	+	27.5518i	−0.156993	+	0.960978i
$823$	−30.9304	+	20.6670i	−1.07817	+	0.720407i	−0.962062	−	0.272830i	$-0.912040\pi$
$823$	−30.9304	+	20.6670i	−1.07817	+	0.720407i	−0.116104	+	0.993237i	$0.537040\pi$
$824$	−2.84306	−	5.25484i	−0.0990427	−	0.183061i
$825$	−5.96094	+	1.44798i	−0.207533	+	0.0504121i
$826$	−0.756671	−	1.05218i	−0.0263280	−	0.0366100i
$827$	−7.45579	+	37.4828i	−0.259263	+	1.30340i	0.603325	+	0.797496i	$0.293842\pi$
$827$	−7.45579	+	37.4828i	−0.259263	+	1.30340i	−0.862588	+	0.505908i	$0.831158\pi$
$828$	−10.6204	+	18.5392i	−0.369083	+	0.644281i
$829$	1.42135	+	1.42135i	0.0493656	+	0.0493656i	0.731359	−	0.681993i	$-0.238887\pi$
$829$	1.42135	+	1.42135i	0.0493656	+	0.0493656i	−0.681993	+	0.731359i	$0.738887\pi$
$830$	−31.4634	+	42.9866i	−1.09211	+	1.49209i
$831$	−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
$835$	1.61983	+	4.96273i	0.0560566	+	0.171742i
$836$	−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	0.664432	−	0.747348i	$-0.268673\pi$
$839$	28.7422	+	5.71717i	0.992290	+	0.197379i	0.327858	+	0.944727i	$0.393673\pi$
$840$	−0.397162	+	2.30933i	−0.0137034	+	0.0796794i
$841$	−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
$845$	−19.4867	+	2.33285i	−0.670364	+	0.0802524i
$846$	−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
$850$	26.1229	+	12.9457i	0.896009	+	0.444035i
$851$	−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	$-0.0122354\pi$
$853$	1.79203	+	9.00915i	0.0613580	+	0.308468i	−0.937903	+	0.346897i	$0.887235\pi$
$854$	−1.61634	+	1.73159i	−0.0553099	+	0.0592538i
$855$	−2.12564	−	17.7559i	−0.0726954	−	0.607239i
$856$	−1.48746	−	0.138904i	−0.0508403	−	0.00474765i
$857$	−0.806870	−	1.20757i	−0.0275622	−	0.0412497i	0.817433	−	0.576024i	$-0.195397\pi$
$857$	−0.806870	−	1.20757i	−0.0275622	−	0.0412497i	−0.844995	+	0.534774i	$0.820397\pi$
$858$	−3.24521	+	1.47699i	−0.110790	+	0.0504236i
$859$	27.4739	−	11.3801i	0.937399	−	0.388283i	0.138918	−	0.990304i	$-0.455637\pi$
$859$	27.4739	−	11.3801i	0.937399	−	0.388283i	0.798481	+	0.602021i	$0.205637\pi$
$860$	−33.5422	−	6.96458i	−1.14378	−	0.237490i
$861$	−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	$-0.571053\pi$
$863$	22.1448	−	22.1448i	0.753818	−	0.753818i	0.975190	+	0.221371i	$0.0710533\pi$
$864$	10.5298	+	27.2768i	0.358231	+	0.927977i
$865$	−36.1015	+	11.7835i	−1.22749	+	0.400652i
$866$	−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
$870$	9.60698	−	13.1255i	0.325707	−	0.444995i
$871$	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
$875$	3.17098	+	2.28446i	0.107199	+	0.0772289i
$876$	−7.27089	+	3.61616i	−0.245661	+	0.122179i
$877$	19.1332	+	28.6349i	0.646083	+	0.966931i	0.999505	+	0.0314670i	$0.0100179\pi$
$877$	19.1332	+	28.6349i	0.646083	+	0.966931i	−0.353422	+	0.935464i	$0.614982\pi$
$878$	2.79630	−	17.1165i	0.0943705	−	0.577655i
$879$	3.27625	+	2.18912i	0.110505	+	0.0738372i
$880$	10.3343	−	0.625426i	0.348368	−	0.0210831i
$881$	18.7176	−	3.72317i	0.630613	−	0.125437i	0.130573	−	0.991439i	$-0.458318\pi$
$881$	18.7176	−	3.72317i	0.630613	−	0.125437i	0.500041	+	0.866002i	$0.333318\pi$
$882$	6.40086	−	17.0941i	0.215528	−	0.575588i
$883$	2.13355			0.0717996			0.0358998	−	0.999355i	$-0.488570\pi$
$883$	2.13355			0.0717996			0.0358998	+	0.999355i	$0.488570\pi$
$884$	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	−0.995901	−	0.0904522i	$-0.971169\pi$
$887$	−3.28868	−	16.5333i	−0.110423	−	0.555134i	0.885478	−	0.464682i	$-0.153831\pi$
$888$	−16.4528	+	20.2560i	−0.552120	+	0.679746i
$889$	−1.10526	−	0.738508i	−0.0370691	−	0.0247688i
$890$	−22.3856	+	13.6098i	−0.750368	+	0.456201i
