LMFDB - Embedded newform 240.2.y.f.187.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,2,Mod(163,240)] 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("240.163"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.5
Root			$1.40751 - 0.137540i$ of defining polynomial
Character	$\chi$	$=$	240.187
Dual form			240.2.y.f.163.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.137540 + 1.40751i) q^{2} -1.00000 q^{3} +(-1.96217 - 0.387177i) q^{4} +(-1.76195 - 1.37678i) q^{5} +(0.137540 - 1.40751i) q^{6} +(0.159531 + 0.159531i) q^{7} +(0.814832 - 2.70851i) q^{8} +1.00000 q^{9} +(2.18017 - 2.29061i) q^{10} +(1.60861 - 1.60861i) q^{11} +(1.96217 + 0.387177i) q^{12} -4.36332i q^{13} +(-0.246483 + 0.202600i) q^{14} +(1.76195 + 1.37678i) q^{15} +(3.70019 + 1.51941i) q^{16} +(-4.63479 - 4.63479i) q^{17} +(-0.137540 + 1.40751i) q^{18} +(3.97920 - 3.97920i) q^{19} +(2.92419 + 3.38365i) q^{20} +(-0.159531 - 0.159531i) q^{21} +(2.04289 + 2.48539i) q^{22} +(-5.58779 + 5.58779i) q^{23} +(-0.814832 + 2.70851i) q^{24} +(1.20897 + 4.85164i) q^{25} +(6.14142 + 0.600131i) q^{26} -1.00000 q^{27} +(-0.251259 - 0.374793i) q^{28} +(-6.25463 - 6.25463i) q^{29} +(-2.18017 + 2.29061i) q^{30} +1.69754i q^{31} +(-2.64751 + 4.99907i) q^{32} +(-1.60861 + 1.60861i) q^{33} +(7.16098 - 5.88604i) q^{34} +(-0.0614476 - 0.500725i) q^{35} +(-1.96217 - 0.387177i) q^{36} +0.609145i q^{37} +(5.05346 + 6.14806i) q^{38} +4.36332i q^{39} +(-5.16472 + 3.65044i) q^{40} +0.538520i q^{41} +(0.246483 - 0.202600i) q^{42} +0.592259i q^{43} +(-3.77919 + 2.53355i) q^{44} +(-1.76195 - 1.37678i) q^{45} +(-7.09632 - 8.63341i) q^{46} +(4.85568 - 4.85568i) q^{47} +(-3.70019 - 1.51941i) q^{48} -6.94910i q^{49} +(-6.99501 + 1.03434i) q^{50} +(4.63479 + 4.63479i) q^{51} +(-1.68938 + 8.56156i) q^{52} -4.82837 q^{53} +(0.137540 - 1.40751i) q^{54} +(-5.04901 + 0.619600i) q^{55} +(0.562083 - 0.302101i) q^{56} +(-3.97920 + 3.97920i) q^{57} +(9.66371 - 7.94319i) q^{58} +(5.78762 + 5.78762i) q^{59} +(-2.92419 - 3.38365i) q^{60} +(1.65469 - 1.65469i) q^{61} +(-2.38930 - 0.233479i) q^{62} +(0.159531 + 0.159531i) q^{63} +(-6.67210 - 4.41397i) q^{64} +(-6.00733 + 7.68798i) q^{65} +(-2.04289 - 2.48539i) q^{66} -0.485302i q^{67} +(7.29974 + 10.8887i) q^{68} +(5.58779 - 5.58779i) q^{69} +(0.713227 - 0.0176184i) q^{70} +6.86042 q^{71} +(0.814832 - 2.70851i) q^{72} +(-0.160991 - 0.160991i) q^{73} +(-0.857378 - 0.0837818i) q^{74} +(-1.20897 - 4.85164i) q^{75} +(-9.34851 + 6.26719i) q^{76} +0.513248 q^{77} +(-6.14142 - 0.600131i) q^{78} -7.13706 q^{79} +(-4.42767 - 7.77147i) q^{80} +1.00000 q^{81} +(-0.757972 - 0.0740679i) q^{82} -6.88217 q^{83} +(0.251259 + 0.374793i) q^{84} +(1.78521 + 14.5474i) q^{85} +(-0.833610 - 0.0814592i) q^{86} +(6.25463 + 6.25463i) q^{87} +(-3.04620 - 5.66770i) q^{88} +17.0238 q^{89} +(2.18017 - 2.29061i) q^{90} +(0.696085 - 0.696085i) q^{91} +(13.1276 - 8.80070i) q^{92} -1.69754i q^{93} +(6.16657 + 7.50227i) q^{94} +(-12.4896 + 1.53269i) q^{95} +(2.64751 - 4.99907i) q^{96} +(9.64079 + 9.64079i) q^{97} +(9.78092 + 0.955778i) q^{98} +(1.60861 - 1.60861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 20 q^{9} + 8 q^{10} + 8 q^{11} - 2 q^{12} + 10 q^{14} + 26 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 4 q^{21} - 10 q^{22} - 16 q^{23} - 6 q^{24} + 4 q^{25}+ \cdots + 8 q^{99}+O(q^{100}) $ 20 * q - 20 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 20 * q^9 + 8 * q^10 + 8 * q^11 - 2 * q^12 + 10 * q^14 + 26 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 4 * q^21 - 10 * q^22 - 16 * q^23 - 6 * q^24 + 4 * q^25 - 20 * q^26 - 20 * q^27 + 6 * q^28 - 8 * q^30 - 10 * q^32 - 8 * q^33 + 6 * q^34 - 28 * q^35 + 2 * q^36 - 2 * q^38 + 6 * q^40 - 10 * q^42 + 22 * q^44 - 18 * q^46 - 26 * q^48 - 52 * q^50 - 12 * q^51 + 8 * q^53 - 4 * q^55 - 26 * q^56 - 16 * q^57 - 22 * q^58 - 16 * q^59 + 10 * q^60 - 12 * q^61 + 4 * q^62 - 4 * q^63 + 26 * q^64 + 4 * q^65 + 10 * q^66 + 2 * q^68 + 16 * q^69 - 10 * q^70 + 6 * q^72 - 20 * q^73 - 8 * q^74 - 4 * q^75 + 26 * q^76 + 20 * q^78 + 48 * q^79 - 54 * q^80 + 20 * q^81 - 8 * q^82 - 24 * q^83 - 6 * q^84 + 4 * q^85 + 4 * q^86 + 34 * q^88 + 40 * q^89 + 8 * q^90 - 24 * q^91 + 82 * q^92 + 58 * q^94 - 72 * q^95 + 10 * q^96 - 28 * q^97 + 70 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.137540	+	1.40751i	−0.0972554	+	0.995259i
$2$	−0.137540	+	1.40751i	−0.0972554	+	0.995259i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.96217	−	0.387177i	−0.981083	−	0.193589i
$5$	−1.76195	−	1.37678i	−0.787970	−	0.615714i
$5$	−1.76195	−	1.37678i	−0.787970	−	0.615714i
$6$	0.137540	−	1.40751i	0.0561504	−	0.574613i
$7$	0.159531	+	0.159531i	0.0602971	+	0.0602971i	0.736612	−	0.676315i	$-0.236424\pi$
$7$	0.159531	+	0.159531i	0.0602971	+	0.0602971i	−0.676315	+	0.736612i	$0.736424\pi$
$8$	0.814832	−	2.70851i	0.288087	−	0.957604i
$9$	1.00000			0.333333
$10$	2.18017	−	2.29061i	0.689429	−	0.724353i
$11$	1.60861	−	1.60861i	0.485015	−	0.485015i	−0.421714	−	0.906729i	$-0.638571\pi$
$11$	1.60861	−	1.60861i	0.485015	−	0.485015i	0.906729	+	0.421714i	$0.138571\pi$
$12$	1.96217	+	0.387177i	0.566428	+	0.111768i
$13$		−	4.36332i		−	1.21017i	−0.796162	−	0.605084i	$-0.793139\pi$
$13$		−	4.36332i		−	1.21017i	0.796162	−	0.605084i	$-0.206861\pi$
$14$	−0.246483	+	0.202600i	−0.0658754	+	0.0541470i
$15$	1.76195	+	1.37678i	0.454935	+	0.355483i
$16$	3.70019	+	1.51941i	0.925047	+	0.379853i
$17$	−4.63479	−	4.63479i	−1.12410	−	1.12410i	−0.991118	−	0.132983i	$-0.957545\pi$
$17$	−4.63479	−	4.63479i	−1.12410	−	1.12410i	−0.132983	−	0.991118i	$-0.542455\pi$
$18$	−0.137540	+	1.40751i	−0.0324185	+	0.331753i
$19$	3.97920	−	3.97920i	0.912891	−	0.912891i	−0.0836074	−	0.996499i	$-0.526644\pi$
$19$	3.97920	−	3.97920i	0.912891	−	0.912891i	0.996499	+	0.0836074i	$0.0266442\pi$
$20$	2.92419	+	3.38365i	0.653868	+	0.756608i
$21$	−0.159531	−	0.159531i	−0.0348125	−	0.0348125i
$22$	2.04289	+	2.48539i	0.435546	+	0.529886i
$23$	−5.58779	+	5.58779i	−1.16513	+	1.16513i	−0.181799	+	0.983336i	$0.558192\pi$
$23$	−5.58779	+	5.58779i	−1.16513	+	1.16513i	−0.983336	+	0.181799i	$0.941808\pi$
$24$	−0.814832	+	2.70851i	−0.166327	+	0.552873i
$25$	1.20897	+	4.85164i	0.241793	+	0.970328i
$26$	6.14142	+	0.600131i	1.20443	+	0.117695i
$27$	−1.00000			−0.192450
$28$	−0.251259	−	0.374793i	−0.0474836	−	0.0708292i
$29$	−6.25463	−	6.25463i	−1.16146	−	1.16146i	−0.984157	−	0.177299i	$-0.943264\pi$
