LMFDB - Embedded newform 270.2.r.a.113.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [270,2,Mod(23,270)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("270.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(270, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([22, 27])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	270.r (of order $36$ , degree $12$ , 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.7
Character	$\chi$	$=$	270.113
Dual form			270.2.r.a.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+(-0.996195 - 0.0871557i) q^{2} +(1.12178 - 1.31970i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.30964 + 1.81241i) q^{5} +(-1.23253 + 1.21691i) q^{6} +(-3.63487 - 2.54517i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-0.483211 - 2.96083i) q^{9} +(1.46262 - 1.69137i) q^{10} +(1.06118 - 2.91557i) q^{11} +(1.33390 - 1.10485i) q^{12} +(-0.443416 - 5.06827i) q^{13} +(3.39922 + 2.85228i) q^{14} +(0.922704 + 3.76146i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-2.90525 + 0.778460i) q^{17} +(0.223319 + 2.99168i) q^{18} +(4.83096 - 2.78915i) q^{19} +(-1.60447 + 1.55746i) q^{20} +(-7.43639 + 1.94182i) q^{21} +(-1.31125 + 2.81199i) q^{22} +(3.26865 + 4.66812i) q^{23} +(-1.42512 + 0.984393i) q^{24} +(-1.56967 - 4.74722i) q^{25} +5.08763i q^{26} +(-4.44946 - 2.68371i) q^{27} +(-3.13769 - 3.13769i) q^{28} +(-0.945635 + 0.793482i) q^{29} +(-0.591359 - 3.82757i) q^{30} +(-0.863767 + 4.89867i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-2.65727 - 4.67108i) q^{33} +(2.96205 - 0.522288i) q^{34} +(9.37328 - 3.25463i) q^{35} +(0.0382726 - 2.99976i) q^{36} +(-0.154906 - 0.578116i) q^{37} +(-5.05567 + 2.35750i) q^{38} +(-7.18600 - 5.10032i) q^{39} +(1.73410 - 1.41169i) q^{40} +(0.230916 - 0.275195i) q^{41} +(7.57733 - 1.28631i) q^{42} +(0.843535 + 1.80897i) q^{43} +(1.55134 - 2.68701i) q^{44} +(5.99907 + 3.00185i) q^{45} +(-2.84936 - 4.93524i) q^{46} +(4.62779 - 6.60916i) q^{47} +(1.50549 - 0.856439i) q^{48} +(4.34030 + 11.9249i) q^{49} +(1.14995 + 4.86597i) q^{50} +(-2.23173 + 4.70732i) q^{51} +(0.443416 - 5.06827i) q^{52} +(-5.61053 + 5.61053i) q^{53} +(4.19863 + 3.06129i) q^{54} +(3.89445 + 5.74166i) q^{55} +(2.85228 + 3.39922i) q^{56} +(1.73844 - 9.50423i) q^{57} +(1.01119 - 0.708045i) q^{58} +(-4.22275 + 1.53695i) q^{59} +(0.255514 + 3.86455i) q^{60} +(0.293531 + 1.66470i) q^{61} +(1.28743 - 4.80474i) q^{62} +(-5.77939 + 11.9921i) q^{63} +(0.866025 + 0.500000i) q^{64} +(9.76650 + 5.83397i) q^{65} +(2.24004 + 4.88490i) q^{66} +(8.65868 - 0.757536i) q^{67} +(-2.99629 + 0.262142i) q^{68} +(9.82723 + 0.922974i) q^{69} +(-9.62127 + 2.42531i) q^{70} +(4.54040 + 2.62140i) q^{71} +(-0.299573 + 2.98501i) q^{72} +(0.146181 - 0.545555i) q^{73} +(0.103930 + 0.589417i) q^{74} +(-8.02573 - 3.25386i) q^{75} +(5.24190 - 1.90789i) q^{76} +(-11.2779 + 7.89686i) q^{77} +(6.71414 + 5.70721i) q^{78} +(4.05065 + 4.82738i) q^{79} +(-1.85054 + 1.25519i) q^{80} +(-8.53301 + 2.86141i) q^{81} +(-0.254023 + 0.254023i) q^{82} +(1.20341 - 13.7551i) q^{83} +(-7.66061 + 0.621003i) q^{84} +(2.39395 - 6.28502i) q^{85} +(-0.682663 - 1.87560i) q^{86} +(-0.0136388 + 2.13807i) q^{87} +(-1.77963 + 2.54157i) q^{88} +(-6.98069 - 12.0909i) q^{89} +(-5.71462 - 3.51328i) q^{90} +(-11.2878 + 19.5511i) q^{91} +(2.40838 + 5.16480i) q^{92} +(5.49581 + 6.63515i) q^{93} +(-5.18620 + 6.18068i) q^{94} +(-1.27173 + 12.4085i) q^{95} +(-1.57441 + 0.721968i) q^{96} +(13.7632 - 6.41791i) q^{97} +(-3.28446 - 12.2578i) q^{98} +(-9.14529 - 1.73314i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100})$ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	1.12178	−	1.31970i	0.647661	−	0.761929i
$3$	1.12178	−	1.31970i	0.647661	−	0.761929i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−1.30964	+	1.81241i	−0.585690	+	0.810535i
$5$	−1.30964	+	1.81241i	−0.585690	+	0.810535i
$6$	−1.23253	+	1.21691i	−0.503179	+	0.496800i
$7$	−3.63487	−	2.54517i	−1.37385	−	0.961983i	−0.999396	−	0.0347383i	$-0.988940\pi$
$7$	−3.63487	−	2.54517i	−1.37385	−	0.961983i	−0.374457	−	0.927244i	$-0.622171\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−0.483211	−	2.96083i	−0.161070	−	0.986943i
$10$	1.46262	−	1.69137i	0.462522	−	0.534859i
$11$	1.06118	−	2.91557i	0.319959	−	0.879079i	−0.670579	−	0.741838i	$-0.733954\pi$
$11$	1.06118	−	2.91557i	0.319959	−	0.879079i	0.990538	−	0.137241i	$-0.0438234\pi$
$12$	1.33390	−	1.10485i	0.385065	−	0.318944i
$13$	−0.443416	−	5.06827i	−0.122981	−	1.40568i	−0.767477	−	0.641077i	$-0.778488\pi$
$13$	−0.443416	−	5.06827i	−0.122981	−	1.40568i	0.644495	−	0.764608i	$-0.277067\pi$
$14$	3.39922	+	2.85228i	0.908479	+	0.762304i
$15$	0.922704	+	3.76146i	0.238241	+	0.971206i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−2.90525	+	0.778460i	−0.704627	+	0.188804i	−0.593302	−	0.804980i	$-0.702176\pi$
$17$	−2.90525	+	0.778460i	−0.704627	+	0.188804i	−0.111325	+	0.993784i	$0.535509\pi$
$18$	0.223319	+	2.99168i	0.0526368	+	0.705145i
$19$	4.83096	−	2.78915i	1.10830	−	0.639876i	0.169910	−	0.985460i	$-0.445652\pi$
$19$	4.83096	−	2.78915i	1.10830	−	0.639876i	0.938388	+	0.345584i	$0.112319\pi$
$20$	−1.60447	+	1.55746i	−0.358770	+	0.348259i
$21$	−7.43639	+	1.94182i	−1.62275	+	0.423740i
$22$	−1.31125	+	2.81199i	−0.279560	+	0.599519i
$23$	3.26865	+	4.66812i	0.681561	+	0.973370i	0.999679	+	0.0253193i	$0.00806026\pi$
$23$	3.26865	+	4.66812i	0.681561	+	0.973370i	−0.318118	+	0.948051i	$0.603051\pi$
$24$	−1.42512	+	0.984393i	−0.290902	+	0.200938i
$25$	−1.56967	−	4.74722i	−0.313934	−	0.949445i
$26$			5.08763i			0.997766i
$27$	−4.44946	−	2.68371i	−0.856299	−	0.516480i
$28$	−3.13769	−	3.13769i	−0.592968	−	0.592968i
$29$	−0.945635	+	0.793482i	−0.175600	+	0.147346i	−0.726352	−	0.687323i	$-0.758786\pi$
$29$	−0.945635	+	0.793482i	−0.175600	+	0.147346i	0.550752	+	0.834669i	$0.314341\pi$
$30$	−0.591359	−	3.82757i	−0.107967	−	0.698816i
$31$	−0.863767	+	4.89867i	−0.155137	+	0.879827i	0.803523	+	0.595274i	$0.202956\pi$
$31$	−0.863767	+	4.89867i	−0.155137	+	0.879827i	−0.958660	+	0.284553i	$0.908155\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	−2.65727	−	4.67108i	−0.462571	−	0.813131i
$34$	2.96205	−	0.522288i	0.507987	−	0.0895717i
$35$	9.37328	−	3.25463i	1.58437	−	0.550133i
$36$	0.0382726	−	2.99976i	0.00637876	−	0.499959i
$37$	−0.154906	−	0.578116i	−0.0254663	−	0.0950417i	0.952023	−	0.306026i	$-0.0989996\pi$
$37$	−0.154906	−	0.578116i	−0.0254663	−	0.0950417i	−0.977489	+	0.210985i	$0.932333\pi$
$38$	−5.05567	+	2.35750i	−0.820137	+	0.382436i
$39$	−7.18600	−	5.10032i	−1.15068	−	0.816704i
$40$	1.73410	−	1.41169i	0.274186	−	0.223208i
$41$	0.230916	−	0.275195i	0.0360631	−	0.0429783i	−0.747711	−	0.664024i	$-0.768847\pi$
$41$	0.230916	−	0.275195i	0.0360631	−	0.0429783i	0.783775	+	0.621045i	$0.213292\pi$
$42$	7.57733	−	1.28631i	1.16921	−	0.198481i
$43$	0.843535	+	1.80897i	0.128638	+	0.275865i	0.960069	−	0.279763i	$-0.0902558\pi$
$43$	0.843535	+	1.80897i	0.128638	+	0.275865i	−0.831431	+	0.555628i	$0.812478\pi$
$44$	1.55134	−	2.68701i	0.233874	−	0.405082i
$45$	5.99907	+	3.00185i	0.894289	+	0.447490i
$46$	−2.84936	−	4.93524i	−0.420115	−	0.727661i
$47$	4.62779	−	6.60916i	0.675032	−	0.964046i	−0.324801	−	0.945782i	$-0.605297\pi$
$47$	4.62779	−	6.60916i	0.675032	−	0.964046i	0.999833	−	0.0182633i	$-0.00581370\pi$
$48$	1.50549	−	0.856439i	0.217299	−	0.123616i
$49$	4.34030	+	11.9249i	0.620043	+	1.70355i
$50$	1.14995	+	4.86597i	0.162627	+	0.688151i
$51$	−2.23173	+	4.70732i	−0.312504	+	0.659157i
$52$	0.443416	−	5.06827i	0.0614907	−	0.702842i
$53$	−5.61053	+	5.61053i	−0.770665	+	0.770665i	−0.978223	−	0.207557i	$-0.933449\pi$
$53$	−5.61053	+	5.61053i	−0.770665	+	0.770665i	0.207557	+	0.978223i	$0.433449\pi$
$54$	4.19863	+	3.06129i	0.571361	+	0.416589i
$55$	3.89445	+	5.74166i	0.525128	+	0.774205i
$56$	2.85228	+	3.39922i	0.381152	+	0.454239i
$57$	1.73844	−	9.50423i	0.230261	−	1.25887i
$58$	1.01119	−	0.708045i	0.132776	−	0.0929709i
$59$	−4.22275	+	1.53695i	−0.549755	+	0.200094i	−0.601938	−	0.798543i	$-0.705604\pi$
$59$	−4.22275	+	1.53695i	−0.549755	+	0.200094i	0.0521828	+	0.998638i	$0.483382\pi$
$60$	0.255514	+	3.86455i	0.0329868	+	0.498911i
$61$	0.293531	+	1.66470i	0.0375829	+	0.213143i	0.997816	−	0.0660570i	$-0.0210419\pi$
$61$	0.293531	+	1.66470i	0.0375829	+	0.213143i	−0.960233	+	0.279200i	$0.909931\pi$
$62$	1.28743	−	4.80474i	0.163503	−	0.610203i
$63$	−5.77939	+	11.9921i	−0.728135	+	1.51086i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	9.76650	+	5.83397i	1.21139	+	0.723615i
$66$	2.24004	+	4.88490i	0.275730	+	0.601290i
$67$	8.65868	−	0.757536i	1.05783	−	0.0925478i	0.455056	−	0.890463i	$-0.349619\pi$
$67$	8.65868	−	0.757536i	1.05783	−	0.0925478i	0.602770	+	0.797915i	$0.294064\pi$
$68$	−2.99629	+	0.262142i	−0.363354	+	0.0317894i
$69$	9.82723	+	0.922974i	1.18306	+	0.111113i
$70$	−9.62127	+	2.42531i	−1.14996	+	0.289880i
$71$	4.54040	+	2.62140i	0.538847	+	0.311103i	0.744611	−	0.667498i	$-0.232635\pi$
