LMFDB - Embedded newform 117.2.z.b.5.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(5,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	117.5
Dual form			117.2.z.b.47.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0389963 - 0.145536i) q^{2} +(1.36970 - 1.06015i) q^{3} +(1.71239 + 0.988649i) q^{4} +(-1.38592 + 0.371357i) q^{5} +(-0.100877 - 0.240683i) q^{6} +(-0.436407 + 1.62869i) q^{7} +(0.423741 - 0.423741i) q^{8} +(0.752165 - 2.90418i) q^{9} +0.216183i q^{10} +(-3.71098 - 0.994354i) q^{11} +(3.39358 - 0.461236i) q^{12} +(-3.21493 - 1.63225i) q^{13} +(0.220016 + 0.127026i) q^{14} +(-1.50461 + 1.97793i) q^{15} +(1.93215 + 3.34659i) q^{16} +3.06669 q^{17} +(-0.393331 - 0.222719i) q^{18} +(1.58615 - 1.58615i) q^{19} +(-2.74038 - 0.734283i) q^{20} +(1.12891 + 2.69348i) q^{21} +(-0.289429 + 0.501306i) q^{22} +(-0.462786 + 0.801569i) q^{23} +(0.131170 - 1.02963i) q^{24} +(-2.54725 + 1.47066i) q^{25} +(-0.362922 + 0.404237i) q^{26} +(-2.04862 - 4.77526i) q^{27} +(-2.35751 + 2.35751i) q^{28} +(-7.75127 + 4.47520i) q^{29} +(0.229187 + 0.296107i) q^{30} +(0.341835 + 1.27575i) q^{31} +(1.72008 - 0.460894i) q^{32} +(-6.13710 + 2.57223i) q^{33} +(0.119590 - 0.446315i) q^{34} -2.41931i q^{35} +(4.15921 - 4.22946i) q^{36} +(0.0790729 + 0.0790729i) q^{37} +(-0.168989 - 0.292697i) q^{38} +(-6.13392 + 1.17261i) q^{39} +(-0.429913 + 0.744631i) q^{40} +(4.70308 - 1.26019i) q^{41} +(0.436023 - 0.0592617i) q^{42} +(5.68065 - 3.27972i) q^{43} +(-5.37158 - 5.37158i) q^{44} +(0.0360434 + 4.30428i) q^{45} +(0.0986104 + 0.0986104i) q^{46} +(6.90396 + 1.84991i) q^{47} +(6.19436 + 2.53545i) q^{48} +(3.59998 + 2.07845i) q^{49} +(0.114700 + 0.428068i) q^{50} +(4.20046 - 3.25115i) q^{51} +(-3.89149 - 5.97348i) q^{52} -8.93473i q^{53} +(-0.774863 + 0.111931i) q^{54} +5.51239 q^{55} +(0.505221 + 0.875068i) q^{56} +(0.490997 - 3.85412i) q^{57} +(0.349032 + 1.30261i) q^{58} +(3.83604 + 14.3163i) q^{59} +(-4.53195 + 1.89947i) q^{60} +(-0.662501 - 1.14749i) q^{61} +0.198998 q^{62} +(4.40177 + 2.49245i) q^{63} +7.46031i q^{64} +(5.06179 + 1.06828i) q^{65} +(0.135028 + 0.993478i) q^{66} +(-2.93507 - 10.9538i) q^{67} +(5.25138 + 3.03188i) q^{68} +(0.215904 + 1.58853i) q^{69} +(-0.352097 - 0.0943440i) q^{70} +(8.77081 + 8.77081i) q^{71} +(-0.911896 - 1.54934i) q^{72} +(-11.7401 - 11.7401i) q^{73} +(0.0145915 - 0.00842442i) q^{74} +(-1.92986 + 4.71483i) q^{75} +(4.28426 - 1.14796i) q^{76} +(3.23900 - 5.61011i) q^{77} +(-0.0685427 + 0.938435i) q^{78} +(-4.14278 - 7.17550i) q^{79} +(-3.92059 - 3.92059i) q^{80} +(-7.86850 - 4.36884i) q^{81} -0.733610i q^{82} +(2.02034 - 7.54003i) q^{83} +(-0.729771 + 5.72839i) q^{84} +(-4.25020 + 1.13884i) q^{85} +(-0.255794 - 0.954637i) q^{86} +(-5.87254 + 14.3472i) q^{87} +(-1.99384 + 1.15115i) q^{88} +(6.10608 - 6.10608i) q^{89} +(0.627835 + 0.162606i) q^{90} +(4.06145 - 4.52381i) q^{91} +(-1.58494 + 0.915066i) q^{92} +(1.82070 + 1.38500i) q^{93} +(0.538458 - 0.932637i) q^{94} +(-1.60926 + 2.78731i) q^{95} +(1.86738 - 2.45483i) q^{96} +(6.12255 + 1.64053i) q^{97} +(0.442876 - 0.442876i) q^{98} +(-5.67905 + 10.0294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.0389963	−	0.145536i	0.0275746	−	0.102910i	−0.950767	−	0.309906i	$-0.899702\pi$
$2$	0.0389963	−	0.145536i	0.0275746	−	0.102910i	0.978342	+	0.206997i	$0.0663690\pi$
$3$	1.36970	−	1.06015i	0.790798	−	0.612078i
$3$	1.36970	−	1.06015i	0.790798	−	0.612078i
$4$	1.71239	+	0.988649i	0.856195	+	0.494325i
$5$	−1.38592	+	0.371357i	−0.619803	+	0.166076i	−0.555038	−	0.831825i	$-0.687296\pi$
$5$	−1.38592	+	0.371357i	−0.619803	+	0.166076i	−0.0647648	+	0.997901i	$0.520630\pi$
$6$	−0.100877	−	0.240683i	−0.0411828	−	0.0982585i
$7$	−0.436407	+	1.62869i	−0.164946	+	0.615588i	0.833101	+	0.553121i	$0.186563\pi$
$7$	−0.436407	+	1.62869i	−0.164946	+	0.615588i	−0.998047	+	0.0624670i	$0.980103\pi$
$8$	0.423741	−	0.423741i	0.149815	−	0.149815i
$9$	0.752165	−	2.90418i	0.250722	−	0.968059i
$10$			0.216183i			0.0683632i
$11$	−3.71098	−	0.994354i	−1.11890	−	0.299809i	−0.348463	−	0.937322i	$-0.613296\pi$
$11$	−3.71098	−	0.994354i	−1.11890	−	0.299809i	−0.770439	+	0.637513i	$0.779963\pi$
$12$	3.39358	−	0.461236i	0.979642	−	0.133147i
$13$	−3.21493	−	1.63225i	−0.891661	−	0.452704i
$13$	−3.21493	−	1.63225i	−0.891661	−	0.452704i
$14$	0.220016	+	0.127026i	0.0588017	+	0.0339492i
$15$	−1.50461	+	1.97793i	−0.388488	+	0.510700i
$16$	1.93215	+	3.34659i	0.483038	+	0.836647i
$17$	3.06669			0.743782			0.371891	−	0.928276i	$-0.378709\pi$
$17$	3.06669			0.743782			0.371891	+	0.928276i	$0.378709\pi$
$18$	−0.393331	−	0.222719i	−0.0927091	−	0.0524955i
$19$	1.58615	−	1.58615i	0.363889	−	0.363889i	−0.501354	−	0.865242i	$-0.667164\pi$
$19$	1.58615	−	1.58615i	0.363889	−	0.363889i	0.865242	+	0.501354i	$0.167164\pi$
$20$	−2.74038	−	0.734283i	−0.612768	−	0.164191i
$21$	1.12891	+	2.69348i	0.246349	+	0.587766i
$22$	−0.289429	+	0.501306i	−0.0617065	+	0.106879i
$23$	−0.462786	+	0.801569i	−0.0964976	+	0.167139i	−0.910233	−	0.414097i	$-0.864097\pi$
$23$	−0.462786	+	0.801569i	−0.0964976	+	0.167139i	0.813735	+	0.581236i	$0.197431\pi$
$24$	0.131170	−	1.02963i	0.0267749	−	0.210172i
$25$	−2.54725	+	1.47066i	−0.509451	+	0.294132i
$26$	−0.362922	+	0.404237i	−0.0711748	+	0.0792774i
$27$	−2.04862	−	4.77526i	−0.394257	−	0.919000i
$28$	−2.35751	+	2.35751i	−0.445527	+	0.445527i
$29$	−7.75127	+	4.47520i	−1.43937	+	0.831023i	−0.997806	−	0.0662050i	$-0.978911\pi$
$29$	−7.75127	+	4.47520i	−1.43937	+	0.831023i	−0.441568	+	0.897228i	$0.645578\pi$
$30$	0.229187	+	0.296107i	0.0418436	+	0.0540614i
$31$	0.341835	+	1.27575i	0.0613955	+	0.229131i	0.989805	−	0.142427i	$-0.0454905\pi$
$31$	0.341835	+	1.27575i	0.0613955	+	0.229131i	−0.928410	+	0.371558i	$0.878824\pi$
$32$	1.72008	−	0.460894i	0.304070	−	0.0814753i
$33$	−6.13710	+	2.57223i	−1.06833	+	0.447767i
$34$	0.119590	−	0.446315i	0.0205095	−	0.0765424i
$35$		−	2.41931i		−	0.408937i
$36$	4.15921	−	4.22946i	0.693202	−	0.704910i
$37$	0.0790729	+	0.0790729i	0.0129995	+	0.0129995i	0.713577	−	0.700577i	$-0.247074\pi$
$37$	0.0790729	+	0.0790729i	0.0129995	+	0.0129995i	−0.700577	+	0.713577i	$0.747074\pi$
$38$	−0.168989	−	0.292697i	−0.0274136	−	0.0474817i
$39$	−6.13392	+	1.17261i	−0.982213	+	0.187768i
$40$	−0.429913	+	0.744631i	−0.0679752	+	0.117736i
$41$	4.70308	−	1.26019i	0.734497	−	0.196808i	0.127866	−	0.991791i	$-0.459187\pi$
$41$	4.70308	−	1.26019i	0.734497	−	0.196808i	0.606631	+	0.794984i	$0.292521\pi$
$42$	0.436023	−	0.0592617i	0.0672797	−	0.00914428i
$43$	5.68065	−	3.27972i	0.866291	−	0.500153i	0.000176765	−	1.00000i	$-0.499944\pi$
$43$	5.68065	−	3.27972i	0.866291	−	0.500153i	0.866114	+	0.499847i	$0.166610\pi$
$44$	−5.37158	−	5.37158i	−0.809796	−	0.809796i
$45$	0.0360434	+	4.30428i	0.00537304	+	0.641645i
$46$	0.0986104	+	0.0986104i	0.0145393	+	0.0145393i
$47$	6.90396	+	1.84991i	1.00705	+	0.269837i	0.724395	−	0.689385i	$-0.242119\pi$
$47$	6.90396	+	1.84991i	1.00705	+	0.269837i	0.282652	+	0.959223i	$0.408786\pi$
$48$	6.19436	+	2.53545i	0.894078	+	0.365961i
$49$	3.59998	+	2.07845i	0.514284	+	0.296922i
$50$	0.114700	+	0.428068i	0.0162211	+	0.0605379i
$51$	4.20046	−	3.25115i	0.588181	−	0.455253i
$52$	−3.89149	−	5.97348i	−0.539653	−	0.828373i
$53$		−	8.93473i		−	1.22728i	−0.789586	−	0.613640i	$-0.789705\pi$
$53$		−	8.93473i		−	1.22728i	0.789586	−	0.613640i	$-0.210295\pi$
$54$	−0.774863	+	0.111931i	−0.105445	+	0.0152319i
$55$	5.51239			0.743290
$56$	0.505221	+	0.875068i	0.0675130	+	0.116936i
$57$	0.490997	−	3.85412i	0.0650341	−	0.510490i
$58$	0.349032	+	1.30261i	0.0458302	+	0.171041i
$59$	3.83604	+	14.3163i	0.499410	+	1.86382i	0.503778	+	0.863833i	$0.331943\pi$
$59$	3.83604	+	14.3163i	0.499410	+	1.86382i	−0.00436825	+	0.999990i	$0.501390\pi$
$60$	−4.53195	+	1.89947i	−0.585073	+	0.245220i
$61$	−0.662501	−	1.14749i	−0.0848246	−	0.146920i	0.820492	−	0.571658i	$-0.193700\pi$
$61$	−0.662501	−	1.14749i	−0.0848246	−	0.146920i	−0.905316	+	0.424738i	$0.860366\pi$
$62$	0.198998			0.0252727
$63$	4.40177	+	2.49245i	0.554570	+	0.314019i
$64$			7.46031i			0.932538i
$65$	5.06179	+	1.06828i	0.627837	+	0.132504i
$66$	0.135028	+	0.993478i	0.0166208	+	0.122289i
$67$	−2.93507	−	10.9538i	−0.358576	−	1.33822i	−0.875924	−	0.482449i	$-0.839747\pi$
$67$	−2.93507	−	10.9538i	−0.358576	−	1.33822i	0.517348	−	0.855775i	$-0.326919\pi$
$68$	5.25138	+	3.03188i	0.636823	+	0.367670i
$69$	0.215904	+	1.58853i	0.0259918	+	0.191237i
$70$	−0.352097	−	0.0943440i	−0.0420836	−	0.0112763i
$71$	8.77081	+	8.77081i	1.04090	+	1.04090i	0.999127	+	0.0417763i	$0.0133017\pi$
$71$	8.77081	+	8.77081i	1.04090	+	1.04090i	0.0417763	+	0.999127i	$0.486698\pi$
$72$	−0.911896	−	1.54934i	−0.107468	−	0.182592i
$73$	−11.7401	−	11.7401i	−1.37408	−	1.37408i	−0.854304	−	0.519773i	$-0.826017\pi$
$73$	−11.7401	−	11.7401i	−1.37408	−	1.37408i	−0.519773	−	0.854304i	$-0.673983\pi$
$74$	0.0145915	−	0.00842442i	0.00169623	−	0.000979319i
$75$	−1.92986	+	4.71483i	−0.222841	+	0.544422i
$76$	4.28426	−	1.14796i	0.491439	−	0.131681i
$77$	3.23900	−	5.61011i	0.369118	−	0.639331i
$78$	−0.0685427	+	0.938435i	−0.00776093	+	0.106257i
$79$	−4.14278	−	7.17550i	−0.466099	−	0.807307i	0.533152	−	0.846020i	$-0.321008\pi$