$29$	−6.25463	−	6.25463i	−1.16146	−	1.16146i	−0.177299	−	0.984157i	$-0.556736\pi$
$30$	−2.18017	+	2.29061i	−0.398042	+	0.418205i
$31$			1.69754i			0.304886i	0.988312	+	0.152443i	$0.0487141\pi$
$31$			1.69754i			0.304886i	−0.988312	+	0.152443i	$0.951286\pi$
$32$	−2.64751	+	4.99907i	−0.468018	+	0.883719i
$33$	−1.60861	+	1.60861i	−0.280024	+	0.280024i
$34$	7.16098	−	5.88604i	1.22810	−	1.00945i
$35$	−0.0614476	−	0.500725i	−0.0103865	−	0.0846380i
$36$	−1.96217	−	0.387177i	−0.327028	−	0.0645296i
$37$			0.609145i			0.100143i	0.998746	+	0.0500714i	$0.0159449\pi$
$37$			0.609145i			0.100143i	−0.998746	+	0.0500714i	$0.984055\pi$
$38$	5.05346	+	6.14806i	0.819780	+	0.997347i
$39$			4.36332i			0.698691i
$40$	−5.16472	+	3.65044i	−0.816614	+	0.577185i
$41$			0.538520i			0.0841026i	0.999115	+	0.0420513i	$0.0133893\pi$
$41$			0.538520i			0.0841026i	−0.999115	+	0.0420513i	$0.986611\pi$
$42$	0.246483	−	0.202600i	0.0380332	−	0.0312618i
$43$			0.592259i			0.0903186i	0.998980	+	0.0451593i	$0.0143795\pi$
$43$			0.592259i			0.0903186i	−0.998980	+	0.0451593i	$0.985620\pi$
$44$	−3.77919	+	2.53355i	−0.569734	+	0.381947i
$45$	−1.76195	−	1.37678i	−0.262657	−	0.205238i
$46$	−7.09632	−	8.63341i	−1.04630	−	1.27293i
$47$	4.85568	−	4.85568i	0.708274	−	0.708274i	−0.257898	−	0.966172i	$-0.583030\pi$
$47$	4.85568	−	4.85568i	0.708274	−	0.708274i	0.966172	+	0.257898i	$0.0830298\pi$
$48$	−3.70019	−	1.51941i	−0.534076	−	0.219308i
$49$		−	6.94910i		−	0.992729i
$50$	−6.99501	+	1.03434i	−0.989244	+	0.146277i
$51$	4.63479	+	4.63479i	0.649000	+	0.649000i
$52$	−1.68938	+	8.56156i	−0.234275	+	1.18728i
$53$	−4.82837			−0.663227			−0.331613	−	0.943415i	$-0.607593\pi$
$53$	−4.82837			−0.663227			−0.331613	+	0.943415i	$0.607593\pi$
$54$	0.137540	−	1.40751i	0.0187168	−	0.191538i
$55$	−5.04901	+	0.619600i	−0.680808	+	0.0835468i
$56$	0.562083	−	0.302101i	0.0751115	−	0.0403700i
$57$	−3.97920	+	3.97920i	−0.527058	+	0.527058i
$58$	9.66371	−	7.94319i	1.26891	−	1.04299i
$59$	5.78762	+	5.78762i	0.753483	+	0.753483i	0.975128	−	0.221644i	$-0.0711424\pi$
$59$	5.78762	+	5.78762i	0.753483	+	0.753483i	−0.221644	+	0.975128i	$0.571142\pi$
$60$	−2.92419	−	3.38365i	−0.377511	−	0.436828i
$61$	1.65469	−	1.65469i	0.211861	−	0.211861i	−0.593197	−	0.805058i	$-0.702134\pi$
$61$	1.65469	−	1.65469i	0.211861	−	0.211861i	0.805058	+	0.593197i	$0.202134\pi$
$62$	−2.38930	−	0.233479i	−0.303441	−	0.0296518i
$63$	0.159531	+	0.159531i	0.0200990	+	0.0200990i
$64$	−6.67210	−	4.41397i	−0.834012	−	0.551746i
$65$	−6.00733	+	7.68798i	−0.745117	+	0.953576i
$66$	−2.04289	−	2.48539i	−0.251462	−	0.305930i
$67$		−	0.485302i		−	0.0592891i	−0.999561	−	0.0296446i	$-0.990562\pi$
$67$		−	0.485302i		−	0.0592891i	0.999561	−	0.0296446i	$-0.00943754\pi$
$68$	7.29974	+	10.8887i	0.885223	+	1.32045i
$69$	5.58779	−	5.58779i	0.672691	−	0.672691i
$70$	0.713227	−	0.0176184i	0.0852469	−	0.00210580i
$71$	6.86042			0.814182			0.407091	−	0.913388i	$-0.366543\pi$
$71$	6.86042			0.814182			0.407091	+	0.913388i	$0.366543\pi$
$72$	0.814832	−	2.70851i	0.0960288	−	0.319201i
$73$	−0.160991	−	0.160991i	−0.0188426	−	0.0188426i	0.697623	−	0.716465i	$-0.254241\pi$
$73$	−0.160991	−	0.160991i	−0.0188426	−	0.0188426i	−0.716465	+	0.697623i	$0.754241\pi$
$74$	−0.857378	−	0.0837818i	−0.0996681	−	0.00973943i
$75$	−1.20897	−	4.85164i	−0.139599	−	0.560219i
$76$	−9.34851	+	6.26719i	−1.07235	+	0.718897i
$77$	0.513248			0.0584900
$78$	−6.14142	−	0.600131i	−0.695379	−	0.0679515i
$79$	−7.13706			−0.802982			−0.401491	−	0.915863i	$-0.631508\pi$
$79$	−7.13706			−0.802982			−0.401491	+	0.915863i	$0.631508\pi$
$80$	−4.42767	−	7.77147i	−0.495028	−	0.868877i
$81$	1.00000			0.111111
$82$	−0.757972	−	0.0740679i	−0.0837040	−	0.00817943i
$83$	−6.88217			−0.755417			−0.377708	−	0.925925i	$-0.623288\pi$
$83$	−6.88217			−0.755417			−0.377708	+	0.925925i	$0.623288\pi$
$84$	0.251259	+	0.374793i	0.0274147	+	0.0408933i
$85$	1.78521	+	14.5474i	0.193633	+	1.57788i
$86$	−0.833610	−	0.0814592i	−0.0898905	−	0.00878397i
$87$	6.25463	+	6.25463i	0.670567	+	0.670567i
$88$	−3.04620	−	5.66770i	−0.324726	−	0.604179i
$89$	17.0238			1.80451			0.902257	−	0.431198i	$-0.141909\pi$
$89$	17.0238			1.80451			0.902257	+	0.431198i	$0.141909\pi$
$90$	2.18017	−	2.29061i	0.229810	−	0.241451i
$91$	0.696085	−	0.696085i	0.0729696	−	0.0729696i
$92$	13.1276	−	8.80070i	1.36865	−	0.917536i
$93$		−	1.69754i		−	0.176026i
$94$	6.16657	+	7.50227i	0.636033	+	0.773800i
$95$	−12.4896	+	1.53269i	−1.28141	+	0.157251i
$96$	2.64751	−	4.99907i	0.270210	−	0.510215i
$97$	9.64079	+	9.64079i	0.978874	+	0.978874i	0.999781	−	0.0209077i	$-0.00665561\pi$
$97$	9.64079	+	9.64079i	0.978874	+	0.978874i	−0.0209077	+	0.999781i	$0.506656\pi$
$98$	9.78092	+	0.955778i	0.988022	+	0.0965482i
$99$	1.60861	−	1.60861i	0.161672	−	0.161672i
$100$	−0.493746	−	9.98780i	−0.0493746	−	0.998780i
$101$	−4.00201	−	4.00201i	−0.398214	−	0.398214i	0.479388	−	0.877603i	$-0.340859\pi$
$101$	−4.00201	−	4.00201i	−0.398214	−	0.398214i	−0.877603	+	0.479388i	$0.840859\pi$
$102$	−7.16098	+	5.88604i	−0.709042	+	0.582805i
$103$	−8.06640	+	8.06640i	−0.794806	+	0.794806i	−0.982271	−	0.187465i	$-0.939973\pi$
$103$	−8.06640	+	8.06640i	−0.794806	+	0.794806i	0.187465	+	0.982271i	$0.439973\pi$
$104$	−11.8181	−	3.55537i	−1.15886	−	0.348633i
$105$	0.0614476	+	0.500725i	0.00599667	+	0.0488658i
$106$	0.664093	−	6.79597i	0.0645024	−	0.660083i
$107$	4.50489			0.435504			0.217752	−	0.976004i	$-0.430128\pi$
$107$	4.50489			0.435504			0.217752	+	0.976004i	$0.430128\pi$
$108$	1.96217	+	0.387177i	0.188809	+	0.0372562i
$109$	0.813992	+	0.813992i	0.0779663	+	0.0779663i	0.745015	−	0.667048i	$-0.232443\pi$
$109$	0.813992	+	0.813992i	0.0779663	+	0.0779663i	−0.667048	+	0.745015i	$0.732443\pi$
$110$	−0.177653	−	7.19175i	−0.0169385	−	0.685706i
$111$		−	0.609145i		−	0.0578175i
$112$	0.347901	+	0.832688i	0.0328736	+	0.0786816i
$113$	7.69423	−	7.69423i	0.723813	−	0.723813i	−0.245567	−	0.969380i	$-0.578974\pi$
$113$	7.69423	−	7.69423i	0.723813	−	0.723813i	0.969380	+	0.245567i	$0.0789741\pi$
$114$	−5.05346	−	6.14806i	−0.473300	−	0.575819i
$115$	17.5386	−	2.15228i	1.63548	−	0.200702i
$116$	9.85097	+	14.6943i	0.914640	+	1.36433i
$117$		−	4.36332i		−	0.403389i
$118$	−8.94215	+	7.35010i	−0.823192	+	0.676631i
$119$		−	1.47878i		−	0.135560i
$120$	5.16472	−	3.65044i	0.471472	−	0.333238i
$121$			5.82472i			0.529520i
$122$	2.10140	+	2.55657i	0.190252	+	0.231461i
$123$		−	0.538520i		−	0.0485567i
$124$	0.657247	−	3.33085i	0.0590226	−	0.299119i
