LMFDB - Embedded newform 544.2.x.a.77.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(77,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.15
Character	$\chi$	$=$	544.77
Dual form			544.2.x.a.325.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08558 - 0.906372i) q^{2} +(0.0709706 - 0.0709706i) q^{3} +(0.356979 + 1.96788i) q^{4} +4.13663i q^{5} +(-0.141370 + 0.0127187i) q^{6} +(-1.05288 - 0.436118i) q^{7} +(1.39610 - 2.45986i) q^{8} +2.98993i q^{9} +(3.74933 - 4.49066i) q^{10} +(-1.46992 - 1.46992i) q^{11} +(0.164997 + 0.114327i) q^{12} +(0.796050 - 1.92184i) q^{13} +(0.747705 + 1.42774i) q^{14} +(0.293579 + 0.293579i) q^{15} +(-3.74513 + 1.40499i) q^{16} +(3.59022 + 2.02739i) q^{17} +(2.70999 - 3.24581i) q^{18} +(-4.64149 + 1.92257i) q^{19} +(-8.14041 + 1.47669i) q^{20} +(-0.105675 + 0.0437721i) q^{21} +(0.263424 + 2.92801i) q^{22} +(-4.14931 - 1.71870i) q^{23} +(-0.0754952 - 0.273660i) q^{24} -12.1117 q^{25} +(-2.60608 + 1.36479i) q^{26} +(0.425109 + 0.425109i) q^{27} +(0.482372 - 2.22763i) q^{28} +(-0.0567121 - 0.0567121i) q^{29} +(-0.0526125 - 0.584797i) q^{30} +(-8.68138 - 3.59595i) q^{31} +(5.33909 + 1.86925i) q^{32} -0.208642 q^{33} +(-2.05991 - 5.45498i) q^{34} +(1.80406 - 4.35538i) q^{35} +(-5.88383 + 1.06734i) q^{36} +9.83922 q^{37} +(6.78128 + 2.11981i) q^{38} +(-0.0798977 - 0.192890i) q^{39} +(10.1755 + 5.77517i) q^{40} +(-3.38846 + 8.18046i) q^{41} +(0.154393 + 0.0482628i) q^{42} +(-3.21310 + 7.75710i) q^{43} +(2.36789 - 3.41735i) q^{44} -12.3682 q^{45} +(2.94664 + 5.62662i) q^{46} -0.385124 q^{47} +(-0.166082 + 0.365507i) q^{48} +(-4.03139 - 4.03139i) q^{49} +(13.1483 + 10.9777i) q^{50} +(0.398686 - 0.110915i) q^{51} +(4.06612 + 0.880479i) q^{52} +(-3.84049 - 1.59078i) q^{53} +(-0.0761840 - 0.846798i) q^{54} +(6.08050 - 6.08050i) q^{55} +(-2.54272 + 1.98107i) q^{56} +(-0.192964 + 0.465855i) q^{57} +(0.0101634 + 0.112968i) q^{58} +(11.8591 + 4.91222i) q^{59} +(-0.472928 + 0.682532i) q^{60} +6.02168 q^{61} +(6.16509 + 11.7723i) q^{62} +(1.30396 - 3.14804i) q^{63} +(-4.10179 - 6.86843i) q^{64} +(7.94993 + 3.29297i) q^{65} +(0.226498 + 0.189107i) q^{66} +(-2.58048 + 6.22983i) q^{67} +(-2.70804 + 7.78887i) q^{68} +(-0.416457 + 0.172502i) q^{69} +(-5.90605 + 3.09298i) q^{70} +(14.5522 - 6.02773i) q^{71} +(7.35479 + 4.17425i) q^{72} +(-7.59896 + 3.14759i) q^{73} +(-10.6813 - 8.91800i) q^{74} +(-0.859577 + 0.859577i) q^{75} +(-5.44030 - 8.44759i) q^{76} +(0.906591 + 2.18870i) q^{77} +(-0.0880947 + 0.281815i) q^{78} +(2.10664 + 5.08589i) q^{79} +(-5.81192 - 15.4922i) q^{80} -8.90944 q^{81} +(11.0930 - 5.80936i) q^{82} +(0.109122 - 0.0451999i) q^{83} +(-0.123862 - 0.192331i) q^{84} +(-8.38658 + 14.8514i) q^{85} +(10.5189 - 5.50871i) q^{86} -0.00804979 q^{87} +(-5.66794 + 1.56363i) q^{88} +(-3.36692 - 3.36692i) q^{89} +(13.4267 + 11.2102i) q^{90} +(-1.67629 + 1.67629i) q^{91} +(1.90099 - 8.77891i) q^{92} +(-0.871330 + 0.360917i) q^{93} +(0.418084 + 0.349066i) q^{94} +(-7.95295 - 19.2001i) q^{95} +(0.511581 - 0.246257i) q^{96} +(-2.64025 + 6.37414i) q^{97} +(0.722467 + 8.03034i) q^{98} +(4.39494 - 4.39494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−1.08558	−	0.906372i	−0.767623	−	0.640902i
$2$	−1.08558	−	0.906372i	−0.767623	−	0.640902i
$3$	0.0709706	−	0.0709706i	0.0409749	−	0.0409749i	−0.686322	−	0.727297i	$-0.740776\pi$
$3$	0.0709706	−	0.0709706i	0.0409749	−	0.0409749i	0.727297	+	0.686322i	$0.240776\pi$
$4$	0.356979	+	1.96788i	0.178490	+	0.983942i
$5$			4.13663i			1.84996i	0.380018	+	0.924979i	$0.375918\pi$
$5$			4.13663i			1.84996i	−0.380018	+	0.924979i	$0.624082\pi$
$6$	−0.141370	+	0.0127187i	−0.0577142	+	0.00519238i
$7$	−1.05288	−	0.436118i	−0.397952	−	0.164837i	0.174727	−	0.984617i	$-0.444096\pi$
$7$	−1.05288	−	0.436118i	−0.397952	−	0.164837i	−0.572679	+	0.819780i	$0.694096\pi$
$8$	1.39610	−	2.45986i	0.493597	−	0.869691i
$9$			2.98993i			0.996642i
$10$	3.74933	−	4.49066i	1.18564	−	1.42007i
$11$	−1.46992	−	1.46992i	−0.443196	−	0.443196i	0.449888	−	0.893085i	$-0.351464\pi$
$11$	−1.46992	−	1.46992i	−0.443196	−	0.443196i	−0.893085	+	0.449888i	$0.851464\pi$
$12$	0.164997	+	0.114327i	0.0476305	+	0.0330033i
$13$	0.796050	−	1.92184i	0.220785	−	0.533021i	−0.774212	−	0.632926i	$-0.781854\pi$
$13$	0.796050	−	1.92184i	0.220785	−	0.533021i	0.994997	+	0.0999046i	$0.0318538\pi$
$14$	0.747705	+	1.42774i	0.199833	+	0.381581i
$15$	0.293579	+	0.293579i	0.0758019	+	0.0758019i
$16$	−3.74513	+	1.40499i	−0.936283	+	0.351247i
$17$	3.59022	+	2.02739i	0.870756	+	0.491715i
$17$	3.59022	+	2.02739i	0.870756	+	0.491715i
$18$	2.70999	−	3.24581i	0.638750	−	0.765045i
$19$	−4.64149	+	1.92257i	−1.06483	+	0.441067i	−0.845164	−	0.534508i	$-0.820497\pi$
$19$	−4.64149	+	1.92257i	−1.06483	+	0.441067i	−0.219667	+	0.975575i	$0.570497\pi$
$20$	−8.14041	+	1.47669i	−1.82025	+	0.330198i
$21$	−0.105675	+	0.0437721i	−0.0230602	+	0.00955186i
$22$	0.263424	+	2.92801i	0.0561623	+	0.624253i
$23$	−4.14931	−	1.71870i	−0.865192	−	0.358374i	−0.0944560	−	0.995529i	$-0.530111\pi$
$23$	−4.14931	−	1.71870i	−0.865192	−	0.358374i	−0.770736	+	0.637155i	$0.780111\pi$
$24$	−0.0754952	−	0.273660i	−0.0154104	−	0.0558606i
$25$	−12.1117			−2.42235
$26$	−2.60608	+	1.36479i	−0.511094	+	0.267658i
$27$	0.425109	+	0.425109i	0.0818122	+	0.0818122i
$28$	0.482372	−	2.22763i	0.0911598	−	0.420983i
$29$	−0.0567121	−	0.0567121i	−0.0105312	−	0.0105312i	0.701822	−	0.712353i	$-0.252370\pi$
$29$	−0.0567121	−	0.0567121i	−0.0105312	−	0.0105312i	−0.712353	+	0.701822i	$0.752370\pi$
$30$	−0.0526125	−	0.584797i	−0.00960569	−	0.106769i
$31$	−8.68138	−	3.59595i	−1.55922	−	0.645851i	−0.574268	−	0.818667i	$-0.694713\pi$
$31$	−8.68138	−	3.59595i	−1.55922	−	0.645851i	−0.984954	+	0.172816i	$0.944713\pi$
$32$	5.33909	+	1.86925i	0.943827	+	0.330440i
$33$	−0.208642			−0.0363199
$34$	−2.05991	−	5.45498i	−0.353271	−	0.935521i
$35$	1.80406	−	4.35538i	0.304942	−	0.736194i
$36$	−5.88383	+	1.06734i	−0.980638	+	0.177890i
$37$	9.83922			1.61756			0.808779	−	0.588112i	$-0.200129\pi$
$37$	9.83922			1.61756			0.808779	+	0.588112i	$0.200129\pi$
$38$	6.78128	+	2.11981i	1.10007	+	0.343879i
$39$	−0.0798977	−	0.192890i	−0.0127939	−	0.0308871i
$40$	10.1755	+	5.77517i	1.60889	+	0.913135i
$41$	−3.38846	+	8.18046i	−0.529188	+	1.27757i	0.402868	+	0.915258i	$0.368013\pi$
$41$	−3.38846	+	8.18046i	−0.529188	+	1.27757i	−0.932056	+	0.362315i	$0.881987\pi$
$42$	0.154393	+	0.0482628i	0.0238234	+	0.00744712i
$43$	−3.21310	+	7.75710i	−0.489992	+	1.18295i	0.464731	+	0.885452i	$0.346151\pi$
$43$	−3.21310	+	7.75710i	−0.489992	+	1.18295i	−0.954724	+	0.297495i	$0.903849\pi$
$44$	2.36789	−	3.41735i	0.356974	−	0.515185i
$45$	−12.3682			−1.84375
$46$	2.94664	+	5.62662i	0.434458	+	0.829599i
$47$	−0.385124			−0.0561761			−0.0280881	−	0.999605i	$-0.508942\pi$
$47$	−0.385124			−0.0561761			−0.0280881	+	0.999605i	$0.508942\pi$
$48$	−0.166082	+	0.365507i	−0.0239718	+	0.0527564i
$49$	−4.03139	−	4.03139i	−0.575912	−	0.575912i
$50$	13.1483	+	10.9777i	1.85945	+	1.55249i
$51$	0.398686	−	0.110915i	0.0558271	−	0.0155312i
$52$	4.06612	+	0.880479i	0.563870	+	0.122100i
$53$	−3.84049	−	1.59078i	−0.527532	−	0.218511i	0.102990	−	0.994682i	$-0.467159\pi$
$53$	−3.84049	−	1.59078i	−0.527532	−	0.218511i	−0.630522	+	0.776171i	$0.717159\pi$
$54$	−0.0761840	−	0.846798i	−0.0103673	−	0.115235i
$55$	6.08050	−	6.08050i	0.819895	−	0.819895i
$56$	−2.54272	+	1.98107i	−0.339785	+	0.264732i
$57$	−0.192964	+	0.465855i	−0.0255586	+	0.0617040i
$58$	0.0101634	+	0.112968i	0.00133452	+	0.0148334i
$59$	11.8591	+	4.91222i	1.54393	+	0.639516i	0.982206	−	0.187808i	$-0.0601384\pi$
$59$	11.8591	+	4.91222i	1.54393	+	0.639516i	0.561724	+	0.827325i	$0.310138\pi$
$60$	−0.472928	+	0.682532i	−0.0610548	+	0.0881145i
$61$	6.02168			0.770998			0.385499	−	0.922708i	$-0.374029\pi$
$61$	6.02168			0.770998			0.385499	+	0.922708i	$0.374029\pi$
$62$	6.16509	+	11.7723i	0.782968	+	1.49508i
$63$	1.30396	−	3.14804i	0.164284	−	0.396616i
$64$	−4.10179	−	6.86843i	−0.512723	−	0.858554i
$65$	7.94993	+	3.29297i	0.986067	+	0.408442i
$66$	0.226498	+	0.189107i	0.0278800	+	0.0232775i
$67$	−2.58048	+	6.22983i	−0.315256	+	0.761094i	0.684238	+	0.729259i	$0.260135\pi$
$67$	−2.58048	+	6.22983i	−0.315256	+	0.761094i	−0.999493	+	0.0318352i	$0.989865\pi$
$68$	−2.70804	+	7.78887i	−0.328398	+	0.944539i
$69$	−0.416457	+	0.172502i	−0.0501355	+	0.0207668i
$70$	−5.90605	+	3.09298i	−0.705909	+	0.369682i
$71$	14.5522	−	6.02773i	1.72703	−	0.715359i	0.727457	−	0.686153i	$-0.240702\pi$
$71$	14.5522	−	6.02773i	1.72703	−	0.715359i	0.999573	−	0.0292063i	$-0.00929796\pi$
$72$	7.35479	+	4.17425i	0.866770	+	0.491940i
$73$	−7.59896	+	3.14759i	−0.889391	+	0.368398i	−0.780132	−	0.625615i	$-0.784848\pi$
$73$	−7.59896	+	3.14759i	−0.889391	+	0.368398i	−0.109259	+	0.994013i	$0.534848\pi$
$74$	−10.6813	−	8.91800i	−1.24167	−	1.03670i
$75$	−0.859577	+	0.859577i	−0.0992554	+	0.0992554i
$76$	−5.44030	−	8.44759i	−0.624046	−	0.969005i
$77$	0.906591	+	2.18870i	0.103316	+	0.249426i
$78$	−0.0880947	+	0.281815i	−0.00997476	+	0.0319093i
