LMFDB - Embedded newform 784.2.w.f.411.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(19,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			411.7
Character	$\chi$	$=$	784.411
Dual form			784.2.w.f.227.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.252874 - 1.39142i) q^{2} +(2.61463 + 0.700587i) q^{3} +(-1.87211 + 0.703710i) q^{4} +(-0.120751 - 0.450647i) q^{5} +(0.313640 - 3.81521i) q^{6} +(1.45257 + 2.42694i) q^{8} +(3.74737 + 2.16355i) q^{9} +(-0.596506 + 0.281972i) q^{10} +(-1.93537 - 0.518581i) q^{11} +(-5.38787 + 0.528362i) q^{12} +(4.51607 + 4.51607i) q^{13} -1.26287i q^{15} +(3.00959 - 2.63484i) q^{16} +(4.68066 - 2.70238i) q^{17} +(2.06279 - 5.76128i) q^{18} +(0.510379 + 1.90476i) q^{19} +(0.543183 + 0.758687i) q^{20} +(-0.232159 + 2.82405i) q^{22} +(0.951245 - 1.64761i) q^{23} +(2.09763 + 7.36320i) q^{24} +(4.14162 - 2.39117i) q^{25} +(5.14176 - 7.42576i) q^{26} +(2.54010 + 2.54010i) q^{27} +(-1.12415 + 1.12415i) q^{29} +(-1.75718 + 0.319347i) q^{30} +(0.434075 + 0.751840i) q^{31} +(-4.42722 - 3.52132i) q^{32} +(-4.69696 - 2.71179i) q^{33} +(-4.94377 - 5.82941i) q^{34} +(-8.53799 - 1.41333i) q^{36} +(-7.90732 + 2.11876i) q^{37} +(2.52126 - 1.19182i) q^{38} +(8.64394 + 14.9717i) q^{39} +(0.918297 - 0.947649i) q^{40} -3.24226 q^{41} +(6.35727 - 6.35727i) q^{43} +(3.98816 - 0.391099i) q^{44} +(0.522499 - 1.94999i) q^{45} +(-2.53306 - 0.906947i) q^{46} +(1.49266 - 2.58536i) q^{47} +(9.71488 - 4.78065i) q^{48} +(-4.37443 - 5.15808i) q^{50} +(14.1314 - 3.78650i) q^{51} +(-11.6326 - 5.27658i) q^{52} +(-1.81663 + 6.77976i) q^{53} +(2.89203 - 4.17668i) q^{54} +0.934789i q^{55} +5.33780i q^{57} +(1.84843 + 1.27990i) q^{58} +(2.22228 - 8.29366i) q^{59} +(0.888694 + 2.36423i) q^{60} +(-0.469703 + 0.125856i) q^{61} +(0.936361 - 0.794103i) q^{62} +(-3.78011 + 7.05059i) q^{64} +(1.48984 - 2.58047i) q^{65} +(-2.58551 + 7.22120i) q^{66} +(-1.03224 + 3.85238i) q^{67} +(-6.86102 + 8.35298i) q^{68} +(3.64144 - 3.64144i) q^{69} -12.1916 q^{71} +(0.192498 + 12.2373i) q^{72} +(7.79109 + 13.4946i) q^{73} +(4.94765 + 10.4666i) q^{74} +(12.5040 - 3.35044i) q^{75} +(-2.29588 - 3.20676i) q^{76} +(18.6462 - 15.8133i) q^{78} +(-1.07130 - 0.618516i) q^{79} +(-1.55079 - 1.03810i) q^{80} +(-1.62878 - 2.82113i) q^{81} +(0.819885 + 4.51136i) q^{82} +(-9.03560 + 9.03560i) q^{83} +(-1.78301 - 1.78301i) q^{85} +(-10.4532 - 7.23805i) q^{86} +(-3.72680 + 2.15167i) q^{87} +(-1.55269 - 5.45031i) q^{88} +(1.16364 - 2.01548i) q^{89} +(-2.84539 - 0.233913i) q^{90} +(-0.621399 + 3.75390i) q^{92} +(0.608215 + 2.26989i) q^{93} +(-3.97479 - 1.42315i) q^{94} +(0.796746 - 0.460002i) q^{95} +(-9.10855 - 12.3086i) q^{96} -4.69704i q^{97} +(-6.13058 - 6.13058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.252874	−	1.39142i	−0.178809	−	0.983884i
$2$	−0.252874	−	1.39142i	−0.178809	−	0.983884i
$3$	2.61463	+	0.700587i	1.50955	+	0.404484i	0.916287	−	0.400521i	$-0.131171\pi$
$3$	2.61463	+	0.700587i	1.50955	+	0.404484i	0.593268	+	0.805005i	$0.297838\pi$
$4$	−1.87211	+	0.703710i	−0.936055	+	0.351855i
$5$	−0.120751	−	0.450647i	−0.0540013	−	0.201536i	0.933655	−	0.358175i	$-0.116601\pi$
$5$	−0.120751	−	0.450647i	−0.0540013	−	0.201536i	−0.987656	+	0.156639i	$0.949934\pi$
$6$	0.313640	−	3.81521i	0.128043	−	1.55755i
$7$		0			0
$7$		0			0
$8$	1.45257	+	2.42694i	0.513559	+	0.858054i
$9$	3.74737	+	2.16355i	1.24912	+	0.721182i
$10$	−0.596506	+	0.281972i	−0.188632	+	0.0891674i
$11$	−1.93537	−	0.518581i	−0.583536	−	0.156358i	−0.0450390	−	0.998985i	$-0.514341\pi$
$11$	−1.93537	−	0.518581i	−0.583536	−	0.156358i	−0.538497	+	0.842627i	$0.681008\pi$
$12$	−5.38787	+	0.528362i	−1.55535	+	0.152525i
$13$	4.51607	+	4.51607i	1.25253	+	1.25253i	0.954581	+	0.297952i	$0.0963035\pi$
$13$	4.51607	+	4.51607i	1.25253	+	1.25253i	0.297952	+	0.954581i	$0.403696\pi$
$14$		0			0
$15$		−	1.26287i		−	0.326072i
$16$	3.00959	−	2.63484i	0.752396	−	0.658711i
$17$	4.68066	−	2.70238i	1.13523	−	0.655424i	0.189983	−	0.981787i	$-0.439157\pi$
$17$	4.68066	−	2.70238i	1.13523	−	0.655424i	0.945244	+	0.326364i	$0.105823\pi$
$18$	2.06279	−	5.76128i	0.486204	−	1.35795i
$19$	0.510379	+	1.90476i	0.117089	+	0.436982i	0.999435	−	0.0336198i	$-0.0107035\pi$
$19$	0.510379	+	1.90476i	0.117089	+	0.436982i	−0.882346	+	0.470602i	$0.844037\pi$
$20$	0.543183	+	0.758687i	0.121459	+	0.169648i
$21$		0			0
$22$	−0.232159	+	2.82405i	−0.0494966	+	0.602090i
$23$	0.951245	−	1.64761i	0.198348	−	0.343549i	−0.749645	−	0.661841i	$-0.769776\pi$
$23$	0.951245	−	1.64761i	0.198348	−	0.343549i	0.947993	+	0.318291i	$0.103109\pi$
$24$	2.09763	+	7.36320i	0.428177	+	1.50301i
$25$	4.14162	−	2.39117i	0.828325	−	0.478234i
$26$	5.14176	−	7.42576i	1.00838	−	1.45631i
$27$	2.54010	+	2.54010i	0.488843	+	0.488843i
$28$		0			0
$29$	−1.12415	+	1.12415i	−0.208749	+	0.208749i	−0.803736	−	0.594986i	$-0.797157\pi$
$29$	−1.12415	+	1.12415i	−0.208749	+	0.208749i	0.594986	+	0.803736i	$0.297157\pi$
$30$	−1.75718	+	0.319347i	−0.320817	+	0.0583046i
$31$	0.434075	+	0.751840i	0.0779622	+	0.135035i	0.902371	−	0.430961i	$-0.141825\pi$
$31$	0.434075	+	0.751840i	0.0779622	+	0.135035i	−0.824408	+	0.565995i	$0.808492\pi$
$32$	−4.42722	−	3.52132i	−0.782630	−	0.622487i
$33$	−4.69696	−	2.71179i	−0.817636	−	0.472062i
$34$	−4.94377	−	5.82941i	−0.847849	−	0.999736i
$35$		0			0
$36$	−8.53799	−	1.41333i	−1.42300	−	0.235555i
$37$	−7.90732	+	2.11876i	−1.29996	+	0.348322i	−0.841433	−	0.540361i	$-0.818288\pi$
$37$	−7.90732	+	2.11876i	−1.29996	+	0.348322i	−0.458522	+	0.888683i	$0.651621\pi$
$38$	2.52126	−	1.19182i	0.409003	−	0.193338i
$39$	8.64394	+	14.9717i	1.38414	+	2.39740i
$40$	0.918297	−	0.947649i	0.145196	−	0.149836i
$41$	−3.24226			−0.506356			−0.253178	−	0.967420i	$-0.581476\pi$
$41$	−3.24226			−0.506356			−0.253178	+	0.967420i	$0.581476\pi$
$42$		0			0
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	−0.0300731	−	0.999548i	$-0.509574\pi$
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	0.999548	+	0.0300731i	$0.00957401\pi$
$44$	3.98816	−	0.391099i	0.601237	−	0.0589604i
$45$	0.522499	−	1.94999i	0.0778895	−	0.290688i
$46$	−2.53306	−	0.906947i	−0.373479	−	0.133722i
$47$	1.49266	−	2.58536i	0.217727	−	0.377114i	−0.736386	−	0.676562i	$-0.763469\pi$
$47$	1.49266	−	2.58536i	0.217727	−	0.377114i	0.954113	+	0.299448i	$0.0968025\pi$
$48$	9.71488	−	4.78065i	1.40222	−	0.690028i
$49$		0			0
$50$	−4.37443	−	5.15808i	−0.618638	−	0.729463i
$51$	14.1314	−	3.78650i	1.97880	−	0.530217i
$52$	−11.6326	−	5.27658i	−1.61315	−	0.731729i
$53$	−1.81663	+	6.77976i	−0.249533	+	0.931272i	0.721517	+	0.692397i	$0.243445\pi$
$53$	−1.81663	+	6.77976i	−0.249533	+	0.931272i	−0.971050	+	0.238875i	$0.923221\pi$
$54$	2.89203	−	4.17668i	0.393555	−	0.568374i
$55$			0.934789i			0.126047i
$56$		0			0
$57$			5.33780i			0.707009i
$58$	1.84843	+	1.27990i	0.242711	+	0.168059i
$59$	2.22228	−	8.29366i	0.289316	−	1.07974i	−0.656311	−	0.754491i	$-0.727884\pi$
$59$	2.22228	−	8.29366i	0.289316	−	1.07974i	0.945627	−	0.325253i	$-0.105449\pi$
$60$	0.888694	+	2.36423i	0.114730	+	0.305221i
$61$	−0.469703	+	0.125856i	−0.0601393	+	0.0161143i	−0.288763	−	0.957401i	$-0.593244\pi$
$61$	−0.469703	+	0.125856i	−0.0601393	+	0.0161143i	0.228624	+	0.973515i	$0.426577\pi$
$62$	0.936361	−	0.794103i	0.118918	−	0.100851i
$63$		0			0
$64$	−3.78011	+	7.05059i	−0.472513	+	0.881323i
$65$	1.48984	−	2.58047i	0.184792	−	0.320068i
$66$	−2.58551	+	7.22120i	−0.318254	+	0.888868i
$67$	−1.03224	+	3.85238i	−0.126108	+	0.470643i	−0.999877	−	0.0156996i	$-0.995002\pi$
$67$	−1.03224	+	3.85238i	−0.126108	+	0.470643i	0.873768	+	0.486342i	$0.161669\pi$
$68$	−6.86102	+	8.35298i	−0.832020	+	1.01295i
$69$	3.64144	−	3.64144i	0.438378	−	0.438378i
$70$		0			0
$71$	−12.1916			−1.44687			−0.723437	−	0.690390i	$-0.757439\pi$
$71$	−12.1916			−1.44687			−0.723437	+	0.690390i	$0.757439\pi$
$72$	0.192498	+	12.2373i	0.0226862	+	1.44219i
$73$	7.79109	+	13.4946i	0.911878	+	1.57942i	0.811408	+	0.584480i	$0.198701\pi$
$73$	7.79109	+	13.4946i	0.911878	+	1.57942i	0.100470	+	0.994940i	$0.467965\pi$
$74$	4.94765	+	10.4666i	0.575152	+	1.21672i
$75$	12.5040	−	3.35044i	1.44384	−	0.386876i
$76$	−2.29588	−	3.20676i	−0.263356	−	0.367841i
$77$		0			0
$78$	18.6462	−	15.8133i	2.11126	−	1.79051i
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	0.438522	−	0.898720i	$-0.355502\pi$
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	−0.559053	+	0.829132i	$0.688835\pi$
$80$	−1.55079	−	1.03810i	−0.173384	−	0.116063i
$81$	−1.62878	−	2.82113i	−0.180976	−	0.313459i
$82$	0.819885	+	4.51136i	0.0905412	+	0.498196i