$79$	−4.14278	−	7.17550i	−0.466099	−	0.807307i	−0.999250	+	0.0387130i	$0.987674\pi$
$80$	−3.92059	−	3.92059i	−0.438335	−	0.438335i
$81$	−7.86850	−	4.36884i	−0.874277	−	0.485427i
$82$		−	0.733610i		−	0.0810137i
$83$	2.02034	−	7.54003i	0.221762	−	0.827625i	−0.761915	−	0.647678i	$-0.775740\pi$
$83$	2.02034	−	7.54003i	0.221762	−	0.827625i	0.983676	−	0.179948i	$-0.0575929\pi$
$84$	−0.729771	+	5.72839i	−0.0796245	+	0.625019i
$85$	−4.25020	+	1.13884i	−0.460999	+	0.123524i
$86$	−0.255794	−	0.954637i	−0.0275830	−	0.102941i
$87$	−5.87254	+	14.3472i	−0.629603	+	1.53818i
$88$	−1.99384	+	1.15115i	−0.212544	+	0.122713i
$89$	6.10608	−	6.10608i	0.647244	−	0.647244i	−0.305082	−	0.952326i	$-0.598684\pi$
$89$	6.10608	−	6.10608i	0.647244	−	0.647244i	0.952326	+	0.305082i	$0.0986840\pi$
$90$	0.627835	+	0.162606i	0.0661796	+	0.0171401i
$91$	4.06145	−	4.52381i	0.425756	−	0.474224i
$92$	−1.58494	+	0.915066i	−0.165242	+	0.0954023i
$93$	1.82070	+	1.38500i	0.188797	+	0.143617i
$94$	0.538458	−	0.932637i	0.0555377	−	0.0961941i
$95$	−1.60926	+	2.78731i	−0.165106	+	0.285972i
$96$	1.86738	−	2.45483i	0.190588	−	0.250545i
$97$	6.12255	+	1.64053i	0.621651	+	0.166571i	0.555878	−	0.831264i	$-0.312382\pi$
$97$	6.12255	+	1.64053i	0.621651	+	0.166571i	0.0657729	+	0.997835i	$0.479049\pi$
$98$	0.442876	−	0.442876i	0.0447373	−	0.0447373i
$99$	−5.67905	+	10.0294i	−0.570766	+	1.00800i
$100$	−5.81586			−0.581586
$101$	−1.08342	−	1.87653i	−0.107804	−	0.186722i	0.807076	−	0.590447i	$-0.201049\pi$
$101$	−1.08342	−	1.87653i	−0.107804	−	0.186722i	−0.914880	+	0.403725i	$0.867715\pi$
$102$	−0.309358	−	0.738101i	−0.0306310	−	0.0730829i
$103$	6.94675	+	4.01071i	0.684484	+	0.395187i	0.801542	−	0.597938i	$-0.204013\pi$
$103$	6.94675	+	4.01071i	0.684484	+	0.395187i	−0.117059	+	0.993125i	$0.537347\pi$
$104$	−2.05395	+	0.670647i	−0.201406	+	0.0657623i
$105$	−2.56483	−	3.31373i	−0.250301	−	0.323387i
$106$	−1.30033	−	0.348422i	−0.126299	−	0.0338417i
$107$			14.0499i			1.35826i	0.734019	+	0.679129i	$0.237642\pi$
$107$			14.0499i			1.35826i	−0.734019	+	0.679129i	$0.762358\pi$
$108$	1.21302	−	10.2025i	0.116723	−	0.981735i
$109$	−8.70457	+	8.70457i	−0.833747	+	0.833747i	−0.988027	−	0.154280i	$-0.950694\pi$
$109$	−8.70457	+	8.70457i	−0.833747	+	0.833747i	0.154280	+	0.988027i	$0.450694\pi$
$110$	0.214963	−	0.802252i	0.0204959	−	0.0764917i
$111$	0.192135	+	0.0244772i	0.0182367	+	0.00232327i
$112$	−6.29377	+	1.68641i	−0.594706	+	0.159351i
$113$	−6.10197	−	3.52298i	−0.574025	−	0.331414i	0.184730	−	0.982789i	$-0.440859\pi$
$113$	−6.10197	−	3.52298i	−0.574025	−	0.331414i	−0.758755	+	0.651376i	$0.774192\pi$
$114$	−0.541767	−	0.221754i	−0.0507411	−	0.0207692i
$115$	0.343717	−	1.28277i	0.0320518	−	0.119619i
$116$	−17.6976			−1.64318
$117$	−7.15850	+	8.10900i	−0.661803	+	0.749678i
$118$	2.23313			0.205576
$119$	−1.33833	+	4.99471i	−0.122684	+	0.457864i
$120$	0.200568	+	1.47569i	0.0183093	+	0.134712i
$121$	3.25636	+	1.88006i	0.296032	+	0.170914i
$122$	−0.192836	+	0.0516702i	−0.0174585	+	0.00467800i
$123$	5.10583	−	6.71204i	0.460377	−	0.605205i
$124$	−0.675911	+	2.52253i	−0.0606986	+	0.226530i
$125$	8.05698	−	8.05698i	0.720638	−	0.720638i
$126$	0.534395	−	0.543420i	0.0476076	−	0.0484117i
$127$			0.337751i			0.0299706i	0.999888	+	0.0149853i	$0.00477015\pi$
$127$			0.337751i			0.0299706i	−0.999888	+	0.0149853i	$0.995230\pi$
$128$	4.52590	+	1.21271i	0.400037	+	0.107190i
$129$	4.30379	−	10.5146i	0.378928	−	0.925757i
$130$	0.352865	−	0.695014i	0.0309483	−	0.0609568i
$131$	3.97418	+	2.29449i	0.347225	+	0.200471i	0.663463	−	0.748209i	$-0.269086\pi$
$131$	3.97418	+	2.29449i	0.347225	+	0.200471i	−0.316237	+	0.948680i	$0.602420\pi$
$132$	−13.0521	−	1.66278i	−1.13604	−	0.144727i
$133$	1.89115	+	3.27557i	0.163983	+	0.284028i
$134$	−1.70864			−0.147604
$135$	4.61255	+	5.85737i	0.396985	+	0.504122i
$136$	1.29948	−	1.29948i	0.111430	−	0.111430i
$137$	−13.7339	−	3.67998i	−1.17336	−	0.314402i	−0.381072	−	0.924545i	$-0.624445\pi$
$137$	−13.7339	−	3.67998i	−1.17336	−	0.314402i	−0.792291	+	0.610144i	$0.791112\pi$
$138$	0.239609	+	0.0305250i	0.0203968	+	0.00259846i
$139$	−3.71796	+	6.43969i	−0.315353	+	0.546207i	−0.979512	−	0.201383i	$-0.935456\pi$
$139$	−3.71796	+	6.43969i	−0.315353	+	0.546207i	0.664159	+	0.747591i	$0.268790\pi$
$140$	2.39184	−	4.14280i	0.202148	−	0.350130i
$141$	11.4176	−	4.78541i	0.961531	−	0.403004i
$142$	1.61850	−	0.934441i	0.135821	−	0.0784165i
$143$	10.3075	+	9.25402i	0.861957	+	0.773860i
$144$	11.1724	−	3.09413i	0.931032	−	0.257844i
$145$	9.08075	−	9.08075i	0.754116	−	0.754116i
$146$	−2.16643	+	1.25079i	−0.179295	+	0.103516i
$147$	7.13438	−	0.969663i	0.588433	−	0.0799765i
$148$	0.0572283	+	0.213579i	0.00470414	+	0.0175561i
$149$	−18.5659	+	4.97473i	−1.52098	+	0.407545i	−0.920064	−	0.391767i	$-0.871864\pi$
$149$	−18.5659	+	4.97473i	−1.52098	+	0.407545i	−0.600916	+	0.799312i	$0.705197\pi$
$150$	0.610921	+	0.464726i	0.0498815	+	0.0379447i
$151$	−1.21912	+	4.54980i	−0.0992103	+	0.370258i	−0.997624	−	0.0688920i	$-0.978054\pi$
$151$	−1.21912	+	4.54980i	−0.0992103	+	0.370258i	0.898414	+	0.439150i	$0.144720\pi$
$152$		−	1.34424i		−	0.109032i
$153$	2.30666	−	8.90622i	0.186482	−	0.720025i
$154$	−0.690165	−	0.690165i	−0.0556151	−	0.0556151i
$155$	−0.947514	−	1.64114i	−0.0761062	−	0.131820i
$156$	−11.6630	−	4.05633i	−0.933785	−	0.324766i
$157$	1.45800	−	2.52533i	0.116361	−	0.201543i	−0.801962	−	0.597375i	$-0.796210\pi$
$157$	1.45800	−	2.52533i	0.116361	−	0.201543i	0.918323	+	0.395832i	$0.129544\pi$
$158$	−1.20585	+	0.323106i	−0.0959321	+	0.0257049i
$159$	−9.47215	−	12.2379i	−0.751191	−	0.970530i
$160$	−2.21274	+	1.27752i	−0.174932	+	0.100997i
$161$	−1.10355	−	1.10355i	−0.0869717	−	0.0869717i
$162$	−0.942667	+	0.974782i	−0.0740629	+	0.0765861i
$163$	10.7515	+	10.7515i	0.842122	+	0.842122i	0.989135	−	0.147013i	$-0.0469659\pi$
$163$	10.7515	+	10.7515i	0.842122	+	0.842122i	−0.147013	+	0.989135i	$0.546966\pi$
$164$	9.29939	+	2.49176i	0.726160	+	0.194574i
$165$	7.55033	−	5.84396i	0.587792	−	0.454951i
$166$	−1.01856	−	0.588066i	−0.0790557	−	0.0456428i
$167$	−0.564722	−	2.10757i	−0.0436995	−	0.163089i	0.940628	−	0.339439i	$-0.110237\pi$
$167$	−0.564722	−	2.10757i	−0.0436995	−	0.163089i	−0.984327	+	0.176351i	$0.943571\pi$
$168$	1.61970	+	0.662973i	0.124963	+	0.0511494i
$169$	7.67153	+	10.4951i	0.590118	+	0.807317i
$170$			0.662968i			0.0508473i
$171$	−3.41342	−	5.79952i	−0.261031	−	0.443500i
$172$	12.9700			0.988952
$173$	−1.74974	−	3.03064i	−0.133030	−	0.230416i	0.791813	−	0.610764i	$-0.209137\pi$
$173$	−1.74974	−	3.03064i	−0.133030	−	0.230416i	−0.924843	+	0.380348i	$0.875804\pi$
$174$	1.85903	+	1.41416i	0.140932	+	0.107207i
$175$	−1.28361	−	4.79050i	−0.0970319	−	0.362128i
$176$	−3.84249	−	14.3404i	−0.289639	−	1.08095i
$177$	20.4317	+	15.5423i	1.53574	+	1.16823i
$178$	−0.650542	−	1.12677i	−0.0487602	−	0.0844551i
$179$	−14.2162			−1.06257			−0.531285	−	0.847193i	$-0.678291\pi$
$179$	−14.2162			−1.06257			−0.531285	+	0.847193i	$0.678291\pi$
$180$	−4.19371	+	7.40625i	−0.312580	+	0.552029i
$181$			5.70433i			0.424000i	0.977270	+	0.212000i	$0.0679976\pi$
$181$			5.70433i			0.424000i	−0.977270	+	0.212000i	$0.932002\pi$
$182$	−0.499997	−	0.767500i	−0.0370622	−	0.0568909i
$183$	−2.12394	−	0.869363i	−0.157006	−	0.0642651i
$184$	0.143556	+	0.535759i	0.0105831	+	0.0394967i
$185$	−0.138953	−	0.0802246i	−0.0102160	−	0.00589823i
$186$	0.272568	−	0.210967i	0.0199856	−	0.0154689i
$187$	−11.3804	−	3.04938i	−0.832220	−	0.222993i
$188$	9.99337	+	9.99337i	0.728841	+	0.728841i
$189$	8.67148	−	1.25262i	0.630757	−	0.0911145i
$190$	0.342900	+	0.342900i	0.0248766	+	0.0248766i
$191$	17.5844	−	10.1523i	1.27236	−	0.734598i	0.296929	−	0.954900i	$-0.404038\pi$
$191$	17.5844	−	10.1523i	1.27236	−	0.734598i	0.975432	+	0.220302i	$0.0707042\pi$
$192$	7.90904	+	10.2184i	0.570786	+	0.737449i
$193$	−12.0248	+	3.22203i	−0.865563	+	0.231927i	−0.664168	−	0.747583i	$-0.731214\pi$
$193$	−12.0248	+	3.22203i	−0.865563	+	0.231927i	−0.201395	+	0.979510i	$0.564547\pi$
$194$	0.477514	−	0.827079i	0.0342835	−	0.0593808i
$195$	8.06568	−	3.90302i	0.577595	−	0.279501i
$196$	4.10972	+	7.11824i	0.293551	+	0.508446i
$197$	10.6984	+	10.6984i	0.762230	+	0.762230i	0.976725	−	0.214495i	$-0.0688106\pi$
$197$	10.6984	+	10.6984i	0.762230	+	0.762230i	−0.214495	+	0.976725i	$0.568811\pi$
$198$	1.23818	+	1.21762i	0.0879938	+	0.0865324i
$199$			17.6661i			1.25232i	0.779696	+	0.626158i	$0.215373\pi$
$199$			17.6661i			1.25232i	−0.779696	+	0.626158i	$0.784627\pi$
$200$	−0.456198	+	1.70255i	−0.0322581	+	0.120389i
$201$	−15.6329	−	11.8919i	−1.10266	−	0.838789i
$202$	−0.315352	+	0.0844984i	−0.0221881	+	0.00594529i
$203$	−3.90602	−	14.5774i	−0.274149	−	1.02314i
$204$	10.4071	−	1.41447i	0.728641	−	0.0990327i
$205$	−6.05012	+	3.49304i	−0.422559	+	0.243964i
$206$	0.854601	−	0.854601i	0.0595429	−	0.0595429i
$207$	1.97981	+	1.94693i	0.137606	+	0.135321i
$208$	−0.749273	−	13.9128i	−0.0519527	−	0.964679i
$209$	−7.46338	+	4.30899i	−0.516253	+	0.298059i
$210$	−0.582286	+	0.244052i	−0.0401815	+	0.0168412i
$211$	10.5424	−	18.2599i	0.725767	−	1.25707i	−0.232890	−	0.972503i	$-0.574818\pi$
