LMFDB - Embedded newform 357.2.bj.a.26.15

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			26.15
Character	$\chi$	$=$	357.26
Dual form			357.2.bj.a.206.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14393 + 0.306515i) q^{2} +(1.09234 + 1.34417i) q^{3} +(-0.517430 + 0.298738i) q^{4} +(-1.89391 - 2.46819i) q^{5} +(-1.66156 - 1.20282i) q^{6} +(2.58352 - 0.570481i) q^{7} +(2.17516 - 2.17516i) q^{8} +(-0.613608 + 2.93658i) q^{9} +(2.92304 + 2.24293i) q^{10} +(-0.185916 + 0.242290i) q^{11} +(-0.966763 - 0.369193i) q^{12} +5.07508 q^{13} +(-2.78050 + 1.44447i) q^{14} +(1.24890 - 5.24184i) q^{15} +(-1.22403 + 2.12009i) q^{16} +(2.53439 + 3.25221i) q^{17} +(-0.198181 - 3.54731i) q^{18} +(-0.768532 + 0.205928i) q^{19} +(1.71731 + 0.711333i) q^{20} +(3.58889 + 2.84954i) q^{21} +(0.138409 - 0.334149i) q^{22} +(6.19991 + 0.816233i) q^{23} +(5.29980 + 0.547790i) q^{24} +(-1.21098 + 4.51945i) q^{25} +(-5.80553 + 1.55559i) q^{26} +(-4.61754 + 2.38293i) q^{27} +(-1.16636 + 1.06698i) q^{28} +(-0.0644789 - 0.0267080i) q^{29} +(0.178055 + 6.37910i) q^{30} +(-8.12245 + 1.06934i) q^{31} +(-0.841960 + 3.14224i) q^{32} +(-0.528763 + 0.0147589i) q^{33} +(-3.89601 - 2.94347i) q^{34} +(-6.30101 - 5.29618i) q^{35} +(-0.559769 - 1.70278i) q^{36} +(5.01490 - 3.84807i) q^{37} +(0.816026 - 0.471133i) q^{38} +(5.54369 + 6.82179i) q^{39} +(-9.48829 - 1.24916i) q^{40} +(-1.93309 - 4.66688i) q^{41} +(-4.97886 - 2.15962i) q^{42} +(6.17268 + 6.17268i) q^{43} +(0.0238170 - 0.180908i) q^{44} +(8.41016 - 4.04712i) q^{45} +(-7.34244 + 0.966651i) q^{46} +(10.3483 + 5.97457i) q^{47} +(-4.18683 + 0.670534i) q^{48} +(6.34910 - 2.94769i) q^{49} -5.54111i q^{50} +(-1.60313 + 6.95916i) q^{51} +(-2.62600 + 1.51612i) q^{52} +(1.97667 - 7.37703i) q^{53} +(4.55173 - 4.14125i) q^{54} +0.950128 q^{55} +(4.37868 - 6.86045i) q^{56} +(-1.11630 - 0.808099i) q^{57} +(0.0819457 + 0.0107884i) q^{58} +(1.41134 - 5.26719i) q^{59} +(0.919722 + 3.08538i) q^{60} +(-0.594921 + 4.51887i) q^{61} +(8.96373 - 3.71290i) q^{62} +(0.0899962 + 7.93674i) q^{63} -8.74871i q^{64} +(-9.61176 - 12.5263i) q^{65} +(0.600343 - 0.178957i) q^{66} +(-5.35595 - 9.27677i) q^{67} +(-2.28293 - 0.925670i) q^{68} +(5.67522 + 9.22536i) q^{69} +(8.83126 + 4.12710i) q^{70} +(-1.68899 + 4.07758i) q^{71} +(5.05284 + 7.72223i) q^{72} +(-0.922615 - 7.00796i) q^{73} +(-4.55720 + 5.93905i) q^{74} +(-7.39773 + 3.30898i) q^{75} +(0.336143 - 0.336143i) q^{76} +(-0.342095 + 0.732023i) q^{77} +(-8.43257 - 6.10442i) q^{78} +(-1.62598 + 12.3505i) q^{79} +(7.55101 - 0.994109i) q^{80} +(-8.24697 - 3.60381i) q^{81} +(3.64178 + 4.74606i) 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} +(-0.0345323 - 0.115845i) q^{87} +(0.122624 + 0.931419i) q^{88} +(-6.23181 - 3.59794i) q^{89} +(-8.38012 + 7.20745i) q^{90} +(13.1116 - 2.89524i) q^{91} +(-3.45186 + 1.42981i) q^{92} +(-10.3098 - 9.74991i) q^{93} +(-13.6690 - 3.66259i) q^{94} +(1.96380 + 1.50688i) q^{95} +(-5.14342 + 2.30064i) q^{96} +(-8.24731 - 3.41615i) q^{97} +(-6.35941 + 5.31804i) q^{98} +(-0.597425 - 0.694628i) 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 $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.14393	+	0.306515i	−0.808880	+	0.216739i	−0.639479	−	0.768809i	$-0.720850\pi$
$2$	−1.14393	+	0.306515i	−0.808880	+	0.216739i	−0.169401	+	0.985547i	$0.554183\pi$
$3$	1.09234	+	1.34417i	0.630660	+	0.776059i
$3$	1.09234	+	1.34417i	0.630660	+	0.776059i
$4$	−0.517430	+	0.298738i	−0.258715	+	0.149369i
$5$	−1.89391	−	2.46819i	−0.846983	−	1.10381i	−0.993413	−	0.114589i	$-0.963445\pi$
$5$	−1.89391	−	2.46819i	−0.846983	−	1.10381i	0.146430	−	0.989221i	$-0.453222\pi$
$6$	−1.66156	−	1.20282i	−0.678330	−	0.491050i
$7$	2.58352	−	0.570481i	0.976477	−	0.215621i
$7$	2.58352	−	0.570481i	0.976477	−	0.215621i
$8$	2.17516	−	2.17516i	0.769036	−	0.769036i
$9$	−0.613608	+	2.93658i	−0.204536	+	0.978859i
$10$	2.92304	+	2.24293i	0.924346	+	0.709275i
$11$	−0.185916	+	0.242290i	−0.0560558	+	0.0730533i	−0.820540	−	0.571589i	$-0.806327\pi$
$11$	−0.185916	+	0.242290i	−0.0560558	+	0.0730533i	0.764484	+	0.644643i	$0.222994\pi$
$12$	−0.966763	−	0.369193i	−0.279080	−	0.106577i
$13$	5.07508			1.40757			0.703787	−	0.710411i	$-0.251491\pi$
$13$	5.07508			1.40757			0.703787	+	0.710411i	$0.251491\pi$
$14$	−2.78050	+	1.44447i	−0.743119	+	0.386052i
$15$	1.24890	−	5.24184i	0.322463	−	1.35344i
$16$	−1.22403	+	2.12009i	−0.306009	+	0.530023i
$17$	2.53439	+	3.25221i	0.614680	+	0.788777i
$17$	2.53439	+	3.25221i	0.614680	+	0.788777i
$18$	−0.198181	−	3.54731i	−0.0467117	−	0.836110i
$19$	−0.768532	+	0.205928i	−0.176313	+	0.0472430i	−0.345896	−	0.938273i	$-0.612425\pi$
$19$	−0.768532	+	0.205928i	−0.176313	+	0.0472430i	0.169582	+	0.985516i	$0.445758\pi$
$20$	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
$23$	6.19991	+	0.816233i	1.29277	+	0.170196i	0.745357	−	0.666666i	$-0.232279\pi$
$23$	6.19991	+	0.816233i	1.29277	+	0.170196i	0.547414	+	0.836862i	$0.315612\pi$
$24$	5.29980	+	0.547790i	1.08182	+	0.111817i
$25$	−1.21098	+	4.51945i	−0.242197	+	0.903890i
$26$	−5.80553	+	1.55559i	−1.13856	+	0.305076i
$27$	−4.61754	+	2.38293i	−0.888645	+	0.458595i
$28$	−1.16636	+	1.06698i	−0.220422	+	0.201640i
$29$	−0.0644789	−	0.0267080i	−0.0119734	−	0.00495956i	0.376689	−	0.926340i	$-0.377063\pi$
$29$	−0.0644789	−	0.0267080i	−0.0119734	−	0.00495956i	−0.388662	+	0.921380i	$0.627063\pi$
$30$	0.178055	+	6.37910i	0.0325082	+	1.16466i
$31$	−8.12245	+	1.06934i	−1.45884	+	0.192059i	−0.817822	−	0.575471i	$-0.804819\pi$
$31$	−8.12245	+	1.06934i	−1.45884	+	0.192059i	−0.641013	+	0.767530i	$0.721485\pi$
$32$	−0.841960	+	3.14224i	−0.148839	+	0.555474i
$33$	−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
$36$	−0.559769	−	1.70278i	−0.0932948	−	0.283797i
$37$	5.01490	−	3.84807i	0.824444	−	0.632618i	−0.107911	−	0.994161i	$-0.534416\pi$
$37$	5.01490	−	3.84807i	0.824444	−	0.632618i	0.932356	+	0.361542i	$0.117750\pi$
$38$	0.816026	−	0.471133i	0.132377	−	0.0764279i
$39$	5.54369	+	6.82179i	0.887701	+	1.09236i
$40$	−9.48829	−	1.24916i	−1.50023	−	0.197509i
$41$	−1.93309	−	4.66688i	−0.301897	−	0.728845i	−0.999918	−	0.0127676i	$-0.995936\pi$
$41$	−1.93309	−	4.66688i	−0.301897	−	0.728845i	0.698021	−	0.716077i	$-0.254064\pi$
$42$	−4.97886	−	2.15962i	−0.768255	−	0.333237i
$43$	6.17268	+	6.17268i	0.941325	+	0.941325i	0.998372	−	0.0570466i	$-0.0181684\pi$
$43$	6.17268	+	6.17268i	0.941325	+	0.941325i	−0.0570466	+	0.998372i	$0.518168\pi$
$44$	0.0238170	−	0.180908i	0.00359055	−	0.0272730i
$45$	8.41016	−	4.04712i	1.25371	−	0.603308i
$46$	−7.34244	+	0.966651i	−1.08258	+	0.142525i
$47$	10.3483	+	5.97457i	1.50945	+	0.871480i	0.999939	+	0.0110148i	$0.00350619\pi$
$47$	10.3483	+	5.97457i	1.50945	+	0.871480i	0.509509	+	0.860465i	$0.329827\pi$
$48$	−4.18683	+	0.670534i	−0.604316	+	0.0967832i
$49$	6.34910	−	2.94769i	0.907015	−	0.421099i
$50$		−	5.54111i		−	0.783632i
$51$	−1.60313	+	6.95916i	−0.224483	+	0.974478i
$52$	−2.62600	+	1.51612i	−0.364160	+	0.210248i
$53$	1.97667	−	7.37703i	0.271516	−	1.01331i	−0.686624	−	0.727013i	$-0.740908\pi$
$53$	1.97667	−	7.37703i	0.271516	−	1.01331i	0.958140	−	0.286300i	$-0.0924254\pi$
$54$	4.55173	−	4.14125i	0.619412	−	0.563552i
$55$	0.950128			0.128115
$56$	4.37868	−	6.86045i	0.585125	−	0.916767i
$57$	−1.11630	−	0.808099i	−0.147857	−	0.107035i
$58$	0.0819457	+	0.0107884i	0.0107600	+	0.00141658i
$59$	1.41134	−	5.26719i	0.183741	−	0.685729i	−0.811156	−	0.584830i	$-0.801161\pi$
$59$	1.41134	−	5.26719i	0.183741	−	0.685729i	0.994897	−	0.100900i	$-0.0321721\pi$
$60$	0.919722	+	3.08538i	0.118736	+	0.398320i
$61$	−0.594921	+	4.51887i	−0.0761718	+	0.578582i	0.910214	+	0.414137i	$0.135917\pi$
$61$	−0.594921	+	4.51887i	−0.0761718	+	0.578582i	−0.986386	+	0.164445i	$0.947417\pi$
$62$	8.96373	−	3.71290i	1.13840	−	0.471539i
$63$	0.0899962	+	7.93674i	0.0113385	+	0.999936i
$64$		−	8.74871i		−	1.09359i
$65$	−9.61176	−	12.5263i	−1.19219	−	1.55369i
$66$	0.600343	−	0.178957i	0.0738972	−	0.0220281i
$67$	−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	$-0.393717\pi$
$68$	−2.28293	−	0.925670i	−0.276846	−	0.112254i
$69$	5.67522	+	9.22536i	0.683216	+	1.11060i
$70$	8.83126	+	4.12710i	1.05554	+	0.493282i
$71$	−1.68899	+	4.07758i	−0.200446	+	0.483919i	−0.991856	−	0.127367i	$-0.959347\pi$
$71$	−1.68899	+	4.07758i	−0.200446	+	0.483919i	0.791410	+	0.611286i	$0.209347\pi$
$72$	5.05284	+	7.72223i	0.595482	+	0.910073i
$73$	−0.922615	−	7.00796i	−0.107984	−	0.820220i	−0.956640	−	0.291274i	$-0.905921\pi$
$73$	−0.922615	−	7.00796i	−0.107984	−	0.820220i	0.848656	−	0.528946i	$-0.177412\pi$
$74$	−4.55720	+	5.93905i	−0.529763	+	0.690401i
$75$	−7.39773	+	3.30898i	−0.854216	+	0.382089i
$76$	0.336143	−	0.336143i	0.0385582	−	0.0385582i
$77$	−0.342095	+	0.732023i	−0.0389853	+	0.0834217i
$78$	−8.43257	−	6.10442i	−0.954800	−	0.691190i
$79$	−1.62598	+	12.3505i	−0.182937	+	1.38954i	0.615820	+	0.787887i	$0.288825\pi$
