LMFDB - Embedded newform 555.2.bi.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(47,555)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("555.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bi (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	555.47
Dual form			555.2.bi.a.248.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.658434 - 2.45731i) q^{2} +(-0.842875 - 1.51313i) q^{3} +(-3.87278 + 2.23595i) q^{4} +(1.16787 - 1.90685i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(1.02555 - 3.82742i) q^{7} +(4.44664 + 4.44664i) q^{8} +(-1.57912 + 2.55076i) q^{9} +O(q^{10})$	\(q+(-0.658434 - 2.45731i) q^{2} +(-0.842875 - 1.51313i) q^{3} +(-3.87278 + 2.23595i) q^{4} +(1.16787 - 1.90685i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(1.02555 - 3.82742i) q^{7} +(4.44664 + 4.44664i) q^{8} +(-1.57912 + 2.55076i) q^{9} +(-5.45469 - 1.61428i) q^{10} +2.14211i q^{11} +(6.64755 + 3.97539i) q^{12} +(-3.78308 - 1.01367i) q^{13} -10.0804 q^{14} +(-3.86968 - 0.159900i) q^{15} +(3.52705 - 6.10903i) q^{16} +(-0.255289 - 0.952752i) q^{17} +(7.30775 + 2.20089i) q^{18} +(-5.86684 + 3.38722i) q^{19} +(-0.259272 + 9.99611i) q^{20} +(-6.65579 + 1.67424i) q^{21} +(5.26382 - 1.41044i) q^{22} +(-2.15463 - 2.15463i) q^{23} +(2.98038 - 10.4763i) q^{24} +(-2.27217 - 4.45390i) q^{25} +9.96365i q^{26} +(5.19063 + 0.239450i) q^{27} +(4.58617 + 17.1158i) q^{28} +10.6695 q^{29} +(2.15501 + 9.61428i) q^{30} +2.81981 q^{31} +(-5.18565 - 1.38949i) q^{32} +(3.24129 - 1.80553i) q^{33} +(-2.17311 + 1.25465i) q^{34} +(-6.10061 - 6.42550i) q^{35} +(0.412230 - 13.4094i) q^{36} +(0.629511 - 6.05010i) q^{37} +(12.1864 + 12.1864i) q^{38} +(1.65485 + 6.57870i) q^{39} +(13.6722 - 3.28599i) q^{40} +(5.90944 - 3.41181i) q^{41} +(8.49652 + 15.2530i) q^{42} +(-0.705507 + 0.705507i) q^{43} +(-4.78965 - 8.29591i) q^{44} +(3.01971 + 5.99011i) q^{45} +(-3.87590 + 6.71326i) q^{46} +(-4.99749 + 4.99749i) q^{47} +(-12.2166 - 0.187737i) q^{48} +(-7.53519 - 4.35044i) q^{49} +(-9.44855 + 8.51601i) q^{50} +(-1.22646 + 1.18934i) q^{51} +(16.9176 - 4.53305i) q^{52} +(-11.7157 + 3.13921i) q^{53} +(-2.82929 - 12.9126i) q^{54} +(4.08468 + 2.50170i) q^{55} +(21.5794 - 12.4589i) q^{56} +(10.0703 + 6.02229i) q^{57} +(-7.02519 - 26.2184i) q^{58} +(2.10057 - 3.63830i) q^{59} +(15.3440 - 8.03316i) q^{60} +(-3.30306 - 5.72107i) q^{61} +(-1.85666 - 6.92914i) q^{62} +(8.14334 + 8.65991i) q^{63} -0.450563i q^{64} +(-6.35107 + 6.02994i) q^{65} +(-6.57092 - 6.77602i) q^{66} +(-1.43666 + 5.36169i) q^{67} +(3.11898 + 3.11898i) q^{68} +(-1.44415 + 5.07631i) q^{69} +(-11.7726 + 19.2218i) q^{70} +(5.69974 - 3.29075i) q^{71} +(-18.3641 + 4.32051i) q^{72} +(1.32554 - 1.32554i) q^{73} +(-15.2815 + 2.43669i) q^{74} +(-4.82418 + 7.19217i) q^{75} +(15.1473 - 26.2359i) q^{76} +(8.19874 + 2.19685i) q^{77} +(15.0763 - 8.39811i) q^{78} +(-6.83148 + 3.94416i) q^{79} +(-7.52988 - 13.8601i) q^{80} +(-4.01274 - 8.05593i) q^{81} +(-12.2749 - 12.2749i) q^{82} +(12.0465 - 3.22785i) q^{83} +(22.0329 - 21.3660i) q^{84} +(-2.11490 - 0.625890i) q^{85} +(2.19818 + 1.26912i) q^{86} +(-8.99309 - 16.1444i) q^{87} +(-9.52519 + 9.52519i) q^{88} +(2.22383 - 3.85179i) q^{89} +(12.7313 - 11.3644i) q^{90} +(-7.75951 + 13.4399i) q^{91} +(13.1620 + 3.52675i) q^{92} +(-2.37674 - 4.26673i) q^{93} +(15.5709 + 8.98987i) q^{94} +(-0.392769 + 15.1430i) q^{95} +(2.26838 + 9.01773i) q^{96} +(-4.28162 - 4.28162i) q^{97} +(-5.72896 + 21.3808i) q^{98} +(-5.46400 - 3.38265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 16 q^{6} - 4 q^{7}+O(q^{10}) $ 288 * q - 16 * q^6 - 4 * q^7	$ 288 q - 16 q^{6} - 4 q^{7} - 16 q^{10} - 18 q^{12} - 20 q^{13} + 6 q^{15} + 112 q^{16} + 20 q^{18} - 4 q^{21} - 12 q^{22} - 36 q^{25} + 48 q^{27} - 28 q^{28} - 16 q^{30} - 80 q^{31} + 2 q^{33} - 16 q^{36} - 36 q^{37} + 8 q^{40} - 32 q^{42} - 16 q^{43} + 76 q^{45} - 24 q^{46} + 112 q^{48} + 48 q^{55} + 2 q^{57} - 60 q^{58} - 56 q^{60} + 16 q^{61} - 36 q^{63} - 36 q^{70} - 58 q^{72} - 48 q^{73} - 88 q^{75} + 16 q^{76} + 20 q^{78} - 56 q^{81} - 136 q^{82} + 144 q^{85} + 16 q^{87} + 144 q^{88} - 42 q^{90} - 22 q^{93} - 80 q^{96} + 56 q^{97}+O(q^{100}) $ 288 * q - 16 * q^6 - 4 * q^7 - 16 * q^10 - 18 * q^12 - 20 * q^13 + 6 * q^15 + 112 * q^16 + 20 * q^18 - 4 * q^21 - 12 * q^22 - 36 * q^25 + 48 * q^27 - 28 * q^28 - 16 * q^30 - 80 * q^31 + 2 * q^33 - 16 * q^36 - 36 * q^37 + 8 * q^40 - 32 * q^42 - 16 * q^43 + 76 * q^45 - 24 * q^46 + 112 * q^48 + 48 * q^55 + 2 * q^57 - 60 * q^58 - 56 * q^60 + 16 * q^61 - 36 * q^63 - 36 * q^70 - 58 * q^72 - 48 * q^73 - 88 * q^75 + 16 * q^76 + 20 * q^78 - 56 * q^81 - 136 * q^82 + 144 * q^85 + 16 * q^87 + 144 * q^88 - 42 * q^90 - 22 * q^93 - 80 * q^96 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.658434	−	2.45731i	−0.465583	−	1.73758i	−0.654949	−	0.755673i	$-0.727310\pi$
$2$	−0.658434	−	2.45731i	−0.465583	−	1.73758i	0.189366	−	0.981907i	$-0.439357\pi$
$3$	−0.842875	−	1.51313i	−0.486634	−	0.873606i
$3$	−0.842875	−	1.51313i	−0.486634	−	0.873606i
$4$	−3.87278	+	2.23595i	−1.93639	+	1.11798i
$5$	1.16787	−	1.90685i	0.522287	−	0.852770i
$5$	1.16787	−	1.90685i	0.522287	−	0.852770i
$6$	−3.16325	+	3.06750i	−1.29139	+	1.25230i
$7$	1.02555	−	3.82742i	0.387623	−	1.44663i	−0.446368	−	0.894850i	$-0.647283\pi$
$7$	1.02555	−	3.82742i	0.387623	−	1.44663i	0.833991	−	0.551778i	$-0.186051\pi$
$8$	4.44664	+	4.44664i	1.57213	+	1.57213i
$9$	−1.57912	+	2.55076i	−0.526375	+	0.850253i
$10$	−5.45469	−	1.61428i	−1.72492	−	0.510480i
$11$			2.14211i			0.645870i	0.946421	+	0.322935i	$0.104670\pi$
$11$			2.14211i			0.645870i	−0.946421	+	0.322935i	$0.895330\pi$
$12$	6.64755	+	3.97539i	1.91898	+	1.14760i
$13$	−3.78308	−	1.01367i	−1.04924	−	0.281143i	−0.307302	−	0.951612i	$-0.599426\pi$
$13$	−3.78308	−	1.01367i	−1.04924	−	0.281143i	−0.741937	+	0.670469i	$0.766093\pi$
$14$	−10.0804			−2.69410
$15$	−3.86968	−	0.159900i	−0.999147	−	0.0412859i
$16$	3.52705	−	6.10903i	0.881763	−	1.52726i
$17$	−0.255289	−	0.952752i	−0.0619167	−	0.231076i	0.928033	−	0.372499i	$-0.121499\pi$
$17$	−0.255289	−	0.952752i	−0.0619167	−	0.231076i	−0.989949	+	0.141423i	$0.954832\pi$
$18$	7.30775	+	2.20089i	1.72245	+	0.518755i
$19$	−5.86684	+	3.38722i	−1.34595	+	0.777082i	−0.987673	−	0.156534i	$-0.949968\pi$
$19$	−5.86684	+	3.38722i	−1.34595	+	0.777082i	−0.358274	+	0.933617i	$0.616635\pi$
$20$	−0.259272	+	9.99611i	−0.0579750	+	2.23520i
$21$	−6.65579	+	1.67424i	−1.45241	+	0.365349i
$22$	5.26382	−	1.41044i	1.12225	−	0.300706i
$23$	−2.15463	−	2.15463i	−0.449270	−	0.449270i	0.445841	−	0.895112i	$-0.352905\pi$
$23$	−2.15463	−	2.15463i	−0.449270	−	0.449270i	−0.895112	+	0.445841i	$0.852905\pi$
$24$	2.98038	−	10.4763i	0.608368	−	2.13847i
$25$	−2.27217	−	4.45390i	−0.454433	−	0.890781i
$26$			9.96365i			1.95403i
$27$	5.19063	+	0.239450i	0.998938	+	0.0460821i
$28$	4.58617	+	17.1158i	0.866705	+	3.23459i
$29$	10.6695			1.98128			0.990642	−	0.136485i	$-0.0435806\pi$
$29$	10.6695			1.98128			0.990642	+	0.136485i	$0.0435806\pi$
$30$	2.15501	+	9.61428i	0.393449	+	1.75532i
$31$	2.81981			0.506452			0.253226	−	0.967407i	$-0.418508\pi$
$31$	2.81981			0.506452			0.253226	+	0.967407i	$0.418508\pi$
$32$	−5.18565	−	1.38949i	−0.916703	−	0.245630i
$33$	3.24129	−	1.80553i	0.564236	−	0.314302i
$34$	−2.17311	+	1.25465i	−0.372686	+	0.215170i
$35$	−6.10061	−	6.42550i	−1.03119	−	1.08611i
$36$	0.412230	−	13.4094i	0.0687051	−	2.23489i
$37$	0.629511	−	6.05010i	0.103491	−	0.994630i
$37$	0.629511	−	6.05010i	0.103491	−	0.994630i
$38$	12.1864	+	12.1864i	1.97689	+	1.97689i
$39$	1.65485	+	6.57870i	0.264987	+	1.05343i
$40$	13.6722	−	3.28599i	2.16176	−	0.519561i
$41$	5.90944	−	3.41181i	0.922899	−	0.532836i	0.0383401	−	0.999265i	$-0.487793\pi$
$41$	5.90944	−	3.41181i	0.922899	−	0.532836i	0.884559	+	0.466429i	$0.154460\pi$
$42$	8.49652	+	15.2530i	1.31104	+	2.35358i
$43$	−0.705507	+	0.705507i	−0.107589	+	0.107589i	−0.758852	−	0.651263i	$-0.774239\pi$
$43$	−0.705507	+	0.705507i	−0.107589	+	0.107589i	0.651263	+	0.758852i	$0.274239\pi$
$44$	−4.78965	−	8.29591i	−0.722067	−	1.25066i
$45$	3.01971	+	5.99011i	0.450152	+	0.892952i
$46$	−3.87590	+	6.71326i	−0.571471	+	0.989816i
$47$	−4.99749	+	4.99749i	−0.728959	+	0.728959i	−0.970412	−	0.241453i	$-0.922376\pi$
$47$	−4.99749	+	4.99749i	−0.728959	+	0.728959i	0.241453	+	0.970412i	$0.422376\pi$
$48$	−12.2166	−	0.187737i	−1.76332	−	0.0270975i
$49$	−7.53519	−	4.35044i	−1.07646	−	0.621492i
$50$	−9.44855	+	8.51601i	−1.33623	+	1.20435i
$51$	−1.22646	+	1.18934i	−0.171739	+	0.166540i
$52$	16.9176	−	4.53305i	2.34605	−	0.628621i
$53$	−11.7157	+	3.13921i	−1.60927	+	0.431204i	−0.947826	−	0.318788i	$-0.896724\pi$
$53$	−11.7157	+	3.13921i	−1.60927	+	0.431204i	−0.661448	+	0.749991i	$0.730058\pi$
$54$	−2.82929	−	12.9126i	−0.385017	−	1.75719i
$55$	4.08468	+	2.50170i	0.550778	+	0.337329i
$56$	21.5794	−	12.4589i	2.88367	−	1.66489i
$57$	10.0703	+	6.02229i	1.33385	+	0.797672i
$58$	−7.02519	−	26.2184i	−0.922452	−	3.44264i
$59$	2.10057	−	3.63830i	0.273472	−	0.473667i	−0.696277	−	0.717773i	$-0.745161\pi$
$59$	2.10057	−	3.63830i	0.273472	−	0.473667i	0.969748	+	0.244107i	$0.0784947\pi$
$60$	15.3440	−	8.03316i	1.98090	−	1.03708i
$61$	−3.30306	−	5.72107i	−0.422914	−	0.732508i	0.573309	−	0.819339i	$-0.305659\pi$
$61$	−3.30306	−	5.72107i	−0.422914	−	0.732508i	−0.996223	+	0.0868311i	$0.972326\pi$
$62$	−1.85666	−	6.92914i	−0.235796	−	0.880001i
$63$	8.14334	+	8.65991i	1.02596	+	1.09105i