$79$	2.10664	+	5.08589i	0.237016	+	0.572207i	0.996971	−	0.0777678i	$-0.0247793\pi$
$79$	2.10664	+	5.08589i	0.237016	+	0.572207i	−0.759955	+	0.649975i	$0.774779\pi$
$80$	−5.81192	−	15.4922i	−0.649792	−	1.73208i
$81$	−8.90944			−0.989938
$82$	11.0930	−	5.80936i	1.22502	−	0.641537i
$83$	0.109122	−	0.0451999i	0.0119777	−	0.00496133i	−0.376687	−	0.926341i	$-0.622937\pi$
$83$	0.109122	−	0.0451999i	0.0119777	−	0.00496133i	0.388664	+	0.921379i	$0.372937\pi$
$84$	−0.123862	−	0.192331i	−0.0135145	−	0.0209850i
$85$	−8.38658	+	14.8514i	−0.909652	+	1.61086i
$86$	10.5189	−	5.50871i	1.13428	−	0.594020i
$87$	−0.00804979			−0.000863028
$88$	−5.66794	+	1.56363i	−0.604204	+	0.166683i
$89$	−3.36692	−	3.36692i	−0.356893	−	0.356893i	0.505774	−	0.862666i	$-0.331207\pi$
$89$	−3.36692	−	3.36692i	−0.356893	−	0.356893i	−0.862666	+	0.505774i	$0.831207\pi$
$90$	13.4267	+	11.2102i	1.41530	+	1.18166i
$91$	−1.67629	+	1.67629i	−0.175723	+	0.175723i
$92$	1.90099	−	8.77891i	0.198192	−	0.915264i
$93$	−0.871330	+	0.360917i	−0.0903527	+	0.0374253i
$94$	0.418084	+	0.349066i	0.0431221	+	0.0360034i
$95$	−7.95295	−	19.2001i	−0.815956	−	1.96989i
$96$	0.511581	−	0.246257i	0.0522130	−	0.0251335i
$97$	−2.64025	+	6.37414i	−0.268077	+	0.647196i	−0.999393	−	0.0348437i	$-0.988907\pi$
$97$	−2.64025	+	6.37414i	−0.268077	+	0.647196i	0.731316	+	0.682039i	$0.238907\pi$
$98$	0.722467	+	8.03034i	0.0729802	+	0.811187i
$99$	4.39494	−	4.39494i	0.441708	−	0.441708i
$100$	−4.32364	−	23.8345i	−0.432364	−	2.38345i
$101$	−1.05173	+	0.435642i	−0.104651	+	0.0433480i	−0.434395	−	0.900723i	$-0.643038\pi$
$101$	−1.05173	+	0.435642i	−0.104651	+	0.0433480i	0.329744	+	0.944071i	$0.393038\pi$
$102$	−0.533336	−	0.240950i	−0.0528082	−	0.0238576i
$103$	−10.6940	+	10.6940i	−1.05371	+	1.05371i	−0.0552415	+	0.998473i	$0.517593\pi$
$103$	−10.6940	+	10.6940i	−1.05371	+	1.05371i	−0.998473	+	0.0552415i	$0.982407\pi$
$104$	−3.61607	−	4.64125i	−0.354585	−	0.455112i
$105$	−0.181069	−	0.437140i	−0.0176705	−	0.0426605i
$106$	2.72733	+	5.20784i	0.264902	+	0.505830i
$107$	9.85063			0.952296			0.476148	−	0.879365i	$-0.342033\pi$
$107$	9.85063			0.952296			0.476148	+	0.879365i	$0.342033\pi$
$108$	−0.684810	+	0.988320i	−0.0658959	+	0.0951011i
$109$		−	8.22170i		−	0.787496i	−0.919218	−	0.393748i	$-0.871178\pi$
$109$		−	8.22170i		−	0.787496i	0.919218	−	0.393748i	$-0.128822\pi$
$110$	−12.1121	+	1.08969i	−1.15484	+	0.103898i
$111$	0.698296	−	0.698296i	0.0662793	−	0.0662793i
$112$	4.55592	+	0.154034i	0.430494	+	0.0145548i
$113$	2.70762	+	6.53677i	0.254712	+	0.614928i	0.998573	−	0.0534060i	$-0.0170077\pi$
$113$	2.70762	+	6.53677i	0.254712	+	0.614928i	−0.743861	+	0.668334i	$0.767008\pi$
$114$	0.631716	−	0.330828i	0.0591656	−	0.0309848i
$115$	7.10964	−	17.1642i	0.662977	−	1.60057i
$116$	0.0913578	−	0.131848i	0.00848236	−	0.0122418i
$117$	5.74615	+	2.38013i	0.531231	+	0.220043i
$118$	−8.42178	−	16.0814i	−0.775288	−	1.48041i
$119$	−2.89589	−	3.70036i	−0.265466	−	0.339212i
$120$	1.13203	−	0.312296i	0.103340	−	0.0285086i
$121$		−	6.67869i		−	0.607154i
$122$	−6.53703	−	5.45789i	−0.591835	−	0.494134i
$123$	0.340091	+	0.821053i	0.0306650	+	0.0740319i
$124$	3.97733	−	18.3676i	0.357175	−	1.64946i
$125$		−	29.4186i		−	2.63128i
$126$	−4.26885	+	2.23558i	−0.380299	+	0.199162i
$127$	1.80969	+	1.80969i	0.160584	+	0.160584i	0.782825	−	0.622242i	$-0.213778\pi$
$127$	1.80969	+	1.80969i	0.160584	+	0.160584i	−0.622242	+	0.782825i	$0.713778\pi$
$128$	−1.77253	+	11.1740i	−0.156671	+	0.987651i
$129$	0.322491	+	0.778562i	0.0283937	+	0.0685485i
$130$	−5.64565	−	10.7804i	−0.495156	−	0.945502i
$131$	7.10259	+	7.10259i	0.620556	+	0.620556i	0.945674	−	0.325118i	$-0.105404\pi$
$131$	7.10259	+	7.10259i	0.620556	+	0.620556i	−0.325118	+	0.945674i	$0.605404\pi$
$132$	−0.0744808	−	0.410583i	−0.00648272	−	0.0357366i
$133$	5.72540			0.496455
$134$	8.44786	−	4.42412i	0.729784	−	0.382186i
$135$	−1.75852	+	1.75852i	−0.151349	+	0.151349i
$136$	9.99942	−	6.00097i	0.857443	−	0.514579i
$137$	2.37223	+	2.37223i	0.202673	+	0.202673i	0.801144	−	0.598471i	$-0.204225\pi$
$137$	2.37223	+	2.37223i	0.202673	+	0.202673i	−0.598471	+	0.801144i	$0.704225\pi$
$138$	0.608449	+	0.190200i	0.0517947	+	0.0161909i
$139$			5.67775i			0.481580i	0.970577	+	0.240790i	$0.0774066\pi$
$139$			5.67775i			0.481580i	−0.970577	+	0.240790i	$0.922593\pi$
$140$	9.21490	+	1.99540i	0.778801	+	0.168642i
$141$	−0.0273325	+	0.0273325i	−0.00230181	+	0.00230181i
$142$	−21.2610	−	6.64613i	−1.78418	−	0.557731i
$143$	−3.99507	+	1.65481i	−0.334084	+	0.138382i
$144$	−4.20081	−	11.1977i	−0.350067	−	0.933139i
$145$	0.234597	−	0.234597i	0.0194822	−	0.0194822i
$146$	11.1022	+	3.47051i	0.918824	+	0.287222i
$147$	−0.572220			−0.0471959
$148$	3.51240	+	19.3624i	0.288717	+	1.59158i
$149$	11.1370	−	4.61311i	0.912381	−	0.377921i	0.123413	−	0.992355i	$-0.460616\pi$
$149$	11.1370	−	4.61311i	0.912381	−	0.377921i	0.788968	+	0.614435i	$0.210616\pi$
$150$	1.71224	−	0.154045i	0.139804	−	0.0125777i
$151$	−18.7792			−1.52823			−0.764115	−	0.645080i	$-0.776824\pi$
$151$	−18.7792			−1.52823			−0.764115	+	0.645080i	$0.776824\pi$
$152$	−1.75076	+	14.1015i	−0.142006	+	1.14378i
$153$	−6.06176	+	10.7345i	−0.490064	+	0.867832i
$154$	0.999601	−	3.19773i	0.0805502	−	0.257680i
$155$	14.8751	−	35.9117i	1.19480	−	2.88450i
$156$	0.351063	−	0.226087i	0.0281076	−	0.0181015i
$157$	−12.8608	−	5.32712i	−1.02640	−	0.425150i	−0.194990	−	0.980805i	$-0.562468\pi$
$157$	−12.8608	−	5.32712i	−1.02640	−	0.425150i	−0.831413	+	0.555655i	$0.812468\pi$
$158$	2.32277	−	7.43056i	0.184790	−	0.591143i
$159$	−0.385461	+	0.159663i	−0.0305691	+	0.0126621i
$160$	−7.73241	+	22.0859i	−0.611301	+	1.74604i
$161$	3.61918	+	3.61918i	0.285231	+	0.285231i
$162$	9.67193	+	8.07527i	0.759899	+	0.634453i
$163$	15.1615			1.18754			0.593770	−	0.804635i	$-0.297639\pi$
$163$	15.1615			1.18754			0.593770	+	0.804635i	$0.297639\pi$
$164$	−17.3078	−	3.74783i	−1.35151	−	0.292657i
$165$		−	0.863075i		−	0.0671903i
$166$	−0.159429	−	0.0498371i	−0.0123741	−	0.00386811i
$167$	4.82552	−	1.99880i	0.373410	−	0.154672i	−0.188082	−	0.982153i	$-0.560227\pi$
$167$	4.82552	−	1.99880i	0.373410	−	0.154672i	0.561493	+	0.827482i	$0.310227\pi$
$168$	−0.0398605	+	0.321056i	−0.00307531	+	0.0247700i
$169$	6.13263	+	6.13263i	0.471741	+	0.471741i
$170$	22.5652	−	8.52108i	1.73067	−	0.653537i
$171$	−5.74833	−	13.8777i	−0.439586	−	1.06125i
$172$	−16.4121	−	3.55387i	−1.25141	−	0.270980i
$173$	15.4920	+	15.4920i	1.17783	+	1.17783i	0.980295	+	0.197538i	$0.0632944\pi$
$173$	15.4920	+	15.4920i	1.17783	+	1.17783i	0.197538	+	0.980295i	$0.436706\pi$
$174$	0.00873871	+	0.00729610i	0.000662480	+	0.000553116i
$175$	12.7522	+	5.28214i	0.963977	+	0.399292i
$176$	7.57024	+	3.43982i	0.570629	+	0.259286i
$177$	1.19027	−	0.493028i	0.0894665	−	0.0370582i
$178$	0.603387	+	6.70675i	0.0452258	+	0.502692i
$179$	−1.68363	−	4.06465i	−0.125841	−	0.303806i	0.848386	−	0.529378i	$-0.177575\pi$
$179$	−1.68363	−	4.06465i	−0.125841	−	0.303806i	−0.974226	+	0.225572i	$0.927575\pi$
$180$	−4.41520	−	24.3392i	−0.329090	−	1.81414i
$181$	0.859418	+	0.859418i	0.0638800	+	0.0638800i	0.738325	−	0.674445i	$-0.235617\pi$
$181$	0.859418	+	0.859418i	0.0638800	+	0.0638800i	−0.674445	+	0.738325i	$0.735617\pi$
$182$	3.33910	−	0.300409i	0.247511	−	0.0222678i
$183$	0.427363	−	0.427363i	0.0315916	−	0.0315916i
$184$	−10.0206	+	7.80723i	−0.738731	+	0.575556i
$185$			40.7013i			2.99242i
$186$	1.27303	+	0.397944i	0.0933428	+	0.0291787i
$187$	−2.29722	−	8.25742i	−0.167990	−	0.603842i
$188$	−0.137481	−	0.757879i	−0.0100269	−	0.0552740i
$189$	−0.262192	−	0.632987i	−0.0190716	−	0.0460430i
$190$	−8.76887	+	28.0517i	−0.636161	+	2.03508i
$191$			20.6078i			1.49113i	0.666435	+	0.745563i	$0.267820\pi$
$191$			20.6078i			1.49113i	−0.666435	+	0.745563i	$0.732180\pi$
$192$	−0.778563	−	0.196351i	−0.0561880	−	0.0141704i
$193$	22.4951	−	9.31777i	1.61923	−	0.670708i	0.625267	−	0.780411i	$-0.284990\pi$
$193$	22.4951	−	9.31777i	1.61923	−	0.670708i	0.993964	+	0.109703i	$0.0349901\pi$
$194$	8.64355	−	4.52660i	0.620571	−	0.324991i
$195$	0.797916	−	0.330507i	0.0571399	−	0.0236681i
$196$	6.49418	−	9.37242i	0.463870	−	0.669459i
$197$	0.561695	+	0.561695i	0.0400191	+	0.0400191i	0.726833	−	0.686814i	$-0.240991\pi$
$197$	0.561695	+	0.561695i	0.0400191	+	0.0400191i	−0.686814	+	0.726833i	$0.740991\pi$
$198$	−8.75452	+	0.787620i	−0.622157	+	0.0559737i
$199$	1.06839	+	2.57931i	0.0757359	+	0.182843i	0.957213	−	0.289384i	$-0.0934504\pi$
$199$	1.06839	+	2.57931i	0.0757359	+	0.182843i	−0.881477	+	0.472227i	$0.843450\pi$
$200$	−16.9092	+	29.7931i	−1.19566	+	2.10669i
$201$	0.258997	+	0.625273i	0.0182682	+	0.0441034i
$202$	1.53660	+	0.480336i	0.108115	+	0.0337963i
$203$	0.0349780	+	0.0844443i	0.00245497	+	0.00592683i
$204$	0.360590	+	0.744973i	0.0252463	+	0.0521585i
$205$	−33.8396	−	14.0168i	−2.36346	−	0.978976i
$206$	21.3020	−	1.91648i	1.48418	−	0.133528i
$207$	5.13879	−	12.4061i	0.357171	−	0.862287i
$208$	−0.281159	+	8.31597i	−0.0194949	+	0.576609i
$209$	9.64861	+	3.99659i	0.667408	+	0.276450i
$210$	−0.199646	+	0.638667i	−0.0137769	+	0.0440722i