$71$	4.54040	+	2.62140i	0.538847	+	0.311103i	−0.205765	+	0.978601i	$0.565968\pi$
$72$	−0.299573	+	2.98501i	−0.0353050	+	0.351786i
$73$	0.146181	−	0.545555i	0.0171092	−	0.0638524i	−0.956843	−	0.290604i	$-0.906144\pi$
$73$	0.146181	−	0.545555i	0.0171092	−	0.0638524i	0.973953	+	0.226751i	$0.0728105\pi$
$74$	0.103930	+	0.589417i	0.0120816	+	0.0685184i
$75$	−8.02573	−	3.25386i	−0.926732	−	0.375723i
$76$	5.24190	−	1.90789i	0.601287	−	0.218850i
$77$	−11.2779	+	7.89686i	−1.28523	+	0.899931i
$78$	6.71414	+	5.70721i	0.760226	+	0.646214i
$79$	4.05065	+	4.82738i	0.455734	+	0.543122i	0.944162	−	0.329482i	$-0.106874\pi$
$79$	4.05065	+	4.82738i	0.455734	+	0.543122i	−0.488428	+	0.872604i	$0.662430\pi$
$80$	−1.85054	+	1.25519i	−0.206897	+	0.140334i
$81$	−8.53301	+	2.86141i	−0.948113	+	0.317934i
$82$	−0.254023	+	0.254023i	−0.0280521	+	0.0280521i
$83$	1.20341	−	13.7551i	0.132092	−	1.50982i	−0.583968	−	0.811777i	$-0.698500\pi$
$83$	1.20341	−	13.7551i	0.132092	−	1.50982i	0.716059	−	0.698039i	$-0.245944\pi$
$84$	−7.66061	+	0.621003i	−0.835841	+	0.0677569i
$85$	2.39395	−	6.28502i	0.259661	−	0.681706i
$86$	−0.682663	−	1.87560i	−0.0736135	−	0.202251i
$87$	−0.0136388	+	2.13807i	−0.00146223	+	0.229225i
$88$	−1.77963	+	2.54157i	−0.189709	+	0.270933i
$89$	−6.98069	−	12.0909i	−0.739952	−	1.28163i	−0.952516	−	0.304487i	$-0.901515\pi$
$89$	−6.98069	−	12.0909i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$90$	−5.71462	−	3.51328i	−0.602374	−	0.370332i
$91$	−11.2878	+	19.5511i	−1.18329	+	2.04951i
$92$	2.40838	+	5.16480i	0.251091	+	0.538467i
$93$	5.49581	+	6.63515i	0.569889	+	0.688033i
$94$	−5.18620	+	6.18068i	−0.534916	+	0.637488i
$95$	−1.27173	+	12.4085i	−0.130477	+	1.27308i
$96$	−1.57441	+	0.721968i	−0.160687	+	0.0736856i
$97$	13.7632	−	6.41791i	1.39745	−	0.651640i	0.429562	−	0.903037i	$-0.358668\pi$
$97$	13.7632	−	6.41791i	1.39745	−	0.651640i	0.967884	+	0.251398i	$0.0808902\pi$
$98$	−3.28446	−	12.2578i	−0.331781	−	1.23822i
$99$	−9.14529	−	1.73314i	−0.919136	−	0.174187i
$100$	−0.721477	−	4.94767i	−0.0721477	−	0.494767i
$101$	12.9642	−	2.28593i	1.28998	−	0.227459i	0.513770	−	0.857928i	$-0.328249\pi$
$101$	12.9642	−	2.28593i	1.28998	−	0.227459i	0.776214	+	0.630469i	$0.217138\pi$
$102$	2.63350	−	4.49490i	0.260756	−	0.445062i
$103$	10.4924	+	4.89268i	1.03385	+	0.482090i	0.864059	−	0.503391i	$-0.167914\pi$
$103$	10.4924	+	4.89268i	1.03385	+	0.482090i	0.169787	+	0.985481i	$0.445692\pi$
$104$	−0.883457	+	5.01034i	−0.0866301	+	0.491304i
$105$	6.21964	−	16.0209i	0.606975	−	1.56348i
$106$	6.07817	−	5.10019i	0.590364	−	0.495374i
$107$	0.623217	+	0.623217i	0.0602487	+	0.0602487i	0.736589	−	0.676340i	$-0.236435\pi$
$107$	0.623217	+	0.623217i	0.0602487	+	0.0602487i	−0.676340	+	0.736589i	$0.736435\pi$
$108$	−3.91584	−	3.41558i	−0.376802	−	0.328664i
$109$		−	19.3629i		−	1.85463i	−0.374277	−	0.927317i	$-0.622109\pi$
$109$		−	19.3629i		−	1.85463i	0.374277	−	0.927317i	$-0.377891\pi$
$110$	−3.37921	−	6.05924i	−0.322195	−	0.577725i
$111$	−0.936710	−	0.444091i	−0.0889086	−	0.0421513i
$112$	−2.54517	−	3.63487i	−0.240496	−	0.343463i
$113$	5.50579	−	11.8072i	0.517941	−	1.11073i	−0.457245	−	0.889341i	$-0.651164\pi$
$113$	5.50579	−	11.8072i	0.517941	−	1.11073i	0.975186	−	0.221387i	$-0.0710585\pi$
$114$	−2.56017	+	9.31655i	−0.239782	+	0.872575i
$115$	−12.7413	−	0.189427i	−1.18813	−	0.0176641i
$116$	−1.06906	+	0.617220i	−0.0992593	+	0.0573074i
$117$	−14.7920	+	3.76192i	−1.36752	+	0.347790i
$118$	4.34063	−	1.16307i	0.399588	−	0.107069i
$119$	12.5415	+	4.56475i	1.14968	+	0.418450i
$120$	0.0822752	−	3.87211i	0.00751066	−	0.353474i
$121$	1.05202	+	0.882752i	0.0956384	+	0.0802501i
$122$	−0.147326	−	1.68395i	−0.0133383	−	0.152457i
$123$	−0.104137	−	0.613449i	−0.00938975	−	0.0553129i
$124$	−1.70129	+	4.67425i	−0.152780	+	0.419760i
$125$	10.6596	+	3.37228i	0.953426	+	0.301626i
$126$	6.80258	−	11.4428i	0.606022	−	1.01940i
$127$	−10.4924	−	2.81142i	−0.931047	−	0.249473i	−0.238746	−	0.971082i	$-0.576736\pi$
$127$	−10.4924	−	2.81142i	−0.931047	−	0.249473i	−0.692301	+	0.721609i	$0.743403\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	3.33355	+	0.916054i	0.293503	+	0.0806540i
$130$	−9.22088	−	6.66298i	−0.808724	−	0.584382i
$131$	2.41953	+	0.426628i	0.211395	+	0.0372747i	0.278343	−	0.960482i	$-0.410215\pi$
$131$	2.41953	+	0.426628i	0.211395	+	0.0372747i	−0.0669475	+	0.997756i	$0.521326\pi$
$132$	−1.80577	−	5.06154i	−0.157172	−	0.440551i
$133$	−24.6588	−	2.15736i	−2.13819	−	0.187067i
$134$	−8.69175			−0.750853
$135$	10.6912	−	4.54955i	0.920151	−	0.391563i
$136$	3.00774			0.257912
$137$	−6.93208	−	0.606478i	−0.592247	−	0.0518149i	−0.212907	−	0.977072i	$-0.568293\pi$
$137$	−6.93208	−	0.606478i	−0.592247	−	0.0518149i	−0.379340	+	0.925257i	$0.623849\pi$
$138$	−9.70939	−	1.77596i	−0.826518	−	0.151180i
$139$	15.1508	+	2.67150i	1.28508	+	0.226594i	0.774134	−	0.633022i	$-0.218186\pi$
$139$	15.1508	+	2.67150i	1.28508	+	0.226594i	0.510942	+	0.859615i	$0.329297\pi$
$140$	9.79604	−	1.57753i	0.827916	−	0.133326i
$141$	−3.53074	−	13.5213i	−0.297342	−	1.13870i
$142$	−4.29465	−	3.00715i	−0.360399	−	0.252354i
$143$	−15.2475	−	4.08554i	−1.27506	−	0.341650i
$144$	0.558593	−	2.94754i	0.0465494	−	0.245628i
$145$	−0.199672	−	2.75306i	−0.0165818	−	0.228629i
$146$	−0.193173	+	0.530738i	−0.0159871	+	0.0439242i
$147$	20.6061	+	7.64922i	1.69956	+	0.630897i
$148$	−0.0521636	−	0.596232i	−0.00428782	−	0.0490100i
$149$	−11.7199	−	9.83419i	−0.960134	−	0.805648i	0.0208405	−	0.999783i	$-0.493366\pi$
$149$	−11.7199	−	9.83419i	−0.960134	−	0.805648i	−0.980975	+	0.194134i	$0.937810\pi$
$150$	7.71160	+	3.94096i	0.629650	+	0.321778i
$151$	−15.0661	−	5.48361i	−1.22606	−	0.446250i	−0.353815	−	0.935316i	$-0.615116\pi$
$151$	−15.0661	−	5.48361i	−1.22606	−	0.446250i	−0.872247	+	0.489066i	$0.837338\pi$
$152$	−5.38823	+	1.44377i	−0.437043	+	0.117105i
$153$	3.70874	+	8.22580i	0.299834	+	0.665016i
$154$	11.9232	−	6.88388i	0.960801	−	0.554719i
$155$	−7.74717	−	7.98101i	−0.622268	−	0.641050i
$156$	−6.19117	−	6.27067i	−0.495691	−	0.502055i
$157$	−9.62532	+	20.6416i	−0.768184	+	1.64738i	−0.00602994	+	0.999982i	$0.501919\pi$
$157$	−9.62532	+	20.6416i	−0.768184	+	1.64738i	−0.762155	+	0.647395i	$0.775858\pi$
$158$	−3.61450	−	5.16205i	−0.287554	−	0.410670i
$159$	1.11042	+	13.6980i	0.0880621	+	1.08632i
$160$	1.95290	−	1.08912i	0.154390	−	0.0861028i
$161$		−	25.2873i		−	1.99292i
$162$	8.74993	−	2.10682i	0.687460	−	0.165527i
$163$	11.0646	+	11.0646i	0.866643	+	0.866643i	0.992099	−	0.125456i	$-0.0400393\pi$
$163$	11.0646	+	11.0646i	0.866643	+	0.866643i	−0.125456	+	0.992099i	$0.540039\pi$
$164$	0.275195	−	0.230916i	0.0214892	−	0.0180315i
$165$	11.9460	+	1.30139i	0.929994	+	0.101313i
$166$	−2.39767	+	13.5979i	−0.186095	+	1.05540i
$167$	0.927334	+	0.432423i	0.0717593	+	0.0334619i	0.458167	−	0.888866i	$-0.348506\pi$
$167$	0.927334	+	0.432423i	0.0717593	+	0.0334619i	−0.386407	+	0.922328i	$0.626284\pi$
$168$	7.68558	+	0.0490265i	0.592955	+	0.00378247i
$169$	−12.6882	+	2.23728i	−0.976017	+	0.172098i
$170$	−2.93262	+	6.05246i	−0.224922	+	0.464202i
$171$	−10.5926	−	12.9559i	−0.810035	−	0.990762i
$172$	0.516596	+	1.92796i	0.0393901	+	0.147006i
$173$	−0.915017	+	0.426680i	−0.0695675	+	0.0324398i	−0.457091	−	0.889420i	$-0.651108\pi$
$173$	−0.915017	+	0.426680i	−0.0695675	+	0.0324398i	0.387523	+	0.921860i	$0.373331\pi$
$174$	0.199932	−	2.12874i	0.0151568	−	0.161380i
$175$	−6.37692	+	21.2506i	−0.482050	+	1.60640i
$176$	1.99437	−	2.37680i	0.150331	−	0.179158i
$177$	−2.70868	+	7.29688i	−0.203597	+	0.548467i
$178$	5.90034	+	12.6533i	0.442249	+	0.948406i
$179$	−4.56812	+	7.91221i	−0.341437	+	0.591387i	−0.984700	−	0.174259i	$-0.944247\pi$
$179$	−4.56812	+	7.91221i	−0.341437	+	0.591387i	0.643263	+	0.765646i	$0.277580\pi$
$180$	5.38667	+	3.99797i	0.401499	+	0.297991i
$181$	0.245003	+	0.424357i	0.0182109	+	0.0315422i	0.874987	−	0.484146i	$-0.160870\pi$
$181$	0.245003	+	0.424357i	0.0182109	+	0.0315422i	−0.856776	+	0.515688i	$0.827536\pi$
$182$	12.9489	−	18.4929i	0.959834	−	1.37078i
$183$	2.52618	+	1.48006i	0.186741	+	0.109409i
$184$	−1.94908	−	5.35505i	−0.143688	−	0.394779i
$185$	1.25066	+	0.476373i	0.0919500	+	0.0350236i
$186$	−4.89660	−	7.08889i	−0.359036	−	0.519783i
$187$	−0.813344	+	9.29657i	−0.0594776	+	0.679833i
$188$	5.70515	−	5.70515i	0.416091	−	0.416091i
$189$	9.34274	+	21.0796i	0.679584	+	1.53331i
$190$	2.34837	−	12.2504i	0.170368	−	0.888739i
$191$	−4.31791	−	5.14588i	−0.312433	−	0.372343i	0.586861	−	0.809688i	$-0.300363\pi$
$191$	−4.31791	−	5.14588i	−0.312433	−	0.372343i	−0.899294	+	0.437345i	$0.855919\pi$
$192$	1.63134	−	0.582002i	0.117732	−	0.0420024i
$193$	−6.71078	+	4.69894i	−0.483053	+	0.338237i	−0.789604	−	0.613617i	$-0.789714\pi$
$193$	−6.71078	+	4.69894i	−0.483053	+	0.338237i	0.306551	+	0.951854i	$0.400825\pi$
$194$	−14.2702	+	5.19394i	−1.02454	+	0.372903i
$195$	18.6550	−	6.34440i	1.33591	−	0.454332i
$196$	2.20363	+	12.4974i	0.157402	+	0.892671i
$197$	−5.02384	+	18.7492i	−0.357934	+	1.33583i	0.518818	+	0.854885i	$0.326372\pi$