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	−0.999967	−	0.00818066i	$-0.997396\pi$
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	0.00818066	+	0.999967i	$0.497396\pi$
$84$		0			0
$85$	−1.78301	−	1.78301i	−0.193395	−	0.193395i
$86$	−10.4532	−	7.23805i	−1.12720	−	0.780499i
$87$	−3.72680	+	2.15167i	−0.399554	+	0.230683i
$88$	−1.55269	−	5.45031i	−0.165517	−	0.581005i
$89$	1.16364	−	2.01548i	0.123345	−	0.213640i	−0.797740	−	0.603002i	$-0.793971\pi$
$89$	1.16364	−	2.01548i	0.123345	−	0.213640i	0.921085	+	0.389362i	$0.127304\pi$
$90$	−2.84539	−	0.233913i	−0.299930	−	0.0246566i
$91$		0			0
$92$	−0.621399	+	3.75390i	−0.0647854	+	0.391371i
$93$	0.608215	+	2.26989i	0.0630689	+	0.235376i
$94$	−3.97479	−	1.42315i	−0.409968	−	0.146786i
$95$	0.796746	−	0.460002i	0.0817444	−	0.0471952i
$96$	−9.10855	−	12.3086i	−0.929637	−	1.25624i
$97$		−	4.69704i		−	0.476912i	−0.971153	−	0.238456i	$-0.923359\pi$
$97$		−	4.69704i		−	0.476912i	0.971153	−	0.238456i	$-0.0766414\pi$
$98$		0			0
$99$	−6.13058	−	6.13058i	−0.616146	−	0.616146i
$100$	−6.07089	+	7.39103i	−0.607089	+	0.739103i
$101$	−5.35584	−	1.43509i	−0.532926	−	0.142797i	−0.0176866	−	0.999844i	$-0.505630\pi$
$101$	−5.35584	−	1.43509i	−0.532926	−	0.142797i	−0.515239	+	0.857047i	$0.672297\pi$
$102$	−8.84210	−	18.7053i	−0.875498	−	1.85210i
$103$	0.958115	+	0.553168i	0.0944059	+	0.0545053i	0.546460	−	0.837485i	$-0.315975\pi$
$103$	0.958115	+	0.553168i	0.0944059	+	0.0545053i	−0.452054	+	0.891991i	$0.649308\pi$
$104$	−4.40036	+	17.5201i	−0.431491	+	1.71799i
$105$		0			0
$106$	9.89289	+	0.813273i	0.960882	+	0.0789921i
$107$	−1.60020	−	5.97202i	−0.154697	−	0.577337i	−0.999131	−	0.0416773i	$-0.986730\pi$
$107$	−1.60020	−	5.97202i	−0.154697	−	0.577337i	0.844434	−	0.535659i	$-0.179937\pi$
$108$	−6.54284	−	2.96785i	−0.629585	−	0.285582i
$109$	−10.5236	−	2.81979i	−1.00798	−	0.270087i	−0.283194	−	0.959063i	$-0.591394\pi$
$109$	−10.5236	−	2.81979i	−1.00798	−	0.270087i	−0.724785	+	0.688975i	$0.758061\pi$
$110$	1.30069	−	0.236384i	0.124015	−	0.0225383i
$111$	−22.1591			−2.10324
$112$		0			0
$113$	−2.81872			−0.265163			−0.132582	−	0.991172i	$-0.542327\pi$
$113$	−2.81872			−0.265163			−0.132582	+	0.991172i	$0.542327\pi$
$114$	7.42713	−	1.34979i	0.695615	−	0.126420i
$115$	−0.857352	−	0.229727i	−0.0799485	−	0.0214221i
$116$	1.31346	−	2.89561i	0.121951	−	0.268850i
$117$	7.15267	+	26.6941i	0.661264	+	2.46787i
$118$	−12.1019	−	0.994875i	−1.11407	−	0.0915857i
$119$		0			0
$120$	3.06491	−	1.83440i	0.279787	−	0.167457i
$121$	−6.04954	−	3.49271i	−0.549958	−	0.317519i
$122$	0.293895	+	0.621729i	0.0266080	+	0.0562887i
$123$	−8.47731	−	2.27149i	−0.764373	−	0.204813i
$124$	−1.34171	−	1.10206i	−0.120489	−	0.0989683i
$125$	−3.22716	−	3.22716i	−0.288646	−	0.288646i
$126$		0			0
$127$			9.34725i			0.829434i	0.909950	+	0.414717i	$0.136119\pi$
$127$			9.34725i			0.829434i	−0.909950	+	0.414717i	$0.863881\pi$
$128$	10.7662	+	3.47681i	0.951610	+	0.307310i
$129$	21.0757	−	12.1681i	1.85561	−	1.07134i
$130$	−3.96727	−	1.42046i	−0.347952	−	0.124582i
$131$	−4.80174	−	17.9203i	−0.419530	−	1.56571i	−0.775586	−	0.631242i	$-0.782545\pi$
$131$	−4.80174	−	17.9203i	−0.419530	−	1.56571i	0.356056	−	0.934465i	$-0.384121\pi$
$132$	10.7015	+	1.77147i	0.931449	+	0.154187i
$133$		0			0
$134$	5.62131	+	0.462116i	0.485607	+	0.0399207i
$135$	0.837971	−	1.45141i	0.0721211	−	0.124917i
$136$	13.3575	+	7.43431i	1.14540	+	0.637487i
$137$	13.1541	−	7.59453i	1.12383	−	0.648844i	0.181455	−	0.983399i	$-0.441919\pi$
$137$	13.1541	−	7.59453i	1.12383	−	0.648844i	0.942376	+	0.334555i	$0.108586\pi$
$138$	−5.98761	−	4.14595i	−0.509699	−	0.352927i
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	0.657507	−	0.753448i	$-0.271611\pi$
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	−0.753448	+	0.657507i	$0.771611\pi$
$140$		0			0
$141$	5.71402	−	5.71402i	0.481207	−	0.481207i
$142$	3.08294	+	16.9636i	0.258714	+	1.42356i
$143$	−6.39833	−	11.0822i	−0.535055	−	0.926742i
$144$	16.9786	−	3.36236i	1.41489	−	0.280196i
$145$	0.642337	+	0.370853i	0.0533431	+	0.0307977i
$146$	16.8065	−	14.2531i	1.39091	−	1.17960i
$147$		0			0
$148$	13.3124	−	9.53101i	1.09427	−	0.783444i
$149$	−9.81380	+	2.62960i	−0.803978	+	0.215425i	−0.637330	−	0.770591i	$-0.719961\pi$
$149$	−9.81380	+	2.62960i	−0.803978	+	0.215425i	−0.166648	+	0.986016i	$0.553294\pi$
$150$	−7.82382	−	16.5511i	−0.638813	−	1.35139i
$151$	−5.83900	−	10.1134i	−0.475171	−	0.823020i	0.524425	−	0.851457i	$-0.324280\pi$
$151$	−5.83900	−	10.1134i	−0.475171	−	0.823020i	−0.999596	+	0.0284368i	$0.990947\pi$
$152$	−3.88139	+	4.00545i	−0.314822	+	0.324885i
$153$	23.3869			1.89072
$154$		0			0
$155$	0.286400	−	0.286400i	0.0230042	−	0.0230042i
$156$	−26.7182	−	21.9459i	−2.13916	−	1.75708i
$157$	−0.576431	+	2.15127i	−0.0460042	+	0.171690i	−0.985106	−	0.171950i	$-0.944993\pi$
$157$	−0.576431	+	2.15127i	−0.0460042	+	0.171690i	0.939101	+	0.343640i	$0.111660\pi$
$158$	−0.589712	+	1.64704i	−0.0469150	+	0.131031i
$159$	−9.49962	+	16.4538i	−0.753369	+	1.30487i
$160$	−1.05228	+	2.42032i	−0.0831902	+	0.191343i
$161$		0			0
$162$	−3.51350	+	2.97971i	−0.276047	+	0.234108i
$163$	−14.1740	+	3.79792i	−1.11020	+	0.297476i	−0.766910	−	0.641755i	$-0.778207\pi$
$163$	−14.1740	+	3.79792i	−1.11020	+	0.297476i	−0.343286	+	0.939231i	$0.611540\pi$
$164$	6.06987	−	2.28161i	0.473977	−	0.178164i
$165$	−0.654901	+	2.44412i	−0.0509839	+	0.190275i
$166$	14.8572	+	10.2875i	1.15314	+	0.798462i
$167$			5.94995i			0.460421i	0.973141	+	0.230210i	$0.0739415\pi$
$167$			5.94995i			0.460421i	−0.973141	+	0.230210i	$0.926059\pi$
$168$		0			0
$169$			27.7898i			2.13768i
$170$	−2.03004	+	2.93180i	−0.155697	+	0.224859i
$171$	−2.20846	+	8.24207i	−0.168885	+	0.630287i
$172$	−7.42783	+	16.3752i	−0.566367	+	1.24860i
$173$	8.87194	−	2.37723i	0.674521	−	0.180737i	0.0947304	−	0.995503i	$-0.469801\pi$
$173$	8.87194	−	2.37723i	0.674521	−	0.180737i	0.579790	+	0.814766i	$0.303134\pi$
$174$	3.93629	+	4.64144i	0.298409	+	0.351867i
$175$		0			0
$176$	−7.19105	+	3.53868i	−0.542045	+	0.266738i
$177$	11.6209	−	20.1279i	0.873478	−	1.51291i
$178$	−3.09863	−	1.10945i	−0.232252	−	0.0831566i
$179$	−0.984716	+	3.67501i	−0.0736011	+	0.274683i	−0.992912	−	0.118848i	$-0.962080\pi$
$179$	−0.984716	+	3.67501i	−0.0736011	+	0.274683i	0.919311	+	0.393531i	$0.128747\pi$
$180$	0.394053	+	4.01828i	0.0293710	+	0.299505i
$181$	−5.13439	+	5.13439i	−0.381636	+	0.381636i	−0.871691	−	0.490055i	$-0.836977\pi$
$181$	−5.13439	+	5.13439i	−0.381636	+	0.381636i	0.490055	+	0.871691i	$0.336977\pi$
$182$		0			0
$183$	−1.31627			−0.0973015
$184$	5.38039	−	0.0846358i	0.396648	−	0.00623943i
$185$	1.90963	+	3.30757i	0.140398	+	0.243177i
$186$	3.00457	−	1.42028i	0.220306	−	0.104140i
$187$	−10.4602	+	2.80281i	−0.764927	+	0.204962i
$188$	−0.975077	+	5.89048i	−0.0711148	+	0.429607i
$189$		0			0
$190$	−0.841533	−	0.992287i	−0.0610512	−	0.0719881i
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.165791	−	0.986161i	$-0.553018\pi$
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.936936	+	0.349501i	$0.886351\pi$
$192$	−14.8231	+	15.7864i	−1.06977	+	1.13928i
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	0.959793	−	0.280708i	$-0.0905692\pi$
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	−0.722997	+	0.690851i	$0.757236\pi$
$194$	−6.53557	+	1.18776i	−0.469226	+	0.0852763i
$195$	5.70321	−	5.70321i	0.408415	−	0.408415i
$196$		0			0
$197$	14.8776	+	14.8776i	1.05998	+	1.05998i	0.998082	+	0.0619015i	$0.0197165\pi$
$197$	14.8776	+	14.8776i	1.05998	+	1.05998i	0.0619015	+	0.998082i	$0.480284\pi$
$198$	−6.97996	+	10.0805i	−0.496044	+	0.716389i
$199$	−6.43322	+	3.71422i	−0.456039	+	0.263294i	−0.710377	−	0.703821i	$-0.751476\pi$
$199$	−6.43322	+	3.71422i	−0.456039	+	0.263294i	0.254338	+	0.967115i	$0.418142\pi$
$200$	11.8192	+	6.57816i	0.835744	+	0.465146i
$201$	−5.39785	+	9.34935i	−0.380735	+	0.659452i
$202$	−0.642465	+	7.81512i	−0.0452037	+	0.549870i
$203$		0			0
$204$	−23.7910	+	17.0332i	−1.66570	+	1.19256i
$205$	0.391505	+	1.46112i	0.0273439	+	0.102049i
$206$	0.527407	−	1.47302i	0.0367462	−	0.102630i
$207$	7.12934	−	4.11612i	0.495523	−	0.286090i
$208$	25.4906	+	1.69236i	1.76746	+	0.117344i
$209$		−	3.95109i		−	0.273303i
$210$		0			0
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	0.319820	−	0.947478i	$-0.396378\pi$
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	−0.947478	+	0.319820i	$0.896378\pi$
$212$	−1.37005	−	13.9708i	−0.0940955	−	0.959521i
$213$	−31.8764	−	8.54126i	−2.18414	−	0.585237i
$214$	−7.90494	+	3.73672i	−0.540371	+	0.255437i
$215$	−3.63253	−	2.09724i	−0.247736	−	0.143031i
$216$	−2.47502	+	9.85435i	−0.168404	+	0.670504i