$125$	4.54949	−	10.2128i	0.406919	−	0.913464i
$126$	−0.246483	+	0.202600i	−0.0219585	+	0.0180490i
$127$	12.0279	−	12.0279i	1.06731	−	1.06731i	0.0697405	−	0.997565i	$-0.477783\pi$
$127$	12.0279	−	12.0279i	1.06731	−	1.06731i	0.997565	−	0.0697405i	$-0.0222171\pi$
$128$	7.13038	−	8.78395i	0.630242	−	0.776398i
$129$		−	0.592259i		−	0.0521455i
$130$	−9.99465	−	9.51277i	−0.876589	−	0.834325i
$131$	13.2235	+	13.2235i	1.15534	+	1.15534i	0.985466	+	0.169874i	$0.0543361\pi$
$131$	13.2235	+	13.2235i	1.15534	+	1.15534i	0.169874	+	0.985466i	$0.445664\pi$
$132$	3.77919	−	2.53355i	0.328936	−	0.220517i
$133$	1.26961			0.110089
$134$	0.683068	+	0.0667484i	0.0590080	+	0.00576618i
$135$	1.76195	+	1.37678i	0.151645	+	0.118494i
$136$	−16.3300	+	8.77682i	−1.40028	+	0.752606i
$137$	4.88182	−	4.88182i	0.417082	−	0.417082i	−0.467115	−	0.884197i	$-0.654706\pi$
$137$	4.88182	−	4.88182i	0.417082	−	0.417082i	0.884197	+	0.467115i	$0.154706\pi$
$138$	7.09632	+	8.63341i	0.604079	+	0.734925i
$139$	−9.86643	−	9.86643i	−0.836860	−	0.836860i	0.151584	−	0.988444i	$-0.451562\pi$
$139$	−9.86643	−	9.86643i	−0.836860	−	0.836860i	−0.988444	+	0.151584i	$0.951562\pi$
$140$	−0.0732991	+	1.00630i	−0.00619490	+	0.0850476i
$141$	−4.85568	+	4.85568i	−0.408922	+	0.408922i
$142$	−0.943581	+	9.65611i	−0.0791836	+	0.810322i
$143$	−7.01890	−	7.01890i	−0.586950	−	0.586950i
$144$	3.70019	+	1.51941i	0.308349	+	0.126618i
$145$	2.40914	+	19.6316i	0.200068	+	1.63032i
$146$	0.248739	−	0.204454i	0.0205858	−	0.0169207i
$147$			6.94910i			0.573152i
$148$	0.235847	−	1.19524i	0.0193865	−	0.0982484i
$149$	−11.2851	+	11.2851i	−0.924515	+	0.924515i	−0.997344	−	0.0728290i	$-0.976797\pi$
$149$	−11.2851	+	11.2851i	−0.924515	+	0.924515i	0.0728290	+	0.997344i	$0.476797\pi$
$150$	6.99501	−	1.03434i	0.571140	−	0.0844532i
$151$	1.52546			0.124140			0.0620701	−	0.998072i	$-0.480230\pi$
$151$	1.52546			0.124140			0.0620701	+	0.998072i	$0.480230\pi$
$152$	−7.53534	−	14.0201i	−0.611197	−	1.13718i
$153$	−4.63479	−	4.63479i	−0.374700	−	0.374700i
$154$	−0.0705920	+	0.722401i	−0.00568847	+	0.0582127i
$155$	2.33713	−	2.99098i	0.187723	−	0.240241i
$156$	1.68938	−	8.56156i	0.135259	−	0.685474i
$157$	11.8705			0.947366			0.473683	−	0.880695i	$-0.342924\pi$
$157$	11.8705			0.947366			0.473683	+	0.880695i	$0.342924\pi$
$158$	0.981630	−	10.0455i	0.0780943	−	0.799175i
$159$	4.82837			0.382914
$160$	11.5474	−	5.16310i	0.912902	−	0.408179i
$161$	−1.78285			−0.140508
$162$	−0.137540	+	1.40751i	−0.0108062	+	0.110584i
$163$	−6.57461			−0.514963			−0.257481	−	0.966283i	$-0.582893\pi$
$163$	−6.57461			−0.514963			−0.257481	+	0.966283i	$0.582893\pi$
$164$	0.208503	−	1.05666i	0.0162813	−	0.0825117i
$165$	5.04901	−	0.619600i	0.393065	−	0.0482358i
$166$	0.946573	−	9.68672i	0.0734683	−	0.751836i
$167$	−18.2166	−	18.2166i	−1.40964	−	1.40964i	−0.761636	−	0.648005i	$-0.775604\pi$
$167$	−18.2166	−	18.2166i	−1.40964	−	1.40964i	−0.648005	−	0.761636i	$-0.724396\pi$
$168$	−0.562083	+	0.302101i	−0.0433656	+	0.0233076i
$169$	−6.03860			−0.464507
$170$	−20.7211	+	0.511859i	−1.58923	+	0.0392578i
$171$	3.97920	−	3.97920i	0.304297	−	0.304297i
$172$	0.229309	−	1.16211i	0.0174847	−	0.0886100i
$173$		−	4.84309i		−	0.368213i	−0.982906	−	0.184106i	$-0.941061\pi$
$173$		−	4.84309i		−	0.368213i	0.982906	−	0.184106i	$-0.0589391\pi$
$174$	−9.66371	+	7.94319i	−0.732604	+	0.602172i
$175$	−0.581119	+	0.966854i	−0.0439285	+	0.0730873i
$176$	8.39632	−	3.50803i	0.632896	−	0.264427i
$177$	−5.78762	−	5.78762i	−0.435024	−	0.435024i
$178$	−2.34144	+	23.9611i	−0.175499	+	1.79596i
$179$	5.14531	−	5.14531i	0.384579	−	0.384579i	−0.488170	−	0.872749i	$-0.662335\pi$
$179$	5.14531	−	5.14531i	0.384579	−	0.384579i	0.872749	+	0.488170i	$0.162335\pi$
$180$	2.92419	+	3.38365i	0.217956	+	0.252203i
$181$	−11.6902	−	11.6902i	−0.868925	−	0.868925i	0.123429	−	0.992353i	$-0.460611\pi$
$181$	−11.6902	−	11.6902i	−0.868925	−	0.868925i	−0.992353	+	0.123429i	$0.960611\pi$
$182$	0.884007	+	1.07549i	0.0655270	+	0.0797204i
$183$	−1.65469	+	1.65469i	−0.122318	+	0.122318i
$184$	10.5815	+	19.6877i	0.780078	+	1.45140i
$185$	0.838658	−	1.07329i	0.0616593	−	0.0789096i
$186$	2.38930	+	0.233479i	0.175192	+	0.0171195i
$187$	−14.9112			−1.09041
$188$	−11.4077	+	7.64764i	−0.831989	+	0.557762i
$189$	−0.159531	−	0.159531i	−0.0116042	−	0.0116042i
$190$	−0.439457	−	17.7901i	−0.0318816	−	1.29063i
$191$			15.8153i			1.14436i	0.820129	+	0.572179i	$0.193902\pi$
$191$			15.8153i			1.14436i	−0.820129	+	0.572179i	$0.806098\pi$
$192$	6.67210	+	4.41397i	0.481517	+	0.318551i
$193$	−1.54170	+	1.54170i	−0.110974	+	0.110974i	−0.760413	−	0.649439i	$-0.775004\pi$
$193$	−1.54170	+	1.54170i	−0.110974	+	0.110974i	0.649439	+	0.760413i	$0.275004\pi$
$194$	−14.8955	+	12.2435i	−1.06943	+	0.879033i
$195$	6.00733	−	7.68798i	0.430194	−	0.550547i
$196$	−2.69053	+	13.6353i	−0.192181	+	0.973949i
$197$			5.98026i			0.426076i	0.977044	+	0.213038i	$0.0683358\pi$
$197$			5.98026i			0.426076i	−0.977044	+	0.213038i	$0.931664\pi$
$198$	2.04289	+	2.48539i	0.145182	+	0.176629i
$199$			12.5564i			0.890102i	0.895505	+	0.445051i	$0.146815\pi$
$199$			12.5564i			0.890102i	−0.895505	+	0.445051i	$0.853185\pi$
$200$	14.1258	+	0.678770i	0.998848	+	0.0479963i
$201$			0.485302i			0.0342306i
$202$	6.18330	−	5.08243i	0.435055	−	0.357598i
$203$		−	1.99561i		−	0.140065i
$204$	−7.29974	−	10.8887i	−0.511084	−	0.762362i
$205$	0.741422	−	0.948847i	0.0517832	−	0.0662704i
$206$	−10.2441	−	12.4630i	−0.713739	−	0.868338i
$207$	−5.58779	+	5.58779i	−0.388378	+	0.388378i
$208$	6.62969	−	16.1451i	0.459686	−	1.11946i
$209$		−	12.8020i		−	0.885533i
$210$	−0.713227	+	0.0176184i	−0.0492173	+	0.00121578i
$211$	−18.4049	−	18.4049i	−1.26705	−	1.26705i	−0.947605	−	0.319443i	$-0.896504\pi$
$211$	−18.4049	−	18.4049i	−1.26705	−	1.26705i	−0.319443	−	0.947605i	$-0.603496\pi$
$212$	9.47405	+	1.86943i	0.650681	+	0.128393i
$213$	−6.86042			−0.470068
$214$	−0.619602	+	6.34067i	−0.0423551	+	0.433440i
$215$	0.815409	−	1.04353i	0.0556104	−	0.0711684i
$216$	−0.814832	+	2.70851i	−0.0554423	+	0.184291i
$217$	−0.270810	+	0.270810i	−0.0183838	+	0.0183838i
$218$	−1.25766	+	1.03374i	−0.0851793	+	0.0700140i
$219$	0.160991	+	0.160991i	0.0108788	+	0.0108788i
$220$	10.1469	+	0.739104i	0.684103	+	0.0498303i
$221$	−20.2231	+	20.2231i	−1.36035	+	1.36035i
$222$	0.857378	+	0.0837818i	0.0575434	+	0.00562306i
$223$	11.6149	+	11.6149i	0.777792	+	0.777792i	0.979455	−	0.201663i	$-0.0646345\pi$
