LMFDB - Embedded newform 357.2.bj.a.257.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(26,357)] 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("357.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 20, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bj (of order $24$, degree $8$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$44$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			257.15
Character	$\chi$	$=$	357.257
Dual form			357.2.bj.a.332.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.306515 - 1.14393i) q^{2} +(1.72287 + 0.178077i) q^{3} +(0.517430 - 0.298738i) q^{4} +(3.08447 + 0.406079i) q^{5} +(-0.324378 - 2.02543i) q^{6} +(-2.23021 - 1.42343i) q^{7} +(-2.17516 - 2.17516i) q^{8} +(2.93658 + 0.613608i) q^{9} +(-0.480912 - 3.65289i) q^{10} +(-0.302788 + 0.0398628i) q^{11} +(0.944663 - 0.422545i) q^{12} -5.07508 q^{13} +(-0.944710 + 2.98751i) q^{14} +(5.24184 + 1.24890i) q^{15} +(-1.22403 + 2.12009i) q^{16} +(1.54930 + 3.82095i) q^{17} +(-0.198181 - 3.54731i) q^{18} +(-0.205928 - 0.768532i) q^{19} +(1.71731 - 0.711333i) q^{20} +(-3.58889 - 2.84954i) q^{21} +(0.138409 + 0.334149i) q^{22} +(3.80683 + 4.96116i) q^{23} +(-3.36018 - 4.13487i) q^{24} +(4.51945 + 1.21098i) q^{25} +(1.55559 + 5.80553i) q^{26} +(4.95008 + 1.58010i) q^{27} +(-1.57921 - 0.0702757i) q^{28} +(0.0644789 - 0.0267080i) q^{29} +(-0.178055 - 6.37910i) q^{30} +(-4.98730 + 6.49958i) q^{31} +(-3.14224 - 0.841960i) q^{32} +(-0.528763 + 0.0147589i) q^{33} +(3.89601 - 2.94347i) q^{34} +(-6.30101 - 5.29618i) q^{35} +(1.70278 - 0.559769i) q^{36} +(0.825075 - 6.26706i) q^{37} +(-0.816026 + 0.471133i) q^{38} +(-8.74372 - 0.903755i) q^{39} +(-5.82595 - 7.59252i) q^{40} +(-1.93309 + 4.66688i) q^{41} +(-2.15962 + 4.97886i) q^{42} +(6.17268 - 6.17268i) q^{43} +(-0.144763 + 0.111080i) q^{44} +(8.80862 + 3.08514i) q^{45} +(4.50836 - 5.87541i) q^{46} +(-10.3483 - 5.97457i) q^{47} +(-2.48639 + 3.43467i) q^{48} +(2.94769 + 6.34910i) q^{49} -5.54111i q^{50} +(1.98882 + 6.85891i) q^{51} +(-2.62600 + 1.51612i) q^{52} +(7.37703 + 1.97667i) q^{53} +(0.290254 - 6.14686i) q^{54} -0.950128 q^{55} +(1.75488 + 7.94727i) q^{56} +(-0.217929 - 1.36075i) q^{57} +(-0.0503158 - 0.0655728i) q^{58} +(-5.26719 - 1.41134i) q^{59} +(3.08538 - 0.919722i) q^{60} +(3.61600 - 2.77465i) q^{61} +(8.96373 + 3.71290i) q^{62} +(-5.67576 - 5.54849i) q^{63} +8.74871i q^{64} +(-15.6540 - 2.06088i) q^{65} +(0.178957 + 0.600343i) q^{66} +(-5.35595 - 9.27677i) q^{67} +(1.94312 + 1.51424i) q^{68} +(5.67522 + 9.22536i) q^{69} +(-4.12710 + 8.83126i) q^{70} +(1.68899 + 4.07758i) q^{71} +(-5.05284 - 7.72223i) q^{72} +(5.60776 + 4.30299i) q^{73} +(-7.42197 + 0.977121i) q^{74} +(7.57079 + 2.89118i) q^{75} +(-0.336143 - 0.336143i) q^{76} +(0.732023 + 0.342095i) q^{77} +(1.64625 + 10.2792i) q^{78} +(-9.88287 + 7.58339i) q^{79} +(-4.63643 + 6.04231i) q^{80} +(8.24697 + 3.60381i) q^{81} +(5.93110 + 0.780844i) q^{82} +(4.41883 + 4.41883i) q^{83} +(-2.70826 - 0.402297i) q^{84} +(3.22717 + 12.4148i) q^{85} +(-8.95312 - 5.16909i) q^{86} +(0.115845 - 0.0345323i) q^{87} +(0.745320 + 0.571904i) q^{88} +(6.23181 + 3.59794i) q^{89} +(0.829205 - 11.0221i) q^{90} +(11.3185 + 7.22403i) q^{91} +(3.45186 + 1.42981i) q^{92} +(-9.74991 + 10.3098i) q^{93} +(-3.66259 + 13.6690i) q^{94} +(-0.323094 - 2.45414i) q^{95} +(-5.26374 - 2.01015i) q^{96} +(8.24731 - 3.41615i) q^{97} +(6.35941 - 5.31804i) q^{98} +(-0.913619 - 0.0687327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) $ 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.306515	−	1.14393i	−0.216739	−	0.808880i	−0.985547	−	0.169401i	$-0.945817\pi$
$2$	−0.306515	−	1.14393i	−0.216739	−	0.808880i	0.768809	−	0.639479i	$-0.220850\pi$
$3$	1.72287	+	0.178077i	0.994701	+	0.102813i
$3$	1.72287	+	0.178077i	0.994701	+	0.102813i
$4$	0.517430	−	0.298738i	0.258715	−	0.149369i
$5$	3.08447	+	0.406079i	1.37942	+	0.181604i	0.783476	−	0.621423i	$-0.213445\pi$
$5$	3.08447	+	0.406079i	1.37942	+	0.181604i	0.595943	+	0.803027i	$0.296778\pi$
$6$	−0.324378	−	2.02543i	−0.132427	−	0.826877i
$7$	−2.23021	−	1.42343i	−0.842941	−	0.538006i
$7$	−2.23021	−	1.42343i	−0.842941	−	0.538006i
$8$	−2.17516	−	2.17516i	−0.769036	−	0.769036i
$9$	2.93658	+	0.613608i	0.978859	+	0.204536i
$10$	−0.480912	−	3.65289i	−0.152078	−	1.15514i
$11$	−0.302788	+	0.0398628i	−0.0912939	+	0.0120191i	−0.176035	−	0.984384i	$-0.556327\pi$
$11$	−0.302788	+	0.0398628i	−0.0912939	+	0.0120191i	0.0847408	+	0.996403i	$0.472994\pi$
$12$	0.944663	−	0.422545i	0.272701	−	0.121978i
$13$	−5.07508			−1.40757			−0.703787	−	0.710411i	$-0.748509\pi$
$13$	−5.07508			−1.40757			−0.703787	+	0.710411i	$0.748509\pi$
$14$	−0.944710	+	2.98751i	−0.252484	+	0.798444i
$15$	5.24184	+	1.24890i	1.35344	+	0.322463i
$16$	−1.22403	+	2.12009i	−0.306009	+	0.530023i
$17$	1.54930	+	3.82095i	0.375761	+	0.926717i
$17$	1.54930	+	3.82095i	0.375761	+	0.926717i
$18$	−0.198181	−	3.54731i	−0.0467117	−	0.836110i
$19$	−0.205928	−	0.768532i	−0.0472430	−	0.176313i	0.938273	−	0.345896i	$-0.112425\pi$
$19$	−0.205928	−	0.768532i	−0.0472430	−	0.176313i	−0.985516	+	0.169582i	$0.945758\pi$
$20$	1.71731	−	0.711333i	0.384002	−	0.159059i
$21$	−3.58889	−	2.84954i	−0.783160	−	0.621820i
$22$	0.138409	+	0.334149i	0.0295089	+	0.0712408i
$23$	3.80683	+	4.96116i	0.793780	+	1.03447i	0.998451	+	0.0556429i	$0.0177208\pi$
$23$	3.80683	+	4.96116i	0.793780	+	1.03447i	−0.204671	+	0.978831i	$0.565612\pi$
$24$	−3.36018	−	4.13487i	−0.685894	−	0.844027i
$25$	4.51945	+	1.21098i	0.903890	+	0.242197i
$26$	1.55559	+	5.80553i	0.305076	+	1.13856i
$27$	4.95008	+	1.58010i	0.952643	+	0.304091i
$28$	−1.57921	−	0.0702757i	−0.298443	−	0.0132809i
$29$	0.0644789	−	0.0267080i	0.0119734	−	0.00495956i	−0.376689	−	0.926340i	$-0.622937\pi$
$29$	0.0644789	−	0.0267080i	0.0119734	−	0.00495956i	0.388662	+	0.921380i	$0.372937\pi$
$30$	−0.178055	−	6.37910i	−0.0325082	−	1.16466i
$31$	−4.98730	+	6.49958i	−0.895746	+	1.16736i	0.0894613	+	0.995990i	$0.471485\pi$
$31$	−4.98730	+	6.49958i	−0.895746	+	1.16736i	−0.985207	+	0.171368i	$0.945181\pi$
$32$	−3.14224	−	0.841960i	−0.555474	−	0.148839i
$33$	−0.528763	+	0.0147589i	−0.0920458	+	0.00256920i
$34$	3.89601	−	2.94347i	0.668160	−	0.504800i
$35$	−6.30101	−	5.29618i	−1.06506	−	0.895217i
$36$	1.70278	−	0.559769i	0.283797	−	0.0932948i
$37$	0.825075	−	6.26706i	0.135641	−	1.03030i	−0.779283	−	0.626673i	$-0.784416\pi$
$37$	0.825075	−	6.26706i	0.135641	−	1.03030i	0.914924	−	0.403626i	$-0.132250\pi$
$38$	−0.816026	+	0.471133i	−0.132377	+	0.0764279i
$39$	−8.74372	−	0.903755i	−1.40012	−	0.144717i
$40$	−5.82595	−	7.59252i	−0.921163	−	1.20048i
$41$	−1.93309	+	4.66688i	−0.301897	+	0.728845i	0.698021	+	0.716077i	$0.254064\pi$
$41$	−1.93309	+	4.66688i	−0.301897	+	0.728845i	−0.999918	+	0.0127676i	$0.995936\pi$
$42$	−2.15962	+	4.97886i	−0.333237	+	0.768255i
$43$	6.17268	−	6.17268i	0.941325	−	0.941325i	−0.0570466	−	0.998372i	$-0.518168\pi$
$43$	6.17268	−	6.17268i	0.941325	−	0.941325i	0.998372	+	0.0570466i	$0.0181684\pi$
$44$	−0.144763	+	0.111080i	−0.0218238	+	0.0167460i
$45$	8.80862	+	3.08514i	1.31311	+	0.459905i
$46$	4.50836	−	5.87541i	0.664722	−	0.866283i
$47$	−10.3483	−	5.97457i	−1.50945	−	0.871480i	−0.999939	−	0.0110148i	$-0.996494\pi$
$47$	−10.3483	−	5.97457i	−1.50945	−	0.871480i	−0.509509	−	0.860465i	$-0.670173\pi$
$48$	−2.48639	+	3.43467i	−0.358880	+	0.495752i
$49$	2.94769	+	6.34910i	0.421099	+	0.907015i
$50$		−	5.54111i		−	0.783632i
$51$	1.98882	+	6.85891i	0.278491	+	0.960439i
$52$	−2.62600	+	1.51612i	−0.364160	+	0.210248i
$53$	7.37703	+	1.97667i	1.01331	+	0.271516i	0.727013	−	0.686624i	$-0.240908\pi$
$53$	7.37703	+	1.97667i	1.01331	+	0.271516i	0.286300	+	0.958140i	$0.407575\pi$
$54$	0.290254	−	6.14686i	0.0394986	−	0.836482i
$55$	−0.950128			−0.128115
$56$	1.75488	+	7.94727i	0.234506	+	1.06200i
$57$	−0.217929	−	1.36075i	−0.0288654	−	0.180236i
$58$	−0.0503158	−	0.0655728i	−0.00660679	−	0.00861014i
$59$	−5.26719	−	1.41134i	−0.685729	−	0.183741i	−0.100900	−	0.994897i	$-0.532172\pi$
$59$	−5.26719	−	1.41134i	−0.685729	−	0.183741i	−0.584830	+	0.811156i	$0.698839\pi$
$60$	3.08538	−	0.919722i	0.398320	−	0.118736i
$61$	3.61600	−	2.77465i	0.462981	−	0.355258i	−0.350780	−	0.936458i	$-0.614083\pi$
$61$	3.61600	−	2.77465i	0.462981	−	0.355258i	0.813761	+	0.581200i	$0.197417\pi$
$62$	8.96373	+	3.71290i	1.13840	+	0.471539i
$63$	−5.67576	−	5.54849i	−0.715079	−	0.699044i
$64$			8.74871i			1.09359i
$65$	−15.6540	−	2.06088i	−1.94163	−	0.255621i
$66$	0.178957	+	0.600343i	0.0220281	+	0.0738972i
$67$	−5.35595	−	9.27677i	−0.654333	−	1.13334i	−0.982061	−	0.188566i	$-0.939616\pi$
$67$	−5.35595	−	9.27677i	−0.654333	−	1.13334i	0.327727	−	0.944772i	$-0.393717\pi$
$68$	1.94312	+	1.51424i	0.235638	+	0.183628i
$69$	5.67522	+	9.22536i	0.683216	+	1.11060i
$70$	−4.12710	+	8.83126i	−0.493282	+	1.05554i
$71$	1.68899	+	4.07758i	0.200446	+	0.483919i	0.991856	−	0.127367i	$-0.0406525\pi$
$71$	1.68899	+	4.07758i	0.200446	+	0.483919i	−0.791410	+	0.611286i	$0.790653\pi$
$72$	−5.05284	−	7.72223i	−0.595482	−	0.910073i
$73$	5.60776	+	4.30299i	0.656339	+	0.503627i	0.882408	−	0.470485i	$-0.155921\pi$
$73$	5.60776	+	4.30299i	0.656339	+	0.503627i	−0.226069	+	0.974111i	$0.572588\pi$
$74$	−7.42197	+	0.977121i	−0.862787	+	0.113588i
$75$	7.57079	+	2.89118i	0.874199	+	0.333845i
$76$	−0.336143	−	0.336143i	−0.0385582	−	0.0385582i