$211$			9.28471i			0.639186i	0.947555	+	0.319593i	$0.103546\pi$
$211$			9.28471i			0.639186i	−0.947555	+	0.319593i	$0.896454\pi$
$212$	1.75950	−	8.12552i	0.120843	−	0.558063i
$213$	0.604989	−	1.46057i	0.0414531	−	0.100077i
$214$	−10.6937	−	8.92833i	−0.731004	−	0.610328i
$215$	−32.0883	−	13.2914i	−2.18840	−	0.906466i
$216$	1.63920	−	0.452210i	0.111534	−	0.0307690i
$217$	7.57221	+	7.57221i	0.514035	+	0.514035i
$218$	−7.45192	+	8.92533i	−0.504708	+	0.604500i
$219$	−0.315916	+	0.762690i	−0.0213477	+	0.0515378i
$220$	14.1363	+	9.79511i	0.953072	+	0.660386i
$221$	6.75431	−	5.28591i	0.454344	−	0.355568i
$222$	−1.39097	+	0.125142i	−0.0933561	+	0.00839898i
$223$	15.0993	−	15.0993i	1.01112	−	1.01112i	0.0111836	−	0.999937i	$-0.496440\pi$
$223$	15.0993	−	15.0993i	1.01112	−	1.01112i	0.999937	−	0.0111836i	$-0.00355992\pi$
$224$	−4.80622	−	4.29658i	−0.321129	−	0.287077i
$225$		−	36.2132i		−	2.41421i
$226$	2.98540	−	9.55032i	0.198586	−	0.635278i
$227$			10.4970i			0.696707i	0.937363	+	0.348354i	$0.113259\pi$
$227$			10.4970i			0.696707i	−0.937363	+	0.348354i	$0.886741\pi$
$228$	−0.985633	−	0.213429i	−0.0652751	−	0.0141347i
$229$	−18.0987	−	7.49674i	−1.19600	−	0.495398i	−0.306294	−	0.951937i	$-0.599089\pi$
$229$	−18.0987	−	7.49674i	−1.19600	−	0.495398i	−0.889703	+	0.456539i	$0.849089\pi$
$230$	−23.2752	+	12.1892i	−1.53472	+	0.803730i
$231$	0.219675	+	0.0909924i	0.0144536	+	0.00598686i
$232$	−0.218680	+	0.0603276i	−0.0143570	+	0.00396070i
$233$	2.46648	−	1.02165i	0.161585	−	0.0669305i	−0.300425	−	0.953805i	$-0.597129\pi$
$233$	2.46648	−	1.02165i	0.161585	−	0.0669305i	0.462010	+	0.886875i	$0.347129\pi$
$234$	−4.08063	−	7.79198i	−0.266759	−	0.509378i
$235$		−	1.59312i		−	0.103923i
$236$	−5.43321	+	25.0910i	−0.353672	+	1.63328i
$237$	0.510459	+	0.211439i	0.0331579	+	0.0137344i
$238$	−0.210174	+	6.64181i	−0.0136235	+	0.430524i
$239$			13.3331i			0.862447i	0.902245	+	0.431224i	$0.141918\pi$
$239$			13.3331i			0.862447i	−0.902245	+	0.431224i	$0.858082\pi$
$240$	−1.51197	−	0.687018i	−0.0975972	−	0.0443468i
$241$	−2.68479	+	6.48164i	−0.172942	+	0.417519i	−0.986456	−	0.164026i	$-0.947552\pi$
$241$	−2.68479	+	6.48164i	−0.172942	+	0.417519i	0.813514	+	0.581546i	$0.197552\pi$
$242$	−6.05338	+	7.25027i	−0.389126	+	0.466065i
$243$	−1.90764	+	1.90764i	−0.122375	+	0.122375i
$244$	2.14962	+	11.8500i	0.137615	+	0.758617i
$245$	16.6764	−	16.6764i	1.06541	−	1.06541i
$246$	0.374982	−	1.19957i	0.0239080	−	0.0764818i
$247$			10.4506i			0.664958i
$248$	−20.9656	+	16.3346i	−1.33132	+	1.03725i
$249$	0.00453661	−	0.0109523i	0.000287496	−	0.000694076i
$250$	−26.6642	+	31.9363i	−1.68639	+	2.01983i
$251$	−1.40353	−	3.38842i	−0.0885900	−	0.213875i	0.873375	−	0.487049i	$-0.161927\pi$
$251$	−1.40353	−	3.38842i	−0.0885900	−	0.213875i	−0.961965	+	0.273174i	$0.911927\pi$
$252$	6.66046	+	1.44226i	0.419570	+	0.0908537i
$253$	3.57280	+	8.62549i	0.224620	+	0.542280i
$254$	−0.324315	−	3.60481i	−0.0203493	−	0.226186i
$255$	0.458814	+	1.64922i	0.0287320	+	0.103278i
$256$	12.0520	−	10.5237i	0.753251	−	0.657733i
$257$	−2.92885	+	2.92885i	−0.182697	+	0.182697i	−0.792530	−	0.609833i	$-0.791236\pi$
$257$	−2.92885	+	2.92885i	−0.182697	+	0.182697i	0.609833	+	0.792530i	$0.291236\pi$
$258$	0.355576	−	1.13749i	0.0221372	−	0.0708170i
$259$	−10.3595	−	4.29106i	−0.643710	−	0.266634i
$260$	−3.64222	+	16.8201i	−0.225881	+	1.04314i
$261$	0.169565	−	0.169565i	0.0104958	−	0.0104958i
$262$	−1.27286	−	14.1480i	−0.0786374	−	0.874068i
$263$	−19.9376			−1.22940			−0.614702	−	0.788759i	$-0.710724\pi$
$263$	−19.9376			−1.22940			−0.614702	+	0.788759i	$0.710724\pi$
$264$	−0.291286	+	0.513229i	−0.0179274	+	0.0315871i
$265$	6.58049	−	15.8867i	0.404236	−	0.975913i
$266$	−6.21540	−	5.18935i	−0.381091	−	0.318179i
$267$	−0.477905			−0.0292473
$268$	−13.1808	−	2.85416i	−0.805142	−	0.174346i
$269$	7.72062	+	7.72062i	0.470734	+	0.470734i	0.902152	−	0.431418i	$-0.141987\pi$
$269$	7.72062	+	7.72062i	0.470734	+	0.470734i	−0.431418	+	0.902152i	$0.641987\pi$
$270$	3.50289	−	0.315145i	0.213179	−	0.0191791i
$271$			19.1064i			1.16063i	0.814392	+	0.580315i	$0.197071\pi$
$271$			19.1064i			1.16063i	−0.814392	+	0.580315i	$0.802929\pi$
$272$	−16.2943	−	2.54864i	−0.987987	−	0.154534i
$273$			0.237935i			0.0144005i
$274$	−0.425128	−	4.72537i	−0.0256829	−	0.285470i
$275$	17.8032	+	17.8032i	1.07358	+	1.07358i
$276$	−0.488130	−	0.757959i	−0.0293820	−	0.0456238i
$277$	5.80205			0.348612			0.174306	−	0.984692i	$-0.444232\pi$
$277$	5.80205			0.348612			0.174306	+	0.984692i	$0.444232\pi$
$278$	5.14615	−	6.16367i	0.308646	−	0.369672i
$279$	10.7516	−	25.9567i	0.643682	−	1.55399i
$280$	−8.19496	−	10.5183i	−0.489743	−	0.628589i
$281$	−4.44888			−0.265398			−0.132699	−	0.991156i	$-0.542364\pi$
$281$	−4.44888			−0.265398			−0.132699	+	0.991156i	$0.542364\pi$
$282$	0.0544451	−	0.00489827i	0.00324216	−	0.000291688i
$283$	−1.78554	+	1.78554i	−0.106139	+	0.106139i	−0.758182	−	0.652043i	$-0.773912\pi$
$283$	−1.78554	+	1.78554i	−0.106139	+	0.106139i	0.652043	+	0.758182i	$0.273912\pi$
$284$	17.0567	+	26.4853i	1.01213	+	1.57161i
$285$	−1.92707	−	0.798219i	−0.114150	−	0.0472824i
$286$	5.83685	+	1.82458i	0.345140	+	0.107890i
$287$	7.13529	−	7.13529i	0.421183	−	0.421183i
$288$	−5.58893	+	15.9635i	−0.329331	+	0.940658i
$289$	8.77936	+	14.5576i	0.516433	+	0.856328i
$290$	−0.467307	+	0.0420423i	−0.0274412	+	0.00246881i
$291$	0.264996	+	0.639757i	0.0155343	+	0.0375032i
$292$	−8.90677	−	13.8302i	−0.521229	−	0.809354i
$293$	0.0186718	+	0.0450777i	0.00109082	+	0.00263347i	0.924424	−	0.381366i	$-0.124546\pi$
$293$	0.0186718	+	0.0450777i	0.00109082	+	0.00263347i	−0.923333	+	0.384000i	$0.874546\pi$
$294$	0.621192	+	0.518644i	0.0362287	+	0.0302480i
$295$	−20.3200	+	49.0569i	−1.18308	+	2.85621i
$296$	13.7366	−	24.2031i	0.798423	−	1.40678i
$297$		−	1.24975i		−	0.0725178i
$298$	−16.2714	−	5.08638i	−0.942574	−	0.294646i
$299$	−6.60613	+	6.60613i	−0.382042	+	0.382042i
$300$	−1.99840	−	1.38470i	−0.115378	−	0.0799455i
$301$	6.76602	−	6.76602i	0.389987	−	0.389987i
$302$	20.3864	+	17.0209i	1.17310	+	0.979446i
$303$	−0.0437244	+	0.105560i	−0.00251190	+	0.00606426i
$304$	14.6818	−	13.7215i	0.842059	−	0.786982i
$305$			24.9095i			1.42631i
$306$	16.3100	−	6.15897i	0.932380	−	0.352085i
$307$	11.4054	+	4.72427i	0.650940	+	0.269628i	0.683621	−	0.729838i	$-0.260404\pi$
$307$	11.4054	+	4.72427i	0.650940	+	0.269628i	−0.0326804	+	0.999466i	$0.510404\pi$
$308$	−3.98348	+	2.56539i	−0.226980	+	0.146177i
$309$			1.51793i			0.0863517i
$310$	−48.6975	+	25.5027i	−2.76583	+	1.44846i
$311$	4.36087	−	1.80633i	0.247283	−	0.102428i	−0.255600	−	0.966783i	$-0.582273\pi$
$311$	4.36087	−	1.80633i	0.247283	−	0.102428i	0.502882	+	0.864355i	$0.332273\pi$
$312$	−0.586028	−	0.0727579i	−0.0331773	−	0.00411910i
$313$	1.14599	+	0.474685i	0.0647753	+	0.0268308i	0.414836	−	0.909896i	$-0.363839\pi$
$313$	1.14599	+	0.474685i	0.0647753	+	0.0268308i	−0.350061	+	0.936727i	$0.613839\pi$
$314$	9.13311	+	17.4397i	0.515411	+	0.984179i
$315$	13.0223	+	5.39400i	0.733722	+	0.303918i
$316$	−9.25641	+	5.96119i	−0.520714	+	0.335343i
$317$		−	10.3091i		−	0.579019i	−0.957175	−	0.289510i	$-0.906508\pi$
$317$		−	10.3091i		−	0.579019i	0.957175	−	0.289510i	$-0.0934923\pi$
$318$	0.563164	+	0.176044i	0.0315807	+	0.00987204i
$319$			0.166724i			0.00933476i
$320$	28.4122	−	16.9676i	1.58829	−	0.948517i
$321$	0.699105	−	0.699105i	0.0390203	−	0.0390203i
$322$	−0.648595	−	7.20924i	−0.0361448	−	0.401755i
$323$	−20.5618	−	2.50768i	−1.14409	−	0.139531i
$324$	−3.18048	−	17.5327i	−0.176694	−	0.974041i
$325$	−9.64155	+	23.2768i	−0.534817	+	1.29116i
$326$	−16.4591	−	13.7420i	−0.911583	−	0.761096i
$327$	−0.583499	−	0.583499i	−0.0322676	−	0.0322676i
$328$	15.3921	+	19.7559i	0.849887	+	1.09084i
$329$	0.405490	+	0.167959i	0.0223554	+	0.00925991i
$330$	−0.782267	+	0.936939i	−0.0430624	+	0.0515768i
$331$	13.6990	−	33.0723i	0.752966	−	1.81782i	0.210844	−	0.977520i	$-0.432379\pi$
$331$	13.6990	−	33.0723i	0.752966	−	1.81782i	0.542122	−	0.840300i	$-0.317621\pi$
$332$	0.127903	+	0.198604i	0.00701956	+	0.0108998i
$333$			29.4186i			1.61213i
$334$	−7.05016	−	2.20386i	−0.385768	−	0.120590i
$335$	−25.7705	−	10.6745i	−1.40799	−	0.583210i
$336$	0.334268	−	0.312405i	0.0182358	−	0.0170431i
$337$	−0.950480	+	2.29466i	−0.0517760	+	0.124998i	−0.947651	−	0.319308i	$-0.896550\pi$
$337$	−0.950480	+	2.29466i	−0.0517760	+	0.124998i	0.895875	+	0.444306i	$0.146550\pi$
$338$	−1.09903	−	12.2159i	−0.0597795	−	0.664459i
$339$	0.656081	+	0.271757i	0.0356334	+	0.0147598i
$340$	−32.2197	−	11.2022i	−1.74736	−	0.607523i
$341$	7.47517	+	18.0466i	0.404803	+	0.977281i
$342$	−6.33807	+	20.2755i	−0.342724	+	1.09637i
$343$	5.53924	+	13.3729i	0.299091	+	0.722069i
$344$	14.5955	+	18.7335i	0.786938	+	1.01004i
$345$	−0.713578	−	1.72273i	−0.0384177	−	0.0927486i
$346$	−2.77632	−	30.8593i	−0.149256	−	1.65901i
$347$	17.4365	+	17.4365i	0.936042	+	0.936042i	0.998074	−	0.0620320i	$-0.0197581\pi$
$347$	17.4365	+	17.4365i	0.936042	+	0.936042i	−0.0620320	+	0.998074i	$0.519758\pi$
$348$	−0.00287361	−	0.0158410i	−0.000154042	−	0.000849169i