$891$	−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
$895$	12.0612	+	21.4693i	0.403160	+	0.717640i
$896$	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
$900$	18.6974	+	1.60404i	0.623247	+	0.0534680i
$901$	−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
$905$	−17.2449	−	1.33399i	−0.573241	−	0.0443434i
$906$	0.564766	+	0.349874i	0.0187631	+	0.0116238i
$907$	44.1047	+	8.77296i	1.46447	+	0.291301i	0.862028	−	0.506860i	$-0.169194\pi$
$907$	44.1047	+	8.77296i	1.46447	+	0.291301i	0.602443	+	0.798162i	$0.294194\pi$
$908$	−4.13066	−	5.34573i	−0.137081	−	0.177404i
$909$	−24.3333	+	10.0792i	−0.807086	+	0.334306i
$910$	2.05958	+	0.958285i	0.0682745	+	0.0317669i
$911$	−15.4110	+	10.2973i	−0.510589	+	0.341165i	−0.784029	−	0.620724i	$-0.786839\pi$
$911$	−15.4110	+	10.2973i	−0.510589	+	0.341165i	0.273440	+	0.961889i	$0.411839\pi$
$912$	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
$915$	−8.92764	−	7.01863i	−0.295139	−	0.232029i
$916$	−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	$-0.790115\pi$
$919$		−	37.1432i		−	1.22524i	0.790377	−	0.612621i	$-0.209885\pi$
$920$	14.6391	+	32.8929i	0.482637	+	1.08445i
$921$	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
$925$	18.3276	+	39.4775i	0.602608	+	1.29801i
$926$	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	0.760413	−	0.649440i	$-0.224997\pi$
$929$	37.0147	+	7.36268i	1.21441	+	0.241562i	0.454000	+	0.891002i	$0.349997\pi$
$930$	31.3203	−	4.84770i	1.02703	−	0.158962i
$931$	−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
$935$	−4.32529	+	9.75599i	−0.141452	+	0.319055i
$936$	10.8496	−	1.12406i	0.354630	−	0.0367411i
$937$	−10.5028	+	25.3560i	−0.343112	+	0.828345i	0.654286	+	0.756247i	$0.272969\pi$
$937$	−10.5028	+	25.3560i	−0.343112	+	0.828345i	−0.997398	+	0.0720975i	$0.977031\pi$
$938$	4.35229	−	1.02256i	0.142107	−	0.0333877i
$939$	12.0954	+	12.0954i	0.394719	+	0.394719i
$940$	4.51196	+	23.7200i	0.147164	+	0.773662i
$941$	−6.81317	−	1.35522i	−0.222103	−	0.0441790i	0.0827842	−	0.996567i	$-0.473619\pi$
$941$	−6.81317	−	1.35522i	−0.222103	−	0.0441790i	−0.304887	+	0.952388i	$0.598619\pi$
$942$	−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
$945$	−3.88985	−	1.09143i	−0.126537	−	0.0355043i
$946$	2.02178	−	12.3756i	0.0657336	−	0.402365i
$947$	−30.7100	−	20.5198i	−0.997942	−	0.666804i	−0.0545599	−	0.998511i	$-0.517376\pi$
$947$	−30.7100	−	20.5198i	−0.997942	−	0.666804i	−0.943383	+	0.331707i	$0.892376\pi$
$948$	−15.5588	+	17.8627i	−0.505328	+	0.580153i
$949$	1.53580	+	7.72100i	0.0498543	+	0.250634i
$950$	−26.2597	−	14.7815i	−0.851979	−	0.479576i
$951$	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
$955$	−9.36749	−	7.36443i	−0.303125	−	0.238307i
$956$	−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
$960$	18.3060	+	4.93708i	0.590824	+	0.159343i
$961$	−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
$965$	2.31046	−	29.8681i	0.0743765	−	0.961488i
$966$	−0.682206	−	2.90366i	−0.0219496	−	0.0934239i
$967$	−3.75359	+	9.06197i	−0.120707	+	0.291413i	−0.972671	−	0.232188i	$-0.925412\pi$
$967$	−3.75359	+	9.06197i	−0.120707	+	0.291413i	0.851964	+	0.523601i	$0.175412\pi$
$968$	−2.81571	−	27.1776i	−0.0905003	−	0.873520i
$969$	16.0075	+	9.51839i	0.514235	+	0.305775i
$970$	18.4619	−	16.9459i	0.592777	−	0.544100i
$971$	22.5048	+	9.32181i	0.722215	+	0.299151i	0.713348	−	0.700810i	$-0.247178\pi$
$971$	22.5048	+	9.32181i	0.722215	+	0.299151i	0.00886622	+	0.999961i	$0.497178\pi$
$972$	−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
$975$	−3.74204	+	10.2274i	−0.119841	+	0.327540i