$197$	−5.02384	+	18.7492i	−0.357934	+	1.33583i	−0.876752	+	0.480943i	$0.840294\pi$
$198$	8.95944	+	2.52361i	0.636720	+	0.179345i
$199$	−16.5891	−	9.57774i	−1.17597	−	0.678948i	−0.220893	−	0.975298i	$-0.570897\pi$
$199$	−16.5891	−	9.57774i	−1.17597	−	0.678948i	−0.955079	+	0.296350i	$0.904230\pi$
$200$	0.287513	+	4.99173i	0.0203303	+	0.352968i
$201$	8.71343	−	12.2766i	0.614598	−	0.865928i
$202$	−13.1141	+	1.14733i	−0.922703	+	0.0807261i
$203$	5.45681	−	0.477409i	0.382993	−	0.0335076i
$204$	−3.01524	+	4.24827i	−0.211109	+	0.297439i
$205$	0.196349	+	0.778923i	0.0137136	+	0.0544024i
$206$	−10.0260	−	5.78854i	−0.698547	−	0.403306i
$207$	12.2421	−	11.9336i	0.850882	−	0.829443i
$208$	1.31678	−	4.91427i	0.0913019	−	0.340743i
$209$	−3.00546	−	17.0448i	−0.207892	−	1.17901i
$210$	−7.59229	+	15.4178i	−0.523918	+	1.06393i
$211$	14.6011	−	5.31436i	1.00518	−	0.365856i	0.213600	−	0.976921i	$-0.431481\pi$
$211$	14.6011	−	5.31436i	1.00518	−	0.365856i	0.791580	+	0.611065i	$0.209259\pi$
$212$	−6.49955	+	4.55103i	−0.446391	+	0.312566i
$213$	8.55280	−	3.05132i	0.586028	−	0.209073i
$214$	−0.566528	−	0.675162i	−0.0387271	−	0.0461531i
$215$	−4.38332	−	0.840268i	−0.298940	−	0.0573058i
$216$	3.60325	+	3.74387i	0.245170	+	0.254738i
$217$	15.6076	−	15.6076i	1.05951	−	1.05951i
$218$	−1.68759	+	19.2893i	−0.114298	+	1.30643i
$219$	−0.555985	−	0.804909i	−0.0375700	−	0.0543907i
$220$	2.83826	+	6.33070i	0.191355	+	0.426815i
$221$	5.23368	+	14.3794i	0.352055	+	0.967265i
$222$	0.894440	+	0.524041i	0.0600309	+	0.0351713i
$223$	3.02226	−	4.31623i	0.202385	−	0.289036i	−0.705110	−	0.709098i	$-0.749103\pi$
$223$	3.02226	−	4.31623i	0.202385	−	0.289036i	0.907496	+	0.420061i	$0.137991\pi$
$224$	2.21868	+	3.84287i	0.148242	+	0.256762i
$225$	−13.2972	+	6.94144i	−0.886482	+	0.462762i
$226$	−6.51390	+	11.2824i	−0.433298	+	0.750495i
$227$	12.4885	+	26.7817i	0.828891	+	1.77756i	0.591821	+	0.806070i	$0.298409\pi$
$227$	12.4885	+	26.7817i	0.828891	+	1.77756i	0.237070	+	0.971493i	$0.423813\pi$
$228$	3.36242	−	9.05797i	0.222682	−	0.599879i
$229$	6.53349	−	7.78631i	0.431745	−	0.514534i	−0.505680	−	0.862721i	$-0.668758\pi$
$229$	6.53349	−	7.78631i	0.431745	−	0.514534i	0.937425	+	0.348187i	$0.113203\pi$
$230$	12.6763	+	1.29919i	0.835852	+	0.0856658i
$231$	−2.22985	+	23.7420i	−0.146713	+	1.56211i
$232$	1.11878	−	0.521697i	0.0734516	−	0.0342511i
$233$	1.64017	+	6.12119i	0.107451	+	0.401012i	0.998612	−	0.0526753i	$-0.0167748\pi$
$233$	1.64017	+	6.12119i	0.107451	+	0.401012i	−0.891161	+	0.453688i	$0.850108\pi$
$234$	15.0636	−	2.45840i	0.984738	−	0.160711i
$235$	5.91778	+	17.0431i	0.386033	+	1.11177i
$236$	−4.42548	+	0.780332i	−0.288074	+	0.0507953i
$237$	10.9146	+	0.0696247i	0.708982	+	0.00452261i
$238$	−12.0960	−	5.64045i	−0.784066	−	0.365616i
$239$	2.96781	−	16.8313i	0.191972	−	1.08873i	−0.724694	−	0.689071i	$-0.758019\pi$
$239$	2.96781	−	16.8313i	0.191972	−	1.08873i	0.916666	−	0.399655i	$-0.130870\pi$
$240$	−0.419439	+	3.85020i	−0.0270746	+	0.248530i
$241$	−0.980613	+	0.822832i	−0.0631668	+	0.0530032i	−0.673824	−	0.738891i	$-0.735350\pi$
$241$	−0.980613	+	0.822832i	−0.0631668	+	0.0530032i	0.610658	+	0.791895i	$0.290905\pi$
$242$	−0.971082	−	0.971082i	−0.0624235	−	0.0624235i
$243$	−5.79598	+	14.4709i	−0.371812	+	0.928308i
$244$			1.69038i			0.108216i
$245$	−27.2970	−	7.75092i	−1.74394	−	0.495188i
$246$	0.0502754	+	0.620191i	0.00320544	+	0.0395419i
$247$	−16.2783	−	23.2478i	−1.03576	−	1.47922i
$248$	2.10220	−	4.50819i	0.133490	−	0.286270i
$249$	−16.8026	−	17.0183i	−1.06482	−	1.07849i
$250$	−10.3252	−	4.28850i	−0.653020	−	0.271228i
$251$	5.83227	−	3.36726i	0.368129	−	0.212540i	−0.304511	−	0.952509i	$-0.598493\pi$
$251$	5.83227	−	3.36726i	0.368129	−	0.212540i	0.672641	+	0.739969i	$0.265160\pi$
$252$	−7.77399	+	10.8063i	−0.489716	+	0.680735i
$253$	17.0789	−	4.57627i	1.07374	−	0.287708i
$254$	10.2074	+	3.71519i	0.640470	+	0.233112i
$255$	−5.60884	−	10.2097i	−0.351239	−	0.639357i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.171851	−	1.96427i	−0.0107198	−	0.122528i	0.988949	−	0.148255i	$-0.0473655\pi$
$257$	−0.171851	−	1.96427i	−0.0107198	−	0.122528i	−0.999669	+	0.0257269i	$0.991810\pi$
$258$	−3.24103	−	1.20311i	−0.201778	−	0.0749021i
$259$	−0.908339	+	2.49564i	−0.0564414	+	0.155072i
$260$	8.60507	+	7.44127i	0.533664	+	0.461488i
$261$	2.80631	+	2.41645i	0.173706	+	0.149574i
$262$	−2.37314	−	0.635881i	−0.146613	−	0.0392848i
$263$	−0.156523	−	0.109599i	−0.00965163	−	0.00675815i	0.568741	−	0.822517i	$-0.307431\pi$
$263$	−0.156523	−	0.109599i	−0.00965163	−	0.00675815i	−0.578392	+	0.815759i	$0.696320\pi$
$264$	1.35776	+	5.19967i	0.0835642	+	0.320017i
$265$	−2.82080	−	17.5164i	−0.173280	−	1.07602i
$266$	24.3769	+	4.29831i	1.49465	+	0.263546i
$267$	−23.7872	−	4.35095i	−1.45575	−	0.266274i
$268$	8.65868	+	0.757536i	0.528913	+	0.0462739i
$269$	7.89719			0.481500			0.240750	−	0.970587i	$-0.422607\pi$
$269$	7.89719			0.481500			0.240750	+	0.970587i	$0.422607\pi$
$270$	−11.0470	+	3.60044i	−0.672301	+	0.219116i
$271$	1.68579			0.102404			0.0512022	−	0.998688i	$-0.483695\pi$
$271$	1.68579			0.102404			0.0512022	+	0.998688i	$0.483695\pi$
$272$	−2.99629	−	0.262142i	−0.181677	−	0.0158947i
$273$	13.1391	+	36.8286i	0.795213	+	2.22897i
$274$	6.85284	+	1.20834i	0.413995	+	0.0729985i
$275$	−15.5066	−	0.461179i	−0.935083	−	0.0278101i
$276$	9.51766	+	2.61543i	0.572896	+	0.157431i
$277$	21.9259	+	15.3527i	1.31740	+	0.922453i	0.999669	−	0.0257282i	$-0.00819046\pi$
$277$	21.9259	+	15.3527i	1.31740	+	0.922453i	0.317730	+	0.948181i	$0.397079\pi$
$278$	−14.8603	−	3.98181i	−0.891264	−	0.238813i
$279$	14.9215	+	0.190377i	0.893327	+	0.0113976i
$280$	−9.89625	+	0.717747i	−0.591414	+	0.0428936i
$281$	−1.59078	+	4.37064i	−0.0948981	+	0.260730i	−0.978055	−	0.208348i	$-0.933191\pi$
$281$	−1.59078	+	4.37064i	−0.0948981	+	0.260730i	0.883157	+	0.469078i	$0.155414\pi$
$282$	2.33884	+	13.7776i	0.139276	+	0.820444i
$283$	−2.80478	−	32.0588i	−0.166727	−	1.90570i	−0.374027	−	0.927418i	$-0.622023\pi$
$283$	−2.80478	−	32.0588i	−0.166727	−	1.90570i	0.207301	−	0.978277i	$-0.433532\pi$
$284$	4.01622	+	3.37001i	0.238319	+	0.199973i
$285$	14.9489	+	15.5979i	0.885494	+	0.923941i
$286$	14.8334	+	5.39890i	0.877115	+	0.319244i
$287$	−1.53977	+	0.412580i	−0.0908898	+	0.0243538i
$288$	−0.813362	+	2.88764i	−0.0479278	+	0.170156i
$289$	−6.88794	+	3.97675i	−0.405173	+	0.233927i
$290$	−0.0410330	+	2.75999i	−0.00240954	+	0.162072i
$291$	6.96965	−	25.3628i	0.408568	−	1.48680i
$292$	0.238695	−	0.511883i	0.0139686	−	0.0299557i
$293$	−1.28660	−	1.83746i	−0.0751642	−	0.107346i	0.779810	−	0.626017i	$-0.215316\pi$
$293$	−1.28660	−	1.83746i	−0.0751642	−	0.107346i	−0.854974	+	0.518671i	$0.826427\pi$
$294$	−19.8610	−	9.41605i	−1.15832	−	0.549155i
$295$	2.74470	−	9.66622i	0.159802	−	0.562789i
$296$			0.598510i			0.0347877i
$297$	−12.5462	+	10.1248i	−0.728007	+	0.587502i
$298$	10.8182	+	10.8182i	0.626683	+	0.626683i
$299$	22.2099	−	18.6363i	1.28443	−	1.07777i
$300$	−7.33878	−	4.59808i	−0.423705	−	0.265470i
$301$	1.53798	−	8.72231i	0.0886476	−	0.502745i
$302$	14.5308	+	6.77584i	0.836156	+	0.389906i
$303$	11.5262	−	19.6731i	0.662165	−	1.13019i
$304$	5.49356	−	0.968663i	0.315077	−	0.0555567i
$305$	−3.40154	−	1.64816i	−0.194772	−	0.0943735i
$306$	−2.97770	−	8.51773i	−0.170224	−	0.486926i
$307$	2.15073	+	8.02664i	0.122749	+	0.458104i	0.999749	−	0.0223847i	$-0.00712586\pi$
$307$	2.15073	+	8.02664i	0.122749	+	0.458104i	−0.877001	+	0.480489i	$0.840459\pi$
$308$	−12.4778	+	5.81851i	−0.710990	+	0.331540i
$309$	18.2270	−	8.35828i	1.03690	−	0.475486i
$310$	7.02210	+	8.62585i	0.398829	+	0.489915i
$311$	−1.22596	+	1.46104i	−0.0695177	+	0.0828479i	−0.799682	−	0.600423i	$-0.794999\pi$
$311$	−1.22596	+	1.46104i	−0.0695177	+	0.0828479i	0.730165	+	0.683271i	$0.239443\pi$
$312$	5.62109	+	6.78640i	0.318231	+	0.384204i
$313$	−3.35295	−	7.19043i	−0.189520	−	0.406427i	0.788472	−	0.615071i	$-0.210873\pi$
$313$	−3.35295	−	7.19043i	−0.189520	−	0.406427i	−0.977992	+	0.208644i	$0.933095\pi$
$314$	11.3877	−	19.7241i	0.642647	−	1.11310i
$315$	−14.1657	−	26.1800i	−0.798145	−	1.47508i
$316$	3.15085	+	5.45743i	0.177249	+	0.307004i
$317$	−9.55065	+	13.6397i	−0.536418	+	0.766084i	−0.992287	−	0.123963i	$-0.960440\pi$
$317$	−9.55065	+	13.6397i	−0.536418	+	0.766084i	0.455869	+	0.890047i	$0.349329\pi$
$318$	0.0876647	−	13.7427i	0.00491599	−	0.770650i
$319$	1.30997	+	3.59910i	0.0733440	+	0.201511i
$320$	−2.04039	+	0.914773i	−0.114061	+	0.0511374i
$321$	1.52157	−	0.123345i	0.0849259	−	0.00688447i
$322$	−2.20393	+	25.1911i	−0.122820	+	1.40384i
$323$	−11.8639	+	11.8639i	−0.660126	+	0.660126i
$324$	−8.90026	+	1.33620i	−0.494459	+	0.0742331i
$325$	−23.3642	+	10.0605i	−1.29601	+	0.558057i
$326$	−10.0581	−	11.9868i	−0.557068	−	0.663887i
$327$	−25.5533	−	21.7210i	−1.41310	−	1.20117i
$328$	−0.294274	+	0.206053i	−0.0162486	+	0.0113774i
$329$	−33.6428	+	12.2450i	−1.85479	+	0.675088i
$330$	−11.7871	−	2.33760i	−0.648859	−	0.128680i
$331$	1.08932	+	6.17783i	0.0598744	+	0.339564i	0.999999	−	0.00126593i	$-0.000402958\pi$