$64$		−	0.450563i		−	0.0563204i
$65$	−6.35107	+	6.02994i	−0.787754	+	0.747922i
$66$	−6.57092	−	6.77602i	−0.808824	−	0.834071i
$67$	−1.43666	+	5.36169i	−0.175516	+	0.655034i	0.820947	+	0.571004i	$0.193446\pi$
$67$	−1.43666	+	5.36169i	−0.175516	+	0.655034i	−0.996463	+	0.0840304i	$0.973221\pi$
$68$	3.11898	+	3.11898i	0.378232	+	0.378232i
$69$	−1.44415	+	5.07631i	−0.173855	+	0.611116i
$70$	−11.7726	+	19.2218i	−1.40709	+	2.29745i
$71$	5.69974	−	3.29075i	0.676435	−	0.390540i	−0.122076	−	0.992521i	$-0.538955\pi$
$71$	5.69974	−	3.29075i	0.676435	−	0.390540i	0.798510	+	0.601981i	$0.205622\pi$
$72$	−18.3641	+	4.32051i	−2.16423	+	0.509177i
$73$	1.32554	−	1.32554i	0.155143	−	0.155143i	−0.625267	−	0.780411i	$-0.715010\pi$
$73$	1.32554	−	1.32554i	0.155143	−	0.155143i	0.780411	+	0.625267i	$0.215010\pi$
$74$	−15.2815	+	2.43669i	−1.77643	+	0.283259i
$75$	−4.82418	+	7.19217i	−0.557049	+	0.830480i
$76$	15.1473	−	26.2359i	1.73752	−	3.00947i
$77$	8.19874	+	2.19685i	0.934333	+	0.250354i
$78$	15.0763	−	8.39811i	1.70705	−	0.950898i
$79$	−6.83148	+	3.94416i	−0.768601	+	0.443752i	−0.832375	−	0.554212i	$-0.813020\pi$
$79$	−6.83148	+	3.94416i	−0.768601	+	0.443752i	0.0637741	+	0.997964i	$0.479686\pi$
$80$	−7.52988	−	13.8601i	−0.841867	−	1.54961i
$81$	−4.01274	−	8.05593i	−0.445859	−	0.895103i
$82$	−12.2749	−	12.2749i	−1.35553	−	1.35553i
$83$	12.0465	−	3.22785i	1.32227	−	0.354302i	0.472444	−	0.881360i	$-0.343372\pi$
$83$	12.0465	−	3.22785i	1.32227	−	0.354302i	0.849829	+	0.527058i	$0.176705\pi$
$84$	22.0329	−	21.3660i	2.40399	−	2.33122i
$85$	−2.11490	−	0.625890i	−0.229393	−	0.0678874i
$86$	2.19818	+	1.26912i	0.237036	+	0.136853i
$87$	−8.99309	−	16.1444i	−0.964160	−	1.73086i
$88$	−9.52519	+	9.52519i	−1.01539	+	1.01539i
$89$	2.22383	−	3.85179i	0.235726	−	0.408289i	−0.723758	−	0.690054i	$-0.757587\pi$
$89$	2.22383	−	3.85179i	0.235726	−	0.408289i	0.959483	+	0.281765i	$0.0909200\pi$
$90$	12.7313	−	11.3644i	1.34199	−	1.19792i
$91$	−7.75951	+	13.4399i	−0.813418	+	1.40888i
$92$	13.1620	+	3.52675i	1.37224	+	0.367690i
$93$	−2.37674	−	4.26673i	−0.246457	−	0.442440i
$94$	15.5709	+	8.98987i	1.60602	+	0.927234i
$95$	−0.392769	+	15.1430i	−0.0402973	+	1.55364i
$96$	2.26838	+	9.01773i	0.231515	+	0.920369i
$97$	−4.28162	−	4.28162i	−0.434733	−	0.434733i	0.455502	−	0.890235i	$-0.349460\pi$
$97$	−4.28162	−	4.28162i	−0.434733	−	0.434733i	−0.890235	+	0.455502i	$0.849460\pi$
$98$	−5.72896	+	21.3808i	−0.578712	+	2.15978i
$99$	−5.46400	−	3.38265i	−0.549153	−	0.339970i
$100$	18.7583	+	12.1685i	1.87583	+	1.21685i
$101$		−	4.57343i		−	0.455073i	−0.973770	−	0.227537i	$-0.926933\pi$
$101$		−	4.57343i		−	0.455073i	0.973770	−	0.227537i	$-0.0730671\pi$
$102$	3.73011	+	2.23069i	0.369336	+	0.220871i
$103$	−4.99488	+	4.99488i	−0.492161	+	0.492161i	−0.908986	−	0.416826i	$-0.863143\pi$
$103$	−4.99488	+	4.99488i	−0.492161	+	0.492161i	0.416826	+	0.908986i	$0.363143\pi$
$104$	−12.3146	−	21.3295i	−1.20754	−	2.09153i
$105$	−4.58057	+	14.6469i	−0.447018	+	1.42939i
$106$	15.4280	+	26.7221i	1.49850	+	2.59548i
$107$	−11.0750	−	2.96753i	−1.07066	−	0.286882i	−0.319894	−	0.947453i	$-0.603647\pi$
$107$	−11.0750	−	2.96753i	−1.07066	−	0.286882i	−0.750763	+	0.660572i	$0.770314\pi$
$108$	−20.6376	+	10.6787i	−1.98585	+	1.02755i
$109$	2.59340	+	1.49730i	0.248403	+	0.143416i	0.619033	−	0.785365i	$-0.287525\pi$
$109$	2.59340	+	1.49730i	0.248403	+	0.143416i	−0.370630	+	0.928781i	$0.620858\pi$
$110$	3.45796	−	11.6845i	0.329703	−	1.11408i
$111$	−9.68519	+	4.14695i	−0.919277	+	0.393611i
$112$	−19.7646	−	19.7646i	−1.86758	−	1.86758i
$113$	−2.28386	+	0.611959i	−0.214848	+	0.0575683i	−0.364637	−	0.931150i	$-0.618807\pi$
$113$	−2.28386	+	0.611959i	−0.214848	+	0.0575683i	0.149790	+	0.988718i	$0.452140\pi$
$114$	8.16798	−	28.7112i	0.765002	−	2.68905i
$115$	−6.62487	+	1.59223i	−0.617772	+	0.148476i
$116$	−41.3208	+	23.8566i	−3.83654	+	2.21503i
$117$	8.55960	−	8.04902i	0.791335	−	0.744132i
$118$	−10.3235	−	2.76618i	−0.950357	−	0.254647i
$119$	−3.90839			−0.358282
$120$	−16.4961	−	17.9181i	−1.50588	−	1.63569i
$121$	6.41137			0.582852
$122$	−11.8836	+	11.8836i	−1.07589	+	1.07589i
$123$	−10.1434	−	6.06601i	−0.914602	−	0.546954i
$124$	−10.9205	+	6.30495i	−0.980689	+	0.566201i
$125$	−11.1465	−	0.868891i	−0.996976	−	0.0777160i
$126$	15.9182	−	25.7127i	1.41811	−	2.29067i
$127$	−8.52509	+	2.28429i	−0.756480	+	0.202698i	−0.616390	−	0.787441i	$-0.711406\pi$
$127$	−8.52509	+	2.28429i	−0.756480	+	0.202698i	−0.140089	+	0.990139i	$0.544739\pi$
$128$	−11.4785	+	3.07565i	−1.01456	+	0.271852i
$129$	1.66218	+	0.472870i	0.146347	+	0.0416339i
$130$	18.9992	+	11.6362i	1.66634	+	1.02056i
$131$	−3.76902	−	2.17605i	−0.329301	−	0.190122i	0.326230	−	0.945290i	$-0.394222\pi$
$131$	−3.76902	−	2.17605i	−0.329301	−	0.190122i	−0.655531	+	0.755169i	$0.727555\pi$
$132$	−8.51572	+	14.2398i	−0.741198	+	1.23941i
$133$	6.94756	+	25.9286i	0.602430	+	2.24830i
$134$	14.1213			1.21989
$135$	6.51857	−	9.61812i	0.561029	−	0.827796i
$136$	3.10137	−	5.37172i	0.265940	−	0.460622i
$137$	6.47482	−	6.47482i	0.553181	−	0.553181i	−0.374177	−	0.927357i	$-0.622075\pi$
$137$	6.47482	−	6.47482i	0.553181	−	0.553181i	0.927357	+	0.374177i	$0.122075\pi$
$138$	13.4249	+	0.206306i	1.14281	+	0.0175619i
$139$	−13.5993	−	7.85158i	−1.15348	−	0.665962i	−0.203747	−	0.979024i	$-0.565312\pi$
$139$	−13.5993	−	7.85158i	−1.15348	−	0.665962i	−0.949733	+	0.313062i	$0.898645\pi$
$140$	37.9934	+	11.2439i	3.21103	+	0.950282i
$141$	11.7741	+	3.34959i	0.991560	+	0.282087i
$142$	−11.8393	−	11.8393i	−0.993530	−	0.993530i
$143$	2.17140	−	8.10378i	0.181582	−	0.677672i
$144$	10.0130	+	18.6436i	0.834418	+	1.55363i
$145$	12.4606	−	20.3452i	1.03480	−	1.68958i
$146$	−4.13005	−	2.38449i	−0.341805	−	0.197341i
$147$	−0.231564	+	15.0686i	−0.0190991	+	1.24284i
$148$	11.0898	+	24.8383i	0.911573	+	2.04169i
$149$	5.57789			0.456959			0.228479	−	0.973549i	$-0.426625\pi$
$149$	5.57789			0.456959			0.228479	+	0.973549i	$0.426625\pi$
$150$	20.8498	+	7.11894i	1.70238	+	0.581259i
$151$	2.75763	+	4.77635i	0.224412	+	0.388694i	0.956143	−	0.292900i	$-0.0946204\pi$
$151$	2.75763	+	4.77635i	0.224412	+	0.388694i	−0.731731	+	0.681594i	$0.761287\pi$
$152$	−41.1495	−	11.0260i	−3.33767	−	0.894325i
$153$	2.83337	+	0.853332i	0.229065	+	0.0689878i
$154$		−	21.5933i		−	1.74004i
$155$	3.29316	−	5.37695i	0.264513	−	0.431887i
$156$	−21.1185	−	21.7777i	−1.69083	−	1.74361i
$157$	−11.8471	+	3.17441i	−0.945499	+	0.253346i	−0.698451	−	0.715658i	$-0.746127\pi$
$157$	−11.8471	+	3.17441i	−0.945499	+	0.253346i	−0.247048	+	0.969003i	$0.579460\pi$
$158$	14.1901	+	14.1901i	1.12890	+	1.12890i
$159$	14.6249	+	15.0814i	1.15983	+	1.19603i
$160$	−8.70571	+	8.26553i	−0.688247	+	0.653447i
$161$	−10.4563	+	6.03697i	−0.824075	+	0.475780i
$162$	−17.1538	+	15.1648i	−1.34773	+	1.19146i
$163$	−3.63406	−	13.5625i	−0.284642	−	1.06230i	−0.949101	−	0.314972i	$-0.898005\pi$
$163$	−3.63406	−	13.5625i	−0.284642	−	1.06230i	0.664459	−	0.747325i	$-0.268662\pi$
$164$	−15.2573	+	26.4264i	−1.19139	+	2.06356i
$165$	0.342522	−	8.28927i	0.0266653	−	0.645319i
$166$	−15.8636	−	27.4766i	−1.23126	−	2.13260i
$167$	−1.80299	−	0.483110i	−0.139520	−	0.0373842i	0.188383	−	0.982096i	$-0.439675\pi$
$167$	−1.80299	−	0.483110i	−0.139520	−	0.0373842i	−0.327903	+	0.944711i	$0.606342\pi$
$168$	−37.0407	−	22.1512i	−2.85775	−	1.70900i
$169$	2.02586	+	1.16963i	0.155836	+	0.0899718i
$170$	−0.145484	+	5.60907i	−0.0111581	+	0.430196i
$171$	0.624484	−	20.3137i	0.0477555	−	1.55343i
$172$	1.15480	−	4.30975i	0.0880523	−	0.328616i
$173$	11.8307	−	3.17003i	0.899473	−	0.241013i	0.220683	−	0.975346i	$-0.429171\pi$
$173$	11.8307	−	3.17003i	0.899473	−	0.241013i	0.678790	+	0.734333i	$0.262505\pi$
$174$	−33.7504	+	32.7288i	−2.55861	+	2.48117i
$175$	−19.3772	+	4.12881i	−1.46478	+	0.312109i
$176$	13.0862	+	7.55532i	0.986410	+	0.569504i
$177$	−7.27575	−	0.111809i	−0.546879	−	0.00840407i
$178$	−10.9293	−	2.92849i	−0.819184	−	0.219500i
$179$	2.05604			0.153676			0.0768379	−	0.997044i	$-0.475518\pi$
$179$	2.05604			0.153676			0.0768379	+	0.997044i	$0.475518\pi$
$180$	−25.0882	−	16.4464i	−1.86997	−	1.22585i
$181$	10.5107	+	18.2050i	0.781252	+	1.35317i	0.931213	+	0.364476i	$0.118752\pi$
$181$	10.5107	+	18.2050i	0.781252	+	1.35317i	−0.149961	+	0.988692i	$0.547915\pi$
$182$	38.1350	+	10.2183i	2.82676	+	0.757427i
$183$	−5.87265	+	9.82011i	−0.434119	+	0.725923i
$184$		−	19.1617i		−	1.41262i
$185$	−10.8015	−	8.26611i	−0.794139	−	0.607736i
$186$	−8.91975	+	8.64976i	−0.654028	+	0.634231i
$187$	2.04090	−	0.546857i	0.149245	−	0.0399901i
$188$	8.18005	−	30.5283i	0.596591	−	2.22651i
$189$	6.23974	−	19.6211i	0.453875	−	1.42723i
$190$	37.4697	−	9.00553i	2.71834	−	0.653330i
$191$			11.7294i			0.848713i	0.905495	+	0.424356i	$0.139500\pi$
$191$			11.7294i			0.848713i	−0.905495	+	0.424356i	$0.860500\pi$
$192$	−0.681761	+	0.379769i	−0.0492019	+	0.0274074i
$193$	11.3837	−	11.3837i	0.819416	−	0.819416i	−0.166607	−	0.986023i	$-0.553281\pi$
$193$	11.3837	−	11.3837i	0.819416	−	0.819416i	0.986023	+	0.166607i	$0.0532811\pi$
$194$	−7.70210	+	13.3404i	−0.552979	+	0.957787i
$195$	14.4772	+	4.52751i	1.03674	+	0.324222i
$196$	38.9095			2.77925
$197$	4.70275	+	17.5509i	0.335057	+	1.25045i	0.903807	+	0.427940i	$0.140761\pi$
$197$	4.70275	+	17.5509i	0.335057	+	1.25045i	−0.568750	+	0.822511i	$0.692573\pi$
$198$	−4.71454	+	15.6540i	−0.335048	+	1.11248i
$199$			1.97796i			0.140214i	0.997539	+	0.0701068i	$0.0223340\pi$