$223$	11.6149	+	11.6149i	0.777792	+	0.777792i	−0.201663	+	0.979455i	$0.564634\pi$
$224$	−1.21987	+	0.375147i	−0.0815058	+	0.0250655i
$225$	1.20897	+	4.85164i	0.0805977	+	0.323443i
$226$	9.77144	+	11.8880i	0.649987	+	0.790776i
$227$		−	0.411442i		−	0.0273084i	−0.999907	−	0.0136542i	$-0.995654\pi$
$227$		−	0.411442i		−	0.0273084i	0.999907	−	0.0136542i	$-0.00434640\pi$
$228$	9.34851	−	6.26719i	0.619120	−	0.415055i
$229$	11.2286	−	11.2286i	0.742009	−	0.742009i	−0.230955	−	0.972964i	$-0.574185\pi$
$229$	11.2286	−	11.2286i	0.742009	−	0.742009i	0.972964	+	0.230955i	$0.0741851\pi$
$230$	0.617107	+	24.9817i	0.0406908	+	1.64725i
$231$	−0.513248			−0.0337692
$232$	−22.0372	+	11.8443i	−1.44681	+	0.777615i
$233$	18.9687	+	18.9687i	1.24268	+	1.24268i	0.958884	+	0.283799i	$0.0915947\pi$
$233$	18.9687	+	18.9687i	1.24268	+	1.24268i	0.283799	+	0.958884i	$0.408405\pi$
$234$	6.14142	+	0.600131i	0.401477	+	0.0392318i
$235$	−15.2407	+	1.87029i	−0.994193	+	0.122005i
$236$	−9.11543	−	13.5971i	−0.593364	−	0.885095i
$237$	7.13706			0.463602
$238$	2.08140	+	0.203392i	0.134917	+	0.0131839i
$239$	−11.2094			−0.725076			−0.362538	−	0.931969i	$-0.618090\pi$
$239$	−11.2094			−0.725076			−0.362538	+	0.931969i	$0.618090\pi$
$240$	4.42767	+	7.77147i	0.285805	+	0.501646i
$241$	0.0518990			0.00334311			0.00167156	−	0.999999i	$-0.499468\pi$
$241$	0.0518990			0.00334311			0.00167156	+	0.999999i	$0.499468\pi$
$242$	−8.19835	−	0.801132i	−0.527010	−	0.0514987i
$243$	−1.00000			−0.0641500
$244$	−3.88743	+	2.60611i	−0.248867	+	0.166839i
$245$	−9.56737	+	12.2440i	−0.611237	+	0.782240i
$246$	0.757972	+	0.0740679i	0.0483265	+	0.00472240i
$247$	−17.3625	−	17.3625i	−1.10475	−	1.10475i
$248$	4.59780	+	1.38321i	0.291961	+	0.0878337i
$249$	6.88217			0.436140
$250$	13.7489	+	7.80812i	0.869559	+	0.493829i
$251$	−2.45358	+	2.45358i	−0.154869	+	0.154869i	−0.780288	−	0.625420i	$-0.784928\pi$
$251$	−2.45358	+	2.45358i	−0.154869	+	0.154869i	0.625420	+	0.780288i	$0.284928\pi$
$252$	−0.251259	−	0.374793i	−0.0158279	−	0.0236097i
$253$			17.9772i			1.13022i
$254$	15.2751	+	18.5837i	0.958445	+	1.16605i
$255$	−1.78521	−	14.5474i	−0.111794	−	0.910991i
$256$	11.3828	+	11.2442i	0.711423	+	0.702764i
$257$	−4.52073	−	4.52073i	−0.281995	−	0.281995i	0.551909	−	0.833904i	$-0.313900\pi$
$257$	−4.52073	−	4.52073i	−0.281995	−	0.281995i	−0.833904	+	0.551909i	$0.813900\pi$
$258$	0.833610	+	0.0814592i	0.0518983	+	0.00507143i
$259$	−0.0971776	+	0.0971776i	−0.00603832	+	0.00603832i
$260$	14.7640	−	12.7592i	0.915623	−	0.791291i
$261$	−6.25463	−	6.25463i	−0.387152	−	0.387152i
$262$	−20.4309	+	16.7934i	−1.26223	+	1.03750i
$263$	16.0925	−	16.0925i	0.992304	−	0.992304i	−0.00766695	−	0.999971i	$-0.502440\pi$
$263$	16.0925	−	16.0925i	0.992304	−	0.992304i	0.999971	+	0.00766695i	$0.00244049\pi$
$264$	3.04620	+	5.66770i	0.187481	+	0.348823i
$265$	8.50736	+	6.64759i	0.522603	+	0.408358i
$266$	−0.174622	+	1.78699i	−0.0107068	+	0.109567i
$267$	−17.0238			−1.04184
$268$	−0.187898	+	0.952243i	−0.0114777	+	0.0581675i
$269$	8.32218	+	8.32218i	0.507412	+	0.507412i	0.913731	−	0.406319i	$-0.133188\pi$
$269$	8.32218	+	8.32218i	0.507412	+	0.507412i	−0.406319	+	0.913731i	$0.633188\pi$
$270$	−2.18017	+	2.29061i	−0.132681	+	0.139402i
$271$		−	2.91266i		−	0.176932i	−0.996079	−	0.0884658i	$-0.971804\pi$
$271$		−	2.91266i		−	0.176932i	0.996079	−	0.0884658i	$-0.0281964\pi$
$272$	−10.1074	−	24.1917i	−0.612853	−	1.46684i
$273$	−0.696085	+	0.696085i	−0.0421290	+	0.0421290i
$274$	6.19977	+	7.54266i	0.374542	+	0.455669i
$275$	9.74917	+	5.85966i	0.587897	+	0.353351i
$276$	−13.1276	+	8.80070i	−0.790191	+	0.529740i
$277$		−	0.339665i		−	0.0204085i	−0.999948	−	0.0102042i	$-0.996752\pi$
$277$		−	0.339665i		−	0.0204085i	0.999948	−	0.0102042i	$-0.00324817\pi$
$278$	15.2441	−	12.5301i	0.914282	−	0.751504i
$279$			1.69754i			0.101629i
$280$	−1.40629	−	0.241575i	−0.0840419	−	0.0144369i
$281$		−	20.9850i		−	1.25186i	−0.779878	−	0.625931i	$-0.784719\pi$
$281$		−	20.9850i		−	1.25186i	0.779878	−	0.625931i	$-0.215281\pi$
$282$	−6.16657	−	7.50227i	−0.367214	−	0.446754i
$283$		−	15.6290i		−	0.929047i	−0.885561	−	0.464523i	$-0.846226\pi$
$283$		−	15.6290i		−	0.929047i	0.885561	−	0.464523i	$-0.153774\pi$
$284$	−13.4613	−	2.65620i	−0.798780	−	0.157616i
$285$	12.4896	−	1.53269i	0.739823	−	0.0907890i
$286$	10.8446	−	8.91379i	0.641252	−	0.527084i
$287$	−0.0859106	+	0.0859106i	−0.00507114	+	0.00507114i
$288$	−2.64751	+	4.99907i	−0.156006	+	0.294573i
$289$			25.9625i			1.52721i
$290$	−27.9630	+	0.690752i	−1.64205	+	0.0405624i
$291$	−9.64079	−	9.64079i	−0.565153	−	0.565153i
$292$	0.253559	+	0.378223i	0.0148384	+	0.0221338i
$293$	19.8819			1.16151			0.580756	−	0.814078i	$-0.302757\pi$
$293$	19.8819			1.16151			0.580756	+	0.814078i	$0.302757\pi$
$294$	−9.78092	−	0.955778i	−0.570435	−	0.0557421i
$295$	−2.22925	−	18.1658i	−0.129792	−	1.05765i
$296$	1.64988	+	0.496351i	0.0958972	+	0.0288498i
$297$	−1.60861	+	1.60861i	−0.0933412	+	0.0933412i
$298$	−14.3318	−	17.4361i	−0.830219	−	1.01005i
$299$	24.3813	+	24.3813i	1.41001	+	1.41001i
$300$	0.493746	+	9.98780i	0.0285064	+	0.576646i
$301$	−0.0944836	+	0.0944836i	−0.00544595	+	0.00544595i
$302$	−0.209811	+	2.14710i	−0.0120733	+	0.123552i
$303$	4.00201	+	4.00201i	0.229909	+	0.229909i
$304$	20.7698	−	8.67774i	1.19123	−	0.497703i
$305$	−5.19362	+	0.637346i	−0.297386	+	0.0364943i
$306$	7.16098	−	5.88604i	0.409366	−	0.336482i
$307$			13.0401i			0.744239i	0.928185	+	0.372119i	$0.121369\pi$
$307$			13.0401i			0.744239i	−0.928185	+	0.372119i	$0.878631\pi$
$308$	−1.00708	−	0.198718i	−0.0573835	−	0.0113230i
$309$	8.06640	−	8.06640i	0.458882	−	0.458882i
$310$	3.88838	+	3.70091i	0.220845	+	0.210198i
$311$	23.6036			1.33843			0.669217	−	0.743067i	$-0.266630\pi$
$311$	23.6036			1.33843			0.669217	+	0.743067i	$0.266630\pi$
$312$	11.8181	+	3.55537i	0.669070	+	0.201283i
$313$	−23.0604	−	23.0604i	−1.30345	−	1.30345i	−0.926051	−	0.377399i	$-0.876818\pi$
$313$	−23.0604	−	23.0604i	−1.30345	−	1.30345i	−0.377399	−	0.926051i	$-0.623182\pi$
$314$	−1.63266	+	16.7078i	−0.0921365	+	0.942875i
$315$	−0.0614476	−	0.500725i	−0.00346218	−	0.0282127i
$316$	14.0041	+	2.76331i	0.787792	+	0.155448i
$317$	10.0772			0.565991			0.282996	−	0.959121i	$-0.408672\pi$
$317$	10.0772			0.565991			0.282996	+	0.959121i	$0.408672\pi$
$318$	−0.664093	+	6.79597i	−0.0372405	+	0.381099i
$319$	−20.1226			−1.12665
$320$	5.67888	+	16.9632i	0.317459	+	0.948272i
$321$	−4.50489			−0.251438