$331$	1.08932	+	6.17783i	0.0598744	+	0.339564i	−0.940125	+	0.340830i	$0.889292\pi$
$332$	3.57368	−	13.3371i	0.196131	−	0.731971i
$333$	−1.63685	+	0.738001i	−0.0896989	+	0.0404422i
$334$	−0.886117	−	0.511600i	−0.0484862	−	0.0279935i
$335$	−9.96681	+	16.6852i	−0.544545	+	0.911609i
$336$	−7.65206	−	0.718682i	−0.417454	−	0.0392073i
$337$	−10.2705	+	0.898553i	−0.559470	+	0.0489473i	−0.363384	−	0.931639i	$-0.618379\pi$
$337$	−10.2705	+	0.898553i	−0.559470	+	0.0489473i	−0.196086	+	0.980587i	$0.562823\pi$
$338$	12.8349	−	1.12291i	0.698128	−	0.0610783i
$339$	−9.40566	−	20.5111i	−0.510845	−	1.11401i
$340$	3.44897	−	5.77383i	0.187046	−	0.313130i
$341$	13.3658	+	7.71676i	0.723799	+	0.417886i
$342$	9.42309	+	13.8298i	0.509543	+	0.747830i
$343$	6.53503	−	24.3891i	0.352859	−	1.31689i
$344$	−0.346597	−	1.96565i	−0.0186873	−	0.105981i
$345$	−14.5430	+	16.6022i	−0.782967	+	0.893833i
$346$	0.948723	−	0.345307i	0.0510037	−	0.0185638i
$347$	10.5911	−	7.41594i	0.568558	−	0.398108i	−0.253650	−	0.967296i	$-0.581631\pi$
$347$	10.5911	−	7.41594i	0.568558	−	0.398108i	0.822208	+	0.569188i	$0.192742\pi$
$348$	−0.384703	+	2.10322i	−0.0206223	+	0.112744i
$349$	2.40775	+	2.86944i	0.128884	+	0.153598i	0.826627	−	0.562750i	$-0.190257\pi$
$349$	2.40775	+	2.86944i	0.128884	+	0.153598i	−0.697743	+	0.716348i	$0.745812\pi$
$350$	8.20477	−	20.6140i	0.438563	−	1.10186i
$351$	−11.6288	+	23.7411i	−0.620700	+	1.26720i
$352$	−2.19393	+	2.19393i	−0.116937	+	0.116937i
$353$	−2.49499	+	28.5179i	−0.132795	+	1.51785i	0.578919	+	0.815385i	$0.303475\pi$
$353$	−2.49499	+	28.5179i	−0.132795	+	1.51785i	−0.711714	+	0.702470i	$0.752081\pi$
$354$	3.33434	−	7.03304i	0.177218	−	0.373802i
$355$	−10.6974	+	4.79597i	−0.567757	+	0.254544i
$356$	−4.77507	−	13.1194i	−0.253078	−	0.695327i
$357$	20.0930	−	11.4304i	1.06343	−	0.604961i
$358$	5.24033	−	7.48397i	0.276960	−	0.395540i
$359$	9.70513	+	16.8098i	0.512217	+	0.887186i	0.999900	+	0.0141649i	$0.00450899\pi$
$359$	9.70513	+	16.8098i	0.512217	+	0.887186i	−0.487683	+	0.873021i	$0.662158\pi$
$360$	−5.01772	−	4.45224i	−0.264457	−	0.234654i
$361$	6.05877	−	10.4941i	0.318883	−	0.552321i
$362$	−0.207085	−	0.444096i	−0.0108842	−	0.0233411i
$363$	2.34511	−	0.398098i	0.123086	−	0.0208947i
$364$	−14.5113	+	17.2940i	−0.760601	+	0.906449i
$365$	0.797325	+	0.979422i	0.0417339	+	0.0512653i
$366$	−2.38757	−	1.69460i	−0.124800	−	0.0885779i
$367$	−14.6723	+	6.84182i	−0.765890	+	0.357140i	−0.765984	−	0.642860i	$-0.777748\pi$
$367$	−14.6723	+	6.84182i	−0.765890	+	0.357140i	9.42303e−5		1.00000i	$0.499970\pi$
$368$	1.47494	+	5.50454i	0.0768865	+	0.286944i
$369$	−0.926388	−	0.550726i	−0.0482258	−	0.0286697i
$370$	−1.20438	−	0.583562i	−0.0626126	−	0.0303379i
$371$	34.6733	−	6.11384i	1.80015	−	0.317415i
$372$	4.26013	+	7.48868i	0.220878	+	0.388270i
$373$	−2.93247	−	1.36743i	−0.151837	−	0.0708030i	0.345214	−	0.938524i	$-0.387806\pi$
$373$	−2.93247	−	1.36743i	−0.151837	−	0.0708030i	−0.497052	+	0.867721i	$0.665584\pi$
$374$	1.62050	−	9.19031i	0.0837940	−	0.475219i
$375$	16.4082	−	10.2845i	0.847314	−	0.531091i
$376$	−6.18068	+	5.18620i	−0.318744	+	0.267458i
$377$	4.44089	+	4.44089i	0.228718	+	0.228718i
$378$	−7.46998	−	21.8136i	−0.384214	−	1.12197i
$379$			34.2390i			1.75874i	0.476139	+	0.879370i	$0.342036\pi$
$379$			34.2390i			1.75874i	−0.476139	+	0.879370i	$0.657964\pi$
$380$	−3.40712	+	11.9991i	−0.174782	+	0.615543i
$381$	−15.4804	+	10.6930i	−0.793084	+	0.547817i
$382$	3.85298	+	5.50263i	0.197136	+	0.281539i
$383$	9.49994	−	20.3727i	0.485424	−	1.04100i	−0.499228	−	0.866471i	$-0.666383\pi$
$383$	9.49994	−	20.3727i	0.485424	−	1.04100i	0.984653	−	0.174526i	$-0.0558392\pi$
$384$	−1.67586	+	0.437607i	−0.0855208	+	0.0223315i
$385$	0.457643	−	30.7822i	0.0233237	−	1.56881i
$386$	7.09478	−	4.09618i	0.361115	−	0.208490i
$387$	4.94844	−	3.37168i	0.251543	−	0.171392i
$388$	14.6686	−	3.93044i	0.744686	−	0.199538i
$389$	1.45361	+	0.529072i	0.0737011	+	0.0268250i	0.378608	−	0.925557i	$-0.376403\pi$
$389$	1.45361	+	0.529072i	0.0737011	+	0.0268250i	−0.304906	+	0.952382i	$0.598625\pi$
$390$	−19.1369	+	4.69437i	−0.969036	+	0.237709i
$391$	−13.1302	−	11.0176i	−0.664023	−	0.557182i
$392$	−1.10602	−	12.6419i	−0.0558626	−	0.638512i
$393$	3.27720	−	2.71447i	0.165313	−	0.136927i
$394$	6.63883	−	18.2400i	0.334459	−	0.918920i
$395$	−14.0541	+	1.01930i	−0.707139	+	0.0512868i
$396$	−8.70540	−	3.29487i	−0.437463	−	0.165574i
$397$	−8.93003	−	2.39279i	−0.448185	−	0.120091i	0.0276648	−	0.999617i	$-0.491193\pi$
$397$	−8.93003	−	2.39279i	−0.448185	−	0.120091i	−0.475850	+	0.879526i	$0.657860\pi$
$398$	15.6912	+	10.9871i	0.786531	+	0.550735i
$399$	−30.5089	+	30.1221i	−1.52735	+	1.50799i
$400$	0.148638	−	4.99779i	0.00743192	−	0.249890i
$401$	−8.77551	−	1.54736i	−0.438228	−	0.0772714i	−0.0498185	−	0.998758i	$-0.515864\pi$
$401$	−8.77551	−	1.54736i	−0.438228	−	0.0772714i	−0.388410	+	0.921487i	$0.626975\pi$
$402$	−9.75025	+	11.4705i	−0.486298	+	0.572097i
$403$	25.2108	+	2.20566i	1.25584	+	0.109872i
$404$	13.1642			0.654942
$405$	5.98915	−	19.2128i	0.297603	−	0.954690i
$406$	−5.47766			−0.271851
$407$	−1.84992	−	0.161847i	−0.0916973	−	0.00802248i
$408$	3.37403	−	3.96931i	0.167039	−	0.196510i
$409$	10.9136	+	1.92436i	0.539642	+	0.0951534i	0.436824	−	0.899547i	$-0.356103\pi$
$409$	10.9136	+	1.92436i	0.539642	+	0.0951534i	0.102817	+	0.994700i	$0.467214\pi$
$410$	−0.127715	−	0.793072i	−0.00630737	−	0.0391670i
$411$	−8.57665	+	8.46792i	−0.423055	+	0.417692i
$412$	9.48338	+	6.64034i	0.467213	+	0.327146i
$413$	19.2610	+	5.16096i	0.947770	+	0.253954i
$414$	−13.2356	+	10.8212i	−0.650492	+	0.531835i
$415$	23.3538	+	20.1953i	1.14639	+	0.991350i
$416$	−1.74007	+	4.78081i	−0.0853140	+	0.234398i
$417$	20.5215	−	16.9977i	1.00494	−	0.832380i
$418$	1.50847	+	17.2419i	0.0737817	+	0.843329i
$419$	−16.3946	−	13.7567i	−0.800930	−	0.672060i	0.147494	−	0.989063i	$-0.452879\pi$
$419$	−16.3946	−	13.7567i	−0.800930	−	0.672060i	−0.948425	+	0.317002i	$0.897324\pi$
$420$	8.90715	−	14.6975i	0.434624	−	0.717163i
$421$	−5.73607	−	2.08776i	−0.279559	−	0.101751i	0.198436	−	0.980114i	$-0.436414\pi$
$421$	−5.73607	−	2.08776i	−0.279559	−	0.101751i	−0.477995	+	0.878363i	$0.658636\pi$
$422$	−15.0087	+	4.02157i	−0.730612	+	0.195767i
$423$	−21.8048	−	10.5085i	−1.06019	−	0.510939i
$424$	6.87147	−	3.96724i	0.333708	−	0.192666i
$425$	8.25582	+	12.5700i	0.400466	+	0.609733i
$426$	−8.78620	+	2.29429i	−0.425693	+	0.111158i
$427$	3.16999	−	6.79806i	0.153406	−	0.328981i
$428$	0.505528	+	0.721969i	0.0244356	+	0.0348977i
$429$	−22.4960	+	15.5390i	−1.08612	+	0.750228i
$430$	4.29341	+	1.21910i	0.207047	+	0.0587903i
$431$			6.37864i			0.307248i	0.988129	+	0.153624i	$0.0490945\pi$
$431$			6.37864i			0.307248i	−0.988129	+	0.153624i	$0.950905\pi$
$432$	−3.26324	−	4.04367i	−0.157003	−	0.194551i
$433$	−1.29802	−	1.29802i	−0.0623789	−	0.0623789i	0.675229	−	0.737608i	$-0.264045\pi$
$433$	−1.29802	−	1.29802i	−0.0623789	−	0.0623789i	−0.737608	+	0.675229i	$0.764045\pi$
$434$	−16.9085	+	14.1879i	−0.811634	+	0.681042i
$435$	−3.85720	−	2.82483i	−0.184938	−	0.135440i
$436$	3.36234	−	19.0688i	0.161027	−	0.913229i
$437$	28.8108	+	13.4347i	1.37821	+	0.642670i
$438$	0.483717	+	0.850303i	0.0231129	+	0.0406291i
$439$	36.5242	−	6.44020i	1.74320	−	0.307374i	0.790768	−	0.612116i	$-0.209681\pi$
$439$	36.5242	−	6.44020i	1.74320	−	0.307374i	0.952435	+	0.304742i	$0.0985701\pi$
$440$	−2.27570	−	6.55398i	−0.108490	−	0.312449i
$441$	33.2102	−	18.6131i	1.58144	−	0.886339i
$442$	−3.96052	−	14.7808i	−0.188383	−	0.703053i
$443$	8.63573	−	4.02691i	0.410296	−	0.191324i	−0.206501	−	0.978446i	$-0.566208\pi$
$443$	8.63573	−	4.02691i	0.410296	−	0.191324i	0.616797	+	0.787122i	$0.288430\pi$
$444$	−0.845363	−	0.600002i	−0.0401192	−	0.0284749i
$445$	31.0559	+	3.18289i	1.47219	+	0.150884i
$446$	−3.38694	+	4.03640i	−0.160376	+	0.191129i
$447$	−26.1254	+	4.43497i	−1.23569	+	0.209767i
$448$	−1.87531	−	4.02162i	−0.0886001	−	0.190004i
$449$	−10.1214	+	17.5309i	−0.477661	+	0.827333i	−0.999672	−	0.0256059i	$-0.991849\pi$
$449$	−10.1214	+	17.5309i	−0.477661	+	0.827333i	0.522011	+	0.852939i	$0.325182\pi$
$450$	13.8516	−	5.75609i	0.652972	−	0.271345i
$451$	−0.557308	−	0.965287i	−0.0262426	−	0.0454536i
$452$	7.47244	−	10.6718i	0.351474	−	0.501957i
$453$	−24.1376	+	13.7313i	−1.13408	+	0.645153i
$454$	−10.1068	−	27.7682i	−0.474336	−	1.30323i
$455$	−20.6516	−	46.0631i	−0.968162	−	2.15947i
$456$	−4.13908	+	8.73044i	−0.193830	+	0.408841i
$457$	2.16049	−	24.6946i	0.101064	−	1.15516i	−0.761135	−	0.648593i	$-0.775358\pi$
$457$	2.16049	−	24.6946i	0.101064	−	1.15516i	0.862199	−	0.506570i	$-0.169087\pi$
$458$	−7.18725	+	7.18725i	−0.335838	+	0.335838i
$459$	15.0160	+	4.33313i	0.700885	+	0.202253i
$460$	−12.5149	−	2.39906i	−0.583508	−	0.111857i
$461$	−22.7869	−	27.1564i	−1.06129	−	1.26480i	−0.962960	−	0.269644i	$-0.913094\pi$
$461$	−22.7869	−	27.1564i	−1.06129	−	1.26480i	−0.0983312	−	0.995154i	$-0.531350\pi$
$462$	4.29061	−	23.4573i	0.199617	−	1.09133i
