LMFDB - Embedded newform 555.2.bi.a.158.3

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			158.3
Character	$\chi$	$=$	555.158
Dual form			555.2.bi.a.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45731 + 0.658434i) q^{2} +(1.51313 - 0.842875i) q^{3} +(3.87278 - 2.23595i) q^{4} +(2.23532 - 0.0579781i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(-3.82742 - 1.02555i) q^{7} +(-4.44664 + 4.44664i) q^{8} +(1.57912 - 2.55076i) q^{9} +O(q^{10})$	\(q+(-2.45731 + 0.658434i) q^{2} +(1.51313 - 0.842875i) q^{3} +(3.87278 - 2.23595i) q^{4} +(2.23532 - 0.0579781i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(-3.82742 - 1.02555i) q^{7} +(-4.44664 + 4.44664i) q^{8} +(1.57912 - 2.55076i) q^{9} +(-5.45469 + 1.61428i) q^{10} +2.14211i q^{11} +(3.97539 - 6.64755i) q^{12} +(1.01367 - 3.78308i) q^{13} +10.0804 q^{14} +(3.33346 - 1.97182i) q^{15} +(3.52705 - 6.10903i) q^{16} +(-0.952752 + 0.255289i) q^{17} +(-2.20089 + 7.30775i) q^{18} +(5.86684 - 3.38722i) q^{19} +(8.52725 - 5.22259i) q^{20} +(-6.65579 + 1.67424i) q^{21} +(-1.41044 - 5.26382i) q^{22} +(2.15463 - 2.15463i) q^{23} +(-2.98038 + 10.4763i) q^{24} +(4.99328 - 0.259199i) q^{25} +9.96365i q^{26} +(0.239450 - 5.19063i) q^{27} +(-17.1158 + 4.58617i) q^{28} -10.6695 q^{29} +(-6.89302 + 7.04023i) q^{30} +2.81981 q^{31} +(-1.38949 + 5.18565i) q^{32} +(1.80553 + 3.24129i) q^{33} +(2.17311 - 1.25465i) q^{34} +(-8.61495 - 2.07053i) q^{35} +(0.412230 - 13.4094i) q^{36} +(-6.05010 - 0.629511i) q^{37} +(-12.1864 + 12.1864i) q^{38} +(-1.65485 - 6.57870i) q^{39} +(-9.68184 + 10.1975i) q^{40} +(5.90944 - 3.41181i) q^{41} +(15.2530 - 8.49652i) q^{42} +(-0.705507 - 0.705507i) q^{43} +(4.78965 + 8.29591i) q^{44} +(3.38195 - 5.79331i) q^{45} +(-3.87590 + 6.71326i) q^{46} +(4.99749 + 4.99749i) q^{47} +(0.187737 - 12.2166i) q^{48} +(7.53519 + 4.35044i) q^{49} +(-12.0994 + 3.92467i) q^{50} +(-1.22646 + 1.18934i) q^{51} +(-4.53305 - 16.9176i) q^{52} +(-3.13921 - 11.7157i) q^{53} +(2.82929 + 12.9126i) q^{54} +(0.124195 + 4.78829i) q^{55} +(21.5794 - 12.4589i) q^{56} +(6.02229 - 10.0703i) q^{57} +(26.2184 - 7.02519i) q^{58} +(-2.10057 + 3.63830i) q^{59} +(8.50085 - 15.0899i) q^{60} +(-3.30306 - 5.72107i) q^{61} +(-6.92914 + 1.85666i) q^{62} +(-8.65991 + 8.14334i) q^{63} +0.450563i q^{64} +(2.04655 - 8.51516i) q^{65} +(-6.57092 - 6.77602i) q^{66} +(5.36169 + 1.43666i) q^{67} +(-3.11898 + 3.11898i) q^{68} +(1.44415 - 5.07631i) q^{69} +(22.5329 - 0.584442i) q^{70} +(5.69974 - 3.29075i) q^{71} +(4.32051 + 18.3641i) q^{72} +(1.32554 + 1.32554i) q^{73} +(15.2815 - 2.43669i) q^{74} +(7.33700 - 4.60091i) q^{75} +(15.1473 - 26.2359i) q^{76} +(2.19685 - 8.19874i) q^{77} +(8.39811 + 15.0763i) 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} +(3.22785 + 12.0465i) q^{83} +(-22.0329 + 21.3660i) q^{84} +(-2.11490 + 0.625890i) q^{85} +(2.19818 + 1.26912i) q^{86} +(-16.1444 + 8.99309i) q^{87} +(-9.52519 - 9.52519i) q^{88} +(-2.22383 + 3.85179i) q^{89} +(-4.49599 + 16.4627i) q^{90} +(-7.75951 + 13.4399i) q^{91} +(3.52675 - 13.1620i) q^{92} +(4.26673 - 2.37674i) q^{93} +(-15.5709 - 8.98987i) q^{94} +(12.9179 - 7.91166i) q^{95} +(2.26838 + 9.01773i) q^{96} +(-4.28162 + 4.28162i) q^{97} +(-21.3808 - 5.72896i) 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 $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.45731	+	0.658434i	−1.73758	+	0.465583i	−0.981907	−	0.189366i	$-0.939357\pi$
$2$	−2.45731	+	0.658434i	−1.73758	+	0.465583i	−0.755673	+	0.654949i	$0.772690\pi$
$3$	1.51313	−	0.842875i	0.873606	−	0.486634i
$3$	1.51313	−	0.842875i	0.873606	−	0.486634i
$4$	3.87278	−	2.23595i	1.93639	−	1.11798i
$5$	2.23532	−	0.0579781i	0.999664	−	0.0259286i
$5$	2.23532	−	0.0579781i	0.999664	−	0.0259286i
$6$	−3.16325	+	3.06750i	−1.29139	+	1.25230i
$7$	−3.82742	−	1.02555i	−1.44663	−	0.387623i	−0.551778	−	0.833991i	$-0.686051\pi$
$7$	−3.82742	−	1.02555i	−1.44663	−	0.387623i	−0.894850	+	0.446368i	$0.852717\pi$
$8$	−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	$0.895330\pi$
$12$	3.97539	−	6.64755i	1.14760	−	1.91898i
$13$	1.01367	−	3.78308i	0.281143	−	1.04924i	−0.670469	−	0.741937i	$-0.733907\pi$
$13$	1.01367	−	3.78308i	0.281143	−	1.04924i	0.951612	−	0.307302i	$-0.0994261\pi$
$14$	10.0804			2.69410
$15$	3.33346	−	1.97182i	0.860694	−	0.509122i
$16$	3.52705	−	6.10903i	0.881763	−	1.52726i
$17$	−0.952752	+	0.255289i	−0.231076	+	0.0619167i	−0.372499	−	0.928033i	$-0.621499\pi$
$17$	−0.952752	+	0.255289i	−0.231076	+	0.0619167i	0.141423	+	0.989949i	$0.454832\pi$
$18$	−2.20089	+	7.30775i	−0.518755	+	1.72245i
$19$	5.86684	−	3.38722i	1.34595	−	0.777082i	0.358274	−	0.933617i	$-0.383365\pi$
$19$	5.86684	−	3.38722i	1.34595	−	0.777082i	0.987673	+	0.156534i	$0.0500321\pi$
$20$	8.52725	−	5.22259i	1.90675	−	1.16781i
$21$	−6.65579	+	1.67424i	−1.45241	+	0.365349i
$22$	−1.41044	−	5.26382i	−0.300706	−	1.12225i
$23$	2.15463	−	2.15463i	0.449270	−	0.449270i	−0.445841	−	0.895112i	$-0.647095\pi$
$23$	2.15463	−	2.15463i	0.449270	−	0.449270i	0.895112	+	0.445841i	$0.147095\pi$
$24$	−2.98038	+	10.4763i	−0.608368	+	2.13847i
$25$	4.99328	−	0.259199i	0.998655	−	0.0518397i
$26$			9.96365i			1.95403i
$27$	0.239450	−	5.19063i	0.0460821	−	0.998938i
$28$	−17.1158	+	4.58617i	−3.23459	+	0.866705i
$29$	−10.6695			−1.98128			−0.990642	−	0.136485i	$-0.956419\pi$
$29$	−10.6695			−1.98128			−0.990642	+	0.136485i	$0.956419\pi$
$30$	−6.89302	+	7.04023i	−1.25849	+	1.28536i
$31$	2.81981			0.506452			0.253226	−	0.967407i	$-0.418508\pi$
$31$	2.81981			0.506452			0.253226	+	0.967407i	$0.418508\pi$
$32$	−1.38949	+	5.18565i	−0.245630	+	0.916703i
$33$	1.80553	+	3.24129i	0.314302	+	0.564236i
$34$	2.17311	−	1.25465i	0.372686	−	0.215170i
$35$	−8.61495	−	2.07053i	−1.45619	−	0.349983i
$36$	0.412230	−	13.4094i	0.0687051	−	2.23489i
$37$	−6.05010	−	0.629511i	−0.994630	−	0.103491i
$37$	−6.05010	−	0.629511i	−0.994630	−	0.103491i
$38$	−12.1864	+	12.1864i	−1.97689	+	1.97689i
$39$	−1.65485	−	6.57870i	−0.264987	−	1.05343i
$40$	−9.68184	+	10.1975i	−1.53083	+	1.61236i
$41$	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	$0.154460\pi$
$42$	15.2530	−	8.49652i	2.35358	−	1.31104i
$43$	−0.705507	−	0.705507i	−0.107589	−	0.107589i	0.651263	−	0.758852i	$-0.274239\pi$
$43$	−0.705507	−	0.705507i	−0.107589	−	0.107589i	−0.758852	+	0.651263i	$0.774239\pi$
$44$	4.78965	+	8.29591i	0.722067	+	1.25066i
$45$	3.38195	−	5.79331i	0.504152	−	0.863615i
$46$	−3.87590	+	6.71326i	−0.571471	+	0.989816i
$47$	4.99749	+	4.99749i	0.728959	+	0.728959i	0.970412	−	0.241453i	$-0.0776240\pi$
$47$	4.99749	+	4.99749i	0.728959	+	0.728959i	−0.241453	+	0.970412i	$0.577624\pi$
$48$	0.187737	−	12.2166i	0.0270975	−	1.76332i
$49$	7.53519	+	4.35044i	1.07646	+	0.621492i
$50$	−12.0994	+	3.92467i	−1.71111	+	0.555033i
$51$	−1.22646	+	1.18934i	−0.171739	+	0.166540i
$52$	−4.53305	−	16.9176i	−0.628621	−	2.34605i
$53$	−3.13921	−	11.7157i	−0.431204	−	1.60927i	−0.749991	−	0.661448i	$-0.769942\pi$
$53$	−3.13921	−	11.7157i	−0.431204	−	1.60927i	0.318788	−	0.947826i	$-0.396724\pi$
$54$	2.82929	+	12.9126i	0.385017	+	1.75719i
$55$	0.124195	+	4.78829i	0.0167465	+	0.645653i
$56$	21.5794	−	12.4589i	2.88367	−	1.66489i
$57$	6.02229	−	10.0703i	0.797672	−	1.33385i
$58$	26.2184	−	7.02519i	3.44264	−	0.922452i
$59$	−2.10057	+	3.63830i	−0.273472	+	0.473667i	−0.969748	−	0.244107i	$-0.921505\pi$
$59$	−2.10057	+	3.63830i	−0.273472	+	0.473667i	0.696277	+	0.717773i	$0.254839\pi$
$60$	8.50085	−	15.0899i	1.09745	−	1.94809i
$61$	−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	$0.972326\pi$
$62$	−6.92914	+	1.85666i	−0.880001	+	0.235796i
$63$	−8.65991	+	8.14334i	−1.09105	+	1.02596i
$64$			0.450563i			0.0563204i
$65$	2.04655	−	8.51516i	0.253843	−	1.05618i
$66$	−6.57092	−	6.77602i	−0.808824	−	0.834071i
$67$	5.36169	+	1.43666i	0.655034	+	0.175516i	0.571004	−	0.820947i	$-0.306554\pi$
$67$	5.36169	+	1.43666i	0.655034	+	0.175516i	0.0840304	+	0.996463i	$0.473221\pi$
$68$	−3.11898	+	3.11898i	−0.378232	+	0.378232i
$69$	1.44415	−	5.07631i	0.173855	−	0.611116i
$70$	22.5329	−	0.584442i	2.69320	−	0.0698542i
$71$	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	$0.205622\pi$
$72$	4.32051	+	18.3641i	0.509177	+	2.16423i