$349$	23.6131	−	9.78088i	1.26398	−	0.523558i	0.352852	−	0.935679i	$-0.385212\pi$
$349$	23.6131	−	9.78088i	1.26398	−	0.523558i	0.911129	+	0.412121i	$0.135212\pi$
$350$	−9.05600	−	17.2925i	−0.484064	−	0.924321i
$351$	1.15540	−	0.478581i	0.0616706	−	0.0255448i
$352$	−5.10037	−	10.5957i	−0.271851	−	0.564751i
$353$		−	0.441749i		−	0.0235119i	−0.999931	−	0.0117560i	$-0.996258\pi$
$353$		−	0.441749i		−	0.0235119i	0.999931	−	0.0117560i	$-0.00374213\pi$
$354$	−1.73901	−	0.543609i	−0.0924272	−	0.0288925i
$355$	24.9345	+	60.1972i	1.32339	+	3.19493i
$356$	5.42378	−	7.82762i	0.287460	−	0.414863i
$357$	−0.468141	−	0.0570937i	−0.0247766	−	0.00302172i
$358$	−1.85636	+	5.93850i	−0.0981117	+	0.313860i
$359$		−	25.1841i		−	1.32916i	−0.747215	−	0.664582i	$-0.768609\pi$
$359$		−	25.1841i		−	1.32916i	0.747215	−	0.664582i	$-0.231391\pi$
$360$	−17.2673	+	30.4241i	−0.910068	+	1.60349i
$361$	4.41211	−	4.41211i	0.232217	−	0.232217i
$362$	−0.154017	−	1.71192i	−0.00809494	−	0.0899766i
$363$	−0.473991	−	0.473991i	−0.0248781	−	0.0248781i
$364$	−3.89715	−	2.70035i	−0.204266	−	0.141537i
$365$	−13.0204	−	31.4341i	−0.681521	−	1.64534i
$366$	−0.851287	+	0.0765879i	−0.0444975	+	0.00400331i
$367$	14.6894	−	6.08457i	0.766783	−	0.317612i	0.0352142	−	0.999380i	$-0.488789\pi$
$367$	14.6894	−	6.08457i	0.766783	−	0.317612i	0.731568	+	0.681768i	$0.238789\pi$
$368$	17.9545	+	0.607033i	0.935942	+	0.0316438i
$369$	−24.4590	−	10.1312i	−1.27328	−	0.527411i
$370$	36.8905	−	44.1846i	1.91784	−	2.29705i
$371$	3.34981	+	3.34981i	0.173914	+	0.173914i
$372$	−1.02129	−	1.58584i	−0.0529514	−	0.0822218i
$373$	−0.331150	−	0.799468i	−0.0171463	−	0.0413949i	0.915075	−	0.403285i	$-0.132132\pi$
$373$	−0.331150	−	0.799468i	−0.0171463	−	0.0413949i	−0.932221	+	0.361890i	$0.882132\pi$
$374$	−4.99047	+	11.0463i	−0.258051	+	0.571188i
$375$	−2.08786	−	2.08786i	−0.107817	−	0.107817i
$376$	−0.537673	+	0.947350i	−0.0277284	+	0.0488558i
$377$	−0.154137	+	0.0638456i	−0.00793846	+	0.00328822i
$378$	−0.289091	+	0.924803i	−0.0148692	+	0.0475667i
$379$		−	7.10676i		−	0.365050i	−0.983201	−	0.182525i	$-0.941573\pi$
$379$		−	7.10676i		−	0.365050i	0.983201	−	0.182525i	$-0.0584270\pi$
$380$	34.9446	−	22.5045i	1.79262	−	1.15446i
$381$	0.256869			0.0131598
$382$	18.6783	−	22.3715i	0.955666	−	1.14462i
$383$	13.8901	+	13.8901i	0.709753	+	0.709753i	0.966483	−	0.256730i	$-0.0826452\pi$
$383$	13.8901	+	13.8901i	0.709753	+	0.709753i	−0.256730	+	0.966483i	$0.582645\pi$
$384$	0.667228	+	0.918823i	0.0340493	+	0.0468885i
$385$	−9.05387	+	3.75023i	−0.461428	+	0.191130i
$386$	−32.8656	−	10.2737i	−1.67282	−	0.522918i
$387$	−23.1932	−	9.60692i	−1.17897	−	0.488347i
$388$	−13.4861	−	2.92028i	−0.684652	−	0.148255i
$389$	10.3625	−	25.0172i	0.525399	−	1.26842i	−0.409111	−	0.912485i	$-0.634161\pi$
$389$	10.3625	−	25.0172i	0.525399	−	1.26842i	0.934509	−	0.355939i	$-0.115839\pi$
$390$	−1.16577	−	0.364415i	−0.0590309	−	0.0184529i
$391$	−11.4125	−	14.5828i	−0.577153	−	0.737484i
$392$	−15.5449	+	4.28840i	−0.785134	+	0.216597i
$393$	1.00815			0.0508544
$394$	−0.100662	−	1.11887i	−0.00507126	−	0.0563679i
$395$	−21.0385	+	8.71442i	−1.05856	+	0.438470i
$396$	10.2176	+	7.07983i	0.513456	+	0.355775i
$397$	2.02925			0.101845			0.0509226	−	0.998703i	$-0.483784\pi$
$397$	2.02925			0.101845			0.0509226	+	0.998703i	$0.483784\pi$
$398$	1.17800	−	3.76841i	0.0590476	−	0.188894i
$399$	0.406336	−	0.406336i	0.0203422	−	0.0203422i
$400$	45.3600	−	17.0168i	2.26800	−	0.850841i
$401$	−7.32961	+	3.03602i	−0.366023	+	0.151612i	−0.558112	−	0.829766i	$-0.688474\pi$
$401$	−7.32961	+	3.03602i	−0.366023	+	0.151612i	0.192089	+	0.981378i	$0.438474\pi$
$402$	0.285568	−	0.913533i	0.0142428	−	0.0455629i
$403$	−13.8216	+	13.8216i	−0.688505	+	0.688505i
$404$	−1.23274	−	1.91417i	−0.0613311	−	0.0952336i
$405$		−	36.8551i		−	1.83134i
$406$	0.0385665	−	0.123374i	0.00191402	−	0.00612296i
$407$	−14.4628	−	14.4628i	−0.716896	−	0.716896i
$408$	0.283772	−	1.13556i	0.0140488	−	0.0562185i
$409$	4.01102	−	4.01102i	0.198332	−	0.198332i	−0.600952	−	0.799285i	$-0.705212\pi$
$409$	4.01102	−	4.01102i	0.198332	−	0.198332i	0.799285	+	0.600952i	$0.205212\pi$
$410$	24.0312	+	45.8876i	1.18682	+	2.26623i
$411$	0.336717			0.0166090
$412$	−24.8622	−	17.2271i	−1.22487	−	0.848717i
$413$	−10.3440	−	10.3440i	−0.508994	−	0.508994i
$414$	−16.8232	+	8.81023i	−0.826813	+	0.432999i
$415$	0.186975	+	0.451399i	0.00917826	+	0.0221583i
$416$	7.84258	−	8.77284i	0.384514	−	0.430124i
$417$	0.402954	+	0.402954i	0.0197327	+	0.0197327i
$418$	−6.85197	−	13.0839i	−0.335141	−	0.639952i
$419$			34.6142i			1.69101i	0.533966	+	0.845506i	$0.320701\pi$
$419$			34.6142i			1.69101i	−0.533966	+	0.845506i	$0.679299\pi$
$420$	0.795602	−	0.512373i	0.0388214	−	0.0250012i
$421$	6.41756	+	15.4934i	0.312773	+	0.755100i	0.999600	+	0.0282795i	$0.00900285\pi$
$421$	6.41756	+	15.4934i	0.312773	+	0.755100i	−0.686827	+	0.726821i	$0.740997\pi$
$422$	8.41540	−	10.0793i	0.409655	−	0.490653i
$423$		−	1.15149i		−	0.0559875i
$424$	−9.27483	+	7.22616i	−0.450426	+	0.350933i
$425$	−43.4838	−	24.5552i	−2.10927	−	1.19110i
$426$	−1.98059	+	1.03723i	−0.0959597	+	0.0502538i
$427$	−6.34012	−	2.62616i	−0.306820	−	0.127089i
$428$	3.51647	+	19.3849i	0.169975	+	0.937004i
$429$	−0.166089	+	0.400975i	−0.00801887	+	0.0193593i
$430$	22.7875	+	43.5128i	1.09891	+	2.09837i
$431$	4.64457	+	11.2130i	0.223721	+	0.540110i	0.995390	−	0.0959145i	$-0.0305776\pi$
$431$	4.64457	+	11.2130i	0.223721	+	0.540110i	−0.771669	+	0.636025i	$0.780578\pi$
$432$	−2.18936	−	0.994816i	−0.105336	−	0.0478631i
$433$	−1.21852	+	1.21852i	−0.0585583	+	0.0585583i	−0.735779	−	0.677221i	$-0.763184\pi$
$433$	−1.21852	+	1.21852i	−0.0585583	+	0.0585583i	0.677221	+	0.735779i	$0.263184\pi$
$434$	−1.35702	−	15.0835i	−0.0651391	−	0.724031i
$435$		−	0.0332990i		−	0.00159657i
$436$	16.1793	−	2.93498i	0.774850	−	0.140560i
$437$	22.5633			1.07935
$438$	1.03423	−	0.541625i	0.0494176	−	0.0258798i
$439$	−3.48763	−	8.41988i	−0.166456	−	0.401859i	0.818538	−	0.574453i	$-0.194785\pi$
$439$	−3.48763	−	8.41988i	−0.166456	−	0.401859i	−0.984993	+	0.172594i	$0.944785\pi$
$440$	−6.46815	−	23.4462i	−0.308357	−	1.11775i
$441$	12.0535	−	12.0535i	0.573979	−	0.573979i
$442$	−12.1234	−	0.383633i	−0.576649	−	0.0182475i
$443$	−9.39370	+	3.89100i	−0.446308	+	0.184867i	−0.594506	−	0.804091i	$-0.702653\pi$
$443$	−9.39370	+	3.89100i	−0.446308	+	0.184867i	0.148198	+	0.988958i	$0.452653\pi$
$444$	1.62344	+	1.12489i	0.0770452	+	0.0533848i
$445$	13.9277	−	13.9277i	0.660236	−	0.660236i
$446$	−30.0770	+	2.70595i	−1.42419	+	0.128130i
$447$	0.463007	−	1.11780i	0.0218995	−	0.0528700i
$448$	1.32325	+	9.02051i	0.0625176	+	0.426179i
$449$	−13.0839	−	31.5873i	−0.617467	−	1.49070i	−0.854635	−	0.519229i	$-0.826219\pi$
$449$	−13.0839	−	31.5873i	−0.617467	−	1.49070i	0.237168	−	0.971469i	$-0.423781\pi$
$450$	−32.8226	+	39.3124i	−1.54727	+	1.85320i
$451$	17.0053	−	7.04384i	0.800750	−	0.331682i
$452$	−11.8970	+	7.66177i	−0.559590	+	0.360380i
$453$	−1.33277	+	1.33277i	−0.0626191	+	0.0626191i
$454$	9.51415	−	11.3953i	0.446521	−	0.534809i
$455$	−6.93421	−	6.93421i	−0.325081	−	0.325081i
$456$	0.876540	+	1.12505i	0.0410477	+	0.0526851i
$457$	−7.61516			−0.356222			−0.178111	−	0.984010i	$-0.556999\pi$
$457$	−7.61516			−0.356222			−0.178111	+	0.984010i	$0.556999\pi$
$458$	12.8528	+	24.5425i	0.600573	+	1.14680i
$459$	0.664372	+	2.38810i	0.0310102	+	0.111467i
$460$	36.3151	+	7.86368i	1.69320	+	0.366646i
$461$	−11.5233	+	4.77312i	−0.536696	+	0.222307i	−0.634533	−	0.772896i	$-0.718808\pi$
$461$	−11.5233	+	4.77312i	−0.536696	+	0.222307i	0.0978373	+	0.995202i	$0.468808\pi$
$462$	−0.156003	−	0.297887i	−0.00725789	−	0.0138590i
$463$	16.6351			0.773100			0.386550	−	0.922268i	$-0.373667\pi$
$463$	16.6351			0.773100			0.386550	+	0.922268i	$0.373667\pi$
$464$	0.292074	+	0.132714i	0.0135592	+	0.00616112i
$465$	−1.49298	−	3.60437i	−0.0692353	−	0.167149i
$466$	−3.60356	−	1.12646i	−0.166932	−	0.0521825i
$467$	8.99160	+	21.7076i	0.416082	+	1.00451i	0.983472	+	0.181061i	$0.0579531\pi$
$467$	8.99160	+	21.7076i	0.416082	+	1.00451i	−0.567390	+	0.823449i	$0.692047\pi$
$468$	−2.63257	+	12.1574i	−0.121690	+	0.561976i
$469$	5.43388	−	5.43388i	0.250913	−	0.250913i
$470$	−1.44396	+	1.72946i	−0.0666048	+	0.0797740i
$471$	−1.29081	+	0.534670i	−0.0594773	+	0.0246363i
$472$	28.6400	−	22.3138i	1.31826	−	1.02708i
$473$	16.1253	−	6.67930i	0.741441	−	0.307115i
$474$	−0.362503	−	0.692200i	−0.0166503	−	0.0317938i
$475$	56.2164	−	23.2856i	2.57939	−	1.06842i
$476$	6.24811	−	7.01974i	0.286382	−	0.321749i
$477$	4.75633	−	11.4828i	0.217777	−	0.525761i
$478$	12.0848	−	14.4742i	0.552744	−	0.662034i
$479$	−13.0509	−	5.40585i	−0.596310	−	0.247000i	0.0640528	−	0.997947i	$-0.479597\pi$
$479$	−13.0509	−	5.40585i	−0.596310	−	0.247000i	−0.660363	+	0.750947i	$0.729597\pi$
$480$	1.01867	+	2.11622i	0.0464959	+	0.0965919i
$481$	7.83252	−	18.9094i	0.357132	−	0.862193i
$482$	8.78934	−	4.60295i	0.400343	−	0.209658i
$483$	0.513711			0.0233747
$484$	13.1429	−	2.38415i	0.597404	−	0.108371i
$485$	−26.3675	−	10.9218i	−1.19728	−	0.495932i