$463$	20.2735	−	14.1957i	0.942190	−	0.659729i	0.00186244	−	0.999998i	$-0.499407\pi$
$463$	20.2735	−	14.1957i	0.942190	−	0.659729i	0.940328	+	0.340269i	$0.110518\pi$
$464$	−1.15999	+	0.422203i	−0.0538514	+	0.0196003i
$465$	−19.2232	+	1.27099i	−0.891453	+	0.0589407i
$466$	−1.10043	−	6.24085i	−0.0509764	−	0.289102i
$467$	−9.86375	+	36.8120i	−0.456440	+	1.70346i	0.227380	+	0.973806i	$0.426984\pi$
$467$	−9.86375	+	36.8120i	−0.456440	+	1.70346i	−0.683820	+	0.729651i	$0.739683\pi$
$468$	−15.2205	+	1.13616i	−0.703570	+	0.0525192i
$469$	−33.4013	−	19.2842i	−1.54233	−	0.890463i
$470$	−4.40985	−	17.4940i	−0.203411	−	0.806939i
$471$	16.4432	+	35.8579i	0.757660	+	1.65224i
$472$	4.47665	−	0.391656i	0.206055	−	0.0180274i
$473$	6.16932	−	0.539746i	0.283666	−	0.0248175i
$474$	−10.8670	−	1.02063i	−0.499139	−	0.0468792i
$475$	−20.8238	−	18.5556i	−0.955459	−	0.851389i
$476$	11.5583	+	6.67322i	0.529776	+	0.305866i
$477$	19.3229	+	13.9007i	0.884734	+	0.636472i
$478$	−4.42346	+	16.5086i	−0.202324	+	0.755085i
$479$	−3.17088	−	17.9830i	−0.144881	−	0.821663i	−0.967462	−	0.253015i	$-0.918578\pi$
$479$	−3.17088	−	17.9830i	−0.144881	−	0.821663i	0.822581	−	0.568648i	$-0.192533\pi$
$480$	0.753410	−	3.79900i	0.0343883	−	0.173400i
$481$	−2.86136	+	1.04145i	−0.130467	+	0.0474860i
$482$	1.04860	−	0.734235i	0.0477622	−	0.0334435i
$483$	−33.3716	−	28.3668i	−1.51846	−	1.29074i
$484$	0.882752	+	1.05202i	0.0401251	+	0.0478192i
$485$	−6.39305	+	33.3498i	−0.290293	+	1.51434i
$486$	7.03515	−	13.9107i	0.319121	−	0.631001i
$487$	14.7251	−	14.7251i	0.667257	−	0.667257i	−0.289823	−	0.957080i	$-0.593597\pi$
$487$	14.7251	−	14.7251i	0.667257	−	0.667257i	0.957080	+	0.289823i	$0.0935966\pi$
$488$	0.147326	−	1.68395i	0.00666915	−	0.0762287i
$489$	27.0139	−	2.18987i	1.22161	−	0.0990292i
$490$	26.5176	+	10.1005i	1.19794	+	0.456295i
$491$	4.42963	+	12.1703i	0.199907	+	0.549239i	0.998623	−	0.0524694i	$-0.0167092\pi$
$491$	4.42963	+	12.1703i	0.199907	+	0.549239i	−0.798716	+	0.601708i	$0.794487\pi$
$492$	0.00396911	−	0.622213i	0.000178941	−	0.0280515i
$493$	2.12962	−	3.04141i	0.0959131	−	0.136978i
$494$	14.1902	+	24.5781i	0.638447	+	1.10582i
$495$	15.1182	−	14.3052i	0.679514	−	0.642973i
$496$	−2.48712	+	4.30782i	−0.111675	+	0.193427i
$497$	−9.83189	−	21.0845i	−0.441020	−	0.945771i
$498$	15.2554	+	18.4180i	0.683612	+	0.825332i
$499$	−8.70391	+	10.3729i	−0.389640	+	0.464355i	−0.924832	−	0.380375i	$-0.875795\pi$
$499$	−8.70391	+	10.3729i	−0.389640	+	0.464355i	0.535192	+	0.844731i	$0.320239\pi$
$500$	9.91210	+	5.17207i	0.443282	+	0.231302i
$501$	1.61094	−	0.738718i	0.0719713	−	0.0330035i
$502$	−6.10355	+	2.84613i	−0.272415	+	0.127029i
$503$	−6.38589	−	23.8324i	−0.284733	−	1.06264i	−0.949035	−	0.315172i	$-0.897938\pi$
$503$	−6.38589	−	23.8324i	−0.284733	−	1.06264i	0.664302	−	0.747464i	$-0.268729\pi$
$504$	8.68625	−	10.0877i	0.386916	−	0.449340i
$505$	−12.8354	+	26.4902i	−0.571167	+	1.17880i
$506$	−17.4127	+	3.07034i	−0.774091	+	0.136493i
$507$	−11.2809	+	19.2544i	−0.501002	+	0.855117i
$508$	−9.84477	−	4.59069i	−0.436791	−	0.203679i
$509$	−3.22302	+	18.2786i	−0.142858	+	0.810187i	0.826205	+	0.563370i	$0.190496\pi$
$509$	−3.22302	+	18.2786i	−0.142858	+	0.810187i	−0.969062	+	0.246816i	$0.920616\pi$
$510$	4.69766	+	10.6597i	0.208016	+	0.472020i
$511$	−1.91988	+	1.61097i	−0.0849304	+	0.0712651i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−28.9804	−	0.554661i	−1.27952	−	0.0244889i
$514$			1.97177i			0.0869711i
$515$	−22.6088	+	12.6089i	−0.996264	+	0.555613i
$516$	3.12384	+	1.48100i	0.137519	+	0.0651975i
$517$	−14.3586	−	20.5062i	−0.631490	−	0.901861i
$518$	1.12239	−	2.40698i	0.0493151	−	0.105756i
$519$	−0.463361	+	1.68619i	−0.0203393	+	0.0740155i
$520$	−7.92378	−	8.16294i	−0.347481	−	0.357969i
$521$	31.0099	−	17.9036i	1.35857	−	0.784371i	0.369139	−	0.929374i	$-0.379653\pi$
$521$	31.0099	−	17.9036i	1.35857	−	0.784371i	0.989431	+	0.145004i	$0.0463194\pi$
$522$	−2.58502	−	2.65184i	−0.113143	−	0.116068i
$523$	−3.95334	+	1.05929i	−0.172867	+	0.0463197i	−0.344214	−	0.938891i	$-0.611855\pi$
$523$	−3.95334	+	1.05929i	−0.172867	+	0.0463197i	0.171347	+	0.985211i	$0.445188\pi$
$524$	2.30869	+	0.840294i	0.100855	+	0.0367084i
$525$	20.8909	+	32.2542i	0.911755	+	1.40769i
$526$	0.146375	+	0.122824i	0.00638227	+	0.00535536i
$527$	−1.30396	−	14.9043i	−0.0568012	−	0.649240i
$528$	−0.899410	−	5.29822i	−0.0391418	−	0.230575i
$529$	−3.24079	+	8.90400i	−0.140904	+	0.387131i
$530$	1.28341	+	17.6956i	0.0557478	+	0.768647i
$531$	6.59114	+	11.7602i	0.286031	+	0.510347i
$532$	−23.9095	−	6.40654i	−1.03661	−	0.277759i
$533$	−1.49716	−	1.04832i	−0.0648490	−	0.0454078i
$534$	23.3175	+	6.40759i	1.00904	+	0.277283i
$535$	−1.94572	+	0.313334i	−0.0841207	+	0.0135466i
$536$	−8.55971	−	1.50931i	−0.369723	−	0.0651922i
$537$	5.31731	+	14.9043i	0.229459	+	0.643169i
$538$	−7.86713	−	0.688285i	−0.339176	−	0.0296741i
$539$	39.3737			1.69595
$540$	11.3188	−	2.62393i	0.487083	−	0.112916i
$541$	−0.366352			−0.0157507			−0.00787535	−	0.999969i	$-0.502507\pi$
$541$	−0.366352			−0.0157507			−0.00787535	+	0.999969i	$0.502507\pi$
$542$	−1.67938	−	0.146926i	−0.0721353	−	0.00631102i
$543$	0.834863	+	0.152706i	0.0358274	+	0.00655325i
$544$	2.96205	+	0.522288i	0.126997	+	0.0223929i
$545$	35.0936	+	25.3585i	1.50325	+	1.08624i
$546$	−9.87925	−	37.8336i	−0.422793	−	1.61913i
$547$	12.3209	+	8.62717i	0.526802	+	0.368871i	0.806516	−	0.591213i	$-0.201351\pi$
$547$	12.3209	+	8.62717i	0.526802	+	0.368871i	−0.279713	+	0.960084i	$0.590239\pi$
$548$	−6.72145	−	1.80101i	−0.287126	−	0.0769352i
$549$	4.78705	−	1.67350i	0.204306	−	0.0714231i
$550$	15.4074	+	1.81091i	0.656973	+	0.0772176i
$551$	−2.35518	+	6.47080i	−0.100334	+	0.275666i
$552$	−9.25349	−	3.43500i	−0.393855	−	0.146203i
$553$	−2.43713	−	27.8565i	−0.103637	−	1.18458i
$554$	−20.5044	−	17.2052i	−0.871148	−	0.730980i
$555$	2.03163	−	1.11610i	0.0862379	−	0.0473759i
$556$	14.4567	+	5.26183i	0.613103	+	0.223151i
$557$	−6.83257	+	1.83078i	−0.289505	+	0.0775727i	−0.400649	−	0.916232i	$-0.631215\pi$
$557$	−6.83257	+	1.83078i	−0.289505	+	0.0775727i	0.111144	+	0.993804i	$0.464549\pi$
$558$	−14.8481	−	1.49015i	−0.628571	−	0.0630829i
$559$	8.79429	−	5.07739i	0.371959	−	0.214751i
$560$	9.92115	+	0.147499i	0.419245	+	0.00623297i
$561$	11.3563	+	11.5021i	0.479462	+	0.485619i
$562$	1.96565	−	4.21536i	0.0829161	−	0.177814i
$563$	15.6316	+	22.3243i	0.658795	+	0.940857i	1.00000		0.000868128i	$0.000276334\pi$
$563$	15.6316	+	22.3243i	0.658795	+	0.940857i	−0.341204	+	0.939989i	$0.610835\pi$
$564$	−1.12915	−	13.9290i	−0.0475457	−	0.586517i
$565$	14.1889	+	25.4420i	0.596931	+	1.07035i
$566$			32.1812i			1.35268i
$567$	38.2992	+	11.3171i	1.60842	+	0.475273i
$568$	−3.70722	−	3.70722i	−0.155552	−	0.155552i
$569$	−32.3161	+	27.1164i	−1.35476	+	1.13678i	−0.377199	+	0.926132i	$0.623113\pi$
$569$	−32.3161	+	27.1164i	−1.35476	+	1.13678i	−0.977562	+	0.210647i	$0.932443\pi$
$570$	−13.5325	−	16.8414i	−0.566815	−	0.705410i
$571$	−5.32517	+	30.2005i	−0.222851	+	1.26385i	0.643899	+	0.765111i	$0.277316\pi$
$571$	−5.32517	+	30.2005i	−0.222851	+	1.26385i	−0.866750	+	0.498742i	$0.833795\pi$
$572$	−14.3064	−	6.67117i	−0.598179	−	0.278936i
$573$	−11.6348	−	0.0742184i	−0.486049	−	0.00310052i
$574$	1.56987	−	0.276810i	0.0655251	−	0.0115538i
$575$	17.0299	−	22.8444i	0.710196	−	0.952679i
$576$	1.06194	−	2.80576i	0.0442476	−	0.116907i
$577$	2.76612	+	10.3233i	0.115155	+	0.429765i	0.999298	−	0.0374510i	$-0.0119238\pi$
$577$	2.76612	+	10.3233i	0.115155	+	0.429765i	−0.884143	+	0.467216i	$0.845257\pi$
$578$	7.20832	−	3.36130i	0.299827	−	0.139811i
$579$	−1.32685	+	14.1274i	−0.0551419	+	0.587115i
$580$	0.281425	−	2.74591i	0.0116856	−	0.114018i
$581$	−39.3832	+	46.9351i	−1.63389	+	1.94720i
$582$	−9.15365	+	24.6589i	−0.379431	+	1.02214i
$583$	10.4041	+	22.3117i	0.430895	+	0.924057i
$584$	−0.282400	+	0.489131i	−0.0116858	+	0.0202404i
$585$	12.5541	−	31.7360i	0.519048	−	1.31212i
$586$	1.12156	+	1.94260i	0.0463313	+	0.0802482i
$587$	26.7496	−	38.2024i	1.10407	−	1.57678i	0.329662	−	0.944099i	$-0.393065\pi$
$587$	26.7496	−	38.2024i	1.10407	−	1.57678i	0.774412	−	0.632682i	$-0.218046\pi$
$588$	18.9648	+	11.1112i	0.782095	+	0.458219i
$589$	9.49032	+	26.0744i	0.391042	+	1.07438i
$590$	−3.57672	+	9.39022i	−0.147251	+	0.386589i
$591$	19.1077	+	27.6625i	0.785985	+	1.13788i
$592$	0.0521636	−	0.596232i	0.00214391	−	0.0245050i
$593$	−7.24736	+	7.24736i	−0.297613	+	0.297613i	−0.840078	−	0.542465i	$-0.817491\pi$
$593$	−7.24736	+	7.24736i	−0.297613	+	0.297613i	0.542465	+	0.840078i	$0.317491\pi$
$594$	13.3809	−	8.99282i	0.549027	−	0.368980i
$595$	−24.6981	+	16.7522i	−1.01253	+	0.686775i
$596$	−9.83419	−	11.7199i	−0.402824	−	0.480067i
$597$	−31.2491	+	11.1485i	−1.27894	+	0.456279i
$598$	−23.7497	+	16.6297i	−0.971196	+	0.680039i
$599$	21.6974	−	7.89721i	0.886532	−	0.322671i	0.141689	−	0.989911i	$-0.454747\pi$
$599$	21.6974	−	7.89721i	0.886532	−	0.322671i	0.744843	+	0.667240i	$0.232524\pi$
$600$	6.91010	+	5.22020i	0.282104	+	0.213114i