$322$	0.245213	−	2.50938i	0.0136652	−	0.139842i
$323$	−36.8855			−2.05236
$324$	−1.96217	−	0.387177i	−0.109009	−	0.0215099i
$325$	21.1693	−	5.27511i	1.17426	−	0.292610i
$326$	0.904271	−	9.25382i	0.0500829	−	0.512522i
$327$	−0.813992	−	0.813992i	−0.0450138	−	0.0450138i
$328$	1.45859	+	0.438803i	0.0805371	+	0.0242288i
$329$	1.54926			0.0854137
$330$	0.177653	+	7.19175i	0.00977947	+	0.395893i
$331$	6.16029	−	6.16029i	0.338600	−	0.338600i	−0.517240	−	0.855840i	$-0.673041\pi$
$331$	6.16029	−	6.16029i	0.338600	−	0.338600i	0.855840	+	0.517240i	$0.173041\pi$
$332$	13.5040	+	2.66462i	0.741126	+	0.146240i
$333$			0.609145i			0.0333810i
$334$	28.1455	−	23.1345i	1.54005	−	1.26586i
$335$	−0.668153	+	0.855080i	−0.0365051	+	0.0467180i
$336$	−0.347901	−	0.832688i	−0.0189796	−	0.0454269i
$337$	−18.1642	−	18.1642i	−0.989467	−	0.989467i	0.0104777	−	0.999945i	$-0.496665\pi$
$337$	−18.1642	−	18.1642i	−0.989467	−	0.989467i	−0.999945	+	0.0104777i	$0.996665\pi$
$338$	0.830548	−	8.49938i	0.0451758	−	0.462305i
$339$	−7.69423	+	7.69423i	−0.417893	+	0.417893i
$340$	2.12953	−	29.2355i	0.115490	−	1.58552i
$341$	2.73068	+	2.73068i	0.147875	+	0.147875i
$342$	5.05346	+	6.14806i	0.273260	+	0.332449i
$343$	2.22531	−	2.22531i	0.120156	−	0.120156i
$344$	1.60414	+	0.482591i	0.0864895	+	0.0260196i
$345$	−17.5386	+	2.15228i	−0.944245	+	0.115875i
$346$	6.81669	+	0.666117i	0.366467	+	0.0358107i
$347$	−2.80849			−0.150767			−0.0753837	−	0.997155i	$-0.524018\pi$
$347$	−2.80849			−0.150767			−0.0753837	+	0.997155i	$0.524018\pi$
$348$	−9.85097	−	14.6943i	−0.528067	−	0.787696i
$349$	−13.8516	−	13.8516i	−0.741458	−	0.741458i	0.231401	−	0.972858i	$-0.425669\pi$
$349$	−13.8516	−	13.8516i	−0.741458	−	0.741458i	−0.972858	+	0.231401i	$0.925669\pi$
$350$	−1.28093	−	0.950912i	−0.0684686	−	0.0508284i
$351$			4.36332i			0.232897i
$352$	3.78275	+	12.3004i	0.201621	+	0.655613i
$353$	16.3758	−	16.3758i	0.871595	−	0.871595i	−0.121051	−	0.992646i	$-0.538626\pi$
$353$	16.3758	−	16.3758i	0.871595	−	0.871595i	0.992646	+	0.121051i	$0.0386265\pi$
$354$	8.94215	−	7.35010i	0.475270	−	0.390653i
$355$	−12.0877	−	9.44528i	−0.641551	−	0.501303i
$356$	−33.4034	−	6.59121i	−1.77038	−	0.349334i
$357$			1.47878i			0.0782656i
$358$	6.53439	+	7.94976i	0.345353	+	0.420158i
$359$		−	17.0587i		−	0.900325i	−0.892947	−	0.450162i	$-0.851366\pi$
$359$		−	17.0587i		−	0.900325i	0.892947	−	0.450162i	$-0.148634\pi$
$360$	−5.16472	+	3.65044i	−0.272205	+	0.192395i
$361$		−	12.6681i		−	0.666741i
$362$	18.0619	−	14.8462i	0.949313	−	0.780298i
$363$		−	5.82472i		−	0.305719i
$364$	−1.63534	+	1.09633i	−0.0857153	+	0.0574631i
$365$	0.0620100	+	0.505308i	0.00324575	+	0.0264490i
$366$	−2.10140	−	2.55657i	−0.109842	−	0.133634i
$367$	13.9971	−	13.9971i	0.730643	−	0.730643i	−0.240104	−	0.970747i	$-0.577182\pi$
$367$	13.9971	−	13.9971i	0.730643	−	0.730643i	0.970747	+	0.240104i	$0.0771816\pi$
$368$	−29.1660	+	12.1857i	−1.52038	+	0.635224i
$369$			0.538520i			0.0280342i
$370$	1.39531	+	1.32804i	0.0725388	+	0.0690414i
$371$	−0.770274	−	0.770274i	−0.0399906	−	0.0399906i
$372$	−0.657247	+	3.33085i	−0.0340767	+	0.172696i
$373$	16.4829			0.853450			0.426725	−	0.904381i	$-0.359667\pi$
$373$	16.4829			0.853450			0.426725	+	0.904381i	$0.359667\pi$
$374$	2.05088	−	20.9876i	0.106048	−	1.08524i
$375$	−4.54949	+	10.2128i	−0.234935	+	0.527389i
$376$	−9.19512	−	17.1083i	−0.474202	−	0.882291i
$377$	−27.2910	+	27.2910i	−1.40556	+	1.40556i
$378$	0.246483	−	0.202600i	0.0126777	−	0.0104206i
$379$	9.73283	+	9.73283i	0.499942	+	0.499942i	0.911420	−	0.411478i	$-0.134987\pi$
$379$	9.73283	+	9.73283i	0.499942	+	0.499942i	−0.411478	+	0.911420i	$0.634987\pi$
$380$	25.1002	+	1.82831i	1.28761	+	0.0937902i
$381$	−12.0279	+	12.0279i	−0.616209	+	0.616209i
$382$	−22.2603	−	2.17524i	−1.13893	−	0.111295i
$383$	5.51456	+	5.51456i	0.281781	+	0.281781i	0.833819	−	0.552038i	$-0.186150\pi$
$383$	5.51456	+	5.51456i	0.281781	+	0.281781i	−0.552038	+	0.833819i	$0.686150\pi$
$384$	−7.13038	+	8.78395i	−0.363871	+	0.448254i
$385$	−0.904319	−	0.706628i	−0.0460883	−	0.0360131i
$386$	−1.95792	−	2.38201i	−0.0996553	−	0.121241i
$387$			0.592259i			0.0301062i
$388$	−15.1841	−	22.6495i	−0.770857	−	1.14986i
$389$	−3.72303	+	3.72303i	−0.188765	+	0.188765i	−0.795162	−	0.606397i	$-0.792614\pi$
$389$	−3.72303	+	3.72303i	−0.188765	+	0.188765i	0.606397	+	0.795162i	$0.292614\pi$
$390$	9.99465	+	9.51277i	0.506099	+	0.481698i
$391$	51.7964			2.61946
$392$	−18.8217	−	5.66235i	−0.950641	−	0.285992i
$393$	−13.2235	−	13.2235i	−0.667036	−	0.667036i
$394$	−8.41727	−	0.822524i	−0.424056	−	0.0414382i
$395$	12.5752	+	9.82615i	0.632726	+	0.494407i
$396$	−3.77919	+	2.53355i	−0.189911	+	0.127316i
$397$	30.9797			1.55483			0.777413	−	0.628991i	$-0.216532\pi$
$397$	30.9797			1.55483			0.777413	+	0.628991i	$0.216532\pi$
$398$	−17.6733	−	1.72701i	−0.885883	−	0.0865672i
$399$	−1.26961			−0.0635601
$400$	−2.89824	+	19.7889i	−0.144912	+	0.989445i
$401$	0.563079			0.0281188			0.0140594	−	0.999901i	$-0.495525\pi$
$401$	0.563079			0.0281188			0.0140594	+	0.999901i	$0.495525\pi$
$402$	−0.683068	−	0.0667484i	−0.0340683	−	0.00332911i
$403$	7.40690			0.368964
$404$	6.30311	+	9.40208i	0.313592	+	0.467771i
$405$	−1.76195	−	1.37678i	−0.0875522	−	0.0684126i
$406$	2.80885	+	0.274477i	0.139401	+	0.0136220i
$407$	0.979879	+	0.979879i	0.0485708	+	0.0485708i
$408$	16.3300	−	8.77682i	0.808453	−	0.434517i
$409$	−33.9503			−1.67874			−0.839368	−	0.543563i	$-0.817075\pi$
$409$	−33.9503			−1.67874			−0.839368	+	0.543563i	$0.817075\pi$
$410$	1.23354	+	1.17406i	0.0609200	+	0.0579828i
$411$	−4.88182	+	4.88182i	−0.240803	+	0.240803i
$412$	18.9508	−	12.7045i	0.933636	−	0.625905i
$413$			1.84661i			0.0908657i
$414$	−7.09632	−	8.63341i	−0.348765	−	0.424309i
$415$	12.1261	+	9.47522i	0.595246	+	0.465120i
$416$	21.8126	+	11.5519i	1.06945	+	0.566381i
$417$	9.86643	+	9.86643i	0.483161	+	0.483161i
$418$	18.0189	+	1.76078i	0.881335	+	0.0861228i
$419$	−12.0118	+	12.0118i	−0.586814	+	0.586814i	−0.936767	−	0.349953i	$-0.886197\pi$
$419$	−12.0118	+	12.0118i	−0.586814	+	0.586814i	0.349953	+	0.936767i	$0.386197\pi$
$420$	0.0732991	−	1.00630i	0.00357663	−	0.0491022i
$421$	−5.06683	−	5.06683i	−0.246942	−	0.246942i	0.572772	−	0.819715i	$-0.305868\pi$
$421$	−5.06683	−	5.06683i	−0.246942	−	0.246942i	−0.819715	+	0.572772i	$0.805868\pi$
$422$	28.4365	−	23.3737i	1.38427	−	1.13781i
$423$	4.85568	−	4.85568i	0.236091	−	0.236091i
$424$	−3.93431	+	13.0777i	−0.191067	+	0.635109i