$79$	−1.62598	+	12.3505i	−0.182937	+	1.38954i	−0.798756	+	0.601654i	$0.794508\pi$
$80$	7.55101	−	0.994109i	0.844228	−	0.111145i
$81$	−8.24697	−	3.60381i	−0.916330	−	0.400424i
$82$	3.64178	+	4.74606i	0.402167	+	0.524115i
$83$	4.41883	−	4.41883i	0.485030	−	0.485030i	−0.421704	−	0.906734i	$-0.638568\pi$
$83$	4.41883	−	4.41883i	0.485030	−	0.485030i	0.906734	+	0.421704i	$0.138568\pi$
$84$	−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
$87$	−0.0345323	−	0.115845i	−0.00370225	−	0.0124199i
$88$	0.122624	+	0.931419i	0.0130717	+	0.0992896i
$89$	−6.23181	−	3.59794i	−0.660571	−	0.381381i	0.131924	−	0.991260i	$-0.457885\pi$
$89$	−6.23181	−	3.59794i	−0.660571	−	0.381381i	−0.792494	+	0.609879i	$0.791218\pi$
$90$	−8.38012	+	7.20745i	−0.883342	+	0.759732i
$91$	13.1116	−	2.89524i	1.37446	−	0.303503i
$92$	−3.45186	+	1.42981i	−0.359881	+	0.149068i
$93$	−10.3098	−	9.74991i	−1.06908	−	1.01102i
$94$	−13.6690	−	3.66259i	−1.40985	−	0.377767i
$95$	1.96380	+	1.50688i	0.201482	+	0.154602i
$96$	−5.14342	+	2.30064i	−0.524948	+	0.234808i
$97$	−8.24731	−	3.41615i	−0.837388	−	0.346857i	−0.0775647	−	0.996987i	$-0.524714\pi$
$97$	−8.24731	−	3.41615i	−0.837388	−	0.346857i	−0.759823	+	0.650130i	$0.774714\pi$
$98$	−6.35941	+	5.31804i	−0.642397	+	0.537203i
$99$	−0.597425	−	0.694628i	−0.0600435	−	0.0698127i
$100$	−0.723534	−	2.70027i	−0.0723534	−	0.270027i
$101$	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	$0.795975\pi$
$102$	−0.299219	−	8.45217i	−0.0296271	−	0.836890i
$103$	−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
$105$	0.236171	−	14.2548i	0.0230479	−	1.39113i
$106$			9.04467i			0.878496i
$107$	−15.2896	+	11.7321i	−1.47810	+	1.13419i	−0.517699	+	0.855563i	$0.673211\pi$
$107$	−15.2896	+	11.7321i	−1.47810	+	1.13419i	−0.960401	+	0.278623i	$0.910122\pi$
$108$	1.67738	−	2.61243i	0.161406	−	0.251382i
$109$	1.66984	−	2.17618i	0.159942	−	0.208440i	−0.706507	−	0.707706i	$-0.749730\pi$
$109$	1.66984	−	2.17618i	0.159942	−	0.208440i	0.866449	+	0.499266i	$0.166397\pi$
$110$	−1.08688	+	0.291228i	−0.103630	+	0.0277675i
$111$	10.6504	+	2.53752i	1.01089	+	0.240851i
$112$	−1.95284	+	6.17557i	−0.184526	+	0.583537i
$113$	0.828642	+	2.00052i	0.0779520	+	0.188193i	0.958051	−	0.286597i	$-0.0925241\pi$
$113$	0.828642	+	2.00052i	0.0779520	+	0.188193i	−0.880099	+	0.474790i	$0.842524\pi$
$114$	1.52466	+	0.582246i	0.142797	+	0.0545323i
$115$	−9.72746	−	16.8484i	−0.907090	−	1.57113i
$116$	0.0413420	−	0.00544278i	0.00383851	−	0.000505349i
$117$	−3.11411	+	14.9034i	−0.287899	+	1.37782i
$118$			6.45788i			0.594496i
$119$	8.40296	+	6.95631i	0.770298	+	0.637684i
$120$	−8.68531	−	14.1184i	−0.792856	−	1.28883i
$121$	2.82287	+	10.5351i	0.256625	+	0.957736i
$122$	−0.704554	−	5.35162i	−0.0637873	−	0.484513i
$123$	4.16153	−	7.69621i	0.375232	−	0.693944i
$124$	3.88334	−	2.97979i	0.348735	−	0.267593i
$125$	−0.922984	+	0.382312i	−0.0825542	+	0.0341951i
$126$	−2.53568	−	9.05148i	−0.225896	−	0.806370i
$127$	−4.66809	−	4.66809i	−0.414226	−	0.414226i	0.468982	−	0.883208i	$-0.344621\pi$
$127$	−4.66809	−	4.66809i	−0.414226	−	0.414226i	−0.883208	+	0.468982i	$0.844621\pi$
$128$	0.997688	+	3.72342i	0.0881840	+	0.329107i
$129$	−1.55452	+	15.0398i	−0.136868	+	1.32418i
$130$	14.8347	+	11.3830i	1.30109	+	0.998358i
$131$	−6.70301	−	8.73554i	−0.585645	−	0.763227i	0.402721	−	0.915323i	$-0.368065\pi$
$131$	−6.70301	−	8.73554i	−0.585645	−	0.763227i	−0.988366	+	0.152095i	$0.951398\pi$
$132$	0.269189	−	0.165598i	0.0234299	−	0.0144135i
$133$	−1.86804	+	0.970450i	−0.161979	+	0.0841487i
$134$	8.97029	+	8.97029i	0.774915	+	0.774915i
$135$	14.6267	+	6.88391i	1.25887	+	0.592473i
$136$	12.5868	+	1.56137i	1.07931	+	0.133887i
$137$	−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	$0.481041\pi$
$138$	−9.31975	−	8.81361i	−0.793350	−	0.750264i
$139$	0.119840	−	0.289319i	0.0101647	−	0.0245397i	−0.918716	−	0.394920i	$-0.870772\pi$
$139$	0.119840	−	0.289319i	0.0101647	−	0.0245397i	0.928880	+	0.370380i	$0.120772\pi$
$140$	4.84250	+	0.858047i	0.409266	+	0.0725182i
$141$	3.27290	+	20.4361i	0.275628	+	1.72103i
$142$	0.682244	−	5.18215i	0.0572526	−	0.434877i
$143$	−0.943539	+	1.22964i	−0.0789027	+	0.102828i
$144$	−5.47473	−	4.89538i	−0.456228	−	0.407948i
$145$	0.0561967	+	0.209729i	0.00466688	+	0.0174171i
$146$	3.20345	+	7.73381i	0.265119	+	0.640055i
$147$	10.8976	+	5.31443i	0.898816	+	0.438327i
$148$	−1.44529	+	3.48925i	−0.118802	+	0.286814i
$149$	1.31345	−	2.27495i	0.107602	−	0.186372i	−0.807197	−	0.590283i	$-0.799016\pi$
$149$	1.31345	−	2.27495i	0.107602	−	0.186372i	0.914798	+	0.403911i	$0.132350\pi$
$150$	7.44822	−	6.05275i	0.608145	−	0.494205i
$151$	−8.17586	−	2.19072i	−0.665342	−	0.178278i	−0.0896864	−	0.995970i	$-0.528586\pi$
$151$	−8.17586	−	2.19072i	−0.665342	−	0.178278i	−0.575656	+	0.817692i	$0.695253\pi$
$152$	−1.22376	+	2.11961i	−0.0992598	+	0.171923i
$153$	−11.1055	+	5.44685i	−0.897825	+	0.440352i
$154$	0.166956	−	0.942239i	0.0134537	−	0.0759277i
$155$	18.0225	+	18.0225i	1.44761	+	1.44761i
$156$	−4.90640	−	1.87369i	−0.392826	−	0.150015i
$157$	2.65465	+	4.59799i	0.211864	+	0.366960i	0.952298	−	0.305170i	$-0.0987132\pi$
$157$	2.65465	+	4.59799i	0.211864	+	0.366960i	−0.740434	+	0.672129i	$0.765380\pi$
$158$	−1.92561	−	14.6265i	−0.153194	−	1.16362i
$159$	12.0752	−	5.40120i	0.957626	−	0.428343i
$160$	9.35025	−	3.87300i	0.739202	−	0.306188i
$161$	16.4832	−	1.42818i	1.29906	−	0.112556i
$162$	10.5386	+	1.59468i	0.827988	+	0.125290i
$163$	21.8491	+	2.87649i	1.71135	+	0.225304i	0.921606	−	0.388127i	$-0.126878\pi$
$163$	21.8491	+	2.87649i	1.71135	+	0.225304i	0.789748	+	0.613431i	$0.210211\pi$
$164$	2.39441	+	1.83730i	0.186972	+	0.143469i
$165$	1.03786	+	1.27714i	0.0807972	+	0.0994250i
$166$	−3.70039	+	6.40926i	−0.287206	+	0.497455i
$167$	−3.28642	−	1.36128i	−0.254311	−	0.105339i	0.251886	−	0.967757i	$-0.418949\pi$
$167$	−3.28642	−	1.36128i	−0.254311	−	0.105339i	−0.506197	+	0.862418i	$0.668949\pi$
$168$	14.0046	−	1.60821i	1.08048	−	0.124076i
$169$	12.7565			0.981266
$170$	0.113655	+	15.1908i	0.00871693	+	1.16508i
$171$	−0.133145	−	2.38321i	−0.0101819	−	0.182249i
$172$	−5.03794	−	1.34991i	−0.384140	−	0.102930i
$173$	−8.09322	+	6.21015i	−0.615316	+	0.472149i	−0.868781	−	0.495196i	$-0.835096\pi$
$173$	−8.09322	+	6.21015i	−0.615316	+	0.472149i	0.253465	+	0.967345i	$0.418430\pi$
$174$	0.0750107	+	0.121934i	0.00568655	+	0.00924377i
$175$	−0.550334	+	12.3669i	−0.0416014	+	0.934851i
$176$	−0.286110	−	0.690731i	−0.0215664	−	0.0520658i
$177$	8.62167	−	3.85645i	0.648045	−	0.289869i
$178$	8.23157	+	2.20564i	0.616982	+	0.165320i
$179$	−2.00011	−	0.535928i	−0.149495	−	0.0400571i	0.183295	−	0.983058i	$-0.441324\pi$
$179$	−2.00011	−	0.535928i	−0.149495	−	0.0400571i	−0.332791	+	0.943001i	$0.607990\pi$
$180$	−3.14264	+	4.60653i	−0.234238	+	0.343351i
$181$	−8.39228	−	20.2608i	−0.623793	−	1.50597i	−0.847216	−	0.531248i	$-0.821723\pi$
$181$	−8.39228	−	20.2608i	−0.623793	−	1.50597i	0.223423	−	0.974722i	$-0.428277\pi$
$182$	−14.1112	+	7.33083i	−1.04600	+	0.543397i
$183$	−6.72400	+	4.13645i	−0.497053	+	0.305775i
$184$	15.2612	−	11.7104i	1.12507	−	0.863300i
$185$	−18.9956	−	5.08984i	−1.39658	−	0.374213i
$186$	14.7822	+	7.99309i	1.08388	+	0.586082i
$187$	−1.25916	+	0.00942085i	−0.0920791	+	0.000688920i
$188$	−7.13932			−0.520689
$189$	−10.5701	+	8.79056i	−0.768859	+	0.639419i
$190$	−2.70833	−	1.12183i	−0.196483	−	0.0813859i
$191$	−4.36728	+	7.56435i	−0.316005	+	0.547337i	−0.979651	−	0.200710i	$-0.935675\pi$
$191$	−4.36728	+	7.56435i	−0.316005	+	0.547337i	0.663645	+	0.748047i	$0.269008\pi$
$192$	11.7598	−	9.55652i	0.848689	−	0.689683i
$193$	1.97035	+	1.51190i	0.141829	+	0.108829i	0.677239	−	0.735763i	$-0.263176\pi$
$193$	1.97035	+	1.51190i	0.141829	+	0.108829i	−0.535410	+	0.844592i	$0.679843\pi$
$194$	10.4814	+	1.37991i	0.752523	+	0.0990716i
$195$	6.33825	−	26.6028i	0.453891	−	1.90506i
$196$	−2.40463	+	3.42194i	−0.171759	+	0.244424i
$197$	−3.28149	+	1.35924i	−0.233796	+	0.0968417i	−0.496506	−	0.868033i	$-0.665384\pi$
$197$	−3.28149	+	1.35924i	−0.233796	+	0.0968417i	0.262710	+	0.964875i	$0.415384\pi$
$198$	0.896325	+	0.611485i	0.0636991	+	0.0434564i
$199$	−1.83801	−	13.9610i	−0.130293	−	0.989672i	−0.924274	−	0.381730i	$-0.875329\pi$
$199$	−1.83801	−	13.9610i	−0.130293	−	0.989672i	0.793981	−	0.607942i	$-0.208005\pi$
$200$	7.19646	+	12.4646i	0.508866	+	0.881382i
$201$	6.61911	−	17.3327i	0.466876	−	1.22255i
$202$	−1.97095	−	1.97095i	−0.138676	−	0.138676i
$203$	−0.181819	−	0.0322166i	−0.0127612	−	0.00226117i
$204$	−1.24946	−	4.07979i	−0.0874797	−	0.285643i
$205$	−7.85768	+	13.6099i	−0.548804	+	0.950556i
$206$	15.7089	+	4.20918i	1.09449	+	0.293268i
$207$	−6.20124	+	17.7057i	−0.431016	+	1.23063i
$208$	−6.21208	+	10.7596i	−0.430730	+	0.746046i
$209$	0.0929882	−	0.224493i	0.00643213	−	0.0155285i
$210$	4.09916	+	16.3789i	0.282869	+	1.13025i
$211$	7.22776	+	17.4494i	0.497580	+	1.20126i	0.950783	+	0.309857i	$0.100281\pi$
$211$	7.22776	+	17.4494i	0.497580	+	1.20126i	−0.453204	+	0.891407i	$0.649719\pi$