$199$			1.97796i			0.140214i	−0.997539	+	0.0701068i	$0.977666\pi$
$200$	9.70141	−	29.9084i	0.685993	−	2.11484i
$201$	9.32385	−	2.34538i	0.657654	−	0.165430i
$202$	−11.2383	+	3.01130i	−0.790726	+	0.211874i
$203$	10.9422	−	40.8368i	0.767991	−	2.86618i
$204$	2.09052	−	7.34834i	0.146365	−	0.514487i
$205$	0.395621	−	15.2530i	0.0276313	−	1.06531i
$206$	15.5628	+	8.98517i	1.08431	+	0.626027i
$207$	8.89835	−	2.09351i	0.618478	−	0.145509i
$208$	−19.5357	+	19.5357i	−1.35456	+	1.35456i
$209$	−7.25580	−	12.5674i	−0.501894	−	0.869306i
$210$	39.0080	+	1.61185i	2.69180	+	0.111228i
$211$	−27.2822			−1.87818			−0.939091	−	0.343667i	$-0.888331\pi$
$211$	−27.2822			−1.87818			−0.939091	+	0.343667i	$0.888331\pi$
$212$	38.3532	−	38.3532i	2.63411	−	2.63411i
$213$	−9.78349	−	5.85076i	−0.670354	−	0.400887i
$214$			29.1685i			1.99392i
$215$	0.521358	+	2.16924i	0.0355563	+	0.147941i
$216$	22.0161	+	24.1456i	1.49801	+	1.64290i
$217$	2.89186	−	10.7926i	0.196312	−	0.732648i
$218$	1.97175	−	7.35867i	0.133544	−	0.498392i
$219$	−3.12299	−	0.888452i	−0.211032	−	0.0600360i
$220$	−21.4128	−	0.555389i	−1.44365	−	0.0374443i
$221$			3.86312i			0.259862i
$222$	16.5674	+	21.0690i	1.11193	+	1.41406i
$223$	12.9197	−	12.9197i	0.865165	−	0.865165i	−0.126768	−	0.991932i	$-0.540460\pi$
$223$	12.9197	−	12.9197i	0.865165	−	0.865165i	0.991932	+	0.126768i	$0.0404603\pi$
$224$	−10.6363	+	18.4227i	−0.710670	+	1.23092i
$225$	14.9489	+	1.23752i	0.996591	+	0.0825014i
$226$	3.00754	+	5.20922i	0.200059	+	0.346512i
$227$	−10.9564	−	2.93576i	−0.727203	−	0.194853i	−0.123820	−	0.992305i	$-0.539514\pi$
$227$	−10.9564	−	2.93576i	−0.727203	−	0.194853i	−0.603383	+	0.797451i	$0.706181\pi$
$228$	−52.4657	−	0.806259i	−3.47463	−	0.0533958i
$229$	21.7843	−	12.5771i	1.43954	−	0.831121i	0.441727	−	0.897150i	$-0.354366\pi$
$229$	21.7843	−	12.5771i	1.43954	−	0.831121i	0.997818	+	0.0660284i	$0.0210328\pi$
$230$	8.27464	+	15.2310i	0.545614	+	1.00430i
$231$	−3.58640	−	14.2574i	−0.235968	−	0.938070i
$232$	47.4436	+	47.4436i	3.11483	+	3.11483i
$233$	5.27544	+	5.27544i	0.345606	+	0.345606i	0.858470	−	0.512864i	$-0.171416\pi$
$233$	5.27544	+	5.27544i	0.345606	+	0.345606i	−0.512864	+	0.858470i	$0.671416\pi$
$234$	−25.4149	−	15.7338i	−1.66142	−	1.02855i
$235$	3.69306	+	15.3659i	0.240909	+	1.00236i
$236$			18.7871i			1.22294i
$237$	11.7261	+	7.01248i	0.761692	+	0.455510i
$238$	2.57342	+	9.60412i	0.166810	+	0.622543i
$239$	9.64882	−	16.7122i	0.624130	−	1.08102i	−0.364578	−	0.931173i	$-0.618787\pi$
$239$	9.64882	−	16.7122i	0.624130	−	1.08102i	0.988708	−	0.149852i	$-0.0478798\pi$
$240$	−14.6254	+	23.0760i	−0.944065	+	1.48955i
$241$	−11.5630	−	20.0277i	−0.744840	−	1.29010i	−0.950270	−	0.311429i	$-0.899192\pi$
$241$	−11.5630	−	20.0277i	−0.744840	−	1.29010i	0.205430	−	0.978672i	$-0.434141\pi$
$242$	−4.22147	−	15.7547i	−0.271366	−	1.01275i
$243$	−8.80743	+	12.8619i	−0.564997	+	0.825093i
$244$	25.5841	+	14.7710i	1.63785	+	0.945614i
$245$	−17.0958	+	9.28774i	−1.09221	+	0.593372i
$246$	−8.22728	+	28.9196i	−0.524552	+	1.84385i
$247$	25.6283	−	6.86708i	1.63069	−	0.436942i
$248$	12.5387	+	12.5387i	0.796206	+	0.796206i
$249$	−15.0378	−	15.5072i	−0.952984	−	0.982731i
$250$	5.20412	+	27.9626i	0.329137	+	1.76851i
$251$		−	22.4404i		−	1.41643i	−0.705998	−	0.708214i	$-0.749501\pi$
$251$		−	22.4404i		−	1.41643i	0.705998	−	0.708214i	$-0.250499\pi$
$252$	−50.9005	−	15.3298i	−3.20643	−	0.965687i
$253$	4.61544	−	4.61544i	0.290170	−	0.290170i
$254$	11.2264	+	19.4447i	0.704408	+	1.22007i
$255$	0.835543	+	3.72767i	0.0523237	+	0.233436i
$256$	14.6651	+	25.4007i	0.916567	+	1.58754i
$257$	−3.80065	−	14.1842i	−0.237078	−	0.884786i	−0.977201	−	0.212315i	$-0.931900\pi$
$257$	−3.80065	−	14.1842i	−0.237078	−	0.884786i	0.740123	−	0.672471i	$-0.234767\pi$
$258$	0.0675524	−	4.39584i	0.00420563	−	0.273673i
$259$	−22.5107	−	8.61410i	−1.39874	−	0.535254i
$260$	11.1137	−	37.5533i	0.689240	−	2.32896i
$261$	−16.8485	+	27.2154i	−1.04290	+	1.68459i
$262$	−2.86556	+	10.6944i	−0.177035	+	0.660704i
$263$	0.780816	−	2.91404i	0.0481472	−	0.179688i	−0.937665	−	0.347541i	$-0.887017\pi$
$263$	0.780816	−	2.91404i	0.0481472	−	0.179688i	0.985812	+	0.167853i	$0.0536835\pi$
$264$	22.4414	+	6.38430i	1.38117	+	0.392927i
$265$	−7.69638	+	26.0063i	−0.472785	+	1.59755i
$266$	59.1402	−	34.1446i	3.62612	−	2.09354i
$267$	−7.70267	−	0.118370i	−0.471396	−	0.00724410i
$268$	−6.42460	−	23.9769i	−0.392445	−	1.46462i
$269$	3.49407			0.213037			0.106519	−	0.994311i	$-0.466030\pi$
$269$	3.49407			0.213037			0.106519	+	0.994311i	$0.466030\pi$
$270$	−27.9267	−	9.68525i	−1.69957	−	0.589425i
$271$	−5.79310	+	10.0340i	−0.351906	+	0.609519i	−0.986583	−	0.163258i	$-0.947800\pi$
$271$	−5.79310	+	10.0340i	−0.351906	+	0.609519i	0.634677	+	0.772777i	$0.281133\pi$
$272$	−6.72081	−	1.80083i	−0.407509	−	0.109192i
$273$	26.8766	+	0.413022i	1.62664	+	0.0249972i
$274$	−20.1739	−	11.6474i	−1.21875	−	0.703644i
$275$	9.54074	−	4.86722i	0.575328	−	0.293505i
$276$	−5.75750	−	22.8885i	−0.346561	−	1.37772i
$277$	−4.14980	+	15.4873i	−0.249337	+	0.930539i	0.721816	+	0.692085i	$0.243307\pi$
$277$	−4.14980	+	15.4873i	−0.249337	+	0.930539i	−0.971154	+	0.238455i	$0.923359\pi$
$278$	−10.3395	+	38.5875i	−0.620121	+	2.31432i
$279$	−4.45282	+	7.19265i	−0.266584	+	0.430612i
$280$	1.44468	−	55.6991i	0.0863364	−	3.32866i
$281$	6.41726	+	3.70501i	0.382822	+	0.221022i	0.679045	−	0.734096i	$-0.262394\pi$
$281$	6.41726	+	3.70501i	0.382822	+	0.221022i	−0.296223	+	0.955119i	$0.595727\pi$
$282$	0.478511	−	31.1381i	0.0284949	−	1.85425i
$283$	10.8823	+	2.91592i	0.646888	+	0.173333i	0.567322	−	0.823496i	$-0.307980\pi$
$283$	10.8823	+	2.91592i	0.646888	+	0.173333i	0.0795668	+	0.996830i	$0.474646\pi$
$284$	−14.7159	+	25.4887i	−0.873228	+	1.51247i
$285$	23.2444	−	12.1694i	1.37688	−	0.720851i
$286$	−21.3432			−1.26205
$287$	−6.99800	−	26.1169i	−0.413079	−	1.54163i
$288$	11.7330	−	11.0332i	0.691376	−	0.650136i
$289$	13.8799	−	8.01355i	0.816463	−	0.471385i
$290$	−58.1990	−	17.2236i	−3.41756	−	1.01140i
$291$	−2.86978	+	10.0875i	−0.168229	+	0.591341i
$292$	−2.16969	+	8.09739i	−0.126971	+	0.473864i
$293$	0.629827	−	2.35054i	0.0367949	−	0.137320i	−0.945085	−	0.326824i	$-0.894021\pi$
$293$	0.629827	−	2.35054i	0.0367949	−	0.137320i	0.981880	+	0.189504i	$0.0606881\pi$
$294$	37.1807	−	9.35265i	2.16842	−	0.545458i
$295$	−4.48451	−	8.25454i	−0.261098	−	0.480598i
$296$	29.7018	−	24.1034i	1.72638	−	1.40098i
$297$	−0.512927	+	11.1189i	−0.0297630	+	0.645184i
$298$	−3.67267	−	13.7066i	−0.212752	−	0.794002i
$299$	5.96704	+	10.3352i	0.345083	+	0.597701i
$300$	2.60167	−	38.6403i	0.150208	−	2.23090i
$301$	1.97674	+	3.42381i	0.113937	+	0.197345i
$302$	9.92125	−	9.92125i	0.570904	−	0.570904i
$303$	−6.92019	+	3.85483i	−0.397555	+	0.221454i
$304$			47.7876i			2.74081i
$305$	−14.7668	−	0.383010i	−0.845543	−	0.0219311i
$306$	0.231313	−	7.52433i	0.0132233	−	0.430138i
$307$	15.8399	+	15.8399i	0.904033	+	0.904033i	0.995782	−	0.0917488i	$-0.0292457\pi$
$307$	15.8399	+	15.8399i	0.904033	+	0.904033i	−0.0917488	+	0.995782i	$0.529246\pi$
$308$	−36.6640	+	9.82408i	−2.08912	+	0.559779i
$309$	11.7680	+	3.34785i	0.669457	+	0.190452i
$310$	−15.3812	−	4.55195i	−0.873591	−	0.258534i
$311$	−24.8138	−	14.3262i	−1.40706	−	0.812367i	−0.411957	−	0.911203i	$-0.635155\pi$
$311$	−24.8138	−	14.3262i	−1.40706	−	0.812367i	−0.995104	+	0.0988363i	$0.968488\pi$
$312$	−21.8946	+	36.6116i	−1.23954	+	2.07273i
$313$	1.89362	+	7.06710i	0.107034	+	0.399456i	0.998568	−	0.0534975i	$-0.0170369\pi$
$313$	1.89362	+	7.06710i	0.107034	+	0.399456i	−0.891534	+	0.452954i	$0.850370\pi$
$314$	15.6010	+	27.0218i	0.880416	+	1.52493i
$315$	26.0235	−	5.41451i	1.46626	−	0.305073i
$316$	17.6379	−	30.5497i	0.992208	−	1.71855i
$317$	1.84115	+	6.87126i	0.103409	+	0.385928i	0.998160	−	0.0606377i	$-0.0193134\pi$
$317$	1.84115	+	6.87126i	0.103409	+	0.385928i	−0.894751	+	0.446566i	$0.852647\pi$
$318$	27.4301	−	45.8680i	1.53821	−	2.57215i
$319$			22.8553i			1.27965i
$320$	−0.859158	−	0.526199i	−0.0480284	−	0.0294154i
$321$	4.84455	+	19.2591i	0.270397	+	1.07494i
$322$	21.7195	+	21.7195i	1.21038	+	1.21038i
$323$	4.72492	+	4.72492i	0.262902	+	0.262902i
$324$	33.5531	+	22.2266i	1.86406	+	1.23481i
$325$	4.08099	+	19.1527i	0.226372	+	1.06240i
$326$	−30.9345	+	17.8600i	−1.71330	+	0.989175i
$327$	0.0796981	−	5.18620i	0.00440731	−	0.286797i
$328$	41.4483	+	11.1060i	2.28860	+	0.613228i
$329$	14.0023	+	24.2527i	0.771972	+	1.33709i
$330$	−20.5948	+	4.61626i	−1.13371	+	0.254117i
$331$	−7.68711	+	13.3145i	−0.422522	+	0.731830i	−0.996185	−	0.0872616i	$-0.972188\pi$
$331$	−7.68711	+	13.3145i	−0.422522	+	0.731830i	0.573663	+	0.819091i	$0.305522\pi$
$332$	−39.4361	+	39.4361i	−2.16434	+	2.16434i
$333$	14.4383	+	11.1596i	0.791212	+	0.611542i
$334$			4.74860i			0.259832i
$335$	8.54611	+	9.00124i	0.466924	+	0.491790i
$336$	−13.2473	+	46.5656i	−0.722702	+	2.54036i
$337$	4.04300	−	15.0887i	0.220236	−	0.821934i	−0.764021	−	0.645192i	$-0.776778\pi$
$337$	4.04300	−	15.0887i	0.220236	−	0.821934i	0.984257	−	0.176742i	$-0.0565558\pi$
$338$	1.54025	−	5.74830i	0.0837787	−	0.312666i
$339$	2.85098	+	2.93998i	0.154844	+	0.159678i
$340$	9.59000	−	2.30488i	0.520091	−	0.124999i
$341$			6.04033i			0.327102i
$342$	−50.3283	+	11.8407i	−2.72144	+	0.640272i
$343$	−4.76565	+	4.76565i	−0.257321	+	0.257321i
$344$	−6.27428			−0.338286
$345$	7.99319	+	8.68224i	0.430339	+	0.467436i