$73$	1.32554	+	1.32554i	0.155143	+	0.155143i	0.780411	−	0.625267i	$-0.215010\pi$
$73$	1.32554	+	1.32554i	0.155143	+	0.155143i	−0.625267	+	0.780411i	$0.715010\pi$
$74$	15.2815	−	2.43669i	1.77643	−	0.283259i
$75$	7.33700	−	4.60091i	0.847204	−	0.531267i
$76$	15.1473	−	26.2359i	1.73752	−	3.00947i
$77$	2.19685	−	8.19874i	0.250354	−	0.934333i
$78$	8.39811	+	15.0763i	0.950898	+	1.70705i
$79$	6.83148	−	3.94416i	0.768601	−	0.443752i	−0.0637741	−	0.997964i	$-0.520314\pi$
$79$	6.83148	−	3.94416i	0.768601	−	0.443752i	0.832375	+	0.554212i	$0.186980\pi$
$80$	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
$83$	3.22785	+	12.0465i	0.354302	+	1.32227i	0.881360	+	0.472444i	$0.156628\pi$
$83$	3.22785	+	12.0465i	0.354302	+	1.32227i	−0.527058	+	0.849829i	$0.676705\pi$
$84$	−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
$87$	−16.1444	+	8.99309i	−1.73086	+	0.964160i
$88$	−9.52519	−	9.52519i	−1.01539	−	1.01539i
$89$	−2.22383	+	3.85179i	−0.235726	+	0.408289i	−0.959483	−	0.281765i	$-0.909080\pi$
$89$	−2.22383	+	3.85179i	−0.235726	+	0.408289i	0.723758	+	0.690054i	$0.242413\pi$
$90$	−4.49599	+	16.4627i	−0.473919	+	1.73532i
$91$	−7.75951	+	13.4399i	−0.813418	+	1.40888i
$92$	3.52675	−	13.1620i	0.367690	−	1.37224i
$93$	4.26673	−	2.37674i	0.442440	−	0.246457i
$94$	−15.5709	−	8.98987i	−1.60602	−	0.927234i
$95$	12.9179	−	7.91166i	1.32535	−	0.811720i
$96$	2.26838	+	9.01773i	0.231515	+	0.920369i
$97$	−4.28162	+	4.28162i	−0.434733	+	0.434733i	−0.890235	−	0.455502i	$-0.849460\pi$
$97$	−4.28162	+	4.28162i	−0.434733	+	0.434733i	0.455502	+	0.890235i	$0.349460\pi$
$98$	−21.3808	−	5.72896i	−2.15978	−	0.578712i
$99$	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	$-0.0730671\pi$
$102$	2.23069	−	3.73011i	0.220871	−	0.369336i
$103$	−4.99488	−	4.99488i	−0.492161	−	0.492161i	0.416826	−	0.908986i	$-0.363143\pi$
$103$	−4.99488	−	4.99488i	−0.492161	−	0.492161i	−0.908986	+	0.416826i	$0.863143\pi$
$104$	12.3146	+	21.3295i	1.20754	+	2.09153i
$105$	−14.7807	+	4.12834i	−1.44245	+	0.402885i
$106$	15.4280	+	26.7221i	1.49850	+	2.59548i
$107$	−2.96753	+	11.0750i	−0.286882	+	1.07066i	0.660572	+	0.750763i	$0.270314\pi$
$107$	−2.96753	+	11.0750i	−0.286882	+	1.07066i	−0.947453	+	0.319894i	$0.896353\pi$
$108$	−10.6787	−	20.6376i	−1.02755	−	1.98585i
$109$	−2.59340	−	1.49730i	−0.248403	−	0.143416i	0.370630	−	0.928781i	$-0.379142\pi$
$109$	−2.59340	−	1.49730i	−0.248403	−	0.143416i	−0.619033	+	0.785365i	$0.712475\pi$
$110$	−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
$113$	−0.611959	−	2.28386i	−0.0575683	−	0.214848i	0.931150	−	0.364637i	$-0.118807\pi$
$113$	−0.611959	−	2.28386i	−0.0575683	−	0.214848i	−0.988718	+	0.149790i	$0.952140\pi$
$114$	−8.16798	+	28.7112i	−0.765002	+	2.68905i
$115$	4.69135	−	4.94119i	0.437471	−	0.460768i
$116$	−41.3208	+	23.8566i	−3.83654	+	2.21503i
$117$	−8.04902	−	8.55960i	−0.744132	−	0.791335i
$118$	2.76618	−	10.3235i	0.254647	−	0.950357i
$119$	3.90839			0.358282
$120$	−6.05470	+	23.5907i	−0.552716	+	2.15352i
$121$	6.41137			0.582852
$122$	11.8836	+	11.8836i	1.07589	+	1.07589i
$123$	6.06601	−	10.1434i	0.546954	−	0.914602i
$124$	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
$127$	2.28429	+	8.52509i	0.202698	+	0.756480i	0.990139	+	0.140089i	$0.0447389\pi$
$127$	2.28429	+	8.52509i	0.202698	+	0.756480i	−0.787441	+	0.616390i	$0.788594\pi$
$128$	−3.07565	−	11.4785i	−0.271852	−	1.01456i
$129$	−1.66218	−	0.472870i	−0.146347	−	0.0416339i
$130$	0.577673	+	22.2719i	0.0506653	+	1.95337i
$131$	−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	$0.727555\pi$
$132$	14.2398	+	8.51572i	1.23941	+	0.741198i
$133$	−25.9286	+	6.94756i	−2.24830	+	0.602430i
$134$	−14.1213			−1.21989
$135$	0.234303	−	11.6166i	0.0201656	−	0.999797i
$136$	3.10137	−	5.37172i	0.265940	−	0.460622i
$137$	−6.47482	−	6.47482i	−0.553181	−	0.553181i	0.374177	−	0.927357i	$-0.377925\pi$
$137$	−6.47482	−	6.47482i	−0.553181	−	0.553181i	−0.927357	+	0.374177i	$0.877925\pi$
$138$	−0.206306	+	13.4249i	−0.0175619	+	1.14281i
$139$	13.5993	+	7.85158i	1.15348	+	0.665962i	0.949733	−	0.313062i	$-0.101355\pi$
$139$	13.5993	+	7.85158i	1.15348	+	0.665962i	0.203747	+	0.979024i	$0.434688\pi$
$140$	−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
$143$	8.10378	+	2.17140i	0.677672	+	0.181582i
$144$	−10.0130	−	18.6436i	−0.834418	−	1.55363i
$145$	−23.8498	+	0.618599i	−1.98062	+	0.0513719i
$146$	−4.13005	−	2.38449i	−0.341805	−	0.197341i
$147$	15.0686	+	0.231564i	1.24284	+	0.0190991i
$148$	−24.8383	+	11.0898i	−2.04169	+	0.911573i
$149$	−5.57789			−0.456959			−0.228479	−	0.973549i	$-0.573375\pi$
$149$	−5.57789			−0.456959			−0.228479	+	0.973549i	$0.573375\pi$
$150$	−14.9999	+	16.1368i	−1.22474	+	1.31756i
$151$	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	$0.761287\pi$
$152$	−11.0260	+	41.1495i	−0.894325	+	3.33767i
$153$	−0.853332	+	2.83337i	−0.0689878	+	0.229065i
$154$			21.5933i			1.74004i
$155$	6.30316	−	0.163487i	0.506282	−	0.0131316i
$156$	−21.1185	−	21.7777i	−1.69083	−	1.74361i
$157$	3.17441	+	11.8471i	0.253346	+	0.945499i	0.969003	+	0.247048i	$0.0794604\pi$
$157$	3.17441	+	11.8471i	0.253346	+	0.945499i	−0.715658	+	0.698451i	$0.753873\pi$
$158$	−14.1901	+	14.1901i	−1.12890	+	1.12890i
$159$	−14.6249	−	15.0814i	−1.15983	−	1.19603i
$160$	−2.80530	+	11.6721i	−0.221778	+	0.922763i
$161$	−10.4563	+	6.03697i	−0.824075	+	0.475780i
$162$	15.1648	+	17.1538i	1.19146	+	1.34773i
$163$	13.5625	−	3.63406i	1.06230	−	0.284642i	0.314972	−	0.949101i	$-0.398005\pi$
$163$	13.5625	−	3.63406i	1.06230	−	0.284642i	0.747325	+	0.664459i	$0.231338\pi$
$164$	15.2573	−	26.4264i	1.19139	−	2.06356i
$165$	4.22385	+	7.14062i	0.328826	+	0.555897i
$166$	−15.8636	−	27.4766i	−1.23126	−	2.13260i
$167$	−0.483110	+	1.80299i	−0.0373842	+	0.139520i	−0.982096	−	0.188383i	$-0.939675\pi$
$167$	−0.483110	+	1.80299i	−0.0373842	+	0.139520i	0.944711	+	0.327903i	$0.106342\pi$
$168$	22.1512	−	37.0407i	1.70900	−	2.85775i
$169$	−2.02586	−	1.16963i	−0.155836	−	0.0899718i
$170$	4.78486	−	2.93053i	0.366982	−	0.224761i
$171$	0.624484	−	20.3137i	0.0477555	−	1.55343i
$172$	−4.30975	−	1.15480i	−0.328616	−	0.0880523i
$173$	3.17003	+	11.8307i	0.241013	+	0.899473i	0.975346	+	0.220683i	$0.0708286\pi$
$173$	3.17003	+	11.8307i	0.241013	+	0.899473i	−0.734333	+	0.678790i	$0.762505\pi$
$174$	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
$177$	−0.111809	+	7.27575i	−0.00840407	+	0.546879i
$178$	2.92849	−	10.9293i	0.219500	−	0.819184i
$179$	−2.05604			−0.153676			−0.0768379	−	0.997044i	$-0.524482\pi$
$179$	−2.05604			−0.153676			−0.0768379	+	0.997044i	$0.524482\pi$
$180$	0.144016	−	29.9981i	0.0107343	−	2.23593i
$181$	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	$0.547915\pi$
$182$	10.2183	−	38.1350i	0.757427	−	2.82676i
$183$	−9.82011	−	5.87265i	−0.725923	−	0.434119i
$184$			19.1617i			1.41262i
$185$	−13.5604	−	1.05638i	−0.996979	−	0.0776669i
$186$	−8.91975	+	8.64976i	−0.654028	+	0.634231i
$187$	−0.546857	−	2.04090i	−0.0399901	−	0.149245i
$188$	30.5283	+	8.18005i	2.22651	+	0.596591i
$189$	−6.23974	+	19.6211i	−0.453875	+	1.42723i
$190$	−26.5339	+	27.9470i	−1.92497	+	2.02749i
$191$			11.7294i			0.848713i	0.905495	+	0.424356i	$0.139500\pi$
$191$			11.7294i			0.848713i	−0.905495	+	0.424356i	$0.860500\pi$
$192$	0.379769	+	0.681761i	0.0274074	+	0.0492019i
$193$	11.3837	+	11.3837i	0.819416	+	0.819416i	0.986023	−	0.166607i	$-0.0532811\pi$
$193$	11.3837	+	11.3837i	0.819416	+	0.819416i	−0.166607	+	0.986023i	$0.553281\pi$
$194$	7.70210	−	13.3404i	0.552979	−	0.957787i
$195$	−4.08052	−	14.6095i	−0.292212	−	1.04621i
$196$	38.9095			2.77925
$197$	17.5509	−	4.70275i	1.25045	−	0.335057i	0.427940	−	0.903807i	$-0.359239\pi$
$197$	17.5509	−	4.70275i	1.25045	−	0.335057i	0.822511	+	0.568750i	$0.192573\pi$
$198$	−15.6540	−	4.71454i	−1.11248	−	0.335048i
$199$		−	1.97796i		−	0.140214i	−0.997539	−	0.0701068i	$-0.977666\pi$
$199$		−	1.97796i		−	0.140214i	0.997539	−	0.0701068i	$-0.0223340\pi$
$200$	−21.0508	+	23.3559i	−1.48851	+	1.65151i
$201$	9.32385	−	2.34538i	0.657654	−	0.165430i
$202$	3.01130	+	11.2383i	0.211874	+	0.790726i
$203$	40.8368	+	10.9422i	2.86618	+	0.767991i
$204$	−2.09052	+	7.34834i	−0.146365	+	0.514487i
$205$	13.0116	−	7.96910i	0.908773	−	0.556586i
$206$	15.5628	+	8.98517i	1.08431	+	0.626027i