$212$	1.18101	+	4.40760i	0.0811123	+	0.302715i
$213$	−7.32591	+	2.18379i	−0.501963	+	0.149631i
$214$	13.8941	−	18.1072i	0.949783	−	1.23778i
$215$	3.54486	−	26.9259i	0.241757	−	1.83633i
$216$	−4.86063	+	15.2272i	−0.330724	+	1.03608i
$217$	−20.3744	+	7.39636i	−1.38311	+	0.502098i
$218$	−1.24315	+	3.00122i	−0.0841965	+	0.203268i
$219$	8.41211	−	8.89520i	0.568438	−	0.601082i
$220$	−0.491624	+	0.283839i	−0.0331453	+	0.0191365i
$221$	12.8622	+	16.5052i	0.865208	+	1.11026i
$222$	−12.9611	+	0.361773i	−0.869893	+	0.0242806i
$223$	10.8718	+	10.8718i	0.728030	+	0.728030i	0.970227	−	0.242197i	$-0.0778679\pi$
$223$	10.8718	+	10.8718i	0.728030	+	0.728030i	−0.242197	+	0.970227i	$0.577868\pi$
$224$	−0.382631	+	8.59834i	−0.0255656	+	0.574501i
$225$	−12.5287	−	6.32932i	−0.835243	−	0.421954i
$226$	−1.56109	−	2.03446i	−0.103842	−	0.135330i
$227$	−5.00862	−	3.84325i	−0.332434	−	0.255085i	0.429034	−	0.903288i	$-0.358854\pi$
$227$	−5.00862	−	3.84325i	−0.332434	−	0.255085i	−0.761468	+	0.648203i	$0.775521\pi$
$228$	0.819015	+	0.0846538i	0.0542406	+	0.00560634i
$229$	1.20936	+	4.51338i	0.0799166	+	0.298253i	0.994303	−	0.106590i	$-0.0339931\pi$
$229$	1.20936	+	4.51338i	0.0799166	+	0.298253i	−0.914387	+	0.404842i	$0.867326\pi$
$230$	16.2918	+	16.2918i	1.07425	+	1.07425i
$231$	−1.35765	+	0.339779i	−0.0893267	+	0.0223558i
$232$	−0.198346	+	0.0821578i	−0.0130221	+	0.00539392i
$233$	−9.97577	+	7.65467i	−0.653534	+	0.501474i	−0.881493	−	0.472196i	$-0.843461\pi$
$233$	−9.97577	+	7.65467i	−0.653534	+	0.501474i	0.227959	+	0.973671i	$0.426795\pi$
$234$	−1.00578	−	18.0029i	−0.0657502	−	1.17689i
$235$	−4.85229	−	36.8568i	−0.316528	−	2.40427i
$236$	0.843241	+	3.14702i	0.0548903	+	0.204854i
$237$	−18.3774	+	11.3053i	−1.19374	+	0.734359i
$238$	−11.7446	−	5.38189i	−0.761289	−	0.348856i
$239$		−	2.62685i		−	0.169917i	−0.996384	−	0.0849586i	$-0.972924\pi$
$239$		−	2.62685i		−	0.169917i	0.996384	−	0.0849586i	$-0.0270758\pi$
$240$	9.58449	+	9.06397i	0.618676	+	0.585077i
$241$	−14.4894	+	1.90757i	−0.933344	+	0.122877i	−0.581835	−	0.813307i	$-0.697665\pi$
$241$	−14.4894	+	1.90757i	−0.933344	+	0.122877i	−0.351510	+	0.936184i	$0.614332\pi$
$242$	−6.45832	−	11.1861i	−0.415157	−	0.719072i
$243$	−4.16431	−	15.0219i	−0.267140	−	0.963658i
$244$	−1.04213	−	2.51592i	−0.0667155	−	0.161066i
$245$	−19.3001	−	10.0881i	−1.23304	−	0.644508i
$246$	−2.40149	+	10.0795i	−0.153113	+	0.642644i
$247$	−3.90036	+	1.04510i	−0.248174	+	0.0664981i
$248$	−15.3417	+	19.9936i	−0.974196	+	1.26960i
$249$	10.7665	+	1.11283i	0.682301	+	0.0705229i
$250$	0.938643	−	0.720246i	0.0593650	−	0.0455524i
$251$		−	8.06462i		−	0.509034i	−0.967068	−	0.254517i	$-0.918083\pi$
$251$		−	8.06462i		−	0.509034i	0.967068	−	0.254517i	$-0.0819166\pi$
$252$	−2.41757	−	4.07982i	−0.152293	−	0.257005i
$253$	−1.35043	+	1.35043i	−0.0849007	+	0.0849007i
$254$	6.77080	+	3.90912i	0.424837	+	0.245280i
$255$	20.2128	−	9.22320i	1.26577	−	0.577579i
$256$	6.46614	+	11.1997i	0.404134	+	0.699980i
$257$	−1.01902	−	3.80303i	−0.0635646	−	0.237226i	0.926833	−	0.375473i	$-0.122520\pi$
$257$	−1.01902	−	3.80303i	−0.0635646	−	0.237226i	−0.990398	+	0.138247i	$0.955853\pi$
$258$	−2.83166	−	17.6809i	−0.176291	−	1.10077i
$259$	10.7608	−	12.8024i	0.668645	−	0.795505i
$260$	8.71549	+	3.61007i	0.540511	+	0.223887i
$261$	0.117995	−	0.172959i	0.00730370	−	0.0107059i
$262$	10.3453	+	7.93826i	0.639137	+	0.490427i
$263$	14.2736	+	3.82461i	0.880151	+	0.235836i	0.670472	−	0.741935i	$-0.266092\pi$
$263$	14.2736	+	3.82461i	0.880151	+	0.235836i	0.209679	+	0.977770i	$0.432758\pi$
$264$	−1.11804	+	1.18225i	−0.0688108	+	0.0727624i
$265$	−21.9516	+	9.09264i	−1.34847	+	0.558556i
$266$	1.83944	−	1.68271i	0.112784	−	0.103173i
$267$	−1.97097	−	12.3068i	−0.120622	−	0.753164i
$268$	5.54265	+	3.20005i	0.338571	+	0.195474i
$269$	−1.65012	−	12.5339i	−0.100610	−	0.764206i	−0.965160	−	0.261660i	$-0.915730\pi$
$269$	−1.65012	−	12.5339i	−0.100610	−	0.764206i	0.864550	−	0.502546i	$-0.167603\pi$
$270$	−18.8420	−	3.39139i	−1.14669	−	0.206393i
$271$	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
$275$	−0.869879	−	1.13365i	−0.0524557	−	0.0683616i
$276$	−5.69249	−	3.07807i	−0.342648	−	0.185278i
$277$	9.41250	−	1.23918i	0.565543	−	0.0744551i	0.157667	−	0.987492i	$-0.449603\pi$
$277$	9.41250	−	1.23918i	0.565543	−	0.0744551i	0.407876	+	0.913037i	$0.366270\pi$
$278$	−0.0484076	+	0.367693i	−0.00290330	+	0.0220527i
$279$	1.84379	−	24.5084i	0.110385	−	1.46728i
$280$	−25.2258	+	2.18567i	−1.50753	+	0.130619i
$281$	−8.90961	+	8.90961i	−0.531503	+	0.531503i	−0.921019	−	0.389516i	$-0.872642\pi$
$281$	−8.90961	+	8.90961i	−0.531503	+	0.531503i	0.389516	+	0.921019i	$0.372642\pi$
$282$	−10.0079	−	22.3742i	−0.595964	−	1.33237i
$283$	−8.26982	+	10.7774i	−0.491590	+	0.640652i	−0.971605	−	0.236608i	$-0.923964\pi$
$283$	−8.26982	+	10.7774i	−0.491590	+	0.640652i	0.480016	+	0.877260i	$0.340631\pi$
$284$	−0.344195	−	2.61442i	−0.0204242	−	0.155137i
$285$	0.119623	+	4.28571i	0.00708588	+	0.253863i
$286$	0.702437	−	1.69583i	0.0415360	−	0.100277i
$287$	−7.65653	−	10.9542i	−0.451950	−	0.646605i
$288$	−8.71079	−	4.40058i	−0.513288	−	0.259307i
$289$	−4.15373	+	16.4847i	−0.244337	+	0.969690i
$290$	−0.128570	−	0.222690i	−0.00754990	−	0.0130768i
$291$	−4.41693	−	14.8174i	−0.258925	−	0.868612i
$292$	2.57093	+	3.35051i	0.150452	+	0.196074i
$293$		−	28.0797i		−	1.64043i	−0.572054	−	0.820216i	$-0.693853\pi$
$293$		−	28.0797i		−	1.64043i	0.572054	−	0.820216i	$-0.306147\pi$
$294$	−14.0950	−	2.73907i	−0.822036	−	0.159746i
$295$	−15.6734	+	6.49213i	−0.912540	+	0.377986i
$296$	2.53805	−	19.2784i	0.147521	−	1.12053i
$297$	0.281112	−	1.56181i	0.0163118	−	0.0906254i
$298$	−0.805181	+	3.00498i	−0.0466429	+	0.174074i
$299$	31.4650	+	4.14245i	1.81967	+	0.239564i
$300$	2.83928	−	3.92215i	0.163926	−	0.226445i
$301$	19.4686	+	12.4258i	1.12215	+	0.716212i
$302$	10.0241			0.576821
$303$	−1.45435	+	3.80833i	−0.0835501	+	0.218783i
$304$	0.504125	−	1.88142i	0.0289136	−	0.107907i
$305$	12.2802	−	7.08997i	0.703161	−	0.405970i
$306$	11.0343	−	9.63481i	0.630791	−	0.550785i
$307$		−	11.2866i		−	0.644158i	−0.946713	−	0.322079i	$-0.895618\pi$
$307$		−	11.2866i		−	0.644158i	0.946713	−	0.322079i	$-0.104382\pi$
$308$	−0.0416731	−	0.480967i	−0.00237454	−	0.0274056i
$309$	−3.76135	−	23.4859i	−0.213976	−	1.33607i
$310$	−26.1407	−	15.0923i	−1.48469	−	0.857187i
$311$	−31.2688	+	4.11662i	−1.77309	+	0.233432i	−0.944980	−	0.327129i	$-0.893919\pi$
$311$	−31.2688	+	4.11662i	−1.77309	+	0.233432i	−0.828113	+	0.560561i	$0.810586\pi$
$312$	26.8969	+	2.78008i	1.52274	+	0.157391i
$313$	0.0348538	−	0.264741i	0.00197005	−	0.0149640i	−0.990432	−	0.138004i	$-0.955931\pi$
$313$	0.0348538	−	0.264741i	0.00197005	−	0.0149640i	0.992402	+	0.123040i	$0.0392645\pi$
$314$	−4.44609	−	4.44609i	−0.250907	−	0.250907i
$315$	19.4190	−	15.2536i	1.09414	−	0.859444i
$316$	−2.84824	−	6.87626i	−0.160226	−	0.386820i
$317$	−3.41045	−	0.448994i	−0.191550	−	0.0252180i	0.0341408	−	0.999417i	$-0.489131\pi$
$317$	−3.41045	−	0.448994i	−0.191550	−	0.0252180i	−0.225691	+	0.974199i	$0.572464\pi$
$318$	−12.1576	+	9.87982i	−0.681765	+	0.554033i
$319$	0.0184588	−	0.0106572i	0.00103349	−	0.000596687i
$320$	−21.5935	+	16.5693i	−1.20711	+	0.926251i
$321$	−32.4713	−	7.73646i	−1.81237	−	0.431807i
$322$	−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
$325$	−6.14584	+	22.9366i	−0.340910	+	1.27229i
$326$	−25.8755	+	3.40657i	−1.43311	+	0.188673i
$327$	4.74918	−	0.132560i	0.262631	−	0.00733059i
$328$	−14.3560	−	5.94645i	−0.792678	−	0.328338i
$329$	30.1433	+	9.53191i	1.66185	+	0.525511i
$330$	−1.57870	−	1.14284i	−0.0869044	−	0.0629110i
$331$	−9.68928	+	2.59624i	−0.532571	+	0.142702i	−0.515075	−	0.857145i	$-0.672236\pi$
$331$	−9.68928	+	2.59624i	−0.532571	+	0.142702i	−0.0174958	+	0.999847i	$0.505569\pi$
$332$	−0.966361	+	3.60651i	−0.0530359	+	0.197933i
$333$	8.22297	+	17.0878i	0.450616	+	0.936408i
$334$	4.17668	+	0.549871i	0.228538	+	0.0300876i
$335$	−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	0.517552	−	0.855652i	$-0.326844\pi$
$337$	5.11219	+	2.11754i	0.278479	+	0.115350i	−0.239073	+	0.971002i	$0.576844\pi$
$338$	−14.5925	+	3.91004i	−0.793726	+	0.212678i
$339$	−1.78389	+	3.29907i	−0.0968876	+	0.179181i
$340$	2.03893	+	7.38784i	0.110576	+	0.400662i
$341$	1.25100	−	2.16680i	0.0677456	−	0.117339i
$342$	0.882799	+	2.68541i	0.0477363	+	0.145211i
$343$	14.7214	−	11.2374i	0.794881	−	0.606765i
$344$	26.8532			1.44783
$345$	12.0216	−	31.4795i	0.647221	−	1.69480i
$346$	7.35457	−	9.58466i	0.395384	−	0.515274i
$347$	4.08676	+	3.13588i	0.219389	+	0.168343i	0.712609	−	0.701562i	$-0.247513\pi$
$347$	4.08676	+	3.13588i	0.219389	+	0.168343i	−0.493220	+	0.869905i	$0.664180\pi$
$348$	0.0524754	+	0.0496255i	0.00281297	+	0.00266021i
$349$	−16.9637	+	16.9637i	−0.908047	+	0.908047i	−0.996114	−	0.0880677i	$-0.971931\pi$
$349$	−16.9637	+	16.9637i	−0.908047	+	0.908047i	0.0880677	+	0.996114i	$0.471931\pi$