$425$	16.8830	−	28.0896i	0.818947	−	1.36255i
$426$	0.943581	−	9.65611i	0.0457167	−	0.467840i
$427$	0.527948			0.0255492
$428$	−8.83934	−	1.74419i	−0.427266	−	0.0843087i
$429$	7.01890	+	7.01890i	0.338876	+	0.338876i
$430$	1.35663	+	1.29122i	0.0654226	+	0.0622683i
$431$			17.0195i			0.819798i	0.912131	+	0.409899i	$0.134436\pi$
$431$			17.0195i			0.819798i	−0.912131	+	0.409899i	$0.865564\pi$
$432$	−3.70019	−	1.51941i	−0.178025	−	0.0731027i
$433$	24.6355	−	24.6355i	1.18390	−	1.18390i	0.205180	−	0.978724i	$-0.434222\pi$
$433$	24.6355	−	24.6355i	1.18390	−	1.18390i	0.978724	−	0.205180i	$-0.0657780\pi$
$434$	−0.343920	−	0.418414i	−0.0165087	−	0.0200845i
$435$	−2.40914	−	19.6316i	−0.115509	−	0.941264i
$436$	−1.28203	−	1.91235i	−0.0613980	−	0.0915847i
$437$			44.4699i			2.12728i
$438$	−0.248739	+	0.204454i	−0.0118852	+	0.00976918i
$439$			27.5012i			1.31256i	0.754516	+	0.656281i	$0.227871\pi$
$439$			27.5012i			1.31256i	−0.754516	+	0.656281i	$0.772129\pi$
$440$	−2.43590	+	14.1802i	−0.116127	+	0.676014i
$441$		−	6.94910i		−	0.330910i
$442$	−25.6827	−	31.2457i	−1.22160	−	1.48620i
$443$			38.2663i			1.81809i	0.416701	+	0.909044i	$0.363186\pi$
$443$			38.2663i			1.81809i	−0.416701	+	0.909044i	$0.636814\pi$
$444$	−0.235847	+	1.19524i	−0.0111928	+	0.0567238i
$445$	−29.9951	−	23.4379i	−1.42190	−	1.11106i
$446$	−17.9456	+	14.7506i	−0.849750	+	0.698461i
$447$	11.2851	−	11.2851i	0.533769	−	0.533769i
$448$	−0.360242	−	1.76857i	−0.0170198	−	0.0835571i
$449$			19.7738i			0.933184i	0.884473	+	0.466592i	$0.154518\pi$
$449$			19.7738i			0.933184i	−0.884473	+	0.466592i	$0.845482\pi$
$450$	−6.99501	+	1.03434i	−0.329748	+	0.0487591i
$451$	0.866270	+	0.866270i	0.0407911	+	0.0407911i
$452$	−18.0764	+	12.1183i	−0.850242	+	0.569998i
$453$	−1.52546			−0.0716723
$454$	0.579109	+	0.0565897i	0.0271789	+	0.00265589i
$455$	−2.18483	+	0.268116i	−0.102426	+	0.0125695i
$456$	7.53534	+	14.0201i	0.352875	+	0.656551i
$457$	3.78901	−	3.78901i	0.177242	−	0.177242i	−0.612910	−	0.790153i	$-0.710001\pi$
$457$	3.78901	−	3.78901i	0.177242	−	0.177242i	0.790153	+	0.612910i	$0.210001\pi$
$458$	14.2600	+	17.3488i	0.666327	+	0.810656i
$459$	4.63479	+	4.63479i	0.216333	+	0.216333i
$460$	−35.2469	−	2.56740i	−1.64339	−	0.119706i
$461$	−3.32447	+	3.32447i	−0.154836	+	0.154836i	−0.780274	−	0.625438i	$-0.784920\pi$
$461$	−3.32447	+	3.32447i	−0.154836	+	0.154836i	0.625438	+	0.780274i	$0.284920\pi$
$462$	0.0705920	−	0.722401i	0.00328424	−	0.0336091i
$463$	8.53272	+	8.53272i	0.396549	+	0.396549i	0.877014	−	0.480465i	$-0.159532\pi$
$463$	8.53272	+	8.53272i	0.396549	+	0.396549i	−0.480465	+	0.877014i	$0.659532\pi$
$464$	−13.6399	−	32.6467i	−0.633218	−	1.51558i
$465$	−2.33713	+	2.99098i	−0.108382	+	0.138703i
$466$	−29.3076	+	24.0897i	−1.35765	+	1.11593i
$467$			12.6255i			0.584240i	0.956382	+	0.292120i	$0.0943606\pi$
$467$			12.6255i			0.584240i	−0.956382	+	0.292120i	$0.905639\pi$
$468$	−1.68938	+	8.56156i	−0.0780916	+	0.395758i
$469$	0.0774208	−	0.0774208i	0.00357496	−	0.00357496i
$470$	−0.536255	−	21.7087i	−0.0247356	−	1.00135i
$471$	−11.8705			−0.546962
$472$	20.3918	−	10.9599i	0.938607	−	0.504471i
$473$	0.952716	+	0.952716i	0.0438059	+	0.0438059i
$474$	−0.981630	+	10.0455i	−0.0450878	+	0.461404i
$475$	24.1164	+	14.4949i	1.10653	+	0.665073i
$476$	−0.572552	+	2.90162i	−0.0262429	+	0.132996i
$477$	−4.82837			−0.221076
$478$	1.54174	−	15.7773i	0.0705175	−	0.721639i
$479$	24.0308			1.09800			0.548998	−	0.835824i	$-0.315009\pi$
$479$	24.0308			1.09800			0.548998	+	0.835824i	$0.315009\pi$
$480$	−11.5474	+	5.16310i	−0.527064	+	0.235662i
$481$	2.65790			0.121190
$482$	−0.00713819	+	0.0730484i	−0.000325135	+	0.00332726i
$483$	1.78285			0.0811225
$484$	2.25520	−	11.4291i	0.102509	−	0.519503i
$485$	−3.71340	−	30.2599i	−0.168617	−	1.37403i
$486$	0.137540	−	1.40751i	0.00623894	−	0.0638459i
$487$	24.5449	+	24.5449i	1.11223	+	1.11223i	0.992848	+	0.119387i	$0.0380930\pi$
$487$	24.5449	+	24.5449i	1.11223	+	1.11223i	0.119387	+	0.992848i	$0.461907\pi$
$488$	−3.13345	−	5.83003i	−0.141845	−	0.263913i
$489$	6.57461			0.297314
$490$	−15.9176	−	15.1502i	−0.719086	−	0.684416i
$491$	16.6457	−	16.6457i	0.751211	−	0.751211i	−0.223494	−	0.974705i	$-0.571746\pi$
$491$	16.6457	−	16.6457i	0.751211	−	0.751211i	0.974705	+	0.223494i	$0.0717463\pi$
$492$	−0.208503	+	1.05666i	−0.00940002	+	0.0476381i
$493$			57.9778i			2.61119i
$494$	26.8260	−	22.0499i	1.20696	−	0.992072i
$495$	−5.04901	+	0.619600i	−0.226936	+	0.0278489i
$496$	−2.57926	+	6.28120i	−0.115812	+	0.282034i
$497$	1.09445	+	1.09445i	0.0490928	+	0.0490928i
$498$	−0.946573	+	9.68672i	−0.0424170	+	0.434073i
$499$	−18.8910	+	18.8910i	−0.845677	+	0.845677i	−0.989590	−	0.143914i	$-0.954031\pi$
$499$	−18.8910	+	18.8910i	−0.845677	+	0.845677i	0.143914	+	0.989590i	$0.454031\pi$
$500$	−12.8810	+	18.2778i	−0.576057	+	0.817409i
$501$	18.2166	+	18.2166i	0.813857	+	0.813857i
$502$	−3.11597	−	3.79090i	−0.139073	−	0.169196i
$503$	13.4812	−	13.4812i	0.601095	−	0.601095i	−0.339508	−	0.940603i	$-0.610261\pi$
$503$	13.4812	−	13.4812i	0.601095	−	0.601095i	0.940603	+	0.339508i	$0.110261\pi$
$504$	0.562083	−	0.302101i	0.0250372	−	0.0134567i
$505$	1.54148	+	12.5612i	0.0685949	+	0.558967i
$506$	−25.3031	−	2.47258i	−1.12486	−	0.109920i
$507$	6.03860			0.268183
$508$	−28.2577	+	18.9438i	−1.25373	+	0.840497i
$509$	−24.1930	−	24.1930i	−1.07233	−	1.07233i	−0.997171	−	0.0751624i	$-0.976052\pi$
$509$	−24.1930	−	24.1930i	−1.07233	−	1.07233i	−0.0751624	−	0.997171i	$-0.523948\pi$
$510$	20.7211	−	0.511859i	0.917545	−	0.0226655i
$511$		−	0.0513661i		−	0.00227230i
$512$	−17.3919	+	14.4748i	−0.768622	+	0.639703i
$513$	−3.97920	+	3.97920i	−0.175686	+	0.175686i
$514$	6.98475	−	5.74119i	0.308084	−	0.253233i
$515$	25.3183	−	3.10699i	1.11566	−	0.136910i
$516$	−0.229309	+	1.16211i	−0.0100948	+	0.0511590i
$517$		−	15.6218i		−	0.687048i
$518$	−0.123413	−	0.150144i	−0.00542244	−	0.00659695i
$519$			4.84309i			0.212588i
$520$	15.9280	+	22.5353i	0.698490	+	0.988240i
$521$			0.863518i			0.0378314i	0.999821	+	0.0189157i	$0.00602142\pi$
$521$			0.863518i			0.0378314i	−0.999821	+	0.0189157i	$0.993979\pi$
$522$	9.66371	−	7.94319i	0.422969	−	0.347664i
$523$			23.9267i			1.04624i	0.852259	+	0.523121i	$0.175232\pi$
$523$			23.9267i			1.04624i	−0.852259	+	0.523121i	$0.824768\pi$
$524$	−20.8268	−	31.0665i	−0.909823	−	1.35714i
$525$	0.581119	−	0.966854i	0.0253621	−	0.0421970i
$526$	20.4369	+	24.8636i	0.891093	+	1.08411i
$527$	7.86772	−	7.86772i	0.342723	−	0.342723i