$346$	−15.5795	−	26.9845i	−0.837559	−	1.45069i
$347$	−10.1193	+	10.1193i	−0.543230	+	0.543230i	−0.924474	−	0.381244i	$-0.875496\pi$
$347$	−10.1193	+	10.1193i	−0.543230	+	0.543230i	0.381244	+	0.924474i	$0.375496\pi$
$348$	70.9263	+	42.4156i	3.80205	+	2.27372i
$349$	12.1994	+	7.04335i	0.653021	+	0.377022i	0.789613	−	0.613605i	$-0.210281\pi$
$349$	12.1994	+	7.04335i	0.653021	+	0.377022i	−0.136591	+	0.990627i	$0.543615\pi$
$350$	22.9044	+	44.8972i	1.22429	+	2.39985i
$351$	−19.3939	−	6.16747i	−1.03517	−	0.329195i
$352$	2.97644	−	11.1082i	0.158645	−	0.592071i
$353$	29.0947	−	7.79590i	1.54855	−	0.414934i	0.619536	−	0.784968i	$-0.287321\pi$
$353$	29.0947	−	7.79590i	1.54855	−	0.414934i	0.929018	+	0.370035i	$0.120654\pi$
$354$	4.51585	+	17.9524i	0.240015	+	0.954158i
$355$	0.381582	−	14.7117i	0.0202523	−	0.780817i
$356$			19.8895i			1.05414i
$357$	3.29429	+	5.91390i	0.174352	+	0.312997i
$358$	−1.35377	−	5.05233i	−0.0715489	−	0.267024i
$359$	−13.5708			−0.716239			−0.358119	−	0.933676i	$-0.616582\pi$
$359$	−13.5708			−0.716239			−0.358119	+	0.933676i	$0.616582\pi$
$360$	−13.2083	+	40.0634i	−0.696138	+	2.11153i
$361$	13.4466	−	23.2901i	0.707714	−	1.22580i
$362$	37.8148	−	37.8148i	1.98750	−	1.98750i
$363$	−5.40399	−	9.70124i	−0.283636	−	0.509183i
$364$		−	69.3995i		−	3.63752i
$365$	−0.979554	−	4.07567i	−0.0512722	−	0.213330i
$366$	27.9978	+	7.96503i	1.46347	+	0.416339i
$367$	−3.07735	+	11.4848i	−0.160636	+	0.599502i	0.837920	+	0.545792i	$0.183771\pi$
$367$	−3.07735	+	11.4848i	−0.160636	+	0.599502i	−0.998557	+	0.0537098i	$0.982895\pi$
$368$	−20.7621	+	5.56320i	−1.08230	+	0.290002i
$369$	−0.629018	+	20.4612i	−0.0327454	+	1.06517i
$370$	−13.2003	+	31.9852i	−0.686253	+	1.66283i
$371$			48.0603i			2.49516i
$372$	18.7448	+	11.2098i	0.971873	+	0.581203i
$373$	−16.4445	−	4.40629i	−0.851464	−	0.228149i	−0.193408	−	0.981118i	$-0.561954\pi$
$373$	−16.4445	−	4.40629i	−0.851464	−	0.228149i	−0.658056	+	0.752969i	$0.728621\pi$
$374$	−2.68759	−	4.65505i	−0.138972	−	0.240707i
$375$	8.08038	+	17.5985i	0.417269	+	0.908783i
$376$	−44.4441			−2.29203
$377$	−40.3638	−	10.8154i	−2.07884	−	0.557024i
$378$	−52.3237	−	2.41375i	−2.69124	−	0.124150i
$379$	−5.13883	−	2.96690i	−0.263964	−	0.152400i	0.362178	−	0.932109i	$-0.382033\pi$
$379$	−5.13883	−	2.96690i	−0.263964	−	0.152400i	−0.626141	+	0.779709i	$0.715367\pi$
$380$	−32.3380	−	59.5239i	−1.65890	−	3.05351i
$381$	10.6420	+	10.9742i	0.545207	+	0.562225i
$382$	28.8229	−	7.72307i	1.47471	−	0.395146i
$383$	7.16383	−	26.7358i	0.366054	−	1.36613i	−0.499931	−	0.866065i	$-0.666641\pi$
$383$	7.16383	−	26.7358i	0.366054	−	1.36613i	0.865986	−	0.500069i	$-0.166692\pi$
$384$	14.3288	+	14.7760i	0.731212	+	0.754037i
$385$	13.7641	−	13.0682i	0.701484	−	0.666015i
$386$	−35.4687	−	20.4778i	−1.80531	−	1.04229i
$387$	−0.685495	−	2.91366i	−0.0348457	−	0.148110i
$388$	26.1553	+	7.00829i	1.32783	+	0.355792i
$389$	4.23146	+	7.32910i	0.214543	+	0.371600i	0.953131	−	0.302557i	$-0.0978403\pi$
$389$	4.23146	+	7.32910i	0.214543	+	0.371600i	−0.738588	+	0.674157i	$0.764507\pi$
$390$	1.59318	−	38.5561i	0.0806739	−	1.95237i
$391$	−1.50277	+	2.60288i	−0.0759984	+	0.131633i
$392$	−14.1614	−	52.8511i	−0.715260	−	2.66939i
$393$	−0.115826	+	7.53715i	−0.00584265	+	0.380199i
$394$	40.0316	−	23.1122i	2.01676	−	1.16438i
$395$	−0.457349	+	17.6329i	−0.0230117	+	0.887206i
$396$	28.7243	+	0.883042i	1.44345	+	0.0443745i
$397$	−14.3266	−	14.3266i	−0.719032	−	0.719032i	0.249375	−	0.968407i	$-0.419775\pi$
$397$	−14.3266	−	14.3266i	−0.719032	−	0.719032i	−0.968407	+	0.249375i	$0.919775\pi$
$398$	4.86045	−	1.30235i	0.243632	−	0.0652811i
$399$	33.3775	−	32.3672i	1.67096	−	1.62038i
$400$	−35.2231	−	1.82841i	−1.76115	−	0.0914206i
$401$		−	18.1609i		−	0.906910i	−0.891279	−	0.453455i	$-0.850191\pi$
$401$		−	18.1609i		−	0.906910i	0.891279	−	0.453455i	$-0.149809\pi$
$402$	−11.9025	−	21.3673i	−0.593641	−	1.06570i
$403$	−10.6676	−	2.85837i	−0.531389	−	0.142385i
$404$	10.2260	+	17.7119i	0.508761	+	0.881199i
$405$	−20.0478	−	1.75657i	−0.996183	−	0.0872848i
$406$	−107.553			−5.33778
$407$	12.9600	+	1.34848i	0.642402	+	0.0668417i
$408$	−10.7422	−	0.165079i	−0.531817	−	0.00817262i
$409$	−24.5785	−	14.1904i	−1.21533	−	0.701671i	−0.251414	−	0.967880i	$-0.580896\pi$
$409$	−24.5785	−	14.1904i	−1.21533	−	0.701671i	−0.963915	+	0.266208i	$0.914229\pi$
$410$	−37.7417	+	9.07091i	−1.86393	+	0.447980i
$411$	−15.2547	−	4.33978i	−0.752459	−	0.214065i
$412$	8.17577	−	30.5124i	0.402792	−	1.50324i
$413$	−11.7711	−	11.7711i	−0.579216	−	0.579216i
$414$	−11.0034	−	20.4876i	−0.540786	−	1.00691i
$415$	7.91369	−	26.7406i	0.388468	−	1.31264i
$416$	18.2093	+	10.5131i	0.892783	+	0.515449i
$417$	−0.417922	+	27.1954i	−0.0204657	+	1.33177i
$418$	−26.1045	+	26.1045i	−1.27682	+	1.27682i
$419$	−3.98331	+	6.89929i	−0.194597	+	0.337052i	−0.946768	−	0.321915i	$-0.895673\pi$
$419$	−3.98331	+	6.89929i	−0.194597	+	0.337052i	0.752171	+	0.658968i	$0.229007\pi$
$420$	−15.0102	−	66.9662i	−0.732424	−	3.26761i
$421$	−3.39995			−0.165703			−0.0828517	−	0.996562i	$-0.526403\pi$
$421$	−3.39995			−0.165703			−0.0828517	+	0.996562i	$0.526403\pi$
$422$	17.9635	+	67.0407i	0.874450	+	3.26349i
$423$	−4.85574	−	20.6391i	−0.236094	−	1.00351i
$424$	−66.0544	−	38.1365i	−3.20789	−	1.85207i
$425$	−3.66341	+	3.30184i	−0.177701	+	0.160163i
$426$	−7.93534	+	27.8934i	−0.384468	+	1.35144i
$427$	−25.2844	+	6.77493i	−1.22360	+	0.327862i
$428$	49.5261	−	13.2705i	2.39394	−	0.641453i
$429$	−14.0923	+	3.54486i	−0.680382	+	0.171147i
$430$	4.98721	−	2.70944i	0.240504	−	0.130661i
$431$	21.9765	−	12.6882i	1.05857	−	0.611167i	0.133536	−	0.991044i	$-0.457367\pi$
$431$	21.9765	−	12.6882i	1.05857	−	0.611167i	0.925037	+	0.379877i	$0.124034\pi$
$432$	19.7704	−	30.8652i	0.951205	−	1.48500i
$433$	18.9039	−	18.9039i	0.908466	−	0.908466i	−0.0876826	−	0.996148i	$-0.527946\pi$
$433$	18.9039	−	18.9039i	0.908466	−	0.908466i	0.996148	+	0.0876826i	$0.0279461\pi$
$434$	−28.4248			−1.36443
$435$	−41.2877	−	1.70605i	−1.97959	−	0.0817991i
$436$	−13.3916			−0.641340
$437$	19.9391	+	5.34265i	0.953814	+	0.255574i
$438$	−0.126921	+	8.25913i	−0.00606451	+	0.394636i
$439$	14.1171	−	8.15049i	0.673771	−	0.389002i	−0.123733	−	0.992316i	$-0.539487\pi$
$439$	14.1171	−	8.15049i	0.673771	−	0.389002i	0.797504	+	0.603314i	$0.206153\pi$
$440$	7.03895	+	29.2873i	0.335569	+	1.39622i
$441$	22.9959	−	12.3506i	1.09504	−	0.588122i
$442$	9.49288	−	2.54361i	0.451530	−	0.120987i
$443$	16.2639	+	16.2639i	0.772719	+	0.772719i	0.978581	−	0.205862i	$-0.0659998\pi$
$443$	16.2639	+	16.2639i	0.772719	+	0.772719i	−0.205862	+	0.978581i	$0.566000\pi$
$444$	28.2362	−	37.7158i	1.34003	−	1.78991i
$445$	−4.74765	−	8.73890i	−0.225060	−	0.414264i
$446$	−40.2543	−	23.2409i	−1.90610	−	1.10049i
$447$	−4.70147	−	8.44008i	−0.222372	−	0.399202i
$448$	−1.72449	−	0.462077i	−0.0814747	−	0.0218311i
$449$	5.68903	+	9.85369i	0.268482	+	0.465024i	0.968470	−	0.249130i	$-0.0801447\pi$
$449$	5.68903	+	9.85369i	0.268482	+	0.465024i	−0.699988	+	0.714155i	$0.746811\pi$
$450$	−6.80187	−	37.5488i	−0.320643	−	1.77007i
$451$	7.30847	+	12.6586i	0.344143	+	0.596072i
$452$	7.47659	−	7.47659i	0.351669	−	0.351669i
$453$	4.90290	−	8.19851i	0.230358	−	0.385200i
$454$			28.8563i			1.35429i
$455$	16.5657	+	30.4922i	0.776614	+	1.42950i
$456$	18.0002	+	71.5581i	0.842935	+	3.35101i
$457$	−1.20317	+	4.49029i	−0.0562820	+	0.210047i	−0.988340	−	0.152261i	$-0.951345\pi$
$457$	−1.20317	+	4.49029i	−0.0562820	+	0.210047i	0.932058	+	0.362308i	$0.118011\pi$
$458$	−45.2494	−	45.2494i	−2.11437	−	2.11437i
$459$	−1.09698	−	5.00651i	−0.0512024	−	0.233684i
$460$	22.0965	−	20.9792i	1.03026	−	0.978163i
$461$	3.57336	+	2.06308i	0.166428	+	0.0960872i	0.580900	−	0.813975i	$-0.302701\pi$
$461$	3.57336	+	2.06308i	0.166428	+	0.0960872i	−0.414473	+	0.910062i	$0.636034\pi$
$462$	−32.6735	+	18.2005i	−1.52011	+	0.846762i
$463$	−9.28940	−	2.48909i	−0.431715	−	0.115678i	0.0364160	−	0.999337i	$-0.488406\pi$
$463$	−9.28940	−	2.48909i	−0.431715	−	0.115678i	−0.468131	+	0.883659i	$0.655073\pi$
$464$	37.6320	−	65.1806i	1.74702	−	3.02593i
$465$	−10.9118	−	0.450886i	−0.506020	−	0.0209093i
$466$	9.48986	−	16.4369i	0.439609	−	0.761425i
$467$	18.0356	−	18.0356i	0.834587	−	0.834587i	−0.153553	−	0.988140i	$-0.549072\pi$
$467$	18.0356	−	18.0356i	0.834587	−	0.834587i	0.988140	+	0.153553i	$0.0490717\pi$
$468$	−15.1522	+	50.3109i	−0.700412	+	2.32562i
$469$	19.0480	+	10.9974i	0.879557	+	0.507813i
$470$	35.3271	−	19.1924i	1.62952	−	0.885280i
$471$	14.7889	+	15.2505i	0.681436	+	0.702707i
$472$	25.5187	−	6.83772i	1.17459	−	0.314732i
$473$	−1.51127	−	1.51127i	−0.0694884	−	0.0694884i
$474$	9.51098	−	33.4319i	0.436854	−	1.53558i
$475$	28.4168	+	18.4340i	1.30385	+	0.845811i
$476$	15.1363	−	8.73897i	0.693773	−	0.400550i
$477$	10.4932	−	34.8411i	0.480449	−	1.59526i
$478$	−47.4202	−	12.7062i	−2.16895	−	0.581169i
$479$	12.5409	−	21.7215i	0.573010	−	0.992482i	−0.423245	−	0.906015i	$-0.639109\pi$
$479$	12.5409	−	21.7215i	0.573010	−	0.992482i	0.996255	−	0.0864665i	$-0.0275576\pi$
$480$	19.8446	+	6.20607i	0.905780	+	0.283267i
$481$	−8.51433	+	22.2499i	−0.388220	+	1.01451i
$482$	−41.6009	+	41.6009i	−1.89487	+	1.89487i
$483$	17.9481	+	10.7334i	0.816667	+	0.488386i
$484$	−24.8298	+	14.3355i	−1.12863	+	0.651614i
$485$	−13.1648	+	3.16405i	−0.597782	+	0.143672i
$486$	37.4048	+	13.1738i	1.69672	+	0.597578i
$487$	12.9020	+	12.9020i	0.584644	+	0.584644i	0.936176	−	0.351532i	$-0.114339\pi$