$350$	−3.16110	−	14.3156i	−0.168968	−	0.765199i
$351$	−23.4344	+	12.0936i	−1.25083	+	0.645507i
$352$	−0.604800	−	0.788191i	−0.0322360	−	0.0420107i
$353$	5.30340	−	3.06192i	0.282272	−	0.162970i	−0.352180	−	0.935932i	$-0.614559\pi$
$353$	5.30340	−	3.06192i	0.282272	−	0.162970i	0.634451	+	0.772963i	$0.281226\pi$
$354$	−8.68052	+	7.05417i	−0.461364	+	0.374925i
$355$	13.2630	−	3.55382i	0.703929	−	0.188617i
$356$	4.29936			0.227866
$357$	−0.171645	+	18.8937i	−0.00908443	+	0.999959i
$358$	2.45225			0.129606
$359$	−1.57827	+	0.422896i	−0.0832978	+	0.0223196i	−0.300227	−	0.953868i	$-0.597063\pi$
$359$	−1.57827	+	0.422896i	−0.0832978	+	0.0223196i	0.216929	+	0.976187i	$0.430396\pi$
$360$	9.49033	−	27.0966i	0.500184	−	1.42812i
$361$	−15.9062	+	9.18348i	−0.837171	+	0.483341i
$362$	15.8104	+	20.6045i	0.830975	+	1.08295i
$363$	−11.0775	+	15.3023i	−0.581417	+	0.803161i
$364$	−5.91939	+	5.41500i	−0.310260	+	0.283823i
$365$	−15.5497	+	15.5497i	−0.813906	+	0.813906i
$366$	6.42390	−	6.79281i	0.335783	−	0.355066i
$367$	10.3486	+	7.94079i	0.540194	+	0.414506i	0.842493	−	0.538708i	$-0.181087\pi$
$367$	10.3486	+	7.94079i	0.540194	+	0.414506i	−0.302298	+	0.953213i	$0.597754\pi$
$368$	−9.31939	+	12.1453i	−0.485807	+	0.633116i
$369$	14.8908	−	2.81302i	0.775185	−	0.146440i
$370$	23.2897			1.21077
$371$	0.898302	−	20.1863i	0.0466375	−	1.04802i
$372$	8.24727	+	1.96496i	0.427601	+	0.101878i
$373$	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	$-0.0516133\pi$
$374$	1.43750	−	0.396729i	0.0743316	−	0.0205144i
$375$	−1.52210	−	0.823038i	−0.0786010	−	0.0425015i
$376$	35.5048	−	9.51348i	1.83102	−	0.490620i
$377$	−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	−0.805531	−	0.592554i	$-0.798120\pi$
$379$	3.56389	−	8.60399i	0.183065	−	0.441957i	0.988595	+	0.150597i	$0.0481196\pi$
$380$	−1.46629	−	0.193041i	−0.0752191	−	0.00990279i
$381$	1.17561	−	11.3738i	0.0602281	−	0.582699i
$382$	2.67727	−	9.99171i	0.136981	−	0.511220i
$383$	18.3958	−	4.92914i	0.939982	−	0.251867i	0.243876	−	0.969806i	$-0.421581\pi$
$383$	18.3958	−	4.92914i	0.939982	−	0.251867i	0.696106	+	0.717939i	$0.254914\pi$
$384$	−3.91512	+	5.40829i	−0.199792	+	0.275991i
$385$	2.45467	−	0.542030i	0.125102	−	0.0276244i
$386$	−2.71736	−	1.12557i	−0.138310	−	0.0572898i
$387$	−21.9142	+	14.3389i	−1.11396	+	0.728890i
$388$	5.28794	−	0.696170i	0.268454	−	0.0353427i
$389$	−1.25267	+	4.67502i	−0.0635127	+	0.237033i	−0.990384	−	0.138347i	$-0.955821\pi$
$389$	−1.25267	+	4.67502i	−0.0635127	+	0.237033i	0.926871	+	0.375380i	$0.122488\pi$
$390$	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
$393$	4.42014	−	18.5521i	0.222967	−	0.935832i
$394$	3.33716	−	2.56070i	0.168124	−	0.129006i
$395$	33.5629	−	19.3776i	1.68873	−	0.974991i
$396$	0.516637	+	0.180947i	0.0259620	+	0.00909295i
$397$	−30.3821	−	3.99989i	−1.52484	−	0.200749i	−0.678979	−	0.734158i	$-0.737577\pi$
$397$	−30.3821	−	3.99989i	−1.52484	−	0.200749i	−0.845857	+	0.533409i	$0.820911\pi$
$398$	6.38181	+	15.4071i	0.319891	+	0.772286i
$399$	−3.34498	−	1.45091i	−0.167458	−	0.0726364i
$400$	−8.09936	−	8.09936i	−0.404968	−	0.404968i
$401$	2.08520	−	15.8386i	0.104130	−	0.790944i	−0.857091	−	0.515165i	$-0.827731\pi$
$401$	2.08520	−	15.8386i	0.104130	−	0.790944i	0.961221	−	0.275779i	$-0.0889360\pi$
$402$	−2.25907	+	21.8562i	−0.112672	+	1.09009i
$403$	−41.2221	+	5.42699i	−2.05342	+	0.270338i
$404$	−1.21783	−	0.703114i	−0.0605893	−	0.0349813i
$405$	6.72413	+	27.1804i	0.334125	+	1.35061i
$406$	0.217862	−	0.0188765i	0.0108123	−	0.000936827i
$407$			1.93048i			0.0956903i
$408$	11.6502	+	18.6244i	0.576773	+	0.922044i
$409$	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	$0.0957654\pi$
$410$	4.81699	−	17.9772i	0.237894	−	0.887833i
$411$	−16.9528	−	6.47404i	−0.836220	−	0.319341i
$412$	8.20479			0.404221
$413$	0.641386	−	14.4130i	0.0315605	−	0.709217i
$414$	1.66673	−	22.1548i	0.0819154	−	1.08885i
$415$	−19.2754	−	2.53766i	−0.946192	−	0.124569i
$416$	−4.27302	+	15.9471i	−0.209502	+	0.781872i
$417$	0.519800	−	0.154948i	0.0254547	−	0.00758782i
$418$	−0.0375613	+	0.285307i	−0.00183718	+	0.0139548i
$419$	23.8135	−	9.86386i	1.16336	−	0.481881i	0.284370	−	0.958714i	$-0.408215\pi$
$419$	23.8135	−	9.86386i	1.16336	−	0.481881i	0.878994	+	0.476833i	$0.158215\pi$
$420$	4.13626	+	7.44643i	0.201829	+	0.363349i
$421$			22.0637i			1.07532i	0.843161	+	0.537660i	$0.180692\pi$
$421$			22.0637i			1.07532i	−0.843161	+	0.537660i	$0.819308\pi$
$422$	−13.6165	−	17.7454i	−0.662842	−	0.863833i
$423$	−23.8945	+	26.7224i	−1.16179	+	1.29929i
$424$	−11.7467	−	20.3458i	−0.570468	−	0.988080i
$425$	−17.7673	+	7.51568i	−0.861841	+	0.364564i
$426$	7.71096	−	4.74360i	0.373597	−	0.229828i
$427$	1.04094	+	12.0140i	0.0503747	+	0.581397i
$428$	4.40645	−	10.6381i	0.212994	−	0.514213i
$429$	−2.68352	+	0.0749028i	−0.129561	+	0.00361634i
$430$	4.19811	+	31.8878i	0.202451	+	1.53777i
$431$	−8.16054	+	10.6350i	−0.393080	+	0.512271i	−0.947409	−	0.320026i	$-0.896308\pi$
$431$	−8.16054	+	10.6350i	−0.393080	+	0.512271i	0.554329	+	0.832298i	$0.312975\pi$
$432$	0.599994	−	12.7064i	0.0288672	−	0.611336i
$433$	−10.0272	+	10.0272i	−0.481876	+	0.481876i	−0.905730	−	0.423855i	$-0.860677\pi$
$433$	−10.0272	+	10.0272i	−0.481876	+	0.481876i	0.423855	+	0.905730i	$0.360677\pi$
$434$	21.0398	−	14.7060i	1.00994	−	0.705909i
$435$	−0.220527	+	0.304633i	−0.0105734	+	0.0146060i
$436$	−0.213917	+	1.62486i	−0.0102448	+	0.0778168i
$437$	−4.93292	+	0.649431i	−0.235973	+	0.0310665i
$438$	−6.89635	+	12.7539i	−0.329520	+	0.609405i
$439$	−19.5753	−	25.5110i	−0.934277	−	1.21757i	−0.975851	−	0.218438i	$-0.929904\pi$
$439$	−19.5753	−	25.5110i	−0.934277	−	1.21757i	0.0415736	−	0.999135i	$-0.486763\pi$
$440$	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	$0.613239\pi$
$444$	−6.26890	+	1.86870i	−0.297509	+	0.0886846i
$445$	2.92209	+	22.1955i	0.138520	+	1.05217i
$446$	−15.7689	−	9.10421i	−0.746681	−	0.431097i
$447$	4.49266	−	0.719514i	0.212495	−	0.0340318i
$448$	−4.99097	−	22.6024i	−0.235801	−	1.06786i
$449$	−13.1988	+	5.46710i	−0.622888	+	0.258009i	−0.671728	−	0.740798i	$-0.734448\pi$
$449$	−13.1988	+	5.46710i	−0.622888	+	0.258009i	0.0488401	+	0.998807i	$0.484448\pi$
$450$	16.2719	+	3.40007i	0.767065	+	0.160281i
$451$	1.49013	+	0.399280i	0.0701676	+	0.0188014i
$452$	−1.02639	−	0.787580i	−0.0482775	−	0.0370447i
$453$	−5.98608	−	13.3828i	−0.281250	−	0.628778i
$454$	6.90751	+	2.86119i	0.324186	+	0.134282i
$455$	−31.9781	−	26.8785i	−1.49916	−	1.26008i
$456$	−4.18588	+	0.670381i	−0.196022	+	0.0313935i
$457$	−5.46980	−	20.4136i	−0.255867	−	0.954907i	−0.967606	−	0.252464i	$-0.918759\pi$
$457$	−5.46980	−	20.4136i	−0.255867	−	0.954907i	0.711740	−	0.702443i	$-0.247908\pi$
$458$	−2.76684	−	4.79230i	−0.129286	−	0.223930i
$459$	−19.4524	−	8.97791i	−0.907962	−	0.419053i
$460$	10.0665	+	5.81192i	0.469355	+	0.270982i
$461$	15.4525	−	15.4525i	0.719695	−	0.719695i	−0.248848	−	0.968543i	$-0.580052\pi$
$461$	15.4525	−	15.4525i	0.719695	−	0.719695i	0.968543	+	0.248848i	$0.0800519\pi$
$462$	1.44890	−	0.804822i	0.0674092	−	0.0374437i
$463$			14.1526i			0.657725i	0.944378	+	0.328862i	$0.106665\pi$
$463$			14.1526i			0.657725i	−0.944378	+	0.328862i	$0.893335\pi$
$464$	0.135548	−	0.104010i	0.00629265	−	0.00482852i
$465$	−4.53878	+	43.9121i	−0.210481	+	2.03637i
$466$	9.06529	−	11.8141i	0.419942	−	0.547279i
$467$	−5.95186	+	1.59480i	−0.275419	+	0.0737983i	−0.393885	−	0.919160i	$-0.628869\pi$
$467$	−5.95186	+	1.59480i	−0.275419	+	0.0737983i	0.118466	+	0.992958i	$0.462202\pi$
$468$	−2.84087	−	8.64175i	−0.131319	−	0.399465i
$469$	−19.1294	−	20.9112i	−0.883313	−	0.965590i
$470$	16.8478	+	40.6742i	0.777132	+	1.87616i
$471$	−3.28073	+	8.59087i	−0.151168	+	0.395846i
$472$	−8.38710	−	14.5269i	−0.386047	−	0.668654i
$473$	−2.64318	+	0.347981i	−0.121534	+	0.0160002i
$474$	17.5571	−	18.5654i	0.806426	−	0.852737i
$475$		−	3.72272i		−	0.170810i
$476$	−6.42606	−	1.08912i	−0.294538	−	0.0499196i
$477$	20.4503	+	10.3312i	0.936356	+	0.473035i
$478$	0.805170	+	3.00493i	0.0368276	+	0.137442i
$479$	1.24660	+	9.46883i	0.0569584	+	0.432642i	0.996037	+	0.0889396i	$0.0283478\pi$
$479$	1.24660	+	9.46883i	0.0569584	+	0.432642i	−0.939079	+	0.343702i	$0.888319\pi$
$480$	15.4196	+	8.33775i	0.703805	+	0.380564i
$481$	25.4510	−	19.5293i	1.16047	−	0.890458i
$482$	15.9901	−	6.62333i	0.728331	−	0.301685i
$483$	19.9249	+	20.5962i	0.906614	+	0.937162i
$484$	−4.60787	−	4.60787i	−0.209449	−	0.209449i
$485$	7.18796	+	26.8258i	0.326389	+	1.21810i
$486$	9.36811	+	15.9076i	0.424946	+	0.721583i
$487$	−0.00382137	−	0.00293224i	−0.000173163	−	0.000132872i	0.608675	−	0.793420i	$-0.291701\pi$
$487$	−0.00382137	−	0.00293224i	−0.000173163	−	0.000132872i	−0.608848	+	0.793287i	$0.708368\pi$
$488$	8.53523	+	11.1233i	0.386372	+	0.503530i
$489$	20.0000	+	32.5111i	0.904433	+	1.47020i
$490$	25.1701	+	5.62435i	1.13707	+	0.254082i
$491$	5.12548	+	5.12548i	0.231310	+	0.231310i	0.813239	−	0.581929i	$-0.197702\pi$