$207$	−2.09351	−	8.89835i	−0.145509	−	0.618478i
$208$	−19.5357	−	19.5357i	−1.35456	−	1.35456i
$209$	7.25580	+	12.5674i	0.501894	+	0.869306i
$210$	33.6026	−	19.8767i	2.31880	−	1.37163i
$211$	−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
$213$	5.85076	−	9.78349i	0.400887	−	0.670354i
$214$		−	29.1685i		−	1.99392i
$215$	−1.61794	−	1.53613i	−0.110342	−	0.104763i
$216$	22.0161	+	24.1456i	1.49801	+	1.64290i
$217$	−10.7926	−	2.89186i	−0.732648	−	0.196312i
$218$	7.35867	+	1.97175i	0.498392	+	0.133544i
$219$	3.12299	+	0.888452i	0.211032	+	0.0600360i
$220$	11.1874	+	18.2663i	0.754252	+	1.23151i
$221$			3.86312i			0.259862i
$222$	21.0690	−	16.5674i	1.41406	−	1.11193i
$223$	12.9197	+	12.9197i	0.865165	+	0.865165i	0.991932	−	0.126768i	$-0.0404603\pi$
$223$	12.9197	+	12.9197i	0.865165	+	0.865165i	−0.126768	+	0.991932i	$0.540460\pi$
$224$	10.6363	−	18.4227i	0.710670	−	1.23092i
$225$	7.22385	−	13.1459i	0.481590	−	0.876397i
$226$	3.00754	+	5.20922i	0.200059	+	0.346512i
$227$	−2.93576	+	10.9564i	−0.194853	+	0.727203i	0.797451	+	0.603383i	$0.206181\pi$
$227$	−2.93576	+	10.9564i	−0.194853	+	0.727203i	−0.992305	+	0.123820i	$0.960486\pi$
$228$	0.806259	−	52.4657i	0.0533958	−	3.47463i
$229$	−21.7843	+	12.5771i	−1.43954	+	0.831121i	−0.997818	−	0.0660284i	$-0.978967\pi$
$229$	−21.7843	+	12.5771i	−1.43954	+	0.831121i	−0.441727	+	0.897150i	$0.645634\pi$
$230$	−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	$-0.828584\pi$
$233$	−5.27544	+	5.27544i	−0.345606	+	0.345606i	0.512864	+	0.858470i	$0.328584\pi$
$234$	25.4149	+	15.7338i	1.66142	+	1.02855i
$235$	11.4607	+	10.8812i	0.747615	+	0.709813i
$236$			18.7871i			1.22294i
$237$	7.01248	−	11.7261i	0.455510	−	0.761692i
$238$	−9.60412	+	2.57342i	−0.622543	+	0.166810i
$239$	−9.64882	+	16.7122i	−0.624130	+	1.08102i	0.364578	+	0.931173i	$0.381213\pi$
$239$	−9.64882	+	16.7122i	−0.624130	+	1.08102i	−0.988708	+	0.149852i	$0.952120\pi$
$240$	−0.288644	−	27.3189i	−0.0186319	−	1.76343i
$241$	−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	$-0.434141\pi$
$242$	−15.7547	+	4.22147i	−1.01275	+	0.271366i
$243$	−12.8619	−	8.80743i	−0.825093	−	0.564997i
$244$	−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
$247$	−6.86708	−	25.6283i	−0.436942	−	1.63069i
$248$	−12.5387	+	12.5387i	−0.796206	+	0.796206i
$249$	15.0378	+	15.5072i	0.952984	+	0.982731i
$250$	−26.8183	+	9.47438i	−1.69614	+	0.599213i
$251$		−	22.4404i		−	1.41643i	−0.705998	−	0.708214i	$-0.749501\pi$
$251$		−	22.4404i		−	1.41643i	0.705998	−	0.708214i	$-0.250499\pi$
$252$	−15.3298	+	50.9005i	−0.965687	+	3.20643i
$253$	4.61544	+	4.61544i	0.290170	+	0.290170i
$254$	−11.2264	−	19.4447i	−0.704408	−	1.22007i
$255$	−2.67257	+	2.72965i	−0.167363	+	0.170937i
$256$	14.6651	+	25.4007i	0.916567	+	1.58754i
$257$	−14.1842	+	3.80065i	−0.884786	+	0.237078i	−0.672471	−	0.740123i	$-0.734767\pi$
$257$	−14.1842	+	3.80065i	−0.884786	+	0.237078i	−0.212315	+	0.977201i	$0.568100\pi$
$258$	4.39584	+	0.0675524i	0.273673	+	0.00420563i
$259$	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
$262$	10.6944	+	2.86556i	0.660704	+	0.177035i
$263$	2.91404	+	0.780816i	0.179688	+	0.0481472i	0.347541	−	0.937665i	$-0.387017\pi$
$263$	2.91404	+	0.780816i	0.179688	+	0.0481472i	−0.167853	+	0.985812i	$0.553683\pi$
$264$	−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
$267$	−0.118370	+	7.70267i	−0.00724410	+	0.471396i
$268$	23.9769	−	6.42460i	1.46462	−	0.392445i
$269$	−3.49407			−0.213037			−0.106519	−	0.994311i	$-0.533970\pi$
$269$	−3.49407			−0.213037			−0.106519	+	0.994311i	$0.533970\pi$
$270$	7.07300	+	28.6998i	0.430449	+	1.74662i
$271$	−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	$0.281133\pi$
$272$	−1.80083	+	6.72081i	−0.109192	+	0.407509i
$273$	−0.413022	+	26.8766i	−0.0249972	+	1.62664i
$274$	20.1739	+	11.6474i	1.21875	+	0.703644i
$275$	0.555231	+	10.6961i	0.0334817	+	0.645001i
$276$	−5.75750	−	22.8885i	−0.346561	−	1.37772i
$277$	15.4873	+	4.14980i	0.930539	+	0.249337i	0.692085	−	0.721816i	$-0.256693\pi$
$277$	15.4873	+	4.14980i	0.930539	+	0.249337i	0.238455	+	0.971154i	$0.423359\pi$
$278$	−38.5875	−	10.3395i	−2.31432	−	0.620121i
$279$	4.45282	−	7.19265i	0.266584	−	0.430612i
$280$	47.5145	−	29.1007i	2.83953	−	1.73910i
$281$	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	$0.595727\pi$
$282$	−31.1381	−	0.478511i	−1.85425	−	0.0284949i
$283$	−2.91592	+	10.8823i	−0.173333	+	0.646888i	0.823496	+	0.567322i	$0.192020\pi$
$283$	−2.91592	+	10.8823i	−0.173333	+	0.646888i	−0.996830	+	0.0795668i	$0.974646\pi$
$284$	14.7159	−	25.4887i	0.873228	−	1.51247i
$285$	12.8779	−	22.8595i	0.762819	−	1.35408i
$286$	−21.3432			−1.26205
$287$	−26.1169	+	6.99800i	−1.54163	+	0.413079i
$288$	11.0332	+	11.7330i	0.650136	+	0.691376i
$289$	−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
$292$	8.09739	+	2.16969i	0.473864	+	0.126971i
$293$	2.35054	+	0.629827i	0.137320	+	0.0367949i	0.326824	−	0.945085i	$-0.394021\pi$
$293$	2.35054	+	0.629827i	0.137320	+	0.0367949i	−0.189504	+	0.981880i	$0.560688\pi$
$294$	−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
$297$	11.1189	+	0.512927i	0.645184	+	0.0297630i
$298$	13.7066	−	3.67267i	0.794002	−	0.212752i
$299$	−5.96704	−	10.3352i	−0.345083	−	0.597701i
$300$	18.1272	−	34.2235i	1.04657	−	1.97589i
$301$	1.97674	+	3.42381i	0.113937	+	0.197345i
$302$	−9.92125	−	9.92125i	−0.570904	−	0.570904i
$303$	−3.85483	−	6.92019i	−0.221454	−	0.397555i
$304$		−	47.7876i		−	2.74081i
$305$	−7.71508	−	12.5969i	−0.441764	−	0.721296i
$306$	0.231313	−	7.52433i	0.0132233	−	0.430138i
$307$	15.8399	−	15.8399i	0.904033	−	0.904033i	−0.0917488	−	0.995782i	$-0.529246\pi$
$307$	15.8399	−	15.8399i	0.904033	−	0.904033i	0.995782	+	0.0917488i	$0.0292457\pi$
$308$	−9.82408	−	36.6640i	−0.559779	−	2.08912i
$309$	−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	$0.968488\pi$
$312$	36.6116	+	21.8946i	2.07273	+	1.23954i
$313$	−7.06710	+	1.89362i	−0.399456	+	0.107034i	−0.452954	−	0.891534i	$-0.649630\pi$
$313$	−7.06710	+	1.89362i	−0.399456	+	0.107034i	0.0534975	+	0.998568i	$0.482963\pi$
$314$	−15.6010	−	27.0218i	−0.880416	−	1.52493i
$315$	−18.8855	+	18.7050i	−1.06408	+	1.05391i
$316$	17.6379	−	30.5497i	0.992208	−	1.71855i
$317$	6.87126	−	1.84115i	0.385928	−	0.103409i	−0.0606377	−	0.998160i	$-0.519313\pi$
$317$	6.87126	−	1.84115i	0.385928	−	0.103409i	0.446566	+	0.894751i	$0.352647\pi$
$318$	45.8680	+	27.4301i	2.57215	+	1.53821i
$319$		−	22.8553i		−	1.27965i
$320$	0.0261228	+	1.00715i	0.00146031	+	0.0563015i
$321$	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
$327$	−5.18620	−	0.0796981i	−0.286797	−	0.00440731i
$328$	−11.1060	+	41.4483i	−0.613228	+	2.28860i
$329$	−14.0023	−	24.2527i	−0.771972	−	1.33709i
$330$	−15.0809	−	14.7656i	−0.830178	−	0.812819i
$331$	−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
$333$	−11.1596	+	14.4383i	−0.611542	+	0.791212i
$334$		−	4.74860i		−	0.259832i
$335$	12.0684	+	2.90053i	0.659365	+	0.158473i
$336$	−13.2473	+	46.5656i	−0.722702	+	2.54036i
$337$	−15.0887	−	4.04300i	−0.821934	−	0.220236i	−0.176742	−	0.984257i	$-0.556556\pi$
$337$	−15.0887	−	4.04300i	−0.821934	−	0.220236i	−0.645192	+	0.764021i	$0.723222\pi$
$338$	5.74830	+	1.54025i	0.312666	+	0.0837787i
$339$	−2.85098	−	2.93998i	−0.154844	−	0.159678i
$340$	−6.79108	+	7.15275i	−0.368298	+	0.387912i
$341$			6.04033i			0.327102i
$342$	11.8407	+	50.3283i	0.640272	+	2.72144i
$343$	−4.76565	−	4.76565i	−0.257321	−	0.257321i
$344$	6.27428			0.338286
$345$	2.93381	−	11.4309i	0.157951	−	0.615418i
$346$	−15.5795	−	26.9845i	−0.837559	−	1.45069i
$347$	10.1193	+	10.1193i	0.543230	+	0.543230i	0.924474	−	0.381244i	$-0.124504\pi$
$347$	10.1193	+	10.1193i	0.543230	+	0.543230i	−0.381244	+	0.924474i	$0.624504\pi$
$348$	−42.4156	+	70.9263i	−2.27372	+	3.80205i
$349$	−12.1994	−	7.04335i	−0.653021	−	0.377022i	0.136591	−	0.990627i	$-0.456385\pi$
$349$	−12.1994	−	7.04335i	−0.653021	−	0.377022i	−0.789613	+	0.613605i	$0.789719\pi$
$350$	50.3343	−	2.61283i	2.69048	−	0.139661i
$351$	−19.3939	−	6.16747i	−1.03517	−	0.329195i
$352$	−11.1082	−	2.97644i	−0.592071	−	0.158645i
$353$	7.79590	+	29.0947i	0.414934	+	1.54855i	0.784968	+	0.619536i	$0.212679\pi$
$353$	7.79590	+	29.0947i	0.414934	+	1.54855i	−0.370035	+	0.929018i	$0.620654\pi$