$211$	10.5424	−	18.2599i	0.725767	−	1.25707i	0.958657	−	0.284563i	$-0.0918485\pi$
$212$	8.83331	−	15.2997i	0.606675	−	1.05079i
$213$	21.3118	+	2.71502i	1.46026	+	0.186030i
$214$	2.04477	+	0.547895i	0.139778	+	0.0374533i
$215$	−6.65499	+	6.65499i	−0.453866	+	0.453866i
$216$	−2.89156	−	1.15539i	−0.196746	−	0.0786144i
$217$	−2.22698			−0.151177
$218$	0.927384	+	1.60628i	0.0628104	+	0.108791i
$219$	−28.5268	−	3.63418i	−1.92766	−	0.245575i
$220$	9.43936	+	5.44982i	0.636402	+	0.367427i
$221$	−9.85920	−	5.00561i	−0.663202	−	0.336713i
$222$	0.0110549	−	0.0270081i	0.000741955	−	0.00181267i
$223$	19.5048	+	5.22631i	1.30614	+	0.349979i	0.843769	−	0.536706i	$-0.180332\pi$
$223$	19.5048	+	5.22631i	1.30614	+	0.349979i	0.462372	+	0.886686i	$0.346998\pi$
$224$			3.00262i			0.200621i
$225$	2.35510	+	8.50385i	0.157006	+	0.566924i
$226$	−0.750675	+	0.750675i	−0.0499342	+	0.0499342i
$227$	3.62460	−	13.5272i	0.240573	−	0.897830i	−0.734984	−	0.678084i	$-0.762810\pi$
$227$	3.62460	−	13.5272i	0.240573	−	0.897830i	0.975557	−	0.219746i	$-0.0705229\pi$
$228$	4.65115	−	6.11433i	0.308030	−	0.404931i
$229$	−12.0378	+	3.22551i	−0.795478	+	0.213148i	−0.633598	−	0.773663i	$-0.718423\pi$
$229$	−12.0378	+	3.22551i	−0.795478	+	0.213148i	−0.161880	+	0.986810i	$0.551756\pi$
$230$	−0.173286	−	0.100047i	−0.0114261	−	0.00659688i
$231$	−1.51109	−	11.1180i	−0.0994227	−	0.731510i
$232$	−1.38821	+	5.18085i	−0.0911401	+	0.340140i
$233$	−21.5604			−1.41247			−0.706235	−	0.707978i	$-0.749608\pi$
$233$	−21.5604			−1.41247			−0.706235	+	0.707978i	$0.749608\pi$
$234$	0.900999	+	1.35804i	0.0589001	+	0.0887780i
$235$	−10.2553			−0.668984
$236$	−7.58500	+	28.3076i	−0.493741	+	1.84267i
$237$	−13.2815	−	5.43633i	−0.862724	−	0.353128i
$238$	0.674721	+	0.389550i	0.0437356	+	0.0252508i
$239$	−16.5914	+	4.44565i	−1.07321	+	0.287565i	−0.751811	−	0.659379i	$-0.770819\pi$
$239$	−16.5914	+	4.44565i	−1.07321	+	0.287565i	−0.321398	+	0.946944i	$0.604153\pi$
$240$	−9.52645	−	1.21363i	−0.614930	−	0.0783392i
$241$	2.90879	−	10.8558i	0.187372	−	0.699282i	−0.806738	−	0.590909i	$-0.798769\pi$
$241$	2.90879	−	10.8558i	0.187372	−	0.699282i	0.994110	−	0.108373i	$-0.0345640\pi$
$242$	0.400602	−	0.400602i	0.0257517	−	0.0257517i
$243$	−15.4091	+	2.35777i	−0.988495	+	0.151251i
$244$		−	2.61992i		−	0.167724i
$245$	−5.76114	−	1.54369i	−0.368066	−	0.0986230i
$246$	−0.777737	−	1.00483i	−0.0495867	−	0.0640655i
$247$	−7.68837	+	2.51037i	−0.489199	+	0.159731i
$248$	0.685436	+	0.395737i	0.0435252	+	0.0251293i
$249$	−5.22629	−	12.4695i	−0.331203	−	0.790220i
$250$	−0.858390	−	1.48678i	−0.0542894	−	0.0940319i
$251$	−21.0928			−1.33137			−0.665684	−	0.746234i	$-0.731860\pi$
$251$	−21.0928			−1.33137			−0.665684	+	0.746234i	$0.731860\pi$
$252$	5.07338	+	8.61985i	0.319593	+	0.543000i
$253$	2.51443	−	2.51443i	0.158081	−	0.158081i
$254$	0.0491550	+	0.0131711i	0.00308426	+	0.000826426i
$255$	−4.61416	+	6.06571i	−0.288950	+	0.379850i
$256$	−7.10732	+	12.3102i	−0.444207	+	0.769390i
$257$	1.29490	−	2.24283i	0.0807734	−	0.139904i	−0.822809	−	0.568318i	$-0.807594\pi$
$257$	1.29490	−	2.24283i	0.0807734	−	0.139904i	0.903582	+	0.428414i	$0.140928\pi$
$258$	−1.36242	−	1.03639i	−0.0848206	−	0.0645227i
$259$	−0.163294	+	0.0942776i	−0.0101466	+	0.00585812i
$260$	7.61160	+	6.83365i	0.472051	+	0.423805i
$261$	7.16653	+	25.8771i	0.443597	+	1.60175i
$262$	0.488910	−	0.488910i	0.0302050	−	0.0302050i
$263$	6.85025	−	3.95500i	0.422405	−	0.243875i	−0.273701	−	0.961815i	$-0.588248\pi$
$263$	6.85025	−	3.95500i	0.422405	−	0.243875i	0.696106	+	0.717939i	$0.254915\pi$
$264$	−1.51058	+	3.69050i	−0.0929700	+	0.227134i
$265$	3.31797	+	12.3828i	0.203821	+	0.760672i
$266$	0.550462	−	0.147496i	0.0337510	−	0.00904354i
$267$	1.89015	−	14.8369i	0.115675	−	0.908002i
$268$	5.80352	−	21.6590i	0.354506	−	1.32304i
$269$		−	6.62634i		−	0.404015i	−0.979384	−	0.202007i	$-0.935253\pi$
$269$		−	6.62634i		−	0.404015i	0.979384	−	0.202007i	$-0.0647465\pi$
$270$	1.03233	−	0.442878i	0.0628258	−	0.0269527i
$271$	−6.37767	−	6.37767i	−0.387416	−	0.387416i	0.486349	−	0.873765i	$-0.338328\pi$
$271$	−6.37767	−	6.37767i	−0.387416	−	0.387416i	−0.873765	+	0.486349i	$0.838328\pi$
$272$	5.92532	+	10.2630i	0.359275	+	0.622283i
$273$	0.767060	−	10.5020i	0.0464246	−	0.635611i
$274$	−1.07114	+	1.85527i	−0.0647099	+	0.112081i
$275$	10.9152	−	2.92471i	0.658209	−	0.176367i
$276$	−1.20079	+	2.93364i	−0.0722790	+	0.176585i
$277$	−24.8880	+	14.3691i	−1.49537	+	0.863354i	−0.999986	−	0.00531870i	$-0.998307\pi$
$277$	−24.8880	+	14.3691i	−1.49537	+	0.863354i	−0.495387	+	0.868673i	$0.664974\pi$
$278$	0.792222	+	0.792222i	0.0475143	+	0.0475143i
$279$	3.96211	−	0.0331781i	0.237206	−	0.00198632i
$280$	−1.02516	−	1.02516i	−0.0612650	−	0.0612650i
$281$	20.6283	+	5.52733i	1.23058	+	0.329733i	0.814805	−	0.579735i	$-0.196844\pi$
$281$	20.6283	+	5.52733i	1.23058	+	0.329733i	0.415774	+	0.909468i	$0.363511\pi$
$282$	−0.251208	−	1.84828i	−0.0149592	−	0.110064i
$283$	16.1273	+	9.31112i	0.958670	+	0.553488i	0.895763	−	0.444531i	$-0.146630\pi$
$283$	16.1273	+	9.31112i	0.958670	+	0.553488i	0.0629065	+	0.998019i	$0.479963\pi$
$284$	6.34780	+	23.6903i	0.376672	+	1.40576i
$285$	0.750769	+	5.52384i	0.0444717	+	0.327204i
$286$	1.74875	−	1.13924i	0.103406	−	0.0673648i
$287$			8.20983i			0.484611i
$288$	−0.0447338	−	5.34208i	−0.00263596	−	0.314785i
$289$	−7.59539			−0.446788
$290$	−0.967463	−	1.67569i	−0.0568114	−	0.0984002i
$291$	10.1253	−	4.24378i	0.593555	−	0.248775i
$292$	−8.49681	−	31.7105i	−0.497238	−	1.85572i
$293$	0.308685	+	1.15203i	0.0180335	+	0.0673021i	0.974356	−	0.225011i	$-0.0722418\pi$
$293$	0.308685	+	1.15203i	0.0180335	+	0.0673021i	−0.956323	+	0.292313i	$0.905575\pi$
$294$	0.137093	−	1.07612i	0.00799544	−	0.0627608i
$295$	−10.6329	−	18.4167i	−0.619072	−	1.07226i
$296$	0.0670129			0.00389504
$297$	2.85409	+	19.7580i	0.165611	+	1.14647i
$298$			2.89601i			0.167761i
$299$	2.79618	−	1.82161i	0.161707	−	0.105346i
$300$	−7.96599	+	6.16568i	−0.459917	+	0.355976i
$301$	2.86259	+	10.6833i	0.164997	+	0.615777i
$302$	0.614620	+	0.354851i	0.0353674	+	0.0204194i
$303$	−3.47336	−	1.42170i	−0.199539	−	0.0816748i
$304$	8.37289	+	2.24351i	0.480218	+	0.128674i
$305$	1.34430	+	1.34430i	0.0769745	+	0.0769745i
$306$	−1.20623	−	0.683012i	−0.0689554	−	0.0390452i
$307$	−8.36696	−	8.36696i	−0.477527	−	0.477527i	0.426813	−	0.904340i	$-0.359636\pi$
$307$	−8.36696	−	8.36696i	−0.477527	−	0.477527i	−0.904340	+	0.426813i	$0.859636\pi$
$308$	11.0929	−	6.40446i	0.632074	−	0.364928i
$309$	13.7669	−	1.87112i	0.783173	−	0.106444i
$310$	−0.275795	+	0.0738991i	−0.0156641	+	0.00419719i
$311$	2.59632	−	4.49695i	0.147224	−	0.254999i	−0.782977	−	0.622051i	$-0.786300\pi$
$311$	2.59632	−	4.49695i	0.147224	−	0.254999i	0.930200	+	0.367052i	$0.119633\pi$
$312$	−2.10231	+	3.09608i	−0.119020	+	0.175281i
$313$	5.50069	+	9.52747i	0.310917	+	0.538525i	0.978561	−	0.205956i	$-0.0660304\pi$
$313$	5.50069	+	9.52747i	0.310917	+	0.538525i	−0.667644	+	0.744481i	$0.732697\pi$
$314$	−0.310671	−	0.310671i	−0.0175322	−	0.0175322i
$315$	−7.02609	−	1.81972i	−0.395875	−	0.102529i
$316$		−	16.3830i		−	0.921616i
$317$	8.76274	−	32.7030i	0.492165	−	1.83678i	−0.0531987	−	0.998584i	$-0.516942\pi$
$317$	8.76274	−	32.7030i	0.492165	−	1.83678i	0.545363	−	0.838200i	$-0.316392\pi$
$318$	−2.15044	+	0.901308i	−0.120591	+	0.0505428i
$319$	33.2147	−	8.89986i	1.85967	−	0.498296i
$320$	−2.77043	−	10.3394i	−0.154872	−	0.577990i
$321$	14.8950	+	19.2442i	0.831359	+	1.07411i
$322$	−0.203640	+	0.117572i	−0.0113484	+	0.00655202i
$323$	4.86425	−	4.86425i	0.270654	−	0.270654i
$324$	−9.15468	−	15.2603i	−0.508594	−	0.847797i
$325$	10.5897	−	0.570309i	0.587412	−	0.0316350i
$326$	1.98400	−	1.14546i	0.109884	−	0.0634413i
$327$	−2.69452	+	21.1508i	−0.149007	+	1.16964i
$328$	1.45889	−	2.52688i	0.0805539	−	0.139524i
$329$	−6.02588	+	10.4371i	−0.332217	+	0.575417i
$330$	−0.556072	−	1.32674i	−0.0306108	−	0.0730346i
$331$	−8.51608	−	2.28188i	−0.468086	−	0.125423i	0.0170637	−	0.999854i	$-0.494568\pi$
$331$	−8.51608	−	2.28188i	−0.468086	−	0.125423i	−0.485150	+	0.874431i	$0.661235\pi$
$332$	10.9141	−	10.9141i	0.598987	−	0.598987i
$333$	0.289118	−	0.170166i	0.0158435	−	0.00932503i
$334$	−0.328750			−0.0179884
$335$	8.13556	+	14.0912i	0.444493	+	0.769885i
$336$	−6.83274	+	8.98222i	−0.372757	+	0.490020i
$337$	−8.75095	−	5.05236i	−0.476694	−	0.275220i	0.242343	−	0.970191i	$-0.422084\pi$
$337$	−8.75095	−	5.05236i	−0.476694	−	0.275220i	−0.719038	+	0.694971i	$0.755417\pi$
$338$	1.82658	−	0.707215i	0.0993530	−	0.0384674i
$339$	−12.0928	+	1.64358i	−0.656789	+	0.0892670i
$340$	−8.40391	−	2.25182i	−0.455766	−	0.122122i
$341$		−	5.07418i		−	0.274782i
$342$	−0.977151	+	0.270617i	−0.0528383	+	0.0146333i
$343$	−13.3022	+	13.3022i	−0.718253	+	0.718253i
$344$	1.01737	−	3.79688i	0.0548529	−	0.204714i
$345$	−0.889139	−	2.12140i	−0.0478696	−	0.114213i
$346$	−0.509302	+	0.136467i	−0.0273802	+	0.00733651i
$347$	−1.09771	−	0.633764i	−0.0589282	−	0.0340222i	0.470246	−	0.882535i	$-0.344165\pi$
$347$	−1.09771	−	0.633764i	−0.0589282	−	0.0340222i	−0.529175	+	0.848513i	$0.677498\pi$
$348$	−24.2404	+	18.7621i	−1.29942	+	1.00575i
$349$	5.55096	−	20.7165i	0.297136	−	1.10893i	−0.642370	−	0.766395i	$-0.722049\pi$