$601$	−1.22918	−	6.97100i	−0.0501391	−	0.284353i	0.949421	−	0.314006i	$-0.101671\pi$
$601$	−1.22918	−	6.97100i	−0.0501391	−	0.284353i	−0.999560	+	0.0296525i	$0.990560\pi$
$602$	−2.29232	+	8.55507i	−0.0934282	+	0.348679i
$603$	−6.42691	−	25.2708i	−0.261724	−	1.02911i
$604$	−13.8850	−	8.01650i	−0.564972	−	0.326187i
$605$	−2.97768	+	0.750608i	−0.121060	+	0.0305166i
$606$	−13.1970	+	18.5937i	−0.536091	+	0.755317i
$607$	36.7043	−	3.21121i	1.48978	−	0.130339i	0.687020	−	0.726638i	$-0.258918\pi$
$607$	36.7043	−	3.21121i	1.48978	−	0.130339i	0.802762	+	0.596299i	$0.203363\pi$
$608$	−5.55708	+	0.486182i	−0.225369	+	0.0197173i
$609$	5.49132	−	7.73690i	0.222519	−	0.313515i
$610$	3.24495	+	1.93835i	0.131384	+	0.0784817i
$611$	−35.5490	−	20.5243i	−1.43816	−	0.830322i
$612$	2.22400	+	8.74484i	0.0898998	+	0.353489i
$613$	−11.0838	+	41.3653i	−0.447671	+	1.67073i	0.261117	+	0.965307i	$0.415909\pi$
$613$	−11.0838	+	41.3653i	−0.447671	+	1.67073i	−0.708787	+	0.705422i	$0.750757\pi$
$614$	−1.44298	−	8.18354i	−0.0582339	−	0.330261i
$615$	1.24821	+	0.614660i	0.0503325	+	0.0247855i
$616$	12.9375	−	4.70885i	0.521265	−	0.189725i
$617$	−2.39325	+	1.67577i	−0.0963488	+	0.0674641i	−0.620758	−	0.784002i	$-0.713175\pi$
$617$	−2.39325	+	1.67577i	−0.0963488	+	0.0674641i	0.524409	+	0.851466i	$0.324286\pi$
$618$	−18.8862	+	6.73788i	−0.759713	+	0.271037i
$619$	−21.4009	−	25.5046i	−0.860175	−	1.02512i	−0.999392	−	0.0348549i	$-0.988903\pi$
$619$	−21.4009	−	25.5046i	−0.860175	−	1.02512i	0.139217	−	0.990262i	$-0.455541\pi$
$620$	−6.24359	−	9.20504i	−0.250749	−	0.369683i
$621$	−2.01586	−	29.5427i	−0.0808935	−	1.18551i
$622$	1.34863	−	1.34863i	0.0540752	−	0.0540752i
$623$	−5.39945	+	61.7160i	−0.216324	+	2.47260i
$624$	−5.00823	−	7.25049i	−0.200489	−	0.290252i
$625$	−20.0723	+	14.9032i	−0.802891	+	0.596126i
$626$	2.71351	+	7.45529i	0.108453	+	0.297973i
$627$	−25.8655	−	15.1543i	−1.03297	−	0.605203i
$628$	−13.0635	+	18.6566i	−0.521289	+	0.744478i
$629$	0.900081	+	1.55899i	0.0358886	+	0.0621608i
$630$	11.8300	+	27.3150i	0.471320	+	1.08826i
$631$	0.339476	−	0.587990i	0.0135143	−	0.0234075i	−0.859189	−	0.511658i	$-0.829031\pi$
$631$	0.339476	−	0.587990i	0.0135143	−	0.0234075i	0.872703	+	0.488251i	$0.162365\pi$
$632$	−2.66321	−	5.71127i	−0.105937	−	0.227182i
$633$	9.36588	−	25.2306i	0.372260	−	1.00283i
$634$	10.7031	−	12.7554i	0.425074	−	0.506583i
$635$	18.8367	−	15.3345i	0.747512	−	0.608532i
$636$	−1.28508	+	13.6827i	−0.0509568	+	0.542555i
$637$	58.5139	−	27.2855i	2.31841	−	1.08109i
$638$	−0.991298	−	3.69958i	−0.0392459	−	0.146468i
$639$	5.56755	−	14.7100i	0.220249	−	0.581920i
$640$	2.11235	−	0.733460i	0.0834981	−	0.0289926i
$641$	−0.101929	+	0.0179728i	−0.00402596	+	0.000709885i	−0.175661	−	0.984451i	$-0.556206\pi$
$641$	−0.101929	+	0.0179728i	−0.00402596	+	0.000709885i	0.171635	+	0.985161i	$0.445095\pi$
$642$	−1.52653	−	0.00973778i	−0.0602474	−	0.000384319i
$643$	−23.7203	−	11.0609i	−0.935436	−	0.436201i	−0.105726	−	0.994395i	$-0.533717\pi$
$643$	−23.7203	−	11.0609i	−0.935436	−	0.436201i	−0.829710	+	0.558194i	$0.811494\pi$
$644$	4.39109	−	24.9031i	0.173033	−	0.981321i
$645$	−6.02603	+	4.84207i	−0.237275	+	0.190656i
$646$	12.8528	−	10.7848i	0.505686	−	0.424321i
$647$	3.62858	+	3.62858i	0.142654	+	0.142654i	0.774827	−	0.632173i	$-0.217837\pi$
$647$	3.62858	+	3.62858i	0.142654	+	0.142654i	−0.632173	+	0.774827i	$0.717837\pi$
$648$	8.98285	−	0.555403i	0.352880	−	0.0218183i
$649$			13.9427i			0.547300i
$650$	24.1521	−	7.98590i	0.947324	−	0.313233i
$651$	−3.08901	−	38.1057i	−0.121068	−	1.49348i
$652$	8.97513	+	12.8178i	0.351493	+	0.501984i
$653$	7.31060	−	15.6776i	0.286086	−	0.613513i	−0.709773	−	0.704431i	$-0.751202\pi$
$653$	7.31060	−	15.6776i	0.286086	−	0.613513i	0.995858	+	0.0909179i	$0.0289801\pi$
$654$	23.5629	+	23.8655i	0.921383	+	0.933213i
$655$	−3.94194	+	3.82645i	−0.154025	+	0.149512i
$656$	0.311113	−	0.179621i	0.0121469	−	0.00701302i
$657$	−1.68593	−	0.169199i	−0.0657744	−	0.00660107i
$658$	34.5820	−	9.26623i	1.34815	−	0.361235i
$659$	−0.834066	−	0.303575i	−0.0324906	−	0.0118256i	0.325724	−	0.945465i	$-0.394392\pi$
$659$	−0.834066	−	0.303575i	−0.0324906	−	0.0118256i	−0.358214	+	0.933639i	$0.616614\pi$
$660$	11.5385	+	3.35602i	0.449136	+	0.130633i
$661$	20.3875	+	17.1071i	0.792980	+	0.665389i	0.946481	−	0.322759i	$-0.104610\pi$
$661$	20.3875	+	17.1071i	0.792980	+	0.665389i	−0.153501	+	0.988148i	$0.549055\pi$
$662$	−0.546740	−	6.24926i	−0.0212496	−	0.242885i
$663$	24.8476	+	9.22369i	0.964999	+	0.358218i
$664$	−4.72249	+	12.9749i	−0.183268	+	0.503525i
$665$	36.2042	−	41.8665i	1.40394	−	1.62351i
$666$	1.69494	−	0.592532i	0.0656777	−	0.0229602i
$667$	−6.79503	−	1.82072i	−0.263104	−	0.0704986i
$668$	0.838157	+	0.586884i	0.0324292	+	0.0227072i
$669$	−2.30581	−	8.83034i	−0.0891479	−	0.341401i
$670$	11.3831	−	15.7530i	0.439767	−	0.608593i
$671$	5.16505	+	0.910737i	0.199394	+	0.0351586i
$672$	7.56031	+	1.38287i	0.291645	+	0.0533453i
$673$	−11.6515	−	1.01938i	−0.449133	−	0.0392940i	−0.139654	−	0.990200i	$-0.544599\pi$
$673$	−11.6515	−	1.01938i	−0.449133	−	0.0392940i	−0.309479	+	0.950906i	$0.600155\pi$
$674$	10.3097			0.397116
$675$	−5.75599	+	25.3351i	−0.221548	+	0.975149i
$676$	−12.8840			−0.495537
$677$	−8.80303	−	0.770165i	−0.338328	−	0.0295999i	−0.0832740	−	0.996527i	$-0.526538\pi$
$677$	−8.80303	−	0.770165i	−0.338328	−	0.0295999i	−0.255054	+	0.966927i	$0.582093\pi$
$678$	7.58221	+	21.2528i	0.291193	+	0.816209i
$679$	−66.3623	−	11.7015i	−2.54675	−	0.449061i
$680$	−3.93906	+	5.45126i	−0.151056	+	0.209046i
$681$	49.3531	+	13.5621i	1.89122	+	0.519702i
$682$	−12.6424	−	8.85230i	−0.484102	−	0.338972i
$683$	9.23383	+	2.47420i	0.353323	+	0.0946725i	0.431115	−	0.902297i	$-0.358120\pi$
$683$	9.23383	+	2.47420i	0.353323	+	0.0946725i	−0.0777922	+	0.996970i	$0.524787\pi$
$684$	−8.18189	−	14.5984i	−0.312842	−	0.558185i
$685$	10.1777	−	11.7695i	0.388871	−	0.449690i
$686$	−8.63581	+	23.7267i	−0.329717	+	0.905890i
$687$	−2.94643	−	17.3568i	−0.112414	−	0.662202i
$688$	0.173961	+	1.98838i	0.00663219	+	0.0758062i
$689$	30.9235	+	25.9479i	1.17809	+	0.988535i
$690$	15.9346	−	15.2715i	0.606620	−	0.581377i
$691$	−22.9766	−	8.36278i	−0.874069	−	0.318135i	−0.134255	−	0.990947i	$-0.542864\pi$
$691$	−22.9766	−	8.36278i	−0.874069	−	0.318135i	−0.739814	+	0.672811i	$0.765087\pi$
$692$	−0.975208	+	0.261306i	−0.0370719	+	0.00993337i
$693$	28.8309	+	29.5760i	1.09519	+	1.12350i
$694$	−11.1971	+	6.46464i	−0.425036	+	0.245395i
$695$	−24.6840	+	23.9608i	−0.936318	+	0.908886i
$696$	0.566547	−	2.06169i	0.0214749	−	0.0781480i
$697$	−0.456642	+	0.979272i	−0.0172965	+	0.0370926i
$698$	−2.14850	−	3.06837i	−0.0813218	−	0.116140i
$699$	9.91804	+	4.70211i	0.375135	+	0.177850i
$700$	−9.97017	+	19.8205i	−0.376837	+	0.749143i
$701$		−	21.3548i		−	0.806559i	−0.915077	−	0.403280i	$-0.867870\pi$
$701$		−	21.3548i		−	0.806559i	0.915077	−	0.403280i	$-0.132130\pi$
$702$	13.6537	−	22.6372i	0.515327	−	0.854386i
$703$	−2.36080	−	2.36080i	−0.0890392	−	0.0890392i
$704$	2.37680	−	1.99437i	0.0895789	−	0.0751657i
$705$	29.1302	+	11.3090i	1.09711	+	0.425920i
$706$	4.97100	−	28.1919i	0.187086	−	1.06102i
$707$	−52.9412	−	24.6869i	−1.99106	−	0.928447i
$708$	−3.93462	+	6.71567i	−0.147872	+	0.252390i
$709$	31.1737	−	5.49676i	1.17075	−	0.206435i	0.445735	−	0.895165i	$-0.352942\pi$
$709$	31.1737	−	5.49676i	1.17075	−	0.206435i	0.725018	+	0.688730i	$0.241831\pi$
$710$	11.0747	−	3.84539i	0.415624	−	0.144315i
$711$	12.3357	−	14.3259i	0.462626	−	0.537264i
$712$	3.61347	+	13.4857i	0.135421	+	0.505397i
$713$	−25.6909	+	11.9799i	−0.962133	+	0.448650i
$714$	−21.0127	+	9.63570i	−0.786382	+	0.360607i
$715$	27.3734	−	22.2841i	1.02371	−	0.833377i
$716$	−5.87266	+	6.99876i	−0.219472	+	0.261556i
$717$	−18.8830	−	22.7976i	−0.705198	−	0.851394i
$718$	−8.20313	−	17.5917i	−0.306138	−	0.656515i
$719$	−4.10372	+	7.10784i	−0.153043	+	0.265078i	−0.932345	−	0.361571i	$-0.882241\pi$
$719$	−4.10372	+	7.10784i	−0.153043	+	0.265078i	0.779302	+	0.626649i	$0.215574\pi$
$720$	4.61059	+	4.87262i	0.171827	+	0.181592i
$721$	−25.6858	−	44.4892i	−0.956590	−	1.65686i
$722$	−6.95034	+	9.92611i	−0.258665	+	0.369412i
$723$	−0.0141432	+	2.21715i	−0.000525993	+	0.0824567i
$724$	0.167592	+	0.460454i	0.00622850	+	0.0171127i
$725$	5.25117	+	3.24364i	0.195024	+	0.120466i
$726$	−2.37088	+	0.192194i	−0.0879916	+	0.00713298i
$727$	−0.514111	+	5.87631i	−0.0190673	+	0.217940i	0.980683	+	0.195603i	$0.0626664\pi$
$727$	−0.514111	+	5.87631i	−0.0190673	+	0.217940i	−0.999750	+	0.0223375i	$0.992889\pi$
$728$	15.9634	−	15.9634i	0.591643	−	0.591643i
$729$	12.5954	+	23.8821i	0.466496	+	0.884523i
$730$	−0.708929	−	1.04519i	−0.0262386	−	0.0386841i
$731$	−3.85889	−	4.59885i	−0.142726	−	0.170095i
$732$	2.23079	+	1.89624i	0.0824525	+	0.0700870i
$733$	−33.2312	+	23.2687i	−1.22742	+	0.859449i	−0.993614	−	0.112834i	$-0.964007\pi$
$733$	−33.2312	+	23.2687i	−1.22742	+	0.859449i	−0.233807	+	0.972283i	$0.575118\pi$
$734$	15.2128	−	5.53701i	0.561515	−	0.204375i