$491$	5.12548	+	5.12548i	0.231310	+	0.231310i	−0.581929	+	0.813239i	$0.697702\pi$
$492$	0.145854	+	5.22545i	0.00657560	+	0.235582i
$493$	−0.0765546	−	0.277387i	−0.00344785	−	0.0124929i
$494$	4.14140	−	2.39104i	0.186330	−	0.107578i
$495$	−0.583006	+	2.79012i	−0.0262042	+	0.125407i
$496$	7.67506	−	18.5292i	0.344620	−	0.831987i
$497$	−2.03735	+	11.4980i	−0.0913875	+	0.515756i
$498$	−12.6572	+	2.02710i	−0.567184	+	0.0908364i
$499$	3.22455	−	24.4929i	0.144351	−	1.09645i	−0.753907	−	0.656981i	$-0.771833\pi$
$499$	3.22455	−	24.4929i	0.144351	−	1.09645i	0.898257	−	0.439470i	$-0.144834\pi$
$500$	0.363368	−	0.473550i	0.0162503	−	0.0211778i
$501$	−1.76008	−	5.90449i	−0.0786344	−	0.263793i
$502$	2.47193	+	9.22535i	0.110327	+	0.411748i
$503$	−6.21482	−	15.0039i	−0.277105	−	0.668990i	0.722648	−	0.691216i	$-0.242925\pi$
$503$	−6.21482	−	15.0039i	−0.277105	−	0.668990i	−0.999753	+	0.0222257i	$0.992925\pi$
$504$	17.4595	+	17.0680i	0.777706	+	0.760267i
$505$	2.80213	−	6.76493i	0.124693	−	0.301035i
$506$	1.13087	−	1.95872i	0.0502732	−	0.0870757i
$507$	13.9343	+	17.1469i	0.618845	+	0.761520i
$508$	3.80994	+	1.02087i	0.169039	+	0.0452938i
$509$	−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	$0.981759\pi$
$510$	−20.2949	+	16.7462i	−0.898673	+	0.741534i
$511$	−6.38150	−	17.5788i	−0.282301	−	0.777642i
$512$	−16.2811	−	16.2811i	−0.719531	−	0.719531i
$513$	3.05801	−	2.78224i	0.135015	−	0.122839i
$514$	2.33137	+	4.03805i	0.102832	+	0.178111i
$515$	5.57644	+	42.3572i	0.245727	+	1.86648i
$516$	−3.68860	−	8.24643i	−0.162382	−	0.363029i
$517$	−3.37149	+	1.39652i	−0.148278	+	0.0614187i
$518$	−8.38547	+	17.9434i	−0.368437	+	0.788389i
$519$	−17.1880	−	4.09514i	−0.754471	−	0.179757i
$520$	−48.1538	−	6.33957i	−2.11169	−	0.278009i
$521$	−32.5720	−	24.9934i	−1.42701	−	1.09498i	−0.979670	−	0.200616i	$-0.935706\pi$
$521$	−32.5720	−	24.9934i	−1.42701	−	1.09498i	−0.447337	−	0.894365i	$-0.647628\pi$
$522$	−0.0819633	+	0.234020i	−0.00358744	+	0.0102428i
$523$	8.40522	−	14.5583i	0.367535	−	0.636588i	−0.621645	−	0.783299i	$-0.713535\pi$
$523$	8.40522	−	14.5583i	0.367535	−	0.636588i	0.989179	+	0.146711i	$0.0468686\pi$
$524$	6.07797	+	2.51758i	0.265518	+	0.109981i
$525$	−17.2244	+	12.7691i	−0.751736	+	0.557288i
$526$	−17.5003			−0.763051
$527$	−24.0632	−	23.7058i	−1.04821	−	1.03264i
$528$	0.615934	−	1.13909i	0.0268051	−	0.0495726i
$529$	15.5563	+	4.16831i	0.676362	+	0.181231i
$530$	22.3240	−	17.1298i	0.969693	−	0.744072i
$531$	14.6015	+	7.37649i	0.633651	+	0.320112i
$532$	0.676667	−	1.06019i	0.0293373	−	0.0459652i
$533$	−9.81057	−	23.6848i	−0.424943	−	1.02590i
$534$	6.02686	+	13.4740i	0.260808	+	0.583075i
$535$	57.9142	+	15.5181i	2.50385	+	0.670905i
$536$	−31.8285	−	8.52843i	−1.37478	−	0.368372i
$537$	−1.46441	−	3.27391i	−0.0631940	−	0.141280i
$538$	5.72945	+	13.8321i	0.247014	+	0.596345i
$539$	−0.466202	+	2.08635i	−0.0200808	+	0.0898655i
$540$	−9.62480	+	0.807626i	−0.414185	+	0.0347547i
$541$	14.1069	−	10.8246i	0.606503	−	0.465386i	−0.259283	−	0.965801i	$-0.583486\pi$
$541$	14.1069	−	10.8246i	0.606503	−	0.465386i	0.865785	+	0.500416i	$0.166819\pi$
$542$	−22.7475	−	6.09516i	−0.977087	−	0.261810i
$543$	18.0668	−	33.4122i	0.775320	−	1.43386i
$544$	−12.3531	+	5.22543i	−0.529633	+	0.224038i
$545$	−8.53375			−0.365546
$546$	−25.2681	−	10.9602i	−1.08138	−	0.469055i
$547$	27.7079	+	11.4770i	1.18471	+	0.490721i	0.886027	−	0.463633i	$-0.153454\pi$
$547$	27.7079	+	11.4770i	1.18471	+	0.490721i	0.298678	+	0.954354i	$0.403454\pi$
$548$	3.12992	−	5.42118i	0.133703	−	0.231581i
$549$	−12.9050	−	4.51985i	−0.550771	−	0.192902i
$550$	1.34256	+	1.03018i	0.0572469	+	0.0439271i
$551$	0.0550540	+	0.00724800i	0.00234538	+	0.000308775i
$552$	32.4112	+	7.72213i	1.37951	+	0.328676i
$553$	2.84500	+	32.8353i	0.120982	+	1.39630i
$554$	−10.3874	+	4.30260i	−0.441319	+	0.182800i
$555$	−13.9079	−	31.0931i	−0.590356	−	1.31983i
$556$	0.0244219	+	0.185503i	0.00103572	+	0.00786707i
$557$	2.67352	+	4.63068i	0.113281	+	0.196208i	0.917091	−	0.398678i	$-0.130531\pi$
$557$	2.67352	+	4.63068i	0.113281	+	0.196208i	−0.803810	+	0.594886i	$0.797197\pi$
$558$	5.40300	+	28.6010i	0.228727	+	1.21078i
$559$	31.3269	+	31.3269i	1.32498	+	1.32498i
$560$	18.9410	−	6.87600i	0.800404	−	0.290564i
$561$	−1.38809	−	1.68224i	−0.0586053	−	0.0710244i
$562$	7.46103	−	12.9229i	0.314725	−	0.545119i
$563$	37.7661	+	10.1194i	1.59165	+	0.426482i	0.942508	−	0.334184i	$-0.108461\pi$
$563$	37.7661	+	10.1194i	1.59165	+	0.426482i	0.649144	+	0.760665i	$0.275127\pi$
$564$	−7.79854	−	9.59649i	−0.328378	−	0.404085i
$565$	3.36829	−	5.83405i	0.141705	−	0.245440i
$566$	6.15664	−	14.8634i	0.258783	−	0.624757i
$567$	−23.3621	−	4.60576i	−0.981115	−	0.193424i
$568$	5.19557	+	12.5432i	0.218001	+	0.526301i
$569$	−7.98316	−	29.7936i	−0.334672	−	1.24901i	−0.904225	−	0.427057i	$-0.859550\pi$
$569$	−7.98316	−	29.7936i	−0.334672	−	1.24901i	0.569553	−	0.821954i	$-0.307116\pi$
$570$	−1.45047	−	4.86588i	−0.0607536	−	0.203809i
$571$	17.4620	−	22.7569i	0.730763	−	0.952349i	−0.269179	−	0.963090i	$-0.586752\pi$
$571$	17.4620	−	22.7569i	0.730763	−	0.952349i	0.999942	+	0.0107414i	$0.00341915\pi$
$572$	0.120873	−	0.918125i	0.00505397	−	0.0383887i
$573$	−14.9383	+	2.39242i	−0.624058	+	0.0999449i
$574$	12.1161	+	10.1840i	0.505718	+	0.425070i
$575$	−11.1969	+	27.0317i	−0.466944	+	1.12730i
$576$	25.6913	+	5.36827i	1.07047	+	0.223678i
$577$	−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	$0.559492\pi$
$578$	−0.301243	−	20.1305i	−0.0125301	−	0.837320i
$579$	0.120022	+	4.30000i	0.00498796	+	0.178702i
$580$	−0.0917319	−	0.0917319i	−0.00380896	−	0.00380896i
$581$	8.89526	−	13.9370i	0.369038	−	0.578203i
$582$	9.59441	+	15.5962i	0.397701	+	0.646483i
$583$	1.41989	+	1.85044i	0.0588058	+	0.0766372i
$584$	−17.2503	−	13.2366i	−0.713822	−	0.547735i
$585$	42.6822	−	20.5394i	1.76469	−	0.849201i
$586$	8.60684	+	32.1212i	0.355545	+	1.32691i
$587$	−1.56011	−	1.56011i	−0.0643927	−	0.0643927i	0.674177	−	0.738570i	$-0.264498\pi$
$587$	−1.56011	−	1.56011i	−0.0643927	−	0.0643927i	−0.738570	+	0.674177i	$0.764498\pi$
$588$	−7.22634	+	0.505672i	−0.298009	+	0.0208535i
$589$	6.02216	−	2.49446i	0.248139	−	0.102782i
$590$	15.9393	−	12.2307i	0.656211	−	0.503528i
$591$	−5.41154	−	2.92615i	−0.222601	−	0.120366i
$592$	2.01984	+	15.3422i	0.0830149	+	0.630561i
$593$	1.46469	+	5.46628i	0.0601474	+	0.224473i	0.989457	−	0.144829i	$-0.0462633\pi$
$593$	1.46469	+	5.46628i	0.0601474	+	0.224473i	−0.929309	+	0.369303i	$0.879597\pi$
$594$	0.157145	+	1.87276i	0.00644775	+	0.0768404i
$595$	1.25506	−	33.9148i	0.0514526	−	1.39037i
$596$			1.56951i			0.0642894i
$597$	16.7583	−	17.7207i	0.685873	−	0.725261i
$598$	−37.2635	+	4.90583i	−1.52382	+	0.200614i
$599$	11.5169	+	19.9479i	0.470568	+	0.815047i	0.999433	−	0.0336583i	$-0.0107158\pi$
$599$	11.5169	+	19.9479i	0.470568	+	0.815047i	−0.528866	+	0.848706i	$0.677382\pi$
$600$	−8.89369	+	23.2888i	−0.363083	+	0.950763i
$601$	−14.0871	−	34.0092i	−0.574624	−	1.38726i	−0.897581	−	0.440850i	$-0.854677\pi$
$601$	−14.0871	−	34.0092i	−0.574624	−	1.38726i	0.322957	−	0.946414i	$-0.395323\pi$
$602$	−26.0794	−	8.24683i	−1.06292	−	0.336116i
$603$	30.5284	−	10.0359i	1.24321	−	0.408692i
$604$	4.88488	−	1.30890i	0.198763	−	0.0532584i
$605$	20.6564	−	26.9199i	0.839801	−	1.09445i
$606$	0.496362	−	4.80224i	0.0201633	−	0.195078i
$607$	5.93190	−	4.55171i	0.240768	−	0.184748i	−0.481328	−	0.876541i	$-0.659845\pi$
$607$	5.93190	−	4.55171i	0.240768	−	0.184748i	0.722096	+	0.691793i	$0.243179\pi$
$608$		−	2.58829i		−	0.104969i
$609$	−0.155302	−	0.279587i	−0.00629316	−	0.0113294i
$610$	−11.8745	+	11.8745i	−0.480783	+	0.480783i
$611$	52.5182	+	30.3214i	2.12466	+	1.22667i
$612$	4.11912	−	6.13599i	0.166506	−	0.248033i
$613$	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	$0.568707\pi$
$614$	3.45950	+	12.9110i	0.139614	+	0.521046i
$615$	−26.8773	+	4.30448i	−1.08380	+	0.173574i
$616$	0.848156	+	2.33638i	0.0341732	+	0.0941354i
$617$	−37.8275	−	15.6687i	−1.52288	−	0.630796i	−0.544712	−	0.838623i	$-0.683361\pi$
$617$	−37.8275	−	15.6687i	−1.52288	−	0.630796i	−0.978166	+	0.207827i	$0.933361\pi$
$618$	11.5015	+	25.7133i	0.462658	+	1.03434i
$619$	−29.3507	−	22.5216i	−1.17970	−	0.905218i	−0.182746	−	0.983160i	$-0.558498\pi$
$619$	−29.3507	−	22.5216i	−1.17970	−	0.905218i	−0.996958	+	0.0779419i	$0.975165\pi$
$620$	−14.7094	−	3.94138i	−0.590744	−	0.158289i
$621$	−30.5733	+	11.0050i	−1.22687	+	0.441614i
$622$	34.5075	−	14.2935i	1.38363	−	0.573116i
$623$	−18.1525	−	5.74020i	−0.727266	−	0.229976i
$624$	−21.2485	+	3.40301i	−0.850620	+	0.136230i
$625$	22.9518	+	13.2512i	0.918073	+	0.530050i
$626$	0.0412767	+	0.313528i	0.00164975	+	0.0125311i
$627$	0.403332	−	0.120230i	0.0161075	−	0.00480151i
$628$	−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	−0.0846337	−	0.996412i	$-0.526972\pi$
$631$	22.9036	−	22.9036i	0.911778	−	0.911778i	0.996412	+	0.0846337i	$0.0269720\pi$