$486$	3.79992	−	0.341868i	0.172368	−	0.0155075i
$487$	11.6215	−	28.0567i	0.526619	−	1.27137i	−0.407107	−	0.913381i	$-0.633462\pi$
$487$	11.6215	−	28.0567i	0.526619	−	1.27137i	0.933726	−	0.357990i	$-0.116538\pi$
$488$	8.40690	−	14.8125i	0.380562	−	0.670529i
$489$	1.07602	−	1.07602i	0.0486593	−	0.0486593i
$490$	−33.2186	+	2.98858i	−1.50066	+	0.135010i
$491$	−5.74027	−	2.37770i	−0.259055	−	0.107304i	0.249376	−	0.968407i	$-0.419774\pi$
$491$	−5.74027	−	2.37770i	−0.259055	−	0.107304i	−0.508431	+	0.861103i	$0.669774\pi$
$492$	−1.49433	+	0.962359i	−0.0673697	+	0.0433865i
$493$	−0.0886312	−	0.318587i	−0.00399175	−	0.0143484i
$494$	9.47217	−	11.3450i	0.426173	−	0.510437i
$495$	18.1803	+	18.1803i	0.817142	+	0.817142i
$496$	37.5652	+	1.27006i	1.68673	+	0.0570275i
$497$	−17.9506			−0.805193
$498$	−0.0148518	+	0.00777781i	−0.000665523	+	0.000348532i
$499$	−29.9145			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$499$	−29.9145			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$500$	57.8924	−	10.5018i	2.58903	−	0.469656i
$501$	0.200615	−	0.484327i	0.00896280	−	0.0216381i
$502$	−1.54752	+	4.95053i	−0.0690693	+	0.220953i
$503$	3.20292	−	7.73253i	0.142811	−	0.344776i	−0.836248	−	0.548351i	$-0.815256\pi$
$503$	3.20292	−	7.73253i	0.142811	−	0.344776i	0.979059	+	0.203574i	$0.0652559\pi$
$504$	−5.92326	−	7.60254i	−0.263843	−	0.338644i
$505$	−1.80209	−	4.35063i	−0.0801920	−	0.193601i
$506$	3.93934	−	12.6020i	0.175125	−	0.560226i
$507$	0.870474			0.0386591
$508$	−2.91523	+	4.20727i	−0.129343	+	0.186668i
$509$	−1.16375	+	2.80954i	−0.0515823	+	0.124531i	−0.947570	−	0.319548i	$-0.896469\pi$
$509$	−1.16375	+	2.80954i	−0.0515823	+	0.124531i	0.895988	+	0.444079i	$0.146469\pi$
$510$	0.996723	−	2.20622i	0.0441356	−	0.0976929i
$511$	9.37353			0.414660
$512$	−22.6219	+	0.500755i	−0.999755	+	0.0221304i
$513$	−2.79044	−	1.15584i	−0.123201	−	0.0510315i
$514$	5.83414	−	0.524881i	0.257333	−	0.0231515i
$515$	−44.2373	−	44.2373i	−1.94933	−	1.94933i
$516$	−1.41700	+	0.912555i	−0.0623798	+	0.0401730i
$517$	0.566100	+	0.566100i	0.0248971	+	0.0248971i
$518$	7.35684	+	14.0479i	0.323241	+	0.617229i
$519$	2.19895			0.0965232
$520$	19.1992	−	14.9584i	0.841939	−	0.655967i
$521$	−37.6661	−	15.6018i	−1.65018	−	0.683528i	−0.652916	−	0.757430i	$-0.726455\pi$
$521$	−37.6661	−	15.6018i	−1.65018	−	0.683528i	−0.997265	+	0.0739028i	$0.976455\pi$
$522$	−0.337766	+	0.0303878i	−0.0147836	+	0.00133004i
$523$	−16.3055	+	6.75397i	−0.712991	+	0.295331i	−0.709542	−	0.704663i	$-0.751098\pi$
$523$	−16.3055	+	6.75397i	−0.712991	+	0.295331i	−0.00344958	+	0.999994i	$0.501098\pi$
$524$	−11.4416	+	16.5125i	−0.499828	+	0.721354i
$525$	1.27991	−	0.530156i	0.0558599	−	0.0231379i
$526$	21.6439	+	18.0709i	0.943719	+	0.787928i
$527$	−23.8777	−	30.5108i	−1.04013	−	1.32907i
$528$	0.781391	−	0.293139i	0.0340057	−	0.0127572i
$529$	−2.00059	−	2.00059i	−0.0869821	−	0.0869821i
$530$	−21.5429	+	11.2820i	−0.935765	+	0.490057i
$531$	−14.6872	+	35.4580i	−0.637369	+	1.53875i
$532$	2.04385	+	11.2669i	0.0886121	+	0.488483i
$533$	13.0241	+	13.0241i	0.564137	+	0.564137i
$534$	0.518805	+	0.433159i	0.0224509	+	0.0187446i
$535$			40.7484i			1.76171i
$536$	11.7219	+	15.0451i	0.506307	+	0.649849i
$537$	−0.407959	−	0.168982i	−0.0176047	−	0.00729212i
$538$	−1.38362	−	15.3791i	−0.0596519	−	0.663041i
$539$			11.8516i			0.510485i
$540$	−4.08832	−	2.83281i	−0.175933	−	0.121905i
$541$	−16.5876	+	16.5876i	−0.713156	+	0.713156i	−0.967194	−	0.254038i	$-0.918241\pi$
$541$	−16.5876	+	16.5876i	−0.713156	+	0.713156i	0.254038	+	0.967194i	$0.418241\pi$
$542$	17.3175	−	20.7416i	0.743850	−	0.890926i
$543$	0.121987			0.00523496
$544$	15.3788	+	17.5355i	0.659361	+	0.751827i
$545$	34.0102			1.45683
$546$	0.215658	−	0.258298i	0.00922931	−	0.0110542i
$547$	−12.1485	+	12.1485i	−0.519431	+	0.519431i	−0.917399	−	0.397968i	$-0.869716\pi$
$547$	−12.1485	+	12.1485i	−0.519431	+	0.519431i	0.397968	+	0.917399i	$0.369716\pi$
$548$	−3.82143	+	5.51511i	−0.163244	+	0.235594i
$549$			18.0044i			0.768409i
$550$	−3.19053	−	35.4632i	−0.136044	−	1.51216i
$551$	0.372261	+	0.154196i	0.0158589	+	0.00656896i
$552$	−0.157087	+	1.26525i	−0.00668606	+	0.0538528i
$553$		−	6.27359i		−	0.266780i
$554$	−6.29861	−	5.25882i	−0.267602	−	0.223426i
$555$	2.88859	+	2.88859i	0.122614	+	0.122614i
$556$	−11.1732	+	2.02684i	−0.473847	+	0.0859571i
$557$	−9.58768	+	23.1467i	−0.406243	+	0.980758i	0.579874	+	0.814706i	$0.303102\pi$
$557$	−9.58768	+	23.1467i	−0.406243	+	0.980758i	−0.986117	+	0.166051i	$0.946898\pi$
$558$	−35.1982	+	18.4332i	−1.49006	+	0.780339i
$559$	12.3501	+	12.3501i	0.522353	+	0.522353i
$560$	−0.637181	+	18.8462i	−0.0269258	+	0.796396i
$561$	−0.749070	−	0.422999i	−0.0316258	−	0.0178590i
$562$	4.82963	+	4.03234i	0.203726	+	0.170094i
$563$	−22.0983	+	9.15342i	−0.931333	+	0.385771i	−0.796184	−	0.605055i	$-0.793151\pi$
$563$	−22.0983	+	9.15342i	−0.931333	+	0.385771i	−0.135149	+	0.990825i	$0.543151\pi$
$564$	−0.0635443	−	0.0440300i	−0.00267570	−	0.00185400i
$565$	−27.0402	+	11.2004i	−1.13759	+	0.471206i
$566$	3.55672	−	0.319988i	0.149500	−	0.0134501i
$567$	9.38058	+	3.88557i	0.393948	+	0.163178i
$568$	5.48908	−	44.2117i	0.230316	−	1.85508i
$569$	−32.3759			−1.35727			−0.678633	−	0.734477i	$-0.737427\pi$
$569$	−32.3759			−1.35727			−0.678633	+	0.734477i	$0.737427\pi$
$570$	1.36851	+	2.61318i	0.0573207	+	0.109454i
$571$	−20.0286	−	20.0286i	−0.838170	−	0.838170i	0.150448	−	0.988618i	$-0.451928\pi$
$571$	−20.0286	−	20.0286i	−0.838170	−	0.838170i	−0.988618	+	0.150448i	$0.951928\pi$
$572$	−4.68263	−	7.27109i	−0.195791	−	0.304020i
$573$	1.46255	+	1.46255i	0.0610988	+	0.0610988i
$574$	−14.2132	+	1.27872i	−0.593246	+	0.0533727i
$575$	50.2554	+	20.8165i	2.09579	+	0.868106i
$576$	20.5361	−	12.2640i	0.855671	−	0.511002i
$577$	25.3973			1.05730			0.528652	−	0.848839i	$-0.322698\pi$
$577$	25.3973			1.05730			0.528652	+	0.848839i	$0.322698\pi$
$578$	3.66386	−	23.7608i	0.152396	−	0.988319i
$579$	0.935202	−	2.25778i	0.0388657	−	0.0938301i
$580$	0.545406	+	0.377914i	0.0226468	+	0.0156920i
$581$	−0.134605			−0.00558437
$582$	0.292183	−	0.934694i	0.0121114	−	0.0387443i
$583$	3.30688	+	7.98352i	0.136957	+	0.330644i
$584$	−2.86632	+	23.0867i	−0.118609	+	0.955335i
$585$	−9.84573	+	23.7697i	−0.407071	+	0.982756i
$586$	0.0205874	−	0.0658592i	0.000850457	−	0.00272062i
$587$	6.33647	−	15.2976i	0.261534	−	0.631399i	−0.737500	−	0.675347i	$-0.763994\pi$
$587$	6.33647	−	15.2976i	0.261534	−	0.631399i	0.999034	+	0.0439483i	$0.0139937\pi$
$588$	−0.204271	−	1.12606i	−0.00842398	−	0.0464380i
$589$	47.2080			1.94517
$590$	66.5229	−	34.8378i	2.73871	−	1.43425i
$591$	0.0797277			0.00327956
$592$	−36.8492	+	13.8240i	−1.51449	+	0.568162i
$593$	8.47926	+	8.47926i	0.348202	+	0.348202i	0.859439	−	0.511238i	$-0.170813\pi$
$593$	8.47926	+	8.47926i	0.348202	+	0.348202i	−0.511238	+	0.859439i	$0.670813\pi$
$594$	−1.13274	+	1.35671i	−0.0464768	+	0.0556663i
$595$	15.3070	−	11.9793i	0.627528	−	0.491101i
$596$	13.0537	+	20.2696i	0.534702	+	0.830275i
$597$	0.258880	+	0.107231i	0.0105952	+	0.00438869i
$598$	13.1591	−	1.18389i	0.538116	−	0.0484127i
$599$	−16.7026	+	16.7026i	−0.682451	+	0.682451i	−0.960552	−	0.278101i	$-0.910295\pi$
$599$	−16.7026	+	16.7026i	−0.682451	+	0.682451i	0.278101	+	0.960552i	$0.410295\pi$
$600$	0.914377	+	3.31450i	0.0373293	+	0.135314i
$601$	−2.90606	+	7.01586i	−0.118541	+	0.286183i	−0.972002	−	0.234974i	$-0.924499\pi$
$601$	−2.90606	+	7.01586i	−0.118541	+	0.286183i	0.853461	+	0.521157i	$0.174499\pi$
$602$	−13.4776	+	1.21254i	−0.549306	+	0.0494195i
$603$	−18.6267	−	7.71544i	−0.758539	−	0.314197i
$604$	−6.70379	−	36.9553i	−0.272773	−	1.50369i
$605$	27.6273			1.12321
$606$	0.143143	−	0.0749635i	0.00581479	−	0.00304518i
$607$	14.2670	−	34.4435i	0.579078	−	1.39802i	−0.314563	−	0.949237i	$-0.601858\pi$
$607$	14.2670	−	34.4435i	0.579078	−	1.39802i	0.893641	−	0.448782i	$-0.148142\pi$
$608$	−28.3751	+	1.58864i	−1.15076	+	0.0644281i
$609$	0.00847547	+	0.00351066i	0.000343444	+	0.000142259i
$610$	22.5773	−	27.0413i	0.914127	−	1.09487i
$611$	−0.306578	+	0.740145i	−0.0124028	+	0.0299431i
$612$	−23.2882	−	8.09684i	−0.941368	−	0.327295i
$613$	−20.6678	+	8.56089i	−0.834765	+	0.345771i	−0.758787	−	0.651338i	$-0.774208\pi$
$613$	−20.6678	+	8.56089i	−0.834765	+	0.345771i	−0.0759778	+	0.997110i	$0.524208\pi$
$614$	−8.09955	−	15.4661i	−0.326871	−	0.624162i
$615$	−3.39640	+	1.40683i	−0.136956	+	0.0567290i
$616$	6.64959	+	0.825576i	0.267920	+	0.0332634i
$617$	27.3537	−	11.3303i	1.10122	−	0.456140i	0.243313	−	0.969948i	$-0.421766\pi$
$617$	27.3537	−	11.3303i	1.10122	−	0.456140i	0.857905	+	0.513808i	$0.171766\pi$
$618$	1.37580	−	1.64783i	0.0553430	−	0.0662856i
$619$	−6.53307	+	6.53307i	−0.262586	+	0.262586i	−0.826104	−	0.563518i	$-0.809448\pi$
$619$	−6.53307	+	6.53307i	−0.262586	+	0.262586i	0.563518	+	0.826104i	$0.309448\pi$
$620$	75.9801	+	16.4528i	3.05144	+	0.660759i
$621$	−1.03327	−	2.49455i	−0.0414639	−	0.100103i
$622$	−6.37130	−	1.99165i	−0.255466	−	0.0798579i
$623$	2.07659	+	5.01334i	0.0831969	+	0.200855i
$624$	0.570236	+	0.610144i	0.0228277	+	0.0244253i