$354$	−4.51585	−	17.9524i	−0.240015	−	0.954158i
$355$	12.5499	−	7.68632i	0.666081	−	0.407947i
$356$			19.8895i			1.05414i
$357$	5.91390	−	3.29429i	0.312997	−	0.174352i
$358$	5.05233	−	1.35377i	0.267024	−	0.0715489i
$359$	13.5708			0.716239			0.358119	−	0.933676i	$-0.383418\pi$
$359$	13.5708			0.716239			0.358119	+	0.933676i	$0.383418\pi$
$360$	10.7224	+	40.7991i	0.565121	+	2.15030i
$361$	13.4466	−	23.2901i	0.707714	−	1.22580i
$362$	−37.8148	−	37.8148i	−1.98750	−	1.98750i
$363$	9.70124	−	5.40399i	0.509183	−	0.283636i
$364$			69.3995i			3.63752i
$365$	3.03986	+	2.88616i	0.159114	+	0.151068i
$366$	27.9978	+	7.96503i	1.46347	+	0.416339i
$367$	11.4848	+	3.07735i	0.599502	+	0.160636i	0.545792	−	0.837920i	$-0.316229\pi$
$367$	11.4848	+	3.07735i	0.599502	+	0.160636i	0.0537098	+	0.998557i	$0.482895\pi$
$368$	−5.56320	−	20.7621i	−0.290002	−	1.08230i
$369$	0.629018	−	20.4612i	0.0327454	−	1.06517i
$370$	34.0176	−	6.33276i	1.76849	−	0.329224i
$371$			48.0603i			2.49516i
$372$	11.2098	−	18.7448i	0.581203	−	0.971873i
$373$	4.40629	−	16.4445i	0.228149	−	0.851464i	−0.752969	−	0.658056i	$-0.771379\pi$
$373$	4.40629	−	16.4445i	0.228149	−	0.851464i	0.981118	−	0.193408i	$-0.0619542\pi$
$374$	2.68759	+	4.65505i	0.138972	+	0.240707i
$375$	16.1338	−	10.7099i	0.833144	−	0.553055i
$376$	−44.4441			−2.29203
$377$	−10.8154	+	40.3638i	−0.557024	+	2.07884i
$378$	2.41375	−	52.3237i	0.124150	−	2.69124i
$379$	5.13883	+	2.96690i	0.263964	+	0.152400i	0.626141	−	0.779709i	$-0.284633\pi$
$379$	5.13883	+	2.96690i	0.263964	+	0.152400i	−0.362178	+	0.932109i	$0.617967\pi$
$380$	32.3380	−	59.5239i	1.65890	−	3.05351i
$381$	10.6420	+	10.9742i	0.545207	+	0.562225i
$382$	−7.72307	−	28.8229i	−0.395146	−	1.47471i
$383$	26.7358	+	7.16383i	1.36613	+	0.366054i	0.866065	−	0.499931i	$-0.166641\pi$
$383$	26.7358	+	7.16383i	1.36613	+	0.366054i	0.500069	+	0.865986i	$0.333308\pi$
$384$	−14.3288	−	14.7760i	−0.731212	−	0.754037i
$385$	4.43530	−	18.4541i	0.226044	−	0.940511i
$386$	−35.4687	−	20.4778i	−1.80531	−	1.04229i
$387$	−2.91366	+	0.685495i	−0.148110	+	0.0348457i
$388$	−7.00829	+	26.1553i	−0.355792	+	1.32783i
$389$	−4.23146	−	7.32910i	−0.214543	−	0.371600i	0.738588	−	0.674157i	$-0.235493\pi$
$389$	−4.23146	−	7.32910i	−0.214543	−	0.371600i	−0.953131	+	0.302557i	$0.902160\pi$
$390$	19.6465	+	33.2134i	0.994840	+	1.68182i
$391$	−1.50277	+	2.60288i	−0.0759984	+	0.131633i
$392$	−52.8511	+	14.1614i	−2.66939	+	0.715260i
$393$	−7.53715	−	0.115826i	−0.380199	−	0.00584265i
$394$	−40.0316	+	23.1122i	−2.01676	+	1.16438i
$395$	15.0418	−	9.21251i	0.756837	−	0.463532i
$396$	28.7243	+	0.883042i	1.44345	+	0.0443745i
$397$	−14.3266	+	14.3266i	−0.719032	+	0.719032i	−0.968407	−	0.249375i	$-0.919775\pi$
$397$	−14.3266	+	14.3266i	−0.719032	+	0.719032i	0.249375	+	0.968407i	$0.419775\pi$
$398$	1.30235	+	4.86045i	0.0652811	+	0.243632i
$399$	−33.3775	+	32.3672i	−1.67096	+	1.62038i
$400$	16.0281	−	31.4183i	0.801404	−	1.57091i
$401$		−	18.1609i		−	0.906910i	−0.891279	−	0.453455i	$-0.850191\pi$
$401$		−	18.1609i		−	0.906910i	0.891279	−	0.453455i	$-0.149809\pi$
$402$	−21.3673	+	11.9025i	−1.06570	+	0.593641i
$403$	2.85837	−	10.6676i	0.142385	−	0.531389i
$404$	−10.2260	−	17.7119i	−0.508761	−	0.881199i
$405$	−9.43680	−	17.7749i	−0.468918	−	0.883242i
$406$	−107.553			−5.33778
$407$	1.34848	−	12.9600i	0.0668417	−	0.642402i
$408$	0.165079	−	10.7422i	0.00817262	−	0.531817i
$409$	24.5785	+	14.1904i	1.21533	+	0.701671i	0.963915	−	0.266208i	$-0.0857709\pi$
$409$	24.5785	+	14.1904i	1.21533	+	0.701671i	0.251414	+	0.967880i	$0.419104\pi$
$410$	−26.7265	+	28.1499i	−1.31993	+	1.39022i
$411$	−15.2547	−	4.33978i	−0.752459	−	0.214065i
$412$	−30.5124	−	8.17577i	−1.50324	−	0.402792i
$413$	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
$417$	27.1954	+	0.417922i	1.33177	+	0.0204657i
$418$	−26.1045	−	26.1045i	−1.27682	−	1.27682i
$419$	3.98331	−	6.89929i	0.194597	−	0.337052i	−0.752171	−	0.658968i	$-0.770993\pi$
$419$	3.98331	−	6.89929i	0.194597	−	0.337052i	0.946768	+	0.321915i	$0.104327\pi$
$420$	−48.0118	+	49.0372i	−2.34273	+	2.39277i
$421$	−3.39995			−0.165703			−0.0828517	−	0.996562i	$-0.526403\pi$
$421$	−3.39995			−0.165703			−0.0828517	+	0.996562i	$0.526403\pi$
$422$	67.0407	−	17.9635i	3.26349	−	0.874450i
$423$	20.6391	−	4.85574i	1.00351	−	0.236094i
$424$	66.0544	+	38.1365i	3.20789	+	1.85207i
$425$	−4.69118	+	1.52168i	−0.227556	+	0.0738124i
$426$	−7.93534	+	27.8934i	−0.384468	+	1.35144i
$427$	6.77493	+	25.2844i	0.327862	+	1.22360i
$428$	13.2705	+	49.5261i	0.641453	+	2.39394i
$429$	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	$0.124034\pi$
$432$	−30.8652	−	19.7704i	−1.48500	−	0.951205i
$433$	18.9039	+	18.9039i	0.908466	+	0.908466i	0.996148	−	0.0876826i	$-0.0279461\pi$
$433$	18.9039	+	18.9039i	0.908466	+	0.908466i	−0.0876826	+	0.996148i	$0.527946\pi$
$434$	28.4248			1.36443
$435$	−35.5664	+	21.0384i	−1.70528	+	1.00871i
$436$	−13.3916			−0.641340
$437$	5.34265	−	19.9391i	0.255574	−	0.953814i
$438$	−8.25913	−	0.126921i	−0.394636	−	0.00606451i
$439$	−14.1171	+	8.15049i	−0.673771	+	0.389002i	−0.797504	−	0.603314i	$-0.793847\pi$
$439$	−14.1171	+	8.15049i	−0.673771	+	0.389002i	0.123733	+	0.992316i	$0.460513\pi$
$440$	−21.8441	−	20.7396i	−1.04137	−	0.988719i
$441$	22.9959	−	12.3506i	1.09504	−	0.588122i
$442$	−2.54361	−	9.49288i	−0.120987	−	0.451530i
$443$	−16.2639	+	16.2639i	−0.772719	+	0.772719i	−0.978581	−	0.205862i	$-0.934000\pi$
$443$	−16.2639	+	16.2639i	−0.772719	+	0.772719i	0.205862	+	0.978581i	$0.434000\pi$
$444$	−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
$447$	−8.44008	+	4.70147i	−0.399202	+	0.222372i
$448$	0.462077	−	1.72449i	0.0218311	−	0.0814747i
$449$	−5.68903	−	9.85369i	−0.268482	−	0.465024i	0.699988	−	0.714155i	$-0.253189\pi$
$449$	−5.68903	−	9.85369i	−0.268482	−	0.465024i	−0.968470	+	0.249130i	$0.919855\pi$
$450$	−9.09549	+	37.0601i	−0.428766	+	1.74703i
$451$	7.30847	+	12.6586i	0.344143	+	0.596072i
$452$	−7.47659	−	7.47659i	−0.351669	−	0.351669i
$453$	8.19851	+	4.90290i	0.385200	+	0.230358i
$454$		−	28.8563i		−	1.35429i
$455$	−16.5657	+	30.4922i	−0.776614	+	1.42950i
$456$	18.0002	+	71.5581i	0.842935	+	3.35101i
$457$	4.49029	+	1.20317i	0.210047	+	0.0562820i	0.362308	−	0.932058i	$-0.381989\pi$
$457$	4.49029	+	1.20317i	0.210047	+	0.0562820i	−0.152261	+	0.988340i	$0.548655\pi$
$458$	45.2494	−	45.2494i	2.11437	−	2.11437i
$459$	1.09698	+	5.00651i	0.0512024	+	0.233684i
$460$	7.12030	−	29.6258i	0.331986	−	1.38131i
$461$	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	$0.636034\pi$
$462$	18.2005	+	32.6735i	0.846762	+	1.52011i
$463$	2.48909	−	9.28940i	0.115678	−	0.431715i	−0.883659	−	0.468131i	$-0.844927\pi$
$463$	2.48909	−	9.28940i	0.115678	−	0.431715i	0.999337	+	0.0364160i	$0.0115941\pi$
$464$	−37.6320	+	65.1806i	−1.74702	+	3.02593i
$465$	9.39970	−	5.56015i	0.435901	−	0.257846i
$466$	9.48986	−	16.4369i	0.439609	−	0.761425i
$467$	−18.0356	−	18.0356i	−0.834587	−	0.834587i	0.153553	−	0.988140i	$-0.450928\pi$
$467$	−18.0356	−	18.0356i	−0.834587	−	0.834587i	−0.988140	+	0.153553i	$0.950928\pi$
$468$	−50.3109	−	15.1522i	−2.32562	−	0.700412i
$469$	−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
$472$	−6.83772	−	25.5187i	−0.314732	−	1.17459i
$473$	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
$477$	−34.8411	−	10.4932i	−1.59526	−	0.480449i
$478$	12.7062	−	47.4202i	0.581169	−	2.16895i
$479$	−12.5409	+	21.7215i	−0.573010	+	0.992482i	0.423245	+	0.906015i	$0.360891\pi$
$479$	−12.5409	+	21.7215i	−0.573010	+	0.992482i	−0.996255	+	0.0864665i	$0.972442\pi$
$480$	5.59337	+	20.0260i	0.255301	+	0.914056i
$481$	−8.51433	+	22.2499i	−0.388220	+	1.01451i
$482$	41.6009	+	41.6009i	1.89487	+	1.89487i
$483$	−10.7334	+	17.9481i	−0.488386	+	0.816667i
$484$	24.8298	−	14.3355i	1.12863	−	0.651614i
$485$	−9.32254	+	9.81902i	−0.423315	+	0.445859i
$486$	37.4048	+	13.1738i	1.69672	+	0.597578i
$487$	12.9020	−	12.9020i	0.584644	−	0.584644i	−0.351532	−	0.936176i	$-0.614339\pi$
$487$	12.9020	−	12.9020i	0.584644	−	0.584644i	0.936176	+	0.351532i	$0.114339\pi$
$488$	40.1271	+	10.7520i	1.81647	+	0.486721i
$489$	17.4588	−	16.9303i	0.789513	−	0.765614i
$490$	−48.1249	−	11.5664i	−2.17406	−	0.522518i