$735$	−40.8502	+	27.3290i	−1.50678	+	1.00805i
$736$	−0.989573	−	5.61215i	−0.0364761	−	0.206866i
$737$	6.97978	−	26.0489i	0.257104	−	0.959524i
$738$	0.874864	+	0.629371i	0.0322042	+	0.0231675i
$739$	−5.31652	−	3.06949i	−0.195571	−	0.112913i	0.399017	−	0.916944i	$-0.369352\pi$
$739$	−5.31652	−	3.06949i	−0.195571	−	0.112913i	−0.594588	+	0.804031i	$0.702685\pi$
$740$	1.14893	+	0.686310i	0.0422357	+	0.0252292i
$741$	−48.9409	−	4.59653i	−1.79789	−	0.168858i
$742$	−35.0742	+	3.06860i	−1.28762	+	0.112652i
$743$	7.74465	−	0.677569i	0.284124	−	0.0248576i	0.0557968	−	0.998442i	$-0.482230\pi$
$743$	7.74465	−	0.677569i	0.284124	−	0.0248576i	0.228327	+	0.973585i	$0.426675\pi$
$744$	−3.59124	−	7.83148i	−0.131661	−	0.287116i
$745$	33.1725	−	8.36206i	1.21535	−	0.306362i
$746$	2.80213	+	1.61781i	0.102593	+	0.0592322i
$747$	−41.3079	+	3.08351i	−1.51138	+	0.112820i
$748$	−2.41532	+	9.01410i	−0.0883129	+	0.329588i
$749$	−0.679124	−	3.85151i	−0.0248147	−	0.140731i
$750$	−17.2421	+	8.81534i	−0.629592	+	0.321891i
$751$	−9.55059	+	3.47613i	−0.348506	+	0.126846i	−0.510341	−	0.859972i	$-0.670481\pi$
$751$	−9.55059	+	3.47613i	−0.348506	+	0.126846i	0.161835	+	0.986818i	$0.448259\pi$
$752$	6.60916	−	4.62779i	0.241011	−	0.168758i
$753$	2.09876	−	11.4742i	0.0764831	−	0.418142i
$754$	−4.03694	−	4.81104i	−0.147017	−	0.175208i
$755$	29.6698	−	20.1244i	1.07979	−	0.732402i
$756$	5.54037	+	22.3817i	0.201501	+	0.814014i
$757$	−29.0503	+	29.0503i	−1.05585	+	1.05585i	−0.0575070	+	0.998345i	$0.518315\pi$
$757$	−29.0503	+	29.0503i	−1.05585	+	1.05585i	−0.998345	+	0.0575070i	$0.981685\pi$
$758$	2.98413	−	34.1087i	0.108388	−	1.23888i
$759$	13.1195	−	27.6726i	0.476207	−	1.00445i
$760$	4.43995	−	11.6565i	0.161054	−	0.422827i
$761$	−12.8115	−	35.1993i	−0.464416	−	1.27597i	−0.922133	−	0.386874i	$-0.873555\pi$
$761$	−12.8115	−	35.1993i	−0.464416	−	1.27597i	0.457717	−	0.889098i	$-0.348667\pi$
$762$	16.3534	−	9.30307i	0.592422	−	0.337015i
$763$	−49.2819	+	70.3819i	−1.78413	+	2.54800i
$764$	−3.35873	−	5.81750i	−0.121515	−	0.210470i
$765$	−19.7657	−	4.05110i	−0.714629	−	0.146468i
$766$	−11.2394	+	19.4672i	−0.406096	+	0.703378i
$767$	9.66213	+	20.7205i	0.348879	+	0.748174i
$768$	1.70762	−	0.289881i	0.0616185	−	0.0104602i
$769$	1.89455	−	2.25784i	0.0683193	−	0.0814198i	−0.730802	−	0.682589i	$-0.760854\pi$
$769$	1.89455	−	2.25784i	0.0683193	−	0.0814198i	0.799122	+	0.601169i	$0.205298\pi$
$770$	−3.13875	+	30.6252i	−0.113113	+	1.10366i
$771$	−2.78502	−	1.97669i	−0.100300	−	0.0711887i
$772$	−7.42479	+	3.46224i	−0.267224	+	0.124609i
$773$	−5.09577	−	19.0177i	−0.183282	−	0.684018i	−0.994992	−	0.0999568i	$-0.968130\pi$
$773$	−5.09577	−	19.0177i	−0.183282	−	0.684018i	0.811710	−	0.584061i	$-0.198537\pi$
$774$	−5.22347	+	2.92756i	−0.187754	+	0.105229i
$775$	24.6109	−	3.58880i	0.884050	−	0.128913i
$776$	−14.9554	+	2.63703i	−0.536866	+	0.0946639i
$777$	2.27454	+	3.99830i	0.0815985	+	0.143438i
$778$	−1.40197	−	0.653750i	−0.0502631	−	0.0234381i
$779$	0.347985	−	1.97352i	0.0124678	−	0.0707087i
$780$	19.4733	−	3.00862i	0.697254	−	0.107726i
$781$	12.4611	−	10.4561i	0.445893	−	0.374148i
$782$	12.1200	+	12.1200i	0.433410	+	0.433410i
$783$	6.33704	−	0.992756i	0.226467	−	0.0354782i
$784$			12.6902i			0.453221i
$785$	−24.8053	−	44.4781i	−0.885339	−	1.58749i
$786$	−3.50131	+	2.41851i	−0.124888	+	0.0862654i
$787$	−7.86375	−	11.2306i	−0.280312	−	0.400328i	0.654164	−	0.756353i	$-0.273021\pi$
$787$	−7.86375	−	11.2306i	−0.280312	−	0.400328i	−0.934476	+	0.356025i	$0.884132\pi$
$788$	−8.20329	+	17.5920i	−0.292230	+	0.626689i
$789$	−0.320222	+	0.0836177i	−0.0114002	+	0.00297687i
$790$	14.0895	+	0.209470i	0.501281	+	0.00745260i
$791$	−50.0641	+	28.9045i	−1.78008	+	1.02773i
$792$	8.38510	+	4.04106i	0.297952	+	0.143593i
$793$	8.30699	−	2.22585i	0.294990	−	0.0790423i
$794$	8.68750	+	3.16199i	0.308308	+	0.112215i
$795$	−26.2807	−	15.9270i	−0.932079	−	0.564871i
$796$	−14.6739	−	12.3129i	−0.520104	−	0.436419i
$797$	−3.93848	−	45.0171i	−0.139508	−	1.59459i	−0.667021	−	0.745039i	$-0.732431\pi$
$797$	−3.93848	−	45.0171i	−0.139508	−	1.59459i	0.527513	−	0.849547i	$-0.323125\pi$
$798$	33.0181	−	27.3484i	1.16883	−	0.968124i
$799$	−8.29992	+	22.8038i	−0.293630	+	0.806742i
$800$	−0.583659	+	4.96582i	−0.0206355	+	0.175568i
$801$	−32.4260	+	26.5111i	−1.14572	+	0.936723i
$802$	8.60726	+	2.30631i	0.303933	+	0.0814385i
$803$	−1.43548	−	1.00513i	−0.0506570	−	0.0354704i
$804$	10.7129	−	10.5771i	0.377814	−	0.373024i
$805$	45.8310	+	33.1173i	1.61533	+	1.16723i
$806$	−24.9226	−	4.39453i	−0.877861	−	0.154791i
$807$	8.85892	−	10.4219i	0.311849	−	0.366869i
$808$	−13.1141	−	1.14733i	−0.461352	−	0.0403630i
$809$	−25.6186			−0.900702			−0.450351	−	0.892852i	$-0.648701\pi$
$809$	−25.6186			−0.900702			−0.450351	+	0.892852i	$0.648701\pi$
$810$	−7.64086	+	18.6177i	−0.268472	+	0.654158i
$811$	6.51385			0.228732			0.114366	−	0.993439i	$-0.463516\pi$
$811$	6.51385			0.228732			0.114366	+	0.993439i	$0.463516\pi$
$812$	5.45681	+	0.477409i	0.191497	+	0.0167538i
$813$	1.89109	−	2.22474i	0.0663234	−	0.0780249i
$814$	1.82878	+	0.322463i	0.0640986	+	0.0113023i
$815$	−34.5442	+	5.56291i	−1.21003	+	0.194860i
$816$	−3.70714	+	3.66014i	−0.129776	+	0.128131i
$817$	9.12057	+	6.38629i	0.319088	+	0.223428i
$818$	−10.7043	−	2.86822i	−0.374268	−	0.100285i
$819$	63.3418	+	23.9740i	2.21334	+	0.837720i
$820$	0.0581077	+	0.801185i	0.00202921	+	0.0279786i
$821$	4.38626	−	12.0512i	0.153082	−	0.420588i	−0.839319	−	0.543640i	$-0.817046\pi$
$821$	4.38626	−	12.0512i	0.153082	−	0.420588i	0.992400	+	0.123051i	$0.0392680\pi$
$822$	9.28204	−	7.68819i	0.323748	−	0.268156i
$823$	−2.88989	−	33.0316i	−0.100735	−	1.15141i	−0.863367	−	0.504576i	$-0.831649\pi$
$823$	−2.88989	−	33.0316i	−0.100735	−	1.15141i	0.762632	−	0.646832i	$-0.223907\pi$
$824$	−8.86855	−	7.44160i	−0.308951	−	0.259240i
$825$	−18.0036	+	19.9467i	−0.626806	+	0.694455i
$826$	−18.7379	−	6.82002i	−0.651973	−	0.237299i
$827$	38.6520	−	10.3568i	1.34406	−	0.360140i	0.486122	−	0.873891i	$-0.338411\pi$
$827$	38.6520	−	10.3568i	1.34406	−	0.360140i	0.857939	+	0.513751i	$0.171744\pi$
$828$	14.1283	−	9.62650i	0.490993	−	0.334544i
$829$	−5.73770	+	3.31267i	−0.199279	+	0.115054i	−0.596319	−	0.802748i	$-0.703371\pi$
$829$	−5.73770	+	3.31267i	−0.199279	+	0.115054i	0.397040	+	0.917801i	$0.370037\pi$
$830$	−21.5048	−	22.1539i	−0.746443	−	0.768973i
$831$	44.8570	−	11.7132i	1.55607	−	0.406327i
$832$	2.15012	−	4.61096i	0.0745422	−	0.159856i
$833$	−21.8927	−	31.2660i	−0.758537	−	1.08330i
$834$	−21.9248	+	15.1444i	−0.759195	+	0.524409i
$835$	−1.99821	+	1.11439i	−0.0691507	+	0.0385651i
$836$		−	17.3078i		−	0.598602i
$837$	16.9899	−	19.4783i	0.587257	−	0.673269i
$838$	15.1333	+	15.1333i	0.522770	+	0.522770i
$839$	23.7978	−	19.9687i	0.821591	−	0.689397i	−0.131753	−	0.991283i	$-0.542061\pi$
$839$	23.7978	−	19.9687i	0.821591	−	0.689397i	0.953344	+	0.301886i	$0.0976161\pi$
$840$	−10.1542	+	13.8652i	−0.350354	+	0.478396i
$841$	−4.77118	+	27.0587i	−0.164524	+	0.933060i
$842$	5.53228	+	2.57975i	0.190655	+	0.0889039i
$843$	3.98341	+	7.00225i	0.137196	+	0.241170i
$844$	15.3021	−	2.69817i	0.526720	−	0.0928749i
$845$	12.5622	−	25.9263i	0.432152	−	0.891893i
$846$	20.8060	+	12.3689i	0.715323	+	0.425251i
$847$	−1.57722	−	5.88626i	−0.0541939	−	0.202254i
$848$	−7.19109	+	3.35326i	−0.246943	+	0.115151i
$849$	−45.4543	−	32.2615i	−1.55999	−	1.10721i
$850$	−7.12886	−	13.2417i	−0.244518	−	0.454186i
$851$	2.19238	−	2.61278i	0.0751539	−	0.0895649i
$852$	8.95272	−	1.51979i	0.306715	−	0.0520671i
$853$	13.3417	+	28.6114i	0.456811	+	0.979635i	0.990949	+	0.134237i	$0.0428585\pi$
$853$	13.3417	+	28.6114i	0.456811	+	0.979635i	−0.534138	+	0.845397i	$0.679364\pi$
$854$	−3.75042	+	6.49591i	−0.128337	+	0.222285i
$855$	37.3539	−	2.23053i	1.27748	−	0.0762825i
$856$	−0.440681	−	0.763282i	−0.0150622	−	0.0260884i
$857$	7.77494	−	11.1038i	0.265587	−	0.379297i	−0.664103	−	0.747641i	$-0.731186\pi$
$857$	7.77494	−	11.1038i	0.265587	−	0.379297i	0.929690	+	0.368344i	$0.120075\pi$
$858$	23.7647	−	13.5192i	0.811314	−	0.461537i
$859$	12.4029	+	34.0766i	0.423181	+	1.16268i	0.949877	+	0.312625i	$0.101208\pi$
$859$	12.4029	+	34.0766i	0.423181	+	1.16268i	−0.526696	+	0.850054i	$0.676569\pi$
$860$	−4.17082	−	1.58866i	−0.142224	−	0.0541728i
$861$	−1.18280	+	2.49486i	−0.0403099	+	0.0850246i
$862$	0.555935	−	6.35437i	0.0189352	−	0.216431i
$863$	4.37666	−	4.37666i	0.148983	−	0.148983i	−0.628680	−	0.777664i	$-0.716405\pi$
$863$	4.37666	−	4.37666i	0.148983	−	0.148983i	0.777664	+	0.628680i	$0.216405\pi$
$864$	2.89840	+	4.31269i	0.0986054	+	0.146721i
$865$	0.425027	−	2.21719i	0.0144514	−	0.0753866i
$866$	1.17995	+	1.40621i	0.0400964	+	0.0477850i
$867$	−2.47865	+	13.5511i	−0.0841792	+	0.460218i
$868$	18.0807	−	12.6603i	0.613700	−	0.429717i
$869$	18.3731	−	6.68725i	0.623263	−	0.226849i
$870$	3.59632	+	3.15025i	0.121927	+	0.106804i
$871$	−7.67880	−	43.5486i	−0.260186	−	1.47559i
$872$	−5.01150	+	18.7032i	−0.169711	+	0.633369i
$873$	−25.6529	−	37.6494i	−0.868218	−	1.27424i