$77$	0.732023	+	0.342095i	0.0834217	+	0.0389853i
$78$	1.64625	+	10.2792i	0.186401	+	1.16389i
$79$	−9.88287	+	7.58339i	−1.11191	+	0.853198i	−0.990240	−	0.139372i	$-0.955492\pi$
$79$	−9.88287	+	7.58339i	−1.11191	+	0.853198i	−0.121670	+	0.992571i	$0.538825\pi$
$80$	−4.63643	+	6.04231i	−0.518368	+	0.675551i
$81$	8.24697	+	3.60381i	0.916330	+	0.400424i
$82$	5.93110	+	0.780844i	0.654981	+	0.0862298i
$83$	4.41883	+	4.41883i	0.485030	+	0.485030i	0.906734	−	0.421704i	$-0.138568\pi$
$83$	4.41883	+	4.41883i	0.485030	+	0.485030i	−0.421704	+	0.906734i	$0.638568\pi$
$84$	−2.70826	−	0.402297i	−0.295496	−	0.0438942i
$85$	3.22717	+	12.4148i	0.350036	+	1.34657i
$86$	−8.95312	−	5.16909i	−0.965440	−	0.557397i
$87$	0.115845	−	0.0345323i	0.0124199	−	0.00370225i
$88$	0.745320	+	0.571904i	0.0794514	+	0.0609652i
$89$	6.23181	+	3.59794i	0.660571	+	0.381381i	0.792494	−	0.609879i	$-0.208782\pi$
$89$	6.23181	+	3.59794i	0.660571	+	0.381381i	−0.131924	+	0.991260i	$0.542115\pi$
$90$	0.829205	−	11.0221i	0.0874058	−	1.16183i
$91$	11.3185	+	7.22403i	1.18650	+	0.757284i
$92$	3.45186	+	1.42981i	0.359881	+	0.149068i
$93$	−9.74991	+	10.3098i	−1.01102	+	1.06908i
$94$	−3.66259	+	13.6690i	−0.377767	+	1.40985i
$95$	−0.323094	−	2.45414i	−0.0331487	−	0.251790i
$96$	−5.26374	−	2.01015i	−0.537228	−	0.205160i
$97$	8.24731	−	3.41615i	0.837388	−	0.346857i	0.0775647	−	0.996987i	$-0.475286\pi$
$97$	8.24731	−	3.41615i	0.837388	−	0.346857i	0.759823	+	0.650130i	$0.225286\pi$
$98$	6.35941	−	5.31804i	0.642397	−	0.537203i
$99$	−0.913619	−	0.0687327i	−0.0918222	−	0.00690790i
$100$	2.70027	−	0.723534i	0.270027	−	0.0723534i
$101$	1.17681	+	2.03829i	0.117097	+	0.202817i	0.918616	−	0.395152i	$-0.129308\pi$
$101$	1.17681	+	2.03829i	0.117097	+	0.202817i	−0.801519	+	0.597969i	$0.795975\pi$
$102$	7.23649	−	4.37743i	0.716520	−	0.433430i
$103$	−11.8926	−	6.86620i	−1.17181	−	0.676547i	−0.217707	−	0.976014i	$-0.569858\pi$
$103$	−11.8926	−	6.86620i	−1.17181	−	0.676547i	−0.954107	+	0.299467i	$0.903191\pi$
$104$	11.0391	+	11.0391i	1.08248	+	1.08248i
$105$	−9.91270	−	10.2467i	−0.967381	−	0.999975i
$106$		−	9.04467i		−	0.878496i
$107$	2.51551	−	19.1072i	0.243184	−	1.84716i	−0.238906	−	0.971043i	$-0.576789\pi$
$107$	2.51551	−	19.1072i	0.243184	−	1.84716i	0.482090	−	0.876122i	$-0.339878\pi$
$108$	3.03335	−	0.661184i	0.291885	−	0.0636225i
$109$	−2.71954	+	0.358035i	−0.260485	+	0.0342935i	−0.259638	−	0.965706i	$-0.583603\pi$
$109$	−2.71954	+	0.358035i	−0.260485	+	0.0342935i	−0.000847501		1.00000i	$0.500270\pi$
$110$	0.291228	+	1.08688i	0.0277675	+	0.103630i
$111$	2.53752	−	10.6504i	0.240851	−	1.01089i
$112$	5.74766	−	2.98592i	0.543103	−	0.282143i
$113$	−0.828642	+	2.00052i	−0.0779520	+	0.188193i	−0.958051	−	0.286597i	$-0.907476\pi$
$113$	−0.828642	+	2.00052i	−0.0779520	+	0.188193i	0.880099	+	0.474790i	$0.157476\pi$
$114$	−1.48981	+	0.666386i	−0.139533	+	0.0624128i
$115$	9.72746	+	16.8484i	0.907090	+	1.57113i
$116$	0.0253846	−	0.0330818i	0.00235690	−	0.00307157i
$117$	−14.9034	−	3.11411i	−1.37782	−	0.287899i
$118$			6.45788i			0.594496i
$119$	1.98359	−	10.7269i	0.181835	−	0.983329i
$120$	−8.68531	−	14.1184i	−0.792856	−	1.28883i
$121$	−10.5351	+	2.82287i	−0.957736	+	0.256625i
$122$	−4.28236	−	3.28597i	−0.387707	−	0.297498i
$123$	−4.16153	+	7.69621i	−0.375232	+	0.693944i
$124$	−0.638906	+	4.85297i	−0.0573754	+	0.435810i
$125$	−0.922984	−	0.382312i	−0.0825542	−	0.0341951i
$126$	−4.60737	+	8.19336i	−0.410457	+	0.729923i
$127$	−4.66809	+	4.66809i	−0.414226	+	0.414226i	−0.883208	−	0.468982i	$-0.844621\pi$
$127$	−4.66809	+	4.66809i	−0.414226	+	0.414226i	0.468982	+	0.883208i	$0.344621\pi$
$128$	3.72342	−	0.997688i	0.329107	−	0.0881840i
$129$	11.7340	−	9.53553i	1.03312	−	0.839556i
$130$	2.44067	+	18.5387i	0.214061	+	1.62595i
$131$	10.9167	+	1.43721i	0.953797	+	0.125570i	0.591332	−	0.806428i	$-0.298602\pi$
$131$	10.9167	+	1.43721i	0.953797	+	0.125570i	0.362464	+	0.931998i	$0.381935\pi$
$132$	−0.269189	+	0.165598i	−0.0234299	+	0.0144135i
$133$	−0.634690	+	2.00711i	−0.0550346	+	0.174039i
$134$	−8.97029	+	8.97029i	−0.774915	+	0.774915i
$135$	14.6267	+	6.88391i	1.25887	+	0.592473i
$136$	4.94121	−	11.6812i	0.423705	−	1.00165i
$137$	−9.07346	+	5.23857i	−0.775198	+	0.447561i	−0.834726	−	0.550666i	$-0.814374\pi$
$137$	−9.07346	+	5.23857i	−0.775198	+	0.447561i	0.0595276	+	0.998227i	$0.481041\pi$
$138$	8.81361	−	9.31975i	0.750264	−	0.793350i
$139$	−0.119840	−	0.289319i	−0.0101647	−	0.0245397i	0.918716	−	0.394920i	$-0.129228\pi$
$139$	−0.119840	−	0.289319i	−0.0101647	−	0.0245397i	−0.928880	+	0.370380i	$0.879228\pi$
$140$	−4.84250	−	0.858047i	−0.409266	−	0.0725182i
$141$	−16.7648	−	12.1362i	−1.41185	−	1.02205i
$142$	4.14676	−	3.18192i	0.347988	−	0.267021i
$143$	1.53667	−	0.202307i	0.128503	−	0.0169177i
$144$	−4.89538	+	5.47473i	−0.407948	+	0.456228i
$145$	0.209729	−	0.0561967i	0.0174171	−	0.00466688i
$146$	3.20345	−	7.73381i	0.265119	−	0.640055i
$147$	3.94787	+	11.4636i	0.325615	+	0.945503i
$148$	−1.44529	−	3.48925i	−0.118802	−	0.286814i
$149$	−1.31345	+	2.27495i	−0.107602	+	0.186372i	−0.914798	−	0.403911i	$-0.867650\pi$
$149$	−1.31345	+	2.27495i	−0.107602	+	0.186372i	0.807197	+	0.590283i	$0.200984\pi$
$150$	0.986745	−	9.54663i	0.0805674	−	0.779479i
$151$	2.19072	−	8.17586i	0.178278	−	0.665342i	−0.817692	−	0.575656i	$-0.804747\pi$
$151$	2.19072	−	8.17586i	0.178278	−	0.665342i	0.995970	−	0.0896864i	$-0.0285865\pi$
$152$	−1.22376	+	2.11961i	−0.0992598	+	0.171923i
$153$	2.20508	+	12.1712i	0.178270	+	0.983982i
$154$	0.166956	−	0.942239i	0.0134537	−	0.0759277i
$155$	−18.0225	+	18.0225i	−1.44761	+	1.44761i
$156$	−4.79424	+	2.14445i	−0.383847	+	0.171694i
$157$	−2.65465	−	4.59799i	−0.211864	−	0.366960i	0.740434	−	0.672129i	$-0.234620\pi$
$157$	−2.65465	−	4.59799i	−0.211864	−	0.366960i	−0.952298	+	0.305170i	$0.901287\pi$
$158$	11.7041	+	8.98088i	0.931129	+	0.714480i
$159$	12.3577	+	4.71923i	0.980028	+	0.374259i
$160$	−9.35025	−	3.87300i	−0.739202	−	0.306188i
$161$	−1.42818	−	16.4832i	−0.112556	−	1.29906i
$162$	1.59468	−	10.5386i	0.125290	−	0.827988i
$163$	−13.4157	−	17.4836i	−1.05080	−	1.36942i	−0.926121	−	0.377226i	$-0.876878\pi$
$163$	−13.4157	−	17.4836i	−1.05080	−	1.36942i	−0.124675	−	0.992198i	$-0.539789\pi$
$164$	0.393940	+	2.99227i	0.0307615	+	0.233657i
$165$	−1.63695	−	0.169196i	−0.127436	−	0.0131719i
$166$	3.70039	−	6.40926i	0.287206	−	0.497455i
$167$	−3.28642	+	1.36128i	−0.254311	+	0.105339i	−0.506197	−	0.862418i	$-0.668949\pi$
$167$	−3.28642	+	1.36128i	−0.254311	+	0.105339i	0.251886	+	0.967757i	$0.418949\pi$
$168$	1.60821	+	14.0046i	0.124076	+	1.08048i
$169$	12.7565			0.981266
$170$	13.2124	−	7.49696i	1.01335	−	0.574991i
$171$	−0.133145	−	2.38321i	−0.0101819	−	0.182249i
$172$	1.34991	−	5.03794i	0.102930	−	0.384140i
$173$	−1.33153	+	10.1140i	−0.101235	+	0.768954i	0.863243	+	0.504789i	$0.168430\pi$
$173$	−1.33153	+	10.1140i	−0.101235	+	0.768954i	−0.964477	+	0.264165i	$0.914904\pi$
$174$	−0.0750107	−	0.121934i	−0.00568655	−	0.00924377i
$175$	−8.35559	−	9.13388i	−0.631623	−	0.690456i
$176$	0.286110	−	0.690731i	0.0215664	−	0.0520658i
$177$	−8.82336	−	3.36952i	−0.663205	−	0.253269i
$178$	2.20564	−	8.23157i	0.165320	−	0.616982i
$179$	−0.535928	+	2.00011i	−0.0400571	+	0.149495i	−0.983058	−	0.183295i	$-0.941324\pi$
$179$	−0.535928	+	2.00011i	−0.0400571	+	0.149495i	0.943001	+	0.332791i	$0.107990\pi$
$180$	5.47949	−	1.03513i	0.408417	−	0.0771540i
$181$	8.39228	−	20.2608i	0.623793	−	1.50597i	−0.223423	−	0.974722i	$-0.571723\pi$
$181$	8.39228	−	20.2608i	0.623793	−	1.50597i	0.847216	−	0.531248i	$-0.178277\pi$
$182$	4.79448	−	15.1618i	0.355391	−	1.12387i
$183$	6.72400	−	4.13645i	0.497053	−	0.305775i
$184$	2.51085	−	19.0718i	0.185102	−	1.40599i
$185$	5.08984	−	18.9956i	0.374213	−	1.39658i
$186$	14.7822	+	7.99309i	1.08388	+	0.586082i
$187$	−0.621423	−	1.09518i	−0.0454429	−	0.0800873i
$188$	−7.13932			−0.520689
$189$	−8.79056	−	10.5701i	−0.639419	−	0.768859i
$190$	−2.70833	+	1.12183i	−0.196483	+	0.0813859i
$191$	4.36728	−	7.56435i	0.316005	−	0.547337i	−0.663645	−	0.748047i	$-0.730992\pi$
$191$	4.36728	−	7.56435i	0.316005	−	0.547337i	0.979651	+	0.200710i	$0.0643249\pi$
$192$	−1.55794	+	15.0729i	−0.112435	+	1.08779i
$193$	0.324171	+	2.46232i	0.0233343	+	0.177242i	0.999143	−	0.0413828i	$-0.0131763\pi$
$193$	0.324171	+	2.46232i	0.0233343	+	0.177242i	−0.975809	+	0.218625i	$0.929843\pi$
$194$	−6.43575	−	8.38724i	−0.462060	−	0.602168i
$195$	−26.6028	−	6.33825i	−1.90506	−	0.453891i
$196$	3.42194	+	2.40463i	0.244424	+	0.171759i
$197$	3.28149	+	1.35924i	0.233796	+	0.0968417i	0.496506	−	0.868033i	$-0.334616\pi$
$197$	3.28149	+	1.35924i	0.233796	+	0.0968417i	−0.262710	+	0.964875i	$0.584616\pi$
$198$	0.201412	+	1.06618i	0.0143138	+	0.0757703i
$199$	11.1716	+	8.57228i	0.791934	+	0.607673i	0.923484	−	0.383637i	$-0.125329\pi$
$199$	11.1716	+	8.57228i	0.791934	+	0.607673i	−0.131550	+	0.991310i	$0.541995\pi$
$200$	−7.19646	−	12.4646i	−0.508866	−	0.881382i
$201$	−7.57563	−	16.9365i	−0.534344	−	1.19461i
$202$	1.97095	−	1.97095i	0.138676	−	0.138676i
$203$	−0.181819	−	0.0322166i	−0.0127612	−	0.00226117i
$204$	3.07809	+	2.95486i	0.215510	+	0.206882i
$205$	−7.85768	+	13.6099i	−0.548804	+	0.950556i
$206$	−4.20918	+	15.7089i	−0.293268	+	1.09449i
$207$	8.13485	+	16.9047i	0.565411	+	1.17496i
$208$	6.21208	−	10.7596i	0.430730	−	0.746046i
$209$	0.0929882	+	0.224493i	0.00643213	+	0.0155285i