$491$			31.4811i			1.42072i	0.703838	+	0.710361i	$0.251468\pi$
$491$			31.4811i			1.42072i	−0.703838	+	0.710361i	$0.748532\pi$
$492$	0.812112	−	52.8466i	0.0366128	−	2.38251i
$493$	10.1654	−	2.72382i	0.457828	−	0.122675i
$494$	33.7491	+	58.4551i	1.51844	+	2.63002i
$495$	12.4099	+	7.24451i	0.557783	+	0.325616i
$496$	9.94560	−	17.2263i	0.446571	−	0.773483i
$497$	−25.1901	+	6.74967i	−1.12993	+	0.302764i
$498$	−47.1631	−	28.2046i	−2.11343	−	1.26388i
$499$	−14.3170	+	8.26595i	−0.640919	+	0.370035i	−0.784969	−	0.619536i	$-0.787321\pi$
$499$	−14.3170	+	8.26595i	−0.640919	+	0.370035i	0.144049	+	0.989571i	$0.453988\pi$
$500$	41.2252	−	28.2881i	1.84365	−	1.26508i
$501$	0.788687	+	3.13536i	0.0352360	+	0.140078i
$502$	14.7756	+	55.1431i	0.659465	+	2.46116i
$503$	−8.03756	−	29.9966i	−0.358377	−	1.33748i	−0.876181	−	0.481982i	$-0.839917\pi$
$503$	−8.03756	−	29.9966i	−0.358377	−	1.33748i	0.517804	−	0.855499i	$-0.326750\pi$
$504$	2.29698	−	74.7180i	0.102316	−	3.32821i
$505$	−0.265159	−	10.2231i	−0.0117994	−	0.454920i
$506$	−14.3805	−	8.30260i	−0.639292	−	0.369096i
$507$	−4.05125	−	0.0622570i	−0.179922	−	0.00276493i
$508$	27.9082	+	27.9082i	1.23823	+	1.23823i
$509$	10.5285	−	18.2358i	0.466666	−	0.808289i	−0.532609	−	0.846361i	$-0.678788\pi$
$509$	10.5285	−	18.2358i	0.466666	−	0.808289i	0.999275	+	0.0380726i	$0.0121218\pi$
$510$	4.77004	−	8.46730i	0.211221	−	0.374939i
$511$	−3.71399	−	6.43282i	−0.164297	−	0.284571i
$512$	−35.9556	−	35.9556i	−1.58903	−	1.58903i
$513$	−16.1770	−	31.2637i	−0.714233	−	1.38033i
$514$	32.3525	−	18.6787i	1.42701	−	0.823883i
$515$	−11.4547	−	10.8756i	−0.504756	−	0.479234i
$516$	−7.49457	+	1.88523i	−0.329930	+	0.0829926i
$517$	−10.7052	+	10.7052i	−0.470813	+	0.470813i
$518$	−60.9875	−	6.34573i	−2.67964	−	0.278815i
$519$	14.7685	+	15.2295i	0.648265	+	0.668500i
$520$	28.7636	+	46.9641i	1.26137	+	2.05951i
$521$	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	$0.0925689\pi$
$522$	23.4825	−	77.9703i	1.02780	−	3.41267i
$523$	−3.69871	+	13.8038i	−0.161733	+	0.603597i	0.836701	+	0.547660i	$0.184481\pi$
$523$	−3.69871	+	13.8038i	−0.161733	+	0.603597i	−0.998434	+	0.0559370i	$0.982185\pi$
$524$	−19.4621			−0.850207
$525$	−32.8003	+	10.0851i	−1.43152	+	0.440150i
$526$	−7.67482			−0.334638
$527$	−2.68658	+	0.719866i	−0.117029	+	0.0313579i
$528$	26.1693	+	0.402153i	1.13887	+	0.0175015i
$529$			13.7152i			0.596312i
$530$	36.0358	+	58.8379i	1.56529	+	2.55575i
$531$	5.96336	+	11.1034i	0.258788	+	0.481846i
$532$	−84.8815	+	84.8815i	−3.68008	+	3.68008i
$533$	−6.91694	−	25.8144i	−0.299606	−	1.11814i
$534$	−4.78083	−	19.0058i	−0.206887	−	0.822460i
$535$	−5.99126	+	24.9281i	−0.259025	+	1.07774i
$536$	−30.2298	+	17.4532i	−1.30573	+	0.753863i
$537$	−3.11106	+	1.73299i	−0.134252	+	0.0747839i
$538$	8.58601	−	2.30061i	0.370169	−	0.0991865i
$539$	−9.31912	+	16.1412i	−0.401403	+	0.695250i
$540$	−25.0667	−	45.5124i	−1.07870	−	1.95854i
$541$	15.2900			0.657370			0.328685	−	0.944440i	$-0.393395\pi$
$541$	15.2900			0.657370			0.328685	+	0.944440i	$0.393395\pi$
$542$	7.62875	−	28.4709i	0.327683	−	1.22293i
$543$	31.2486	+	18.6874i	1.34100	+	0.801952i
$544$		−	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	0.467913	−	0.883775i	$-0.345006\pi$
$547$	31.6133	−	31.6133i	1.35169	−	1.35169i	0.883775	−	0.467913i	$-0.154994\pi$
$548$	−39.5529	−	10.5982i	−1.68962	−	0.452731i
$549$	−19.8090	−	0.608968i	−0.845428	−	0.0259901i
$550$	−8.40708	−	25.9181i	−0.358479	−	1.10515i
$551$	−62.5965	+	36.1401i	−2.66670	+	1.53962i
$552$	16.1509	+	28.9941i	0.687428	+	1.23407i
$553$	−30.1919	+	8.08989i	−1.28389	+	0.344017i
$554$	−40.7893			−1.73297
$555$	−21.4090	+	9.83126i	−0.908762	+	0.417314i
$556$	70.2229			2.97812
$557$	8.44527	−	2.26290i	0.357838	−	0.0958823i	−0.0754213	−	0.997152i	$-0.524030\pi$
$557$	8.44527	−	2.26290i	0.357838	−	0.0958823i	0.433259	+	0.901269i	$0.357364\pi$
$558$	−6.20608	+	20.6064i	−0.262724	+	0.872340i
$559$	−3.38415	+	1.95384i	−0.143134	+	0.0826386i
$560$	−43.0343	+	45.3261i	−1.81853	+	1.91538i
$561$	−2.54769	−	2.62721i	−0.107563	−	0.110921i
$562$	−18.2087	−	4.87901i	−0.768088	−	0.205808i
$563$	−3.03484	+	3.03484i	−0.127903	+	0.127903i	−0.768161	−	0.640257i	$-0.778828\pi$
$563$	−3.03484	+	3.03484i	−0.127903	+	0.127903i	0.640257	+	0.768161i	$0.278828\pi$
$564$	53.0881	−	13.3541i	2.23541	−	0.562309i
$565$	−1.50034	−	5.06967i	−0.0631196	−	0.213283i
$566$		−	28.6612i		−	1.20472i
$567$	7.09663	+	34.9487i	0.298030	+	1.46771i
$568$	−10.7119	+	39.9775i	−0.449463	+	1.67742i
$569$	10.6341			0.445803			0.222901	−	0.974841i	$-0.428447\pi$
$569$	10.6341			0.445803			0.222901	+	0.974841i	$0.428447\pi$
$570$	−16.5934	+	64.6521i	−0.695021	+	2.70798i
$571$	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	$-0.0423339\pi$
$572$	36.2393	−	9.71029i	1.51524	−	0.406008i
$573$	9.88646	+	17.7482i	0.413013	+	0.741441i
$574$	59.5695	−	34.3925i	2.48638	−	1.43551i
$575$	10.2002	−	11.3171i	0.425376	−	0.471956i
$576$	1.14928	+	0.711495i	0.0478866	+	0.0296456i
$577$	5.12314	+	19.1198i	0.213279	+	0.795968i	0.986765	+	0.162155i	$0.0518445\pi$
$577$	5.12314	+	19.1198i	0.213279	+	0.795968i	−0.773486	+	0.633813i	$0.781489\pi$
$578$	28.8307	−	28.8307i	1.19920	−	1.19920i
$579$	26.8200	+	7.62998i	1.11460	+	0.317091i
$580$	−90.9819	+	55.7227i	−3.77782	+	2.31376i
$581$		−	49.4173i		−	2.05017i
$582$	0.409966	−	26.6777i	0.0169936	−	1.10583i
$583$	25.0963	−	6.72453i	1.03938	−	0.278501i
$584$	−11.7884			−0.487809
$585$	−18.4884	−	18.6667i	−0.764400	−	0.771775i
$586$	−6.19071			−0.255736
$587$	4.77470	−	17.8194i	0.197073	−	0.735486i	−0.794648	−	0.607071i	$-0.792344\pi$
$587$	4.77470	−	17.8194i	0.197073	−	0.735486i	0.991721	−	0.128415i	$-0.0409889\pi$
$588$	58.8751	−	32.7958i	2.42797	−	1.35248i
$589$	16.5434	−	9.55132i	0.681658	−	0.393555i
$590$	5.58475	−	23.2367i	0.229920	−	0.956640i
$591$	22.5930	−	21.9091i	0.929351	−	0.901220i
$592$	−25.1847	+	34.7399i	−1.03509	+	1.42780i
$593$	0.318297	−	0.318297i	0.0130709	−	0.0130709i	−0.700541	−	0.713612i	$-0.747058\pi$
$593$	0.318297	−	0.318297i	0.0130709	−	0.0130709i	0.713612	+	0.700541i	$0.247058\pi$
$594$	−27.6603	+	6.06064i	−1.13492	+	0.248671i
$595$	8.73649	−	0.226601i	0.358161	−	0.00928973i
$596$	−21.6020	+	12.4719i	−0.884850	+	0.510869i
$597$	−1.66717	−	2.99291i	−0.0682327	−	0.122491i
$598$	21.4679	+	21.4679i	0.877889	+	0.877889i
$599$	−4.99391	−	8.64970i	−0.204046	−	0.353417i	0.745783	−	0.666189i	$-0.232076\pi$
$599$	−4.99391	−	8.64970i	−0.204046	−	0.353417i	−0.949828	+	0.312772i	$0.898742\pi$
$600$	−12.1664	+	53.0836i	−0.496693	+	2.16713i
$601$	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
$603$	12.1313	−	11.4077i	0.494026	−	0.464558i
$604$	21.3594	+	12.3318i	0.869100	+	0.501775i
$605$	14.3314	−	0.371719i	0.582656	−	0.0151125i
$606$	14.0290	+	14.4669i	0.569889	+	0.587678i
$607$	−11.1154	−	41.4832i	−0.451159	−	1.68375i	−0.699140	−	0.714985i	$-0.746433\pi$
$607$	−11.1154	−	41.4832i	−0.451159	−	1.68375i	0.247980	−	0.968765i	$-0.420233\pi$
$608$	9.41304	+	35.1299i	0.381749	+	1.42471i
$609$	71.0143	−	17.8634i	2.87764	−	0.723860i
$610$	27.2526	+	25.8746i	1.10342	+	1.04763i
$611$	23.9718	−	13.8401i	0.969794	−	0.559911i
$612$	3.03051	+	12.8810i	0.122501	+	0.520685i
$613$	−37.5213	+	10.0538i	−1.51547	+	0.406069i	−0.918248	−	0.396005i	$-0.870396\pi$
$613$	−37.5213	+	10.0538i	−1.51547	+	0.406069i	−0.597224	+	0.802075i	$0.703730\pi$
$614$	−28.4941	+	49.3532i	−1.14993	+	1.99173i
$615$	12.9714	−	23.0255i	0.523056	−	0.928477i
$616$	26.6883	+	46.2255i	1.07530	+	1.86248i
$617$	13.1847	−	3.53284i	0.530797	−	0.142227i	0.0165408	−	0.999863i	$-0.494735\pi$
$617$	13.1847	−	3.53284i	0.530797	−	0.142227i	0.514256	+	0.857637i	$0.328068\pi$
$618$	31.1219	+	0.478261i	1.25191	+	0.0192385i
$619$		−	31.4725i		−	1.26499i	−0.774566	−	0.632493i	$-0.782032\pi$
$619$		−	31.4725i		−	1.26499i	0.774566	−	0.632493i	$-0.217968\pi$
$620$	24.0452	−	14.7267i	0.965679	−	0.591439i
$621$	−10.6679	−	11.6998i	−0.428090	−	0.469497i
$622$	70.4080	+	18.8658i	2.82310	+	0.756449i
$623$	12.4617	−	12.4617i	0.499269	−	0.499269i
$624$	−46.0262	−	13.0939i	−1.84252	−	0.524176i
$625$	24.8656	−	2.58850i	0.994625	−	0.103540i
$626$	16.1192	−	9.30644i	0.644254	−	0.371960i