$349$	5.55096	−	20.7165i	0.297136	−	1.10893i	0.939506	−	0.342533i	$-0.111285\pi$
$350$	−0.747248			−0.0399421
$351$	−1.20825	+	18.6960i	−0.0644914	+	0.997918i
$352$	−6.84147			−0.364652
$353$	−1.64267	+	6.13052i	−0.0874304	+	0.326295i	−0.995763	−	0.0919532i	$-0.970689\pi$
$353$	−1.64267	+	6.13052i	−0.0874304	+	0.326295i	0.908333	+	0.418248i	$0.137356\pi$
$354$	3.05872	−	2.36745i	0.162569	−	0.125829i
$355$	−15.4127	−	8.89855i	−0.818024	−	0.472286i
$356$	16.4928	−	4.41923i	0.874115	−	0.234219i
$357$	3.46203	+	8.26008i	0.183230	+	0.437170i
$358$	−0.554380	+	2.06898i	−0.0292999	+	0.109349i
$359$	0.342346	−	0.342346i	0.0180683	−	0.0180683i	−0.698015	−	0.716083i	$-0.745933\pi$
$359$	0.342346	−	0.342346i	0.0180683	−	0.0180683i	0.716083	+	0.698015i	$0.245933\pi$
$360$	1.83917	+	1.80863i	0.0969330	+	0.0953231i
$361$			13.9682i			0.735170i
$362$	0.830187	+	0.222448i	0.0436337	+	0.0116916i
$363$	6.45338	−	0.877106i	0.338714	−	0.0460361i
$364$	11.4273	−	3.73118i	0.598951	−	0.195567i
$365$	20.6307	+	11.9111i	1.07986	+	0.623456i
$366$	−0.209349	+	0.275208i	−0.0109429	+	0.0143853i
$367$	−5.55996	−	9.63013i	−0.290227	−	0.502688i	0.683636	−	0.729823i	$-0.260398\pi$
$367$	−5.55996	−	9.63013i	−0.290227	−	0.502688i	−0.973863	+	0.227135i	$0.927064\pi$
$368$	−3.57669			−0.186448
$369$	−0.122312	−	14.6064i	−0.00636732	−	0.760381i
$370$	−0.0170942	+	0.0170942i	−0.000888687	+	0.000888687i
$371$	14.5519	+	3.89918i	0.755499	+	0.202435i
$372$	1.74847	+	4.17168i	0.0906538	+	0.216292i
$373$	8.42329	−	14.5896i	0.436141	−	0.755419i	−0.561247	−	0.827649i	$-0.689678\pi$
$373$	8.42329	−	14.5896i	0.436141	−	0.755419i	0.997388	+	0.0722297i	$0.0230115\pi$
$374$	−0.887590	+	1.53735i	−0.0458962	+	0.0794946i
$375$	2.49405	−	19.5773i	0.128792	−	1.01097i
$376$	3.70938	−	2.14161i	0.191296	−	0.110445i
$377$	32.2244	−	1.73544i	1.65964	−	0.0893799i
$378$	0.155855	−	1.31086i	0.00801629	−	0.0674234i
$379$	15.6371	−	15.6371i	0.803226	−	0.803226i	−0.180372	−	0.983598i	$-0.557730\pi$
$379$	15.6371	−	15.6371i	0.803226	−	0.803226i	0.983598	+	0.180372i	$0.0577303\pi$
$380$	−5.51135	+	3.18198i	−0.282726	+	0.163232i
$381$	0.358067	+	0.462619i	0.0183443	+	0.0237007i
$382$	−0.791808	−	2.95507i	−0.0405124	−	0.151194i
$383$	−13.0599	+	3.49940i	−0.667331	+	0.178811i	−0.576552	−	0.817060i	$-0.695602\pi$
$383$	−13.0599	+	3.49940i	−0.667331	+	0.178811i	−0.0907786	+	0.995871i	$0.528936\pi$
$384$	7.48479	−	3.13708i	0.381957	−	0.160088i
$385$	−2.40565	+	8.97799i	−0.122603	+	0.457561i
$386$			1.87569i			0.0954700i
$387$	−5.25211	−	18.9645i	−0.266980	−	0.964020i
$388$	8.86229	+	8.86229i	0.449915	+	0.449915i
$389$	−12.3282	−	21.3531i	−0.625065	−	1.08264i	−0.988528	−	0.151036i	$-0.951739\pi$
$389$	−12.3282	−	21.3531i	−0.625065	−	1.08264i	0.363463	−	0.931609i	$-0.381594\pi$
$390$	−0.253499	−	1.32605i	−0.0128364	−	0.0671472i
$391$	−1.41922	+	2.45817i	−0.0717732	+	0.124315i
$392$	2.40619	−	0.644736i	0.121531	−	0.0325641i
$393$	7.87594	−	1.07045i	0.397289	−	0.0539972i
$394$	1.97420	−	1.13981i	0.0994590	−	0.0574227i
$395$	8.40623	+	8.40623i	0.422963	+	0.422963i
$396$	−19.6403	+	11.5597i	−0.986964	+	0.580897i
$397$	−7.04299	−	7.04299i	−0.353478	−	0.353478i	0.507924	−	0.861402i	$-0.330413\pi$
$397$	−7.04299	−	7.04299i	−0.353478	−	0.353478i	−0.861402	+	0.507924i	$0.830413\pi$
$398$	2.57106	+	0.688912i	0.128875	+	0.0345321i
$399$	6.06290	+	2.48165i	0.303525	+	0.124238i
$400$	−9.84337	−	5.68307i	−0.492168	−	0.284154i
$401$	3.69639	+	13.7951i	0.184589	+	0.688896i	0.994718	+	0.102644i	$0.0327304\pi$
$401$	3.69639	+	13.7951i	0.184589	+	0.688896i	−0.810129	+	0.586252i	$0.800603\pi$
$402$	−2.34032	+	1.81141i	−0.116725	+	0.0903450i
$403$	0.983360	−	4.65940i	0.0489846	−	0.232101i
$404$		−	4.28447i		−	0.213160i
$405$	12.5275	+	3.13286i	0.622497	+	0.155673i
$406$	−2.27387			−0.112850
$407$	−0.214812	−	0.372064i	−0.0106478	−	0.0184425i
$408$	0.402258	−	3.15755i	0.0199147	−	0.156322i
$409$	8.98055	+	33.5159i	0.444060	+	1.65725i	0.718407	+	0.695623i	$0.244871\pi$
$409$	8.98055	+	33.5159i	0.444060	+	1.65725i	−0.274348	+	0.961631i	$0.588462\pi$
$410$	0.272431	+	1.01673i	0.0134544	+	0.0502126i
$411$	−22.7126	+	9.51948i	−1.12033	+	0.469561i
$412$	7.93037	+	13.7358i	0.390701	+	0.676714i
$413$	−24.9909			−1.22972
$414$	0.360553	−	0.212211i	0.0177202	−	0.0104296i
$415$			11.2002i			0.549794i
$416$	−6.28222	−	1.32585i	−0.308011	−	0.0650054i
$417$	1.73454	+	12.7620i	0.0849410	+	0.624960i
$418$	0.336069	+	1.25423i	0.0164377	+	0.0613462i
$419$	−3.81943	−	2.20515i	−0.186591	−	0.107729i	0.403794	−	0.914850i	$-0.367691\pi$
$419$	−3.81943	−	2.20515i	−0.186591	−	0.107729i	−0.590386	+	0.807121i	$0.701024\pi$
$420$	−1.11587	−	8.21011i	−0.0544489	−	0.400612i
$421$	15.4473	+	4.13909i	0.752854	+	0.201727i	0.614784	−	0.788696i	$-0.289243\pi$
$421$	15.4473	+	4.13909i	0.752854	+	0.201727i	0.138071	+	0.990422i	$0.455910\pi$
$422$	−2.24637	−	2.24637i	−0.109352	−	0.109352i
$423$	10.5654	−	18.6589i	0.513707	−	0.907227i
$424$	−3.78601	−	3.78601i	−0.183865	−	0.183865i
$425$	−7.81165	+	4.51006i	−0.378921	+	0.218770i
$426$	1.22621	−	2.99576i	0.0594102	−	0.145145i
$427$	2.15802	−	0.578241i	0.104434	−	0.0279830i
$428$	−13.8904	+	24.0590i	−0.671420	+	1.16293i
$429$	23.9289	+	1.74775i	1.15530	+	0.0843821i
$430$	0.709021	+	1.22806i	0.0341921	+	0.0592224i
$431$	−14.2709	−	14.2709i	−0.687404	−	0.687404i	0.274254	−	0.961657i	$-0.411569\pi$
$431$	−14.2709	−	14.2709i	−0.687404	−	0.687404i	−0.961657	+	0.274254i	$0.911569\pi$
$432$	12.0226	−	16.0824i	0.578437	−	0.773766i
$433$			4.58585i			0.220382i	0.993910	+	0.110191i	$0.0351462\pi$
$433$			4.58585i			0.220382i	−0.993910	+	0.110191i	$0.964854\pi$
$434$	−0.0868441	+	0.324106i	−0.00416865	+	0.0155576i
$435$	2.81096	−	22.0649i	0.134775	−	1.05793i
$436$	−23.5114	+	6.29986i	−1.12599	+	0.301709i
$437$	0.537362	+	2.00546i	0.0257055	+	0.0959342i
$438$	−1.64134	+	4.00996i	−0.0784264	+	0.191603i
$439$	11.0799	−	6.39700i	0.528816	−	0.305312i	−0.211718	−	0.977331i	$-0.567906\pi$
$439$	11.0799	−	6.39700i	0.528816	−	0.305312i	0.740534	+	0.672019i	$0.234573\pi$
$440$	2.33582	−	2.33582i	0.111356	−	0.111356i
$441$	8.74398	−	8.89166i	0.416380	−	0.423412i
$442$	−1.11297	+	1.23967i	−0.0529386	+	0.0589651i
$443$	−21.2323	+	12.2585i	−1.00878	+	0.582418i	−0.910833	−	0.412774i	$-0.864560\pi$
$443$	−21.2323	+	12.2585i	−1.00878	+	0.582418i	−0.0979439	+	0.995192i	$0.531227\pi$
$444$	0.304812	+	0.231869i	0.0144657	+	0.0110040i
$445$	−6.19502	+	10.7301i	−0.293672	+	0.508655i
$446$	1.52123	−	2.63485i	0.0720325	−	0.124764i
$447$	−20.1558	+	26.4966i	−0.953338	+	1.25324i
$448$	−12.1506	−	3.25573i	−0.574060	−	0.153819i
$449$	5.90689	−	5.90689i	0.278763	−	0.278763i	−0.553852	−	0.832615i	$-0.686843\pi$
$449$	5.90689	−	5.90689i	0.278763	−	0.278763i	0.832615	+	0.553852i	$0.186843\pi$
$450$	1.32946	−	0.0111327i	0.0626713	−	0.000524800i
$451$	−18.7061			−0.880836
$452$	−6.96597	−	12.0654i	−0.327652	−	0.567510i
$453$	3.15365	+	7.52432i	0.148171	+	0.353523i
$454$	−1.82735	−	1.05502i	−0.0857617	−	0.0495146i
$455$	−3.94891	+	7.77789i	−0.185128	+	0.364633i
$456$	−1.42509	−	1.84120i	−0.0667360	−	0.0862222i
$457$	−6.69728	−	1.79453i	−0.313285	−	0.0839446i	0.0987503	−	0.995112i	$-0.468515\pi$
$457$	−6.69728	−	1.79453i	−0.313285	−	0.0839446i	−0.412036	+	0.911168i	$0.635182\pi$
$458$			1.87771i			0.0877398i
$459$	−6.28249	−	14.6443i	−0.293242	−	0.683536i
$460$	1.85679	−	1.85679i	0.0865732	−	0.0865732i
$461$	−2.31973	+	8.65737i	−0.108041	+	0.403214i	−0.998672	−	0.0515119i	$-0.983596\pi$
$461$	−2.31973	+	8.65737i	−0.108041	+	0.403214i	0.890632	+	0.454726i	$0.150263\pi$
$462$	−1.67700	−	0.213642i	−0.0780210	−	0.00993952i
$463$	−10.1651	+	2.72374i	−0.472414	+	0.126583i	−0.487168	−	0.873308i	$-0.661970\pi$
$463$	−10.1651	+	2.72374i	−0.472414	+	0.126583i	0.0147539	+	0.999891i	$0.495304\pi$
$464$	−29.9533	−	17.2935i	−1.39055	−	0.802832i
$465$	−3.03767	−	1.24337i	−0.140869	−	0.0576599i
$466$	−0.840776	+	3.13782i	−0.0389482	+	0.145357i
$467$	29.6962			1.37418			0.687088	−	0.726574i	$-0.258889\pi$
$467$	29.6962			1.37418			0.687088	+	0.726574i	$0.258889\pi$
$468$	−20.2751	+	6.80854i	−0.937217	+	0.314725i
$469$	19.1213			0.882942
$470$	−0.399920	+	1.49252i	−0.0184469	+	0.0688449i
$471$	−0.680203	−	5.00465i	−0.0313421	−	0.230602i
$472$	7.69189	+	4.44092i	0.354048	+	0.204410i
$473$	−24.3420	+	6.52241i	−1.11925	+	0.299901i
$474$	−1.30911	+	1.72094i	−0.0601295	+	0.0790453i
$475$	−1.70765	+	6.37302i	−0.0783522	+	0.292414i
$476$	−7.22975	+	7.22975i	−0.331375	+	0.331375i
$477$	−25.9480	−	6.72039i	−1.18808	−	0.307706i
$478$			2.58801i			0.118373i
$479$	−34.1360	−	9.14672i	−1.55972	−	0.417925i	−0.627142	−	0.778905i	$-0.715775\pi$
$479$	−34.1360	−	9.14672i	−1.55972	−	0.417925i	−0.932573	+	0.360980i	$0.882442\pi$
$480$	−1.67642	+	4.09566i	−0.0765179	+	0.186941i
$481$	−0.125147	−	0.383280i	−0.00570622	−	0.0174761i
$482$	−1.46648	−	0.846670i	−0.0667961	−	0.0385648i
$483$	−2.68146	−	0.341605i	−0.122010	−	0.0155436i
$484$	3.71744	+	6.43879i	0.168974	+	0.292672i
$485$	−9.09460			−0.412965
$486$	−0.257758	+	2.33453i	−0.0116921	+	0.105896i