$632$	23.3276	+	30.4011i	0.927923	+	1.20929i
$633$	−15.5598	+	28.7759i	−0.618448	+	1.14374i
$634$	4.03893	−	0.531736i	0.160407	−	0.0211179i
$635$	−2.68080	+	20.3627i	−0.106384	+	0.808069i
$636$	−4.63452	+	6.40206i	−0.183771	+	0.253858i
$637$	32.2222	−	14.9598i	1.27669	−	0.592728i
$638$	−0.0178489	+	0.0178489i	−0.000706646	+	0.000706646i
$639$	−10.9377	−	7.46187i	−0.432690	−	0.295187i
$640$	7.30059	−	9.51432i	0.288581	−	0.376086i
$641$	−2.62579	−	19.9448i	−0.103712	−	0.787774i	−0.961700	−	0.274104i	$-0.911619\pi$
$641$	−2.62579	−	19.9448i	−0.103712	−	0.787774i	0.857988	−	0.513670i	$-0.171714\pi$
$642$	39.5162	−	1.10298i	1.55958	−	0.0435313i
$643$	−12.2316	+	29.5297i	−0.482367	+	1.16454i	0.476114	+	0.879383i	$0.342045\pi$
$643$	−12.2316	+	29.5297i	−0.482367	+	1.16454i	−0.958482	+	0.285154i	$0.907955\pi$
$644$	−8.10225	+	5.66314i	−0.319273	+	0.223159i
$645$	40.0652	−	24.6472i	1.57757	−	0.970482i
$646$	3.60035	+	1.45985i	0.141654	+	0.0574372i
$647$	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	$0.555824\pi$
$648$	−25.7774	+	10.0996i	−1.01263	+	0.396751i
$649$	1.01380	+	1.32121i	0.0397951	+	0.0518620i
$650$		−	28.1216i		−	1.10302i
$651$	−32.1977	−	19.3075i	−1.26193	−	0.756720i
$652$	−12.1647	+	5.03878i	−0.476406	+	0.197334i
$653$	3.06130	−	23.2529i	0.119798	−	0.909955i	−0.820986	−	0.570948i	$-0.806576\pi$
$653$	3.06130	−	23.2529i	0.119798	−	0.909955i	0.940784	−	0.339007i	$-0.110091\pi$
$654$	−5.39210	+	1.60733i	−0.210848	+	0.0628517i
$655$	−8.86608	+	33.0887i	−0.346426	+	1.29288i
$656$	12.2604	+	1.61411i	0.478687	+	0.0630204i
$657$	21.1455	+	1.59081i	0.824966	+	0.0620632i
$658$	−37.4034	−	1.66447i	−1.45814	−	0.0648878i
$659$	33.2924			1.29689			0.648443	−	0.761263i	$-0.275420\pi$
$659$	33.2924			1.29689			0.648443	+	0.761263i	$0.275420\pi$
$660$	−0.918548	−	0.350781i	−0.0357544	−	0.0136541i
$661$	−7.42877	+	27.7245i	−0.288946	+	1.07836i	0.656962	+	0.753924i	$0.271841\pi$
$661$	−7.42877	+	27.7245i	−0.288946	+	1.07836i	−0.945908	+	0.324436i	$0.894826\pi$
$662$	10.2881	−	5.93981i	0.399857	−	0.230857i
$663$	−8.13602	+	35.3183i	−0.315977	+	1.37165i
$664$		−	19.2233i		−	0.746011i
$665$	5.93316	+	2.77273i	0.230078	+	0.107522i
$666$	−14.6442	−	17.0268i	−0.567450	−	0.659775i
$667$	−0.377963	−	0.218217i	−0.0146348	−	0.00844940i
$668$	2.10716	−	0.277413i	0.0815284	−	0.0107334i
$669$	−2.73794	+	26.4893i	−0.105855	+	1.02413i
$670$	5.15148	−	39.1293i	0.199019	−	1.51170i
$671$	−0.984274	−	0.984274i	−0.0379975	−	0.0379975i
$672$	−11.9756	+	8.87795i	−0.461970	+	0.342474i
$673$	2.51498	+	6.07169i	0.0969453	+	0.234047i	0.964911	−	0.262578i	$-0.0845726\pi$
$673$	2.51498	+	6.07169i	0.0969453	+	0.234047i	−0.867966	+	0.496624i	$0.834573\pi$
$674$	−6.49704	−	0.855351i	−0.250257	−	0.0329469i
$675$	−5.17778	−	23.7544i	−0.199293	−	0.914308i
$676$	−6.60057	+	3.81084i	−0.253868	+	0.146571i
$677$	−14.0897	+	10.8114i	−0.541510	+	0.415515i	−0.842968	−	0.537964i	$-0.819193\pi$
$677$	−14.0897	+	10.8114i	−0.541510	+	0.415515i	0.301458	+	0.953480i	$0.402527\pi$
$678$	1.02943	−	4.32069i	0.0395349	−	0.165935i
$679$	−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
$682$	−0.766901	+	2.86211i	−0.0293662	+	0.109596i
$683$	−9.52042	+	1.25339i	−0.364289	+	0.0479595i	−0.310449	−	0.950590i	$-0.600479\pi$
$683$	−9.52042	+	1.25339i	−0.364289	+	0.0479595i	−0.0538399	+	0.998550i	$0.517146\pi$
$684$	0.780850	+	1.19337i	0.0298565	+	0.0456296i
$685$	30.1141	+	12.4737i	1.15060	+	0.476595i
$686$	−13.3958	+	17.3672i	−0.511454	+	0.663081i
$687$	−4.74575	+	6.55571i	−0.181062	+	0.250116i
$688$	−20.6422	+	5.53107i	−0.786977	+	0.210870i
$689$	10.0318	−	37.4390i	0.382180	−	1.42631i
$690$	−4.10291	+	39.6952i	−0.156195	+	1.51117i
$691$	22.3893	+	2.94760i	0.851728	+	0.112132i	0.543736	−	0.839257i	$-0.317009\pi$
$691$	22.3893	+	2.94760i	0.851728	+	0.112132i	0.307993	+	0.951389i	$0.400343\pi$
$692$	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
$695$	−0.941061	+	0.252156i	−0.0356965	+	0.00956484i
$696$	−0.327095	−	0.176868i	−0.0123985	−	0.00670417i
$697$	10.2785	−	18.1145i	0.389325	−	0.686136i
$698$	14.2056	−	24.6049i	0.537692	−	0.931309i
$699$	−21.1861	−	5.04769i	−0.801332	−	0.190921i
$700$	−3.40971	−	6.56341i	−0.128875	−	0.248074i
$701$	30.6702			1.15840			0.579198	−	0.815187i	$-0.303366\pi$
$701$	30.6702			1.15840			0.579198	+	0.815187i	$0.303366\pi$
$702$	23.1004	−	21.0172i	0.871868	−	0.793242i
$703$	−3.06169	+	3.99007i	−0.115474	+	0.150488i
$704$	2.11973	+	1.62652i	0.0798903	+	0.0613020i
$705$	44.2416	−	46.7823i	1.66624	−	1.76192i
$706$	−5.12819	+	5.12819i	−0.193002	+	0.193002i
$707$	4.20311	+	4.59461i	0.158074	+	0.172798i
$708$	−3.30904	+	4.57106i	−0.124361	+	0.171791i
$709$	−8.11127	−	10.5708i	−0.304625	−	0.396995i	0.615807	−	0.787897i	$-0.288830\pi$
$709$	−8.11127	−	10.5708i	−0.304625	−	0.396995i	−0.920432	+	0.390902i	$0.872163\pi$
$710$	−14.0827	+	8.13063i	−0.528513	+	0.305137i
$711$	−35.2705	−	12.3532i	−1.32275	−	0.463280i
$712$	−21.3813	+	5.72910i	−0.801298	+	0.214707i
$713$	−51.2313			−1.91863
$714$	−5.59484	−	21.6656i	−0.209381	−	0.810815i
$715$	4.82198			0.180332
$716$	1.19502	−	0.320204i	0.0446599	−	0.0119666i
$717$	3.53095	−	2.86941i	0.131866	−	0.107160i
$718$	1.67580	−	0.967525i	0.0625404	−	0.0361077i
$719$	26.3658	+	34.3606i	0.983278	+	1.28143i	0.959498	+	0.281715i	$0.0909034\pi$
$719$	26.3658	+	34.3606i	0.983278	+	1.28143i	0.0237798	+	0.999717i	$0.492430\pi$
$720$	−1.71408	+	22.7841i	−0.0638799	+	0.849114i
$721$	−34.6418	−	10.9544i	−1.29013	−	0.407964i
$722$	15.3807	−	15.3807i	0.572412	−	0.572412i
$723$	−18.3914	−	17.3926i	−0.683983	−	0.646837i
$724$	10.3951	+	7.97642i	0.386330	+	0.296441i
$725$	0.198789	−	0.259066i	0.00738282	−	0.00962148i
$726$	7.98147	−	20.9001i	0.296220	−	0.775676i
$727$	0.499312			0.0185184			0.00925922	−	0.999957i	$-0.497053\pi$
$727$	0.499312			0.0185184			0.00925922	+	0.999957i	$0.497053\pi$
$728$	22.2221	−	34.8174i	0.823608	−	1.29042i
$729$	15.6433	−	22.0065i	0.579381	−	0.815057i
$730$	13.0215	−	22.5539i	0.481947	−	0.834757i
$731$	−4.43087	+	35.7188i	−0.163882	+	1.32111i
$732$	2.24348	−	4.14904i	0.0829216	−	0.153353i
$733$	−39.3837	+	10.5528i	−1.45467	+	0.389778i	−0.897645	−	0.440718i	$-0.854724\pi$
$733$	−39.3837	+	10.5528i	−1.45467	+	0.389778i	−0.557025	+	0.830496i	$0.688057\pi$
$734$	−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
$737$	3.24343	+	0.427006i	0.119473	+	0.0157290i
$738$	−16.1718	+	7.78215i	−0.595292	+	0.286465i
$739$	−12.8341	+	47.8975i	−0.472110	+	1.76194i	0.160060	+	0.987107i	$0.448831\pi$
$739$	−12.8341	+	47.8975i	−0.472110	+	1.76194i	−0.632170	+	0.774830i	$0.717836\pi$
$740$	11.3494	−	3.04106i	0.417212	−	0.111792i
$741$	−5.66530	−	4.10117i	−0.208120	−	0.150660i
$742$	5.15981	+	23.3671i	0.189423	+	0.857832i
$743$	31.0765	+	12.8723i	1.14008	+	0.472239i	0.871197	−	0.490933i	$-0.163344\pi$
$743$	31.0765	+	12.8723i	1.14008	+	0.472239i	0.268887	+	0.963172i	$0.413344\pi$
$744$	−43.6332	+	1.21790i	−1.59967	+	0.0446503i
$745$	−8.10258	+	1.06672i	−0.296856	+	0.0390818i
$746$	−7.49742	+	27.9807i	−0.274500	+	1.02445i
$747$	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
$750$	1.99345	+	0.474949i	0.0727905	+	0.0173427i
$751$	−13.8556	+	10.6317i	−0.505597	+	0.387958i	−0.829828	−	0.558020i	$-0.811561\pi$
$751$	−13.8556	+	10.6317i	−0.505597	+	0.387958i	0.324231	+	0.945978i	$0.394895\pi$
$752$	−25.3332	+	14.6262i	−0.923809	+	0.533361i
$753$	10.8403	−	8.80927i	0.395041	−	0.321028i
$754$	0.415881	+	0.0547518i	0.0151455	+	0.00199394i
$755$	10.0772	+	24.3286i	0.366749	+	0.885409i
$756$	2.84319	−	7.70617i	0.103406	−	0.280271i
$757$	−38.0611	−	38.0611i	−1.38335	−	1.38335i	−0.838586	−	0.544769i	$-0.816618\pi$
$757$	−38.0611	−	38.0611i	−1.38335	−	1.38335i	−0.544769	−	0.838586i	$-0.683382\pi$
$758$	−1.43958	+	10.9347i	−0.0522881	+	0.397167i
$759$	−3.29033	−	0.340090i	−0.119431	−	0.0123445i
$760$	7.54929	−	0.993883i	0.273842	−	0.0360519i
$761$	−19.1409	−	11.0510i	−0.693857	−	0.400598i	0.111199	−	0.993798i	$-0.464531\pi$
$761$	−19.1409	−	11.0510i	−0.693857	−	0.400598i	−0.805055	+	0.593200i	$0.797864\pi$
$762$	2.14144	+	13.3712i	0.0775762	+	0.484387i
$763$	3.07259	−	6.57480i	0.111235	−	0.238024i
$764$		−	5.21869i		−	0.188806i
$765$	34.4767	+	17.0946i	1.24651	+	0.618058i
$766$	−19.5326	+	11.2772i	−0.705743	+	0.407461i
$767$	7.16266	−	26.7314i	0.258629	−	0.965215i
$768$	−7.99113	+	20.9254i	−0.288355	+	0.755081i
$769$	−27.7315			−1.00002			−0.500012	−	0.866018i	$-0.666671\pi$
$769$	−27.7315			−1.00002			−0.500012	+	0.866018i	$0.666671\pi$
$770$	−2.64183	+	1.37244i	−0.0952049	+	0.0494592i
$771$	3.99882	−	5.52392i	0.144014	−	0.198939i
$772$	−1.47118	−	0.193684i	−0.0529489	−	0.00697086i
$773$	−13.2052	+	49.2825i	−0.474958	+	1.77257i	0.146597	+	0.989196i	$0.453168\pi$
$773$	−13.2052	+	49.2825i	−0.474958	+	1.77257i	−0.621555	+	0.783370i	$0.713499\pi$
$774$	20.6731	−	23.1197i	0.743080	−	0.831022i
$775$	5.00332	−	38.0040i	0.179725	−	1.36514i