$627$	21.5717	+	12.9004i	0.861492	+	0.515192i
$628$	38.7833	+	38.7833i	1.54762	+	1.54762i
$629$	5.92495	−	0.944757i	0.236243	−	0.0376699i
$630$	34.0915	−	58.3989i	1.35824	−	2.32667i
$631$	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	$0.0769594\pi$
$632$	−12.8389	+	47.9154i	−0.510704	+	1.90597i
$633$	−41.2815	+	22.9955i	−1.64079	+	0.913988i
$634$	−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
$638$	15.0487	+	56.1626i	0.595784	+	2.22350i
$639$	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	$0.778379\pi$
$642$	−24.5854	−	44.1358i	−0.970309	−	1.74190i
$643$	24.0313	+	24.0313i	0.947704	+	0.947704i	0.998699	−	0.0509951i	$-0.0162393\pi$
$643$	24.0313	+	24.0313i	0.947704	+	0.947704i	−0.0509951	+	0.998699i	$0.516239\pi$
$644$	−26.9967	+	46.7597i	−1.06382	+	1.84259i
$645$	−3.74291	−	0.960644i	−0.147377	−	0.0378253i
$646$	8.49955	−	14.7216i	0.334410	−	0.579216i
$647$	9.67868	−	36.1213i	0.380508	−	1.42008i	−0.464619	−	0.885511i	$-0.653809\pi$
$647$	9.67868	−	36.1213i	0.380508	−	1.42008i	0.845127	−	0.534566i	$-0.179525\pi$
$648$	53.6650	+	17.9786i	2.10816	+	0.706267i
$649$	−7.79364	−	4.49966i	−0.305927	−	0.176627i
$650$	2.58256	+	49.7512i	0.101296	+	1.95140i
$651$	−18.7681	+	4.72103i	−0.735578	+	0.185032i
$652$	44.3990	−	44.3990i	1.73880	−	1.73880i
$653$	−7.41911	−	1.98794i	−0.290332	−	0.0777943i	0.110713	−	0.993852i	$-0.464686\pi$
$653$	−7.41911	−	1.98794i	−0.290332	−	0.0777943i	−0.401046	+	0.916058i	$0.631353\pi$
$654$	12.7966	−	3.21892i	0.500385	−	0.125870i
$655$	−8.55112	−	4.64563i	−0.334120	−	0.181520i
$656$		−	48.1346i		−	1.87934i
$657$	5.47434	−	1.28794i	0.213574	−	0.0502474i
$658$	50.3768	+	50.3768i	1.96389	+	1.96389i
$659$	13.0966	+	22.6840i	0.510171	+	0.883642i	0.999931	+	0.0117845i	$0.00375122\pi$
$659$	13.0966	+	22.6840i	0.510171	+	0.883642i	−0.489760	+	0.871858i	$0.662915\pi$
$660$	32.3241	+	18.2097i	1.25821	+	0.708813i
$661$	−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	$-0.407177\pi$
$662$	10.1229	−	37.7792i	0.393438	−	1.46833i
$663$	3.25613	+	5.84540i	0.126458	+	0.227017i
$664$	−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
$668$	2.16042	+	8.06280i	0.0835891	+	0.311959i
$669$	30.4388	+	8.65947i	1.17683	+	0.334794i
$670$	−31.5655	+	0.818724i	−1.21948	+	0.0316301i
$671$	12.2551	−	7.07551i	0.473105	−	0.273147i
$672$	0.566148	−	36.8410i	0.0218396	−	1.42117i
$673$	7.77808	−	29.0282i	0.299823	−	1.11896i	−0.637488	−	0.770461i	$-0.720026\pi$
$673$	7.77808	−	29.0282i	0.299823	−	1.11896i	0.937311	−	0.348495i	$-0.113307\pi$
$674$	39.7396			1.53071
$675$	−0.149766	−	25.9803i	−0.00576451	−	0.999983i
$676$	−10.4610			−0.402345
$677$	−22.0923	−	22.0923i	−0.849076	−	0.849076i	0.140942	−	0.990018i	$-0.454987\pi$
$677$	−22.0923	−	22.0923i	−0.849076	−	0.849076i	−0.990018	+	0.140942i	$0.954987\pi$
$678$	8.94153	+	5.34724i	0.343397	+	0.205360i
$679$	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
$682$	−3.97716	−	14.8430i	−0.152293	−	0.568366i
$683$	−2.58551	−	9.64927i	−0.0989320	−	0.369219i	0.898654	−	0.438658i	$-0.144546\pi$
$683$	−2.58551	−	9.64927i	−0.0989320	−	0.369219i	−0.997586	+	0.0694385i	$0.977879\pi$
$684$	−43.0020	−	80.0670i	−1.64422	−	3.06144i
$685$	−14.8487	−	14.0979i	−0.567338	−	0.538652i
$686$	14.8485	+	8.57281i	0.566920	+	0.327311i
$687$	−22.3615	+	37.3923i	−0.853143	+	1.42660i
$688$	−6.79832	+	1.82161i	−0.259184	+	0.0694481i
$689$	−47.5036			−1.80974
$690$	0.317193	+	30.0209i	0.0120753	+	1.14288i
$691$	−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
$693$	−17.4439	−	18.5505i	−0.662640	−	0.704673i
$694$	−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
$698$	34.6154	+	9.27516i	1.31021	+	0.351070i
$699$	−3.53589	+	12.4290i	−0.133740	+	0.470107i
$700$	−84.2754	+	27.3364i	−3.18531	+	1.03322i
$701$	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	$0.447995\pi$
$702$	51.7176	+	2.38579i	1.95196	+	0.0900459i
$703$	−37.6273	+	16.7998i	−1.41914	+	0.633616i
$704$	−0.965155			−0.0363757
$705$	26.5131	+	6.80476i	0.998540	+	0.256282i
$706$	−38.3139	−	66.3615i	−1.44196	−	2.49755i
$707$	−4.69030	+	17.5044i	−0.176397	+	0.658322i
$708$	15.8352	+	28.4274i	0.595123	+	1.06837i
$709$		−	5.38431i		−	0.202212i	−0.994876	−	0.101106i	$-0.967762\pi$
$709$		−	5.38431i		−	0.202212i	0.994876	−	0.101106i	$-0.0322381\pi$
$710$	−25.7781	+	27.1510i	−0.967436	+	1.01896i
$711$	0.727163	−	23.6538i	0.0272707	−	0.887085i
$712$	−7.23894	−	27.0161i	−0.271291	−	1.01247i
$713$	6.07563	−	6.07563i	0.227534	−	0.227534i
$714$	−12.3632	+	11.9890i	−0.462682	+	0.448677i
$715$	18.2404	+	4.38393i	0.682152	+	0.163950i
$716$	−7.96260	+	4.59721i	−0.297576	+	0.171806i
$717$	−0.513585	+	33.4205i	−0.0191802	+	1.24811i
$718$	−33.3476	+	8.93546i	−1.24452	+	0.333469i
$719$	−7.84705	+	13.5915i	−0.292646	+	0.506877i	−0.974434	−	0.224672i	$-0.927869\pi$
$719$	−7.84705	+	13.5915i	−0.292646	+	0.506877i	0.681789	+	0.731549i	$0.261202\pi$
$720$	−23.4632	−	41.0937i	−0.874420	−	1.53147i
$721$	13.9950	+	24.2400i	0.521201	+	0.902746i
$722$	−17.7074	+	66.0847i	−0.659000	+	2.45942i
$723$	−34.3772	−	20.5584i	−1.27850	−	0.764575i
$724$	81.4111	+	47.0027i	3.02562	+	1.74684i
$725$	−53.2760	+	2.76553i	−1.97862	+	0.102709i
$726$	−20.2808	+	19.6669i	−0.752690	+	0.729907i
$727$	−33.3393	−	8.93325i	−1.23649	−	0.331316i	−0.419385	−	0.907808i	$-0.637754\pi$
$727$	−33.3393	−	8.93325i	−1.23649	−	0.331316i	−0.817102	+	0.576493i	$0.804421\pi$
$728$	−25.2585	−	94.2660i	−0.936143	−	3.49373i
$729$	−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
$732$	−51.1621	−	0.786226i	−1.89100	−	0.0290597i
$733$	4.52850	−	16.9006i	0.167264	−	0.624238i	−0.830476	−	0.557054i	$-0.811932\pi$
$733$	4.52850	−	16.9006i	0.167264	−	0.624238i	0.997741	−	0.0671844i	$-0.0214016\pi$
$734$	−30.2479			−1.11647
$735$	33.6965	−	0.356028i	1.24291	−	0.0131323i
$736$	8.17931	+	14.1670i	0.301493	+	0.522202i
$737$	−3.07748	+	11.4853i	−0.113360	+	0.423067i
$738$	11.9267	+	50.6937i	0.439027	+	1.86606i
$739$			1.94114i			0.0714062i	0.999362	+	0.0357031i	$0.0113671\pi$
$739$			1.94114i			0.0714062i	−0.999362	+	0.0357031i	$0.988633\pi$
$740$	−54.8784	+	26.2292i	−2.01737	+	0.964205i
$741$	−31.9922	−	32.9909i	−1.17526	−	1.21195i
$742$	−31.6445	−	118.099i	−1.16171	−	4.33555i
$743$	−18.0219	−	4.82896i	−0.661160	−	0.177157i	−0.0873905	−	0.996174i	$-0.527853\pi$
$743$	−18.0219	−	4.82896i	−0.661160	−	0.177157i	−0.573769	+	0.819017i	$0.694519\pi$
$744$	−8.40411	+	29.5412i	−0.308110	+	1.08303i
$745$	−12.4684	+	0.323395i	−0.456805	+	0.0118483i
$746$			43.3105i			1.58571i
$747$	35.8248	+	10.7894i	1.31076	+	0.394765i
$748$	−6.68120	−	6.68120i	−0.244289	−	0.244289i
$749$	22.7159	−	39.3451i	0.830022	−	1.43764i
$750$	−32.5939	+	36.9405i	−1.19016	+	1.34888i
$751$	−8.06988			−0.294474			−0.147237	−	0.989101i	$-0.547038\pi$
$751$	−8.06988			−0.294474			−0.147237	+	0.989101i	$0.547038\pi$
$752$	48.1563	−	12.9034i	1.75608	−	0.470540i
$753$	−18.9145	−	33.9553i	−0.689282	−	1.23740i
$754$		−	106.308i		−	3.87149i
$755$	6.44109	+	10.5168i	0.234415	+	0.382744i
$756$	19.7068	+	89.9402i	0.716728	+	3.27109i
$757$	−6.66386	−	24.8699i	−0.242202	−	0.903911i	−0.974769	−	0.223216i	$-0.928345\pi$
$757$	−6.66386	−	24.8699i	−0.242202	−	0.903911i	0.732567	−	0.680695i	$-0.238322\pi$
$758$	−14.5812	−	3.90702i	−0.529613	−	0.141909i
$759$	10.8740	+	3.09352i	0.394701	+	0.112288i
$760$	−22.2608	+	92.6215i	−0.807484	+	3.35973i
$761$	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	$0.529240\pi$
$762$	−33.3765	−	19.9599i	−1.20910	−	0.723072i
$763$	8.39048	+	8.39048i	0.303756	+	0.303756i
$764$	26.2265	+	45.4256i	0.948840	+	1.64344i
$765$	−1.74319	+	6.38296i	−0.0630253	+	0.230776i
$766$	−70.4149			−2.54419
$767$	11.6347	+	11.6347i	0.420105	+	0.420105i
$768$	43.5997	+	26.0737i	1.57327	+	0.940852i
$769$			31.6099i			1.13988i	0.821685	+	0.569942i	$0.193034\pi$
$769$			31.6099i			1.13988i	−0.821685	+	0.569942i	$0.806966\pi$
$770$	1.25194	+	48.2679i	0.0451167	+	1.73945i
$771$	−18.2591	+	17.7064i	−0.657585	+	0.637680i
$772$	69.5399	+	18.6332i	2.50280	+	0.670622i
$773$	−28.9522	−	7.75772i	−1.04134	−	0.279026i	−0.302671	−	0.953095i	$-0.597878\pi$
$773$	−28.9522	−	7.75772i	−1.04134	−	0.279026i	−0.738668	+	0.674069i	$0.764545\pi$