$487$	12.9020	+	12.9020i	0.584644	+	0.584644i	−0.351532	+	0.936176i	$0.614339\pi$
$488$	10.7520	−	40.1271i	0.486721	−	1.81647i
$489$	−17.4588	+	16.9303i	−0.789513	+	0.765614i
$490$	34.0793	+	35.8942i	1.53954	+	1.62153i
$491$			31.4811i			1.42072i	0.703838	+	0.710361i	$0.251468\pi$
$491$			31.4811i			1.42072i	−0.703838	+	0.710361i	$0.748532\pi$
$492$	52.8466	+	0.812112i	2.38251	+	0.0366128i
$493$	−2.72382	−	10.1654i	−0.122675	−	0.457828i
$494$	−33.7491	−	58.4551i	−1.51844	−	2.63002i
$495$	−12.8315	+	6.46854i	−0.576731	+	0.290739i
$496$	9.94560	−	17.2263i	0.446571	−	0.773483i
$497$	−6.74967	−	25.1901i	−0.302764	−	1.12993i
$498$	−28.2046	+	47.1631i	−1.26388	+	2.11343i
$499$	14.3170	−	8.26595i	0.640919	−	0.370035i	−0.144049	−	0.989571i	$-0.546012\pi$
$499$	14.3170	−	8.26595i	0.640919	−	0.370035i	0.784969	+	0.619536i	$0.212679\pi$
$500$	45.1108	−	21.5581i	2.01742	−	0.964106i
$501$	0.788687	+	3.13536i	0.0352360	+	0.140078i
$502$	−55.1431	+	14.7756i	−2.46116	+	0.659465i
$503$	−29.9966	+	8.03756i	−1.33748	+	0.358377i	−0.855499	−	0.517804i	$-0.826750\pi$
$503$	−29.9966	+	8.03756i	−1.33748	+	0.358377i	−0.481982	+	0.876181i	$0.660083\pi$
$504$	−2.29698	+	74.7180i	−0.102316	+	3.32821i
$505$	−8.72085	−	5.34116i	−0.388073	−	0.237679i
$506$	−14.3805	−	8.30260i	−0.639292	−	0.369096i
$507$	0.0622570	−	4.05125i	0.00276493	−	0.179922i
$508$	27.9082	−	27.9082i	1.23823	−	1.23823i
$509$	−10.5285	+	18.2358i	−0.466666	+	0.808289i	−0.999275	−	0.0380726i	$-0.987878\pi$
$509$	−10.5285	+	18.2358i	−0.466666	+	0.808289i	0.532609	+	0.846361i	$0.321212\pi$
$510$	8.60988	−	4.50761i	0.381252	−	0.199600i
$511$	−3.71399	−	6.43282i	−0.164297	−	0.284571i
$512$	35.9556	−	35.9556i	1.58903	−	1.58903i
$513$	−31.2637	+	16.1770i	−1.38033	+	0.714233i
$514$	−32.3525	+	18.6787i	−1.42701	+	0.823883i
$515$	3.69113	+	15.3579i	0.162651	+	0.676749i
$516$	−7.49457	+	1.88523i	−0.329930	+	0.0829926i
$517$	−10.7052	−	10.7052i	−0.470813	−	0.470813i
$518$	−6.34573	+	60.9875i	−0.278815	+	2.67964i
$519$	−14.7685	−	15.2295i	−0.648265	−	0.668500i
$520$	−55.0539	−	1.42795i	−2.41427	−	0.0626198i
$521$	27.1326	−	15.6650i	1.18870	−	0.686296i	0.230688	−	0.973028i	$-0.425902\pi$
$521$	27.1326	−	15.6650i	1.18870	−	0.686296i	0.958011	+	0.286732i	$0.0925689\pi$
$522$	77.9703	+	23.4825i	3.41267	+	1.02780i
$523$	13.8038	+	3.69871i	0.603597	+	0.161733i	0.547660	−	0.836701i	$-0.315519\pi$
$523$	13.8038	+	3.69871i	0.603597	+	0.161733i	0.0559370	+	0.998434i	$0.482185\pi$
$524$	19.4621			0.850207
$525$	22.5800	+	25.8401i	0.985470	+	1.12776i
$526$	−7.67482			−0.334638
$527$	−0.719866	−	2.68658i	−0.0313579	−	0.117029i
$528$	0.402153	−	26.1693i	0.0175015	−	1.13887i
$529$		−	13.7152i		−	0.596312i
$530$	68.9730	+	1.78897i	2.99600	+	0.0777080i
$531$	5.96336	+	11.1034i	0.258788	+	0.481846i
$532$	−84.8815	−	84.8815i	−3.68008	−	3.68008i
$533$	−25.8144	+	6.91694i	−1.11814	+	0.299606i
$534$	4.78083	+	19.0058i	0.206887	+	0.822460i
$535$	−18.5927	+	17.6526i	−0.803834	+	0.763190i
$536$	−30.2298	+	17.4532i	−1.30573	+	0.753863i
$537$	−1.73299	−	3.11106i	−0.0747839	−	0.134252i
$538$	−2.30061	−	8.58601i	−0.0991865	−	0.370169i
$539$	9.31912	−	16.1412i	0.401403	−	0.695250i
$540$	−3.73935	+	51.8241i	−0.160916	+	2.23015i
$541$	15.2900			0.657370			0.328685	−	0.944440i	$-0.393395\pi$
$541$	15.2900			0.657370			0.328685	+	0.944440i	$0.393395\pi$
$542$	28.4709	+	7.62875i	1.22293	+	0.327683i
$543$	18.6874	−	31.2486i	0.801952	−	1.34100i
$544$			5.29536i			0.227037i
$545$	5.88389	−	3.19658i	0.252038	−	0.136927i
$546$	−16.6815	−	66.3160i	−0.713903	−	2.83806i
$547$	31.6133	+	31.6133i	1.35169	+	1.35169i	0.883775	+	0.467913i	$0.154994\pi$
$547$	31.6133	+	31.6133i	1.35169	+	1.35169i	0.467913	+	0.883775i	$0.345006\pi$
$548$	−10.5982	+	39.5529i	−0.452731	+	1.68962i
$549$	19.8090	+	0.608968i	0.845428	+	0.0259901i
$550$	−18.2422	−	20.2398i	−0.777851	−	0.863028i
$551$	−62.5965	+	36.1401i	−2.66670	+	1.53962i
$552$	−28.9941	+	16.1509i	−1.23407	+	0.687428i
$553$	8.08989	+	30.1919i	0.344017	+	1.28389i
$554$	40.7893			1.73297
$555$	−3.40342	+	23.3113i	−0.144467	+	0.989510i
$556$	70.2229			2.97812
$557$	2.26290	+	8.44527i	0.0958823	+	0.357838i	0.997152	−	0.0754213i	$-0.0240302\pi$
$557$	2.26290	+	8.44527i	0.0958823	+	0.357838i	−0.901269	+	0.433259i	$0.857364\pi$
$558$	20.6064	+	6.20608i	0.872340	+	0.262724i
$559$	3.38415	−	1.95384i	0.143134	−	0.0826386i
$560$	−60.7707	+	14.6057i	−2.56803	+	0.617205i
$561$	−2.54769	−	2.62721i	−0.107563	−	0.110921i
$562$	4.87901	−	18.2087i	0.205808	−	0.768088i
$563$	3.03484	+	3.03484i	0.127903	+	0.127903i	0.768161	−	0.640257i	$-0.221172\pi$
$563$	3.03484	+	3.03484i	0.127903	+	0.127903i	−0.640257	+	0.768161i	$0.721172\pi$
$564$	−53.0881	+	13.3541i	−2.23541	+	0.562309i
$565$	−1.50034	+	5.06967i	−0.0631196	+	0.213283i
$566$		−	28.6612i		−	1.20472i
$567$	−34.9487	+	7.09663i	−1.46771	+	0.298030i
$568$	39.9775	+	10.7119i	1.67742	+	0.449463i
$569$	−10.6341			−0.445803			−0.222901	−	0.974841i	$-0.571553\pi$
$569$	−10.6341			−0.445803			−0.222901	+	0.974841i	$0.571553\pi$
$570$	−45.2088	−	49.1060i	−1.89359	−	2.05682i
$571$	14.5864	−	25.2644i	0.610423	−	1.05728i	−0.380746	−	0.924680i	$-0.624333\pi$
$571$	14.5864	−	25.2644i	0.610423	−	1.05728i	0.991169	−	0.132604i	$-0.0423339\pi$
$572$	9.71029	+	36.2393i	0.406008	+	1.51524i
$573$	17.7482	−	9.88646i	0.741441	−	0.413013i
$574$	−59.5695	+	34.3925i	−2.48638	+	1.43551i
$575$	−4.70083	+	14.4922i	−0.196038	+	0.604365i
$576$	1.14928	+	0.711495i	0.0478866	+	0.0296456i
$577$	−19.1198	+	5.12314i	−0.795968	+	0.213279i	−0.633813	−	0.773486i	$-0.718511\pi$
$577$	−19.1198	+	5.12314i	−0.795968	+	0.213279i	−0.162155	+	0.986765i	$0.551845\pi$
$578$	−28.8307	−	28.8307i	−1.19920	−	1.19920i
$579$	−26.8200	−	7.62998i	−1.11460	−	0.317091i
$580$	−2.76632	+	106.654i	−0.114865	+	4.42856i
$581$		−	49.4173i		−	2.05017i
$582$	26.6777	+	0.409966i	1.10583	+	0.0169936i
$583$	−6.72453	−	25.0963i	−0.278501	−	1.03938i
$584$	11.7884			0.487809
$585$	−5.35179	−	25.7221i	−0.221269	−	1.06348i
$586$	−6.19071			−0.255736
$587$	17.8194	+	4.77470i	0.735486	+	0.197073i	0.607071	−	0.794648i	$-0.292344\pi$
$587$	17.8194	+	4.77470i	0.735486	+	0.197073i	0.128415	+	0.991721i	$0.459011\pi$
$588$	−32.7958	−	58.8751i	−1.35248	−	2.42797i
$589$	−16.5434	+	9.55132i	−0.681658	+	0.393555i
$590$	−17.3312	+	16.4549i	−0.713515	+	0.677437i
$591$	22.5930	−	21.9091i	0.929351	−	0.901220i
$592$	−34.7399	−	25.1847i	−1.42780	−	1.03509i
$593$	−0.318297	−	0.318297i	−0.0130709	−	0.0130709i	0.700541	−	0.713612i	$-0.252942\pi$
$593$	−0.318297	−	0.318297i	−0.0130709	−	0.0130709i	−0.713612	+	0.700541i	$0.752942\pi$
$594$	27.6603	−	6.06064i	1.13492	−	0.248671i
$595$	−4.56449	+	7.45272i	−0.187126	+	0.305532i
$596$	−21.6020	+	12.4719i	−0.884850	+	0.510869i
$597$	2.99291	−	1.66717i	0.122491	−	0.0682327i
$598$	21.4679	−	21.4679i	0.877889	−	0.877889i
$599$	4.99391	+	8.64970i	0.204046	+	0.353417i	0.949828	−	0.312772i	$-0.101258\pi$
$599$	4.99391	+	8.64970i	0.204046	+	0.353417i	−0.745783	+	0.666189i	$0.767924\pi$
$600$	−53.4324	+	10.5296i	−2.18137	+	0.429868i
$601$	19.2573	−	33.3546i	0.785520	−	1.36056i	−0.143168	−	0.989698i	$-0.545729\pi$
$601$	19.2573	−	33.3546i	0.785520	−	1.36056i	0.928688	−	0.370862i	$-0.120938\pi$
$602$	7.11180	−	7.11180i	0.289855	−	0.289855i
$603$	−11.4077	−	12.1313i	−0.464558	−	0.494026i
$604$	−21.3594	−	12.3318i	−0.869100	−	0.501775i
$605$	7.48764	−	12.2255i	0.304416	−	0.497039i
$606$	14.0290	+	14.4669i	0.569889	+	0.587678i
$607$	41.4832	−	11.1154i	1.68375	−	0.451159i	0.714985	−	0.699140i	$-0.246433\pi$
$607$	41.4832	−	11.1154i	1.68375	−	0.451159i	0.968765	+	0.247980i	$0.0797668\pi$
$608$	35.1299	−	9.41304i	1.42471	−	0.381749i
$609$	−71.0143	+	17.8634i	−2.87764	+	0.723860i
$610$	8.78177	+	36.5387i	0.355563	+	1.47941i
$611$	23.9718	−	13.8401i	0.969794	−	0.559911i
$612$	−12.8810	+	3.03051i	−0.520685	+	0.122501i
$613$	10.0538	+	37.5213i	0.406069	+	1.51547i	0.802075	+	0.597224i	$0.203730\pi$
$613$	10.0538	+	37.5213i	0.406069	+	1.51547i	−0.396005	+	0.918248i	$0.629604\pi$
$614$	28.4941	−	49.3532i	1.14993	−	1.99173i
$615$	−23.4132	+	12.2577i	−0.944110	+	0.494279i
$616$	26.6883	+	46.2255i	1.07530	+	1.86248i
$617$	3.53284	+	13.1847i	0.142227	+	0.530797i	0.999863	+	0.0165408i	$0.00526535\pi$
$617$	3.53284	+	13.1847i	0.142227	+	0.530797i	−0.857637	+	0.514256i	$0.828068\pi$
$618$	0.478261	−	31.1219i	0.0192385	−	1.25191i
$619$			31.4725i			1.26499i	0.774566	+	0.632493i	$0.217968\pi$
$619$			31.4725i			1.26499i	−0.774566	+	0.632493i	$0.782032\pi$
$620$	−0.731097	+	28.1871i	−0.0293616	+	1.13202i
$621$	−10.6679	−	11.6998i	−0.428090	−	0.469497i
$622$	−18.8658	+	70.4080i	−0.756449	+	2.82310i
$623$	−12.4617	−	12.4617i	−0.499269	−	0.499269i
$624$	46.0262	+	13.0939i	1.84252	+	0.524176i
$625$	−14.6745	+	20.2400i	−0.586981	+	0.809601i
$626$	16.1192	−	9.30644i	0.644254	−	0.371960i
$627$	−12.9004	+	21.5717i	−0.515192	+	0.861492i
$628$	38.7833	−	38.7833i	1.54762	−	1.54762i
$629$	−5.92495	+	0.944757i	−0.236243	+	0.0376699i
$630$	−30.4399	−	60.3827i	−1.21275	−	2.40570i
$631$	6.98599	−	12.1001i	0.278108	−	0.481697i	−0.692807	−	0.721123i	$-0.743626\pi$
$631$	6.98599	−	12.1001i	0.278108	−	0.481697i	0.970914	+	0.239427i	$0.0769594\pi$
$632$	−47.9154	−	12.8389i	−1.90597	−	0.510704i
$633$	22.9955	+	41.2815i	0.913988	+	1.64079i
$634$	15.6725	−	9.04854i	0.622436	−	0.359363i
$635$	−5.60038	+	18.9238i	−0.222244	+	0.750970i