$776$	−25.3699	+	10.5086i	−0.910727	+	0.377236i
$777$	28.9631	+	0.479854i	1.03905	+	0.0172147i
$778$		−	5.73184i		−	0.205497i
$779$	2.44668	+	3.18858i	0.0876614	+	0.114243i
$780$	4.66767	+	15.6585i	0.167129	+	0.560666i
$781$	−0.673948	−	1.16731i	−0.0241157	−	0.0417697i
$782$	−21.7524	−	21.4293i	−0.777863	−	0.766310i
$783$	0.361377	−	0.0303235i	0.0129146	−	0.00108367i
$784$	−1.52215	+	17.0688i	−0.0543625	+	0.609598i
$785$	6.32106	−	15.2604i	0.225608	−	0.544667i
$786$	0.630178	+	22.5772i	0.0224777	+	0.805301i
$787$	−6.32018	−	48.0065i	−0.225290	−	1.71125i	−0.613515	−	0.789683i	$-0.710245\pi$
$787$	−6.32018	−	48.0065i	−0.225290	−	1.71125i	0.388225	−	0.921564i	$-0.373088\pi$
$788$	1.29188	−	1.68362i	0.0460215	−	0.0599763i
$789$	10.4507	+	23.3640i	0.372053	+	0.831781i
$790$	−32.4541	+	32.4541i	−1.15466	+	1.15466i
$791$	3.28206	+	4.69564i	0.116697	+	0.166958i
$792$	−2.81043	−	0.211432i	−0.0998641	−	0.00751290i
$793$	−3.01927	+	22.9336i	−0.107218	+	0.814398i
$794$	35.9810	−	4.73699i	1.27692	−	0.168110i
$795$	−36.2006	−	19.5745i	−1.28390	−	0.694237i
$796$	5.12173	+	6.67477i	0.181535	+	0.236581i
$797$	26.7260	−	26.7260i	0.946685	−	0.946685i	−0.0519639	−	0.998649i	$-0.516548\pi$
$797$	26.7260	−	26.7260i	0.946685	−	0.946685i	0.998649	+	0.0519639i	$0.0165481\pi$
$798$	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
$801$	14.3895	−	16.0925i	0.508428	−	0.568600i
$802$	2.46946	+	18.7574i	0.0871997	+	0.662348i
$803$	1.86949	+	1.07935i	0.0659729	+	0.0380895i
$804$	1.75301	+	10.9458i	0.0618238	+	0.386029i
$805$	−34.7427	−	37.9789i	−1.22452	−	1.33858i
$806$	45.4917	−	18.8433i	1.60238	−	0.663726i
$807$	15.0453	−	15.9093i	0.529619	−	0.560033i
$808$	6.99336	+	1.87387i	0.246026	+	0.0659223i
$809$	−33.4626	−	25.6767i	−1.17648	−	0.902746i	−0.179764	−	0.983710i	$-0.557534\pi$
$809$	−33.4626	−	25.6767i	−1.17648	−	0.902746i	−0.996717	+	0.0809637i	$0.974200\pi$
$810$	−16.0231	−	29.0314i	−0.562995	−	1.02006i
$811$	−5.55830	−	2.30232i	−0.195178	−	0.0808455i	0.282953	−	0.959134i	$-0.408686\pi$
$811$	−5.55830	−	2.30232i	−0.195178	−	0.0808455i	−0.478132	+	0.878288i	$0.658686\pi$
$812$	0.103703	−	0.0376463i	0.00363925	−	0.00132113i
$813$	5.44667	+	34.0091i	0.191023	+	1.19275i
$814$	−0.591720	−	2.20833i	−0.0207398	−	0.0774019i
$815$	−34.2805	−	59.3756i	−1.20080	−	2.07984i
$816$	−12.7918	−	11.9170i	−0.447802	−	0.417180i
$817$	−6.01503	−	3.47278i	−0.210439	−	0.121497i
$818$	−22.9972	+	22.9972i	−0.804077	+	0.804077i
$819$	0.456738	+	40.2796i	0.0159597	+	1.40748i
$820$		−	9.38955i		−	0.327897i
$821$	−11.7972	+	9.05227i	−0.411723	+	0.315927i	−0.793772	−	0.608216i	$-0.791885\pi$
$821$	−11.7972	+	9.05227i	−0.411723	+	0.315927i	0.382048	+	0.924142i	$0.375219\pi$
$822$	21.3772	+	2.20956i	0.745615	+	0.0770671i
$823$	1.90668	−	2.48483i	0.0664626	−	0.0866157i	−0.758939	−	0.651162i	$-0.774282\pi$
$823$	1.90668	−	2.48483i	0.0664626	−	0.0866157i	0.825402	+	0.564546i	$0.190949\pi$
$824$	−40.8035	+	10.9333i	−1.42146	+	0.380878i
$825$	0.573621	−	2.40759i	0.0199709	−	0.0838216i
$826$	3.68410	+	16.6840i	0.128186	+	0.580512i
$827$	−11.6938	−	28.2313i	−0.406633	−	0.981700i	−0.986017	−	0.166645i	$-0.946707\pi$
$827$	−11.6938	−	28.2313i	−0.406633	−	0.981700i	0.579384	−	0.815055i	$-0.303293\pi$
$828$	−2.08065	−	11.0140i	−0.0723076	−	0.382762i
$829$	15.9606	+	27.6445i	0.554334	+	0.960134i	0.997955	+	0.0639197i	$0.0203601\pi$
$829$	15.9606	+	27.6445i	0.554334	+	0.960134i	−0.443621	+	0.896214i	$0.646307\pi$
$830$	22.8275	−	3.00530i	0.792355	−	0.104315i
$831$	11.9473	+	11.2984i	0.414447	+	0.391939i
$832$		−	44.4004i		−	1.53931i
$833$	25.6776	+	13.1780i	0.889677	+	0.456591i
$834$	−0.547120	+	0.336575i	−0.0189452	+	0.0116546i
$835$	2.86429	+	10.6897i	0.0991227	+	0.369931i
$836$	0.0189499	+	0.143939i	0.000655395	+	0.00497822i
$837$	34.9575	−	24.2930i	1.20831	−	0.839688i
$838$	−24.2175	+	18.5827i	−0.836579	+	0.641930i
$839$	15.2664	−	6.32357i	0.527056	−	0.218314i	−0.103257	−	0.994655i	$-0.532926\pi$
$839$	15.2664	−	6.32357i	0.527056	−	0.218314i	0.630313	+	0.776341i	$0.282926\pi$
$840$	−30.4929	−	31.5203i	−1.05211	−	1.08755i
$841$	−20.5027	−	20.5027i	−0.706988	−	0.706988i
$842$	−6.76286	−	25.2393i	−0.233064	−	0.869805i
$843$	−21.7084	−	2.24379i	−0.747676	−	0.0772801i
$844$	−8.95265	−	6.86961i	−0.308163	−	0.236462i
$845$	−24.1596	−	31.4854i	−0.831116	−	1.08313i
$846$	19.1428	−	37.8926i	0.658144	−	1.30277i
$847$	13.3030	+	25.6072i	0.457096	+	0.879873i
$848$	13.2205	+	13.2205i	0.453992	+	0.453992i
$849$	−23.5202	+	0.656499i	−0.807210	+	0.0225310i
$850$	18.0209	−	14.0433i	0.618111	−	0.481683i
$851$	34.2328	−	19.7643i	1.17349	−	0.677513i
$852$	3.13826	−	3.31848i	0.107515	−	0.113689i
$853$	9.06411	−	21.8827i	0.310349	−	0.749249i	−0.689343	−	0.724435i	$-0.742101\pi$
$853$	9.06411	−	21.8827i	0.310349	−	0.749249i	0.999692	−	0.0248140i	$-0.00789934\pi$
$854$	−4.87322	−	13.4241i	−0.166758	−	0.459362i
$855$	−5.63007	+	4.84222i	−0.192544	+	0.165601i
$856$	−7.73808	+	58.7766i	−0.264482	+	2.00894i
$857$	5.50527	−	7.17460i	0.188056	−	0.245080i	−0.689804	−	0.723996i	$-0.742303\pi$
$857$	5.50527	−	7.17460i	0.188056	−	0.245080i	0.877861	+	0.478916i	$0.158970\pi$
$858$	3.04679	−	0.908221i	0.104016	−	0.0310061i
$859$	−3.96269	−	14.7890i	−0.135205	−	0.504593i	−0.999997	−	0.00246241i	$-0.999216\pi$
$859$	−3.96269	−	14.7890i	−0.135205	−	0.504593i	0.864792	−	0.502131i	$-0.167450\pi$
$860$	6.20957	+	14.9912i	0.211745	+	0.511197i
$861$	6.36083	−	22.2573i	0.216776	−	0.758528i
$862$	6.07529	−	14.6670i	0.206925	−	0.499561i
$863$	5.14360	−	8.90897i	0.175090	−	0.303265i	−0.765102	−	0.643909i	$-0.777312\pi$
$863$	5.14360	−	8.90897i	0.175090	−	0.303265i	0.940192	+	0.340644i	$0.110645\pi$
$864$	−3.59996	−	16.5157i	−0.122473	−	0.561876i
$865$	30.6557	+	8.21417i	1.04233	+	0.279290i
$866$	8.39690	−	14.5439i	0.285338	−	0.494221i
$867$	−26.6956	+	12.4235i	−0.906631	+	0.421925i
$868$	8.33276	−	9.91372i	0.282832	−	0.336493i
$869$	−2.69012	−	2.69012i	−0.0912560	−	0.0912560i
$870$	0.158892	−	0.416073i	0.00538696	−	0.0141062i
$871$	−27.1819	−	47.0804i	−0.921023	−	1.59526i
$872$	−1.10137	−	8.36571i	−0.0372970	−	0.283299i
$873$	15.0924	−	22.1227i	0.510800	−	0.748740i
$874$	5.44384	−	2.25491i	0.184141	−	0.0762736i
$875$	−2.16644	+	1.51425i	−0.0732391	+	0.0511912i
$876$	−1.69534	+	7.11566i	−0.0572803	+	0.240416i
$877$	−6.77480	−	0.891919i	−0.228769	−	0.0301180i	0.0152702	−	0.999883i	$-0.495139\pi$
$877$	−6.77480	−	0.891919i	−0.228769	−	0.0301180i	−0.244039	+	0.969765i	$0.578472\pi$
$878$	30.2122	+	23.1827i	1.01961	+	0.782377i
$879$	37.7440	−	30.6724i	1.27307	−	1.03456i
$880$	−1.16299	+	2.01436i	−0.0392044	+	0.0679040i
$881$	51.6944	+	21.4125i	1.74163	+	0.721406i	0.998642	+	0.0520986i	$0.0165910\pi$
$881$	51.6944	+	21.4125i	1.74163	+	0.721406i	0.742986	+	0.669307i	$0.233409\pi$
$882$	−11.7147	−	21.9381i	−0.394453	−	0.738694i
$883$	2.04518			0.0688259			0.0344130	−	0.999408i	$-0.489044\pi$
$883$	2.04518			0.0688259			0.0344130	+	0.999408i	$0.489044\pi$
$884$	−11.5860	−	4.69785i	−0.389681	−	0.158006i
$885$	−25.8471	−	13.9762i	−0.868842	−	0.469804i
$886$	−8.04466	−	2.15556i	−0.270265	−	0.0724174i
$887$	−24.0204	+	18.4315i	−0.806526	+	0.618869i	−0.927515	−	0.373785i	$-0.878060\pi$
$887$	−24.0204	+	18.4315i	−0.806526	+	0.618869i	0.120990	+	0.992654i	$0.461393\pi$
$888$	28.6859	−	17.6469i	0.962636	−	0.592191i
$889$	−14.7231	−	9.39702i	−0.493798	−	0.315166i
$890$	−10.1459	−	24.4944i	−0.340092	−	0.821054i
$891$	2.40641	−	1.32816i	0.0806179	−	0.0444949i
$892$	−8.87322	−	2.37757i	−0.297097	−	0.0796070i
$893$	−9.18330	−	2.46066i	−0.307307	−	0.0823427i
$894$	−4.91874	+	2.20014i	−0.164507	+	0.0735836i
$895$	2.46526	+	5.95166i	0.0824045	+	0.198942i
$896$	4.70168	+	9.05035i	0.157072	+	0.302351i
$897$	28.8022	+	46.8194i	0.961677	+	1.56326i
$898$	13.4227	−	10.2996i	0.447921	−	0.343702i
$899$	0.552287	+	0.147985i	0.0184198	+	0.00493557i
$900$	8.37350	−	0.467810i	0.279117	−	0.0155937i
$901$	29.0013	−	12.2677i	0.966173	−	0.408697i
$902$	−1.82699			−0.0608321
$903$	4.56378	+	39.7424i	0.151873	+	1.32254i
$904$	6.15388	+	2.54902i	0.204675	+	0.0847792i
$905$	−34.1132	+	59.0858i	−1.13396	+	1.96408i
$906$	10.9497	+	13.4741i	0.363778	+	0.447648i
$907$	27.3335	+	20.9737i	0.907593	+	0.696421i	0.953136	−	0.302541i	$-0.0978351\pi$
$907$	27.3335	+	20.9737i	0.907593	+	0.696421i	−0.0455428	+	0.998962i	$0.514502\pi$
$908$	3.73973	+	0.492345i	0.124107	+	0.0163390i
$909$	−6.70769	+	2.20508i	−0.222480	+	0.0731377i
$910$	44.8194	+	20.9453i	1.48575	+	0.694332i
$911$	−27.9559	+	11.5797i	−0.926221	+	0.383653i	−0.794244	−	0.607599i	$-0.792133\pi$
$911$	−27.9559	+	11.5797i	−0.926221	+	0.383653i	−0.131977	+	0.991253i	$0.542133\pi$
$912$	3.07963	−	1.37751i	0.101977	−	0.0456139i
$913$	0.249109	+	1.89217i	0.00824431	+	0.0626217i
$914$	12.5141	+	21.6751i	0.413931	+	0.716949i
$915$	22.9442	+	8.76208i	0.758513	+	0.289665i
$916$	−1.97408	−	1.97408i	−0.0652253	−	0.0652253i