$210$	−8.68310	+	14.4802i	−0.599191	+	0.999228i
$211$	7.22776	−	17.4494i	0.497580	−	1.20126i	−0.453204	−	0.891407i	$-0.649719\pi$
$211$	7.22776	−	17.4494i	0.497580	−	1.20126i	0.950783	−	0.309857i	$-0.100281\pi$
$212$	4.40760	−	1.18101i	0.302715	−	0.0811123i
$213$	2.18379	+	7.32591i	0.149631	+	0.501963i
$214$	−22.6283	+	2.97908i	−1.54684	+	0.203645i
$215$	21.5461	−	16.5329i	1.46943	−	1.12753i
$216$	−7.33024	−	14.2042i	−0.498760	−	0.966474i
$217$	20.3744	−	7.39636i	1.38311	−	0.502098i
$218$	1.24315	+	3.00122i	0.0841965	+	0.203268i
$219$	8.89520	+	8.41211i	0.601082	+	0.568438i
$220$	−0.491624	+	0.283839i	−0.0331453	+	0.0191365i
$221$	−7.86283	−	19.3916i	−0.528911	−	1.30442i
$222$	−12.9611	+	0.361773i	−0.869893	+	0.0242806i
$223$	−10.8718	+	10.8718i	−0.728030	+	0.728030i	−0.970227	−	0.242197i	$-0.922132\pi$
$223$	−10.8718	+	10.8718i	−0.728030	+	0.728030i	0.242197	+	0.970227i	$0.422132\pi$
$224$	5.80938	+	6.35051i	0.388156	+	0.424311i
$225$	12.5287	+	6.32932i	0.835243	+	0.421954i
$226$	2.54244	+	0.334719i	0.169121	+	0.0222651i
$227$	−0.824041	−	6.25922i	−0.0546935	−	0.415439i	−0.996788	−	0.0800901i	$-0.974479\pi$
$227$	−0.824041	−	6.25922i	−0.0546935	−	0.415439i	0.942094	−	0.335349i	$-0.108854\pi$
$228$	−0.519272	−	0.638991i	−0.0343896	−	0.0423182i
$229$	4.51338	−	1.20936i	0.298253	−	0.0799166i	−0.106590	−	0.994303i	$-0.533993\pi$
$229$	4.51338	−	1.20936i	0.298253	−	0.0799166i	0.404842	+	0.914387i	$0.367326\pi$
$230$	16.2918	−	16.2918i	1.07425	−	1.07425i
$231$	1.20026	+	0.719742i	0.0789715	+	0.0473555i
$232$	−0.198346	−	0.0821578i	−0.0130221	−	0.00539392i
$233$	1.64126	−	12.4666i	0.107522	−	0.816714i	−0.849681	−	0.527298i	$-0.823205\pi$
$233$	1.64126	−	12.4666i	0.107522	−	0.816714i	0.957203	−	0.289417i	$-0.0934614\pi$
$234$	1.00578	+	18.0029i	0.0657502	+	1.17689i
$235$	−29.4928	−	22.6306i	−1.92390	−	1.47626i
$236$	−3.14702	+	0.843241i	−0.204854	+	0.0548903i
$237$	−18.3774	+	11.3053i	−1.19374	+	0.734359i
$238$	−12.8788	+	1.01885i	−0.834806	+	0.0660425i
$239$		−	2.62685i		−	0.169917i	−0.996384	−	0.0849586i	$-0.972924\pi$
$239$		−	2.62685i		−	0.169917i	0.996384	−	0.0849586i	$-0.0270758\pi$
$240$	−9.06397	+	9.58449i	−0.585077	+	0.618676i
$241$	−8.89670	+	11.5944i	−0.573087	+	0.746861i	−0.986514	−	0.163676i	$-0.947665\pi$
$241$	−8.89670	+	11.5944i	−0.573087	+	0.746861i	0.413427	+	0.910537i	$0.364332\pi$
$242$	6.45832	+	11.1861i	0.415157	+	0.719072i
$243$	13.5667	+	7.67750i	0.870306	+	0.492512i
$244$	1.04213	−	2.51592i	0.0667155	−	0.161066i
$245$	6.51384	+	20.7806i	0.416154	+	1.32763i
$246$	10.0795	+	2.40149i	0.642644	+	0.153113i
$247$	1.04510	+	3.90036i	0.0664981	+	0.248174i
$248$	24.9858	−	3.28945i	1.58660	−	0.208880i
$249$	6.82619	+	8.39997i	0.432592	+	0.532327i
$250$	−0.154430	+	1.17301i	−0.00976701	+	0.0741878i
$251$			8.06462i			0.509034i	0.967068	+	0.254517i	$0.0819166\pi$
$251$			8.06462i			0.509034i	−0.967068	+	0.254517i	$0.918083\pi$
$252$	−4.59435	−	1.17539i	−0.289417	−	0.0740423i
$253$	−1.35043	−	1.35043i	−0.0849007	−	0.0849007i
$254$	6.77080	+	3.90912i	0.424837	+	0.245280i
$255$	3.34922	+	21.9637i	0.209736	+	1.37542i
$256$	6.46614	+	11.1997i	0.404134	+	0.699980i
$257$	3.80303	−	1.01902i	0.237226	−	0.0635646i	−0.138247	−	0.990398i	$-0.544147\pi$
$257$	3.80303	−	1.01902i	0.237226	−	0.0635646i	0.375473	+	0.926833i	$0.377480\pi$
$258$	−14.5046	−	10.5000i	−0.903016	−	0.653703i
$259$	−10.7608	+	12.8024i	−0.668645	+	0.795505i
$260$	−8.71549	+	3.61007i	−0.540511	+	0.223887i
$261$	0.205736	−	0.0388655i	0.0127347	−	0.00240571i
$262$	−1.70206	−	12.9285i	−0.105154	−	0.798723i
$263$	3.82461	−	14.2736i	0.235836	−	0.880151i	−0.741935	−	0.670472i	$-0.766092\pi$
$263$	3.82461	−	14.2736i	0.235836	−	0.880151i	0.977770	−	0.209679i	$-0.0672418\pi$
$264$	1.18225	+	1.11804i	0.0727624	+	0.0688108i
$265$	21.9516	+	9.09264i	1.34847	+	0.558556i
$266$	2.49054	+	0.110830i	0.152705	+	0.00679544i
$267$	10.0959	+	7.30853i	0.617859	+	0.447275i
$268$	−5.54265	−	3.20005i	−0.338571	−	0.195474i
$269$	−10.0296	−	7.69600i	−0.611517	−	0.469233i	0.255976	−	0.966683i	$-0.417603\pi$
$269$	−10.0296	−	7.69600i	−0.611517	−	0.469233i	−0.867493	+	0.497450i	$0.834270\pi$
$270$	3.39139	−	18.8420i	0.206393	−	1.14669i
$271$	17.2212	+	9.94269i	1.04612	+	0.603975i	0.921560	−	0.388237i	$-0.126916\pi$
$271$	17.2212	+	9.94269i	1.04612	+	0.603975i	0.124557	+	0.992213i	$0.460249\pi$
$272$	−9.99716	−	1.39232i	−0.606167	−	0.0844218i
$273$	18.2139	+	14.4616i	1.10236	+	0.875258i
$274$	8.77369	+	8.77369i	0.530038	+	0.530038i
$275$	−1.41671	−	0.186513i	−0.0854307	−	0.0112472i
$276$	5.69249	+	3.07807i	0.342648	+	0.185278i
$277$	−5.77941	+	7.53188i	−0.347251	+	0.452547i	−0.934027	−	0.357203i	$-0.883730\pi$
$277$	−5.77941	+	7.53188i	−0.347251	+	0.452547i	0.586775	+	0.809750i	$0.300397\pi$
$278$	−0.294227	+	0.225769i	−0.0176466	+	0.0135407i
$279$	−18.6338	+	16.0263i	−1.11558	+	0.959467i
$280$	2.18567	+	25.2258i	0.130619	+	1.50753i
$281$	8.90961	+	8.90961i	0.531503	+	0.531503i	0.921019	−	0.389516i	$-0.127358\pi$
$281$	8.90961	+	8.90961i	0.531503	+	0.531503i	−0.389516	+	0.921019i	$0.627358\pi$
$282$	−8.74429	+	22.8976i	−0.520715	+	1.36353i
$283$	−13.4684	+	1.77315i	−0.800616	+	0.105403i	−0.519722	−	0.854336i	$-0.673964\pi$
$283$	−13.4684	+	1.77315i	−0.800616	+	0.105403i	−0.280894	+	0.959739i	$0.590631\pi$
$284$	2.09206	+	1.60529i	0.124141	+	0.0952566i
$285$	−0.119623	−	4.28571i	−0.00708588	−	0.253863i
$286$	−0.702437	−	1.69583i	−0.0415360	−	0.100277i
$287$	10.9542	−	7.65653i	0.646605	−	0.451950i
$288$	−8.71079	−	4.40058i	−0.513288	−	0.259307i
$289$	−12.1993	+	11.8396i	−0.717608	+	0.696447i
$290$	−0.128570	−	0.222690i	−0.00754990	−	0.0130768i
$291$	14.8174	−	4.41693i	0.868612	−	0.258925i
$292$	4.18709	+	0.551241i	0.245031	+	0.0322589i
$293$			28.0797i			1.64043i	0.572054	+	0.820216i	$0.306147\pi$
$293$			28.0797i			1.64043i	−0.572054	+	0.820216i	$0.693853\pi$
$294$	11.9035	−	8.02984i	0.694225	−	0.468310i
$295$	−15.6734	−	6.49213i	−0.912540	−	0.377986i
$296$	−15.4266	+	11.8372i	−0.896650	+	0.688024i
$297$	−1.56181	−	0.281112i	−0.0906254	−	0.0163118i
$298$	3.00498	+	0.805181i	0.174074	+	0.0466429i
$299$	−19.3200	−	25.1783i	−1.11730	−	1.45610i
$300$	4.78106	−	0.765701i	0.276034	−	0.0442078i
$301$	−22.5528	+	4.98000i	−1.29992	+	0.287043i
$302$	−10.0241			−0.576821
$303$	1.66452	+	3.72128i	0.0956240	+	0.213782i
$304$	1.88142	+	0.504125i	0.107907	+	0.0289136i
$305$	12.2802	−	7.08997i	0.703161	−	0.405970i
$306$	13.2471	−	6.25310i	0.757285	−	0.357466i
$307$		−	11.2866i		−	0.644158i	−0.946713	−	0.322079i	$-0.895618\pi$
$307$		−	11.2866i		−	0.644158i	0.946713	−	0.322079i	$-0.104382\pi$
$308$	0.480967	−	0.0416731i	0.0274056	−	0.00237454i
$309$	−19.2667	−	13.9474i	−1.09605	−	0.793439i
$310$	26.1407	+	15.0923i	1.48469	+	0.857187i
$311$	19.1995	−	25.0213i	1.08870	−	1.41883i	0.189188	−	0.981941i	$-0.439414\pi$
$311$	19.1995	−	25.0213i	1.08870	−	1.41883i	0.899517	−	0.436887i	$-0.143919\pi$
$312$	17.0532	+	20.9848i	0.965447	+	1.18803i
$313$	−0.211845	+	0.162555i	−0.0119742	+	0.00918813i	−0.614731	−	0.788737i	$-0.710736\pi$
$313$	−0.211845	+	0.162555i	−0.0119742	+	0.00918813i	0.602757	+	0.797925i	$0.294069\pi$
$314$	−4.44609	+	4.44609i	−0.250907	+	0.250907i
$315$	−15.2536	−	19.4190i	−0.859444	−	1.09414i
$316$	−2.84824	+	6.87626i	−0.160226	+	0.386820i
$317$	−2.09406	−	2.72904i	−0.117614	−	0.153278i	0.730836	−	0.682553i	$-0.239131\pi$
$317$	−2.09406	−	2.72904i	−0.117614	−	0.153278i	−0.848450	+	0.529275i	$0.822464\pi$
$318$	1.61065	−	15.5828i	0.0903206	−	0.873841i
$319$	−0.0184588	+	0.0106572i	−0.00103349	+	0.000596687i
$320$	−3.55266	+	26.9852i	−0.198600	+	1.50852i
$321$	7.73646	−	32.4713i	0.431807	−	1.81237i
$322$	−18.4179	+	6.68608i	−1.02639	+	0.372600i
$323$	2.61748	−	1.97753i	0.145641	−	0.110033i
$324$	5.34382	−	0.598966i	0.296879	−	0.0332759i
$325$	−22.9366	−	6.14584i	−1.27229	−	0.340910i
$326$	−15.8879	+	20.7056i	−0.879951	+	1.14677i
$327$	−4.74918	+	0.132560i	−0.262631	+	0.00733059i
$328$	14.3560	−	5.94645i	0.792678	−	0.328338i
$329$	14.5744	+	28.0546i	0.803514	+	1.54670i
$330$	0.308201	+	1.92441i	0.0169659	+	0.105936i
$331$	2.59624	+	9.68928i	0.142702	+	0.532571i	0.999847	+	0.0174958i	$0.00556937\pi$
$331$	2.59624	+	9.68928i	0.142702	+	0.532571i	−0.857145	+	0.515075i	$0.827764\pi$
$332$	3.60651	+	0.966361i	0.197933	+	0.0530359i
$333$	6.26841	−	17.8974i	0.343507	−	0.980774i
$334$	2.56454	+	3.34218i	0.140326	+	0.182876i
$335$	−12.7532	−	30.7889i	−0.696781	−	1.68218i
$336$	10.4342	−	4.12084i	0.569233	−	0.224810i
$337$	5.11219	−	2.11754i	0.278479	−	0.115350i	−0.239073	−	0.971002i	$-0.576844\pi$
$337$	5.11219	−	2.11754i	0.278479	−	0.115350i	0.517552	+	0.855652i	$0.326844\pi$
$338$	−3.91004	−	14.5925i	−0.212678	−	0.793726i
$339$	−1.78389	+	3.29907i	−0.0968876	+	0.179181i
$340$	5.37860	+	5.45969i	0.291695	+	0.296093i
$341$	1.25100	−	2.16680i	0.0677456	−	0.117339i
$342$	−2.68541	+	0.882799i	−0.145211	+	0.0477363i
$343$	2.46353	−	18.3557i	0.133018	−	0.991114i
$344$	−26.8532			−1.44783
$345$	13.7588	+	30.7600i	0.740751	+	1.65606i
$346$	11.9778	−	1.57691i	0.643933	−	0.0847754i
$347$	−0.672373	−	5.10718i	−0.0360949	−	0.274168i	−0.999969	−	0.00781150i	$-0.997513\pi$
$347$	−0.672373	−	5.10718i	−0.0360949	−	0.274168i	0.963875	−	0.266356i	$-0.0858198\pi$
$348$	0.0496255	−	0.0524754i	0.00266021	−	0.00281297i