$487$	8.09264	−	8.09264i	0.366713	−	0.366713i	−0.499564	−	0.866277i	$-0.666507\pi$
$487$	8.09264	−	8.09264i	0.366713	−	0.366713i	0.866277	+	0.499564i	$0.166507\pi$
$488$	−0.766966	−	0.205508i	−0.0347189	−	0.00930290i
$489$	26.1245	+	3.32814i	1.18139	+	0.150504i
$490$	−0.449327	+	0.778257i	−0.0202985	+	0.0351581i
$491$	11.7790	−	20.4018i	0.531577	−	0.920719i	−0.467743	−	0.883864i	$-0.654933\pi$
$491$	11.7790	−	20.4018i	0.531577	−	0.920719i	0.999321	−	0.0368548i	$-0.0117339\pi$
$492$	15.3790	−	6.44577i	0.693340	−	0.290598i
$493$	−23.7708	+	13.7241i	−1.07058	+	0.618100i
$494$	0.0655324	+	1.21683i	0.00294844	+	0.0547478i
$495$	4.14623	−	16.0090i	0.186359	−	0.719549i
$496$	−3.60892	+	3.60892i	−0.162045	+	0.162045i
$497$	−18.1126	+	10.4573i	−0.812461	+	0.469075i
$498$	−2.01856	+	0.274352i	−0.0904540	+	0.0122940i
$499$	3.81052	+	14.2211i	0.170582	+	0.636622i	0.997262	+	0.0739490i	$0.0235602\pi$
$499$	3.81052	+	14.2211i	0.170582	+	0.636622i	−0.826680	+	0.562673i	$0.809773\pi$
$500$	21.7622	−	5.83117i	0.973236	−	0.260778i
$501$	−3.00784	−	2.28805i	−0.134380	−	0.102223i
$502$	−0.822542	+	3.06977i	−0.0367119	+	0.137011i
$503$			35.9407i			1.60252i	0.598318	+	0.801258i	$0.295836\pi$
$503$			35.9407i			1.60252i	−0.598318	+	0.801258i	$0.704164\pi$
$504$	2.92136	−	0.809055i	0.130128	−	0.0360382i
$505$	2.19839	+	2.19839i	0.0978271	+	0.0978271i
$506$	−0.267888	−	0.463995i	−0.0119091	−	0.0206271i
$507$	21.6341	+	6.24222i	0.960805	+	0.277227i
$508$	−0.333918	+	0.578362i	−0.0148152	+	0.0256607i
$509$	39.3639	−	10.5475i	1.74478	−	0.467511i	0.761277	−	0.648427i	$-0.224573\pi$
$509$	39.3639	−	10.5475i	1.74478	−	0.467511i	0.983499	+	0.180916i	$0.0579061\pi$
$510$	0.702845	+	0.908068i	0.0311225	+	0.0402099i
$511$	24.2445	−	13.9976i	1.07252	−	0.619217i
$512$	8.14081	+	8.14081i	0.359776	+	0.359776i
$513$	−10.8237	−	4.32487i	−0.477879	−	0.190948i
$514$	−0.275916	−	0.275916i	−0.0121701	−	0.0121701i
$515$	−11.1171	−	2.97881i	−0.489876	−	0.131262i
$516$	17.7650	−	13.7501i	0.782061	−	0.605315i
$517$	−23.7810	−	13.7300i	−1.04589	−	0.603843i
$518$	0.00735295	+	0.0274416i	0.000323070	+	0.00120571i
$519$	−5.60956	−	2.29609i	−0.246232	−	0.100787i
$520$	2.59756	−	1.69221i	0.113911	−	0.0742083i
$521$		−	30.5189i		−	1.33706i	−0.743687	−	0.668528i	$-0.766925\pi$
$521$		−	30.5189i		−	1.33706i	0.743687	−	0.668528i	$-0.233075\pi$
$522$	4.04553	−	0.0338767i	0.177068	−	0.00148274i
$523$	34.8570			1.52419			0.762095	−	0.647465i	$-0.224171\pi$
$523$	34.8570			1.52419			0.762095	+	0.647465i	$0.224171\pi$
$524$	4.53690	+	7.85813i	0.198195	+	0.343284i
$525$	−6.83681	−	5.20074i	−0.298383	−	0.226979i
$526$	−0.308460	−	1.15119i	−0.0134495	−	0.0501943i
$527$	1.04830	+	3.91233i	0.0456649	+	0.170424i
$528$	−20.4660	−	15.5684i	−0.890668	−	0.677528i
$529$	11.0717	+	19.1767i	0.481376	+	0.833768i
$530$	1.93154			0.0839007
$531$	44.4624	−	0.372322i	1.92950	−	0.0161574i
$532$			7.47873i			0.324244i
$533$	−17.1770	−	3.62518i	−0.744018	−	0.157024i
$534$	−2.08559	−	0.853669i	−0.0902525	−	0.0369419i
$535$	−5.21753	−	19.4721i	−0.225574	−	0.841852i
$536$	−5.88530	−	3.39788i	−0.254206	−	0.146766i
$537$	−19.4720	+	15.0713i	−0.840278	+	0.650376i
$538$	−0.964372	−	0.258403i	−0.0415770	−	0.0111405i
$539$	−11.2928	−	11.2928i	−0.486413	−	0.486413i
$540$	2.10761	+	14.5903i	0.0906970	+	0.627867i
$541$	18.9826	+	18.9826i	0.816125	+	0.816125i	0.985544	−	0.169419i	$-0.0541893\pi$
$541$	18.9826	+	18.9826i	0.816125	+	0.816125i	−0.169419	+	0.985544i	$0.554189\pi$
$542$	−1.17689	+	0.679477i	−0.0505517	+	0.0291860i
$543$	6.04745	+	7.81324i	0.259521	+	0.335298i
$544$	5.27495	−	1.41342i	0.226162	−	0.0605999i
$545$	8.83136	−	15.2964i	0.378294	−	0.655224i
$546$	−1.49851	−	0.521175i	−0.0641304	−	0.0223042i
$547$	2.84041	+	4.91974i	0.121447	+	0.210353i	0.920339	−	0.391122i	$-0.127913\pi$
$547$	2.84041	+	4.91974i	0.121447	+	0.210353i	−0.798891	+	0.601475i	$0.794580\pi$
$548$	−19.8795	−	19.8795i	−0.849212	−	0.849212i
$549$	−3.83081	+	1.06092i	−0.163495	+	0.0452791i
$550$		−	1.70260i		−	0.0725993i
$551$	−5.19635	+	19.3930i	−0.221372	+	0.826171i
$552$	0.764614	+	0.581639i	0.0325441	+	0.0247562i
$553$	13.4946	−	3.61588i	0.573850	−	0.153763i
$554$	1.12068	+	4.18244i	0.0476132	+	0.177695i
$555$	−0.275374	+	0.0374273i	−0.0116890	+	0.00158870i
$556$	−12.7332	+	7.35151i	−0.540008	+	0.311774i
$557$	28.9082	−	28.9082i	1.22488	−	1.22488i	0.259004	−	0.965876i	$-0.416606\pi$
$557$	28.9082	−	28.9082i	1.22488	−	1.22488i	0.965876	−	0.259004i	$-0.0833942\pi$
$558$	0.149679	−	0.577925i	0.00633642	−	0.0244655i
$559$	−23.6162	+	1.27185i	−0.998859	+	0.0537935i
$560$	8.09642	−	4.67447i	0.342136	−	0.197532i
$561$	−18.8206	+	7.88823i	−0.794607	+	0.333041i
$562$	1.60885	−	2.78661i	0.0678653	−	0.117546i
$563$	−0.639994	+	1.10850i	−0.0269725	+	0.0467178i	−0.879197	−	0.476459i	$-0.841920\pi$
$563$	−0.639994	+	1.10850i	−0.0269725	+	0.0467178i	0.852224	+	0.523177i	$0.175253\pi$
$564$	24.2824	+	3.09347i	1.02247	+	0.130258i
$565$	9.76514	+	2.61656i	0.410822	+	0.110080i
$566$	1.98401	−	1.98401i	0.0833942	−	0.0833942i
$567$	10.5494	−	10.9088i	0.443032	−	0.458126i
$568$	7.43310			0.311886
$569$	11.6913	+	20.2499i	0.490124	+	0.848920i	0.999935	−	0.0113665i	$-0.00361813\pi$
$569$	11.6913	+	20.2499i	0.490124	+	0.848920i	−0.509811	+	0.860286i	$0.670285\pi$
$570$	0.833196	+	0.106145i	0.0348987	+	0.00444594i
$571$	−8.36082	−	4.82712i	−0.349890	−	0.202009i	0.314747	−	0.949176i	$-0.398080\pi$
$571$	−8.36082	−	4.82712i	−0.349890	−	0.202009i	−0.664637	+	0.747167i	$0.731414\pi$
$572$	8.50150	+	26.0370i	0.355465	+	1.08866i
$573$	13.3223	−	32.5478i	0.556549	−	1.35970i
$574$	1.19483	+	0.320153i	0.0498711	+	0.0133629i
$575$		−	2.72240i		−	0.113532i
$576$	21.6661	+	5.61138i	0.902752	+	0.233808i
$577$	20.1564	−	20.1564i	0.839120	−	0.839120i	−0.149623	−	0.988743i	$-0.547806\pi$
$577$	20.1564	−	20.1564i	0.839120	−	0.839120i	0.988743	+	0.149623i	$0.0478059\pi$
$578$	−0.296192	+	1.10540i	−0.0123200	+	0.0459788i
$579$	−13.0545	+	17.1613i	−0.542528	+	0.713199i
$580$	24.5275	−	6.57212i	1.01845	−	0.272892i
$581$	11.3987	+	6.58104i	0.472898	+	0.273028i
$582$	−0.222775	−	1.63909i	−0.00923434	−	0.0679424i
$583$	−8.88429	+	33.1566i	−0.367950	+	1.37321i
$584$	−9.94954			−0.411715
$585$	6.90978	−	13.8968i	0.285684	−	0.574562i
$586$	0.179699			0.00742330
$587$	−0.314575	+	1.17401i	−0.0129839	+	0.0484566i	−0.972114	−	0.234509i	$-0.924652\pi$
$587$	−0.314575	+	1.17401i	−0.0129839	+	0.0484566i	0.959130	+	0.282966i	$0.0913183\pi$
$588$	13.1755	+	5.39295i	0.543348	+	0.222402i
$589$	2.56573	+	1.48133i	0.105719	+	0.0610370i
$590$	−3.09495	+	0.829288i	−0.127417	+	0.0341413i
$591$	25.9955	+	3.31171i	1.06931	+	0.136226i
$592$	−0.111843	+	0.417405i	−0.00459674	+	0.0171553i
$593$	4.26713	−	4.26713i	0.175230	−	0.175230i	−0.614043	−	0.789273i	$-0.710458\pi$
$593$	4.26713	−	4.26713i	0.175230	−	0.175230i	0.789273	+	0.614043i	$0.210458\pi$
$594$	2.98680	+	0.355115i	0.122550	+	0.0145705i
$595$		−	7.41927i		−	0.304160i
$596$	−36.7104	−	9.83652i	−1.50372	−	0.402919i
$597$	18.7287	+	24.1973i	0.766515	+	0.990328i
$598$	−0.156069	−	0.477982i	−0.00638212	−	0.0195461i
$599$	11.8386	+	6.83504i	0.483714	+	0.279272i	0.721963	−	0.691932i	$-0.243240\pi$
$599$	11.8386	+	6.83504i	0.483714	+	0.279272i	−0.238249	+	0.971204i	$0.576573\pi$
$600$	1.18011	+	2.81563i	0.0481777	+	0.114948i
$601$	−1.98486	−	3.43788i	−0.0809642	−	0.140234i	0.822700	−	0.568476i	$-0.192467\pi$
$601$	−1.98486	−	3.43788i	−0.0809642	−	0.140234i	−0.903664	+	0.428241i	$0.859133\pi$
$602$	1.66644			0.0679191
$603$	−34.0196	+	0.284875i	−1.38538	+	0.0116010i
$604$	−6.58576	+	6.58576i	−0.267971	+	0.267971i
$605$	−5.21123	−	1.39634i	−0.211866	−	0.0567694i
$606$	−0.342358	+	0.450058i	−0.0139073	+	0.0182824i
$607$	1.32037	−	2.28695i	0.0535923	−	0.0928246i	−0.837985	−	0.545694i	$-0.816266\pi$
$607$	1.32037	−	2.28695i	0.0535923	−	0.0928246i	0.891577	+	0.452869i	$0.149600\pi$
$608$	1.99726	−	3.45936i	0.0809996	−	0.140295i
$609$	−20.8044	−	15.8258i	−0.843035	−	0.641293i
$610$	0.248067	−	0.143222i	0.0100439	−	0.00579888i
$611$	−19.1762	−	17.2163i	−0.775787	−	0.696497i
$612$	12.7550	−	12.9705i	0.515592	−	0.524300i
$613$	−34.1691	+	34.1691i	−1.38008	+	1.38008i	−0.535615	+	0.844462i	$0.679920\pi$
$613$	−34.1691	+	34.1691i	−1.38008	+	1.38008i	−0.844462	+	0.535615i	$0.820080\pi$
$614$	−1.54398	+	0.891415i	−0.0623098	+	0.0359746i
$615$	−4.58371	+	11.1984i	−0.184833	+	0.451565i
$616$	−1.00474	−	3.74973i	−0.0404820	−	0.151081i
$617$	−6.28966	+	1.68531i	−0.253212	+	0.0678480i	−0.383192	−	0.923669i	$-0.625175\pi$
$617$	−6.28966	+	1.68531i	−0.253212	+	0.0678480i	0.129980	+	0.991517i	$0.458509\pi$
$618$	0.264543	−	2.07655i	0.0106415	−	0.0835312i
$619$	2.00513	−	7.48326i	0.0805931	−	0.300777i	−0.913850	−	0.406052i	$-0.866905\pi$
$619$	2.00513	−	7.48326i	0.0805931	−	0.300777i	0.994443	+	0.105274i	$0.0335720\pi$
$620$		−	3.74704i		−	0.150485i
$621$	4.77578	+	0.567815i	0.191645	+	0.0227856i
$622$	−0.553222	−	0.553222i	−0.0221822	−	0.0221822i
$623$	7.28020	+	12.6097i	0.291675	+	0.505196i
$624$	−15.7759	−	18.2620i	−0.631542	−	0.731066i
$625$	−0.821044	+	1.42209i	−0.0328418	+	0.0568836i
$626$	1.60110	−	0.429013i	0.0639928	−	0.0171468i