$217$		0			0
$218$	−1.26237	+	15.3558i	−0.0854985	+	1.04003i
$219$	10.9167	+	40.7416i	0.737681	+	2.75306i
$220$	−0.657820	−	1.75003i	−0.0443502	−	0.117987i
$221$	33.3423	+	8.93405i	2.24285	+	0.600969i
$222$	5.60346	+	30.8326i	0.376079	+	2.06935i
$223$	6.72926			0.450624			0.225312	−	0.974287i	$-0.427660\pi$
$223$	6.72926			0.450624			0.225312	+	0.974287i	$0.427660\pi$
$224$		0			0
$225$	20.6936			1.37957
$226$	0.712783	+	3.92203i	0.0474136	+	0.260890i
$227$	7.46500	+	2.00024i	0.495469	+	0.132761i	0.497896	−	0.867236i	$-0.334106\pi$
$227$	7.46500	+	2.00024i	0.495469	+	0.132761i	−0.00242728	+	0.999997i	$0.500773\pi$
$228$	−3.75626	−	9.99294i	−0.248765	−	0.661799i
$229$	3.94509	+	14.7233i	0.260699	+	0.972941i	0.964831	+	0.262872i	$0.0846696\pi$
$229$	3.94509	+	14.7233i	0.260699	+	0.972941i	−0.704132	+	0.710069i	$0.748664\pi$
$230$	−0.102845	+	1.25103i	−0.00678137	+	0.0824905i
$231$		0			0
$232$	−4.36115	−	1.09535i	−0.286323	−	0.0719130i
$233$	12.7954	+	7.38741i	0.838253	+	0.483965i	0.856670	−	0.515865i	$-0.172529\pi$
$233$	12.7954	+	7.38741i	0.838253	+	0.483965i	−0.0184173	+	0.999830i	$0.505863\pi$
$234$	35.3340	−	16.7026i	2.30986	−	1.09189i
$235$	−1.34533	−	0.360479i	−0.0877594	−	0.0235151i
$236$	1.67598	+	17.0905i	0.109097	+	1.11250i
$237$	−2.36773	−	2.36773i	−0.153800	−	0.153800i
$238$		0			0
$239$		−	28.5488i		−	1.84667i	−0.383998	−	0.923334i	$-0.625453\pi$
$239$		−	28.5488i		−	1.84667i	0.383998	−	0.923334i	$-0.374547\pi$
$240$	−3.32746	−	3.80072i	−0.214787	−	0.245335i
$241$	−19.8792	+	11.4772i	−1.28053	+	0.739314i	−0.976945	−	0.213491i	$-0.931517\pi$
$241$	−19.8792	+	11.4772i	−1.28053	+	0.739314i	−0.303584	+	0.952805i	$0.598183\pi$
$242$	−3.33005	+	9.30068i	−0.214064	+	0.597870i
$243$	−5.07143	−	18.9268i	−0.325332	−	1.21416i
$244$	0.790768	−	0.566151i	0.0506238	−	0.0362441i
$245$		0			0
$246$	−1.01690	+	12.3699i	−0.0648354	+	0.788677i
$247$	−6.29713	+	10.9069i	−0.400676	+	0.693992i
$248$	−1.19415	+	2.14557i	−0.0758287	+	0.136244i
$249$	−29.9549	+	17.2945i	−1.89832	+	1.09599i
$250$	−3.67427	+	5.30641i	−0.232382	+	0.335607i
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	0.952732	−	0.303813i	$-0.0982599\pi$
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	−0.303813	+	0.952732i	$0.598260\pi$
$252$		0			0
$253$	−2.69543	+	2.69543i	−0.169460	+	0.169460i
$254$	13.0060	−	2.36368i	0.816067	−	0.148310i
$255$	−3.41276	−	5.91107i	−0.213715	−	0.370165i
$256$	2.11521	−	15.8596i	0.132200	−	0.991223i
$257$	−2.17812	−	1.25754i	−0.135867	−	0.0784431i	0.430526	−	0.902578i	$-0.358328\pi$
$257$	−2.17812	−	1.25754i	−0.135867	−	0.0784431i	−0.566393	+	0.824135i	$0.691662\pi$
$258$	−22.2604	−	26.2482i	−1.38587	−	1.63414i
$259$		0			0
$260$	−0.973233	+	5.87934i	−0.0603574	+	0.364621i
$261$	−6.64475	+	1.78046i	−0.411300	+	0.110207i
$262$	−23.7205	+	11.2128i	−1.46546	+	0.692731i
$263$	−4.54781	−	7.87703i	−0.280430	−	0.485718i	0.691061	−	0.722797i	$-0.257144\pi$
$263$	−4.54781	−	7.87703i	−0.280430	−	0.485718i	−0.971491	+	0.237078i	$0.923810\pi$
$264$	−0.241278	−	15.3383i	−0.0148496	−	0.944008i
$265$	3.27464			0.201159
$266$		0			0
$267$	4.45449	−	4.45449i	0.272611	−	0.272611i
$268$	−0.778486	−	7.93847i	−0.0475536	−	0.484919i
$269$	−1.47548	+	5.50656i	−0.0899615	+	0.335741i	−0.996207	−	0.0870099i	$-0.972269\pi$
$269$	−1.47548	+	5.50656i	−0.0899615	+	0.335741i	0.906246	+	0.422751i	$0.138935\pi$
$270$	−2.23142	−	0.798947i	−0.135800	−	0.0486224i
$271$	5.76007	−	9.97673i	0.349899	−	0.606043i	−0.636332	−	0.771415i	$-0.719549\pi$
$271$	5.76007	−	9.97673i	0.349899	−	0.606043i	0.986231	+	0.165372i	$0.0528825\pi$
$272$	6.96650	−	20.4658i	0.422406	−	1.24092i
$273$		0			0
$274$	−13.8935	−	16.3824i	−0.839338	−	0.989700i
$275$	−9.25560	+	2.48003i	−0.558134	+	0.149551i
$276$	−4.25466	+	9.37969i	−0.256100	+	0.564591i
$277$	5.40800	−	20.1829i	0.324935	−	1.21268i	−0.589442	−	0.807811i	$-0.700652\pi$
$277$	5.40800	−	20.1829i	0.324935	−	1.21268i	0.914377	−	0.404864i	$-0.132681\pi$
$278$	−1.28785	+	1.85991i	−0.0772399	+	0.111550i
$279$			3.75657i			0.224900i
$280$		0			0
$281$		−	19.8360i		−	1.18331i	−0.806190	−	0.591657i	$-0.798474\pi$
$281$		−	19.8360i		−	1.18331i	0.806190	−	0.591657i	$-0.201526\pi$
$282$	−9.39554	−	6.50568i	−0.559496	−	0.387408i
$283$	−5.26602	+	19.6531i	−0.313033	+	1.16825i	0.612775	+	0.790258i	$0.290053\pi$
$283$	−5.26602	+	19.6531i	−0.313033	+	1.16825i	−0.925807	+	0.377996i	$0.876613\pi$
$284$	22.8240	−	8.57933i	1.35435	−	0.509090i
$285$	2.40546	−	0.644542i	0.142487	−	0.0381794i
$286$	−13.8021	+	11.7052i	−0.816134	+	0.692142i
$287$		0			0
$288$	−8.97192	−	22.7742i	−0.528675	−	1.34198i
$289$	6.10572	−	10.5754i	0.359160	−	0.622083i
$290$	0.353583	−	0.987540i	0.0207631	−	0.0579904i
$291$	3.29069	−	12.2810i	0.192903	−	0.719926i
$292$	−24.0820	−	19.7806i	−1.40929	−	1.15757i
$293$	6.75509	−	6.75509i	0.394636	−	0.394636i	−0.481700	−	0.876336i	$-0.659980\pi$
$293$	6.75509	−	6.75509i	0.394636	−	0.394636i	0.876336	+	0.481700i	$0.159980\pi$
$294$		0			0
$295$	−4.00586			−0.233230
$296$	−16.6280	−	16.1130i	−0.966483	−	0.936548i
$297$	−3.59879	−	6.23329i	−0.208823	−	0.361692i
$298$	6.14054	+	12.9902i	0.355712	+	0.752501i
$299$	11.7366	−	3.14481i	0.678745	−	0.181869i
$300$	−21.0512	+	15.0716i	−1.21539	+	0.870159i
$301$		0			0
$302$	−12.5955	+	10.6819i	−0.724791	+	0.614676i
$303$	−12.9981	−	7.50446i	−0.746721	−	0.431120i
$304$	6.55477	+	4.38777i	0.375942	+	0.251656i
$305$	0.113434	+	0.196473i	0.00649520	+	0.0112500i
$306$	−5.91394	−	32.5410i	−0.338078	−	1.86025i
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	−0.771479	−	0.636255i	$-0.780483\pi$
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	0.636255	+	0.771479i	$0.280483\pi$
$308$		0			0
$309$	2.11757	+	2.11757i	0.120464	+	0.120464i
$310$	−0.470926	−	0.326080i	−0.0267468	−	0.0185201i
$311$	13.1239	−	7.57707i	0.744186	−	0.429656i	−0.0794032	−	0.996843i	$-0.525301\pi$
$311$	13.1239	−	7.57707i	0.744186	−	0.429656i	0.823589	+	0.567186i	$0.191968\pi$
$312$	−23.7797	+	42.7258i	−1.34626	+	2.41887i
$313$	3.32791	−	5.76411i	0.188105	−	0.325807i	−0.756514	−	0.653978i	$-0.773099\pi$
$313$	3.32791	−	5.76411i	0.188105	−	0.325807i	0.944618	+	0.328171i	$0.106432\pi$
$314$	3.13909	+	0.258058i	0.177149	+	0.0145630i
$315$		0			0
$316$	2.44085	+	0.404045i	0.137308	+	0.0227293i
$317$	6.86233	+	25.6106i	0.385427	+	1.43843i	0.837493	+	0.546449i	$0.184021\pi$
$317$	6.86233	+	25.6106i	0.385427	+	1.43843i	−0.452065	+	0.891985i	$0.649313\pi$
$318$	25.2964	+	9.05723i	1.41855	+	0.507904i
$319$	2.75861	−	1.59268i	0.154453	−	0.0891732i
$320$	3.63378	+	0.852133i	0.203134	+	0.0476357i
$321$		−	16.7357i		−	0.934094i
$322$		0			0
$323$	7.53630	+	7.53630i	0.419331	+	0.419331i
$324$	5.03451	+	4.13527i	0.279695	+	0.229737i
$325$	29.5026	+	7.90519i	1.63651	+	0.438501i
$326$	8.86876	+	18.7617i	0.491195	+	1.03911i
$327$	−25.5398	−	14.7454i	−1.41235	−	0.815423i
$328$	−4.70960	−	7.86879i	−0.260044	−	0.434481i
$329$		0			0
$330$	3.56641	+	0.293187i	0.196325	+	0.0161394i
$331$	2.45530	+	9.16331i	0.134956	+	0.503661i	0.999998	+	0.00196237i	$0.000624644\pi$
$331$	2.45530	+	9.16331i	0.134956	+	0.503661i	−0.865043	+	0.501699i	$0.832709\pi$
$332$	10.5572	−	23.2741i	0.579401	−	1.27733i
$333$	−34.2157	−	9.16806i	−1.87501	−	0.502407i
$334$	8.27889	−	1.50459i	0.453001	−	0.0823275i
$335$	1.86071			0.101661
$336$		0			0
$337$	−16.0354			−0.873502			−0.436751	−	0.899582i	$-0.643871\pi$
$337$	−16.0354			−0.873502			−0.436751	+	0.899582i	$0.643871\pi$
$338$	38.6673	−	7.02733i	2.10323	−	0.382236i
$339$	−7.36991	−	1.97476i	−0.400278	−	0.107254i
$340$	4.59272	+	2.08327i	0.249075	+	0.112981i
$341$	−0.450207	−	1.68019i	−0.0243801	−	0.0909876i
$342$	12.0267	+	0.988686i	0.650327	+	0.0534620i
$343$		0			0
$344$	24.6631	+	6.19438i	1.32974	+	0.333979i
$345$	−2.08071	−	1.20130i	−0.112022	−	0.0646758i
$346$	−5.55121	−	11.7435i	−0.298435	−	0.631333i
$347$	−3.06636	−	0.821629i	−0.164611	−	0.0441074i	0.175572	−	0.984467i	$-0.443822\pi$
$347$	−3.06636	−	0.821629i	−0.164611	−	0.0441074i	−0.340183	+	0.940359i	$0.610489\pi$
$348$	5.46282	−	6.65074i	0.292838	−	0.356517i
$349$	2.21348	+	2.21348i	0.118485	+	0.118485i	0.763863	−	0.645378i	$-0.223300\pi$
$349$	2.21348	+	2.21348i	0.118485	+	0.118485i	−0.645378	+	0.763863i	$0.723300\pi$
$350$		0			0
$351$			22.9426i			1.22458i
$352$	6.74223	+	9.11093i	0.359362	+	0.485614i
$353$	7.11770	−	4.10941i	0.378837	−	0.218722i	−0.298475	−	0.954417i	$-0.596478\pi$
$353$	7.11770	−	4.10941i	0.378837	−	0.218722i	0.677312	+	0.735696i	$0.263145\pi$
$354$	−30.9451	−	11.0797i	−1.64471	−	0.588879i