$349$	16.9637	+	16.9637i	0.908047	+	0.908047i	0.996114	−	0.0880677i	$-0.0280692\pi$
$349$	16.9637	+	16.9637i	0.908047	+	0.908047i	−0.0880677	+	0.996114i	$0.528069\pi$
$350$	−7.88739	+	12.3579i	−0.421599	+	0.660555i
$351$	−25.1221	−	8.01916i	−1.34092	−	0.428031i
$352$	0.984994	+	0.129677i	0.0525003	+	0.00691180i
$353$	−5.30340	+	3.06192i	−0.282272	+	0.162970i	−0.634451	−	0.772963i	$-0.718774\pi$
$353$	−5.30340	+	3.06192i	−0.282272	+	0.162970i	0.352180	+	0.935932i	$0.385441\pi$
$354$	−1.15000	+	11.1261i	−0.0611218	+	0.591346i
$355$	3.55382	+	13.2630i	0.188617	+	0.703929i
$356$	4.29936			0.227866
$357$	5.32768	−	18.1278i	0.281970	−	0.959423i
$358$	2.45225			0.129606
$359$	−0.422896	−	1.57827i	−0.0223196	−	0.0832978i	0.953868	−	0.300227i	$-0.0970625\pi$
$359$	−0.422896	−	1.57827i	−0.0223196	−	0.0832978i	−0.976187	+	0.216929i	$0.930396\pi$
$360$	−12.4495	−	25.8709i	−0.656147	−	1.36351i
$361$	15.9062	−	9.18348i	0.837171	−	0.483341i
$362$	−25.7492	−	3.38995i	−1.35335	−	0.178172i
$363$	−18.6533	+	2.98739i	−0.979045	+	0.156797i
$364$	8.01462	+	0.356655i	0.420080	+	0.0186938i
$365$	15.5497	+	15.5497i	0.813906	+	0.813906i
$366$	−6.79281	−	6.42390i	−0.355066	−	0.335783i
$367$	−1.70261	−	12.9326i	−0.0888753	−	0.675075i	−0.976656	−	0.214809i	$-0.931087\pi$
$367$	−1.70261	−	12.9326i	−0.0888753	−	0.675075i	0.887781	−	0.460266i	$-0.152246\pi$
$368$	−15.1778	+	1.99820i	−0.791198	+	0.104163i
$369$	−8.54029	+	12.5185i	−0.444590	+	0.651687i
$370$	−23.2897			−1.21077
$371$	−13.6387	−	14.9091i	−0.708086	−	0.774041i
$372$	−1.96496	+	8.24727i	−0.101878	+	0.427601i
$373$	12.2301	−	21.1832i	0.633251	−	1.09682i	−0.353632	−	0.935385i	$-0.615053\pi$
$373$	12.2301	−	21.1832i	0.633251	−	1.09682i	0.986883	−	0.161438i	$-0.0516133\pi$
$374$	−1.06233	+	1.04655i	−0.0549318	+	0.0541159i
$375$	−1.52210	−	0.823038i	−0.0786010	−	0.0425015i
$376$	9.51348	+	35.5048i	0.490620	+	1.83102i
$377$	−0.327236	+	0.135545i	−0.0168535	+	0.00698095i
$378$	−9.39696	+	13.2956i	−0.483327	+	0.683854i
$379$	3.56389	+	8.60399i	0.183065	+	0.441957i	0.988595	−	0.150597i	$-0.0481196\pi$
$379$	3.56389	+	8.60399i	0.183065	+	0.441957i	−0.805531	+	0.592554i	$0.798120\pi$
$380$	−0.900324	−	1.17332i	−0.0461856	−	0.0601903i
$381$	−8.87380	+	7.21124i	−0.454618	+	0.369443i
$382$	−9.99171	−	2.67727i	−0.511220	−	0.136981i
$383$	−4.92914	−	18.3958i	−0.251867	−	0.939982i	−0.969806	−	0.243876i	$-0.921581\pi$
$383$	−4.92914	−	18.3958i	−0.251867	−	0.939982i	0.717939	−	0.696106i	$-0.245086\pi$
$384$	6.59264	−	1.05583i	0.336429	−	0.0538803i
$385$	2.11899	+	1.35244i	0.107994	+	0.0689268i
$386$	2.71736	−	1.12557i	0.138310	−	0.0572898i
$387$	21.9142	−	14.3389i	1.11396	−	0.728890i
$388$	3.24687	−	4.23140i	0.164835	−	0.214817i
$389$	−4.67502	−	1.25267i	−0.237033	−	0.0635127i	0.138347	−	0.990384i	$-0.455821\pi$
$389$	−4.67502	−	1.25267i	−0.237033	−	0.0635127i	−0.375380	+	0.926871i	$0.622488\pi$
$390$	0.903641	+	32.3744i	0.0457577	+	1.63934i
$391$	−13.0584	+	22.2321i	−0.660393	+	1.12432i
$392$	7.39862	−	20.2220i	0.373687	−	1.02137i
$393$	18.5521	+	4.42014i	0.935832	+	0.222967i
$394$	0.549046	−	4.17042i	0.0276605	−	0.210103i
$395$	−33.5629	+	19.3776i	−1.68873	+	0.974991i
$396$	−0.493267	+	0.237369i	−0.0247876	+	0.0119282i
$397$	−18.6551	−	24.3118i	−0.936271	−	1.22017i	−0.975289	−	0.220934i	$-0.929089\pi$
$397$	−18.6551	−	24.3118i	−0.936271	−	1.22017i	0.0390172	−	0.999239i	$-0.487577\pi$
$398$	6.38181	−	15.4071i	0.319891	−	0.772286i
$399$	−1.45091	+	3.34498i	−0.0726364	+	0.167458i
$400$	−8.09936	+	8.09936i	−0.404968	+	0.404968i
$401$	−12.6741	+	9.72516i	−0.632913	+	0.485651i	−0.874691	−	0.484680i	$-0.838936\pi$
$401$	−12.6741	+	9.72516i	−0.632913	+	0.485651i	0.241778	+	0.970331i	$0.422269\pi$
$402$	−17.0521	+	13.8573i	−0.850480	+	0.691137i
$403$	25.3110	−	32.9859i	1.26083	−	1.64314i
$404$	1.21783	+	0.703114i	0.0605893	+	0.0349813i
$405$	23.9741	+	14.4648i	1.19128	+	0.718761i
$406$	0.0188765	+	0.217862i	0.000936827	+	0.0108123i
$407$			1.93048i			0.0956903i
$408$	10.5932	−	19.2452i	0.524442	−	0.952782i
$409$	23.7829	−	13.7311i	1.17599	−	0.678958i	0.220906	−	0.975295i	$-0.429099\pi$
$409$	23.7829	−	13.7311i	1.17599	−	0.678958i	0.955083	+	0.296338i	$0.0957654\pi$
$410$	17.9772	+	4.81699i	0.887833	+	0.237894i
$411$	−16.5653	+	7.40961i	−0.817105	+	0.365489i
$412$	−8.20479			−0.404221
$413$	9.73800	+	10.6451i	0.479176	+	0.523809i
$414$	16.8444	−	14.4872i	0.827855	−	0.712009i
$415$	11.8354	+	15.4242i	0.580976	+	0.757142i
$416$	15.9471	+	4.27302i	0.781872	+	0.209502i
$417$	−0.154948	−	0.519800i	−0.00758782	−	0.0254547i
$418$	0.228302	−	0.175182i	0.0111666	−	0.00856845i
$419$	23.8135	+	9.86386i	1.16336	+	0.481881i	0.878994	−	0.476833i	$-0.158215\pi$
$419$	23.8135	+	9.86386i	1.16336	+	0.481881i	0.284370	+	0.958714i	$0.408215\pi$
$420$	−8.19020	−	2.34064i	−0.399641	−	0.114212i
$421$		−	22.0637i		−	1.07532i	−0.843161	−	0.537660i	$-0.819308\pi$
$421$		−	22.0637i		−	1.07532i	0.843161	−	0.537660i	$-0.180692\pi$
$422$	−22.1762	−	2.91956i	−1.07952	−	0.142122i
$423$	−26.7224	−	23.8945i	−1.29929	−	1.16179i
$424$	−11.7467	−	20.3458i	−0.570468	−	0.988080i
$425$	2.37488	+	19.1448i	0.115199	+	0.928658i
$426$	7.71096	−	4.74360i	0.373597	−	0.229828i
$427$	−12.0140	+	1.04094i	−0.581397	+	0.0503747i
$428$	−4.40645	−	10.6381i	−0.212994	−	0.514213i
$429$	2.68352	−	0.0749028i	0.129561	−	0.00361634i
$430$	−25.5166	−	19.5796i	−1.23052	−	0.944212i
$431$	−13.2905	+	1.74972i	−0.640180	+	0.0842813i	−0.443626	−	0.896212i	$-0.646308\pi$
$431$	−13.2905	+	1.74972i	−0.640180	+	0.0842813i	−0.196553	+	0.980493i	$0.562975\pi$
$432$	−9.40903	+	8.56051i	−0.452692	+	0.411868i
$433$	10.0272	+	10.0272i	0.481876	+	0.481876i	0.905730	−	0.423855i	$-0.139323\pi$
$433$	10.0272	+	10.0272i	0.481876	+	0.481876i	−0.423855	+	0.905730i	$0.639323\pi$
$434$	−14.7060	−	21.0398i	−0.705909	−	1.00994i
$435$	0.371344	−	0.0594719i	0.0178046	−	0.00285146i
$436$	−1.30021	+	0.997689i	−0.0622690	+	0.0477806i
$437$	3.02888	−	3.94731i	0.144891	−	0.188826i
$438$	6.89635	−	12.7539i	0.329520	−	0.609405i
$439$	−31.8808	−	4.19719i	−1.52159	−	0.200321i	−0.677098	−	0.735892i	$-0.736763\pi$
$439$	−31.8808	−	4.19719i	−1.52159	−	0.200321i	−0.844490	+	0.535572i	$0.820096\pi$
$440$	2.06668	+	2.06668i	0.0985253	+	0.0985253i
$441$	4.76027	+	20.4534i	0.226679	+	0.973969i
$442$	−19.7726	+	14.9383i	−0.940486	+	0.710544i
$443$	6.09031	+	3.51624i	0.289359	+	0.167062i	0.637653	−	0.770324i	$-0.279905\pi$
$443$	6.09031	+	3.51624i	0.289359	+	0.167062i	−0.348294	+	0.937385i	$0.613239\pi$
$444$	−1.86870	−	6.26890i	−0.0886846	−	0.297509i
$445$	17.7608	+	13.6284i	0.841943	+	0.646046i
$446$	15.7689	+	9.10421i	0.746681	+	0.431097i
$447$	−2.66802	+	3.68556i	−0.126193	+	0.174321i
$448$	12.4532	−	19.5115i	0.588357	−	0.921830i
$449$	13.1988	+	5.46710i	0.622888	+	0.258009i	0.671728	−	0.740798i	$-0.265552\pi$
$449$	13.1988	+	5.46710i	0.622888	+	0.258009i	−0.0488401	+	0.998807i	$0.515552\pi$
$450$	3.40007	−	16.2719i	0.160281	−	0.767065i
$451$	0.399280	−	1.49013i	0.0188014	−	0.0701676i
$452$	0.168867	+	1.28267i	0.00794285	+	0.0603319i
$453$	5.23025	−	13.6958i	0.245739	−	0.643487i
$454$	−6.90751	+	2.86119i	−0.324186	+	0.134282i
$455$	31.9781	+	26.8785i	1.49916	+	1.26008i
$456$	−2.48583	+	3.43389i	−0.116410	+	0.160807i
$457$	20.4136	−	5.46980i	0.954907	−	0.255867i	0.252464	−	0.967606i	$-0.418759\pi$
$457$	20.4136	−	5.46980i	0.954907	−	0.255867i	0.702443	+	0.711740i	$0.252092\pi$
$458$	−2.76684	−	4.79230i	−0.129286	−	0.223930i
$459$	1.63166	+	21.3621i	0.0761593	+	0.997096i
$460$	10.0665	+	5.81192i	0.469355	+	0.270982i
$461$	15.4525	+	15.4525i	0.719695	+	0.719695i	0.968543	−	0.248848i	$-0.0800519\pi$
$461$	15.4525	+	15.4525i	0.719695	+	0.719695i	−0.248848	+	0.968543i	$0.580052\pi$
$462$	0.455435	−	1.59363i	0.0211888	−	0.0741422i
$463$		−	14.1526i		−	0.657725i	−0.944378	−	0.328862i	$-0.893335\pi$
$463$		−	14.1526i		−	0.657725i	0.944378	−	0.328862i	$-0.106665\pi$
$464$	−0.0223010	+	0.169393i	−0.00103530	+	0.00786386i
$465$	−34.2599	+	27.8411i	−1.58877	+	1.29110i
$466$	−14.7640	+	1.94371i	−0.683928	+	0.0900408i
$467$	1.59480	+	5.95186i	0.0737983	+	0.275419i	0.992958	−	0.118466i	$-0.0377976\pi$
$467$	1.59480	+	5.95186i	0.0737983	+	0.275419i	−0.919160	+	0.393885i	$0.871131\pi$
$468$	−8.64175	+	2.84087i	−0.399465	+	0.131319i
$469$	−1.25994	+	28.3130i	−0.0581788	+	1.30737i
$470$	−16.8478	+	40.6742i	−0.777132	+	1.87616i
$471$	−3.75483	−	8.39449i	−0.173014	−	0.386798i
$472$	8.38710	+	14.5269i	0.386047	+	0.668654i
$473$	−1.62295	+	2.11507i	−0.0746234	+	0.0972511i
$474$	18.5654	+	17.5571i	0.852737	+	0.806426i
$475$		−	3.72272i		−	0.170810i
$476$	−2.17815	−	6.14296i	−0.0998354	−	0.281562i
$477$	20.4503	+	10.3312i	0.936356	+	0.473035i
$478$	−3.00493	+	0.805170i	−0.137442	+	0.0368276i
$479$	7.57695	+	5.81400i	0.346200	+	0.265648i	0.767194	−	0.641415i	$-0.221652\pi$
$479$	7.57695	+	5.81400i	0.346200	+	0.265648i	−0.420995	+	0.907063i	$0.638319\pi$
$480$	−15.4196	−	8.33775i	−0.703805	−	0.380564i
$481$	−4.18732	+	31.8059i	−0.190925	+	1.45022i
$482$	15.9901	+	6.62333i	0.728331	+	0.301685i
$483$	0.474712	−	28.6528i	0.0216002	−	1.30375i
$484$	−4.60787	+	4.60787i	−0.209449	+	0.209449i
$485$	26.8258	−	7.18796i	1.21810	−	0.326389i
$486$	4.62411	−	17.8726i	0.209754	−	0.810719i
$487$	−0.000628709	−	0.00477552i	−2.84895e−5	−	0.000216399i	0.991431	−	0.130634i	$-0.0417014\pi$