$917$	−22.3008	−	18.7445i	−0.736437	−	0.618996i
$918$	25.0041	+	4.30764i	0.825257	+	0.142173i
$919$	−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	$0.260552\pi$
$920$	−57.8069	−	15.4893i	−1.90584	−	0.510668i
$921$	15.1711	−	12.3287i	0.499905	−	0.406245i
$922$	−12.9401	+	22.4130i	−0.426161	+	0.738132i
$923$	−8.57175	+	20.6940i	−0.282143	+	0.681152i
$924$	0.600982	−	0.581393i	0.0197709	−	0.0191264i
$925$	11.3182	+	27.3245i	0.372140	+	0.898425i
$926$	−4.33797	−	16.1895i	−0.142554	−	0.532020i
$927$	27.4605	−	30.7104i	0.901922	−	1.00866i
$928$	0.138212	−	0.180121i	0.00453702	−	0.00591276i
$929$	−5.87548	+	44.6287i	−0.192768	+	1.46422i	0.572180	+	0.820128i	$0.306098\pi$
$929$	−5.87548	+	44.6287i	−0.192768	+	1.46422i	−0.764948	+	0.644092i	$0.777236\pi$
$930$	−8.26767	−	51.6235i	−0.271108	−	1.69280i
$931$	−4.27248	+	3.57285i	−0.140025	+	0.117095i
$932$	2.87501	−	6.94090i	0.0941742	−	0.227357i
$933$	−39.6895	−	37.5340i	−1.29938	−	1.22881i
$934$	6.31967	−	3.64866i	0.206786	−	0.119388i
$935$	2.40800	+	3.09002i	0.0787499	+	0.101054i
$936$	25.6436	+	39.1909i	0.838186	+	1.28100i
$937$	−3.31899	−	3.31899i	−0.108427	−	0.108427i	0.650812	−	0.759239i	$-0.274429\pi$
$937$	−3.31899	−	3.31899i	−0.108427	−	0.108427i	−0.759239	+	0.650812i	$0.774429\pi$
$938$	28.2923	+	18.0575i	0.923775	+	0.589598i
$939$	0.393930	−	0.242336i	0.0128554	−	0.00790834i
$940$	13.5212	+	17.6212i	0.441015	+	0.574741i
$941$	23.4717	+	18.0104i	0.765154	+	0.587124i	0.915880	−	0.401452i	$-0.131494\pi$
$941$	23.4717	+	18.0104i	0.765154	+	0.587124i	−0.150726	+	0.988576i	$0.548161\pi$
$942$	1.11970	−	10.8329i	0.0364817	−	0.352956i
$943$	−8.17569	−	30.5121i	−0.266237	−	0.993611i
$944$	9.43939	+	9.43939i	0.307226	+	0.307226i
$945$	41.7155	+	9.44042i	1.35701	+	0.307097i
$946$	2.91695	−	1.20824i	0.0948382	−	0.0392833i
$947$	13.9012	−	10.6667i	0.451727	−	0.346623i	−0.357706	−	0.933834i	$-0.616441\pi$
$947$	13.9012	−	10.6667i	0.451727	−	0.346623i	0.809433	+	0.587212i	$0.199774\pi$
$948$	6.13166	−	11.3397i	0.199147	−	0.368297i
$949$	−4.68235	−	35.5660i	−0.151995	−	1.15452i
$950$	1.14107	+	4.25853i	0.0370211	+	0.138165i
$951$	−3.12183	−	5.07469i	−0.101232	−	0.164558i
$952$	33.4089	−	3.14669i	1.08279	−	0.101985i
$953$			39.8464i			1.29075i	0.763865	+	0.645376i	$0.223299\pi$
$953$			39.8464i			1.29075i	−0.763865	+	0.645376i	$0.776701\pi$
$954$	−26.5604	−	5.54988i	−0.859924	−	0.179684i
$955$	26.9415	−	3.54692i	0.871807	−	0.114776i
$956$	0.784742	+	1.35921i	0.0253804	+	0.0439601i
$957$	0.0344882	+	0.0131706i	0.00111485	+	0.000425744i
$958$	−4.32835	−	10.4496i	−0.139843	−	0.337610i
$959$	−20.4529	+	18.7102i	−0.660459	+	0.604182i
$960$	−45.8593	−	10.9262i	−1.48010	−	0.352642i
$961$	34.8870	−	9.34795i	1.12539	−	0.301547i
$962$	−23.1281	+	30.1412i	−0.745681	+	0.971791i
$963$	−25.0704	−	52.0979i	−0.807884	−	1.67883i
$964$	6.92738	−	5.31557i	0.223116	−	0.171203i
$965$		−	7.72661i		−	0.248728i
$966$	−29.1057	−	17.4534i	−0.936461	−	0.561553i
$967$	−23.2532	+	23.2532i	−0.747771	+	0.747771i	−0.974060	−	0.226289i	$-0.927341\pi$
$967$	−23.2532	+	23.2532i	−0.747771	+	0.747771i	0.226289	+	0.974060i	$0.427341\pi$
$968$	29.0557	+	16.7753i	0.933887	+	0.539180i
$969$	−0.201026	−	5.67847i	−0.00645788	−	0.182419i
$970$	−16.4450	−	28.4836i	−0.528018	−	0.914554i
$971$	8.25423	+	30.8052i	0.264891	+	0.988586i	0.962317	+	0.271929i	$0.0876617\pi$
$971$	8.25423	+	30.8052i	0.264891	+	0.988586i	−0.697427	+	0.716656i	$0.745672\pi$
$972$	6.64236	+	6.52876i	0.213054	+	0.209410i
$973$	0.144557	−	0.815826i	0.00463429	−	0.0261542i
$974$	0.00527015	+	0.00218297i	0.000168866	+	6.99467e-5i
$975$	−37.5441	+	16.7934i	−1.20237	+	0.537818i
$976$	−8.85222	−	6.79254i	−0.283353	−	0.217424i
$977$	2.87990	+	0.771667i	0.0921362	+	0.0246878i	0.304593	−	0.952483i	$-0.401480\pi$
$977$	2.87990	+	0.771667i	0.0921362	+	0.0246878i	−0.212456	+	0.977171i	$0.568146\pi$
$978$	−32.8438	−	31.0601i	−1.05023	−	0.993191i
$979$	2.03034	−	0.840994i	0.0648899	−	0.0268783i
$980$	13.0002	−	0.545772i	0.415275	−	0.0174341i
$981$	5.36589	+	6.23893i	0.171320	+	0.199194i
$982$	−7.43422	−	4.29215i	−0.237236	−	0.136968i
$983$	−3.81933	−	29.0107i	−0.121818	−	0.925299i	−0.937789	−	0.347206i	$-0.887131\pi$
$983$	−3.81933	−	29.0107i	−0.121818	−	0.925299i	0.815971	−	0.578093i	$-0.196203\pi$
$984$	−7.68851	−	25.7925i	−0.245101	−	0.822235i
$985$	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
$989$	33.2317	+	43.3084i	1.05671	+	1.37713i
$990$	−0.188297	−	3.37040i	−0.00598448	−	0.107118i
$991$	−22.2085	+	2.92381i	−0.705477	+	0.0928778i	−0.474724	−	0.880135i	$-0.657452\pi$
$991$	−22.2085	+	2.92381i	−0.705477	+	0.0928778i	−0.230753	+	0.973012i	$0.574119\pi$
$992$	3.47866	−	26.4230i	0.110447	−	0.838931i
$993$	−14.0737	−	10.1881i	−0.446616	−	0.323310i
$994$	−1.19373	−	13.7774i	−0.0378629	−	0.436992i
$995$	−30.9775	+	30.9775i	−0.982053	+	0.982053i
$996$	−5.90336	+	2.64056i	−0.187055	+	0.0836693i
$997$	9.34501	−	12.1787i	0.295959	−	0.385702i	−0.621577	−	0.783353i	$-0.713508\pi$
$997$	9.34501	−	12.1787i	0.295959	−	0.385702i	0.917537	+	0.397651i	$0.130174\pi$
$998$	3.81877	+	29.0065i	0.120881	+	0.918183i
$999$	−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.26.15	✓	352
3.2	odd	2	inner	357.2.bj.a.26.30	yes	352
7.3	odd	6	inner	357.2.bj.a.332.30	yes	352
17.2	even	8	inner	357.2.bj.a.257.15	yes	352
21.17	even	6	inner	357.2.bj.a.332.15	yes	352
51.2	odd	8	inner	357.2.bj.a.257.30	yes	352
119.87	odd	24	inner	357.2.bj.a.206.30	yes	352
357.206	even	24	inner	357.2.bj.a.206.15	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.15	✓	352	1.1	even	1	trivial
357.2.bj.a.26.30	yes	352	3.2	odd	2	inner
357.2.bj.a.206.15	yes	352	357.206	even	24	inner
357.2.bj.a.206.30	yes	352	119.87	odd	24	inner
357.2.bj.a.257.15	yes	352	17.2	even	8	inner
357.2.bj.a.257.30	yes	352	51.2	odd	8	inner
357.2.bj.a.332.15	yes	352	21.17	even	6	inner
357.2.bj.a.332.30	yes	352	7.3	odd	6	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+(-1.14393 + 0.306515i) q^{2} +(1.09234 + 1.34417i) q^{3} +(-0.517430 + 0.298738i) q^{4} +(-1.89391 - 2.46819i) q^{5} +(-1.66156 - 1.20282i) q^{6} +(2.58352 - 0.570481i) q^{7} +(2.17516 - 2.17516i) q^{8} +(-0.613608 + 2.93658i) q^{9} +(2.92304 + 2.24293i) q^{10} +(-0.185916 + 0.242290i) q^{11} +(-0.966763 - 0.369193i) q^{12} +5.07508 q^{13} +(-2.78050 + 1.44447i) q^{14} +(1.24890 - 5.24184i) q^{15} +(-1.22403 + 2.12009i) q^{16} +(2.53439 + 3.25221i) q^{17} +(-0.198181 - 3.54731i) q^{18} +(-0.768532 + 0.205928i) q^{19} +(1.71731 + 0.711333i) q^{20} +(3.58889 + 2.84954i) q^{21} +(0.138409 - 0.334149i) q^{22} +(6.19991 + 0.816233i) q^{23} +(5.29980 + 0.547790i) q^{24} +(-1.21098 + 4.51945i) q^{25} +(-5.80553 + 1.55559i) q^{26} +(-4.61754 + 2.38293i) q^{27} +(-1.16636 + 1.06698i) q^{28} +(-0.0644789 - 0.0267080i) q^{29} +(0.178055 + 6.37910i) q^{30} +(-8.12245 + 1.06934i) q^{31} +(-0.841960 + 3.14224i) q^{32} +(-0.528763 + 0.0147589i) q^{33} +(-3.89601 - 2.94347i) q^{34} +(-6.30101 - 5.29618i) q^{35} +(-0.559769 - 1.70278i) q^{36} +(5.01490 - 3.84807i) q^{37} +(0.816026 - 0.471133i) q^{38} +(5.54369 + 6.82179i) q^{39} +(-9.48829 - 1.24916i) q^{40} +(-1.93309 - 4.66688i) q^{41} +(-4.97886 - 2.15962i) q^{42} +(6.17268 + 6.17268i) q^{43} +(0.0238170 - 0.180908i) q^{44} +(8.41016 - 4.04712i) q^{45} +(-7.34244 + 0.966651i) q^{46} +(10.3483 + 5.97457i) q^{47} +(-4.18683 + 0.670534i) q^{48} +(6.34910 - 2.94769i) q^{49} -5.54111i q^{50} +(-1.60313 + 6.95916i) q^{51} +(-2.62600 + 1.51612i) q^{52} +(1.97667 - 7.37703i) q^{53} +(4.55173 - 4.14125i) q^{54} +0.950128 q^{55} +(4.37868 - 6.86045i) q^{56} +(-1.11630 - 0.808099i) q^{57} +(0.0819457 + 0.0107884i) q^{58} +(1.41134 - 5.26719i) q^{59} +(0.919722 + 3.08538i) q^{60} +(-0.594921 + 4.51887i) q^{61} +(8.96373 - 3.71290i) q^{62} +(0.0899962 + 7.93674i) q^{63} -8.74871i q^{64} +(-9.61176 - 12.5263i) q^{65} +(0.600343 - 0.178957i) q^{66} +(-5.35595 - 9.27677i) q^{67} +(-2.28293 - 0.925670i) q^{68} +(5.67522 + 9.22536i) q^{69} +(8.83126 + 4.12710i) q^{70} +(-1.68899 + 4.07758i) q^{71} +(5.05284 + 7.72223i) q^{72} +(-0.922615 - 7.00796i) q^{73} +(-4.55720 + 5.93905i) q^{74} +(-7.39773 + 3.30898i) q^{75} +(0.336143 - 0.336143i) q^{76} +(-0.342095 + 0.732023i) q^{77} +(-8.43257 - 6.10442i) q^{78} +(-1.62598 + 12.3505i) q^{79} +(7.55101 - 0.994109i) q^{80} +(-8.24697 - 3.60381i) q^{81} +(3.64178 + 4.74606i) 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} +(-0.0345323 - 0.115845i) q^{87} +(0.122624 + 0.931419i) q^{88} +(-6.23181 - 3.59794i) q^{89} +(-8.38012 + 7.20745i) q^{90} +(13.1116 - 2.89524i) q^{91} +(-3.45186 + 1.42981i) q^{92} +(-10.3098 - 9.74991i) q^{93} +(-13.6690 - 3.66259i) q^{94} +(1.96380 + 1.50688i) q^{95} +(-5.14342 + 2.30064i) q^{96} +(-8.24731 - 3.41615i) q^{97} +(-6.35941 + 5.31804i) q^{98} +(-0.597425 - 0.694628i) 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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