$355$	1.47214	+	5.49410i	0.0781331	+	0.291597i
$356$	−0.760144	+	4.59206i	−0.0402875	+	0.243379i
$357$		0			0
$358$	5.36250	+	0.440840i	0.283417	+	0.0232991i
$359$	15.3319	−	26.5556i	0.809184	−	1.40155i	−0.104245	−	0.994552i	$-0.533243\pi$
$359$	15.3319	−	26.5556i	0.809184	−	1.40155i	0.913430	−	0.406997i	$-0.133424\pi$
$360$	5.49148	−	1.56442i	0.289426	−	0.0824519i
$361$	13.0869	−	7.55570i	0.688782	−	0.397668i
$362$	8.44245	+	5.84574i	0.443725	+	0.307245i
$363$	−13.3703	−	13.3703i	−0.701761	−	0.701761i
$364$		0			0
$365$	5.14051	−	5.14051i	0.269067	−	0.269067i
$366$	0.332851	+	1.83149i	0.0173984	+	0.0957334i
$367$	−8.91168	−	15.4355i	−0.465186	−	0.805726i	0.534024	−	0.845469i	$-0.320679\pi$
$367$	−8.91168	−	15.4355i	−0.465186	−	0.805726i	−0.999210	+	0.0397435i	$0.987346\pi$
$368$	−1.47833	−	7.46499i	−0.0770631	−	0.389140i
$369$	−12.1500	−	7.01478i	−0.632502	−	0.365175i
$370$	4.11933	−	3.49349i	0.214154	−	0.181618i
$371$		0			0
$372$	−2.73599	−	3.82147i	−0.141854	−	0.198134i
$373$	2.39939	−	0.642914i	0.124236	−	0.0332888i	−0.196166	−	0.980571i	$-0.562849\pi$
$373$	2.39939	−	0.642914i	0.124236	−	0.0332888i	0.320401	+	0.947282i	$0.396182\pi$
$374$	6.54501	+	13.8458i	0.338434	+	0.715950i
$375$	−6.17691	−	10.6987i	−0.318974	−	0.552480i
$376$	8.44272	−	0.132807i	0.435400	−	0.00684902i
$377$	−10.1535			−0.522931
$378$		0			0
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	−0.720489	−	0.693466i	$-0.756083\pi$
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	0.693466	+	0.720489i	$0.256083\pi$
$380$	−1.16789	+	1.42185i	−0.0599114	+	0.0729394i
$381$	−6.54856	+	24.4396i	−0.335493	+	1.25208i
$382$	−8.38906	+	23.4303i	−0.429222	+	1.19880i
$383$	−11.8928	+	20.5989i	−0.607692	+	1.05255i	0.383928	+	0.923363i	$0.374571\pi$
$383$	−11.8928	+	20.5989i	−0.607692	+	1.05255i	−0.991620	+	0.129190i	$0.958762\pi$
$384$	25.7139	+	16.6332i	1.31221	+	0.848812i
$385$		0			0
$386$	7.09630	−	6.01819i	0.361192	−	0.306318i
$387$	37.5773	−	10.0688i	1.91016	−	0.511826i
$388$	3.30535	+	8.79338i	0.167804	+	0.446416i
$389$	6.27509	−	23.4190i	0.318160	−	1.18739i	−0.602852	−	0.797853i	$-0.705969\pi$
$389$	6.27509	−	23.4190i	0.318160	−	1.18739i	0.921012	−	0.389535i	$-0.127364\pi$
$390$	−9.37777	−	6.49338i	−0.474862	−	0.328805i
$391$		−	10.2825i		−	0.520009i
$392$		0			0
$393$		−	50.2190i		−	2.53321i
$394$	16.9388	−	24.4631i	0.853366	−	1.23244i
$395$	−0.149372	+	0.557465i	−0.00751574	+	0.0280491i
$396$	15.7913	+	7.16297i	0.793541	+	0.359953i
$397$	−4.07659	+	1.09232i	−0.204598	+	0.0548219i	−0.359662	−	0.933082i	$-0.617108\pi$
$397$	−4.07659	+	1.09232i	−0.204598	+	0.0548219i	0.155064	+	0.987904i	$0.450442\pi$
$398$	6.79485	+	8.01209i	0.340595	+	0.401610i
$399$		0			0
$400$	6.16422	−	18.1090i	0.308211	−	0.905448i
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	−0.998387	−	0.0567812i	$-0.981916\pi$
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	0.548367	+	0.836238i	$0.315250\pi$
$402$	14.3739	+	5.14647i	0.716903	+	0.256683i
$403$	−1.43505	+	5.35568i	−0.0714849	+	0.266785i
$404$	11.0366	−	1.08230i	0.549091	−	0.0538467i
$405$	−1.07466	+	1.07466i	−0.0534002	+	0.0534002i
$406$		0			0
$407$	16.4023			0.813034
$408$	29.7165	+	28.7960i	1.47118	+	1.42562i
$409$	−13.9843	−	24.2215i	−0.691478	−	1.19768i	−0.971354	−	0.237639i	$-0.923626\pi$
$409$	−13.9843	−	24.2215i	−0.691478	−	1.19768i	0.279875	−	0.960036i	$-0.409707\pi$
$410$	1.93403	−	0.914228i	0.0955149	−	0.0451505i
$411$	39.7137	−	10.6412i	1.95893	−	0.524894i
$412$	−2.18297	−	0.361356i	−0.107547	−	0.0178027i
$413$		0			0
$414$	−7.53009	−	8.87905i	−0.370084	−	0.436382i
$415$	5.16292	+	2.98081i	0.253438	+	0.146322i
$416$	−4.09114	−	35.8962i	−0.200584	−	1.75996i
$417$	−2.16503	−	3.74994i	−0.106022	−	0.183635i
$418$	−5.49763	+	0.999130i	−0.268898	+	0.0488690i
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	−0.403596	−	0.914937i	$-0.632240\pi$
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	0.914937	+	0.403596i	$0.132240\pi$
$420$		0			0
$421$	12.3722	+	12.3722i	0.602984	+	0.602984i	0.941103	−	0.338119i	$-0.109791\pi$
$421$	12.3722	+	12.3722i	0.602984	+	0.602984i	−0.338119	+	0.941103i	$0.609791\pi$
$422$	−10.3804	+	14.9915i	−0.505312	+	0.729775i
$423$	11.1871	−	6.45887i	0.543935	−	0.314041i
$424$	−19.0929	+	5.43918i	−0.927232	+	0.264150i
$425$	12.9237	−	22.3845i	0.626891	−	1.08581i
$426$	−3.82377	+	46.5134i	−0.185262	+	2.25358i
$427$		0			0
$428$	7.19831	+	10.0542i	0.347943	+	0.485988i
$429$	−8.96517	−	33.4585i	−0.432842	−	1.61539i
$430$	−1.99957	+	5.58472i	−0.0964281	+	0.269319i
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	−0.756675	−	0.653791i	$-0.773178\pi$
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	0.187862	+	0.982195i	$0.439844\pi$
$432$	14.3374	+	0.951885i	0.689810	+	0.0457976i
$433$		−	19.1575i		−	0.920649i	−0.887751	−	0.460325i	$-0.847733\pi$
$433$		−	19.1575i		−	0.920649i	0.887751	−	0.460325i	$-0.152267\pi$
$434$		0			0
$435$	1.41965	+	1.41965i	0.0680672	+	0.0680672i
$436$	21.6857	−	2.12661i	1.03855	−	0.101846i
$437$	3.62379	+	0.970991i	0.173349	+	0.0464488i
$438$	53.9282	−	25.4922i	2.57679	−	1.21806i
$439$	−7.42387	−	4.28617i	−0.354322	−	0.204568i	0.312265	−	0.949995i	$-0.398912\pi$
$439$	−7.42387	−	4.28617i	−0.354322	−	0.204568i	−0.666587	+	0.745427i	$0.732246\pi$
$440$	−2.26868	+	1.35784i	−0.108155	+	0.0647326i
$441$		0			0
$442$	3.99961	−	48.6524i	0.190242	−	2.31416i
$443$	−5.42088	−	20.2310i	−0.257554	−	0.961204i	−0.966652	−	0.256094i	$-0.917564\pi$
$443$	−5.42088	−	20.2310i	−0.257554	−	0.961204i	0.709098	−	0.705110i	$-0.249102\pi$
$444$	41.4842	−	15.5935i	1.96875	−	0.740037i
$445$	−1.04878	−	0.281020i	−0.0497169	−	0.0133216i
$446$	−1.70166	−	9.36324i	−0.0805758	−	0.443362i
$447$	−27.5017			−1.30079
$448$		0			0
$449$	−24.4270			−1.15278			−0.576391	−	0.817174i	$-0.695539\pi$
$449$	−24.4270			−1.15278			−0.576391	+	0.817174i	$0.695539\pi$
$450$	−5.23288	−	28.7935i	−0.246680	−	1.35734i
$451$	6.27498	+	1.68138i	0.295477	+	0.0791729i
$452$	5.27696	−	1.98356i	0.248207	−	0.0932990i
$453$	−8.18145	−	30.5336i	−0.384398	−	1.43459i
$454$	0.895471	−	10.8928i	0.0420265	−	0.511223i
$455$		0			0
$456$	−12.9545	+	7.75350i	−0.606652	+	0.363091i
$457$	3.12783	+	1.80585i	0.146314	+	0.0844743i	0.571370	−	0.820693i	$-0.306412\pi$
$457$	3.12783	+	1.80585i	0.146314	+	0.0844743i	−0.425056	+	0.905167i	$0.639746\pi$
$458$	19.4887	−	9.21242i	0.910645	−	0.430468i
$459$	18.7537	+	5.02503i	0.875347	+	0.234548i
$460$	1.76672	−	0.173253i	0.0823736	−	0.00807798i
$461$	25.2872	+	25.2872i	1.17774	+	1.17774i	0.980318	+	0.197423i	$0.0632574\pi$
$461$	25.2872	+	25.2872i	1.17774	+	1.17774i	0.197423	+	0.980318i	$0.436743\pi$
$462$		0			0
$463$			8.01165i			0.372333i	0.982518	+	0.186166i	$0.0596064\pi$
$463$			8.01165i			0.372333i	−0.982518	+	0.186166i	$0.940394\pi$
$464$	−0.421267	+	6.34518i	−0.0195568	+	0.294568i
$465$	0.949477	−	0.548181i	0.0440309	−	0.0254213i
$466$	7.04338	−	19.6718i	0.326278	−	0.911281i
$467$	4.79633	+	17.9002i	0.221948	+	0.828321i	0.983604	+	0.180340i	$0.0577197\pi$
$467$	4.79633	+	17.9002i	0.221948	+	0.828321i	−0.761657	+	0.647981i	$0.775614\pi$
$468$	−32.1755	−	44.9409i	−1.48731	−	2.07739i
$469$		0			0
$470$	−0.161380	+	1.96307i	−0.00744390	+	0.0905498i
$471$	−3.01430	+	5.22093i	−0.138892	+	0.240568i
$472$	23.3563	−	6.65374i	1.07506	−	0.306263i
$473$	−15.6004	+	9.00692i	−0.717309	+	0.414139i
$474$	−2.69577	+	3.89325i	−0.123821	+	0.178823i
$475$	6.66840	+	6.66840i	0.305967	+	0.305967i
$476$		0			0
$477$	−21.4759	+	21.4759i	−0.983314	+	0.983314i
$478$	−39.7234	+	7.21926i	−1.81691	+	0.330201i
$479$	−13.6882	−	23.7087i	−0.625432	−	1.08328i	−0.988457	−	0.151501i	$-0.951589\pi$
$479$	−13.6882	−	23.7087i	−0.625432	−	1.08328i	0.363025	−	0.931779i	$-0.381744\pi$
$480$	−4.44697	+	5.59101i	−0.202975	+	0.255193i
$481$	−45.2785	−	26.1415i	−2.06452	−	1.19195i
$482$	20.9966	+	24.7580i	0.956369	+	1.12770i
$483$		0			0
$484$	13.7833	+	2.28160i	0.626512	+	0.103709i
$485$	−2.11671	+	0.567171i	−0.0961148	+	0.0257539i
$486$	−25.0528	+	11.8426i	−1.13642	+	0.537192i
$487$	−9.68012	−	16.7665i	−0.438648	−	0.759761i	0.558938	−	0.829210i	$-0.311209\pi$
$487$	−9.68012	−	16.7665i	−0.438648	−	0.759761i	−0.997585	+	0.0694492i	$0.977876\pi$
$488$	−0.987720	−	0.957127i	−0.0447120	−	0.0433271i
$489$	−39.7206			−1.79623
$490$		0			0
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	−0.979148	−	0.203149i	$-0.934882\pi$
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	0.203149	+	0.979148i	$0.434882\pi$
$492$	17.4689	−	1.71309i	0.787559	−	0.0772321i