$487$	−0.000628709	−	0.00477552i	−2.84895e−5	−	0.000216399i	−0.991459	+	0.130418i	$0.958368\pi$
$488$	−13.9007	−	1.83006i	−0.629255	−	0.0828430i
$489$	−20.0000	−	32.5111i	−0.904433	−	1.47020i
$490$	21.7750	−	13.8209i	0.983693	−	0.624367i
$491$	−5.12548	+	5.12548i	−0.231310	+	0.231310i	−0.813239	−	0.581929i	$-0.802298\pi$
$491$	−5.12548	+	5.12548i	−0.231310	+	0.231310i	0.581929	+	0.813239i	$0.302298\pi$
$492$	0.145854	+	5.22545i	0.00657560	+	0.235582i
$493$	0.201947	+	0.204992i	0.00909525	+	0.00923237i
$494$	4.14140	−	2.39104i	0.186330	−	0.107578i
$495$	−2.79012	−	0.583006i	−0.125407	−	0.0262042i
$496$	−7.67506	−	18.5292i	−0.344620	−	0.831987i
$497$	2.03735	−	11.4980i	0.0913875	−	0.515756i
$498$	7.51664	−	10.3834i	0.336829	−	0.465291i
$499$	19.5992	−	15.0390i	0.877379	−	0.673237i	−0.0685366	−	0.997649i	$-0.521833\pi$
$499$	19.5992	−	15.0390i	0.877379	−	0.673237i	0.945916	+	0.324412i	$0.105166\pi$
$500$	−0.591791	+	0.0779107i	−0.0264657	+	0.00348427i
$501$	−5.90449	+	1.76008i	−0.263793	+	0.0786344i
$502$	9.22535	−	2.47193i	0.411748	−	0.110327i
$503$	−6.21482	+	15.0039i	−0.277105	+	0.668990i	−0.999753	−	0.0222257i	$-0.992925\pi$
$503$	−6.21482	+	15.0039i	−0.277105	+	0.668990i	0.722648	+	0.691216i	$0.242925\pi$
$504$	0.276841	+	24.4146i	0.0123315	+	1.08751i
$505$	2.80213	+	6.76493i	0.124693	+	0.301035i
$506$	−1.13087	+	1.95872i	−0.0502732	+	0.0870757i
$507$	21.9777	+	2.27163i	0.976066	+	0.100887i
$508$	−1.02087	+	3.80994i	−0.0452938	+	0.169039i
$509$	−12.3811	+	21.4446i	−0.548781	+	0.950517i	0.449577	+	0.893241i	$0.351575\pi$
$509$	−12.3811	+	21.4446i	−0.548781	+	0.950517i	−0.998358	+	0.0572754i	$0.981759\pi$
$510$	24.0984	−	10.5635i	1.06709	−	0.467759i
$511$	−6.38150	−	17.5788i	−0.282301	−	0.777642i
$512$	16.2811	−	16.2811i	0.719531	−	0.719531i
$513$	0.195003	−	4.12968i	0.00860960	−	0.182330i
$514$	−2.33137	−	4.03805i	−0.102832	−	0.178111i
$515$	−33.8942	−	26.0080i	−1.49356	−	1.14605i
$516$	3.22287	−	8.43934i	0.141879	−	0.371521i
$517$	3.37149	+	1.39652i	0.148278	+	0.0614187i
$518$	17.9434	+	8.38547i	0.788389	+	0.368437i
$519$	−4.09514	+	17.1880i	−0.179757	+	0.754471i
$520$	29.5671	+	38.5327i	1.29661	+	1.68977i
$521$	−5.35890	−	40.7049i	−0.234778	−	1.78331i	−0.550875	−	0.834588i	$-0.685706\pi$
$521$	−5.35890	−	40.7049i	−0.234778	−	1.78331i	0.316097	−	0.948727i	$-0.397628\pi$
$522$	−0.107520	−	0.223434i	−0.00470604	−	0.00977944i
$523$	−8.40522	+	14.5583i	−0.367535	+	0.636588i	−0.989179	−	0.146711i	$-0.953131\pi$
$523$	−8.40522	+	14.5583i	−0.367535	+	0.636588i	0.621645	+	0.783299i	$0.286465\pi$
$524$	6.07797	−	2.51758i	0.265518	−	0.109981i
$525$	−12.7691	−	17.2244i	−0.557288	−	0.751736i
$526$	−17.5003			−0.763051
$527$	−32.5614	−	8.98643i	−1.41840	−	0.391455i
$528$	0.615934	−	1.13909i	0.0268051	−	0.0495726i
$529$	−4.16831	+	15.5563i	−0.181231	+	0.676362i
$530$	3.67285	−	27.8981i	0.159538	−	1.21181i
$531$	−14.6015	−	7.37649i	−0.633651	−	0.320112i
$532$	0.271194	+	1.22815i	0.0117577	+	0.0532469i
$533$	9.81057	−	23.6848i	0.424943	−	1.02590i
$534$	5.26589	−	13.7892i	0.227877	−	0.596716i
$535$	15.5181	−	57.9142i	0.670905	−	2.50385i
$536$	−8.52843	+	31.8285i	−0.368372	+	1.37478i
$537$	−1.27951	+	3.35050i	−0.0552149	+	0.144585i
$538$	−5.72945	+	13.8321i	−0.247014	+	0.596345i
$539$	−1.14562	−	1.80493i	−0.0493452	−	0.0777437i
$540$	9.62480	−	0.807626i	0.414185	−	0.0347547i
$541$	2.32093	−	17.6292i	0.0997846	−	0.757939i	−0.866265	−	0.499584i	$-0.833486\pi$
$541$	2.32093	−	17.6292i	0.0997846	−	0.757939i	0.966050	−	0.258355i	$-0.0831805\pi$
$542$	6.09516	−	22.7475i	0.261810	−	0.977087i
$543$	18.0668	−	33.4122i	0.775320	−	1.43386i
$544$	−1.65118	−	13.3108i	−0.0707939	−	0.570695i
$545$	−8.53375			−0.365546
$546$	10.9602	−	25.2681i	0.469055	−	1.08138i
$547$	27.7079	−	11.4770i	1.18471	−	0.490721i	0.298678	−	0.954354i	$-0.403454\pi$
$547$	27.7079	−	11.4770i	1.18471	−	0.490721i	0.886027	+	0.463633i	$0.153454\pi$
$548$	−3.12992	+	5.42118i	−0.133703	+	0.231581i
$549$	12.3212	−	5.92918i	0.525856	−	0.253051i
$550$	0.220884	+	1.67778i	0.00941853	+	0.0715408i
$551$	−0.0338040	−	0.0440542i	−0.00144010	−	0.00187677i
$552$	7.72213	−	32.4112i	0.328676	−	1.37951i
$553$	32.8353	−	2.84500i	1.39630	−	0.120982i
$554$	10.3874	+	4.30260i	0.441319	+	0.182800i
$555$	12.1518	−	31.8205i	0.515816	−	1.35071i
$556$	−0.148439	−	0.113901i	−0.00629522	−	0.00483049i
$557$	−2.67352	−	4.63068i	−0.113281	−	0.196208i	0.803810	−	0.594886i	$-0.202803\pi$
$557$	−2.67352	−	4.63068i	−0.113281	−	0.196208i	−0.917091	+	0.398678i	$0.869469\pi$
$558$	24.0444	+	16.4034i	1.01788	+	0.694413i
$559$	−31.3269	+	31.3269i	−1.32498	+	1.32498i
$560$	18.9410	−	6.87600i	0.800404	−	0.290564i
$561$	−0.875606	−	1.99751i	−0.0369681	−	0.0843350i
$562$	7.46103	−	12.9229i	0.314725	−	0.545119i
$563$	−10.1194	+	37.7661i	−0.426482	+	1.59165i	0.334184	+	0.942508i	$0.391539\pi$
$563$	−10.1194	+	37.7661i	−0.426482	+	1.59165i	−0.760665	+	0.649144i	$0.775127\pi$
$564$	−12.3001	−	1.27135i	−0.517929	−	0.0535334i
$565$	−3.36829	+	5.83405i	−0.141705	+	0.245440i
$566$	6.15664	+	14.8634i	0.258783	+	0.624757i
$567$	−13.2627	−	19.7763i	−0.556982	−	0.830525i
$568$	5.19557	−	12.5432i	0.218001	−	0.526301i
$569$	−29.7936	+	7.98316i	−1.24901	+	0.334672i	−0.821954	−	0.569553i	$-0.807116\pi$
$569$	−29.7936	+	7.98316i	−1.24901	+	0.334672i	−0.427057	+	0.904225i	$0.640450\pi$
$570$	−4.86588	+	1.45047i	−0.203809	+	0.0607536i
$571$	−28.4391	+	3.74408i	−1.19014	+	0.156685i	−0.699471	−	0.714661i	$-0.746581\pi$
$571$	−28.4391	+	3.74408i	−1.19014	+	0.156685i	−0.490669	+	0.871346i	$0.663248\pi$
$572$	0.734683	−	0.563742i	0.0307186	−	0.0235712i
$573$	8.87130	−	12.2547i	0.370604	−	0.511947i
$574$	−12.1161	−	10.1840i	−0.505718	−	0.425070i
$575$	11.1969	+	27.0317i	0.466944	+	1.12730i
$576$	−5.36827	+	25.6913i	−0.223678	+	1.07047i
$577$	−27.1354	+	15.6667i	−1.12966	+	0.652211i	−0.943850	−	0.330374i	$-0.892825\pi$
$577$	−27.1354	+	15.6667i	−1.12966	+	0.652211i	−0.185813	+	0.982585i	$0.559492\pi$
$578$	17.2829	+	10.3262i	0.718875	+	0.429511i
$579$	0.120022	+	4.30000i	0.00498796	+	0.178702i
$580$	0.0917319	−	0.0917319i	0.00380896	−	0.00380896i
$581$	−3.56503	−	16.1448i	−0.147902	−	0.669800i
$582$	−9.59441	−	15.5962i	−0.397701	−	0.646483i
$583$	−2.31247	−	0.304442i	−0.0957727	−	0.0126087i
$584$	−2.83810	−	21.5575i	−0.117441	−	0.892056i
$585$	−44.7045	−	15.6573i	−1.84830	−	0.647351i
$586$	32.1212	−	8.60684i	1.32691	−	0.355545i
$587$	−1.56011	+	1.56011i	−0.0643927	+	0.0643927i	−0.738570	−	0.674177i	$-0.764498\pi$
$587$	−1.56011	+	1.56011i	−0.0643927	+	0.0643927i	0.674177	+	0.738570i	$0.264498\pi$
$588$	5.46736	+	4.75223i	0.225470	+	0.195979i
$589$	6.02216	+	2.49446i	0.248139	+	0.102782i
$590$	−2.62241	+	19.9192i	−0.107963	+	0.820059i
$591$	5.41154	+	2.92615i	0.222601	+	0.120366i
$592$	12.2768	+	9.42034i	0.504574	+	0.387173i
$593$	−5.46628	+	1.46469i	−0.224473	+	0.0601474i	−0.369303	−	0.929309i	$-0.620403\pi$
$593$	−5.46628	+	1.46469i	−0.224473	+	0.0601474i	0.144829	+	0.989457i	$0.453737\pi$
$594$	0.157145	+	1.87276i	0.00644775	+	0.0768404i
$595$	10.4743	−	32.2812i	0.429403	−	1.32340i
$596$			1.56951i			0.0642894i
$597$	17.7207	+	16.7583i	0.725261	+	0.685873i
$598$	−22.8803	+	29.8182i	−0.935646	+	1.21936i
$599$	−11.5169	−	19.9479i	−0.470568	−	0.815047i	0.528866	−	0.848706i	$-0.322618\pi$
$599$	−11.5169	−	19.9479i	−0.470568	−	0.815047i	−0.999433	+	0.0336583i	$0.989284\pi$
$600$	−10.1789	−	22.7565i	−0.415552	−	0.929030i
$601$	14.0871	−	34.0092i	0.574624	−	1.38726i	−0.322957	−	0.946414i	$-0.604677\pi$
$601$	14.0871	−	34.0092i	0.574624	−	1.38726i	0.897581	−	0.440850i	$-0.145323\pi$
$602$	12.6095	+	24.2723i	0.513926	+	0.989265i
$603$	−10.0359	−	30.5284i	−0.408692	−	1.24321i
$604$	−1.30890	−	4.88488i	−0.0532584	−	0.198763i
$605$	−33.6415	+	4.42899i	−1.36772	+	0.180064i
$606$	3.74668	−	3.04471i	0.152198	−	0.123683i
$607$	−0.975944	+	7.41303i	−0.0396123	+	0.300886i	0.960158	+	0.279458i	$0.0901546\pi$
$607$	−0.975944	+	7.41303i	−0.0396123	+	0.300886i	−0.999770	+	0.0214281i	$0.993179\pi$
$608$			2.58829i			0.104969i
$609$	−0.307513	−	0.0878829i	−0.0124611	−	0.00356119i
$610$	−11.8745	−	11.8745i	−0.480783	−	0.480783i
$611$	52.5182	+	30.3214i	2.12466	+	1.22667i
$612$	4.77697	+	5.63899i	0.193097	+	0.227943i
$613$	18.2928	+	31.6841i	0.738839	+	1.27971i	0.953018	+	0.302913i	$0.0979592\pi$
$613$	18.2928	+	31.6841i	0.738839	+	1.27971i	−0.214179	+	0.976794i	$0.568707\pi$
$614$	−12.9110	+	3.45950i	−0.521046	+	0.139614i
$615$	−15.9614	+	22.0488i	−0.643625	+	0.889095i
$616$	−0.848156	−	2.33638i	−0.0341732	−	0.0941354i
$617$	37.8275	−	15.6687i	1.52288	−	0.630796i	0.544712	−	0.838623i	$-0.316639\pi$
$617$	37.8275	−	15.6687i	1.52288	−	0.630796i	0.978166	+	0.207827i	$0.0666391\pi$
$618$	−10.0493	+	26.3148i	−0.404241	+	1.05854i
$619$	4.82891	+	36.6792i	0.194090	+	1.47426i	0.760069	+	0.649842i	$0.225165\pi$
$619$	4.82891	+	36.6792i	0.194090	+	1.47426i	−0.565979	+	0.824420i	$0.691502\pi$
$620$	−3.94138	+	14.7094i	−0.158289	+	0.590744i
$621$	11.0050	+	30.5733i	0.441614	+	1.22687i
$622$	−34.5075	−	14.2935i	−1.38363	−	0.573116i
$623$	−8.77685	−	16.8947i	−0.351637	−	0.676872i
$624$	12.6187	−	17.4312i	0.505151	−	0.697808i
$625$	−22.9518	−	13.2512i	−0.918073	−	0.530050i
$626$	0.250885	+	0.192510i	0.0100274	+	0.00769427i
$627$	0.120230	+	0.403332i	0.00480151	+	0.0161075i