$636$	−90.3603	−	25.7064i	−3.58302	−	1.01933i
$637$	24.0963	+	24.0963i	0.954731	+	0.954731i
$638$	56.1626	−	15.0487i	2.22350	−	0.595784i
$639$	−0.606697	+	19.7352i	−0.0240006	+	0.780711i
$640$	−7.54055	+	25.4797i	−0.298066	+	1.00717i
$641$	−15.0760	−	8.70414i	−0.595467	−	0.343793i	0.171789	−	0.985134i	$-0.445045\pi$
$641$	−15.0760	−	8.70414i	−0.595467	−	0.343793i	−0.767256	+	0.641341i	$0.778379\pi$
$642$	44.1358	−	24.5854i	1.74190	−	0.970309i
$643$	24.0313	−	24.0313i	0.947704	−	0.947704i	−0.0509951	−	0.998699i	$-0.516239\pi$
$643$	24.0313	−	24.0313i	0.947704	−	0.947704i	0.998699	+	0.0509951i	$0.0162393\pi$
$644$	26.9967	−	46.7597i	1.06382	−	1.84259i
$645$	2.84290	−	2.61728i	0.111939	−	0.103055i
$646$	8.49955	−	14.7216i	0.334410	−	0.579216i
$647$	36.1213	+	9.67868i	1.42008	+	0.380508i	0.885511	−	0.464619i	$-0.153809\pi$
$647$	36.1213	+	9.67868i	1.42008	+	0.380508i	0.534566	+	0.845127i	$0.320475\pi$
$648$	17.9786	−	53.6650i	0.706267	−	2.10816i
$649$	7.79364	+	4.49966i	0.305927	+	0.176627i
$650$	44.3771	−	22.6391i	1.74061	−	0.887977i
$651$	−18.7681	+	4.72103i	−0.735578	+	0.185032i
$652$	44.3990	+	44.3990i	1.73880	+	1.73880i
$653$	−1.98794	+	7.41911i	−0.0777943	+	0.290332i	−0.993852	−	0.110713i	$-0.964686\pi$
$653$	−1.98794	+	7.41911i	−0.0777943	+	0.290332i	0.916058	+	0.401046i	$0.131353\pi$
$654$	−12.7966	+	3.21892i	−0.500385	+	0.125870i
$655$	−8.55112	+	4.64563i	−0.334120	+	0.181520i
$656$		−	48.1346i		−	1.87934i
$657$	1.28794	+	5.47434i	0.0502474	+	0.213574i
$658$	50.3768	−	50.3768i	1.96389	−	1.96389i
$659$	−13.0966	−	22.6840i	−0.510171	−	0.883642i	−0.999931	−	0.0117845i	$-0.996249\pi$
$659$	−13.0966	−	22.6840i	−0.510171	−	0.883642i	0.489760	−	0.871858i	$-0.337085\pi$
$660$	17.2079	+	32.8684i	0.669817	+	1.27940i
$661$	−17.6297	−	30.5355i	−0.685716	−	1.18769i	−0.973211	−	0.229912i	$-0.926156\pi$
$661$	−17.6297	−	30.5355i	−0.685716	−	1.18769i	0.287496	−	0.957782i	$-0.407177\pi$
$662$	37.7792	+	10.1229i	1.46833	+	0.393438i
$663$	5.84540	−	3.25613i	0.227017	−	0.126458i
$664$	67.9195	+	39.2133i	2.63579	+	1.52177i
$665$	57.5559	+	17.0333i	2.23192	+	0.660522i
$666$	17.9159	−	42.8271i	0.694228	−	1.65952i
$667$	−22.9889	−	22.9889i	−0.890133	−	0.890133i
$668$	8.06280	−	2.16042i	0.311959	−	0.0835891i
$669$	−30.4388	−	8.65947i	−1.17683	−	0.334794i
$670$	16.4918	−	26.9272i	0.637133	−	1.04029i
$671$	12.2551	−	7.07551i	0.473105	−	0.273147i
$672$	36.8410	+	0.566148i	1.42117	+	0.0218396i
$673$	−29.0282	−	7.77808i	−1.11896	−	0.299823i	−0.348495	−	0.937311i	$-0.613307\pi$
$673$	−29.0282	−	7.77808i	−1.11896	−	0.299823i	−0.770461	+	0.637488i	$0.779974\pi$
$674$	−39.7396			−1.53071
$675$	−10.7275	−	23.6626i	−0.412901	−	0.910776i
$676$	−10.4610			−0.402345
$677$	22.0923	−	22.0923i	0.849076	−	0.849076i	−0.140942	−	0.990018i	$-0.545013\pi$
$677$	22.0923	−	22.0923i	0.849076	−	0.849076i	0.990018	+	0.140942i	$0.0450130\pi$
$678$	5.34724	−	8.94153i	0.205360	−	0.343397i
$679$	−20.7786	+	11.9965i	−0.797409	+	0.460384i
$680$	−6.62109	−	12.1873i	−0.253907	−	0.467362i
$681$	4.79270	+	19.0530i	0.183657	+	0.730111i
$682$	14.8430	−	3.97716i	0.568366	−	0.152293i
$683$	−9.64927	+	2.58551i	−0.369219	+	0.0989320i	−0.438658	−	0.898654i	$-0.644546\pi$
$683$	−9.64927	+	2.58551i	−0.369219	+	0.0989320i	0.0694385	+	0.997586i	$0.477879\pi$
$684$	43.0020	+	80.0670i	1.64422	+	3.06144i
$685$	−4.78478	−	19.9082i	−0.182817	−	0.760655i
$686$	14.8485	+	8.57281i	0.566920	+	0.327311i
$687$	−37.3923	−	22.3615i	−1.42660	−	0.853143i
$688$	1.82161	+	6.79832i	0.0694481	+	0.259184i
$689$	47.5036			1.80974
$690$	16.0720	−	25.3584i	0.611849	−	0.965378i
$691$	−11.7546	+	20.3596i	−0.447166	+	0.774515i	−0.998200	−	0.0599680i	$-0.980900\pi$
$691$	−11.7546	+	20.3596i	−0.447166	+	0.774515i	0.551034	+	0.834483i	$0.314233\pi$
$692$	−38.7297	+	38.7297i	−1.47228	+	1.47228i
$693$	−18.5505	+	17.4439i	−0.704673	+	0.662640i
$694$	31.5290	+	18.2033i	1.19682	+	0.690987i
$695$	−30.8540	+	16.7623i	−1.17036	+	0.635830i
$696$	31.7993	−	111.777i	1.20535	−	4.23691i
$697$	−4.75923	−	4.75923i	−0.180269	−	0.180269i
$698$	9.27516	−	34.6154i	0.351070	−	1.31021i
$699$	3.53589	−	12.4290i	0.133740	−	0.470107i
$700$	65.8117	−	59.3164i	2.48745	−	2.24195i
$701$	29.0836	+	16.7914i	1.09847	+	0.634203i	0.935819	−	0.352481i	$-0.114662\pi$
$701$	29.0836	+	16.7914i	1.09847	+	0.634203i	0.162652	+	0.986683i	$0.447995\pi$
$702$	−2.38579	+	51.7176i	−0.0900459	+	1.95196i
$703$	16.7998	+	37.6273i	0.633616	+	1.41914i
$704$	0.965155			0.0363757
$705$	20.1378	−	18.5396i	0.758434	−	0.698242i
$706$	−38.3139	−	66.3615i	−1.44196	−	2.49755i
$707$	−17.5044	−	4.69030i	−0.658322	−	0.176397i
$708$	28.4274	−	15.8352i	1.06837	−	0.595123i
$709$			5.38431i			0.202212i	0.994876	+	0.101106i	$0.0322381\pi$
$709$			5.38431i			0.202212i	−0.994876	+	0.101106i	$0.967762\pi$
$710$	−36.4025	+	8.74903i	−1.36616	+	0.328345i
$711$	0.727163	−	23.6538i	0.0272707	−	0.887085i
$712$	27.0161	−	7.23894i	1.01247	−	0.271291i
$713$	−6.07563	−	6.07563i	−0.227534	−	0.227534i
$714$	12.3632	−	11.9890i	0.462682	−	0.448677i
$715$	−12.9168	−	13.6047i	−0.483060	−	0.508786i
$716$	−7.96260	+	4.59721i	−0.297576	+	0.171806i
$717$	−33.4205	−	0.513585i	−1.24811	−	0.0191802i
$718$	8.93546	+	33.3476i	0.333469	+	1.24452i
$719$	7.84705	−	13.5915i	0.292646	−	0.506877i	−0.681789	−	0.731549i	$-0.738798\pi$
$719$	7.84705	−	13.5915i	0.292646	−	0.506877i	0.974434	+	0.224672i	$0.0721310\pi$
$720$	47.2444	+	2.67991i	1.76069	+	0.0998745i
$721$	13.9950	+	24.2400i	0.521201	+	0.902746i
$722$	−66.0847	−	17.7074i	−2.45942	−	0.659000i
$723$	−20.5584	+	34.3772i	−0.764575	+	1.27850i
$724$	−81.4111	−	47.0027i	−3.02562	−	1.74684i
$725$	−24.2430	−	47.5211i	−0.900361	−	1.76489i
$726$	−20.2808	+	19.6669i	−0.752690	+	0.729907i
$727$	8.93325	−	33.3393i	0.331316	−	1.23649i	−0.576493	−	0.817102i	$-0.695579\pi$
$727$	8.93325	−	33.3393i	0.331316	−	1.23649i	0.907808	−	0.419385i	$-0.137754\pi$
$728$	−94.2660	+	25.2585i	−3.49373	+	0.936143i
$729$	26.8853	+	2.48579i	0.995753	+	0.0920663i
$730$	−9.37022	+	5.09063i	−0.346807	+	0.188413i
$731$	0.852282	+	0.492065i	0.0315228	+	0.0181997i
$732$	0.786226	−	51.1621i	0.0290597	−	1.89100i
$733$	−16.9006	−	4.52850i	−0.624238	−	0.167264i	−0.0671844	−	0.997741i	$-0.521402\pi$
$733$	−16.9006	−	4.52850i	−0.624238	−	0.167264i	−0.557054	+	0.830476i	$0.688068\pi$
$734$	30.2479			1.11647
$735$	28.4631	+	18.0397i	1.04988	+	0.665404i
$736$	8.17931	+	14.1670i	0.301493	+	0.522202i
$737$	−11.4853	−	3.07748i	−0.423067	−	0.113360i
$738$	50.6937	−	11.9267i	1.86606	−	0.439027i
$739$		−	1.94114i		−	0.0714062i	−0.999362	−	0.0357031i	$-0.988633\pi$
$739$		−	1.94114i		−	0.0714062i	0.999362	−	0.0357031i	$-0.0113671\pi$
$740$	60.3143	+	7.86129i	2.21720	+	0.288987i
$741$	−31.9922	−	32.9909i	−1.17526	−	1.21195i
$742$	118.099	−	31.6445i	4.33555	−	1.16171i
$743$	−4.82896	+	18.0219i	−0.177157	+	0.661160i	0.819017	+	0.573769i	$0.194519\pi$
$743$	−4.82896	+	18.0219i	−0.177157	+	0.661160i	−0.996174	+	0.0873905i	$0.972147\pi$
$744$	8.40411	−	29.5412i	0.308110	−	1.08303i
$745$	6.51425	−	10.6362i	0.238663	−	0.389681i
$746$			43.3105i			1.58571i
$747$	−10.7894	+	35.8248i	−0.394765	+	1.31076i
$748$	−6.68120	+	6.68120i	−0.244289	+	0.244289i
$749$	−22.7159	+	39.3451i	−0.830022	+	1.43764i
$750$	37.9246	−	31.4434i	1.38481	−	1.14815i
$751$	−8.06988			−0.294474			−0.147237	−	0.989101i	$-0.547038\pi$
$751$	−8.06988			−0.294474			−0.147237	+	0.989101i	$0.547038\pi$
$752$	12.9034	+	48.1563i	0.470540	+	1.75608i
$753$	−33.9553	+	18.9145i	−1.23740	+	0.689282i
$754$			106.308i			3.87149i
$755$	12.3283	+	0.319764i	0.448674	+	0.0116374i
$756$	19.7068	+	89.9402i	0.716728	+	3.27109i
$757$	24.8699	−	6.66386i	0.903911	−	0.242202i	0.223216	−	0.974769i	$-0.428345\pi$
$757$	24.8699	−	6.66386i	0.903911	−	0.242202i	0.680695	+	0.732567i	$0.261678\pi$
$758$	−3.90702	+	14.5812i	−0.141909	+	0.529613i
$759$	−10.8740	−	3.09352i	−0.394701	−	0.112288i
$760$	−69.0821	+	65.5891i	−2.50587	+	2.37917i
$761$	19.9939	+	11.5435i	0.724779	+	0.418451i	0.816509	−	0.577333i	$-0.195906\pi$
$761$	19.9939	+	11.5435i	0.724779	+	0.418451i	−0.0917303	+	0.995784i	$0.529240\pi$
$762$	19.9599	−	33.3765i	0.723072	−	1.20910i
$763$	8.39048	−	8.39048i	0.303756	−	0.303756i
$764$	−26.2265	−	45.4256i	−0.948840	−	1.64344i
$765$	4.93619	−	4.40624i	0.178468	−	0.159308i
$766$	−70.4149			−2.54419
$767$	−11.6347	+	11.6347i	−0.420105	+	0.420105i
$768$	26.0737	−	43.5997i	0.940852	−	1.57327i
$769$		−	31.6099i		−	1.13988i	−0.821685	−	0.569942i	$-0.806966\pi$
$769$		−	31.6099i		−	1.13988i	0.821685	−	0.569942i	$-0.193034\pi$
$770$	−41.1753	−	25.2182i	−1.48385	−	0.908799i
$771$	−18.2591	+	17.7064i	−0.657585	+	0.637680i
$772$	−18.6332	+	69.5399i	−0.670622	+	2.50280i
$773$	−7.75772	+	28.9522i	−0.279026	+	1.04134i	0.674069	+	0.738668i	$0.264545\pi$
$773$	−7.75772	+	28.9522i	−0.279026	+	1.04134i	−0.953095	+	0.302671i	$0.902122\pi$
$774$	−6.70841	+	3.60293i	−0.241129	+	0.129505i
$775$	−6.40707	−	12.5591i	−0.230149	−	0.451138i
$776$		−	38.0777i		−	1.36691i
$777$	5.93941	+	41.3222i	0.213075	+	1.48242i
$778$	15.2237	−	15.2237i	0.545797	−	0.545797i
$779$	−23.1132	+	40.0332i	−0.828115	+	1.43434i
$780$	−66.1905	+	14.8364i	−2.37000	+	0.531227i
$781$	7.04913	+	12.2095i	0.252238	+	0.436889i
$782$	7.38554	+	1.97895i	0.264107	+	0.0707671i
$783$	55.3817	+	2.55482i	1.97918	+	0.0913017i
$784$	−53.1540	+	30.6885i	−1.89836	+	1.09602i
$785$	−7.78268	+	26.2979i	−0.277776	+	0.938612i