$528$	−8.39632	+	3.50803i	−0.365403	+	0.152667i
$529$		−	39.4468i		−	1.71508i
$530$	−10.5266	+	11.0599i	−0.457248	+	0.480410i
$531$	5.78762	+	5.78762i	0.251161	+	0.251161i
$532$	−2.49119	−	0.491565i	−0.108007	−	0.0213120i
$533$	2.34974			0.101778
$534$	2.34144	−	23.9611i	0.101324	−	1.03690i
$535$	−7.93741	−	6.20223i	−0.343164	−	0.268146i
$536$	−1.31445	−	0.395440i	−0.0567755	−	0.0170804i
$537$	−5.14531	+	5.14531i	−0.222037	+	0.222037i
$538$	−12.8582	+	10.5689i	−0.554355	+	0.455658i
$539$	−11.1784	−	11.1784i	−0.481489	−	0.481489i
$540$	−2.92419	−	3.38365i	−0.125837	−	0.145609i
$541$	−3.73413	+	3.73413i	−0.160543	+	0.160543i	−0.782807	−	0.622264i	$-0.786213\pi$
$541$	−3.73413	+	3.73413i	−0.160543	+	0.160543i	0.622264	+	0.782807i	$0.286213\pi$
$542$	4.09960	+	0.400607i	0.176093	+	0.0172076i
$543$	11.6902	+	11.6902i	0.501674	+	0.501674i
$544$	35.4403	−	10.8990i	1.51949	−	0.467290i
$545$	−0.313530	−	2.55490i	−0.0134302	−	0.109440i
$546$	−0.884007	−	1.07549i	−0.0378320	−	0.0460266i
$547$			33.9579i			1.45193i	0.687730	+	0.725967i	$0.258607\pi$
$547$			33.9579i			1.45193i	−0.687730	+	0.725967i	$0.741393\pi$
$548$	−11.4691	+	7.68881i	−0.489935	+	0.328450i
$549$	1.65469	−	1.65469i	0.0706203	−	0.0706203i
$550$	−9.58842	+	12.9161i	−0.408852	+	0.550745i
$551$	−49.7769			−2.12057
$552$	−10.5815	−	19.6877i	−0.450378	−	0.837965i
$553$	−1.13858	−	1.13858i	−0.0484174	−	0.0484174i
$554$	0.478082	+	0.0467175i	0.0203118	+	0.00198484i
$555$	−0.838658	+	1.07329i	−0.0355990	+	0.0455585i
$556$	15.5395	+	23.1796i	0.659022	+	0.983035i
$557$	17.7955			0.754018			0.377009	−	0.926210i	$-0.376953\pi$
$557$	17.7955			0.754018			0.377009	+	0.926210i	$0.376953\pi$
$558$	−2.38930	−	0.233479i	−0.101147	−	0.00988395i
$559$	2.58422			0.109301
$560$	0.533440	−	1.94614i	0.0225420	−	0.0822395i
$561$	14.9112			0.629550
$562$	29.5366	+	2.88628i	1.24593	+	0.121750i
$563$	−27.7570			−1.16982			−0.584909	−	0.811099i	$-0.698870\pi$
$563$	−27.7570			−1.16982			−0.584909	+	0.811099i	$0.698870\pi$
$564$	11.4077	−	7.64764i	0.480349	−	0.322024i
$565$	−24.1501	+	2.96364i	−1.01600	+	0.124681i
$566$	21.9979	+	2.14961i	0.924643	+	0.0903548i
$567$	0.159531	+	0.159531i	0.00669967	+	0.00669967i
$568$	5.59009	−	18.5815i	0.234555	−	0.779664i
$569$	−31.4665			−1.31915			−0.659573	−	0.751641i	$-0.729263\pi$
$569$	−31.4665			−1.31915			−0.659573	+	0.751641i	$0.729263\pi$
$570$	0.439457	+	17.7901i	0.0184068	+	0.745145i
$571$	−1.60655	+	1.60655i	−0.0672319	+	0.0672319i	−0.739923	−	0.672691i	$-0.765138\pi$
$571$	−1.60655	+	1.60655i	−0.0672319	+	0.0672319i	0.672691	+	0.739923i	$0.265138\pi$
$572$	11.0547	+	16.4898i	0.462220	+	0.689474i
$573$		−	15.8153i		−	0.660696i
$574$	−0.109104	−	0.132736i	−0.00455391	−	0.00554030i
$575$	−33.8654	−	20.3545i	−1.41228	−	0.848841i
$576$	−6.67210	−	4.41397i	−0.278004	−	0.183915i
$577$	−21.8169	−	21.8169i	−0.908250	−	0.908250i	0.0878809	−	0.996131i	$-0.471990\pi$
$577$	−21.8169	−	21.8169i	−0.908250	−	0.908250i	−0.996131	+	0.0878809i	$0.971990\pi$
$578$	−36.5425	−	3.57088i	−1.51997	−	0.148529i
$579$	1.54170	−	1.54170i	0.0640710	−	0.0640710i
$580$	2.87379	−	39.4532i	0.119328	−	1.63821i
$581$	−1.09792	−	1.09792i	−0.0455494	−	0.0455494i
$582$	14.8955	−	12.2435i	0.617438	−	0.507510i
$583$	−7.76697	+	7.76697i	−0.321675	+	0.321675i
$584$	−0.567227	+	0.304866i	−0.0234720	+	0.0126154i
$585$	−6.00733	+	7.68798i	−0.248372	+	0.317859i
$586$	−2.73455	+	27.9839i	−0.112963	+	1.15600i
$587$	−9.52161			−0.392999			−0.196499	−	0.980504i	$-0.562957\pi$
$587$	−9.52161			−0.392999			−0.196499	+	0.980504i	$0.562957\pi$
$588$	2.69053	−	13.6353i	0.110956	−	0.562310i
$589$	6.75484	+	6.75484i	0.278328	+	0.278328i
$590$	25.8751	−	0.639176i	1.06526	−	0.0263145i
$591$		−	5.98026i		−	0.245995i
$592$	−0.925543	+	2.25395i	−0.0380396	+	0.0926368i
$593$	14.3970	−	14.3970i	0.591215	−	0.591215i	−0.346745	−	0.937959i	$-0.612713\pi$
$593$	14.3970	−	14.3970i	0.591215	−	0.591215i	0.937959	+	0.346745i	$0.112713\pi$
$594$	−2.04289	−	2.48539i	−0.0838208	−	0.101977i
$595$	−2.03596	+	2.60555i	−0.0834661	+	0.106817i
$596$	26.5127	−	17.7740i	1.08600	−	0.728050i
$597$		−	12.5564i		−	0.513901i
$598$	−37.6704	+	30.9635i	−1.54046	+	1.26619i
$599$		−	12.1649i		−	0.497045i	−0.968626	−	0.248523i	$-0.920055\pi$
$599$		−	12.1649i		−	0.497045i	0.968626	−	0.248523i	$-0.0799451\pi$
$600$	−14.1258	−	0.678770i	−0.576685	−	0.0277107i
$601$			0.836112i			0.0341057i	0.999855	+	0.0170528i	$0.00542835\pi$
$601$			0.836112i			0.0341057i	−0.999855	+	0.0170528i	$0.994572\pi$
$602$	−0.119991	−	0.145982i	−0.00489048	−	0.00594978i
$603$		−	0.485302i		−	0.0197630i
$604$	−2.99320	−	0.590623i	−0.121792	−	0.0240321i
$605$	8.01935	−	10.2629i	0.326033	−	0.417246i
$606$	−6.18330	+	5.08243i	−0.251179	+	0.206459i
$607$	−20.7652	+	20.7652i	−0.842835	+	0.842835i	−0.989227	−	0.146392i	$-0.953234\pi$
$607$	−20.7652	+	20.7652i	−0.842835	+	0.842835i	0.146392	+	0.989227i	$0.453234\pi$
$608$	9.35733	+	30.4273i	0.379490	+	1.23399i
$609$			1.99561i			0.0808664i
$610$	−0.182741	−	7.39773i	−0.00739898	−	0.299525i
$611$	−21.1869	−	21.1869i	−0.857131	−	0.857131i
$612$	7.29974	+	10.8887i	0.295074	+	0.440150i
$613$	−16.8630			−0.681089			−0.340545	−	0.940228i	$-0.610611\pi$
$613$	−16.8630			−0.681089			−0.340545	+	0.940228i	$0.610611\pi$
$614$	−18.3541	−	1.79354i	−0.740711	−	0.0723812i
$615$	−0.741422	+	0.948847i	−0.0298970	+	0.0382612i
$616$	0.418210	−	1.39014i	0.0168502	−	0.0560103i
$617$	8.57198	−	8.57198i	0.345095	−	0.345095i	−0.513184	−	0.858279i	$-0.671534\pi$
$617$	8.57198	−	8.57198i	0.345095	−	0.345095i	0.858279	+	0.513184i	$0.171534\pi$
$618$	10.2441	+	12.4630i	0.412078	+	0.501335i
$619$	−22.4414	−	22.4414i	−0.901996	−	0.901996i	0.0936130	−	0.995609i	$-0.470158\pi$
$619$	−22.4414	−	22.4414i	−0.901996	−	0.901996i	−0.995609	+	0.0936130i	$0.970158\pi$
$620$	−5.74387	+	4.96391i	−0.230680	+	0.199356i
$621$	5.58779	−	5.58779i	0.224230	−	0.224230i
$622$	−3.24643	+	33.2222i	−0.130170	+	1.33209i
$623$	2.71582	+	2.71582i	0.108807	+	0.108807i
$624$	−6.62969	+	16.1451i	−0.265400	+	0.646322i
$625$	−22.0768	+	11.7309i	−0.883072	+	0.469237i
$626$	35.6294	−	29.2860i	1.42404	−	1.17050i
$627$			12.8020i			0.511262i
$628$	−23.2918	−	4.59598i	−0.929445	−	0.183399i
$629$	2.82326	−	2.82326i	0.112571	−	0.112571i
$630$	0.713227	−	0.0176184i	0.0284156	−	0.000701933i
$631$	0.149433			0.00594882			0.00297441	−	0.999996i	$-0.499053\pi$