$628$	−2.74719	−	1.58609i	−0.109625	−	0.0632920i
$629$	25.2244	−	6.55700i	1.00576	−	0.261445i
$630$	−17.5385	+	23.4013i	−0.698749	+	0.932328i
$631$	22.9036	+	22.9036i	0.911778	+	0.911778i	0.996412	−	0.0846337i	$-0.0269720\pi$
$631$	22.9036	+	22.9036i	0.911778	+	0.911778i	−0.0846337	+	0.996412i	$0.526972\pi$
$632$	37.9920	+	5.00174i	1.51124	+	0.198958i
$633$	15.5598	−	28.7759i	0.618448	−	1.14374i
$634$	−2.47996	+	3.23195i	−0.0984919	+	0.128357i
$635$	−16.2942	+	12.5030i	−0.646616	+	0.496166i
$636$	7.80404	−	1.24984i	0.309450	−	0.0495595i
$637$	−14.9598	−	32.2222i	−0.592728	−	1.27669i
$638$	0.0178489	+	0.0178489i	0.000706646	+	0.000706646i
$639$	2.45781	+	13.0105i	0.0972295	+	0.514687i
$640$	11.8899	−	1.56534i	0.469991	−	0.0618755i
$641$	15.9598	+	12.2464i	0.630376	+	0.483704i	0.873845	−	0.486204i	$-0.161619\pi$
$641$	15.9598	+	12.2464i	0.630376	+	0.483704i	−0.243469	+	0.969909i	$0.578286\pi$
$642$	−39.5162	+	1.10298i	−1.55958	+	0.0435313i
$643$	12.2316	+	29.5297i	0.482367	+	1.16454i	0.958482	+	0.285154i	$0.0920448\pi$
$643$	12.2316	+	29.5297i	0.482367	+	1.16454i	−0.476114	+	0.879383i	$0.657955\pi$
$644$	−5.66314	−	8.10225i	−0.223159	−	0.319273i
$645$	40.0652	−	24.6472i	1.57757	−	0.970482i
$646$	−3.06445	−	2.38807i	−0.120569	−	0.0939573i
$647$	19.4715	+	33.7256i	0.765502	+	1.32589i	0.939981	+	0.341228i	$0.110843\pi$
$647$	19.4715	+	33.7256i	0.765502	+	1.32589i	−0.174478	+	0.984661i	$0.555824\pi$
$648$	−10.0996	−	25.7774i	−0.396751	−	1.01263i
$649$	1.65110	+	0.217371i	0.0648113	+	0.00853257i
$650$			28.1216i			1.10302i
$651$	36.4197	−	9.11477i	1.42740	−	0.357236i
$652$	−12.1647	−	5.03878i	−0.476406	−	0.197334i
$653$	−18.6069	+	14.2776i	−0.728145	+	0.558725i	−0.904949	−	0.425521i	$-0.860091\pi$
$653$	−18.6069	+	14.2776i	−0.728145	+	0.558725i	0.176803	+	0.984246i	$0.443424\pi$
$654$	1.60733	+	5.39210i	0.0628517	+	0.210848i
$655$	33.0887	+	8.86608i	1.29288	+	0.346426i
$656$	−7.52805	−	9.81075i	−0.293921	−	0.383045i
$657$	13.8273	+	16.0770i	0.539454	+	0.627224i
$658$	27.6252	−	25.2712i	1.07694	−	0.985175i
$659$	−33.2924			−1.29689			−0.648443	−	0.761263i	$-0.724580\pi$
$659$	−33.2924			−1.29689			−0.648443	+	0.761263i	$0.724580\pi$
$660$	−0.897551	+	0.401472i	−0.0349371	+	0.0156273i
$661$	−27.7245	−	7.42877i	−1.07836	−	0.288946i	−0.324436	−	0.945908i	$-0.605174\pi$
$661$	−27.7245	−	7.42877i	−1.07836	−	0.288946i	−0.753924	+	0.656962i	$0.771841\pi$
$662$	10.2881	−	5.93981i	0.399857	−	0.230857i
$663$	−10.0934	−	34.8095i	−0.391997	−	1.35189i
$664$		−	19.2233i		−	0.746011i
$665$	−2.77273	+	5.93316i	−0.107522	+	0.230078i
$666$	−22.3948	−	1.68479i	−0.867779	−	0.0652841i
$667$	0.377963	+	0.218217i	0.0146348	+	0.00844940i
$668$	−1.29382	+	1.68615i	−0.0500596	+	0.0652389i
$669$	−20.6668	+	16.7947i	−0.799023	+	0.649322i
$670$	−31.3113	+	24.0260i	−1.20966	+	0.928205i
$671$	−0.984274	+	0.984274i	−0.0379975	+	0.0379975i
$672$	8.87795	+	11.9756i	0.342474	+	0.461970i
$673$	2.51498	−	6.07169i	0.0969453	−	0.234047i	−0.867966	−	0.496624i	$-0.834573\pi$
$673$	2.51498	−	6.07169i	0.0969453	−	0.234047i	0.964911	+	0.262578i	$0.0845726\pi$
$674$	−3.98927	−	5.19892i	−0.153661	−	0.200255i
$675$	20.4582	+	13.1357i	0.787435	+	0.505592i
$676$	6.60057	−	3.81084i	0.253868	−	0.146571i
$677$	−2.31810	+	17.6077i	−0.0890917	+	0.676719i	0.887375	+	0.461049i	$0.152527\pi$
$677$	−2.31810	+	17.6077i	−0.0890917	+	0.676719i	−0.976466	+	0.215670i	$0.930807\pi$
$678$	4.32069	+	1.02943i	0.165935	+	0.0395349i
$679$	−23.2559	−	4.12074i	−0.892480	−	0.158139i
$680$	19.9845	−	34.0237i	0.766371	−	1.30475i
$681$	−0.305096	−	10.9306i	−0.0116913	−	0.418860i
$682$	−2.86211	−	0.766901i	−0.109596	−	0.0293662i
$683$	−5.84568	+	7.61824i	−0.223679	+	0.291504i	−0.891689	−	0.452648i	$-0.850479\pi$
$683$	−5.84568	+	7.61824i	−0.223679	+	0.291504i	0.668011	+	0.744152i	$0.267146\pi$
$684$	−0.780850	−	1.19337i	−0.0298565	−	0.0456296i
$685$	−30.1141	+	12.4737i	−1.15060	+	0.476595i
$686$	−21.7527	+	2.80818i	−0.830522	+	0.107217i
$687$	7.99134	−	1.27984i	0.304889	−	0.0488289i
$688$	5.53107	+	20.6422i	0.210870	+	0.786977i
$689$	−37.4390	−	10.0318i	−1.42631	−	0.382180i
$690$	30.9699	−	25.1675i	1.17900	−	0.958111i
$691$	13.7473	+	17.9159i	0.522973	+	0.681552i	0.977923	−	0.208965i	$-0.0670094\pi$
$691$	13.7473	+	17.9159i	0.522973	+	0.681552i	−0.454950	+	0.890517i	$0.650343\pi$
$692$	2.33247	+	5.63107i	0.0886670	+	0.214061i
$693$	1.93973	+	1.45376i	0.0736842	+	0.0552239i
$694$	−5.63616	+	2.33457i	−0.213946	+	0.0886192i
$695$	−0.252156	−	0.941061i	−0.00956484	−	0.0356965i
$696$	−0.327095	−	0.176868i	−0.0123985	−	0.00670417i
$697$	−20.8269	−	0.155823i	−0.788874	−	0.00590222i
$698$	14.2056	−	24.6049i	0.537692	−	0.931309i
$699$	5.04769	−	21.1861i	0.190921	−	0.801332i
$700$	−7.05206	−	2.23001i	−0.266543	−	0.0842863i
$701$	−30.6702			−1.15840			−0.579198	−	0.815187i	$-0.696634\pi$
$701$	−30.6702			−1.15840			−0.579198	+	0.815187i	$0.696634\pi$
$702$	−1.47306	+	31.1958i	−0.0555972	+	1.17741i
$703$	−4.98635	+	0.656465i	−0.188064	+	0.0247590i
$704$	−0.348748	−	2.64900i	−0.0131439	−	0.0998380i
$705$	−46.7823	−	44.2416i	−1.76192	−	1.66624i
$706$	5.12819	+	5.12819i	0.193002	+	0.193002i
$707$	0.276834	−	6.22092i	0.0104114	−	0.233962i
$708$	−5.57207	+	0.892385i	−0.209411	+	0.0335379i
$709$	13.2102	+	1.73916i	0.496120	+	0.0653155i	0.374435	−	0.927253i	$-0.377837\pi$
$709$	13.2102	+	1.73916i	0.496120	+	0.0653155i	0.121685	+	0.992569i	$0.461170\pi$
$710$	14.0827	−	8.13063i	0.528513	−	0.305137i
$711$	−33.6750	+	16.2050i	−1.26291	+	0.607736i
$712$	−5.72910	−	21.3813i	−0.214707	−	0.801298i
$713$	−51.2313			−1.91863
$714$	−22.3699	−	0.538053i	−0.837172	−	0.0201361i
$715$	4.82198			0.180332
$716$	0.320204	+	1.19502i	0.0119666	+	0.0446599i
$717$	0.467782	−	4.52574i	0.0174696	−	0.169017i
$718$	−1.67580	+	0.967525i	−0.0625404	+	0.0361077i
$719$	−42.9400	−	5.65316i	−1.60139	−	0.210827i	−0.723722	−	0.690092i	$-0.757570\pi$
$719$	−42.9400	−	5.65316i	−1.60139	−	0.210827i	−0.877670	+	0.479265i	$0.840903\pi$
$720$	−17.3228	+	14.8988i	−0.645584	+	0.555244i
$721$	16.7495	+	32.2414i	0.623783	+	1.20073i
$722$	−15.3807	−	15.3807i	−0.572412	−	0.572412i
$723$	−17.3926	+	18.3914i	−0.646837	+	0.683983i
$724$	−1.71025	−	12.9906i	−0.0635608	−	0.482792i
$725$	0.323752	−	0.0426228i	0.0120239	−	0.00158297i
$726$	9.13487	+	20.4224i	0.339027	+	0.757945i
$727$	−0.499312			−0.0185184			−0.00925922	−	0.999957i	$-0.502947\pi$
$727$	−0.499312			−0.0185184			−0.00925922	+	0.999957i	$0.502947\pi$
$728$	−8.90616	−	40.3330i	−0.330084	−	1.49484i
$729$	22.0065	+	15.6433i	0.815057	+	0.579381i
$730$	13.0215	−	22.5539i	0.481947	−	0.834757i
$731$	33.1488	+	14.0222i	1.22605	+	0.518629i
$732$	2.24348	−	4.14904i	0.0829216	−	0.153353i
$733$	−10.5528	−	39.3837i	−0.389778	−	1.45467i	−0.830496	−	0.557025i	$-0.811943\pi$
$733$	−10.5528	−	39.3837i	−0.389778	−	1.45467i	0.440718	−	0.897645i	$-0.354724\pi$
$734$	−14.2721	+	5.91168i	−0.526792	+	0.218204i
$735$	7.52197	+	36.9624i	0.277452	+	1.36338i
$736$	−7.78487	−	18.7943i	−0.286954	−	0.692769i
$737$	1.99151	+	2.59539i	0.0733583	+	0.0956024i
$738$	16.9380	+	5.93238i	0.623497	+	0.218374i
$739$	47.8975	+	12.8341i	1.76194	+	0.472110i	0.987107	−	0.160060i	$-0.0511689\pi$
$739$	47.8975	+	12.8341i	1.76194	+	0.472110i	0.774830	+	0.632170i	$0.217836\pi$
$740$	−3.04106	−	11.3494i	−0.111792	−	0.417212i
$741$	1.10601	+	6.90594i	0.0406302	+	0.253696i
$742$	−12.8745	+	20.1715i	−0.472636	+	0.740521i
$743$	−31.0765	+	12.8723i	−1.14008	+	0.472239i	−0.871197	−	0.490933i	$-0.836656\pi$
$743$	−31.0765	+	12.8723i	−1.14008	+	0.472239i	−0.268887	+	0.963172i	$0.586656\pi$
$744$	43.6332	−	1.21790i	1.59967	−	0.0446503i
$745$	−4.97510	+	6.48368i	−0.182274	+	0.237544i
$746$	−27.9807	−	7.49742i	−1.02445	−	0.274500i
$747$	10.2648	+	15.6877i	0.375570	+	0.573982i
$748$	−0.648714	−	0.381035i	−0.0237193	−	0.0139320i
$749$	−32.8079	+	39.0325i	−1.19878	+	1.42622i
$750$	−0.474949	+	1.99345i	−0.0173427	+	0.0727905i
$751$	−2.27958	+	17.3151i	−0.0831831	+	0.631839i	0.898173	+	0.439642i	$0.144895\pi$
$751$	−2.27958	+	17.3151i	−0.0831831	+	0.631839i	−0.981356	+	0.192197i	$0.938439\pi$
$752$	25.3332	−	14.6262i	0.923809	−	0.533361i
$753$	−1.43612	+	13.8943i	−0.0523352	+	0.506337i
$754$	0.255357	+	0.332788i	0.00929955	+	0.0121194i
$755$	10.0772	−	24.3286i	0.366749	−	0.885409i
$756$	−7.70617	−	2.84319i	−0.280271	−	0.103406i
$757$	−38.0611	+	38.0611i	−1.38335	+	1.38335i	−0.544769	+	0.838586i	$0.683382\pi$
$757$	−38.0611	+	38.0611i	−1.38335	+	1.38335i	−0.838586	+	0.544769i	$0.816618\pi$
$758$	8.74996	−	6.71408i	0.317813	−	0.243866i
$759$	−2.08613	−	2.56709i	−0.0757219	−	0.0931796i
$760$	−4.63537	+	6.04094i	−0.168143	+	0.219128i
$761$	19.1409	+	11.0510i	0.693857	+	0.400598i	0.805055	−	0.593200i	$-0.202136\pi$
$761$	19.1409	+	11.0510i	0.693857	+	0.400598i	−0.111199	+	0.993798i	$0.535469\pi$
$762$	10.9691	+	7.94064i	0.397368	+	0.287659i
$763$	6.57480	+	3.07259i	0.238024	+	0.111235i
$764$		−	5.21869i		−	0.188806i
$765$	1.85904	+	38.4371i	0.0672139	+	1.38970i
$766$	−19.5326	+	11.2772i	−0.705743	+	0.407461i
$767$	26.7314	+	7.16266i	0.965215	+	0.258629i
$768$	9.14593	+	20.4471i	0.330025	+	0.737821i
$769$	27.7315			1.00002			0.500012	−	0.866018i	$-0.333329\pi$
$769$	27.7315			1.00002			0.500012	+	0.866018i	$0.333329\pi$
$770$	0.897595	−	2.83851i	0.0323471	−	0.102293i
$771$	6.73360	−	1.07841i	0.242505	−	0.0388379i