$627$	−5.65444	+	13.8143i	−0.225816	+	0.551691i
$628$	4.99333	−	2.88290i	0.199256	−	0.115040i
$629$	0.242492	+	0.242492i	0.00966880	+	0.00966880i
$630$	−0.538826	+	0.951589i	−0.0214674	+	0.0379122i
$631$	−4.51134	−	4.51134i	−0.179594	−	0.179594i	0.611585	−	0.791179i	$-0.290532\pi$
$631$	−4.51134	−	4.51134i	−0.179594	−	0.179594i	−0.791179	+	0.611585i	$0.790532\pi$
$632$	−4.79602	−	1.28509i	−0.190775	−	0.0511181i
$633$	−4.91835	−	36.1872i	−0.195487	−	1.43831i
$634$	−4.41776	−	2.55059i	−0.175452	−	0.101297i
$635$	−0.125426	−	0.468097i	−0.00497739	−	0.0185759i
$636$	−4.12102	−	30.3207i	−0.163409	−	1.20230i
$637$	−8.18114	−	12.5581i	−0.324149	−	0.497572i
$638$		−	5.18101i		−	0.205118i
$639$	32.0691	−	18.8749i	1.26863	−	0.746679i
$640$	−6.72289			−0.265746
$641$	17.1553	+	29.7138i	0.677593	+	1.17363i	0.975704	+	0.219094i	$0.0703102\pi$
$641$	17.1553	+	29.7138i	0.677593	+	1.17363i	−0.298111	+	0.954531i	$0.596356\pi$
$642$	3.38158	−	1.41731i	0.133460	−	0.0559369i
$643$	3.80807	+	14.2119i	0.150176	+	0.560463i	0.999470	+	0.0325438i	$0.0103608\pi$
$643$	3.80807	+	14.2119i	0.150176	+	0.560463i	−0.849295	+	0.527919i	$0.822972\pi$
$644$	−0.798683	−	2.98073i	−0.0314725	−	0.117457i
$645$	−2.06006	+	16.1706i	−0.0811149	+	0.636718i
$646$	−0.518236	−	0.897612i	−0.0203897	−	0.0353161i
$647$	−14.9387			−0.587300			−0.293650	−	0.955913i	$-0.594870\pi$
$647$	−14.9387			−0.587300			−0.293650	+	0.955913i	$0.594870\pi$
$648$	−5.18546	+	1.48295i	−0.203704	+	0.0582556i
$649$		−	56.9419i		−	2.23516i
$650$	0.329959	−	1.56343i	0.0129421	−	0.0613227i
$651$	−3.05030	+	2.36093i	−0.119551	+	0.0925323i
$652$	7.78130	+	29.0402i	0.304739	+	1.13730i
$653$	8.23077	+	4.75204i	0.322095	+	0.185962i	0.652326	−	0.757939i	$-0.273793\pi$
$653$	8.23077	+	4.75204i	0.322095	+	0.185962i	−0.330231	+	0.943900i	$0.607127\pi$
$654$	2.97313	+	1.21695i	0.116259	+	0.0475867i
$655$	−6.35997	−	1.70415i	−0.248505	−	0.0665866i
$656$	13.3044	+	13.3044i	0.519449	+	0.519449i
$657$	−42.9259	+	25.2649i	−1.67470	+	0.985677i
$658$	1.28399	+	1.28399i	0.0500553	+	0.0500553i
$659$	25.5763	−	14.7665i	0.996310	−	0.575220i	0.0891558	−	0.996018i	$-0.471583\pi$
$659$	25.5763	−	14.7665i	0.996310	−	0.575220i	0.907155	+	0.420798i	$0.138250\pi$
$660$	18.7067	−	2.54251i	0.728159	−	0.0989671i
$661$	−8.81977	+	2.36325i	−0.343049	+	0.0919198i	−0.426230	−	0.904615i	$-0.640159\pi$
$661$	−8.81977	+	2.36325i	−0.343049	+	0.0919198i	0.0831810	+	0.996534i	$0.473492\pi$
$662$	−0.664191	+	1.15041i	−0.0258145	+	0.0447121i
$663$	−18.8109	+	3.59604i	−0.730553	+	0.139659i
$664$	−2.33892	−	4.05112i	−0.0907675	−	0.157214i
$665$	−3.83739	−	3.83739i	−0.148808	−	0.148808i
$666$	−0.0134908	−	0.0487129i	−0.000522757	−	0.00188759i
$667$		−	8.28423i		−	0.320767i
$668$	1.11662	−	4.16729i	0.0432034	−	0.161237i
$669$	32.2565	−	13.5196i	1.24711	−	0.522697i
$670$	2.36804	−	0.634514i	0.0914853	−	0.0245134i
$671$	1.31752	+	4.91706i	0.0508624	+	0.189821i
$672$	3.18323	+	4.11269i	0.122796	+	0.158651i
$673$	22.4590	−	12.9667i	0.865731	−	0.499830i	−0.000196390	−	1.00000i	$-0.500063\pi$
$673$	22.4590	−	12.9667i	0.865731	−	0.499830i	0.865927	+	0.500170i	$0.166729\pi$
$674$	−1.07656	+	1.07656i	−0.0414674	+	0.0414674i
$675$	12.2411	+	9.15099i	0.471162	+	0.352222i
$676$	2.76066	+	25.5562i	0.106179	+	0.982931i
$677$	−13.6638	+	7.88881i	−0.525143	+	0.303192i	−0.739037	−	0.673665i	$-0.764719\pi$
$677$	−13.6638	+	7.88881i	−0.525143	+	0.303192i	0.213893	+	0.976857i	$0.431386\pi$
$678$	−0.232373	+	1.82403i	−0.00892423	+	0.0700514i
$679$	−5.34385	+	9.25583i	−0.205078	+	0.355206i
$680$	−1.31841	+	2.28355i	−0.0505588	+	0.0875703i
$681$	−9.37622	−	22.3708i	−0.359298	−	0.857252i
$682$	−0.738477	−	0.197874i	−0.0282777	−	0.00757700i
$683$	−21.0422	+	21.0422i	−0.805156	+	0.805156i	−0.983896	−	0.178741i	$-0.942798\pi$
$683$	−21.0422	+	21.0422i	−0.805156	+	0.805156i	0.178741	+	0.983896i	$0.442798\pi$
$684$	−0.111420	−	13.3057i	−0.00426026	−	0.508757i
$685$	20.4006			0.779468
$686$	1.41722	+	2.45469i	0.0541096	+	0.0937207i
$687$	−13.0686	+	17.1798i	−0.498599	+	0.655451i
$688$	21.9518	+	12.6739i	0.836903	+	0.483186i
$689$	−14.5837	+	28.7245i	−0.555595	+	1.09432i
$690$	−0.343414	+	0.0466749i	−0.0130736	+	0.00177688i
$691$	−21.8670	−	5.85923i	−0.831858	−	0.222896i	−0.182334	−	0.983237i	$-0.558365\pi$
$691$	−21.8670	−	5.85923i	−0.831858	−	0.222896i	−0.649524	+	0.760341i	$0.725032\pi$
$692$		−	6.91953i		−	0.263041i
$693$	−13.8565	−	13.6264i	−0.526364	−	0.517622i
$694$	−0.135042	+	0.135042i	−0.00512613	+	0.00512613i
$695$	2.76138	−	10.3056i	0.104745	−	0.390914i
$696$	3.59105	+	8.56793i	0.136118	+	0.324766i
$697$	14.4229	−	3.86460i	0.546306	−	0.146382i
$698$	−2.79853	−	1.61573i	−0.105926	−	0.0611564i
$699$	−29.5313	+	22.8573i	−1.11698	+	0.864541i
$700$	2.53808	−	9.47225i	0.0959305	−	0.358018i
$701$	23.1430			0.874097			0.437049	−	0.899438i	$-0.356024\pi$
$701$	23.1430			0.874097			0.437049	+	0.899438i	$0.356024\pi$
$702$	2.67383	+	0.904918i	0.100917	+	0.0341539i
$703$	0.250843			0.00946074
$704$	7.41819	−	27.6850i	0.279583	−	1.04342i
$705$	−14.0467	+	10.8722i	−0.529031	+	0.409470i
$706$	0.828155	+	0.478135i	0.0311680	+	0.0179949i
$707$	3.52910	−	0.945621i	0.132726	−	0.0355637i
$708$	19.6211	+	46.8142i	0.737406	+	1.75939i
$709$	−2.55487	+	9.53489i	−0.0959501	+	0.358090i	−0.997162	−	0.0752886i	$-0.976012\pi$
$709$	−2.55487	+	9.53489i	−0.0959501	+	0.358090i	0.901212	+	0.433379i	$0.142679\pi$
$710$	−1.89610	+	1.89610i	−0.0711595	+	0.0711595i
$711$	−23.9550	+	6.63420i	−0.898382	+	0.248802i
$712$		−	5.17480i		−	0.193934i
$713$	−1.18080	−	0.316393i	−0.0442212	−	0.0118490i
$714$	1.33715	−	0.181737i	0.0500415	−	0.00680135i
$715$	−17.7219	−	8.99759i	−0.662763	−	0.336491i
$716$	−24.3437	−	14.0549i	−0.909768	−	0.525255i
$717$	−18.0122	+	23.6786i	−0.672679	+	0.884293i
$718$	−0.0364735	−	0.0631740i	−0.00136118	−	0.00235763i
$719$	35.2812			1.31577			0.657883	−	0.753120i	$-0.271452\pi$
$719$	35.2812			1.31577			0.657883	+	0.753120i	$0.271452\pi$
$720$	−14.3350	+	8.43716i	−0.534235	+	0.314434i
$721$	−9.56383	+	9.56383i	−0.356176	+	0.356176i
$722$	2.03288	+	0.544710i	0.0756561	+	0.0202720i
$723$	−7.52456	−	17.9529i	−0.279841	−	0.667676i
$724$	−5.63959	+	9.76805i	−0.209594	+	0.363027i
$725$	13.1630	−	22.7989i	0.488860	−	0.846730i
$726$	0.124007	−	0.973404i	0.00460234	−	0.0361264i
$727$	−11.3793	+	6.56985i	−0.422035	+	0.243662i	−0.695948	−	0.718092i	$-0.745015\pi$
$727$	−11.3793	+	6.56985i	−0.422035	+	0.243662i	0.273912	+	0.961755i	$0.411682\pi$
$728$	−0.195920	−	3.63793i	−0.00726129	−	0.134831i
$729$	−18.6063	+	19.5654i	−0.689122	+	0.724645i
$730$	2.53802	−	2.53802i	0.0939363	−	0.0939363i
$731$	17.4208	−	10.0579i	0.644332	−	0.372005i
$732$	−2.77751	−	3.58852i	−0.102660	−	0.132635i
$733$	−12.3633	−	46.1404i	−0.456649	−	1.70424i	−0.683195	−	0.730236i	$-0.739410\pi$
$733$	−12.3633	−	46.1404i	−0.456649	−	1.70424i	0.226547	−	0.974000i	$-0.427256\pi$
$734$	−1.61835	+	0.433636i	−0.0597344	+	0.0160058i
$735$	−9.52760	+	3.99328i	−0.351431	+	0.147294i
$736$	−0.426590	+	1.59206i	−0.0157243	+	0.0586840i
$737$			43.5680i			1.60485i
$738$	−2.13054	−	0.551796i	−0.0784261	−	0.0203119i
$739$	−4.77424	−	4.77424i	−0.175623	−	0.175623i	0.613822	−	0.789445i	$-0.289631\pi$
$739$	−4.77424	−	4.77424i	−0.175623	−	0.175623i	−0.789445	+	0.613822i	$0.789631\pi$
$740$	−0.158628	−	0.274752i	−0.00583128	−	0.0101001i
$741$	−7.86940	+	11.5893i	−0.289089	+	0.425743i
$742$	1.13494	−	1.96578i	0.0416651	−	0.0721661i
$743$	−13.0735	+	3.50304i	−0.479621	+	0.128514i	−0.490526	−	0.871426i	$-0.663195\pi$
$743$	−13.0735	+	3.50304i	−0.479621	+	0.128514i	0.0109050	+	0.999941i	$0.496529\pi$
$744$	1.35838	−	0.184624i	0.0498007	−	0.00676863i
$745$	23.8835	−	13.7892i	0.875025	−	0.505196i
$746$	−1.79483	−	1.79483i	−0.0657135	−	0.0657135i
$747$	−20.3779	−	11.5388i	−0.745590	−	0.422182i
$748$	−16.4730	−	16.4730i	−0.602312	−	0.602312i
$749$	−22.8830	−	6.13149i	−0.836128	−	0.224040i
$750$	−2.75194	−	1.12642i	−0.100487	−	0.0411309i
$751$	23.5636	+	13.6045i	0.859849	+	0.496434i	0.863962	−	0.503558i	$-0.167976\pi$
$751$	23.5636	+	13.6045i	0.859849	+	0.496434i	−0.00411274	+	0.999992i	$0.501309\pi$
$752$	7.14862	+	26.6790i	0.260683	+	0.972884i
$753$	−28.8909	+	22.3616i	−1.05284	+	0.814900i
$754$	1.00406	−	4.75749i	0.0365658	−	0.173258i
$755$		−	6.75840i		−	0.245963i
$756$	16.0874	+	6.42808i	0.585092	+	0.233787i
$757$	−48.6346			−1.76765			−0.883827	−	0.467813i	$-0.845042\pi$
$757$	−48.6346			−1.76765			−0.883827	+	0.467813i	$0.845042\pi$
$758$	−1.66598	−	2.88556i	−0.0605111	−	0.104808i
$759$	0.778348	−	6.10970i	0.0282522	−	0.221768i
$760$	0.499191	+	1.86301i	0.0181076	+	0.0675783i
$761$	2.92145	+	10.9030i	0.105902	+	0.395233i	0.998446	−	0.0557279i	$-0.0177479\pi$
$761$	2.92145	+	10.9030i	0.105902	+	0.395233i	−0.892544	+	0.450961i	$0.851081\pi$
$762$	0.0812910	−	0.0340713i	0.00294486	−	0.00123427i
$763$	−10.3783	−	17.9758i	−0.375721	−	0.650769i
$764$	40.1484			1.45252
$765$	0.110534	+	13.1999i	0.00399637	+	0.477244i
$766$			2.03715i			0.0736054i
$767$	11.0352	−	52.2873i	0.398456	−	1.88798i
$768$	3.31579	+	24.3962i	0.119648	+	0.880321i