$493$	−2.22388	+	8.29964i	−0.100159	+	0.373797i
$494$	16.7685	+	6.00387i	0.754452	+	0.270127i
$495$	−2.02246	+	3.50300i	−0.0909027	+	0.157448i
$496$	3.28737	+	1.11901i	0.147607	+	0.0502449i
$497$		0			0
$498$	31.6388	+	37.3066i	1.41777	+	1.67175i
$499$	2.92484	−	0.783708i	0.130934	−	0.0350836i	−0.192757	−	0.981247i	$-0.561743\pi$
$499$	2.92484	−	0.783708i	0.130934	−	0.0350836i	0.323691	+	0.946163i	$0.395076\pi$
$500$	8.31258	+	3.77061i	0.371750	+	0.168627i
$501$	−4.16846	+	15.5569i	−0.186233	+	0.695031i
$502$	11.7052	−	16.9047i	0.522428	−	0.754493i
$503$		−	34.5673i		−	1.54128i	−0.637272	−	0.770639i	$-0.719937\pi$
$503$		−	34.5673i		−	1.54128i	0.637272	−	0.770639i	$-0.280063\pi$
$504$		0			0
$505$			2.58688i			0.115115i
$506$	4.43209	+	3.06888i	0.197030	+	0.136428i
$507$	−19.4692	+	72.6599i	−0.864656	+	3.22694i
$508$	−6.57775	−	17.4991i	−0.291840	−	0.776396i
$509$	15.2307	−	4.08105i	0.675088	−	0.180889i	0.0950424	−	0.995473i	$-0.469701\pi$
$509$	15.2307	−	4.08105i	0.675088	−	0.180889i	0.580046	+	0.814584i	$0.303035\pi$
$510$	−7.36179	+	6.24334i	−0.325985	+	0.276460i
$511$		0			0
$512$	−22.6022	+	1.06733i	−0.998887	+	0.0471698i
$513$	−3.54187	+	6.13470i	−0.156377	+	0.270854i
$514$	−1.19898	+	3.34869i	−0.0528846	+	0.147704i
$515$	0.133591	−	0.498567i	0.00588671	−	0.0219695i
$516$	−30.8932	+	37.6111i	−1.36000	+	1.65574i
$517$	−4.22957	+	4.22957i	−0.186016	+	0.186016i
$518$		0			0
$519$	24.8623			1.09133
$520$	8.42675	−	0.132556i	0.369537	−	0.00581297i
$521$	7.72095	+	13.3731i	0.338261	+	0.585885i	0.984106	−	0.177584i	$-0.0568281\pi$
$521$	7.72095	+	13.3731i	0.338261	+	0.585885i	−0.645845	+	0.763469i	$0.723495\pi$
$522$	4.15765	+	8.79542i	0.181976	+	0.384965i
$523$	−1.96968	+	0.527773i	−0.0861280	+	0.0230779i	−0.301626	−	0.953426i	$-0.597529\pi$
$523$	−1.96968	+	0.527773i	−0.0861280	+	0.0230779i	0.215498	+	0.976504i	$0.430863\pi$
$524$	21.6001	+	30.1698i	0.943604	+	1.31797i
$525$		0			0
$526$	−9.81025	+	8.31981i	−0.427747	+	0.362761i
$527$	4.06352	+	2.34607i	0.177010	+	0.102197i
$528$	−21.2810	+	4.21439i	−0.926139	+	0.183408i
$529$	9.69026	+	16.7840i	0.421316	+	0.729740i
$530$	−0.828072	−	4.55640i	−0.0359692	−	0.197918i
$531$	26.2714	−	26.2714i	1.14008	−	1.14008i
$532$		0			0
$533$	−14.6423	−	14.6423i	−0.634228	−	0.634228i
$534$	−7.32450	−	5.07165i	−0.316962	−	0.219472i
$535$	−2.49805	+	1.44225i	−0.108000	+	0.0623538i
$536$	−10.8489	+	3.09064i	−0.468601	+	0.133495i
$537$	−5.14933	+	8.91890i	−0.222210	+	0.384879i
$538$	8.03506	+	0.660545i	0.346416	+	0.0284781i
$539$		0			0
$540$	−0.547403	+	3.30688i	−0.0235565	+	0.142306i
$541$	5.40772	+	20.1819i	0.232496	+	0.867686i	0.979262	+	0.202599i	$0.0649389\pi$
$541$	5.40772	+	20.1819i	0.232496	+	0.867686i	−0.746766	+	0.665087i	$0.768394\pi$
$542$	−15.3384	−	5.49183i	−0.658841	−	0.235894i
$543$	−17.0216	+	9.82741i	−0.730466	+	0.421735i
$544$	−30.2383	−	4.51805i	−1.29646	−	0.193710i
$545$			5.08293i			0.217729i
$546$		0			0
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	0.928945	−	0.370217i	$-0.120717\pi$
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	−0.370217	+	0.928945i	$0.620717\pi$
$548$	−19.2816	+	23.4744i	−0.823668	+	1.00278i
$549$	−2.03245	−	0.544592i	−0.0867427	−	0.0232426i
$550$	5.79127	+	12.2513i	0.246941	+	0.522397i
$551$	−2.71498	−	1.56749i	−0.115662	−	0.0667775i
$552$	14.1270	+	3.54814i	0.601285	+	0.151019i
$553$		0			0
$554$	−29.4505	−	2.42106i	−1.25123	−	0.102861i
$555$	2.67572	+	9.98591i	0.113578	+	0.423878i
$556$	2.91359	+	1.32161i	0.123564	+	0.0560489i
$557$	−11.6914	−	3.13271i	−0.495381	−	0.132737i	0.00247440	−	0.999997i	$-0.499212\pi$
$557$	−11.6914	−	3.13271i	−0.495381	−	0.132737i	−0.497856	+	0.867260i	$0.665879\pi$
$558$	5.22697	−	0.949939i	0.221275	−	0.0402141i
$559$	57.4198			2.42860
$560$		0			0
$561$	−29.3132			−1.23760
$562$	−27.6002	+	5.01600i	−1.16424	+	0.211587i
$563$	−27.2040	−	7.28930i	−1.14651	−	0.307207i	−0.364946	−	0.931029i	$-0.618913\pi$
$563$	−27.2040	−	7.28930i	−1.14651	−	0.307207i	−0.781567	+	0.623821i	$0.785579\pi$
$564$	−6.67626	+	14.7183i	−0.281121	+	0.619751i
$565$	0.340362	+	1.27025i	0.0143192	+	0.0534398i
$566$	28.6773	+	2.35750i	1.20540	+	0.0990932i
$567$		0			0
$568$	−17.7091	−	29.5883i	−0.743056	−	1.24150i
$569$	−20.4277	−	11.7940i	−0.856375	−	0.494428i	0.00642167	−	0.999979i	$-0.497956\pi$
$569$	−20.4277	−	11.7940i	−0.856375	−	0.494428i	−0.862797	+	0.505551i	$0.831289\pi$
$570$	−1.50511	−	3.18403i	−0.0630421	−	0.133364i
$571$	21.7673	+	5.83253i	0.910933	+	0.244084i	0.683705	−	0.729758i	$-0.260367\pi$
$571$	21.7673	+	5.83253i	0.910933	+	0.244084i	0.227227	+	0.973842i	$0.427034\pi$
$572$	19.7770	+	16.2446i	0.826919	+	0.679220i
$573$	−33.6826	−	33.6826i	−1.40711	−	1.40711i
$574$		0			0
$575$		−	9.09835i		−	0.379427i
$576$	−29.4197	+	18.2427i	−1.22582	+	0.760114i
$577$	16.2893	−	9.40463i	0.678132	−	0.391520i	−0.121019	−	0.992650i	$-0.538616\pi$
$577$	16.2893	−	9.40463i	0.678132	−	0.391520i	0.799151	+	0.601130i	$0.205283\pi$
$578$	−16.2588	−	5.82138i	−0.676279	−	0.242137i
$579$	4.60942	+	17.2026i	0.191561	+	0.714915i
$580$	−1.46350	−	0.242259i	−0.0607684	−	0.0100593i
$581$		0			0
$582$	−17.9202	−	1.47318i	−0.742816	−	0.0610653i
$583$	7.03171	−	12.1793i	0.291224	−	0.504414i
$584$	−21.4335	+	38.5103i	−0.886924	+	1.59357i
$585$	11.1659	−	6.44666i	0.461655	−	0.266537i
$586$	−11.1074	−	7.69099i	−0.458841	−	0.317712i
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	0.396999	−	0.917819i	$-0.370052\pi$
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	−0.917819	+	0.396999i	$0.870052\pi$
$588$		0			0
$589$	−1.21053	+	1.21053i	−0.0498791	+	0.0498791i
$590$	1.01298	+	5.57384i	0.0417037	+	0.229471i
$591$	28.4763	+	49.3223i	1.17136	+	2.02885i
$592$	−18.2152	+	27.2111i	−0.748638	+	1.11837i
$593$	22.0260	+	12.7167i	0.904498	+	0.522212i	0.878657	−	0.477454i	$-0.158440\pi$
$593$	22.0260	+	12.7167i	0.904498	+	0.522212i	0.0258409	+	0.999666i	$0.491774\pi$
$594$	−7.76310	+	6.58368i	−0.318524	+	0.270132i
$595$		0			0
$596$	16.5220	−	11.8290i	0.676769	−	0.484533i
$597$	−19.4226	+	5.20427i	−0.794914	+	0.212997i
$598$	−7.34364	−	15.5353i	−0.300304	−	0.635286i
$599$	21.1003	+	36.5468i	0.862135	+	1.49326i	0.869864	+	0.493292i	$0.164207\pi$
$599$	21.1003	+	36.5468i	0.862135	+	1.49326i	−0.00772853	+	0.999970i	$0.502460\pi$
$600$	26.2942	+	25.4798i	1.07346	+	1.04021i
$601$	29.8695			1.21840			0.609202	−	0.793015i	$-0.291490\pi$
$601$	29.8695			1.21840			0.609202	+	0.793015i	$0.291490\pi$
$602$		0			0
$603$	−12.2030	+	12.2030i	−0.496944	+	0.496944i
$604$	18.0482	+	14.8245i	0.734369	+	0.603200i
$605$	−0.843492	+	3.14796i	−0.0342928	+	0.127983i
$606$	−7.15498	+	19.9835i	−0.290651	+	0.811775i
$607$	−14.7137	+	25.4850i	−0.597212	+	1.03440i	0.396018	+	0.918243i	$0.370392\pi$
$607$	−14.7137	+	25.4850i	−0.597212	+	1.03440i	−0.993231	+	0.116160i	$0.962942\pi$
$608$	4.44771	−	10.2300i	0.180378	−	0.414882i
$609$		0			0
$610$	0.244692	−	0.207517i	0.00990730	−	0.00840212i
$611$	18.4166	−	4.93472i	0.745058	−	0.199638i
$612$	−43.7828	+	16.4576i	−1.76982	+	0.665258i
$613$	5.94532	−	22.1882i	0.240129	−	0.896175i	−0.735640	−	0.677373i	$-0.763118\pi$
$613$	5.94532	−	22.1882i	0.240129	−	0.896175i	0.975769	−	0.218802i	$-0.0702149\pi$
$614$	3.89584	+	2.69756i	0.157223	+	0.108865i
$615$			4.09456i			0.165108i
$616$		0			0
$617$			31.2064i			1.25632i	0.778084	+	0.628161i	$0.216192\pi$
$617$			31.2064i			1.25632i	−0.778084	+	0.628161i	$0.783808\pi$
$618$	2.41095	−	3.48191i	0.0969828	−	0.140063i
$619$	4.74503	−	17.7087i	0.190719	−	0.711772i	−0.802615	−	0.596498i	$-0.796559\pi$
$619$	4.74503	−	17.7087i	0.190719	−	0.711772i	0.993334	−	0.115275i	$-0.0367748\pi$
$620$	−0.334630	+	0.737714i	−0.0134390	+	0.0296273i
$621$	6.60135	−	1.76883i	0.264903	−	0.0709805i
$622$	−13.8616	−	16.3448i	−0.555799	−	0.655366i
$623$		0			0
$624$	65.4628	+	22.2833i	2.62061	+	0.892046i
$625$	10.8912	−	18.8641i	0.435648	−	0.754565i
$626$	−8.86185	−	3.17293i	−0.354191	−	0.126816i
$627$	2.76808	−	10.3306i	0.110547	−	0.412565i
$628$	−0.434728	−	4.43305i	−0.0173475	−	0.176898i
$629$	−31.2858	+	31.2858i	−1.24745	+	1.24745i
$630$		0			0
$631$	8.10970			0.322842			0.161421	−	0.986886i	$-0.448392\pi$
$631$	8.10970			0.322842			0.161421	+	0.986886i	$0.448392\pi$
$632$	−0.0550316	−	3.49842i	−0.00218904	−	0.139160i
$633$	−17.4508	−	30.2257i	−0.693608	−	1.20136i
$634$	33.8998	−	16.0247i	1.34633	−	0.636421i
$635$	4.21231	−	1.12869i	0.167160	−	0.0447905i
$636$	6.20561	−	37.4883i	0.246068	−	1.48651i
$637$		0			0
$638$	−2.91368	−	3.43564i	−0.115354	−	0.136018i
$639$	−45.6864	−	26.3770i	−1.80732	−	1.04346i