$772$	0.903325	+	1.17724i	0.0325114	+	0.0423697i
$773$	49.2825	+	13.2052i	1.77257	+	0.474958i	0.989196	−	0.146597i	$-0.0468322\pi$
$773$	49.2825	+	13.2052i	1.77257	+	0.474958i	0.783370	+	0.621555i	$0.213499\pi$
$774$	−23.1197	−	20.6731i	−0.831022	−	0.743080i
$775$	−30.4107	+	23.3350i	−1.09239	+	0.838218i
$776$	−25.3699	−	10.5086i	−0.910727	−	0.377236i
$777$	−20.8193	+	20.1407i	−0.746890	+	0.722544i
$778$			5.73184i			0.205497i
$779$	3.98473	+	0.524599i	0.142768	+	0.0187957i
$780$	−15.6585	+	4.66767i	−0.560666	+	0.167129i
$781$	−0.673948	−	1.16731i	−0.0241157	−	0.0417697i
$782$	29.4345	+	8.12345i	1.05257	+	0.290494i
$783$	0.361377	−	0.0303235i	0.0129146	−	0.00108367i
$784$	−17.0688	−	1.52215i	−0.609598	−	0.0543625i
$785$	−6.32106	−	15.2604i	−0.225608	−	0.544667i
$786$	−0.630178	−	22.5772i	−0.0224777	−	0.805301i
$787$	38.4148	+	29.4767i	1.36934	+	1.05073i	0.992211	+	0.124569i	$0.0397549\pi$
$787$	38.4148	+	29.4767i	1.36934	+	1.05073i	0.377128	+	0.926161i	$0.376912\pi$
$788$	2.10400	−	0.276996i	0.0749518	−	0.00986759i
$789$	9.13113	−	23.9106i	0.325077	−	0.851240i
$790$	32.4541	+	32.4541i	1.15466	+	1.15466i
$791$	4.69564	−	3.28206i	0.166958	−	0.116697i
$792$	1.83777	+	2.13678i	0.0653022	+	0.0759270i
$793$	−18.3515	+	14.0816i	−0.651680	+	0.500052i
$794$	−22.0929	+	28.7920i	−0.784047	+	1.02179i
$795$	36.2006	+	19.5745i	1.28390	+	0.694237i
$796$	8.34139	+	1.09816i	0.295653	+	0.0389234i
$797$	26.7260	+	26.7260i	0.946685	+	0.946685i	0.998649	−	0.0519639i	$-0.0165481\pi$
$797$	26.7260	+	26.7260i	0.946685	+	0.946685i	−0.0519639	+	0.998649i	$0.516548\pi$
$798$	4.27114	+	0.634453i	0.151197	+	0.0224594i
$799$	6.79597	−	48.7966i	0.240424	−	1.72630i
$800$	−13.1816	−	7.61040i	−0.466040	−	0.269068i
$801$	16.0925	+	14.3895i	0.568600	+	0.508428i
$802$	15.0097	+	11.5173i	0.530010	+	0.406691i
$803$	−1.86949	−	1.07935i	−0.0659729	−	0.0380895i
$804$	−8.97942	−	6.50030i	−0.316680	−	0.229248i
$805$	2.28830	−	51.4220i	0.0806521	−	1.81239i
$806$	−45.4917	−	18.8433i	−1.60238	−	0.663726i
$807$	−15.9093	−	15.0453i	−0.560033	−	0.529619i
$808$	1.87387	−	6.99336i	0.0659223	−	0.246026i
$809$	5.50542	+	41.8178i	0.193560	+	1.47024i	0.762035	+	0.647535i	$0.224200\pi$
$809$	5.50542	+	41.8178i	0.193560	+	1.47024i	−0.568475	+	0.822700i	$0.692466\pi$
$810$	9.19825	−	31.8584i	0.323194	−	1.11939i
$811$	5.55830	−	2.30232i	0.195178	−	0.0808455i	−0.282953	−	0.959134i	$-0.591314\pi$
$811$	5.55830	−	2.30232i	0.195178	−	0.0808455i	0.478132	+	0.878288i	$0.341314\pi$
$812$	−0.103703	+	0.0376463i	−0.00363925	+	0.00132113i
$813$	27.8994	+	20.1967i	0.978476	+	0.708329i
$814$	2.20833	−	0.591720i	0.0774019	−	0.0207398i
$815$	−34.2805	−	59.3756i	−1.20080	−	2.07984i
$816$	−16.9759	−	4.17905i	−0.594275	−	0.146296i
$817$	−6.01503	−	3.47278i	−0.210439	−	0.121497i
$818$	−22.9972	−	22.9972i	−0.804077	−	0.804077i
$819$	28.8050	+	28.1590i	1.00653	+	0.983956i
$820$			9.38955i			0.327897i
$821$	1.94092	−	14.7428i	0.0677387	−	0.514526i	−0.923616	−	0.383318i	$-0.874781\pi$
$821$	1.94092	−	14.7428i	0.0677387	−	0.514526i	0.991355	−	0.131208i	$-0.0418855\pi$
$822$	13.5536	+	16.6783i	0.472735	+	0.581724i
$823$	−3.10526	+	0.408816i	−0.108243	+	0.0142504i	−0.184453	−	0.982841i	$-0.559051\pi$
$823$	−3.10526	+	0.408816i	−0.108243	+	0.0142504i	0.0762102	+	0.997092i	$0.475718\pi$
$824$	10.9333	+	40.8035i	0.380878	+	1.42146i
$825$	−2.40759	−	0.573621i	−0.0838216	−	0.0199709i
$826$	9.19235	−	14.4024i	0.319843	−	0.501125i
$827$	11.6938	−	28.2313i	0.406633	−	0.981700i	−0.579384	−	0.815055i	$-0.696707\pi$
$827$	11.6938	−	28.2313i	0.406633	−	0.981700i	0.986017	−	0.166645i	$-0.0532933\pi$
$828$	9.25930	+	6.31682i	0.321783	+	0.219525i
$829$	−15.9606	−	27.6445i	−0.554334	−	0.960134i	−0.997955	−	0.0639197i	$-0.979640\pi$
$829$	−15.9606	−	27.6445i	−0.554334	−	0.960134i	0.443621	−	0.896214i	$-0.353693\pi$
$830$	14.0164	−	18.2666i	0.486517	−	0.634041i
$831$	−11.2984	+	11.9473i	−0.391939	+	0.414447i
$832$		−	44.4004i		−	1.53931i
$833$	−19.6928	+	21.0997i	−0.682313	+	0.731060i
$834$	−0.547120	+	0.336575i	−0.0189452	+	0.0116546i
$835$	−10.6897	+	2.86429i	−0.369931	+	0.0991227i
$836$	0.115180	+	0.0883804i	0.00398357	+	0.00305670i
$837$	−34.9575	+	24.2930i	−1.20831	+	0.839688i
$838$	3.98437	−	30.2643i	0.137638	−	1.04546i
$839$	15.2664	+	6.32357i	0.527056	+	0.218314i	0.630313	−	0.776341i	$-0.282926\pi$
$839$	15.2664	+	6.32357i	0.527056	+	0.218314i	−0.103257	+	0.994655i	$0.532926\pi$
$840$	−0.726496	+	43.8500i	−0.0250665	+	1.51297i
$841$	−20.5027	+	20.5027i	−0.706988	+	0.706988i
$842$	−25.2393	+	6.76286i	−0.869805	+	0.233064i
$843$	13.7635	+	16.9367i	0.474041	+	0.583332i
$844$	−1.47293	−	11.1880i	−0.0507004	−	0.385108i
$845$	39.3470	+	5.18013i	1.35358	+	0.178202i
$846$	−19.1428	+	37.8926i	−0.658144	+	1.30277i
$847$	27.5136	+	8.70037i	0.945380	+	0.298948i
$848$	−13.2205	+	13.2205i	−0.453992	+	0.453992i
$849$	−23.5202	+	0.656499i	−0.807210	+	0.0225310i
$850$	21.1723	−	8.58485i	0.726205	−	0.294458i
$851$	34.2328	−	19.7643i	1.17349	−	0.677513i
$852$	3.31848	+	3.13826i	0.113689	+	0.107515i
$853$	−9.06411	−	21.8827i	−0.310349	−	0.749249i	−0.999692	−	0.0248140i	$-0.992101\pi$
$853$	−9.06411	−	21.8827i	−0.310349	−	0.749249i	0.689343	−	0.724435i	$-0.257899\pi$
$854$	4.87322	+	13.4241i	0.166758	+	0.459362i
$855$	0.557090	−	7.40503i	0.0190521	−	0.253247i
$856$	−47.0330	+	36.0897i	−1.60755	+	1.23352i
$857$	−8.96602	+	1.18040i	−0.306274	+	0.0403217i	−0.282097	−	0.959386i	$-0.591030\pi$
$857$	−8.96602	+	1.18040i	−0.306274	+	0.0403217i	−0.0241770	+	0.999708i	$0.507697\pi$
$858$	−0.908221	−	3.04679i	−0.0310061	−	0.104016i
$859$	−14.7890	+	3.96269i	−0.504593	+	0.135205i	−0.502131	−	0.864792i	$-0.667450\pi$
$859$	−14.7890	+	3.96269i	−0.504593	+	0.135205i	−0.00246241	+	0.999997i	$0.500784\pi$
$860$	6.20957	−	14.9912i	0.211745	−	0.511197i
$861$	20.2361	−	11.2405i	0.689644	−	0.383076i
$862$	6.07529	+	14.6670i	0.206925	+	0.499561i
$863$	−5.14360	+	8.90897i	−0.175090	+	0.303265i	−0.940192	−	0.340644i	$-0.889355\pi$
$863$	−5.14360	+	8.90897i	−0.175090	+	0.303265i	0.765102	+	0.643909i	$0.222688\pi$
$864$	−14.2239	−	9.13283i	−0.483908	−	0.310705i
$865$	−8.21417	+	30.6557i	−0.279290	+	1.04233i
$866$	8.39690	−	14.5439i	0.285338	−	0.494221i
$867$	−23.1263	+	18.2257i	−0.785409	+	0.618977i
$868$	8.33276	−	9.91372i	0.282832	−	0.336493i
$869$	2.69012	−	2.69012i	0.0912560	−	0.0912560i
$870$	−0.181854	−	0.406562i	−0.00616542	−	0.0137837i
$871$	27.1819	+	47.0804i	0.921023	+	1.59526i
$872$	6.69423	+	5.13667i	0.226695	+	0.173949i
$873$	26.3150	−	4.97117i	0.890629	−	0.168249i
$874$	−5.44384	−	2.25491i	−0.184141	−	0.0762736i
$875$	1.51425	+	2.16644i	0.0511912	+	0.0732391i
$876$	7.11566	+	1.69534i	0.240416	+	0.0572803i
$877$	4.15983	+	5.42119i	0.140467	+	0.183061i	0.858289	−	0.513166i	$-0.171528\pi$
$877$	4.15983	+	5.42119i	0.140467	+	0.183061i	−0.717822	+	0.696227i	$0.754861\pi$
$878$	4.97066	+	37.7559i	0.167751	+	1.27420i
$879$	−5.00034	+	48.3777i	−0.168657	+	1.63174i
$880$	1.16299	−	2.01436i	0.0392044	−	0.0679040i
$881$	51.6944	−	21.4125i	1.74163	−	0.721406i	0.742986	−	0.669307i	$-0.233409\pi$
$881$	51.6944	−	21.4125i	1.74163	−	0.721406i	0.998642	−	0.0520986i	$-0.0165910\pi$
$882$	21.9381	−	11.7147i	0.738694	−	0.394453i
$883$	2.04518			0.0688259			0.0344130	−	0.999408i	$-0.489044\pi$
$883$	2.04518			0.0688259			0.0344130	+	0.999408i	$0.489044\pi$
$884$	−9.86148	−	7.68488i	−0.331678	−	0.258471i
$885$	−25.8471	−	13.9762i	−0.868842	−	0.469804i
$886$	2.15556	−	8.04466i	0.0724174	−	0.270265i
$887$	−3.95195	+	30.0180i	−0.132693	+	1.00791i	0.787465	+	0.616359i	$0.211393\pi$
$887$	−3.95195	+	30.0180i	−0.132693	+	1.00791i	−0.920158	+	0.391547i	$0.871940\pi$
$888$	−28.6859	+	17.6469i	−0.962636	+	0.592191i
$889$	17.0555	−	3.76613i	0.572024	−	0.126312i
$890$	10.1459	−	24.4944i	0.340092	−	0.821054i
$891$	−2.64074	−	0.762443i	−0.0884681	−	0.0255428i
$892$	−2.37757	+	8.87322i	−0.0796070	+	0.297097i
$893$	−2.46066	+	9.18330i	−0.0823427	+	0.307307i
$894$	5.03381	+	1.92234i	0.168356	+	0.0642927i
$895$	−2.46526	+	5.95166i	−0.0824045	+	0.198942i
$896$	−9.72416	−	3.07498i	−0.324861	−	0.102728i
$897$	−28.8022	−	46.8194i	−0.961677	−	1.56326i
$898$	2.20836	−	16.7742i	0.0736940	−	0.559762i
$899$	−0.147985	+	0.552287i	−0.00493557	+	0.0184198i
$900$	8.37350	−	0.467810i	0.279117	−	0.0155937i
$901$	3.87648	+	31.2497i	0.129144	+	1.04108i
$902$	−1.82699			−0.0608321
$903$	−39.7424	+	4.56378i	−1.32254	+	0.151873i
$904$	6.15388	−	2.54902i	0.204675	−	0.0847792i
$905$	34.1132	−	59.0858i	1.13396	−	1.96408i
$906$	−17.2702	−	1.78506i	−0.573765	−	0.0593046i
$907$	4.49703	+	34.1584i	0.149322	+	1.13421i	0.887898	+	0.460040i	$0.152165\pi$
$907$	4.49703	+	34.1584i	0.149322	+	1.13421i	−0.738577	+	0.674169i	$0.764502\pi$
$908$	−2.29625	−	2.99253i	−0.0762037	−	0.0993106i
$909$	2.20508	+	6.70769i	0.0731377	+	0.222480i
$910$	20.9453	−	44.8194i	0.694332	−	1.48575i
$911$	27.9559	+	11.5797i	0.926221	+	0.383653i	0.794244	−	0.607599i	$-0.207867\pi$
$911$	27.9559	+	11.5797i	0.926221	+	0.383653i	0.131977	+	0.991253i	$0.457867\pi$
$912$	3.15167	+	1.20358i	0.104362	+	0.0398545i
$913$	−1.51411	−	1.16182i	−0.0501099	−	0.0384507i
$914$	−12.5141	−	21.6751i	−0.413931	−	0.716949i
$915$	22.4197	−	10.0283i	0.741174	−	0.331525i
$916$	1.97408	−	1.97408i	0.0652253	−	0.0652253i
$917$	−22.3008	−	18.7445i	−0.736437	−	0.618996i