$769$	−7.07219	−	26.3938i	−0.255030	−	0.951783i	−0.968074	−	0.250664i	$-0.919351\pi$
$769$	−7.07219	−	26.3938i	−0.255030	−	0.951783i	0.713045	−	0.701119i	$-0.247316\pi$
$770$	1.21281	+	0.700217i	0.0437067	+	0.0252341i
$771$	−0.604110	−	4.44479i	−0.0217565	−	0.160075i
$772$	−23.7766	−	6.37091i	−0.855738	−	0.229294i
$773$	−4.24694	−	4.24694i	−0.152752	−	0.152752i	0.626594	−	0.779346i	$-0.284448\pi$
$773$	−4.24694	−	4.24694i	−0.152752	−	0.152752i	−0.779346	+	0.626594i	$0.784448\pi$
$774$	−2.96483	+	0.0248271i	−0.106569	+	0.000892391i
$775$	−2.74693	−	2.74693i	−0.0986726	−	0.0986726i
$776$	3.28954	−	1.89922i	0.118088	−	0.0681779i
$777$	−0.123715	+	0.302248i	−0.00443825	+	0.0108431i
$778$	−3.58840	+	0.961510i	−0.128650	+	0.0344718i
$779$	5.46095	−	9.45865i	0.195659	−	0.338891i
$780$	17.6703	+	1.29063i	0.632699	+	0.0462119i
$781$	−23.8270	−	41.2696i	−0.852597	−	1.47674i
$782$	0.302408	+	0.302408i	0.0108141	+	0.0108141i
$783$	37.2496	+	27.8464i	1.33119	+	0.995148i
$784$			16.0636i			0.573698i
$785$	−1.08288	+	4.04135i	−0.0386495	+	0.144242i
$786$	0.151343	−	1.18798i	0.00539823	−	0.0423738i
$787$	−35.4566	+	9.50056i	−1.26389	+	0.338658i	−0.827687	−	0.561190i	$-0.810344\pi$
$787$	−35.4566	+	9.50056i	−1.26389	+	0.338658i	−0.436203	+	0.899848i	$0.643677\pi$
$788$	7.74288	+	28.8968i	0.275829	+	1.02941i
$789$	5.18992	−	12.6795i	0.184766	−	0.451401i
$790$	1.55122	−	0.895599i	0.0551901	−	0.0318640i
$791$	8.40079	−	8.40079i	0.298698	−	0.298698i
$792$	1.84343	+	6.65633i	0.0655035	+	0.236522i
$793$	0.256912	+	4.77045i	0.00912323	+	0.169404i
$794$	−1.29966	+	0.750360i	−0.0461232	+	0.0266293i
$795$	17.6723	+	13.4432i	0.626772	+	0.476783i
$796$	−17.4656	+	30.2512i	−0.619051	+	1.07223i
$797$	14.1473	−	24.5039i	0.501123	−	0.867971i	−0.498876	−	0.866673i	$-0.666254\pi$
$797$	14.1473	−	24.5039i	0.501123	−	0.867971i	0.999999	−	0.00129761i	$-0.000413043\pi$
$798$	0.597601	−	0.785597i	0.0211548	−	0.0278098i
$799$	21.1723	+	5.67311i	0.749023	+	0.200700i
$800$	−3.70366	+	3.70366i	−0.130944	+	0.130944i
$801$	−13.1404	−	22.3259i	−0.464292	−	0.788848i
$802$	2.15184			0.0759840
$803$	31.8935	+	55.2412i	1.12550	+	1.94942i
$804$	−15.0127	−	35.8190i	−0.529458	−	1.26324i
$805$	1.93924	+	1.11962i	0.0683492	+	0.0394614i
$806$	−0.639763	−	0.324814i	−0.0225347	−	0.0114411i
$807$	−7.02491	−	9.07610i	−0.247288	−	0.319494i
$808$	−1.25425	−	0.336075i	−0.0441244	−	0.0118231i
$809$		−	6.47634i		−	0.227696i	−0.993498	−	0.113848i	$-0.963682\pi$
$809$		−	6.47634i		−	0.227696i	0.993498	−	0.113848i	$-0.0363177\pi$
$810$	0.944471	−	1.70104i	0.0331853	−	0.0597684i
$811$	24.5927	−	24.5927i	0.863568	−	0.863568i	−0.128183	−	0.991751i	$-0.540914\pi$
$811$	24.5927	−	24.5927i	0.863568	−	0.863568i	0.991751	+	0.128183i	$0.0409144\pi$
$812$	7.72336	−	28.8240i	0.271037	−	1.01152i
$813$	−15.4968	−	1.97422i	−0.543497	−	0.0692390i
$814$	−0.0625257	+	0.0167537i	−0.00219152	+	0.000587217i
$815$	−18.8934	−	10.9081i	−0.661805	−	0.382094i
$816$	18.9962	+	7.77546i	0.665000	+	0.272196i
$817$	3.80823	−	14.2125i	0.133233	−	0.497233i
$818$	5.22798			0.182792
$819$	−10.0831	−	15.1978i	−0.352331	−	0.531055i
$820$	−13.8136			−0.482390
$821$	−0.0962679	+	0.359277i	−0.00335977	+	0.0125388i	−0.967585	−	0.252544i	$-0.918733\pi$
$821$	−0.0962679	+	0.359277i	−0.00335977	+	0.0125388i	0.964226	+	0.265083i	$0.0853994\pi$
$822$	0.499721	+	3.67673i	0.0174298	+	0.128241i
$823$	10.4756	+	6.04809i	0.365157	+	0.210823i	0.671340	−	0.741149i	$-0.265719\pi$
$823$	10.4756	+	6.04809i	0.365157	+	0.210823i	−0.306184	+	0.951972i	$0.599052\pi$
$824$	4.64312	−	1.24412i	0.161751	−	0.0433410i
$825$	11.8499	−	15.5777i	0.412560	−	0.542345i
$826$	−0.974555	+	3.63709i	−0.0339091	+	0.126550i
$827$	−14.0652	+	14.0652i	−0.489094	+	0.489094i	−0.908020	−	0.418926i	$-0.862407\pi$
$827$	−14.0652	+	14.0652i	−0.489094	+	0.489094i	0.418926	+	0.908020i	$0.362407\pi$
$828$	1.46538	+	5.29123i	0.0509254	+	0.183883i
$829$			19.5757i			0.679892i	0.940445	+	0.339946i	$0.110409\pi$
$829$			19.5757i			0.679892i	−0.940445	+	0.339946i	$0.889591\pi$
$830$	1.63003	+	0.436765i	0.0565791	+	0.0151603i
$831$	−18.8557	+	46.0663i	−0.654098	+	1.59802i
$832$	12.1771	−	23.9844i	0.422164	−	0.831508i
$833$	11.0401	+	6.37398i	0.382515	+	0.220845i
$834$	1.92498	+	0.245234i	0.0666566	+	0.00849175i
$835$	1.56532	+	2.71121i	0.0541701	+	0.0938254i
$836$	−17.0403			−0.589351
$837$	5.39174	−	4.24588i	0.186366	−	0.146759i
$838$	−0.469873	+	0.469873i	−0.0162315	+	0.0162315i
$839$	36.8125	+	9.86389i	1.27091	+	0.340539i	0.830379	−	0.557198i	$-0.188124\pi$
$839$	36.8125	+	9.86389i	1.27091	+	0.340539i	0.440531	+	0.897738i	$0.354790\pi$
$840$	−2.49098	−	0.317340i	−0.0859471	−	0.0109493i
$841$	25.5547	−	44.2621i	0.881198	−	1.52628i
$842$	1.20477	−	2.08673i	0.0415193	−	0.0719135i
$843$	34.1144	−	14.2983i	1.17496	−	0.492458i
$844$	36.1053	−	20.8454i	1.24280	−	0.717529i
$845$	−14.5296	−	11.6965i	−0.499833	−	0.402373i
$846$	−2.30353	−	2.26528i	−0.0791971	−	0.0778818i
$847$	−4.48314	+	4.48314i	−0.154042	+	0.154042i
$848$	29.9009	−	17.2633i	1.02680	−	0.592823i
$849$	31.9608	−	4.34393i	1.09689	−	0.149083i
$850$	0.351751	+	1.31275i	0.0120650	+	0.0450271i
$851$	−0.0999762	+	0.0267885i	−0.00342714	+	0.000918300i
$852$	33.8099	+	25.7190i	1.15831	+	0.881119i
$853$	−5.73563	+	21.4056i	−0.196384	+	0.732915i	0.795520	+	0.605927i	$0.207198\pi$
$853$	−5.73563	+	21.4056i	−0.196384	+	0.732915i	−0.991904	+	0.126988i	$0.959469\pi$
$854$		−	0.336620i		−	0.0115189i
$855$	6.88443	+	6.77008i	0.235442	+	0.231532i
$856$	5.95353	+	5.95353i	0.203487	+	0.203487i
$857$	7.38003	+	12.7826i	0.252097	+	0.436645i	0.964103	−	0.265529i	$-0.0855465\pi$
$857$	7.38003	+	12.7826i	0.252097	+	0.436645i	−0.712006	+	0.702173i	$0.752213\pi$
$858$	1.18750	−	3.41436i	0.0405405	−	0.116564i
$859$	9.61650	−	16.6563i	0.328111	−	0.568304i	−0.654026	−	0.756472i	$-0.726921\pi$
$859$	9.61650	−	16.6563i	0.328111	−	0.568304i	0.982137	+	0.188167i	$0.0602548\pi$
$860$	−17.9754	+	4.81649i	−0.612955	+	0.164241i
$861$	8.70364	+	11.2450i	0.296619	+	0.383229i
$862$	−2.63344	+	1.52042i	−0.0896954	+	0.0517856i
$863$	17.6630	+	17.6630i	0.601257	+	0.601257i	0.940646	−	0.339389i	$-0.110220\pi$
$863$	17.6630	+	17.6630i	0.601257	+	0.601257i	−0.339389	+	0.940646i	$0.610220\pi$
$864$	−5.72468	−	7.26963i	−0.194758	−	0.247318i
$865$	3.55046	+	3.55046i	0.120719	+	0.120719i
$866$	0.667407	+	0.178831i	0.0226794	+	0.00607693i
$867$	−10.4034	+	8.05225i	−0.353319	+	0.273469i
$868$	−3.81346	−	2.20170i	−0.129437	−	0.0747307i
$869$	8.23877	+	30.7475i	0.279481	+	1.04304i
$870$	−3.10162	−	1.26955i	−0.105155	−	0.0430416i
$871$	−8.44334	+	40.0066i	−0.286092	+	1.35557i
$872$			7.37697i			0.249816i
$873$	9.36957	−	16.5470i	0.317112	−	0.560032i
$874$	0.312822			0.0105814
$875$	9.60623	+	16.6385i	0.324750	+	0.562483i
$876$	−45.2560	−	34.4261i	−1.52906	−	1.16315i
$877$	0.829495	+	3.09572i	0.0280101	+	0.104535i	0.978516	−	0.206172i	$-0.0661008\pi$
$877$	0.829495	+	3.09572i	0.0280101	+	0.104535i	−0.950506	+	0.310707i	$0.899434\pi$
$878$	−0.498918	−	1.86199i	−0.0168377	−	0.0628391i
$879$	1.64413	+	1.25068i	0.0554550	+	0.0421844i
$880$	10.6508	+	18.4477i	0.359038	+	0.621871i
$881$	−51.9363			−1.74978			−0.874890	−	0.484322i	$-0.839066\pi$
$881$	−51.9363			−1.74978			−0.874890	+	0.484322i	$0.839066\pi$
$882$	−0.953075	−	1.61931i	−0.0320917	−	0.0545249i
$883$		−	20.8694i		−	0.702311i	−0.936317	−	0.351155i	$-0.885789\pi$
$883$		−	20.8694i		−	0.702311i	0.936317	−	0.351155i	$-0.114211\pi$
$884$	−11.9340	−	18.3188i	−0.401384	−	0.616129i
$885$	−34.0884	−	13.9530i	−1.14587	−	0.469024i
$886$	0.956071	+	3.56811i	0.0321198	+	0.119873i
$887$	−3.48618	−	2.01275i	−0.117055	−	0.0675815i	0.440330	−	0.897836i	$-0.354862\pi$
$887$	−3.48618	−	2.01275i	−0.117055	−	0.0675815i	−0.557384	+	0.830255i	$0.688195\pi$
$888$	0.0917876	−	0.0710437i	0.00308019	−	0.00238407i
$889$	−0.550094	−	0.147397i	−0.0184495	−	0.00494354i
$890$	1.32003	+	1.32003i	0.0442476	+	0.0442476i
$891$	24.8557	+	24.0368i	0.832696	+	0.805262i
$892$	28.2329	+	28.2329i	0.945309	+	0.945309i
$893$	13.8850	−	8.01650i	0.464643	−	0.268262i
$894$	3.07020	+	3.96667i	0.102683	+	0.132665i
$895$	19.7026	−	5.27929i	0.658585	−	0.176467i
$896$	−3.95027	+	6.84207i	−0.131969	+	0.228578i
$897$	1.89876	−	5.45943i	0.0633979	−	0.182285i
$898$	−0.629319	−	1.09001i	−0.0210007	−	0.0363742i
$899$	−8.35887	−	8.35887i	−0.278784	−	0.278784i
$900$	−4.37449	+	16.8903i	−0.145816	+	0.563010i
$901$		−	27.4001i		−	0.912829i
$902$	−0.729469	+	2.72241i	−0.0242886	+	0.0906465i
$903$	15.2468	+	11.5982i	0.507383	+	0.385964i
$904$	−4.07848	+	1.09283i	−0.135648	+	0.0363469i
$905$	−2.11834	−	7.90576i	−0.0704161	−	0.262796i
$906$	1.21804	−	0.165549i	0.0404667	−	0.00550000i
$907$	26.8997	−	15.5306i	0.893190	−	0.515684i	0.0182055	−	0.999834i	$-0.494205\pi$
$907$	26.8997	−	15.5306i	0.893190	−	0.515684i	0.874985	+	0.484151i	$0.160871\pi$
$908$	19.5804	−	19.5804i	0.649797	−	0.649797i
$909$	−6.26468	+	1.73497i	−0.207786	+	0.0575453i
$910$	0.977972	+	0.878018i	0.0324195	+	0.0291060i
$911$	7.88507	−	4.55245i	0.261244	−	0.150829i	−0.363658	−	0.931533i	$-0.618472\pi$
$911$	7.88507	−	4.55245i	0.261244	−	0.150829i	0.624902	+	0.780703i	$0.285139\pi$