$774$	6.70841	−	3.60293i	0.241129	−	0.129505i
$775$	14.0801	−	0.730890i	0.505771	−	0.0262543i
$776$		−	38.0777i		−	1.36691i
$777$	41.3222	−	5.93941i	1.48242	−	0.213075i
$778$	15.2237	+	15.2237i	0.545797	+	0.545797i
$779$	23.1132	−	40.0332i	0.828115	−	1.43434i
$780$	−48.4692	−	47.4556i	−1.73547	−	1.69918i
$781$	7.04913	+	12.2095i	0.252238	+	0.436889i
$782$	1.97895	−	7.38554i	0.0707671	−	0.264107i
$783$	−2.55482	+	55.3817i	−0.0913017	+	1.97918i
$784$	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	−0.454799	+	0.890594i	$0.650289\pi$
$787$	−37.7430	+	37.7430i	−1.34539	+	1.34539i	−0.890594	+	0.454799i	$0.849711\pi$
$788$	57.4557	−	57.4557i	2.04677	−	2.04677i
$789$	5.06746	−	1.27470i	0.180406	−	0.0453805i
$790$	−30.8966	+	32.5420i	−1.09925	+	1.15779i
$791$			9.36889i			0.333119i
$792$	−39.3379	+	9.25500i	−1.39781	+	0.328862i
$793$	−24.9915	+	6.69646i	−0.887475	+	0.237798i
$794$	25.7718	−	44.6380i	0.914606	−	1.58414i
$795$	−33.5657	−	32.8638i	−1.19045	−	1.16556i
$796$	−4.42262	−	7.66019i	−0.156755	−	0.271508i
$797$	−6.19220	+	1.65920i	−0.219339	+	0.0587717i	−0.366815	−	0.930294i	$-0.619552\pi$
$797$	−6.19220	+	1.65920i	−0.219339	+	0.0587717i	0.147476	+	0.989066i	$0.452885\pi$
$798$	60.7071	−	101.513i	2.14901	−	3.59352i
$799$	−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
$802$	11.9577	+	44.6269i	0.422242	+	1.57583i
$803$	−2.83946	+	2.83946i	−0.100202	+	0.100202i
$804$	30.8651	−	29.9308i	1.08853	−	1.05558i
$805$	−23.0232	+	14.1008i	−0.811461	+	0.496987i
$806$			28.0956i			0.989624i
$807$	−5.28698	+	2.94506i	−0.186111	+	0.103671i
$808$	20.3364	+	20.3364i	0.715432	+	0.715432i
$809$	11.7665	+	20.3802i	0.413688	+	0.716529i	0.995290	−	0.0969449i	$-0.0309071\pi$
$809$	11.7665	+	20.3802i	0.413688	+	0.716529i	−0.581602	+	0.813474i	$0.697574\pi$
$810$	34.8927	+	37.4649i	1.22601	+	1.31638i
$811$	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	$0.650069\pi$
$812$	182.618	−	48.9324i	6.40864	−	1.71719i
$813$	−0.308354	+	20.0655i	−0.0108145	+	0.703729i
$814$	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
$817$	−6.52881	−	1.74939i	−0.228414	−	0.0612034i
$818$	−69.7405	−	18.6869i	−2.43842	−	0.653372i
$819$	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	$0.394425\pi$
$822$	40.3430	+	0.619964i	1.40712	+	0.0216237i
$823$	−24.7150	+	6.62236i	−0.861511	+	0.230841i	−0.662413	−	0.749139i	$-0.730468\pi$
$823$	−24.7150	+	6.62236i	−0.861511	+	0.230841i	−0.199097	+	0.979980i	$0.563801\pi$
$824$	44.4209			1.54748
$825$	9.85564	+	15.7167i	0.343129	+	0.547184i
$826$	−21.1746	+	36.6756i	−0.736760	+	1.27611i
$827$	−5.15249	+	19.2294i	−0.179170	+	0.668670i	0.816634	+	0.577156i	$0.195837\pi$
$827$	−5.15249	+	19.2294i	−0.179170	+	0.668670i	−0.995804	+	0.0915146i	$0.970829\pi$
$828$	−28.0040	−	29.7804i	−0.973205	−	1.03494i
$829$	−0.402867	−	0.232595i	−0.0139921	−	0.00807836i	0.492988	−	0.870036i	$-0.335905\pi$
$829$	−0.402867	−	0.232595i	−0.0139921	−	0.00807836i	−0.506980	+	0.861958i	$0.669238\pi$
$830$	−37.0533	−	60.4992i	−1.28614	−	2.09996i
$831$	26.9320	−	6.77464i	0.934260	−	0.235010i
$832$	1.70452	+	0.456725i	0.0590936	+	0.0158341i
$833$	−8.28978	−	2.22124i	−0.287224	−	0.0769614i
$834$	−67.1028	+	16.8794i	−2.32358	+	0.584487i
$835$	−0.975369	+	4.05826i	−0.0337540	+	0.140442i
$836$	56.2002	+	32.4472i	1.94373	+	1.12221i
$837$	0.675202	−	14.6366i	0.0233384	−	0.505914i
$838$	−5.24549	+	19.5764i	−0.181202	+	0.676256i
$839$	0.122527	−	0.212223i	0.00423010	−	0.00732674i	−0.863903	−	0.503659i	$-0.831987\pi$
$839$	0.122527	−	0.212223i	0.00423010	−	0.00732674i	0.868133	+	0.496332i	$0.165320\pi$
$840$	47.3674	−	84.0819i	1.63433	−	2.90110i
$841$	84.8391			2.92549
$842$	8.35472	−	2.23864i	0.287923	−	0.0771487i
$843$	12.8330	+	0.197209i	0.441992	+	0.00679225i
$844$	−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
$847$	−24.5390	−	6.57521i	−0.843170	−	0.225927i
$848$	−82.6437	−	22.1443i	−2.83800	−	0.760438i
$849$	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
$852$	0.783294	−	50.9713i	0.0268352	−	1.74625i
$853$	−30.2529	+	8.10625i	−1.03584	+	0.277553i	−0.736389	−	0.676559i	$-0.763470\pi$
$853$	−30.2529	+	8.10625i	−1.03584	+	0.277553i	−0.299452	+	0.954111i	$0.596804\pi$
$854$	−33.2962	−	57.6707i	−1.13937	−	1.97345i
$855$	0.218169	−	45.4439i	0.00746121	−	1.55415i
$856$	−36.0509	−	62.4419i	−1.23219	−	2.13422i
$857$	−9.93247	−	9.93247i	−0.339287	−	0.339287i	0.516812	−	0.856099i	$-0.327119\pi$
$857$	−9.93247	−	9.93247i	−0.339287	−	0.339287i	−0.856099	+	0.516812i	$0.827119\pi$
$858$	−32.2950	+	17.9897i	−1.10253	+	0.614157i
$859$			33.4604i			1.14165i	0.821070	+	0.570827i	$0.193377\pi$
$859$			33.4604i			1.14165i	−0.821070	+	0.570827i	$0.806623\pi$
$860$	−9.70062	−	2.33146i	−0.330788	−	0.0795022i
$861$	−33.6198	+	32.6021i	−1.14576	+	1.11108i
$862$	−45.6488	+	45.6488i	−1.55481	+	1.55481i
$863$	−7.98974	−	29.8181i	−0.271974	−	1.01502i	−0.957842	−	0.287294i	$-0.907244\pi$
$863$	−7.98974	−	29.8181i	−0.271974	−	1.01502i	0.685869	−	0.727725i	$-0.259422\pi$
$864$	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
$867$	−14.2476	+	23.8245i	−0.483875	+	0.809123i
$868$	−48.2634	+	12.9321i	−1.63816	+	0.438945i
$869$	8.44881	+	14.6338i	0.286606	+	0.496416i
$870$	73.5453	−	75.1160i	2.49342	−	2.54667i
$871$	10.8700	−	18.8274i	0.368316	−	0.637943i
$872$	18.1899	−	4.87397i	0.615988	−	0.165053i
$873$	4.16017	+	17.6826i	0.140800	+	0.598465i
$874$			52.5142i			1.77632i
$875$	−43.5535	−	8.10575i	−1.47238	−	0.274024i
$876$	14.0812	−	3.54206i	0.475759	−	0.119675i
$877$	−17.7907	+	17.7907i	−0.600749	+	0.600749i	−0.940511	−	0.339762i	$-0.889653\pi$
$877$	−17.7907	+	17.7907i	−0.600749	+	0.600749i	0.339762	+	0.940511i	$0.389653\pi$
$878$	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	$0.143343\pi$
$882$	−48.3761	+	45.4904i	−1.62891	+	1.53174i
$883$	−3.22738	+	12.0448i	−0.108610	+	0.405338i	−0.998730	−	0.0503886i	$-0.983954\pi$
$883$	−3.22738	+	12.0448i	−0.108610	+	0.405338i	0.890120	+	0.455727i	$0.150621\pi$
$884$	8.63775	+	14.9610i	0.290519	+	0.503194i
$885$	0.171905	+	16.2701i	0.00577853	+	0.546913i
$886$	29.2566	−	50.6740i	0.982896	−	1.70243i
$887$	37.6934	+	37.6934i	1.26562	+	1.26562i	0.948328	+	0.317291i	$0.102773\pi$
$887$	37.6934	+	37.6934i	1.26562	+	1.26562i	0.317291	+	0.948328i	$0.397227\pi$
$888$	24.6266	−	61.5065i	0.826414	−	2.06402i
$889$		−	34.9717i		−	1.17291i
$890$	5.91245	−	24.6002i	0.198186	−	0.824600i
$891$	17.2567	−	8.59571i	0.578120	−	0.287967i
$892$	78.9227	+	21.1473i	2.64253	+	0.708064i
$893$	46.2471	+	12.3919i	1.54760	+	0.414679i
$894$	17.6443	−	17.1102i	0.590113	−	0.572250i
$895$	−4.59590	+	0.119205i	−0.153624	+	0.00398460i
$896$			47.0872i			1.57307i
$897$	−17.7402	−	10.6091i	−0.592328	−	0.354226i
$898$	20.4677	+	20.4677i	0.683016	+	0.683016i
$899$	−30.0860			−1.00343
$900$	−1.41731	−	67.0635i	−0.0472437	−	2.23545i
$901$	5.98178	+	10.3607i	0.199282	+	0.345166i
$902$	−26.2941	−	26.2941i	−0.875496	−	0.875496i
$903$	5.87690	+	3.51452i	0.195571	+	0.116956i
$904$	12.8767	+	7.43435i	0.428272	+	0.247263i
$905$	24.5502	+	40.0846i	0.816075	+	1.33246i
$906$	−23.3745	−	6.64977i	−0.776566	−	0.220924i
$907$	−6.00671	−	1.60949i	−0.199449	−	0.0534423i	0.157711	−	0.987485i	$-0.449588\pi$
$907$	−6.00671	−	1.60949i	−0.199449	−	0.0534423i	−0.357161	+	0.934043i	$0.616255\pi$
$908$	13.1284	+	48.9960i	0.435683	+	1.62599i
$909$	−11.6657	−	7.22201i	−0.386927	−	0.239539i
$910$	20.6300	−	85.8363i	0.683879	−	2.84545i
$911$		−	29.6237i		−	0.981477i	−0.871307	−	0.490738i	$-0.836727\pi$
$911$		−	29.6237i		−	0.981477i	0.871307	−	0.490738i	$-0.163273\pi$
$912$	−40.2790	−	72.3089i	−1.33377	−	2.39439i
$913$	−25.8049	+	6.91439i	−0.854017	+	0.228833i
$914$	−11.8262			−0.391178
$915$	−22.2915	−	12.5579i	−0.736935	−	0.415151i
$916$	−56.2438	+	97.4171i	−1.85835	+	3.21875i
$917$	12.1940	+	12.1940i	0.402680	+	0.402680i
$918$	−5.99207	−	11.5803i	−0.197768	−	0.382206i
$919$		−	31.4801i		−	1.03843i	−0.854643	−	0.519216i	$-0.826224\pi$
$919$		−	31.4801i		−	1.03843i	0.854643	−	0.519216i	$-0.173776\pi$
$920$	1.11096	+	42.8325i	0.0366272	+	1.41214i
$921$	10.6168	−	37.3190i	0.349835	−	1.22970i
$922$	−10.1392	−	2.71680i	−0.333918	−	0.0894731i
$923$	−6.67149	−	24.8983i	−0.219595	−	0.819539i