$874$	−27.5303	−	15.8946i	−0.931226	−	0.537644i
$875$	−30.1634	−	39.3884i	−1.01971	−	1.33157i
$876$	−0.407768	−	0.889226i	−0.0137772	−	0.0300442i
$877$	−37.0637	+	3.24266i	−1.25155	+	0.109497i	−0.693591	−	0.720369i	$-0.743972\pi$
$877$	−37.0637	+	3.24266i	−1.25155	+	0.109497i	−0.557962	+	0.829866i	$0.688417\pi$
$878$	−36.9465	+	3.23240i	−1.24688	+	0.109088i
$879$	−3.86818	−	0.363300i	−0.130471	−	0.0122538i
$880$	1.69582	+	6.72738i	0.0571662	+	0.226780i
$881$	20.4902	+	11.8301i	0.690334	+	0.398565i	0.803737	−	0.594985i	$-0.202842\pi$
$881$	20.4902	+	11.8301i	0.690334	+	0.398565i	−0.113403	+	0.993549i	$0.536175\pi$
$882$	−34.7061	+	15.6478i	−1.16862	+	0.526890i
$883$	−8.22323	+	30.6895i	−0.276734	+	1.03278i	0.677937	+	0.735120i	$0.262874\pi$
$883$	−8.22323	+	30.6895i	−0.276734	+	1.03278i	−0.954671	+	0.297664i	$0.903792\pi$
$884$	2.65721	+	15.0698i	0.0893716	+	0.506852i
$885$	−9.67754	−	14.4656i	−0.325307	−	0.486254i
$886$	−8.95384	+	3.25893i	−0.300810	+	0.109486i
$887$	−7.56247	+	5.29530i	−0.253923	+	0.177799i	−0.693607	−	0.720354i	$-0.743979\pi$
$887$	−7.56247	+	5.29530i	−0.253923	+	0.177799i	0.439684	+	0.898153i	$0.355090\pi$
$888$	0.789853	+	0.671397i	0.0265057	+	0.0225306i
$889$	30.9829	+	36.9240i	1.03913	+	1.23839i
$890$	−30.6603	−	5.87748i	−1.02774	−	0.197014i
$891$	−0.712429	+	27.9151i	−0.0238673	+	0.935192i
$892$	3.72585	−	3.72585i	0.124751	−	0.124751i
$893$	3.92266	−	44.8362i	0.131267	−	1.50039i
$894$	26.4125	−	2.14111i	0.883366	−	0.0716096i
$895$	−8.35758	−	18.6415i	−0.279363	−	0.623116i
$896$	1.51767	+	4.16976i	0.0507017	+	0.139302i
$897$	0.320331	−	50.2163i	0.0106955	−	1.67667i
$898$	11.6108	−	16.5820i	0.387459	−	0.553349i
$899$	−3.07020	−	5.31774i	−0.102397	−	0.177356i
$900$	−14.3006	+	4.52694i	−0.476686	+	0.150898i
$901$	11.9324	−	20.6676i	0.397527	−	0.688537i
$902$	0.471057	+	1.01019i	0.0156845	+	0.0336355i
$903$	−9.78554	−	11.8142i	−0.325642	−	0.393152i
$904$	−8.37411	+	9.97988i	−0.278519	+	0.331926i
$905$	−1.08998	−	0.111711i	−0.0362320	−	0.00371339i
$906$	25.2425	−	11.5753i	0.838626	−	0.384564i
$907$	−23.5402	+	10.9770i	−0.781639	+	0.364484i	−0.772125	−	0.635470i	$-0.780806\pi$
$907$	−23.5402	+	10.9770i	−0.781639	+	0.364484i	−0.00951394	+	0.999955i	$0.503028\pi$
$908$	7.64818	+	28.5434i	0.253814	+	0.947246i
$909$	−13.0327	−	37.2801i	−0.432267	−	1.23650i
$910$	16.5583	+	47.6878i	0.548904	+	1.58083i
$911$	−20.1917	+	3.56035i	−0.668982	+	0.117960i	−0.497816	−	0.867283i	$-0.665865\pi$
$911$	−20.1917	+	3.56035i	−0.668982	+	0.117960i	−0.171166	+	0.985242i	$0.554753\pi$
$912$	4.88424	−	8.33648i	0.161733	−	0.276048i
$913$	−38.8269	−	18.1053i	−1.28498	−	0.599198i
$914$	−4.30454	+	24.4123i	−0.142382	+	0.807487i
$915$	−5.99087	+	2.64013i	−0.198052	+	0.0872801i
$916$	7.78631	−	6.53349i	0.257267	−	0.215873i
$917$	−7.70884	−	7.70884i	−0.254568	−	0.254568i
$918$	−14.5812	−	5.62537i	−0.481250	−	0.185665i
$919$		−	28.4664i		−	0.939020i	−0.882927	−	0.469510i	$-0.844431\pi$
$919$		−	28.4664i		−	0.939020i	0.882927	−	0.469510i	$-0.155569\pi$
$920$	12.2581	+	3.48067i	0.404139	+	0.114754i
$921$	13.0054	+	6.16582i	0.428542	+	0.203171i
$922$	20.3333	+	29.0390i	0.669643	+	0.956349i
$923$	11.2727	−	24.1743i	0.371045	−	0.795708i
$924$	−6.31872	+	22.9941i	−0.207871	+	0.756449i
$925$	−2.50130	+	1.64282i	−0.0822421	+	0.0540157i
$926$	−21.4336	+	12.3747i	−0.704352	+	0.406658i
$927$	9.41636	−	33.4304i	0.309274	−	1.09800i
$928$	1.19238	−	0.319496i	0.0391417	−	0.0104880i
$929$	5.40638	+	1.96776i	0.177378	+	0.0645602i	0.429182	−	0.903218i	$-0.358802\pi$
$929$	5.40638	+	1.96776i	0.177378	+	0.0645602i	−0.251805	+	0.967778i	$0.581024\pi$
$930$	19.2608	+	0.409256i	0.631586	+	0.0134200i
$931$	54.2281	+	45.5028i	1.77726	+	1.49129i
$932$	0.552317	+	6.31301i	0.0180917	+	0.206789i
$933$	0.552875	+	3.25686i	0.0181003	+	0.106625i
$934$	13.0346	−	35.8122i	0.426505	−	1.17181i
$935$	−15.7840	−	13.6493i	−0.516193	−	0.446380i
$936$	15.2616	+	0.194717i	0.498842	+	0.00636451i
$937$	25.1757	+	6.74581i	0.822455	+	0.220376i	0.645419	−	0.763828i	$-0.276683\pi$
$937$	25.1757	+	6.74581i	0.822455	+	0.220376i	0.177035	+	0.984204i	$0.443349\pi$
$938$	31.5934	+	22.1220i	1.03156	+	0.722308i
$939$	−13.2505	−	3.64120i	−0.432413	−	0.118826i
$940$	2.86837	+	17.8118i	0.0935559	+	0.580956i
$941$	52.3223	+	9.22584i	1.70566	+	0.300754i	0.939666	−	0.342094i	$-0.111136\pi$
$941$	52.3223	+	9.22584i	1.70566	+	0.300754i	0.765994	+	0.642848i	$0.222247\pi$
$942$	−13.2554	−	37.1545i	−0.431883	−	1.21056i
$943$	2.03943	+	0.178427i	0.0664130	+	0.00581039i
$944$	−4.49375			−0.146259
$945$	−50.4405	−	10.6738i	−1.64083	−	0.347220i
$946$	−6.19289			−0.201348
$947$	51.1947	+	4.47895i	1.66360	+	0.145546i	0.879762	−	0.475414i	$-0.157702\pi$
$947$	51.1947	+	4.47895i	1.66360	+	0.145546i	0.783842	+	0.620961i	$0.213257\pi$
$948$	10.7367	+	1.96387i	0.348713	+	0.0637836i
$949$	−2.82984	−	0.498977i	−0.0918604	−	0.0161975i
$950$	19.1273	+	20.2999i	0.620571	+	0.658615i
$951$	7.28661	+	27.9048i	0.236284	+	0.904875i
$952$	−10.9328	−	7.65520i	−0.354333	−	0.248106i
$953$	−26.0061	−	6.96831i	−0.842419	−	0.225726i	−0.188295	−	0.982113i	$-0.560296\pi$
$953$	−26.0061	−	6.96831i	−0.842419	−	0.225726i	−0.654124	+	0.756387i	$0.726963\pi$
$954$	−18.0378	−	15.5320i	−0.583996	−	0.502865i
$955$	14.9814	−	1.08656i	0.484786	−	0.0351601i
$956$	5.84544	−	16.0602i	0.189055	−	0.519425i
$957$	6.21922	+	2.30865i	0.201039	+	0.0746279i
$958$	1.59150	+	18.1909i	0.0514189	+	0.587721i
$959$	23.6536	+	19.8478i	0.763816	+	0.640918i
$960$	−1.08165	+	3.71888i	−0.0349100	+	0.120026i
$961$	5.87963	+	2.14001i	0.189665	+	0.0690326i
$962$	2.94124	−	0.788103i	0.0948294	−	0.0254095i
$963$	1.54409	−	2.14638i	0.0497577	−	0.0691663i
$964$	−1.10860	+	0.640049i	−0.0357055	+	0.0206146i
$965$	0.272316	−	18.3166i	0.00876615	−	0.589633i
$966$	30.7723	+	31.1674i	0.990083	+	1.00280i
$967$	4.22001	−	9.04984i	0.135706	−	0.291023i	−0.826697	−	0.562647i	$-0.809783\pi$
$967$	4.22001	−	9.04984i	0.135706	−	0.291023i	0.962403	+	0.271624i	$0.0875607\pi$
$968$	−0.787703	−	1.12496i	−0.0253177	−	0.0361575i
$969$	2.34807	+	28.9655i	0.0754309	+	0.930506i
$970$	9.27535	−	32.6657i	0.297814	−	1.04883i
$971$			8.51742i			0.273337i	0.990617	+	0.136668i	$0.0436395\pi$
$971$			8.51742i			0.273337i	−0.990617	+	0.136668i	$0.956360\pi$
$972$	−8.22077	+	13.2446i	−0.263681	+	0.424820i
$973$	−48.2719	−	48.2719i	−1.54753	−	1.54753i
$974$	−15.9524	+	13.3857i	−0.511148	+	0.428904i
$975$	−12.9327	+	42.1194i	−0.414177	+	1.34890i
$976$	−0.293531	+	1.66470i	−0.00939571	+	0.0532857i
$977$	22.3736	+	10.4330i	0.715796	+	0.333781i	0.746168	−	0.665757i	$-0.231891\pi$
$977$	22.3736	+	10.4330i	0.715796	+	0.333781i	−0.0303720	+	0.999539i	$0.509669\pi$
$978$	−27.1020	−	0.172884i	−0.866626	−	0.00552822i
$979$	−42.6597	+	7.52206i	−1.36341	+	0.240406i
$980$	−25.5364	−	12.3732i	−0.815730	−	0.395249i
$981$	−57.3304	+	9.35639i	−1.83042	+	0.298726i
$982$	−3.35206	−	12.5101i	−0.106969	−	0.399213i
$983$	38.7656	−	18.0767i	1.23643	−	0.576557i	0.309182	−	0.951003i	$-0.399945\pi$
$983$	38.7656	−	18.0767i	1.23643	−	0.576557i	0.927249	+	0.374446i	$0.122167\pi$
$984$	−0.0581834	+	0.619499i	−0.00185482	+	0.0197489i
$985$	−27.4019	−	33.6601i	−0.873097	−	1.07250i
$986$	−2.38659	+	2.84423i	−0.0760045	+	0.0905786i
$987$	−21.5802	+	58.1346i	−0.686906	+	1.85045i
$988$	−11.9941	−	25.7213i	−0.381582	−	0.818305i
$989$	−5.68725	+	9.85061i	−0.180844	+	0.313231i
$990$	−16.3075	+	12.9332i	−0.518286	+	0.411043i
$991$	19.3895	+	33.5836i	0.615927	+	1.06682i	0.990221	+	0.139507i	$0.0445519\pi$
$991$	19.3895	+	33.5836i	0.615927	+	1.06682i	−0.374294	+	0.927310i	$0.622115\pi$
$992$	2.85310	−	4.07466i	0.0905862	−	0.129370i
$993$	9.37486	+	5.49261i	0.297502	+	0.174303i
$994$	7.95683	+	21.8612i	0.252375	+	0.693396i
$995$	39.0846	−	17.5229i	1.23907	−	0.555514i
$996$	−13.5921	−	19.6775i	−0.430683	−	0.623507i
$997$	−4.17803	+	47.7552i	−0.132320	+	1.51242i	0.582338	+	0.812947i	$0.302138\pi$
$997$	−4.17803	+	47.7552i	−0.132320	+	1.51242i	−0.714658	+	0.699474i	$0.753418\pi$
$998$	9.57484	−	9.57484i	0.303086	−	0.303086i
$999$	−0.862250	+	2.98803i	−0.0272804	+	0.0945370i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.113.7	✓	216
3.2	odd	2		810.2.s.a.773.15		216
5.2	odd	4	inner	270.2.r.a.167.11	yes	216
15.2	even	4		810.2.s.a.287.2		216
27.11	odd	18	inner	270.2.r.a.173.11	yes	216
27.16	even	9		810.2.s.a.683.2		216
135.92	even	36	inner	270.2.r.a.227.7	yes	216
135.97	odd	36		810.2.s.a.197.15		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.7	✓	216	1.1	even	1	trivial
270.2.r.a.167.11	yes	216	5.2	odd	4	inner
270.2.r.a.173.11	yes	216	27.11	odd	18	inner
270.2.r.a.227.7	yes	216	135.92	even	36	inner
810.2.s.a.197.15		216	135.97	odd	36
810.2.s.a.287.2		216	15.2	even	4
810.2.s.a.683.2		216	27.16	even	9
810.2.s.a.773.15		216	3.2	odd	2

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	270.2.r.a.113.7

Level	$270$
Weight	$2$
Character	270.113
Analytic conductor	$2.156$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$