$625$	61.1354			2.44541
$626$	−0.813827	−	1.55400i	−0.0325271	−	0.0621105i
$627$	0.968408	−	0.401128i	0.0386745	−	0.0160195i
$628$	5.89211	−	27.2102i	0.235121	−	1.08581i
$629$	35.3250	+	19.9480i	1.40850	+	0.795378i
$630$	−9.24778	−	17.6587i	−0.368441	−	0.703538i
$631$	−44.2420			−1.76124			−0.880622	−	0.473819i	$-0.842875\pi$
$631$	−44.2420			−1.76124			−0.880622	+	0.473819i	$0.842875\pi$
$632$	15.4517	+	1.91839i	0.614634	+	0.0763095i
$633$	0.658942	+	0.658942i	0.0261906	+	0.0261906i
$634$	−9.34392	+	11.1914i	−0.371095	+	0.444469i
$635$	−7.48601	+	7.48601i	−0.297073	+	0.297073i
$636$	−0.451800	−	0.701546i	−0.0179150	−	0.0278181i
$637$	−10.9568	+	4.53848i	−0.434126	+	0.179821i
$638$	0.151114	−	0.180993i	0.00598266	−	0.00716557i
$639$	18.0225	+	43.5101i	0.712957	+	1.72123i
$640$	−46.2227	−	7.33230i	−1.82711	−	0.289835i
$641$	−16.5781	+	40.0230i	−0.654795	+	1.58081i	0.150944	+	0.988542i	$0.451769\pi$
$641$	−16.5781	+	40.0230i	−0.654795	+	1.58081i	−0.805738	+	0.592272i	$0.798231\pi$
$642$	−1.39259	+	0.125287i	−0.0549610	+	0.00494468i
$643$	−9.66224	+	9.66224i	−0.381042	+	0.381042i	−0.871477	−	0.490436i	$-0.836838\pi$
$643$	−9.66224	+	9.66224i	−0.381042	+	0.381042i	0.490436	+	0.871477i	$0.336838\pi$
$644$	−5.83015	+	8.41410i	−0.229740	+	0.331562i
$645$	−3.22062	+	1.33403i	−0.126812	+	0.0525272i
$646$	20.0486	+	21.3589i	0.788802	+	0.840355i
$647$	−18.0850	+	18.0850i	−0.710995	+	0.710995i	−0.966743	−	0.255749i	$-0.917678\pi$
$647$	−18.0850	+	18.0850i	−0.710995	+	0.710995i	0.255749	+	0.966743i	$0.417678\pi$
$648$	−12.4385	+	21.9159i	−0.488631	+	0.860939i
$649$	−10.2114	−	24.6525i	−0.400833	−	0.967695i
$650$	31.5641	−	16.5300i	1.23805	−	0.648360i
$651$	1.07481			0.0421251
$652$	5.41234	+	29.8361i	0.211964	+	1.16847i
$653$		−	25.0494i		−	0.980258i	−0.871650	−	0.490129i	$-0.836950\pi$
$653$		−	25.0494i		−	0.980258i	0.871650	−	0.490129i	$-0.163050\pi$
$654$	0.104569	+	1.16230i	0.00408898	+	0.0454497i
$655$	−29.3808	+	29.3808i	−1.14800	+	1.14800i
$656$	1.19678	−	35.3976i	0.0467263	−	1.38205i
$657$	−9.41107	−	22.7203i	−0.367161	−	0.886405i
$658$	−0.287959	−	0.549859i	−0.0112258	−	0.0214357i
$659$	1.81333	−	4.37776i	0.0706372	−	0.170533i	−0.884618	−	0.466317i	$-0.845581\pi$
$659$	1.81333	−	4.37776i	0.0706372	−	0.170533i	0.955255	+	0.295784i	$0.0955807\pi$
$660$	1.69843	−	0.308100i	0.0661113	−	0.0119928i
$661$	−12.8565	−	5.32536i	−0.500062	−	0.207132i	0.118372	−	0.992969i	$-0.462232\pi$
$661$	−12.8565	−	5.32536i	−0.500062	−	0.207132i	−0.618434	+	0.785837i	$0.712232\pi$
$662$	−44.8472	+	23.4863i	−1.74304	+	0.912823i
$663$	0.104214	−	0.854502i	0.00404733	−	0.0331861i
$664$	0.0411607	−	0.331529i	0.00159735	−	0.0128658i
$665$			23.6839i			0.918422i
$666$	26.6642	−	31.9363i	1.03322	−	1.23751i
$667$	0.137845	+	0.332787i	0.00533738	+	0.0128856i
$668$	5.65601	+	8.78254i	0.218838	+	0.339807i
$669$		−	2.14321i		−	0.0828612i
$670$	18.3009	+	34.9457i	0.707027	+	1.35007i
$671$	−8.85137	−	8.85137i	−0.341703	−	0.341703i
$672$	−0.646031	+	0.0361695i	−0.0249212	+	0.00139527i
$673$	−6.49650	−	15.6839i	−0.250422	−	0.604572i	0.747816	−	0.663906i	$-0.231102\pi$
$673$	−6.49650	−	15.6839i	−0.250422	−	0.604572i	−0.998238	+	0.0593340i	$0.981102\pi$
$674$	3.11164	−	1.62956i	0.119856	−	0.0627682i
$675$	−5.14880	−	5.14880i	−0.198178	−	0.198178i
$676$	−9.87908	+	14.2575i	−0.379965	+	0.548366i
$677$	37.7679			1.45154			0.725769	−	0.687938i	$-0.241484\pi$
$677$	37.7679			1.45154			0.725769	+	0.687938i	$0.241484\pi$
$678$	−0.465916	−	0.889668i	−0.0178934	−	0.0341675i
$679$	5.55975	−	5.55975i	0.213364	−	0.213364i
$680$	24.8238	+	41.3639i	0.951950	+	1.58623i
$681$	0.744976	+	0.744976i	0.0285475	+	0.0285475i
$682$	8.24207	−	26.3664i	0.315605	−	1.00962i
$683$			32.4394i			1.24126i	0.784104	+	0.620630i	$0.213123\pi$
$683$			32.4394i			1.24126i	−0.784104	+	0.620630i	$0.786877\pi$
$684$	25.2577	−	16.2661i	0.965751	−	0.621950i
$685$	−9.81304	+	9.81304i	−0.374937	+	0.374937i
$686$	6.10753	−	19.5380i	0.233186	−	0.745964i
$687$	−1.81653	+	0.752430i	−0.0693048	+	0.0287070i
$688$	1.13484	−	33.5657i	0.0432654	−	1.27968i
$689$	−6.11445	+	6.11445i	−0.232942	+	0.232942i
$690$	−0.786786	+	2.51693i	−0.0299524	+	0.0958180i
$691$	−1.57293			−0.0598369			−0.0299185	−	0.999552i	$-0.509525\pi$
$691$	−1.57293			−0.0598369			−0.0299185	+	0.999552i	$0.509525\pi$
$692$	−24.9561	+	36.0167i	−0.948688	+	1.36915i
$693$	−6.54407	+	2.71064i	−0.248588	+	0.102969i
$694$	−3.12481	−	34.7328i	−0.118616	−	1.31844i
$695$	−23.4868			−0.890904
$696$	−0.0112383	+	0.0198013i	−0.000425988	+	0.000750567i
$697$	−28.7503	+	22.4999i	−1.08900	+	0.852245i
$698$	−34.4991	−	10.7843i	−1.30581	−	0.408193i
$699$	0.102541	−	0.247555i	0.00387844	−	0.00936339i
$700$	−5.84236	+	26.9805i	−0.220821	+	1.01977i
$701$	−5.03769	−	2.08668i	−0.190271	−	0.0788128i	0.285514	−	0.958375i	$-0.407836\pi$
$701$	−5.03769	−	2.08668i	−0.190271	−	0.0788128i	−0.475785	+	0.879562i	$0.657836\pi$
$702$	−1.68805	−	0.527681i	−0.0637114	−	0.0199160i
$703$	−45.6686	+	18.9166i	−1.72243	+	0.713452i
$704$	−4.06674	+	16.1253i	−0.153271	+	0.607745i
$705$	−0.113065	−	0.113065i	−0.00425826	−	0.00425826i
$706$	−0.400389	+	0.479555i	−0.0150689	+	0.0180483i
$707$	1.29734			0.0487915
$708$	1.39512	+	2.16632i	0.0524320	+	0.0814153i
$709$		−	33.0464i		−	1.24108i	−0.784174	−	0.620541i	$-0.786913\pi$
$709$		−	33.0464i		−	1.24108i	0.784174	−	0.620541i	$-0.213087\pi$
$710$	27.4926	−	87.9489i	1.03178	−	3.30066i
$711$	−15.2064	+	6.29871i	−0.570286	+	0.236220i
$712$	−12.9827	+	3.58157i	−0.486547	+	0.134225i
$713$	29.8414	+	29.8414i	1.11757	+	1.11757i
$714$	0.456457	+	0.486290i	0.0170825	+	0.0181989i
$715$	−6.84534	−	16.5261i	−0.256001	−	0.618042i
$716$	7.39773	−	4.76418i	0.276466	−	0.178046i
$717$	0.946259	+	0.946259i	0.0353387	+	0.0353387i
$718$	−22.8261	+	27.3394i	−0.851864	+	1.02030i
$719$	−34.5789	−	14.3231i	−1.28958	−	0.534160i	−0.370717	−	0.928746i	$-0.620888\pi$
$719$	−34.5789	−	14.3231i	−1.28958	−	0.534160i	−0.918859	+	0.394586i	$0.870888\pi$
$720$	46.3206	−	17.3772i	1.72627	−	0.647610i
$721$	15.9234	−	6.59569i	0.593019	−	0.245636i
$722$	−8.78873	+	0.790697i	−0.327083	+	0.0294267i
$723$	0.269466	+	0.650547i	0.0100215	+	0.0241941i
$724$	−1.38444	+	1.99803i	−0.0514523	+	0.0742562i
$725$	0.686882	+	0.686882i	0.0255101	+	0.0255101i
$726$	0.0849442	+	0.944169i	0.00315257	+	0.0350414i
$727$	−3.51978	+	3.51978i	−0.130541	+	0.130541i	−0.769359	−	0.638817i	$-0.779424\pi$
$727$	−3.51978	+	3.51978i	−0.130541	+	0.130541i	0.638817	+	0.769359i	$0.279424\pi$
$728$	1.78316	+	6.46372i	0.0660883	+	0.239561i
$729$		−	26.4575i		−	0.979909i
$730$	−14.3562	+	45.9257i	−0.531348	+	1.69979i
$731$	−27.2624	+	21.3355i	−1.00834	+	0.789121i
$732$	0.993560	+	0.688440i	0.0367230	+	0.0254455i
$733$	5.24445	+	12.6612i	0.193708	+	0.467653i	0.990654	−	0.136398i	$-0.0435525\pi$
$733$	5.24445	+	12.6612i	0.193708	+	0.467653i	−0.796946	+	0.604051i	$0.793552\pi$
$734$	−21.4615	−	6.70880i	−0.792158	−	0.247626i
$735$		−	2.36706i		−	0.0873105i
$736$	−18.9409	−	16.9324i	−0.698170	−	0.624137i
$737$	12.9504	−	5.36424i	0.477035	−	0.197594i
$738$	17.3696	+	33.1672i	0.639382	+	1.22090i
$739$	42.4483	−	17.5827i	1.56149	−	0.646789i	0.576141	−	0.817351i	$-0.304558\pi$
$739$	42.4483	−	17.5827i	1.56149	−	0.646789i	0.985347	+	0.170561i	$0.0545580\pi$
$740$	−80.0953	+	14.5295i	−2.94436	+	0.534115i
$741$	0.741688	+	0.741688i	0.0272466	+	0.0272466i
$742$	−0.600322	−	6.67268i	−0.0220385	−	0.244962i
$743$	−7.48096	−	18.0606i	−0.274450	−	0.662581i	0.725213	−	0.688524i	$-0.241741\pi$
$743$	−7.48096	−	18.0606i	−0.274450	−	0.662581i	−0.999663	+	0.0259433i	$0.991741\pi$
$744$	−0.328664	+	2.64722i	−0.0120494	+	0.0970519i
$745$	19.0827	+	46.0698i	0.699137	+	1.68787i
$746$	−0.365124	+	1.16803i	−0.0133681	+	0.0427647i
$747$	0.135144	+	0.326267i	0.00494467	+	0.0119375i
$748$	15.4296	−	7.46840i	0.564161	−	0.273072i
$749$	−10.3715	−	4.29603i	−0.378968	−	0.156974i
$750$	0.374166	+	4.15892i	0.0136626	+	0.151862i
$751$	12.8591	−	31.0447i	0.469236	−	1.13284i	−0.495261	−	0.868744i	$-0.664928\pi$
$751$	12.8591	−	31.0447i	0.469236	−	1.13284i	0.964497	−	0.264092i	$-0.0850724\pi$
$752$	1.44234	−	0.541094i	0.0525967	−	0.0197317i
$753$	−0.340088	−	0.140869i	−0.0123935	−	0.00513355i
$754$	0.225196	+	0.0703958i	0.00820117	+	0.00256366i
$755$		−	77.6827i		−	2.82716i
$756$	1.15205	−	0.741926i	0.0418996	−	0.0269836i
$757$	−13.5848	+	32.7966i	−0.493748	+	1.19201i	0.459051	+	0.888410i	$0.348189\pi$
$757$	−13.5848	+	32.7966i	−0.493748	+	1.19201i	−0.952799	+	0.303602i	$0.901811\pi$
$758$	−6.44137	+	7.71498i	−0.233961	+	0.280221i
$759$	0.865720	+	0.358593i	0.0314237	+	0.0130161i
$760$	−58.3327	−	7.24226i	−2.11595	−	0.262704i
$761$	22.3346	+	22.3346i	0.809628	+	0.809628i	0.984577	−	0.174949i	$-0.0559762\pi$
$761$	22.3346	+	22.3346i	0.809628	+	0.809628i	−0.174949	+	0.984577i	$0.555976\pi$
$762$	−0.278853	−	0.232819i	−0.0101018	−	0.00843415i
$763$	−3.58563	+	8.65648i	−0.129809	+	0.313385i
$764$	−40.5537	+	7.35655i	−1.46718	+	0.266151i
$765$	−44.4047	−	25.0753i	−1.60545	−	0.906598i