$918$	23.9365	−	8.41429i	0.790024	−	0.277713i
$919$	−8.81233	+	15.2634i	−0.290692	+	0.503493i	−0.973974	−	0.226662i	$-0.927219\pi$
$919$	−8.81233	+	15.2634i	−0.290692	+	0.503493i	0.683281	+	0.730155i	$0.260552\pi$
$920$	15.4893	−	57.8069i	0.510668	−	1.90584i
$921$	2.00988	−	19.4453i	0.0662277	−	0.640745i
$922$	12.9401	−	22.4130i	0.426161	−	0.738132i
$923$	−8.57175	−	20.6940i	−0.282143	−	0.681152i
$924$	0.836066	+	0.0138517i	0.0275045	+	0.000455689i
$925$	11.3182	−	27.3245i	0.372140	−	0.898425i
$926$	−16.1895	+	4.33797i	−0.532020	+	0.142554i
$927$	−30.7104	−	27.4605i	−1.00866	−	0.901922i
$928$	−0.225095	+	0.0296343i	−0.00738911	+	0.000972795i
$929$	−35.7118	+	27.4027i	−1.17167	+	0.899052i	−0.996342	−	0.0854587i	$-0.972764\pi$
$929$	−35.7118	+	27.4027i	−1.17167	+	0.899052i	−0.175325	+	0.984511i	$0.556098\pi$
$930$	42.3494	+	30.6572i	1.38869	+	1.00529i
$931$	4.27248	−	3.57285i	0.140025	−	0.117095i
$932$	−2.87501	−	6.94090i	−0.0941742	−	0.227357i
$933$	37.5340	−	39.6895i	1.22881	−	1.29938i
$934$	6.31967	−	3.64866i	0.206786	−	0.119388i
$935$	−1.47203	−	3.63039i	−0.0481407	−	0.118727i
$936$	25.6436	+	39.1909i	0.838186	+	1.28100i
$937$	3.31899	−	3.31899i	0.108427	−	0.108427i	−0.650812	−	0.759239i	$-0.725571\pi$
$937$	3.31899	−	3.31899i	0.108427	−	0.108427i	0.759239	+	0.650812i	$0.225571\pi$
$938$	32.7742	−	7.23706i	1.07012	−	0.236298i
$939$	−0.393930	+	0.242336i	−0.0128554	+	0.00790834i
$940$	−22.0211	−	2.89913i	−0.718248	−	0.0945591i
$941$	3.86167	+	29.3323i	0.125887	+	0.956205i	0.931494	+	0.363756i	$0.118506\pi$
$941$	3.86167	+	29.3323i	0.125887	+	0.956205i	−0.805608	+	0.592449i	$0.798161\pi$
$942$	−8.45178	+	6.86829i	−0.275374	+	0.223781i
$943$	−30.5121	+	8.17569i	−0.993611	+	0.266237i
$944$	9.43939	−	9.43939i	0.307226	−	0.307226i
$945$	−22.8220	−	36.1727i	−0.742399	−	1.17670i
$946$	2.91695	+	1.20824i	0.0948382	+	0.0392833i
$947$	−2.28709	+	17.3721i	−0.0743203	+	0.564519i	0.913257	+	0.407384i	$0.133559\pi$
$947$	−2.28709	+	17.3721i	−0.0743203	+	0.564519i	−0.987577	+	0.157135i	$0.949774\pi$
$948$	−6.13166	+	11.3397i	−0.199147	+	0.368297i
$949$	−28.4599	−	21.8380i	−0.923846	−	0.708892i
$950$	−4.25853	+	1.14107i	−0.138165	+	0.0370211i
$951$	−3.12183	−	5.07469i	−0.101232	−	0.164558i
$952$	−27.6473	+	19.0180i	−0.896053	+	0.616378i
$953$			39.8464i			1.29075i	0.763865	+	0.645376i	$0.223299\pi$
$953$			39.8464i			1.29075i	−0.763865	+	0.645376i	$0.776701\pi$
$954$	5.54988	−	26.5604i	0.179684	−	0.859924i
$955$	16.5425	−	21.5586i	0.535302	−	0.697619i
$956$	−0.784742	−	1.35921i	−0.0253804	−	0.0439601i
$957$	−0.0336999	+	0.0150739i	−0.00108936	+	0.000487269i
$958$	4.32835	−	10.4496i	0.139843	−	0.337610i
$959$	27.6925	+	1.23233i	0.894237	+	0.0397940i
$960$	−10.9262	+	45.8593i	−0.352642	+	1.48010i
$961$	−9.34795	−	34.8870i	−0.301547	−	1.12539i
$962$	37.6671	−	4.95897i	1.21444	−	0.159884i
$963$	19.1113	−	54.5663i	0.615854	−	1.75837i
$964$	−1.13973	+	8.65707i	−0.0367081	+	0.278826i
$965$			7.72661i			0.248728i
$966$	−32.9222	+	8.23946i	−1.05926	+	0.265100i
$967$	−23.2532	−	23.2532i	−0.747771	−	0.747771i	0.226289	−	0.974060i	$-0.427341\pi$
$967$	−23.2532	−	23.2532i	−0.747771	−	0.747771i	−0.974060	+	0.226289i	$0.927341\pi$
$968$	29.0557	+	16.7753i	0.933887	+	0.539180i
$969$	4.86174	−	2.94091i	0.156181	−	0.0944758i
$970$	−16.4450	−	28.4836i	−0.528018	−	0.914554i
$971$	−30.8052	+	8.25423i	−0.988586	+	0.264891i	−0.716656	−	0.697427i	$-0.754328\pi$
$971$	−30.8052	+	8.25423i	−0.988586	+	0.264891i	−0.271929	+	0.962317i	$0.587662\pi$
$972$	9.31339	−	0.0803301i	0.298727	−	0.00257659i
$973$	−0.144557	+	0.815826i	−0.00463429	+	0.0261542i
$974$	−0.00527015	+	0.00218297i	−0.000168866	+	6.99467e-5i
$975$	−38.4224	−	14.6730i	−1.23050	−	0.469911i
$976$	1.45641	+	11.0625i	0.0466185	+	0.354102i
$977$	0.771667	−	2.87990i	0.0246878	−	0.0921362i	−0.952483	−	0.304593i	$-0.901480\pi$
$977$	0.771667	−	2.87990i	0.0246878	−	0.0921362i	0.977171	+	0.212456i	$0.0681464\pi$
$978$	−31.0601	+	32.8438i	−0.993191	+	1.05023i
$979$	−2.03034	−	0.840994i	−0.0648899	−	0.0268783i
$980$	9.57842	+	8.80659i	0.305972	+	0.281316i
$981$	−8.20584	−	0.617336i	−0.261992	−	0.0197100i
$982$	7.43422	+	4.29215i	0.237236	+	0.136968i
$983$	−23.2144	−	17.8130i	−0.740423	−	0.568147i	0.168205	−	0.985752i	$-0.446203\pi$
$983$	−23.2144	−	17.8130i	−0.740423	−	0.568147i	−0.908629	+	0.417605i	$0.862869\pi$
$984$	25.7925	−	7.68851i	0.822235	−	0.245101i
$985$	9.56971	+	5.52508i	0.304916	+	0.176044i
$986$	0.172596	−	0.293846i	0.00549659	−	0.00935797i
$987$	20.1140	+	50.9298i	0.640235	+	1.62111i
$988$	1.70595	+	1.70595i	0.0542736	+	0.0542736i
$989$	54.1220	+	7.12530i	1.72098	+	0.226571i
$990$	0.188297	+	3.37040i	0.00598448	+	0.107118i
$991$	13.6364	−	17.7712i	0.433173	−	0.564522i	−0.524857	−	0.851191i	$-0.675881\pi$
$991$	13.6364	−	17.7712i	0.433173	−	0.564522i	0.958030	+	0.286668i	$0.0925478\pi$
$992$	21.1437	−	16.2241i	0.671312	−	0.515116i
$993$	2.74754	+	17.1557i	0.0871907	+	0.544420i
$994$	−13.7774	+	1.19373i	−0.436992	+	0.0378629i
$995$	30.9775	+	30.9775i	0.982053	+	0.982053i
$996$	6.04146	+	2.30715i	0.191431	+	0.0731049i
$997$	15.2195	−	2.00369i	0.482007	−	0.0634575i	0.114393	−	0.993436i	$-0.463508\pi$
$997$	15.2195	−	2.00369i	0.482007	−	0.0634575i	0.367615	+	0.929978i	$0.380174\pi$
$998$	−23.2109	−	17.8104i	−0.734730	−	0.563778i
$999$	13.9868	−	29.7188i	0.442523	−	0.940260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bj.a.257.15	yes	352
3.2	odd	2	inner	357.2.bj.a.257.30	yes	352
7.3	odd	6	inner	357.2.bj.a.206.30	yes	352
17.9	even	8	inner	357.2.bj.a.26.15	✓	352
21.17	even	6	inner	357.2.bj.a.206.15	yes	352
51.26	odd	8	inner	357.2.bj.a.26.30	yes	352
119.94	odd	24	inner	357.2.bj.a.332.30	yes	352
357.332	even	24	inner	357.2.bj.a.332.15	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.15	✓	352	17.9	even	8	inner
357.2.bj.a.26.30	yes	352	51.26	odd	8	inner
357.2.bj.a.206.15	yes	352	21.17	even	6	inner
357.2.bj.a.206.30	yes	352	7.3	odd	6	inner
357.2.bj.a.257.15	yes	352	1.1	even	1	trivial
357.2.bj.a.257.30	yes	352	3.2	odd	2	inner
357.2.bj.a.332.15	yes	352	357.332	even	24	inner
357.2.bj.a.332.30	yes	352	119.94	odd	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bj (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.306515 - 1.14393i) q^{2} +(1.72287 + 0.178077i) q^{3} +(0.517430 - 0.298738i) q^{4} +(3.08447 + 0.406079i) q^{5} +(-0.324378 - 2.02543i) q^{6} +(-2.23021 - 1.42343i) q^{7} +(-2.17516 - 2.17516i) q^{8} +(2.93658 + 0.613608i) q^{9} +(-0.480912 - 3.65289i) q^{10} +(-0.302788 + 0.0398628i) q^{11} +(0.944663 - 0.422545i) q^{12} -5.07508 q^{13} +(-0.944710 + 2.98751i) q^{14} +(5.24184 + 1.24890i) q^{15} +(-1.22403 + 2.12009i) q^{16} +(1.54930 + 3.82095i) q^{17} +(-0.198181 - 3.54731i) q^{18} +(-0.205928 - 0.768532i) q^{19} +(1.71731 - 0.711333i) q^{20} +(-3.58889 - 2.84954i) q^{21} +(0.138409 + 0.334149i) q^{22} +(3.80683 + 4.96116i) q^{23} +(-3.36018 - 4.13487i) q^{24} +(4.51945 + 1.21098i) q^{25} +(1.55559 + 5.80553i) q^{26} +(4.95008 + 1.58010i) q^{27} +(-1.57921 - 0.0702757i) q^{28} +(0.0644789 - 0.0267080i) q^{29} +(-0.178055 - 6.37910i) q^{30} +(-4.98730 + 6.49958i) q^{31} +(-3.14224 - 0.841960i) q^{32} +(-0.528763 + 0.0147589i) q^{33} +(3.89601 - 2.94347i) q^{34} +(-6.30101 - 5.29618i) q^{35} +(1.70278 - 0.559769i) q^{36} +(0.825075 - 6.26706i) q^{37} +(-0.816026 + 0.471133i) q^{38} +(-8.74372 - 0.903755i) q^{39} +(-5.82595 - 7.59252i) q^{40} +(-1.93309 + 4.66688i) q^{41} +(-2.15962 + 4.97886i) q^{42} +(6.17268 - 6.17268i) q^{43} +(-0.144763 + 0.111080i) q^{44} +(8.80862 + 3.08514i) q^{45} +(4.50836 - 5.87541i) q^{46} +(-10.3483 - 5.97457i) q^{47} +(-2.48639 + 3.43467i) q^{48} +(2.94769 + 6.34910i) q^{49} -5.54111i q^{50} +(1.98882 + 6.85891i) q^{51} +(-2.62600 + 1.51612i) q^{52} +(7.37703 + 1.97667i) q^{53} +(0.290254 - 6.14686i) q^{54} -0.950128 q^{55} +(1.75488 + 7.94727i) q^{56} +(-0.217929 - 1.36075i) q^{57} +(-0.0503158 - 0.0655728i) q^{58} +(-5.26719 - 1.41134i) q^{59} +(3.08538 - 0.919722i) q^{60} +(3.61600 - 2.77465i) q^{61} +(8.96373 + 3.71290i) q^{62} +(-5.67576 - 5.54849i) q^{63} +8.74871i q^{64} +(-15.6540 - 2.06088i) q^{65} +(0.178957 + 0.600343i) q^{66} +(-5.35595 - 9.27677i) q^{67} +(1.94312 + 1.51424i) q^{68} +(5.67522 + 9.22536i) q^{69} +(-4.12710 + 8.83126i) q^{70} +(1.68899 + 4.07758i) q^{71} +(-5.05284 - 7.72223i) q^{72} +(5.60776 + 4.30299i) q^{73} +(-7.42197 + 0.977121i) q^{74} +(7.57079 + 2.89118i) q^{75} +(-0.336143 - 0.336143i) q^{76} +(0.732023 + 0.342095i) q^{77} +(1.64625 + 10.2792i) q^{78} +(-9.88287 + 7.58339i) q^{79} +(-4.63643 + 6.04231i) q^{80} +(8.24697 + 3.60381i) q^{81} +(5.93110 + 0.780844i) q^{82} +(4.41883 + 4.41883i) q^{83} +(-2.70826 - 0.402297i) q^{84} +(3.22717 + 12.4148i) q^{85} +(-8.95312 - 5.16909i) q^{86} +(0.115845 - 0.0345323i) q^{87} +(0.745320 + 0.571904i) q^{88} +(6.23181 + 3.59794i) q^{89} +(0.829205 - 11.0221i) q^{90} +(11.3185 + 7.22403i) q^{91} +(3.45186 + 1.42981i) q^{92} +(-9.74991 + 10.3098i) q^{93} +(-3.66259 + 13.6690i) q^{94} +(-0.323094 - 2.45414i) q^{95} +(-5.26374 - 2.01015i) q^{96} +(8.24731 - 3.41615i) q^{97} +(6.35941 - 5.31804i) q^{98} +(-0.913619 - 0.0687327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) \) 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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