$976$	12.7343	+	14.3246i	0.407616	+	0.458518i
$977$	−11.4274	+	4.73338i	−0.365595	+	0.151434i	−0.557915	−	0.829898i	$-0.688399\pi$
$977$	−11.4274	+	4.73338i	−0.365595	+	0.151434i	0.192321	+	0.981332i	$0.438399\pi$
$978$	0.270951	−	0.123318i	0.00866407	−	0.00394327i
$979$	−5.32767	−	7.97343i	−0.170273	−	0.254832i
$980$	−16.8736	−	25.7170i	−0.539009	−	0.821500i
$981$	−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	$-0.529632\pi$
$983$	6.33908	−	1.26092i	0.202185	−	0.0402171i	0.295144	+	0.955453i	$0.404632\pi$
$984$	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
$990$	−0.293840	+	6.86285i	−0.00933885	+	0.218116i
$991$	−5.89100	+	8.81651i	−0.187134	+	0.280066i	−0.913160	−	0.407602i	$-0.866365\pi$
$991$	−5.89100	+	8.81651i	−0.187134	+	0.280066i	0.726026	+	0.687667i	$0.241365\pi$
$992$	−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
$995$	19.8531	−	39.0932i	0.629387	−	1.23934i
$996$	−21.8342	−	28.2569i	−0.691842	−	0.895354i
$997$	−12.0547	−	2.39783i	−0.381777	−	0.0759402i	0.000471116	−	1.00000i	$-0.499850\pi$
$997$	−12.0547	−	2.39783i	−0.381777	−	0.0759402i	−0.382248	+	0.924060i	$0.624850\pi$
$998$	−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.419.93	yes	832
5.4	even	2	inner	680.2.co.a.419.12	yes	832
8.3	odd	2	inner	680.2.co.a.419.15	yes	832
17.14	odd	16	inner	680.2.co.a.99.90	yes	832
40.19	odd	2	inner	680.2.co.a.419.90	yes	832
85.14	odd	16	inner	680.2.co.a.99.15	yes	832
136.99	even	16	inner	680.2.co.a.99.12	✓	832
680.99	even	16	inner	680.2.co.a.99.93	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.12	✓	832	136.99	even	16	inner
680.2.co.a.99.15	yes	832	85.14	odd	16	inner
680.2.co.a.99.90	yes	832	17.14	odd	16	inner
680.2.co.a.99.93	yes	832	680.99	even	16	inner
680.2.co.a.419.12	yes	832	5.4	even	2	inner
680.2.co.a.419.15	yes	832	8.3	odd	2	inner
680.2.co.a.419.90	yes	832	40.19	odd	2	inner
680.2.co.a.419.93	yes	832	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
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} +(0.265792 + 2.22021i) 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} +(-0.749038 + 3.07229i) 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} +(-0.735389 - 2.25303i) 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} +(-2.51565 + 3.69750i) 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} +(-4.85871 + 1.18023i) 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} +(0.143375 - 3.34864i) 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} +(-5.16543 + 3.64943i) 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} +(-2.05526 - 3.65844i) 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} +(-7.02022 - 0.846435i) 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} +(0.199623 - 2.58058i) 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} +(1.85055 - 4.36386i) 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} +(-3.61244 - 2.83999i) q^{65} +(1.62486 + 0.608427i) q^{66} -9.04379 q^{67} +(-4.05520 - 7.18020i) q^{68} +6.03363i q^{69} +(-0.378945 - 1.03842i) 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} +(4.80676 - 2.23156i) 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} +(-8.65098 + 2.27169i) 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} +(2.02060 - 8.99540i) 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} +(-0.907700 - 5.86453i) 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} +(-2.57435 + 9.17494i) 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

Varieties

Fields

Representations

Groups

Database

Properties

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