$640$	0.266787	−	5.27160i	0.0105457	−	0.208378i
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	−0.997928	−	0.0643416i	$-0.979505\pi$
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	0.443242	−	0.896402i	$-0.353828\pi$
$642$	−23.2864	+	4.23202i	−0.919040	+	0.167024i
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	−0.990721	−	0.135909i	$-0.956605\pi$
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	0.135909	+	0.990721i	$0.456605\pi$
$644$		0			0
$645$	−8.02841	−	8.02841i	−0.316118	−	0.316118i
$646$	8.58043	−	12.3919i	0.337593	−	0.487553i
$647$	39.8543	−	23.0099i	1.56683	−	0.904612i	0.570299	−	0.821437i	$-0.306827\pi$
$647$	39.8543	−	23.0099i	1.56683	−	0.904612i	0.996535	−	0.0831749i	$-0.0265060\pi$
$648$	4.48081	−	8.05083i	0.176023	−	0.316267i
$649$	−8.60188	+	14.8989i	−0.337653	+	0.584833i
$650$	3.53901	−	43.0495i	0.138811	−	1.68854i
$651$		0			0
$652$	23.8627	−	17.0845i	0.934536	−	0.669082i
$653$	7.84001	+	29.2593i	0.306803	+	1.14501i	0.931382	+	0.364043i	$0.118604\pi$
$653$	7.84001	+	29.2593i	0.306803	+	1.14501i	−0.624579	+	0.780962i	$0.714729\pi$
$654$	−14.0587	+	39.2654i	−0.549740	+	1.53540i
$655$	−7.49594	+	4.32778i	−0.292890	+	0.169100i
$656$	−9.75787	+	8.54285i	−0.380981	+	0.333542i
$657$			67.4255i			2.63052i
$658$		0			0
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	0.546096	−	0.837723i	$-0.316113\pi$
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	−0.837723	+	0.546096i	$0.816113\pi$
$660$	−0.493907	−	5.03652i	−0.0192253	−	0.196046i
$661$	−10.2052	−	2.73446i	−0.396934	−	0.106358i	0.0548296	−	0.998496i	$-0.482538\pi$
$661$	−10.2052	−	2.73446i	−0.396934	−	0.106358i	−0.451764	+	0.892137i	$0.649205\pi$
$662$	12.1291	−	5.73352i	0.471412	−	0.222840i
$663$	80.9187	+	46.7184i	3.14262	+	1.81439i
$664$	−35.0537	−	8.80409i	−1.36035	−	0.341665i
$665$		0			0
$666$	−4.10438	+	49.9268i	−0.159041	+	1.93462i
$667$	0.782813	+	2.92150i	0.0303106	+	0.113121i
$668$	−4.18704	−	11.1390i	−0.162001	−	0.430979i
$669$	17.5945	+	4.71443i	0.680242	+	0.182270i
$670$	−0.470525	−	2.58903i	−0.0181780	−	0.100023i
$671$	0.974316			0.0376130
$672$		0			0
$673$	17.2027			0.663115			0.331557	−	0.943435i	$-0.392426\pi$
$673$	17.2027			0.663115			0.331557	+	0.943435i	$0.392426\pi$
$674$	4.05493	+	22.3120i	0.156190	+	0.859425i
$675$	16.5940	+	4.44634i	0.638702	+	0.171140i
$676$	−19.5560	−	52.0255i	−0.752152	−	2.00098i
$677$	−5.18323	−	19.3441i	−0.199208	−	0.743453i	−0.991137	−	0.132841i	$-0.957590\pi$
$677$	−5.18323	−	19.3441i	−0.199208	−	0.743453i	0.791930	−	0.610612i	$-0.209077\pi$
$678$	−0.884065	+	10.7540i	−0.0339523	+	0.413006i
$679$		0			0
$680$	1.73733	−	6.91721i	0.0666235	−	0.265263i
$681$	18.1168	+	10.4598i	0.694238	+	0.400819i
$682$	−2.22401	+	1.05131i	−0.0851618	+	0.0402566i
$683$	−0.930638	−	0.249364i	−0.0356099	−	0.00954164i	0.240970	−	0.970533i	$-0.422534\pi$
$683$	−0.930638	−	0.249364i	−0.0356099	−	0.00954164i	−0.276580	+	0.960991i	$0.589201\pi$
$684$	−1.66555	−	16.9842i	−0.0636840	−	0.649406i
$685$	−5.01082	−	5.01082i	−0.191453	−	0.191453i
$686$		0			0
$687$			41.2597i			1.57416i
$688$	2.38234	−	35.8832i	0.0908259	−	1.36803i
$689$	−38.8219	+	22.4138i	−1.47900	+	0.853899i
$690$	−1.14536	+	3.19893i	−0.0436029	+	0.121781i
$691$	8.97758	+	33.5048i	0.341523	+	1.27458i	0.896622	+	0.442797i	$0.146014\pi$
$691$	8.97758	+	33.5048i	0.341523	+	1.27458i	−0.555099	+	0.831784i	$0.687320\pi$
$692$	−14.9364	+	10.6937i	−0.567795	+	0.406513i
$693$		0			0
$694$	−0.367829	+	4.47437i	−0.0139626	+	0.169845i
$695$	−0.373156	+	0.646326i	−0.0141546	+	0.0245165i
$696$	−10.6354	−	5.91929i	−0.403133	−	0.224370i
$697$	−15.1759	+	8.76183i	−0.574829	+	0.331878i
$698$	2.52015	−	3.63961i	0.0953891	−	0.137761i
$699$	28.2796	+	28.2796i	1.06963	+	1.06963i
$700$		0			0
$701$	32.4969	−	32.4969i	1.22739	−	1.22739i	0.262444	−	0.964947i	$-0.415471\pi$
$701$	32.4969	−	32.4969i	1.22739	−	1.22739i	0.964947	−	0.262444i	$-0.0845286\pi$
$702$	31.9228	−	5.80159i	1.20485	−	0.218967i
$703$	−8.07146	−	13.9802i	−0.304421	−	0.527272i
$704$	10.9722	−	11.6852i	0.413531	−	0.440403i
$705$	−3.26498	−	1.88504i	−0.122966	−	0.0709945i
$706$	−7.51780	−	8.86456i	−0.282936	−	0.333622i
$707$		0			0
$708$	−7.59131	+	45.8594i	−0.285299	+	1.72350i
$709$	4.54454	−	1.21770i	0.170674	−	0.0457319i	−0.172470	−	0.985015i	$-0.555175\pi$
$709$	4.54454	−	1.21770i	0.170674	−	0.0457319i	0.343144	+	0.939283i	$0.388508\pi$
$710$	7.27234	−	3.43768i	0.272926	−	0.129014i
$711$	−2.67638	−	4.63562i	−0.100372	−	0.173849i
$712$	6.58171	−	0.103533i	0.246660	−	0.00388006i
$713$	1.65165			0.0618547
$714$		0			0
$715$	−4.22157	+	4.22157i	−0.157878	+	0.157878i
$716$	−0.742644	−	7.57297i	−0.0277539	−	0.283015i
$717$	20.0009	−	74.6444i	0.746947	−	2.78765i
$718$	−40.8270	−	14.6179i	−1.52365	−	0.545534i
$719$	−9.27548	+	16.0656i	−0.345917	+	0.599146i	−0.985520	−	0.169559i	$-0.945766\pi$
$719$	−9.27548	+	16.0656i	−0.345917	+	0.599146i	0.639603	+	0.768706i	$0.279099\pi$
$720$	−3.56542	−	7.24537i	−0.132875	−	0.270019i
$721$		0			0
$722$	−13.8225	−	16.2987i	−0.514420	−	0.606575i
$723$	−60.0174	+	16.0816i	−2.23207	+	0.598081i
$724$	5.99901	−	13.2252i	0.222952	−	0.491512i
$725$	−1.96778	+	7.34384i	−0.0730813	+	0.272743i
$726$	−15.2228	+	21.9848i	−0.564970	+	0.815933i
$727$		−	5.96613i		−	0.221272i	−0.993861	−	0.110636i	$-0.964711\pi$
$727$		−	5.96613i		−	0.221272i	0.993861	−	0.110636i	$-0.0352887\pi$
$728$		0			0
$729$		−	43.2669i		−	1.60248i
$730$	−8.45252	−	5.85272i	−0.312842	−	0.216619i
$731$	12.5765	−	46.9360i	0.465157	−	1.73599i
$732$	2.46420	−	0.926272i	0.0910795	−	0.0342360i
$733$	−20.8755	+	5.59358i	−0.771055	+	0.206604i	−0.622838	−	0.782351i	$-0.714020\pi$
$733$	−20.8755	+	5.59358i	−0.771055	+	0.206604i	−0.148218	+	0.988955i	$0.547354\pi$
$734$	−19.2237	+	16.3031i	−0.709561	+	0.601760i
$735$		0			0
$736$	−10.0131	+	3.94468i	−0.369089	+	0.145403i
$737$	3.99554	−	6.92048i	0.147178	−	0.254919i
$738$	−6.68811	+	18.6796i	−0.246193	+	0.687605i
$739$	−9.37297	+	34.9804i	−0.344790	+	1.28677i	0.548067	+	0.836434i	$0.315364\pi$
$739$	−9.37297	+	34.9804i	−0.344790	+	1.28677i	−0.892857	+	0.450340i	$0.851303\pi$
$740$	−5.90260	−	4.84831i	−0.216984	−	0.178227i
$741$	−24.1059	+	24.1059i	−0.885552	+	0.885552i
$742$		0			0
$743$	16.2749			0.597067			0.298533	−	0.954399i	$-0.403503\pi$
$743$	16.2749			0.597067			0.298533	+	0.954399i	$0.403503\pi$
$744$	−4.62542	+	4.77326i	−0.169576	+	0.174996i
$745$	2.37004	+	4.10504i	0.0868317	+	0.150397i
$746$	−1.50131	−	3.17598i	−0.0549668	−	0.116281i
$747$	−53.4087	+	14.3108i	−1.95412	+	0.523605i
$748$	17.6103	−	12.6081i	0.643897	−	0.460998i
$749$		0			0
$750$	−13.3245	+	11.3001i	−0.486540	+	0.412622i
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	0.760504	−	0.649334i	$-0.224952\pi$
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	−0.182087	+	0.983282i	$0.558285\pi$
$752$	−2.31974	−	11.7138i	−0.0845921	−	0.427158i
$753$	19.6778	+	34.0830i	0.717101	+	1.24205i
$754$	2.56755	+	14.1278i	0.0935048	+	0.514503i
$755$	−3.85253	+	3.85253i	−0.140208	+	0.140208i
$756$		0			0
$757$	−16.6944	−	16.6944i	−0.606767	−	0.606767i	0.335333	−	0.942100i	$-0.391151\pi$
$757$	−16.6944	−	16.6944i	−0.606767	−	0.606767i	−0.942100	+	0.335333i	$0.891151\pi$
$758$	0.865015	+	0.598956i	0.0314188	+	0.0217551i
$759$	−8.93593	+	5.15916i	−0.324354	+	0.187266i
$760$	2.27372	+	1.26548i	0.0824766	+	0.0459036i
$761$	4.43390	−	7.67974i	0.160729	−	0.278390i	−0.774401	−	0.632695i	$-0.781949\pi$
$761$	4.43390	−	7.67974i	0.160729	−	0.278390i	0.935130	+	0.354304i	$0.115282\pi$
$762$	35.6617	+	2.93167i	1.29189	+	0.106203i
$763$		0			0
$764$	34.7228	+	5.74781i	1.25623	+	0.207949i
$765$	−2.82398	−	10.5392i	−0.102101	−	0.381047i
$766$	31.6691	+	11.3389i	1.14425	+	0.409692i
$767$	47.4908	−	27.4188i	1.71479	−	0.990036i
$768$	16.6415	−	39.9849i	0.600498	−	1.44283i
$769$		−	1.14344i		−	0.0412335i	−0.999787	−	0.0206167i	$-0.993437\pi$
$769$		−	1.14344i		−	0.0412335i	0.999787	−	0.0206167i	$-0.00656298\pi$
$770$		0			0
$771$	−4.81396	−	4.81396i	−0.173370	−	0.173370i
$772$	−10.1683	−	8.35210i	−0.365966	−	0.300599i
$773$	5.25103	+	1.40701i	0.188866	+	0.0506066i	0.352012	−	0.935995i	$-0.385497\pi$
$773$	5.25103	+	1.40701i	0.188866	+	0.0506066i	−0.163146	+	0.986602i	$0.552164\pi$
$774$	−23.5123	−	49.7397i	−0.845132	−	1.78786i
$775$	3.59555	+	2.07589i	0.129156	+	0.0745683i
$776$	11.3995	−	6.82276i	0.409217	−	0.244923i
$777$		0			0
$778$	−34.1725	−	2.80925i	−1.22514	−	0.100716i
$779$	−1.65478	−	6.17573i	−0.0592888	−	0.221269i
$780$	−6.66363	+	14.6904i	−0.238596	+	0.526002i
$781$	23.5952	+	6.32232i	0.844304	+	0.226231i