$766$	−2.48926	−	27.6685i	−0.0899406	−	0.999705i
$767$	18.8810	−	18.8810i	0.681752	−	0.681752i
$768$	0.108464	−	1.60222i	0.00391387	−	0.0578150i
$769$			12.5956i			0.454210i	0.973870	+	0.227105i	$0.0729260\pi$
$769$			12.5956i			0.454210i	−0.973870	+	0.227105i	$0.927074\pi$
$770$	13.2278	+	4.13498i	0.476698	+	0.149014i
$771$			0.415725i			0.0149720i
$772$	26.3666	+	40.9414i	0.948953	+	1.47351i
$773$	−25.1840	−	10.4316i	−0.905807	−	0.375197i	−0.119357	−	0.992851i	$-0.538083\pi$
$773$	−25.1840	−	10.4316i	−0.905807	−	0.375197i	−0.786450	+	0.617654i	$0.788083\pi$
$774$	16.4706	+	31.4507i	0.592025	+	1.13047i
$775$	105.147	+	43.5531i	3.77698	+	1.56447i
$776$	11.9934	+	15.3936i	0.430538	+	0.552598i
$777$	−1.03976	+	0.430684i	−0.0373013	+	0.0154507i
$778$	−33.9243	+	17.7660i	−1.21624	+	0.636943i
$779$		−	44.4840i		−	1.59381i
$780$	0.935240	+	1.45222i	0.0334869	+	0.0519978i
$781$	−30.2508	−	12.5303i	−1.08246	−	0.448369i
$782$	−0.828277	+	26.1748i	−0.0296191	+	0.936008i
$783$		−	0.0482176i		−	0.00172316i
$784$	20.7621	+	9.43403i	0.741504	+	0.336930i
$785$	22.0363	−	53.2004i	0.786510	−	1.89880i
$786$	−1.09443	−	0.913759i	−0.0390370	−	0.0325927i
$787$	26.5696	−	26.5696i	0.947104	−	0.947104i	−0.0515660	−	0.998670i	$-0.516421\pi$
$787$	26.5696	−	26.5696i	0.947104	−	0.947104i	0.998670	+	0.0515660i	$0.0164213\pi$
$788$	−0.904837	+	1.30586i	−0.0322335	+	0.0465195i
$789$	−1.41498	+	1.41498i	−0.0503748	+	0.0503748i
$790$	30.7375	+	9.60846i	1.09359	+	0.341853i
$791$		−	8.06329i		−	0.286698i
$792$	−4.67513	−	16.9467i	−0.166123	−	0.602176i
$793$	4.79356	−	11.5727i	0.170224	−	0.410958i
$794$	−2.20292	−	1.83926i	−0.0781787	−	0.0652728i
$795$	−0.660468	−	1.59451i	−0.0234244	−	0.0565515i
$796$	−4.69440	+	3.02322i	−0.166389	+	0.107155i
$797$	9.39026	+	22.6701i	0.332620	+	0.803016i	0.998383	+	0.0568520i	$0.0181063\pi$
$797$	9.39026	+	22.6701i	0.332620	+	0.803016i	−0.665763	+	0.746164i	$0.731894\pi$
$798$	−0.809402	+	0.0728196i	−0.0286525	+	0.00257779i
$799$	−1.38268	−	0.780798i	−0.0489157	−	0.0276226i
$800$	−64.6656	−	22.6399i	−2.28628	−	0.800441i
$801$	10.0668	−	10.0668i	0.355694	−	0.355694i
$802$	10.7087	+	3.34750i	0.378136	+	0.118204i
$803$	15.7965	+	6.54314i	0.557448	+	0.230902i
$804$	−1.13801	+	0.732885i	−0.0401345	+	0.0258468i
$805$	−14.9712	+	14.9712i	−0.527666	+	0.527666i
$806$	27.5321	−	2.47698i	0.969776	−	0.0872480i
$807$	1.09587			0.0385766
$808$	−0.396712	+	3.19531i	−0.0139563	+	0.112411i
$809$	9.85492	−	23.7919i	0.346480	−	0.836478i	−0.650550	−	0.759464i	$-0.725461\pi$
$809$	9.85492	−	23.7919i	0.346480	−	0.836478i	0.997030	−	0.0770139i	$-0.0245386\pi$
$810$	−33.4044	+	40.0092i	−1.17371	+	1.40578i
$811$	2.46640			0.0866071			0.0433035	−	0.999062i	$-0.486212\pi$
$811$	2.46640			0.0866071			0.0433035	+	0.999062i	$0.486212\pi$
$812$	−0.153690	+	0.0989774i	−0.00539347	+	0.00347343i
$813$	1.35599	+	1.35599i	0.0475567	+	0.0475567i
$814$	2.59189	+	28.8093i	0.0908458	+	1.00977i
$815$			62.7175i			2.19690i
$816$	−1.33730	+	0.975539i	−0.0468147	+	0.0341507i
$817$		−	42.1819i		−	1.47576i
$818$	−7.98978	+	0.718818i	−0.279356	+	0.0251329i
$819$	−5.01199	−	5.01199i	−0.175133	−	0.175133i
$820$	15.5034	−	71.5960i	0.541403	−	2.50024i
$821$	−11.4107			−0.398236			−0.199118	−	0.979976i	$-0.563808\pi$
$821$	−11.4107			−0.398236			−0.199118	+	0.979976i	$0.563808\pi$
$822$	−0.365534	−	0.305191i	−0.0127495	−	0.0106448i
$823$	−13.3471	+	32.2228i	−0.465252	+	1.12322i	0.500961	+	0.865470i	$0.332980\pi$
$823$	−13.3471	+	32.2228i	−0.465252	+	1.12322i	−0.966213	+	0.257747i	$0.917020\pi$
$824$	11.3758	+	41.2358i	0.396295	+	1.43652i
$825$	2.52701			0.0879793
$826$	1.85375	+	20.6047i	0.0645002	+	0.716930i
$827$	14.3142	−	14.3142i	0.497753	−	0.497753i	−0.412985	−	0.910738i	$-0.635514\pi$
$827$	14.3142	−	14.3142i	0.497753	−	0.497753i	0.910738	+	0.412985i	$0.135514\pi$
$828$	26.2483	+	5.68381i	0.912191	+	0.197526i
$829$	8.74352	+	3.62168i	0.303675	+	0.125786i	0.529317	−	0.848424i	$-0.322448\pi$
$829$	8.74352	+	3.62168i	0.303675	+	0.125786i	−0.225642	+	0.974210i	$0.572448\pi$
$830$	0.206158	−	0.659500i	0.00715584	−	0.0228916i
$831$	0.411775	−	0.411775i	0.0142843	−	0.0142843i
$832$	−16.4652	+	2.41534i	−0.570829	+	0.0837368i
$833$	−6.30036	−	22.6468i	−0.218295	−	0.784664i
$834$	−0.0722135	−	0.802665i	−0.00250055	−	0.0277940i
$835$	8.26829	+	19.9614i	0.286136	+	0.690794i
$836$	−4.42046	+	20.4140i	−0.152885	+	0.706034i
$837$	−2.16186	−	5.21920i	−0.0747250	−	0.180402i
$838$	31.3733	−	37.5765i	1.08377	−	1.29806i
$839$	5.30804	−	12.8147i	0.183254	−	0.442414i	−0.805380	−	0.592759i	$-0.798039\pi$
$839$	5.30804	−	12.8147i	0.183254	−	0.442414i	0.988634	+	0.150345i	$0.0480385\pi$
$840$	−1.32809	−	0.164888i	−0.0458235	−	0.00568919i
$841$		−	28.9936i		−	0.999778i
$842$	7.07596	−	22.6360i	0.243854	−	0.780089i
$843$	−0.315740	+	0.315740i	−0.0108747	+	0.0108747i
$844$	−18.2712	+	3.31445i	−0.628921	+	0.114088i
$845$	−25.3684	+	25.3684i	−0.872701	+	0.872701i
$846$	−1.04368	+	1.25004i	−0.0358825	+	0.0429773i
$847$	−2.91270	+	7.03187i	−0.100081	+	0.241618i
$848$	16.6182	+	0.561853i	0.570671	+	0.0192941i
$849$			0.253442i			0.00869811i
$850$	24.9490	+	66.0692i	0.855745	+	2.26616i
$851$	−40.8260	−	16.9107i	−1.39950	−	0.579691i
$852$	3.09020	+	0.669153i	0.105869	+	0.0229248i
$853$			51.3943i			1.75971i	0.475244	+	0.879854i	$0.342360\pi$
$853$			51.3943i			1.75971i	−0.475244	+	0.879854i	$0.657640\pi$
$854$	4.50244	+	8.59743i	0.154070	+	0.294198i
$855$	57.4070	−	23.7787i	1.96328	−	0.813216i
$856$	13.7525	−	24.2311i	0.470051	−	0.828203i
$857$	33.0518	+	13.6905i	1.12903	+	0.467659i	0.867450	−	0.497524i	$-0.165757\pi$
$857$	33.0518	+	13.6905i	1.12903	+	0.467659i	0.261577	+	0.965182i	$0.415757\pi$
$858$	0.543737	−	0.284753i	0.0185629	−	0.00972131i
$859$	−21.2198	−	8.78952i	−0.724010	−	0.299895i	−0.00992191	−	0.999951i	$-0.503158\pi$
$859$	−21.2198	−	8.78952i	−0.724010	−	0.299895i	−0.714088	+	0.700056i	$0.753158\pi$
$860$	14.7011	−	67.8907i	0.501302	−	2.31505i
$861$		−	1.01279i		−	0.0345159i
$862$	5.12107	−	16.3823i	0.174424	−	0.557984i
$863$			12.3720i			0.421148i	0.977578	+	0.210574i	$0.0675332\pi$
$863$			12.3720i			0.421148i	−0.977578	+	0.210574i	$0.932467\pi$
$864$	1.47506	+	3.06433i	0.0501825	+	0.104251i
$865$	−64.0846	+	64.0846i	−2.17894	+	2.17894i
$866$	2.42723	−	0.218371i	0.0824807	−	0.00742056i
$867$	1.65624	+	0.410084i	0.0562488	+	0.0139272i
$868$	−12.1981	+	17.6044i	−0.414031	+	0.597531i
$869$	4.37924	−	10.5724i	0.148556	−	0.358645i
$870$	−0.0301813	+	0.0361488i	−0.00102324	+	0.00122556i
$871$	9.91851	+	9.91851i	0.336076	+	0.336076i
$872$	−20.2242	−	11.4784i	−0.684878	−	0.388706i
$873$	−19.0582	−	7.89416i	−0.645022	−	0.267177i
$874$	−24.4943	−	20.4508i	−0.828533	−	0.691757i
$875$	−12.8300	+	30.9743i	−0.433733	+	1.04712i
$876$	−1.61366	−	0.349422i	−0.0545205	−	0.0118059i
$877$		−	24.2425i		−	0.818612i	−0.912397	−	0.409306i	$-0.865771\pi$
$877$		−	24.2425i		−	0.818612i	0.912397	−	0.409306i	$-0.134229\pi$
$878$	−3.84544	+	12.3016i	−0.129777	+	0.415158i
$879$	0.00452434	+	0.00187404i	0.000152602	+	6.32099e-5i
$880$	−14.2293	+	31.3153i	−0.479668	+	1.05564i
$881$	19.6982	−	47.5556i	0.663648	−	1.60219i	−0.128394	−	0.991723i	$-0.540982\pi$
$881$	19.6982	−	47.5556i	0.663648	−	1.60219i	0.792043	−	0.610466i	$-0.209018\pi$
$882$	−24.0101	+	2.16012i	−0.808463	+	0.0727351i
$883$	−32.0166	−	13.2617i	−1.07745	−	0.446293i	−0.227833	−	0.973700i	$-0.573164\pi$
$883$	−32.0166	−	13.2617i	−1.07745	−	0.446293i	−0.849612	+	0.527408i	$0.823164\pi$
$884$	12.8132	+	11.4047i	0.430954	+	0.383583i
$885$	2.03948	+	4.92373i	0.0685562	+	0.165509i
$886$	13.7243	+	4.29019i	0.461078	+	0.144132i
$887$	−1.15633	−	2.79162i	−0.0388257	−	0.0937334i	0.903277	−	0.429057i	$-0.141154\pi$
$887$	−1.15633	−	2.79162i	−0.0388257	−	0.0937334i	−0.942103	+	0.335324i	$0.891154\pi$
$888$	−0.742814	−	2.69260i	−0.0249272	−	0.0903578i
$889$	−1.11615	−	2.69462i	−0.0374344	−	0.0903747i
$890$	−27.7434	+	2.49599i	−0.929959	+	0.0836658i
$891$	13.0961	+	13.0961i	0.438737	+	0.438737i
$892$	35.1037	+	24.3235i	1.17536	+	0.814410i
$893$	1.78755	−	0.740427i	0.0598180	−	0.0247774i
$894$	−1.51577	+	0.793805i	−0.0506950	+	0.0265488i
$895$	16.8139	−	6.96456i	0.562028	−	0.232800i
$896$	6.73944	−	10.9919i	0.225149	−	0.367212i
$897$			0.937682i			0.0313083i
$898$	−14.4262	+	46.1495i	−0.481409	+	1.54003i
$899$	0.288406	+	0.696273i	0.00961887	+	0.0232220i
$900$	71.2633	−	12.9274i	2.37544	−	0.430912i
$901$	−10.5631	−	13.4975i	−0.351907	−	0.449665i
$902$	−24.8450	−	7.76649i	−0.827249	−	0.258596i
$903$		−	0.960377i		−	0.0319594i
$904$	19.8596	+	2.46566i	0.660522	+	0.0820067i
$905$	−3.55510	+	3.55510i	−0.118175	+	0.118175i
$906$	2.65482	−	0.238847i	0.0882006	−	0.00793515i
$907$	−3.29244	−	3.29244i	−0.109324	−	0.109324i	0.650329	−	0.759653i	$-0.274631\pi$
$907$	−3.29244	−	3.29244i	−0.109324	−	0.109324i	−0.759653	+	0.650329i	$0.774631\pi$
$908$	−20.6568	+	3.74720i	−0.685520	+	0.124355i
$909$	−1.30254	−	3.14460i	−0.0432024	−	0.104300i
$910$	1.24268	+	13.8126i	0.0411946	+	0.457884i