$912$	13.8468	−	5.80358i	0.458514	−	0.192176i
$913$	−14.9949	+	25.9720i	−0.496259	+	0.859546i
$914$	−0.522338	+	0.904717i	−0.0172774	+	0.0299254i
$915$	3.26645	+	0.416131i	0.107986	+	0.0137569i
$916$	−23.8023	−	6.37780i	−0.786449	−	0.210728i
$917$	−5.47138	+	5.47138i	−0.180681	+	0.180681i
$918$	−2.37627	+	0.343258i	−0.0784285	+	0.0113292i
$919$	16.2306			0.535398			0.267699	−	0.963503i	$-0.413737\pi$
$919$	16.2306			0.535398			0.267699	+	0.963503i	$0.413737\pi$
$920$	−0.397915	−	0.689210i	−0.0131189	−	0.0227226i
$921$	−20.3305	−	2.59001i	−0.669911	−	0.0853436i
$922$	1.16950	+	0.675211i	0.0385154	+	0.0222369i
$923$	−13.8814	−	42.5137i	−0.456911	−	1.39935i
$924$	8.40421	−	20.5323i	0.276478	−	0.675463i
$925$	−0.317708	−	0.0851296i	−0.0104462	−	0.00279904i
$926$			1.58561i			0.0521065i
$927$	16.8729	−	17.1579i	0.554179	−	0.563539i
$928$	−11.2702	+	11.2702i	−0.369962	+	0.369962i
$929$	−11.5799	+	43.2167i	−0.379923	+	1.41789i	0.466093	+	0.884736i	$0.345661\pi$
$929$	−11.5799	+	43.2167i	−0.379923	+	1.41789i	−0.846016	+	0.533157i	$0.821005\pi$
$930$	−0.299413	+	0.393604i	−0.00981814	+	0.0129068i
$931$	9.00687	−	2.41338i	0.295188	−	0.0790955i
$932$	−36.9198	−	21.3157i	−1.20935	−	0.698218i
$933$	−1.21126	−	8.91196i	−0.0396550	−	0.291765i
$934$	1.15804	−	4.32187i	0.0378923	−	0.141416i
$935$	16.9048			0.552846
$936$	0.402769	+	6.46947i	0.0131649	+	0.211461i
$937$	7.90837			0.258355			0.129178	−	0.991621i	$-0.458766\pi$
$937$	7.90837			0.258355			0.129178	+	0.991621i	$0.458766\pi$
$938$	0.745662	−	2.78285i	0.0243467	−	0.0908632i
$939$	17.6349	+	7.21824i	0.575492	+	0.235558i
$940$	−17.5611	−	10.1389i	−0.572781	−	0.330695i
$941$	3.94282	−	1.05648i	0.128532	−	0.0344401i	−0.193979	−	0.981006i	$-0.562140\pi$
$941$	3.94282	−	1.05648i	0.128532	−	0.0344401i	0.322512	+	0.946565i	$0.395473\pi$
$942$	−0.754883	−	0.0961687i	−0.0245954	−	0.00313334i
$943$	−1.16639	+	4.35304i	−0.0379830	+	0.141754i
$944$	−40.4989	+	40.4989i	−1.31813	+	1.31813i
$945$	−11.5528	+	4.95624i	−0.375813	+	0.161226i
$946$			3.79699i			0.123451i
$947$	5.10020	+	1.36659i	0.165734	+	0.0444083i	0.340732	−	0.940160i	$-0.389325\pi$
$947$	5.10020	+	1.36659i	0.165734	+	0.0444083i	−0.174998	+	0.984569i	$0.555992\pi$
$948$	−17.3684	−	22.4398i	−0.564101	−	0.728812i
$949$	18.5809	+	56.9064i	0.603160	+	1.84726i
$950$	0.860914	+	0.497049i	0.0279317	+	0.0161264i
$951$	−22.6677	−	54.0832i	−0.735052	−	1.75377i
$952$	1.54936	+	2.68357i	0.0502150	+	0.0869749i
$953$	21.8837			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$953$	21.8837			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$954$	−1.98994	+	3.51431i	−0.0644266	+	0.113780i
$955$	−20.6004	+	20.6004i	−0.666614	+	0.666614i
$956$	−32.8062	−	8.79039i	−1.06103	−	0.284301i
$957$	36.0591	−	47.4027i	1.16562	−	1.53231i
$958$	−2.66236	+	4.61134i	−0.0860169	+	0.148986i
$959$	11.9871	−	20.7623i	0.387084	−	0.670449i
$960$	−14.7560	−	11.2248i	−0.476247	−	0.362279i
$961$	25.3361	−	14.6278i	0.817294	−	0.471865i
$962$	−0.0606614	+	0.00326692i	−0.00195580	+	0.000105330i
$963$	40.8035	+	10.5679i	1.31487	+	0.340545i
$964$	15.7135	−	15.7135i	0.506099	−	0.506099i
$965$	15.4689	−	8.93096i	0.497961	−	0.287498i
$966$	−0.154283	+	0.376928i	−0.00496397	+	0.0121274i
$967$	0.497719	+	1.85751i	0.0160056	+	0.0597335i	0.973467	−	0.228829i	$-0.0734895\pi$
$967$	0.497719	+	1.85751i	0.0160056	+	0.0597335i	−0.957461	+	0.288562i	$0.906823\pi$
$968$	2.17651	−	0.583194i	0.0699556	−	0.0187446i
$969$	1.50574	−	11.8194i	0.0483712	−	0.379694i
$970$	−0.354656	+	1.32359i	−0.0113873	+	0.0424980i
$971$			46.5055i			1.49243i	0.665703	+	0.746217i	$0.268132\pi$
$971$			46.5055i			1.49243i	−0.665703	+	0.746217i	$0.731868\pi$
$972$	−28.7174	−	11.1968i	−0.921112	−	0.359137i
$973$	−8.86574	−	8.86574i	−0.284223	−	0.284223i
$974$	−0.862189	−	1.49336i	−0.0276263	−	0.0478502i
$975$	13.9001	−	12.0078i	0.445161	−	0.384559i
$976$	2.56011	−	4.43424i	0.0819470	−	0.141936i
$977$	−19.7238	+	5.28498i	−0.631020	+	0.169081i	−0.560133	−	0.828403i	$-0.689250\pi$
$977$	−19.7238	+	5.28498i	−0.631020	+	0.169081i	−0.0708877	+	0.997484i	$0.522583\pi$
$978$	1.50313	−	3.67228i	0.0480647	−	0.117427i
$979$	−28.7312	+	16.5879i	−0.918252	+	0.530153i
$980$	−8.33916	−	8.33916i	−0.266385	−	0.266385i
$981$	18.7324	+	31.8269i	0.598078	+	1.01615i
$982$	−2.50986	−	2.50986i	−0.0800929	−	0.0800929i
$983$	−48.0367	−	12.8714i	−1.53213	−	0.410534i	−0.608418	−	0.793616i	$-0.708196\pi$
$983$	−48.0367	−	12.8714i	−1.53213	−	0.410534i	−0.923714	+	0.383083i	$0.874862\pi$
$984$	−0.680620	−	5.00772i	−0.0216974	−	0.159640i
$985$	−18.8001	−	10.8542i	−0.599020	−	0.345845i
$986$	1.07037	+	3.99469i	0.0340877	+	0.127217i
$987$	2.81126	+	20.6841i	0.0894835	+	0.658382i
$988$	−15.6474	−	3.30236i	−0.497809	−	0.105062i
$989$			6.07124i			0.193054i
$990$	−2.16820	−	1.22772i	−0.0689098	−	0.0390194i
$991$	5.40918			0.171828			0.0859141	−	0.996303i	$-0.472619\pi$
$991$	5.40918			0.171828			0.0859141	+	0.996303i	$0.472619\pi$
$992$	1.17597	+	2.03684i	0.0373370	+	0.0646696i
$993$	−14.0836	+	5.90283i	−0.446930	+	0.187321i
$994$	0.815594	+	3.04384i	0.0258691	+	0.0965446i
$995$	−6.56042	−	24.4838i	−0.207979	−	0.776189i
$996$	3.37847	−	26.5195i	0.107051	−	0.840304i
$997$	3.95821	+	6.85582i	0.125358	+	0.217126i	0.921873	−	0.387493i	$-0.126659\pi$
$997$	3.95821	+	6.85582i	0.125358	+	0.217126i	−0.796515	+	0.604619i	$0.793325\pi$
$998$	2.21827			0.0702183
$999$	0.215604	−	0.539584i	0.00682140	−	0.0170717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.5.7	✓	44
3.2	odd	2		351.2.bc.b.44.5		44
9.2	odd	6	inner	117.2.z.b.83.7	yes	44
9.7	even	3		351.2.bc.b.278.5		44
13.8	odd	4	inner	117.2.z.b.86.7	yes	44
39.8	even	4		351.2.bc.b.125.5		44
117.34	odd	12		351.2.bc.b.8.5		44
117.47	even	12	inner	117.2.z.b.47.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.7	✓	44	1.1	even	1	trivial
117.2.z.b.47.7	yes	44	117.47	even	12	inner
117.2.z.b.83.7	yes	44	9.2	odd	6	inner
117.2.z.b.86.7	yes	44	13.8	odd	4	inner
351.2.bc.b.8.5		44	117.34	odd	12
351.2.bc.b.44.5		44	3.2	odd	2
351.2.bc.b.125.5		44	39.8	even	4
351.2.bc.b.278.5		44	9.7	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0389963 - 0.145536i) q^{2} +(1.36970 - 1.06015i) q^{3} +(1.71239 + 0.988649i) q^{4} +(-1.38592 + 0.371357i) q^{5} +(-0.100877 - 0.240683i) q^{6} +(-0.436407 + 1.62869i) q^{7} +(0.423741 - 0.423741i) q^{8} +(0.752165 - 2.90418i) q^{9} +0.216183i q^{10} +(-3.71098 - 0.994354i) q^{11} +(3.39358 - 0.461236i) q^{12} +(-3.21493 - 1.63225i) q^{13} +(0.220016 + 0.127026i) q^{14} +(-1.50461 + 1.97793i) q^{15} +(1.93215 + 3.34659i) q^{16} +3.06669 q^{17} +(-0.393331 - 0.222719i) q^{18} +(1.58615 - 1.58615i) q^{19} +(-2.74038 - 0.734283i) q^{20} +(1.12891 + 2.69348i) q^{21} +(-0.289429 + 0.501306i) q^{22} +(-0.462786 + 0.801569i) q^{23} +(0.131170 - 1.02963i) q^{24} +(-2.54725 + 1.47066i) q^{25} +(-0.362922 + 0.404237i) q^{26} +(-2.04862 - 4.77526i) q^{27} +(-2.35751 + 2.35751i) q^{28} +(-7.75127 + 4.47520i) q^{29} +(0.229187 + 0.296107i) q^{30} +(0.341835 + 1.27575i) q^{31} +(1.72008 - 0.460894i) q^{32} +(-6.13710 + 2.57223i) q^{33} +(0.119590 - 0.446315i) q^{34} -2.41931i q^{35} +(4.15921 - 4.22946i) q^{36} +(0.0790729 + 0.0790729i) q^{37} +(-0.168989 - 0.292697i) q^{38} +(-6.13392 + 1.17261i) q^{39} +(-0.429913 + 0.744631i) q^{40} +(4.70308 - 1.26019i) q^{41} +(0.436023 - 0.0592617i) q^{42} +(5.68065 - 3.27972i) q^{43} +(-5.37158 - 5.37158i) q^{44} +(0.0360434 + 4.30428i) q^{45} +(0.0986104 + 0.0986104i) q^{46} +(6.90396 + 1.84991i) q^{47} +(6.19436 + 2.53545i) q^{48} +(3.59998 + 2.07845i) q^{49} +(0.114700 + 0.428068i) q^{50} +(4.20046 - 3.25115i) q^{51} +(-3.89149 - 5.97348i) q^{52} -8.93473i q^{53} +(-0.774863 + 0.111931i) q^{54} +5.51239 q^{55} +(0.505221 + 0.875068i) q^{56} +(0.490997 - 3.85412i) q^{57} +(0.349032 + 1.30261i) q^{58} +(3.83604 + 14.3163i) q^{59} +(-4.53195 + 1.89947i) q^{60} +(-0.662501 - 1.14749i) q^{61} +0.198998 q^{62} +(4.40177 + 2.49245i) q^{63} +7.46031i q^{64} +(5.06179 + 1.06828i) q^{65} +(0.135028 + 0.993478i) q^{66} +(-2.93507 - 10.9538i) q^{67} +(5.25138 + 3.03188i) q^{68} +(0.215904 + 1.58853i) q^{69} +(-0.352097 - 0.0943440i) q^{70} +(8.77081 + 8.77081i) q^{71} +(-0.911896 - 1.54934i) q^{72} +(-11.7401 - 11.7401i) q^{73} +(0.0145915 - 0.00842442i) q^{74} +(-1.92986 + 4.71483i) q^{75} +(4.28426 - 1.14796i) q^{76} +(3.23900 - 5.61011i) q^{77} +(-0.0685427 + 0.938435i) q^{78} +(-4.14278 - 7.17550i) q^{79} +(-3.92059 - 3.92059i) q^{80} +(-7.86850 - 4.36884i) q^{81} -0.733610i q^{82} +(2.02034 - 7.54003i) q^{83} +(-0.729771 + 5.72839i) q^{84} +(-4.25020 + 1.13884i) q^{85} +(-0.255794 - 0.954637i) q^{86} +(-5.87254 + 14.3472i) q^{87} +(-1.99384 + 1.15115i) q^{88} +(6.10608 - 6.10608i) q^{89} +(0.627835 + 0.162606i) q^{90} +(4.06145 - 4.52381i) q^{91} +(-1.58494 + 0.915066i) q^{92} +(1.82070 + 1.38500i) q^{93} +(0.538458 - 0.932637i) q^{94} +(-1.60926 + 2.78731i) q^{95} +(1.86738 - 2.45483i) q^{96} +(6.12255 + 1.64053i) q^{97} +(0.442876 - 0.442876i) q^{98} +(-5.67905 + 10.0294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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