$786$	18.5974	−	4.67810i	0.663346	−	0.166862i
$787$	−37.7430	−	37.7430i	−1.34539	−	1.34539i	−0.890594	−	0.454799i	$-0.849711\pi$
$787$	−37.7430	−	37.7430i	−1.34539	−	1.34539i	−0.454799	−	0.890594i	$-0.650289\pi$
$788$	−57.4557	−	57.4557i	−2.04677	−	2.04677i
$789$	−5.06746	+	1.27470i	−0.180406	+	0.0453805i
$790$	43.6305	−	10.4862i	1.55231	−	0.373083i
$791$			9.36889i			0.333119i
$792$	−9.25500	−	39.3379i	−0.328862	−	1.39781i
$793$	6.69646	+	24.9915i	0.237798	+	0.887475i
$794$	−25.7718	+	44.6380i	−0.914606	+	1.58414i
$795$	45.8379	−	10.2744i	1.62570	−	0.364396i
$796$	−4.42262	−	7.66019i	−0.156755	−	0.271508i
$797$	−1.65920	−	6.19220i	−0.0587717	−	0.219339i	0.930294	−	0.366815i	$-0.119552\pi$
$797$	−1.65920	−	6.19220i	−0.0587717	−	0.219339i	−0.989066	+	0.147476i	$0.952885\pi$
$798$	−101.513	−	60.7071i	−3.59352	−	2.14901i
$799$	6.03718	+	3.48557i	0.213580	+	0.123310i
$800$	5.59400	+	26.2536i	0.197778	+	0.928203i
$801$	6.31328	+	11.7549i	0.223069	+	0.415339i
$802$	−44.6269	+	11.9577i	−1.57583	+	0.422242i
$803$	2.83946	+	2.83946i	0.100202	+	0.100202i
$804$	−30.8651	+	29.9308i	−1.08853	+	1.05558i
$805$	−0.700023	+	26.9891i	−0.0246726	+	0.951240i
$806$			28.0956i			0.989624i
$807$	−2.94506	−	5.28698i	−0.103671	−	0.186111i
$808$	20.3364	−	20.3364i	0.715432	−	0.715432i
$809$	−11.7665	−	20.3802i	−0.413688	−	0.716529i	0.581602	−	0.813474i	$-0.302426\pi$
$809$	−11.7665	−	20.3802i	−0.413688	−	0.716529i	−0.995290	+	0.0969449i	$0.969093\pi$
$810$	8.88371	+	50.4202i	0.312142	+	1.77159i
$811$	15.5051	+	26.8556i	0.544458	+	0.943029i	0.998641	+	0.0521204i	$0.0165980\pi$
$811$	15.5051	+	26.8556i	0.544458	+	0.943029i	−0.454183	+	0.890908i	$0.650069\pi$
$812$	48.9324	+	182.618i	1.71719	+	6.40864i
$813$	20.0655	+	0.308354i	0.703729	+	0.0108145i
$814$	−5.21965	−	32.7345i	−0.182949	−	1.14734i
$815$	−30.1058	−	8.90960i	−1.05456	−	0.312090i
$816$	2.93990	+	11.6873i	0.102917	+	0.409138i
$817$	1.74939	−	6.52881i	0.0612034	−	0.228414i
$818$	−18.6869	+	69.7405i	−0.653372	+	2.43842i
$819$	−22.0286	−	41.0159i	−0.769742	−	1.43321i
$820$	32.5727	+	59.9560i	1.13749	+	2.09375i
$821$	−9.46662	+	5.46556i	−0.330387	+	0.190749i	−0.656013	−	0.754750i	$-0.727758\pi$
$821$	−9.46662	+	5.46556i	−0.330387	+	0.190749i	0.325626	+	0.945499i	$0.394425\pi$
$822$	−0.619964	+	40.3430i	−0.0216237	+	1.40712i
$823$	6.62236	+	24.7150i	0.230841	+	0.861511i	0.979980	+	0.199097i	$0.0638010\pi$
$823$	6.62236	+	24.7150i	0.230841	+	0.861511i	−0.749139	+	0.662413i	$0.769532\pi$
$824$	−44.4209			−1.54748
$825$	−15.4064	−	10.3339i	−0.536382	−	0.359781i
$826$	−21.1746	+	36.6756i	−0.736760	+	1.27611i
$827$	−19.2294	−	5.15249i	−0.668670	−	0.179170i	−0.0915146	−	0.995804i	$-0.529171\pi$
$827$	−19.2294	−	5.15249i	−0.668670	−	0.179170i	−0.577156	+	0.816634i	$0.695837\pi$
$828$	−29.7804	+	28.0040i	−1.03494	+	0.973205i
$829$	0.402867	+	0.232595i	0.0139921	+	0.00807836i	0.506980	−	0.861958i	$-0.330762\pi$
$829$	0.402867	+	0.232595i	0.0139921	+	0.00807836i	−0.492988	+	0.870036i	$0.664095\pi$
$830$	−70.9205	−	1.83948i	−2.46168	−	0.0638495i
$831$	26.9320	−	6.77464i	0.934260	−	0.235010i
$832$	−0.456725	+	1.70452i	−0.0158341	+	0.0590936i
$833$	−2.22124	+	8.28978i	−0.0769614	+	0.287224i
$834$	67.1028	−	16.8794i	2.32358	−	0.584487i
$835$	−3.02687	+	2.87383i	−0.104749	+	0.0994529i
$836$	56.2002	+	32.4472i	1.94373	+	1.12221i
$837$	14.6366	+	0.675202i	0.505914	+	0.0233384i
$838$	19.5764	+	5.24549i	0.676256	+	0.181202i
$839$	−0.122527	+	0.212223i	−0.00423010	+	0.00732674i	−0.868133	−	0.496332i	$-0.834680\pi$
$839$	−0.122527	+	0.212223i	−0.00423010	+	0.00732674i	0.863903	+	0.503659i	$0.168013\pi$
$840$	−85.4977	+	44.7614i	−2.94995	+	1.54441i
$841$	84.8391			2.92549
$842$	2.23864	+	8.35472i	0.0771487	+	0.287923i
$843$	0.197209	−	12.8330i	0.00679225	−	0.441992i
$844$	105.658	−	61.0016i	3.63690	−	2.09976i
$845$	4.59626	−	2.49704i	0.158116	−	0.0859010i
$846$	−47.5194	+	25.5215i	−1.63375	+	0.877447i
$847$	6.57521	−	24.5390i	0.225927	−	0.843170i
$848$	−22.1443	+	82.6437i	−0.760438	+	2.83800i
$849$	−4.76030	−	18.9242i	−0.163373	−	0.649475i
$850$	10.5258	+	6.82807i	0.361031	+	0.234201i
$851$	−14.3921	+	11.6793i	−0.493354	+	0.400363i
$852$	50.9713	+	0.783294i	1.74625	+	0.0268352i
$853$	8.10625	+	30.2529i	0.277553	+	1.03584i	0.954111	+	0.299452i	$0.0968038\pi$
$853$	8.10625	+	30.2529i	0.277553	+	1.03584i	−0.676559	+	0.736389i	$0.736530\pi$
$854$	33.2962	+	57.6707i	1.13937	+	1.97345i
$855$	−38.0060	−	24.9146i	−1.29978	−	0.852061i
$856$	−36.0509	−	62.4419i	−1.23219	−	2.13422i
$857$	9.93247	−	9.93247i	0.339287	−	0.339287i	−0.516812	−	0.856099i	$-0.672881\pi$
$857$	9.93247	−	9.93247i	0.339287	−	0.339287i	0.856099	+	0.516812i	$0.172881\pi$
$858$	17.9897	+	32.2950i	0.614157	+	1.10253i
$859$		−	33.4604i		−	1.14165i	−0.821070	−	0.570827i	$-0.806623\pi$
$859$		−	33.4604i		−	1.14165i	0.821070	−	0.570827i	$-0.193377\pi$
$860$	−6.86941	−	7.23525i	−0.234245	−	0.246720i
$861$	−33.6198	+	32.6021i	−1.14576	+	1.11108i
$862$	−45.6488	−	45.6488i	−1.55481	−	1.55481i
$863$	−29.8181	+	7.98974i	−1.01502	+	0.271974i	−0.727725	−	0.685869i	$-0.759422\pi$
$863$	−29.8181	+	7.98974i	−1.01502	+	0.271974i	−0.287294	+	0.957842i	$0.592756\pi$
$864$	−26.5841	−	8.45404i	−0.904410	−	0.287612i
$865$	7.77195	−	26.2616i	0.264254	−	0.892921i
$866$	−58.8998	−	34.0058i	−2.00150	−	1.15557i
$867$	−23.8245	−	14.2476i	−0.809123	−	0.483875i
$868$	12.9321	+	48.2634i	0.438945	+	1.63816i
$869$	−8.44881	−	14.6338i	−0.286606	−	0.496416i
$870$	22.9929	+	102.580i	0.779533	+	3.47779i
$871$	10.8700	−	18.8274i	0.368316	−	0.637943i
$872$	4.87397	+	18.1899i	0.165053	+	0.615988i
$873$	17.6826	−	4.16017i	0.598465	−	0.140800i
$874$		−	52.5142i		−	1.77632i
$875$	−14.7570	+	41.7713i	−0.498877	+	1.41213i
$876$	14.0812	−	3.54206i	0.475759	−	0.119675i
$877$	−17.7907	−	17.7907i	−0.600749	−	0.600749i	0.339762	−	0.940511i	$-0.389653\pi$
$877$	−17.7907	−	17.7907i	−0.600749	−	0.600749i	−0.940511	+	0.339762i	$0.889653\pi$
$878$	−29.3234	−	29.3234i	−0.989618	−	0.989618i
$879$	−4.08754	+	1.02821i	−0.137869	+	0.0346805i
$880$	29.6898	−	16.1298i	1.00084	−	0.543736i
$881$	28.8955	−	16.6828i	0.973513	−	0.562058i	0.0732075	−	0.997317i	$-0.476676\pi$
$881$	28.8955	−	16.6828i	0.973513	−	0.562058i	0.900305	+	0.435259i	$0.143343\pi$
$882$	−45.4904	−	48.3761i	−1.53174	−	1.62891i
$883$	12.0448	+	3.22738i	0.405338	+	0.108610i	0.455727	−	0.890120i	$-0.349379\pi$
$883$	12.0448	+	3.22738i	0.405338	+	0.108610i	−0.0503886	+	0.998730i	$0.516046\pi$
$884$	−8.63775	−	14.9610i	−0.290519	−	0.503194i
$885$	−8.71032	+	13.7432i	−0.292794	+	0.461972i
$886$	29.2566	−	50.6740i	0.982896	−	1.70243i
$887$	−37.6934	+	37.6934i	−1.26562	+	1.26562i	−0.317291	+	0.948328i	$0.602773\pi$
$887$	−37.6934	+	37.6934i	−1.26562	+	1.26562i	−0.948328	+	0.317291i	$0.897227\pi$
$888$	−61.5065	−	24.6266i	−2.06402	−	0.826414i
$889$			34.9717i			1.17291i
$890$	−18.3482	+	17.4204i	−0.615032	+	0.583934i
$891$	17.2567	−	8.59571i	0.578120	−	0.287967i
$892$	−21.1473	+	78.9227i	−0.708064	+	2.64253i
$893$	12.3919	−	46.2471i	0.414679	−	1.54760i
$894$	−17.6443	+	17.1102i	−0.590113	+	0.572250i
$895$	2.40119	−	3.92057i	0.0802628	−	0.131050i
$896$			47.0872i			1.57307i
$897$	10.6091	−	17.7402i	0.354226	−	0.592328i
$898$	20.4677	−	20.4677i	0.683016	−	0.683016i
$899$	30.0860			1.00343
$900$	−60.6607	+	28.6323i	−2.02202	+	0.954409i
$901$	5.98178	+	10.3607i	0.199282	+	0.345166i
$902$	26.2941	−	26.2941i	0.875496	−	0.875496i
$903$	3.51452	−	5.87690i	0.116956	−	0.195571i
$904$	−12.8767	−	7.43435i	−0.428272	−	0.247263i
$905$	46.9894	+	1.21878i	1.56198	+	0.0405135i
$906$	−23.3745	−	6.64977i	−0.776566	−	0.220924i
$907$	1.60949	−	6.00671i	0.0534423	−	0.199449i	−0.934043	−	0.357161i	$-0.883745\pi$
$907$	1.60949	−	6.00671i	0.0534423	−	0.199449i	0.987485	+	0.157711i	$0.0504115\pi$
$908$	48.9960	−	13.1284i	1.62599	−	0.435683i
$909$	11.6657	+	7.22201i	0.386927	+	0.239539i
$910$	64.0214	−	60.7843i	2.12229	−	2.01498i
$911$		−	29.6237i		−	0.981477i	−0.871307	−	0.490738i	$-0.836727\pi$
$911$		−	29.6237i		−	0.981477i	0.871307	−	0.490738i	$-0.163273\pi$
$912$	72.3089	−	40.2790i	2.39439	−	1.33377i
$913$	6.91439	+	25.8049i	0.228833	+	0.854017i
$914$	11.8262			0.391178
$915$	11.8670	+	22.6669i	0.392311	+	0.749344i
$916$	−56.2438	+	97.4171i	−1.85835	+	3.21875i
$917$	−12.1940	+	12.1940i	−0.402680	+	0.402680i
$918$	−11.5803	+	5.99207i	−0.382206	+	0.197768i
$919$			31.4801i			1.03843i	0.854643	+	0.519216i	$0.173776\pi$
$919$			31.4801i			1.03843i	−0.854643	+	0.519216i	$0.826224\pi$
$920$	−36.5385	−	22.3783i	−1.20464	−	0.737792i
$921$	10.6168	−	37.3190i	0.349835	−	1.22970i
$922$	2.71680	−	10.1392i	0.0894731	−	0.333918i
$923$	−24.8983	+	6.67149i	−0.819539	+	0.219595i
$924$	45.7682	+	47.1969i	1.50566	+	1.55266i
$925$	−28.3769	+	10.9430i	−0.933027	+	0.359805i
$926$			24.4658i			0.803997i
$927$	−4.85320	−	20.6283i	−0.159400	−	0.677522i
$928$	−55.3285	−	14.8252i	−1.81625	−	0.486662i
$929$	3.36721	+	5.83217i	0.110474	+	0.191347i	0.915962	−	0.401266i	$-0.131430\pi$
$929$	3.36721	+	5.83217i	0.110474	+	0.191347i	−0.805487	+	0.592613i	$0.798096\pi$
$930$	6.07670	+	27.1104i	0.199263	+	0.888986i
$931$	58.9437			1.93180
$932$	−32.2262	−	8.63500i	−1.05561	−	0.282849i
$933$	−0.762554	+	49.6217i	−0.0249649	+	1.62454i
$934$	−56.1942	−	32.4438i	−1.83873	−	1.06159i
$935$	1.34073	−	4.53034i	0.0438464	−	0.148158i
$936$	73.8526	+	2.27037i	2.41395	+	0.0742094i