$782$	−14.3073	+	2.60018i	−0.511628	+	0.0929823i
$783$	−5.71091			−0.204091
$784$		0			0
$785$	1.03907			0.0370859
$786$	−69.8758	+	12.6991i	−2.49239	+	0.452962i
$787$	49.2659	+	13.2008i	1.75614	+	0.470556i	0.985919	−	0.167221i	$-0.0534795\pi$
$787$	49.2659	+	13.2008i	1.75614	+	0.470556i	0.770220	+	0.637778i	$0.220146\pi$
$788$	−38.3220	−	17.3830i	−1.36516	−	0.619242i
$789$	−6.37227	−	23.7816i	−0.226859	−	0.846648i
$790$	0.813442	+	0.0668713i	0.0289410	+	0.00237917i
$791$		0			0
$792$	5.97350	−	23.7836i	0.212259	−	0.845115i
$793$	−2.68959	−	1.55283i	−0.0955101	−	0.0551428i
$794$	2.55074	+	5.39604i	0.0905224	+	0.191498i
$795$	8.56196	+	2.29417i	0.303661	+	0.0813658i
$796$	9.42996	−	11.4806i	0.334236	−	0.406917i
$797$	26.5433	+	26.5433i	0.940211	+	0.940211i	0.998311	−	0.0581002i	$-0.0185043\pi$
$797$	26.5433	+	26.5433i	0.940211	+	0.940211i	−0.0581002	+	0.998311i	$0.518504\pi$
$798$		0			0
$799$		−	16.1349i		−	0.570813i
$800$	−26.7560	−	3.99774i	−0.945966	−	0.141342i
$801$	8.72116	−	5.03516i	0.308147	−	0.177909i
$802$	23.9970	+	8.59196i	0.847362	+	0.303393i
$803$	−8.08063	−	30.1573i	−0.285159	−	1.06423i
$804$	3.52613	−	21.3015i	0.124357	−	0.751247i
$805$		0			0
$806$	7.81490	+	0.642446i	0.275268	+	0.0226292i
$807$	−7.71565	+	13.3639i	−0.271604	+	0.470432i
$808$	−4.29681	−	15.0829i	−0.151161	−	0.530614i
$809$	−17.6346	+	10.1813i	−0.620000	+	0.357957i	−0.776869	−	0.629662i	$-0.783193\pi$
$809$	−17.6346	+	10.1813i	−0.620000	+	0.357957i	0.156869	+	0.987619i	$0.449860\pi$
$810$	1.76706	+	1.22355i	0.0620880	+	0.0429911i
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.991752	+	0.128171i	$0.0409107\pi$
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.128171	+	0.991752i	$0.459089\pi$
$812$		0			0
$813$	22.0500	−	22.0500i	0.773327	−	0.773327i
$814$	−4.14773	−	22.8226i	−0.145378	−	0.799931i
$815$	3.42304	+	5.92889i	0.119904	+	0.207680i
$816$	32.5529	−	48.6299i	1.13958	−	1.70239i
$817$	15.3537	+	8.86446i	0.537158	+	0.310128i
$818$	−30.1660	+	25.5830i	−1.05473	+	0.894490i
$819$		0			0
$820$	−1.76114	−	2.45986i	−0.0615018	−	0.0859022i
$821$	23.6777	−	6.34443i	0.826359	−	0.221422i	0.179234	−	0.983806i	$-0.442638\pi$
$821$	23.6777	−	6.34443i	0.826359	−	0.221422i	0.647125	+	0.762384i	$0.275971\pi$
$822$	−24.8490	−	52.5676i	−0.866710	−	1.83351i
$823$	−5.16976	−	8.95429i	−0.180207	−	0.312127i	0.761744	−	0.647878i	$-0.224343\pi$
$823$	−5.16976	−	8.95429i	−0.180207	−	0.312127i	−0.941951	+	0.335751i	$0.891010\pi$
$824$	0.0492174	+	3.12880i	0.00171457	+	0.108997i
$825$	−25.9374			−0.903024
$826$		0			0
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.161581	−	0.986859i	$-0.448341\pi$
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.986859	−	0.161581i	$-0.0516594\pi$
$828$	−10.4503	+	12.7228i	−0.363174	+	0.442149i
$829$	−9.70111	+	36.2050i	−0.336934	+	1.25745i	0.564824	+	0.825211i	$0.308944\pi$
$829$	−9.70111	+	36.2050i	−0.336934	+	1.25745i	−0.901758	+	0.432242i	$0.857723\pi$
$830$	2.84200	−	7.93757i	0.0986472	−	0.275517i
$831$	28.2798	−	48.9821i	0.981015	−	1.69917i
$832$	−48.9122	+	14.7697i	−1.69573	+	0.512048i
$833$		0			0
$834$	−4.67027	+	3.96073i	−0.161718	+	0.137149i
$835$	2.68133	−	0.718460i	0.0927912	−	0.0248633i
$836$	2.78042	+	7.39687i	0.0961629	+	0.255826i
$837$	−0.807156	+	3.01235i	−0.0278994	+	0.104122i
$838$	−17.2107	−	11.9171i	−0.594534	−	0.411668i
$839$			41.5802i			1.43551i	0.696296	+	0.717754i	$0.254830\pi$
$839$			41.5802i			1.43551i	−0.696296	+	0.717754i	$0.745170\pi$
$840$		0			0
$841$			26.4726i			0.912847i
$842$	14.0863	−	20.3436i	0.485447	−	0.701085i
$843$	13.8968	−	51.8636i	0.478632	−	1.78628i
$844$	23.4844	+	10.6526i	0.808368	+	0.366678i
$845$	12.5234	−	3.35563i	0.430818	−	0.115437i
$846$	−11.8159	−	13.9327i	−0.406241	−	0.479016i
$847$		0			0
$848$	12.3963	+	25.1908i	0.425691	+	0.865056i
$849$	−27.5374	+	47.6961i	−0.945080	+	1.63693i
$850$	−34.4143	−	12.3218i	−1.18040	−	0.422636i
$851$	−4.03092	+	15.0436i	−0.138178	+	0.515688i
$852$	65.6867	−	6.44157i	2.25039	−	0.220685i
$853$	3.78632	−	3.78632i	0.129641	−	0.129641i	−0.639309	−	0.768950i	$-0.720779\pi$
$853$	3.78632	−	3.78632i	0.129641	−	0.129641i	0.768950	+	0.639309i	$0.220779\pi$
$854$		0			0
$855$	3.98094			0.136145
$856$	12.1694	−	12.5583i	0.415940	−	0.429235i
$857$	9.93943	+	17.2156i	0.339524	+	0.588073i	0.984343	−	0.176262i	$-0.0564006\pi$
$857$	9.93943	+	17.2156i	0.339524	+	0.588073i	−0.644819	+	0.764335i	$0.723067\pi$
$858$	−44.2878	+	20.9351i	−1.51196	+	0.714713i
$859$	12.3699	−	3.31449i	0.422054	−	0.113089i	−0.0415399	−	0.999137i	$-0.513226\pi$
$859$	12.3699	−	3.31449i	0.422054	−	0.113089i	0.463594	+	0.886048i	$0.346560\pi$
$860$	8.27634	+	1.37002i	0.282221	+	0.0467173i
$861$		0			0
$862$	12.4727	+	14.7071i	0.424821	+	0.500925i
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	0.812778	−	0.582574i	$-0.197954\pi$
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	−0.0981346	+	0.995173i	$0.531288\pi$
$864$	−2.30109	−	20.1901i	−0.0782848	−	0.686882i
$865$	−2.14258	−	3.71106i	−0.0728500	−	0.126180i
$866$	−26.6561	+	4.84443i	−0.905812	+	0.164620i
$867$	23.3732	−	23.3732i	0.793794	−	0.793794i
$868$		0			0
$869$	1.75262	+	1.75262i	0.0594534	+	0.0594534i
$870$	1.61634	−	2.33433i	0.0547992	−	0.0791413i
$871$	−22.0593	+	12.7359i	−0.747450	+	0.431541i
$872$	−8.44275	−	29.6361i	−0.285908	−	1.00361i
$873$	10.1623	−	17.6016i	0.343941	−	0.595723i
$874$	0.434695	−	5.28776i	0.0147038	−	0.178861i
$875$		0			0
$876$	−49.1075	−	68.5905i	−1.65919	−	2.31746i
$877$	−5.60738	−	20.9270i	−0.189348	−	0.706656i	−0.993658	−	0.112446i	$-0.964132\pi$
$877$	−5.60738	−	20.9270i	−0.189348	−	0.706656i	0.804310	−	0.594210i	$-0.202535\pi$
$878$	−4.08657	+	11.4136i	−0.137915	+	0.385190i
$879$	22.3946	−	12.9295i	0.755349	−	0.436101i
$880$	2.46302	+	2.81333i	0.0830284	+	0.0948372i
$881$		−	15.3375i		−	0.516733i	−0.966047	−	0.258367i	$-0.916816\pi$
$881$		−	15.3375i		−	0.516733i	0.966047	−	0.258367i	$-0.0831842\pi$
$882$		0			0
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.973124	+	0.230282i	$0.0739648\pi$
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.230282	+	0.973124i	$0.426035\pi$
$884$	−68.7075	+	6.73781i	−2.31088	+	0.226617i
$885$	−10.4738	−	2.80645i	−0.352074	−	0.0943378i
$886$	−26.7790	+	12.6586i	−0.899660	+	0.425275i
$887$	−28.0000	−	16.1658i	−0.940148	−	0.542795i	−0.0501414	−	0.998742i	$-0.515967\pi$
$887$	−28.0000	−	16.1658i	−0.940148	−	0.542795i	−0.890007	+	0.455947i	$0.849301\pi$
$888$	−32.1875	−	53.7788i	−1.08014	−	1.80470i
$889$		0			0
$890$	−0.125807	+	1.53036i	−0.00421707	+	0.0512977i
$891$	1.68931	+	6.30459i	0.0565940	+	0.211212i
$892$	−12.5979	+	4.73544i	−0.421809	+	0.158554i
$893$	5.68632	+	1.52364i	0.190285	+	0.0509868i
$894$	6.95447	+	38.2664i	0.232592	+	1.27982i
$895$	1.77504			0.0593330
$896$		0			0
$897$	32.8900			1.09817
$898$	6.17696	+	33.9883i	0.206128	+	1.13420i
$899$	−1.33315	−	0.357216i	−0.0444629	−	0.0119138i
$900$	−38.7407	+	14.5623i	−1.29136	+	0.485410i
$901$	9.81846	+	36.6430i	0.327100	+	1.22075i
$902$	0.752722	−	9.15633i	0.0250629	−	0.304872i
$903$		0			0
$904$	−4.09438	−	6.84088i	−0.136177	−	0.227524i
$905$	2.93378	+	1.69382i	0.0975220	+	0.0563044i
$906$	−40.4162	+	19.1050i	−1.34274	+	0.634721i
$907$	−30.5807	−	8.19408i	−1.01542	−	0.272080i	−0.287525	−	0.957773i	$-0.592832\pi$
$907$	−30.5807	−	8.19408i	−1.01542	−	0.272080i	−0.727891	+	0.685693i	$0.759499\pi$
$908$	−15.3829	+	1.50852i	−0.510499	+	0.0500621i
$909$	−16.9654	−	16.9654i	−0.562707	−	0.562707i
$910$		0			0
$911$			7.17911i			0.237854i	0.992903	+	0.118927i	$0.0379455\pi$
$911$			7.17911i			0.237854i	−0.992903	+	0.118927i	$0.962054\pi$
$912$	14.0643	+	16.0646i	0.465714	+	0.531951i
$913$	22.1729	−	12.8015i	0.733817	−	0.423669i
$914$	1.72176	−	4.80878i	0.0569506	−	0.159060i
$915$	0.158940	+	0.593173i	0.00525441	+	0.0196097i
$916$	−17.7465	−	24.7874i	−0.586362	−	0.818998i
$917$		0			0
$918$	2.24962	−	27.3650i	0.0742484	−	0.903179i
$919$	−1.18242	+	2.04801i	−0.0390044	+	0.0675576i	−0.884869	−	0.465841i	$-0.845752\pi$
$919$	−1.18242	+	2.04801i	−0.0390044	+	0.0675576i	0.845864	+	0.533398i	$0.179085\pi$
$920$	−0.687826	−	2.41444i	−0.0226770	−	0.0796017i
$921$	−7.85475	+	4.53494i	−0.258823	+	0.149431i
$922$	28.7907	−	41.5796i	0.948170	−	1.36935i
$923$	−55.0580	−	55.0580i	−1.81226	−	1.81226i
$924$		0			0
$925$	−27.6828	+	27.6828i	−0.910206	+	0.910206i
$926$	11.1476	−	2.02594i	0.366332	−	0.0665765i
$927$	2.39361	+	4.14585i	0.0786164	+	0.136168i
$928$	8.93535	−	1.01837i	0.293317	−	0.0334298i
$929$	50.6476	+	29.2414i	1.66169	+	0.959379i	0.971906	+	0.235367i	$0.0756294\pi$