$911$	21.9362	−	9.08627i	0.726779	−	0.301042i	0.0115513	−	0.999933i	$-0.496323\pi$
$911$	21.9362	−	9.08627i	0.726779	−	0.301042i	0.715228	+	0.698892i	$0.246323\pi$
$912$	0.0681533	−	2.01580i	0.00225678	−	0.0667498i
$913$	−0.226841	−	0.0939605i	−0.00750733	−	0.00310964i
$914$	8.26689	+	6.90217i	0.273444	+	0.228303i
$915$	1.76784	+	1.76784i	0.0584431	+	0.0584431i
$916$	8.29184	−	38.2924i	0.273970	−	1.26521i
$917$	−4.38062	−	10.5757i	−0.144661	−	0.349242i
$918$	1.44327	−	3.19464i	0.0476352	−	0.105439i
$919$	37.7588	+	37.7588i	1.24555	+	1.24555i	0.957666	+	0.287881i	$0.0929506\pi$
$919$	37.7588	+	37.7588i	1.24555	+	1.24555i	0.287881	+	0.957666i	$0.407049\pi$
$920$	−32.2956	−	41.4517i	−1.06476	−	1.36662i
$921$	1.14473	−	0.474164i	0.0377202	−	0.0156242i
$922$	16.8358	+	5.26282i	0.554456	+	0.173322i
$923$		−	32.7653i		−	1.07848i
$924$	−0.100643	+	0.464777i	−0.00331091	+	0.0152901i
$925$	−119.170			−3.91829
$926$	−18.0588	−	15.0776i	−0.593449	−	0.495481i
$927$	−31.9744	−	31.9744i	−1.05018	−	1.05018i
$928$	−0.196782	−	0.408800i	−0.00645968	−	0.0134195i
$929$	18.1021	−	7.49812i	0.593910	−	0.246005i	−0.0654220	−	0.997858i	$-0.520839\pi$
$929$	18.1021	−	7.49812i	0.593910	−	0.246005i	0.659332	+	0.751852i	$0.270839\pi$
$930$	−1.64615	+	5.26604i	−0.0539794	+	0.172680i
$931$	26.4622	+	10.9610i	0.867265	+	0.359233i
$932$	2.89097	+	4.48904i	0.0946969	+	0.147043i
$933$	0.181297	−	0.437691i	0.00593541	−	0.0143294i
$934$	9.91408	−	31.7152i	0.324398	−	1.03775i
$935$	34.1579	−	9.50278i	1.11708	−	0.310774i
$936$	13.8770	−	10.8118i	0.453584	−	0.353394i
$937$	−16.2634			−0.531304			−0.265652	−	0.964069i	$-0.585587\pi$
$937$	−16.2634			−0.531304			−0.265652	+	0.964069i	$0.585587\pi$
$938$	−10.8240	+	0.973808i	−0.353417	+	0.0317960i
$939$	0.115020	−	0.0476430i	0.00375355	−	0.00155477i
$940$	3.13507	−	0.568710i	0.102255	−	0.0185493i
$941$	−24.8551			−0.810252			−0.405126	−	0.914261i	$-0.632772\pi$
$941$	−24.8551			−0.810252			−0.405126	+	0.914261i	$0.632772\pi$
$942$	1.88589	+	0.589524i	0.0614456	+	0.0192077i
$943$	28.1195	−	28.1195i	0.915698	−	0.915698i
$944$	−51.3157	−	1.73496i	−1.67018	−	0.0564681i
$945$	2.61843	−	1.08459i	0.0851777	−	0.0352818i
$946$	−23.5592	−	7.36456i	−0.765977	−	0.239442i
$947$	30.6430	−	30.6430i	0.995763	−	0.995763i	−0.00422821	−	0.999991i	$-0.501346\pi$
$947$	30.6430	−	30.6430i	0.995763	−	0.995763i	0.999991	+	0.00422821i	$0.00134589\pi$
$948$	−0.233864	+	1.08000i	−0.00759555	+	0.0350769i
$949$			17.1096i			0.555401i
$950$	−82.1330	−	25.6746i	−2.66475	−	0.832993i
$951$	−0.731647	−	0.731647i	−0.0237253	−	0.0237253i
$952$	−13.1453	+	1.95739i	−0.426043	+	0.0634394i
$953$	−8.21263	+	8.21263i	−0.266033	+	0.266033i	−0.827500	−	0.561466i	$-0.810237\pi$
$953$	−8.21263	+	8.21263i	−0.266033	+	0.266033i	0.561466	+	0.827500i	$0.310237\pi$
$954$	−15.5711	+	8.15452i	−0.504132	+	0.264012i
$955$	−85.2468			−2.75852
$956$	−26.2380	+	4.75964i	−0.848598	+	0.153938i
$957$	0.0118325	+	0.0118325i	0.000382491	+	0.000382491i
$958$	9.26809	+	17.6974i	0.299439	+	0.571779i
$959$	−1.46311	−	3.53225i	−0.0472461	−	0.114062i
$960$	0.812231	−	3.22063i	0.0262146	−	0.103945i
$961$	40.5153	+	40.5153i	1.30694	+	1.30694i
$962$	−25.6418	+	13.4285i	−0.826724	+	0.432952i
$963$			29.4526i			0.949098i
$964$	−13.7135	−	2.96953i	−0.441683	−	0.0956422i
$965$	38.5442	+	93.0539i	1.24078	+	2.99551i
$966$	−0.557676	−	0.465613i	−0.0179429	−	0.0149809i
$967$		−	45.1805i		−	1.45291i	−0.687215	−	0.726454i	$-0.741167\pi$
$967$		−	45.1805i		−	1.45291i	0.687215	−	0.726454i	$-0.258833\pi$
$968$	−16.4286	−	9.32415i	−0.528036	−	0.299690i
$969$	−1.63725	+	1.28131i	−0.0525961	+	0.0411616i
$970$	18.7249	+	35.7552i	0.601220	+	1.14803i
$971$	−10.2318	−	4.23815i	−0.328354	−	0.136009i	0.212416	−	0.977179i	$-0.431867\pi$
$971$	−10.2318	−	4.23815i	−0.328354	−	0.136009i	−0.540770	+	0.841171i	$0.681867\pi$
$972$	−4.43499	−	3.07302i	−0.142252	−	0.0985671i
$973$	2.47617	−	5.97800i	0.0793823	−	0.191646i
$974$	−38.0459	+	19.9245i	−1.21907	+	0.638422i
$975$	0.967699	+	2.33623i	0.0309912	+	0.0748193i
$976$	−22.5520	+	8.46039i	−0.721872	+	0.270810i
$977$	−21.4552	+	21.4552i	−0.686411	+	0.686411i	−0.961437	−	0.275026i	$-0.911314\pi$
$977$	−21.4552	+	21.4552i	−0.686411	+	0.686411i	0.275026	+	0.961437i	$0.411314\pi$
$978$	−2.14339	+	0.192834i	−0.0685379	+	0.00616616i
$979$			9.89817i			0.316347i
$980$	38.7703	+	26.8640i	1.23847	+	0.858140i
$981$	24.5823			0.784852
$982$	4.07646	+	7.78400i	0.130085	+	0.248398i
$983$	−1.92051	−	4.63652i	−0.0612548	−	0.147882i	0.890289	−	0.455397i	$-0.150503\pi$
$983$	−1.92051	−	4.63652i	−0.0612548	−	0.147882i	−0.951543	+	0.307515i	$0.900503\pi$
$984$	2.49448	+	0.309700i	0.0795210	+	0.00987288i
$985$	−2.32353	+	2.32353i	−0.0740337	+	0.0740337i
$986$	−0.192542	+	0.426185i	−0.00613177	+	0.0135725i
$987$	0.0406981	−	0.0168577i	0.00129543	−	0.000536586i
$988$	−20.5656	+	3.73066i	−0.654280	+	0.118688i
$989$	26.6643	−	26.6643i	0.847875	−	0.847875i
$990$	−3.25809	−	36.2143i	−0.103549	−	1.15096i
$991$	11.7747	−	28.4265i	0.374034	−	0.902999i	−0.619023	−	0.785372i	$-0.712471\pi$
$991$	11.7747	−	28.4265i	0.374034	−	0.902999i	0.993058	−	0.117627i	$-0.0375286\pi$
$992$	−39.6290	−	35.4268i	−1.25822	−	1.12480i
$993$	−1.37494	−	3.31939i	−0.0436323	−	0.105338i
$994$	19.4868	+	16.2699i	0.618084	+	0.516050i
$995$	−10.6697	+	4.41952i	−0.338251	+	0.140108i
$996$	0.0231724	+	0.00501776i	0.000734246	+	0.000158994i
$997$	19.0854	−	19.0854i	0.604440	−	0.604440i	−0.337047	−	0.941488i	$-0.609428\pi$
$997$	19.0854	−	19.0854i	0.604440	−	0.604440i	0.941488	+	0.337047i	$0.109428\pi$
$998$	32.4747	+	27.1137i	1.02797	+	0.858269i
$999$	4.18274	+	4.18274i	0.132336	+	0.132336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.x.a.77.15	yes	280
17.2	even	8		544.2.v.a.461.52	✓	280
32.5	even	8		544.2.v.a.485.52	yes	280
544.325	even	8	inner	544.2.x.a.325.15	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.v.a.461.52	✓	280	17.2	even	8
544.2.v.a.485.52	yes	280	32.5	even	8
544.2.x.a.77.15	yes	280	1.1	even	1	trivial
544.2.x.a.325.15	yes	280	544.325	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08558 - 0.906372i) q^{2} +(0.0709706 - 0.0709706i) q^{3} +(0.356979 + 1.96788i) q^{4} +4.13663i q^{5} +(-0.141370 + 0.0127187i) q^{6} +(-1.05288 - 0.436118i) q^{7} +(1.39610 - 2.45986i) q^{8} +2.98993i q^{9} +(3.74933 - 4.49066i) q^{10} +(-1.46992 - 1.46992i) q^{11} +(0.164997 + 0.114327i) q^{12} +(0.796050 - 1.92184i) q^{13} +(0.747705 + 1.42774i) q^{14} +(0.293579 + 0.293579i) q^{15} +(-3.74513 + 1.40499i) q^{16} +(3.59022 + 2.02739i) q^{17} +(2.70999 - 3.24581i) q^{18} +(-4.64149 + 1.92257i) q^{19} +(-8.14041 + 1.47669i) q^{20} +(-0.105675 + 0.0437721i) q^{21} +(0.263424 + 2.92801i) q^{22} +(-4.14931 - 1.71870i) q^{23} +(-0.0754952 - 0.273660i) q^{24} -12.1117 q^{25} +(-2.60608 + 1.36479i) q^{26} +(0.425109 + 0.425109i) q^{27} +(0.482372 - 2.22763i) q^{28} +(-0.0567121 - 0.0567121i) q^{29} +(-0.0526125 - 0.584797i) q^{30} +(-8.68138 - 3.59595i) q^{31} +(5.33909 + 1.86925i) q^{32} -0.208642 q^{33} +(-2.05991 - 5.45498i) q^{34} +(1.80406 - 4.35538i) q^{35} +(-5.88383 + 1.06734i) q^{36} +9.83922 q^{37} +(6.78128 + 2.11981i) q^{38} +(-0.0798977 - 0.192890i) q^{39} +(10.1755 + 5.77517i) q^{40} +(-3.38846 + 8.18046i) q^{41} +(0.154393 + 0.0482628i) q^{42} +(-3.21310 + 7.75710i) q^{43} +(2.36789 - 3.41735i) q^{44} -12.3682 q^{45} +(2.94664 + 5.62662i) q^{46} -0.385124 q^{47} +(-0.166082 + 0.365507i) q^{48} +(-4.03139 - 4.03139i) q^{49} +(13.1483 + 10.9777i) q^{50} +(0.398686 - 0.110915i) q^{51} +(4.06612 + 0.880479i) q^{52} +(-3.84049 - 1.59078i) q^{53} +(-0.0761840 - 0.846798i) q^{54} +(6.08050 - 6.08050i) q^{55} +(-2.54272 + 1.98107i) q^{56} +(-0.192964 + 0.465855i) q^{57} +(0.0101634 + 0.112968i) q^{58} +(11.8591 + 4.91222i) q^{59} +(-0.472928 + 0.682532i) q^{60} +6.02168 q^{61} +(6.16509 + 11.7723i) q^{62} +(1.30396 - 3.14804i) q^{63} +(-4.10179 - 6.86843i) q^{64} +(7.94993 + 3.29297i) q^{65} +(0.226498 + 0.189107i) q^{66} +(-2.58048 + 6.22983i) q^{67} +(-2.70804 + 7.78887i) q^{68} +(-0.416457 + 0.172502i) q^{69} +(-5.90605 + 3.09298i) q^{70} +(14.5522 - 6.02773i) q^{71} +(7.35479 + 4.17425i) q^{72} +(-7.59896 + 3.14759i) q^{73} +(-10.6813 - 8.91800i) q^{74} +(-0.859577 + 0.859577i) q^{75} +(-5.44030 - 8.44759i) q^{76} +(0.906591 + 2.18870i) q^{77} +(-0.0880947 + 0.281815i) q^{78} +(2.10664 + 5.08589i) q^{79} +(-5.81192 - 15.4922i) q^{80} -8.90944 q^{81} +(11.0930 - 5.80936i) q^{82} +(0.109122 - 0.0451999i) q^{83} +(-0.123862 - 0.192331i) q^{84} +(-8.38658 + 14.8514i) q^{85} +(10.5189 - 5.50871i) q^{86} -0.00804979 q^{87} +(-5.66794 + 1.56363i) q^{88} +(-3.36692 - 3.36692i) q^{89} +(13.4267 + 11.2102i) q^{90} +(-1.67629 + 1.67629i) q^{91} +(1.90099 - 8.77891i) q^{92} +(-0.871330 + 0.360917i) q^{93} +(0.418084 + 0.349066i) q^{94} +(-7.95295 - 19.2001i) q^{95} +(0.511581 - 0.246257i) q^{96} +(-2.64025 + 6.37414i) q^{97} +(0.722467 + 8.03034i) q^{98} +(4.39494 - 4.39494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

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