$937$	10.0120	−	2.68270i	0.327077	−	0.0876399i	−0.0915442	−	0.995801i	$-0.529180\pi$
$937$	10.0120	−	2.68270i	0.327077	−	0.0876399i	0.418621	+	0.908161i	$0.362514\pi$
$938$	14.4821	−	54.0480i	0.472858	−	1.76473i
$939$	9.09735	−	8.82198i	0.296881	−	0.287894i
$940$	−48.6598	−	51.2512i	−1.58711	−	1.67163i
$941$	7.04406	+	4.06689i	0.229630	+	0.132577i	0.610401	−	0.792092i	$-0.291008\pi$
$941$	7.04406	+	4.06689i	0.229630	+	0.132577i	−0.380771	+	0.924669i	$0.624342\pi$
$942$	27.7377	−	46.3823i	0.903744	−	1.51122i
$943$	−20.0838	−	5.38144i	−0.654019	−	0.175244i
$944$	−14.8177	−	25.6650i	−0.482274	−	0.835323i
$945$	−30.1274	−	34.8132i	−0.980045	−	1.13247i
$946$	−2.71859	+	4.70874i	−0.0883890	+	0.153094i
$947$	−0.175652	−	0.655541i	−0.00570792	−	0.0213022i	0.963013	−	0.269454i	$-0.0868434\pi$
$947$	−0.175652	−	0.655541i	−0.00570792	−	0.0213022i	−0.968721	+	0.248152i	$0.920177\pi$
$948$	−61.0922	−	0.938825i	−1.98418	−	0.0304916i
$949$	−6.35831	+	3.67097i	−0.206399	+	0.119165i
$950$	26.5875	−	81.9665i	0.862612	−	2.65934i
$951$	8.84525	−	8.57751i	0.286827	−	0.278145i
$952$	−17.3792	−	17.3792i	−0.563264	−	0.563264i
$953$	19.5235	−	5.23131i	0.632428	−	0.169459i	0.0716569	−	0.997429i	$-0.477171\pi$
$953$	19.5235	−	5.23131i	0.632428	−	0.169459i	0.560771	+	0.827971i	$0.310505\pi$
$954$	−92.5244	−	2.84438i	−2.99559	−	0.0920902i
$955$	22.3663	+	13.6985i	0.723757	+	0.443272i
$956$			86.2971i			2.79105i
$957$	34.5831	−	19.2642i	1.11791	−	0.622722i
$958$	−61.6339	−	16.5147i	−1.99130	−	0.533567i
$959$	−18.1416	−	31.4221i	−0.585821	−	1.01467i
$960$	−0.0720449	+	1.74354i	−0.00232524	+	0.0562724i
$961$	−23.0487			−0.743506
$962$	60.2811	+	6.27223i	1.94354	+	0.202225i
$963$	25.0582	−	23.5635i	0.807489	−	0.759322i
$964$	89.5621	+	51.7087i	2.88460	+	1.66543i
$965$	−8.41236	−	35.0017i	−0.270803	−	1.12674i
$966$	14.5576	−	51.1712i	0.468383	−	1.64641i
$967$	−1.53190	+	5.71714i	−0.0492627	+	0.183851i	−0.986173	−	0.165719i	$-0.947006\pi$
$967$	−1.53190	+	5.71714i	−0.0492627	+	0.183851i	0.936910	+	0.349570i	$0.113672\pi$
$968$	28.5091	+	28.5091i	0.916317	+	0.916317i
$969$	3.16690	−	11.1319i	0.101736	−	0.357610i
$970$	16.4432	+	30.2666i	0.527959	+	0.971803i
$971$	42.5448	+	24.5632i	1.36533	+	0.788271i	0.990327	−	0.138754i	$-0.0443097\pi$
$971$	42.5448	+	24.5632i	1.36533	+	0.788271i	0.374999	+	0.927025i	$0.377643\pi$
$972$	5.35060	−	69.5044i	0.171621	−	2.22935i
$973$	−43.9981	+	43.9981i	−1.41051	+	1.41051i
$974$	23.2090	−	40.1992i	0.743666	−	1.28807i
$975$	25.5408	−	22.3184i	0.817961	−	0.714762i
$976$	−46.6002			−1.49164
$977$	−7.25628	−	27.0808i	−0.232149	−	0.866392i	−0.979413	−	0.201865i	$-0.935300\pi$
$977$	−7.25628	−	27.0808i	−0.232149	−	0.866392i	0.747264	−	0.664527i	$-0.231367\pi$
$978$	53.0984	+	31.7541i	1.69790	+	1.01538i
$979$	8.25095	+	4.76369i	0.263701	+	0.152248i
$980$	45.4412	−	74.1947i	1.45157	−	2.37006i
$981$	−7.91456	+	4.25072i	−0.252693	+	0.135715i
$982$	77.3587	−	20.7282i	2.46862	−	0.661464i
$983$	43.5861	−	11.6789i	1.39018	−	0.372498i	0.515372	−	0.856966i	$-0.327654\pi$
$983$	43.5861	−	11.6789i	1.39018	−	0.372498i	0.874809	+	0.484469i	$0.160987\pi$
$984$	−18.1308	−	72.0776i	−0.577990	−	2.29775i
$985$	38.9592	+	11.5297i	1.24134	+	0.367367i
$986$	−23.1861	+	13.3865i	−0.738397	+	0.426314i
$987$	24.8953	−	41.6293i	0.792426	−	1.32507i
$988$	−83.8984	+	83.8984i	−2.66916	+	2.66916i
$989$	3.04021			0.0966730
$990$	24.3439	+	27.2717i	0.773699	+	0.866753i
$991$	−27.3204			−0.867860			−0.433930	−	0.900947i	$-0.642873\pi$
$991$	−27.3204			−0.867860			−0.433930	+	0.900947i	$0.642873\pi$
$992$	−14.6225	−	3.91810i	−0.464266	−	0.124400i
$993$	26.6258	+	0.409168i	0.844944	+	0.0129846i
$994$	−57.4557	+	33.1721i	−1.82238	+	1.05215i
$995$	3.77167	+	2.30999i	0.119570	+	0.0732317i
$996$	92.9116	+	26.4322i	2.94402	+	0.837537i
$997$	9.39431	−	2.51720i	0.297521	−	0.0797204i	−0.106971	−	0.994262i	$-0.534115\pi$
$997$	9.39431	−	2.51720i	0.297521	−	0.0797204i	0.404492	+	0.914542i	$0.367449\pi$
$998$	−29.7388	−	29.7388i	−0.941366	−	0.941366i
$999$	4.71626	−	31.2531i	0.149216	−	0.988805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bi.a.47.3	✓	288
3.2	odd	2	inner	555.2.bi.a.47.70	yes	288
5.3	odd	4	inner	555.2.bi.a.158.3	yes	288
15.8	even	4	inner	555.2.bi.a.158.70	yes	288
37.26	even	3	inner	555.2.bi.a.137.70	yes	288
111.26	odd	6	inner	555.2.bi.a.137.3	yes	288
185.63	odd	12	inner	555.2.bi.a.248.70	yes	288
555.248	even	12	inner	555.2.bi.a.248.3	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bi.a.47.3	✓	288	1.1	even	1	trivial
555.2.bi.a.47.70	yes	288	3.2	odd	2	inner
555.2.bi.a.137.3	yes	288	111.26	odd	6	inner
555.2.bi.a.137.70	yes	288	37.26	even	3	inner
555.2.bi.a.158.3	yes	288	5.3	odd	4	inner
555.2.bi.a.158.70	yes	288	15.8	even	4	inner
555.2.bi.a.248.3	yes	288	555.248	even	12	inner
555.2.bi.a.248.70	yes	288	185.63	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bi (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.658434 - 2.45731i) q^{2} +(-0.842875 - 1.51313i) q^{3} +(-3.87278 + 2.23595i) q^{4} +(1.16787 - 1.90685i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(1.02555 - 3.82742i) q^{7} +(4.44664 + 4.44664i) q^{8} +(-1.57912 + 2.55076i) q^{9} +O(q^{10})\)	\(q+(-0.658434 - 2.45731i) q^{2} +(-0.842875 - 1.51313i) q^{3} +(-3.87278 + 2.23595i) q^{4} +(1.16787 - 1.90685i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(1.02555 - 3.82742i) q^{7} +(4.44664 + 4.44664i) q^{8} +(-1.57912 + 2.55076i) q^{9} +(-5.45469 - 1.61428i) q^{10} +2.14211i q^{11} +(6.64755 + 3.97539i) q^{12} +(-3.78308 - 1.01367i) q^{13} -10.0804 q^{14} +(-3.86968 - 0.159900i) q^{15} +(3.52705 - 6.10903i) q^{16} +(-0.255289 - 0.952752i) q^{17} +(7.30775 + 2.20089i) q^{18} +(-5.86684 + 3.38722i) q^{19} +(-0.259272 + 9.99611i) q^{20} +(-6.65579 + 1.67424i) q^{21} +(5.26382 - 1.41044i) q^{22} +(-2.15463 - 2.15463i) q^{23} +(2.98038 - 10.4763i) q^{24} +(-2.27217 - 4.45390i) q^{25} +9.96365i q^{26} +(5.19063 + 0.239450i) q^{27} +(4.58617 + 17.1158i) q^{28} +10.6695 q^{29} +(2.15501 + 9.61428i) q^{30} +2.81981 q^{31} +(-5.18565 - 1.38949i) q^{32} +(3.24129 - 1.80553i) q^{33} +(-2.17311 + 1.25465i) q^{34} +(-6.10061 - 6.42550i) q^{35} +(0.412230 - 13.4094i) q^{36} +(0.629511 - 6.05010i) q^{37} +(12.1864 + 12.1864i) q^{38} +(1.65485 + 6.57870i) q^{39} +(13.6722 - 3.28599i) q^{40} +(5.90944 - 3.41181i) q^{41} +(8.49652 + 15.2530i) q^{42} +(-0.705507 + 0.705507i) q^{43} +(-4.78965 - 8.29591i) q^{44} +(3.01971 + 5.99011i) q^{45} +(-3.87590 + 6.71326i) q^{46} +(-4.99749 + 4.99749i) q^{47} +(-12.2166 - 0.187737i) q^{48} +(-7.53519 - 4.35044i) q^{49} +(-9.44855 + 8.51601i) q^{50} +(-1.22646 + 1.18934i) q^{51} +(16.9176 - 4.53305i) q^{52} +(-11.7157 + 3.13921i) q^{53} +(-2.82929 - 12.9126i) q^{54} +(4.08468 + 2.50170i) q^{55} +(21.5794 - 12.4589i) q^{56} +(10.0703 + 6.02229i) q^{57} +(-7.02519 - 26.2184i) q^{58} +(2.10057 - 3.63830i) q^{59} +(15.3440 - 8.03316i) q^{60} +(-3.30306 - 5.72107i) q^{61} +(-1.85666 - 6.92914i) q^{62} +(8.14334 + 8.65991i) q^{63} -0.450563i q^{64} +(-6.35107 + 6.02994i) q^{65} +(-6.57092 - 6.77602i) q^{66} +(-1.43666 + 5.36169i) q^{67} +(3.11898 + 3.11898i) q^{68} +(-1.44415 + 5.07631i) q^{69} +(-11.7726 + 19.2218i) q^{70} +(5.69974 - 3.29075i) q^{71} +(-18.3641 + 4.32051i) q^{72} +(1.32554 - 1.32554i) q^{73} +(-15.2815 + 2.43669i) q^{74} +(-4.82418 + 7.19217i) q^{75} +(15.1473 - 26.2359i) q^{76} +(8.19874 + 2.19685i) q^{77} +(15.0763 - 8.39811i) q^{78} +(-6.83148 + 3.94416i) q^{79} +(-7.52988 - 13.8601i) q^{80} +(-4.01274 - 8.05593i) q^{81} +(-12.2749 - 12.2749i) q^{82} +(12.0465 - 3.22785i) q^{83} +(22.0329 - 21.3660i) q^{84} +(-2.11490 - 0.625890i) q^{85} +(2.19818 + 1.26912i) q^{86} +(-8.99309 - 16.1444i) q^{87} +(-9.52519 + 9.52519i) q^{88} +(2.22383 - 3.85179i) q^{89} +(12.7313 - 11.3644i) q^{90} +(-7.75951 + 13.4399i) q^{91} +(13.1620 + 3.52675i) q^{92} +(-2.37674 - 4.26673i) q^{93} +(15.5709 + 8.98987i) q^{94} +(-0.392769 + 15.1430i) q^{95} +(2.26838 + 9.01773i) q^{96} +(-4.28162 - 4.28162i) q^{97} +(-5.72896 + 21.3808i) q^{98} +(-5.46400 - 3.38265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 16 q^{6} - 4 q^{7}+O(q^{10}) \) 288 * q - 16 * q^6 - 4 * q^7	\( 288 q - 16 q^{6} - 4 q^{7} - 16 q^{10} - 18 q^{12} - 20 q^{13} + 6 q^{15} + 112 q^{16} + 20 q^{18} - 4 q^{21} - 12 q^{22} - 36 q^{25} + 48 q^{27} - 28 q^{28} - 16 q^{30} - 80 q^{31} + 2 q^{33} - 16 q^{36} - 36 q^{37} + 8 q^{40} - 32 q^{42} - 16 q^{43} + 76 q^{45} - 24 q^{46} + 112 q^{48} + 48 q^{55} + 2 q^{57} - 60 q^{58} - 56 q^{60} + 16 q^{61} - 36 q^{63} - 36 q^{70} - 58 q^{72} - 48 q^{73} - 88 q^{75} + 16 q^{76} + 20 q^{78} - 56 q^{81} - 136 q^{82} + 144 q^{85} + 16 q^{87} + 144 q^{88} - 42 q^{90} - 22 q^{93} - 80 q^{96} + 56 q^{97}+O(q^{100}) \) 288 * q - 16 * q^6 - 4 * q^7 - 16 * q^10 - 18 * q^12 - 20 * q^13 + 6 * q^15 + 112 * q^16 + 20 * q^18 - 4 * q^21 - 12 * q^22 - 36 * q^25 + 48 * q^27 - 28 * q^28 - 16 * q^30 - 80 * q^31 + 2 * q^33 - 16 * q^36 - 36 * q^37 + 8 * q^40 - 32 * q^42 - 16 * q^43 + 76 * q^45 - 24 * q^46 + 112 * q^48 + 48 * q^55 + 2 * q^57 - 60 * q^58 - 56 * q^60 + 16 * q^61 - 36 * q^63 - 36 * q^70 - 58 * q^72 - 48 * q^73 - 88 * q^75 + 16 * q^76 + 20 * q^78 - 56 * q^81 - 136 * q^82 + 144 * q^85 + 16 * q^87 + 144 * q^88 - 42 * q^90 - 22 * q^93 - 80 * q^96 + 56 * q^97

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