$924$	−45.7682	−	47.1969i	−1.50566	−	1.55266i
$925$	−30.3730	−	1.57515i	−0.998658	−	0.0517905i
$926$			24.4658i			0.803997i
$927$	−20.6283	+	4.85320i	−0.677522	+	0.159400i
$928$	14.8252	−	55.3285i	0.486662	−	1.81625i
$929$	−3.36721	−	5.83217i	−0.110474	−	0.191347i	0.805487	−	0.592613i	$-0.201904\pi$
$929$	−3.36721	−	5.83217i	−0.110474	−	0.191347i	−0.915962	+	0.401266i	$0.868570\pi$
$930$	−19.4370	+	19.8521i	−0.637364	+	0.650976i
$931$	58.9437			1.93180
$932$	−8.63500	+	32.2262i	−0.282849	+	1.05561i
$933$	−49.6217	−	0.762554i	−1.62454	−	0.0249649i
$934$	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
$937$	−2.68270	−	10.0120i	−0.0876399	−	0.327077i	0.908161	−	0.418621i	$-0.137486\pi$
$937$	−2.68270	−	10.0120i	−0.0876399	−	0.327077i	−0.995801	+	0.0915442i	$0.970820\pi$
$938$	54.0480	+	14.4821i	1.76473	+	0.472858i
$939$	−9.09735	+	8.82198i	−0.296881	+	0.287894i
$940$	68.7148	+	16.5150i	2.24123	+	0.538660i
$941$	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	$0.624342\pi$
$942$	−46.3823	−	27.7377i	−1.51122	−	0.903744i
$943$	5.38144	−	20.0838i	0.175244	−	0.654019i
$944$	14.8177	+	25.6650i	0.482274	+	0.835323i
$945$	−12.8102	+	44.2212i	−0.416716	+	1.43852i
$946$	−2.71859	+	4.70874i	−0.0883890	+	0.153094i
$947$	−0.655541	+	0.175652i	−0.0213022	+	0.00570792i	−0.269454	−	0.963013i	$-0.586843\pi$
$947$	−0.655541	+	0.175652i	−0.0213022	+	0.00570792i	0.248152	+	0.968721i	$0.420177\pi$
$948$	0.938825	−	61.0922i	0.0304916	−	1.98418i
$949$	6.35831	−	3.67097i	0.206399	−	0.119165i
$950$	−57.6913	+	64.0087i	−1.87175	+	2.07672i
$951$	8.84525	−	8.57751i	0.286827	−	0.278145i
$952$	−17.3792	+	17.3792i	−0.563264	+	0.563264i
$953$	5.23131	+	19.5235i	0.169459	+	0.632428i	0.997429	+	0.0716569i	$0.0228287\pi$
$953$	5.23131	+	19.5235i	0.169459	+	0.632428i	−0.827971	+	0.560771i	$0.810505\pi$
$954$	92.5244	+	2.84438i	2.99559	+	0.0920902i
$955$	0.680051	+	26.2190i	0.0220059	+	0.848428i
$956$			86.2971i			2.79105i
$957$	−19.2642	−	34.5831i	−0.622722	−	1.11791i
$958$	16.5147	−	61.6339i	0.533567	−	1.99130i
$959$	18.1416	+	31.4221i	0.585821	+	1.01467i
$960$	0.888430	+	1.50193i	0.0286740	+	0.0484747i
$961$	−23.0487			−0.743506
$962$	6.27223	−	60.2811i	0.202225	−	1.94354i
$963$	23.5635	+	25.0582i	0.759322	+	0.807489i
$964$	−89.5621	−	51.7087i	−2.88460	−	1.66543i
$965$	26.1062	+	24.7862i	0.840387	+	0.797895i
$966$	14.5576	−	51.1712i	0.468383	−	1.64641i
$967$	5.71714	+	1.53190i	0.183851	+	0.0492627i	0.349570	−	0.936910i	$-0.386328\pi$
$967$	5.71714	+	1.53190i	0.183851	+	0.0492627i	−0.165719	+	0.986173i	$0.552994\pi$
$968$	−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	$0.377643\pi$
$972$	−69.5044	−	5.35060i	−2.22935	−	0.171621i
$973$	−43.9981	−	43.9981i	−1.41051	−	1.41051i
$974$	−23.2090	+	40.1992i	−0.743666	+	1.28807i
$975$	−9.96829	−	32.4203i	−0.319241	−	1.03828i
$976$	−46.6002			−1.49164
$977$	−27.0808	+	7.25628i	−0.866392	+	0.232149i	−0.664527	−	0.747264i	$-0.731367\pi$
$977$	−27.0808	+	7.25628i	−0.866392	+	0.232149i	−0.201865	+	0.979413i	$0.564700\pi$
$978$	−31.7541	+	53.0984i	−1.01538	+	1.69790i
$979$	−8.25095	−	4.76369i	−0.263701	−	0.152248i
$980$	86.9751	−	2.25590i	2.77832	−	0.0720620i
$981$	−7.91456	+	4.25072i	−0.252693	+	0.135715i
$982$	−20.7282	−	77.3587i	−0.661464	−	2.46862i
$983$	11.6789	+	43.5861i	0.372498	+	1.39018i	0.856966	+	0.515372i	$0.172346\pi$
$983$	11.6789	+	43.5861i	0.372498	+	1.39018i	−0.484469	+	0.874809i	$0.660987\pi$
$984$	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
$987$	−41.6293	−	24.8953i	−1.32507	−	0.792426i
$988$	−83.8984	−	83.8984i	−2.66916	−	2.66916i
$989$	−3.04021			−0.0966730
$990$	−35.2650	−	9.63091i	−1.12079	−	0.306090i
$991$	−27.3204			−0.867860			−0.433930	−	0.900947i	$-0.642873\pi$
$991$	−27.3204			−0.867860			−0.433930	+	0.900947i	$0.642873\pi$
$992$	−3.91810	+	14.6225i	−0.124400	+	0.464266i
$993$	−0.409168	+	26.6258i	−0.0129846	+	0.844944i
$994$	57.4557	−	33.1721i	1.82238	−	1.05215i
$995$	−0.114678	−	4.42136i	−0.00363554	−	0.140167i
$996$	92.9116	+	26.4322i	2.94402	+	0.837537i
$997$	−2.51720	−	9.39431i	−0.0797204	−	0.297521i	0.914542	−	0.404492i	$-0.132551\pi$
$997$	−2.51720	−	9.39431i	−0.0797204	−	0.297521i	−0.994262	+	0.106971i	$0.965885\pi$
$998$	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.158.3	yes	288
3.2	odd	2	inner	555.2.bi.a.158.70	yes	288
5.2	odd	4	inner	555.2.bi.a.47.3	✓	288
15.2	even	4	inner	555.2.bi.a.47.70	yes	288
37.26	even	3	inner	555.2.bi.a.248.70	yes	288
111.26	odd	6	inner	555.2.bi.a.248.3	yes	288
185.137	odd	12	inner	555.2.bi.a.137.70	yes	288
555.137	even	12	inner	555.2.bi.a.137.3	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bi.a.47.3	✓	288	5.2	odd	4	inner
555.2.bi.a.47.70	yes	288	15.2	even	4	inner
555.2.bi.a.137.3	yes	288	555.137	even	12	inner
555.2.bi.a.137.70	yes	288	185.137	odd	12	inner
555.2.bi.a.158.3	yes	288	1.1	even	1	trivial
555.2.bi.a.158.70	yes	288	3.2	odd	2	inner
555.2.bi.a.248.3	yes	288	111.26	odd	6	inner
555.2.bi.a.248.70	yes	288	37.26	even	3	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)

\(f(q)\)	\(=\)	\(q+(-2.45731 + 0.658434i) q^{2} +(1.51313 - 0.842875i) q^{3} +(3.87278 - 2.23595i) q^{4} +(2.23532 - 0.0579781i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(-3.82742 - 1.02555i) q^{7} +(-4.44664 + 4.44664i) q^{8} +(1.57912 - 2.55076i) q^{9} +O(q^{10})\)	\(q+(-2.45731 + 0.658434i) q^{2} +(1.51313 - 0.842875i) q^{3} +(3.87278 - 2.23595i) q^{4} +(2.23532 - 0.0579781i) q^{5} +(-3.16325 + 3.06750i) q^{6} +(-3.82742 - 1.02555i) q^{7} +(-4.44664 + 4.44664i) q^{8} +(1.57912 - 2.55076i) q^{9} +(-5.45469 + 1.61428i) q^{10} +2.14211i q^{11} +(3.97539 - 6.64755i) q^{12} +(1.01367 - 3.78308i) q^{13} +10.0804 q^{14} +(3.33346 - 1.97182i) q^{15} +(3.52705 - 6.10903i) q^{16} +(-0.952752 + 0.255289i) q^{17} +(-2.20089 + 7.30775i) q^{18} +(5.86684 - 3.38722i) q^{19} +(8.52725 - 5.22259i) q^{20} +(-6.65579 + 1.67424i) q^{21} +(-1.41044 - 5.26382i) q^{22} +(2.15463 - 2.15463i) q^{23} +(-2.98038 + 10.4763i) q^{24} +(4.99328 - 0.259199i) q^{25} +9.96365i q^{26} +(0.239450 - 5.19063i) q^{27} +(-17.1158 + 4.58617i) q^{28} -10.6695 q^{29} +(-6.89302 + 7.04023i) q^{30} +2.81981 q^{31} +(-1.38949 + 5.18565i) q^{32} +(1.80553 + 3.24129i) q^{33} +(2.17311 - 1.25465i) q^{34} +(-8.61495 - 2.07053i) q^{35} +(0.412230 - 13.4094i) q^{36} +(-6.05010 - 0.629511i) q^{37} +(-12.1864 + 12.1864i) q^{38} +(-1.65485 - 6.57870i) q^{39} +(-9.68184 + 10.1975i) q^{40} +(5.90944 - 3.41181i) q^{41} +(15.2530 - 8.49652i) q^{42} +(-0.705507 - 0.705507i) q^{43} +(4.78965 + 8.29591i) q^{44} +(3.38195 - 5.79331i) q^{45} +(-3.87590 + 6.71326i) q^{46} +(4.99749 + 4.99749i) q^{47} +(0.187737 - 12.2166i) q^{48} +(7.53519 + 4.35044i) q^{49} +(-12.0994 + 3.92467i) q^{50} +(-1.22646 + 1.18934i) q^{51} +(-4.53305 - 16.9176i) q^{52} +(-3.13921 - 11.7157i) q^{53} +(2.82929 + 12.9126i) q^{54} +(0.124195 + 4.78829i) q^{55} +(21.5794 - 12.4589i) q^{56} +(6.02229 - 10.0703i) q^{57} +(26.2184 - 7.02519i) q^{58} +(-2.10057 + 3.63830i) q^{59} +(8.50085 - 15.0899i) q^{60} +(-3.30306 - 5.72107i) q^{61} +(-6.92914 + 1.85666i) q^{62} +(-8.65991 + 8.14334i) q^{63} +0.450563i q^{64} +(2.04655 - 8.51516i) q^{65} +(-6.57092 - 6.77602i) q^{66} +(5.36169 + 1.43666i) q^{67} +(-3.11898 + 3.11898i) q^{68} +(1.44415 - 5.07631i) q^{69} +(22.5329 - 0.584442i) q^{70} +(5.69974 - 3.29075i) q^{71} +(4.32051 + 18.3641i) q^{72} +(1.32554 + 1.32554i) q^{73} +(15.2815 - 2.43669i) q^{74} +(7.33700 - 4.60091i) q^{75} +(15.1473 - 26.2359i) q^{76} +(2.19685 - 8.19874i) q^{77} +(8.39811 + 15.0763i) 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} +(3.22785 + 12.0465i) q^{83} +(-22.0329 + 21.3660i) q^{84} +(-2.11490 + 0.625890i) q^{85} +(2.19818 + 1.26912i) q^{86} +(-16.1444 + 8.99309i) q^{87} +(-9.52519 - 9.52519i) q^{88} +(-2.22383 + 3.85179i) q^{89} +(-4.49599 + 16.4627i) q^{90} +(-7.75951 + 13.4399i) q^{91} +(3.52675 - 13.1620i) q^{92} +(4.26673 - 2.37674i) q^{93} +(-15.5709 - 8.98987i) q^{94} +(12.9179 - 7.91166i) q^{95} +(2.26838 + 9.01773i) q^{96} +(-4.28162 + 4.28162i) q^{97} +(-21.3808 - 5.72896i) 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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