$929$	50.6476	+	29.2414i	1.66169	+	0.959379i	0.689787	+	0.724012i	$0.257704\pi$
$930$	−1.00285	−	1.18250i	−0.0328847	−	0.0387758i
$931$		0			0
$932$	−29.1529	−	4.82581i	−0.954936	−	0.158075i
$933$	39.6224	−	10.6168i	1.29718	−	0.347578i
$934$	23.6938	−	11.2002i	0.775285	−	0.366482i
$935$	2.52615	+	4.37543i	0.0826141	+	0.143092i
$936$	−54.3954	+	56.1341i	−1.77797	+	1.83480i
$937$	13.4613			0.439761			0.219881	−	0.975527i	$-0.429433\pi$
$937$	13.4613			0.439761			0.219881	+	0.975527i	$0.429433\pi$
$938$		0			0
$939$	12.7395	−	12.7395i	0.415738	−	0.415738i
$940$	2.77227	−	0.271863i	0.0904215	−	0.00886719i
$941$	3.99761	−	14.9193i	0.130318	−	0.486355i	−0.869655	−	0.493660i	$-0.835659\pi$
$941$	3.99761	−	14.9193i	0.130318	−	0.486355i	0.999973	+	0.00730539i	$0.00232540\pi$
$942$	8.02675	+	2.87393i	0.261526	+	0.0936377i
$943$	−3.08419	+	5.34197i	−0.100435	+	0.173959i
$944$	−15.1644	−	30.8159i	−0.493558	−	1.00297i
$945$		0			0
$946$	16.4774	+	19.4292i	0.535726	+	0.631697i
$947$	−30.1683	+	8.08357i	−0.980338	+	0.262681i	−0.713187	−	0.700974i	$-0.752749\pi$
$947$	−30.1683	+	8.08357i	−0.980338	+	0.262681i	−0.267151	+	0.963655i	$0.586082\pi$
$948$	6.09884	+	2.76645i	0.198081	+	0.0898502i
$949$	−25.7573	+	96.1276i	−0.836118	+	3.12043i
$950$	7.59229	−	10.9648i	0.246326	−	0.355746i
$951$			71.7697i			2.32729i
$952$		0			0
$953$		−	15.7802i		−	0.511170i	−0.966787	−	0.255585i	$-0.917732\pi$
$953$		−	15.7802i		−	0.511170i	0.966787	−	0.255585i	$-0.0822680\pi$
$954$	35.3128	+	24.4513i	1.14329	+	0.791641i
$955$	−2.12492	+	7.93032i	−0.0687609	+	0.256619i
$956$	20.0901	+	53.4464i	0.649759	+	1.72858i
$957$	8.32855	−	2.23163i	0.269224	−	0.0721383i
$958$	−29.5275	+	25.0415i	−0.953989	+	0.809053i
$959$		0			0
$960$	8.90398	+	4.77378i	0.287375	+	0.154073i
$961$	15.1232	−	26.1941i	0.487844	−	0.844970i
$962$	−24.9241	+	69.6120i	−0.803587	+	2.24438i
$963$	6.92420	−	25.8415i	0.223129	−	0.832729i
$964$	29.1393	−	35.4758i	0.938514	−	1.14260i
$965$	2.17051	−	2.17051i	0.0698712	−	0.0698712i
$966$		0			0
$967$	−44.7046			−1.43760			−0.718801	−	0.695216i	$-0.755309\pi$
$967$	−44.7046			−1.43760			−0.718801	+	0.695216i	$0.755309\pi$
$968$	−0.310759	−	19.7553i	−0.00998816	−	0.634959i
$969$	14.4248	+	24.9844i	0.463390	+	0.802615i
$970$	1.32443	+	2.80181i	0.0425250	+	0.0899608i
$971$	−56.2271	+	15.0660i	−1.80441	+	0.483491i	−0.994653	−	0.103269i	$-0.967070\pi$
$971$	−56.2271	+	15.0660i	−1.80441	+	0.483491i	−0.809761	+	0.586761i	$0.800403\pi$
$972$	22.8133	+	31.8643i	0.731736	+	1.02205i
$973$		0			0
$974$	−20.8814	+	17.7089i	−0.669082	+	0.567431i
$975$	71.5999	+	41.3382i	2.29303	+	1.32388i
$976$	−1.08200	+	1.61637i	−0.0346339	+	0.0517387i
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	0.983259	−	0.182215i	$-0.0583267\pi$
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	−0.649432	+	0.760420i	$0.724993\pi$
$978$	10.0443	+	55.2681i	0.321182	+	1.76728i
$979$	−3.29726	+	3.29726i	−0.105381	+	0.105381i
$980$		0			0
$981$	−33.3351	−	33.3351i	−1.06431	−	1.06431i
$982$	28.2736	+	19.5773i	0.902248	+	0.624737i
$983$	−36.5230	+	21.0866i	−1.16490	+	0.672558i	−0.952474	−	0.304619i	$-0.901471\pi$
$983$	−36.5230	+	21.0866i	−1.16490	+	0.672558i	−0.212430	+	0.977176i	$0.568138\pi$
$984$	−6.80107	−	23.8734i	−0.216810	−	0.761057i
$985$	4.90806	−	8.50102i	0.156384	−	0.270865i
$986$	12.1107	+	0.995592i	0.385682	+	0.0317061i
$987$		0			0
$988$	4.11359	−	24.8503i	0.130871	−	0.790594i
$989$	−4.42695	−	16.5216i	−0.140769	−	0.525356i
$990$	5.38558	+	1.92827i	0.171165	+	0.0612845i
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	−0.716280	−	0.697813i	$-0.754156\pi$
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	0.246184	+	0.969223i	$0.420823\pi$
$992$	0.725721	−	4.85708i	0.0230417	−	0.154213i
$993$			25.6788i			0.814891i
$994$		0			0
$995$	2.45062	+	2.45062i	0.0776898	+	0.0776898i
$996$	43.9086	−	53.4567i	1.39130	−	1.69384i
$997$	27.4427	+	7.35325i	0.869119	+	0.232880i	0.665707	−	0.746214i	$-0.268130\pi$
$997$	27.4427	+	7.35325i	0.869119	+	0.232880i	0.203412	+	0.979093i	$0.434797\pi$
$998$	−1.83008	−	3.87150i	−0.0579303	−	0.122550i
$999$	−25.4673	−	14.7035i	−0.805749	−	0.465199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.f.411.7		56
7.2	even	3		784.2.j.a.587.7		56
7.3	odd	6	inner	784.2.w.f.619.13		56
7.4	even	3		112.2.v.a.59.13	yes	56
7.5	odd	6		784.2.j.a.587.8		56
7.6	odd	2		112.2.v.a.75.7	yes	56
16.3	odd	4	inner	784.2.w.f.19.13		56
28.11	odd	6		448.2.z.a.143.13		56
28.27	even	2		448.2.z.a.271.13		56
56.11	odd	6		896.2.z.a.31.2		56
56.13	odd	2		896.2.z.b.159.13		56
56.27	even	2		896.2.z.a.159.2		56
56.53	even	6		896.2.z.b.31.13		56
112.3	even	12	inner	784.2.w.f.227.7		56
112.11	odd	12		896.2.z.b.479.13		56
112.13	odd	4		448.2.z.a.47.13		56
112.19	even	12		784.2.j.a.195.7		56
112.27	even	4		896.2.z.b.607.13		56
112.51	odd	12		784.2.j.a.195.8		56
112.53	even	12		896.2.z.a.479.2		56
112.67	odd	12		112.2.v.a.3.7	✓	56
112.69	odd	4		896.2.z.a.607.2		56
112.83	even	4		112.2.v.a.19.13	yes	56
112.109	even	12		448.2.z.a.367.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	112.67	odd	12
112.2.v.a.19.13	yes	56	112.83	even	4
112.2.v.a.59.13	yes	56	7.4	even	3
112.2.v.a.75.7	yes	56	7.6	odd	2
448.2.z.a.47.13		56	112.13	odd	4
448.2.z.a.143.13		56	28.11	odd	6
448.2.z.a.271.13		56	28.27	even	2
448.2.z.a.367.13		56	112.109	even	12
784.2.j.a.195.7		56	112.19	even	12
784.2.j.a.195.8		56	112.51	odd	12
784.2.j.a.587.7		56	7.2	even	3
784.2.j.a.587.8		56	7.5	odd	6
784.2.w.f.19.13		56	16.3	odd	4	inner
784.2.w.f.227.7		56	112.3	even	12	inner
784.2.w.f.411.7		56	1.1	even	1	trivial
784.2.w.f.619.13		56	7.3	odd	6	inner
896.2.z.a.31.2		56	56.11	odd	6
896.2.z.a.159.2		56	56.27	even	2
896.2.z.a.479.2		56	112.53	even	12
896.2.z.a.607.2		56	112.69	odd	4
896.2.z.b.31.13		56	56.53	even	6
896.2.z.b.159.13		56	56.13	odd	2
896.2.z.b.479.13		56	112.11	odd	12
896.2.z.b.607.13		56	112.27	even	4

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.252874 - 1.39142i) q^{2} +(2.61463 + 0.700587i) q^{3} +(-1.87211 + 0.703710i) q^{4} +(-0.120751 - 0.450647i) q^{5} +(0.313640 - 3.81521i) q^{6} +(1.45257 + 2.42694i) q^{8} +(3.74737 + 2.16355i) q^{9} +(-0.596506 + 0.281972i) q^{10} +(-1.93537 - 0.518581i) q^{11} +(-5.38787 + 0.528362i) q^{12} +(4.51607 + 4.51607i) q^{13} -1.26287i q^{15} +(3.00959 - 2.63484i) q^{16} +(4.68066 - 2.70238i) q^{17} +(2.06279 - 5.76128i) q^{18} +(0.510379 + 1.90476i) q^{19} +(0.543183 + 0.758687i) q^{20} +(-0.232159 + 2.82405i) q^{22} +(0.951245 - 1.64761i) q^{23} +(2.09763 + 7.36320i) q^{24} +(4.14162 - 2.39117i) q^{25} +(5.14176 - 7.42576i) q^{26} +(2.54010 + 2.54010i) q^{27} +(-1.12415 + 1.12415i) q^{29} +(-1.75718 + 0.319347i) q^{30} +(0.434075 + 0.751840i) q^{31} +(-4.42722 - 3.52132i) q^{32} +(-4.69696 - 2.71179i) q^{33} +(-4.94377 - 5.82941i) q^{34} +(-8.53799 - 1.41333i) q^{36} +(-7.90732 + 2.11876i) q^{37} +(2.52126 - 1.19182i) q^{38} +(8.64394 + 14.9717i) q^{39} +(0.918297 - 0.947649i) q^{40} -3.24226 q^{41} +(6.35727 - 6.35727i) q^{43} +(3.98816 - 0.391099i) q^{44} +(0.522499 - 1.94999i) q^{45} +(-2.53306 - 0.906947i) q^{46} +(1.49266 - 2.58536i) q^{47} +(9.71488 - 4.78065i) q^{48} +(-4.37443 - 5.15808i) q^{50} +(14.1314 - 3.78650i) q^{51} +(-11.6326 - 5.27658i) q^{52} +(-1.81663 + 6.77976i) q^{53} +(2.89203 - 4.17668i) q^{54} +0.934789i q^{55} +5.33780i q^{57} +(1.84843 + 1.27990i) q^{58} +(2.22228 - 8.29366i) q^{59} +(0.888694 + 2.36423i) q^{60} +(-0.469703 + 0.125856i) q^{61} +(0.936361 - 0.794103i) q^{62} +(-3.78011 + 7.05059i) q^{64} +(1.48984 - 2.58047i) q^{65} +(-2.58551 + 7.22120i) q^{66} +(-1.03224 + 3.85238i) q^{67} +(-6.86102 + 8.35298i) q^{68} +(3.64144 - 3.64144i) q^{69} -12.1916 q^{71} +(0.192498 + 12.2373i) q^{72} +(7.79109 + 13.4946i) q^{73} +(4.94765 + 10.4666i) q^{74} +(12.5040 - 3.35044i) q^{75} +(-2.29588 - 3.20676i) q^{76} +(18.6462 - 15.8133i) q^{78} +(-1.07130 - 0.618516i) q^{79} +(-1.55079 - 1.03810i) q^{80} +(-1.62878 - 2.82113i) q^{81} +(0.819885 + 4.51136i) q^{82} +(-9.03560 + 9.03560i) q^{83} +(-1.78301 - 1.78301i) q^{85} +(-10.4532 - 7.23805i) q^{86} +(-3.72680 + 2.15167i) q^{87} +(-1.55269 - 5.45031i) q^{88} +(1.16364 - 2.01548i) q^{89} +(-2.84539 - 0.233913i) q^{90} +(-0.621399 + 3.75390i) q^{92} +(0.608215 + 2.26989i) q^{93} +(-3.97479 - 1.42315i) q^{94} +(0.796746 - 0.460002i) q^{95} +(-9.10855 - 12.3086i) q^{96} -4.69704i q^{97} +(-6.13058 - 6.13058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Introduction

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