$631$	0.149433			0.00594882			0.00297441	+	0.999996i	$0.499053\pi$
$632$	−5.81550	+	19.3308i	−0.231328	+	0.768939i
$633$	18.4049	+	18.4049i	0.731531	+	0.731531i
$634$	−1.38601	+	14.1837i	−0.0550457	+	0.563308i
$635$	−37.7524	+	4.63287i	−1.49816	+	0.183850i
$636$	−9.47405	−	1.86943i	−0.375671	−	0.0741279i
$637$	−30.3212			−1.20137
$638$	2.76766	−	28.3227i	0.109573	−	1.12131i
$639$	6.86042			0.271394
$640$	−24.6569	+	5.65996i	−0.974651	+	0.223730i
$641$	20.6789			0.816766			0.408383	−	0.912811i	$-0.366093\pi$
$641$	20.6789			0.816766			0.408383	+	0.912811i	$0.366093\pi$
$642$	0.619602	−	6.34067i	0.0244537	−	0.250246i
$643$	42.0475			1.65819			0.829097	−	0.559105i	$-0.188855\pi$
$643$	42.0475			1.65819			0.829097	+	0.559105i	$0.188855\pi$
$644$	3.49825	+	0.690279i	0.137850	+	0.0272008i
$645$	−0.815409	+	1.04353i	−0.0321067	+	0.0410891i
$646$	5.07323	−	51.9167i	0.199603	−	2.04263i
$647$	2.09704	+	2.09704i	0.0824431	+	0.0824431i	0.747126	−	0.664683i	$-0.231433\pi$
$647$	2.09704	+	2.09704i	0.0824431	+	0.0824431i	−0.664683	+	0.747126i	$0.731433\pi$
$648$	0.814832	−	2.70851i	0.0320096	−	0.106400i
$649$	18.6201			0.730902
$650$	4.51314	+	30.5215i	0.177020	+	1.19715i
$651$	0.270810	−	0.270810i	0.0106139	−	0.0106139i
$652$	12.9005	+	2.54554i	0.505221	+	0.0996910i
$653$			33.4870i			1.31045i	0.755435	+	0.655223i	$0.227425\pi$
$653$			33.4870i			1.31045i	−0.755435	+	0.655223i	$0.772575\pi$
$654$	1.25766	−	1.03374i	0.0491783	−	0.0404226i
$655$	−5.09337	−	41.5049i	−0.199014	−	1.62173i
$656$	−0.818233	+	1.99262i	−0.0319466	+	0.0777989i
$657$	−0.160991	−	0.160991i	−0.00628086	−	0.00628086i
$658$	−0.213086	+	2.18060i	−0.00830694	+	0.0850088i
$659$	32.5431	−	32.5431i	1.26770	−	1.26770i	0.320427	−	0.947273i	$-0.396174\pi$
$659$	32.5431	−	32.5431i	1.26770	−	1.26770i	0.947273	−	0.320427i	$-0.103826\pi$
$660$	−10.1469	−	0.739104i	−0.394967	−	0.0287696i
$661$	−8.31994	−	8.31994i	−0.323608	−	0.323608i	0.526541	−	0.850149i	$-0.323488\pi$
$661$	−8.31994	−	8.31994i	−0.323608	−	0.323608i	−0.850149	+	0.526541i	$0.823488\pi$
$662$	7.82338	+	9.51795i	0.304064	+	0.369925i
$663$	20.2231	−	20.2231i	0.785399	−	0.785399i
$664$	−5.60781	+	18.6405i	−0.217625	+	0.723390i
$665$	−2.23700	−	1.74797i	−0.0867471	−	0.0677835i
$666$	−0.857378	−	0.0837818i	−0.0332227	−	0.00324648i
$667$	69.8991			2.70650
$668$	28.6909	+	42.7970i	1.11008	+	1.65587i
$669$	−11.6149	−	11.6149i	−0.449059	−	0.449059i
$670$	−1.11164	−	1.05804i	−0.0429462	−	0.0408756i
$671$		−	5.32350i		−	0.205512i
$672$	1.21987	−	0.375147i	0.0470574	−	0.0144716i
$673$	−9.07931	+	9.07931i	−0.349982	+	0.349982i	−0.860103	−	0.510121i	$-0.829601\pi$
$673$	−9.07931	+	9.07931i	−0.349982	+	0.349982i	0.510121	+	0.860103i	$0.329601\pi$
$674$	28.0646	−	23.0680i	1.08101	−	0.888546i
$675$	−1.20897	−	4.85164i	−0.0465331	−	0.186740i
$676$	11.8487	+	2.33801i	0.455720	+	0.0899234i
$677$			10.6497i			0.409301i	0.978835	+	0.204650i	$0.0656058\pi$
$677$			10.6497i			0.409301i	−0.978835	+	0.204650i	$0.934394\pi$
$678$	−9.77144	−	11.8880i	−0.375270	−	0.456555i
$679$			3.07601i			0.118046i
$680$	40.8564	+	7.01838i	1.56677	+	0.269143i
$681$			0.411442i			0.0157665i
$682$	−4.21903	+	3.46788i	−0.161555	+	0.132792i
$683$		−	40.7197i		−	1.55809i	−0.626965	−	0.779047i	$-0.715703\pi$
$683$		−	40.7197i		−	1.55809i	0.626965	−	0.779047i	$-0.284297\pi$
$684$	−9.34851	+	6.26719i	−0.357449	+	0.239632i
$685$	−15.3227	+	1.88036i	−0.585452	+	0.0718450i
$686$	2.82608	+	3.43822i	0.107900	+	0.131272i
$687$	−11.2286	+	11.2286i	−0.428399	+	0.428399i
$688$	−0.899885	+	2.19147i	−0.0343078	+	0.0835490i
$689$			21.0677i			0.802616i
$690$	−0.617107	−	24.9817i	−0.0234929	−	0.951038i
$691$	−23.4396	−	23.4396i	−0.891684	−	0.891684i	0.102997	−	0.994682i	$-0.467157\pi$
$691$	−23.4396	−	23.4396i	−0.891684	−	0.891684i	−0.994682	+	0.102997i	$0.967157\pi$
$692$	−1.87513	+	9.50293i	−0.0712819	+	0.361247i
$693$	0.513248			0.0194967
$694$	0.386279	−	3.95297i	0.0146629	−	0.150053i
$695$	3.80032	+	30.9681i	0.144154	+	1.17469i
$696$	22.0372	−	11.8443i	0.835319	−	0.448956i
$697$	2.49592	−	2.49592i	0.0945399	−	0.0945399i
$698$	21.4014	−	17.5911i	0.810053	−	0.665832i
$699$	−18.9687	−	18.9687i	−0.717463	−	0.717463i
$700$	1.51460	−	1.67213i	0.0572464	−	0.0632007i
$701$	−8.98392	+	8.98392i	−0.339318	+	0.339318i	−0.856111	−	0.516793i	$-0.827126\pi$
$701$	−8.98392	+	8.98392i	−0.339318	+	0.339318i	0.516793	+	0.856111i	$0.327126\pi$
$702$	−6.14142	−	0.600131i	−0.231793	−	0.0226505i
$703$	2.42391	+	2.42391i	0.0914195	+	0.0914195i
$704$	−17.8332	+	3.63246i	−0.672114	+	0.136904i
$705$	15.2407	−	1.87029i	0.573998	−	0.0704394i
$706$	20.7968	+	25.3014i	0.782696	+	0.952231i
$707$		−	1.27689i		−	0.0480223i
$708$	9.11543	+	13.5971i	0.342579	+	0.511010i
$709$	10.0094	−	10.0094i	0.375912	−	0.375912i	−0.493713	−	0.869625i	$-0.664361\pi$
$709$	10.0094	−	10.0094i	0.375912	−	0.375912i	0.869625	+	0.493713i	$0.164361\pi$
$710$	14.9569	−	15.7145i	0.561321	−	0.589755i
$711$	−7.13706			−0.267661
$712$	13.8715	−	46.1091i	0.519856	−	1.72801i
$713$	−9.48547	−	9.48547i	−0.355234	−	0.355234i
$714$	−2.08140	−	0.203392i	−0.0778946	−	0.00761175i
$715$	2.70352	+	22.0305i	0.101106	+	0.823892i
$716$	−12.0881	+	8.10380i	−0.451753	+	0.302853i
$717$	11.2094			0.418623
$718$	24.0103	+	2.34625i	0.896057	+	0.0875614i
$719$	11.6941			0.436118			0.218059	−	0.975936i	$-0.430027\pi$
$719$	11.6941			0.436118			0.218059	+	0.975936i	$0.430027\pi$
$720$	−4.42767	−	7.77147i	−0.165009	−	0.289626i
$721$	−2.57368			−0.0958490
$722$	17.8304	+	1.74237i	0.663580	+	0.0648442i
$723$	−0.0518990			−0.00193015
$724$	18.4119	+	27.4643i	0.684273	+	1.02070i
$725$	22.7836	−	37.9068i	0.846161	−	1.40782i
$726$	8.19835	+	0.801132i	0.304269	+	0.0297328i
$727$	−15.5108	−	15.5108i	−0.575263	−	0.575263i	0.358331	−	0.933594i	$-0.383346\pi$
$727$	−15.5108	−	15.5108i	−0.575263	−	0.575263i	−0.933594	+	0.358331i	$0.883346\pi$
$728$	−1.31816	−	2.45255i	−0.0488544	−	0.0908975i
$729$	1.00000			0.0370370
$730$	−0.719754	+	0.0177796i	−0.0266393	+	0.000658053i
$731$	2.74499	−	2.74499i	0.101527	−	0.101527i
$732$	3.88743	−	2.60611i	0.143683	−	0.0963247i
$733$		−	39.4855i		−	1.45843i	−0.684285	−	0.729214i	$-0.739886\pi$
$733$		−	39.4855i		−	1.45843i	0.684285	−	0.729214i	$-0.260114\pi$
$734$	17.7759	+	21.6262i	0.656120	+	0.798238i
$735$	9.56737	−	12.2440i	0.352898	−	0.451627i
$736$	−13.1400	−	42.7275i	−0.484347	−	1.57496i
$737$	−0.780664	−	0.780664i	−0.0287561	−	0.0287561i
$738$	−0.757972	−	0.0740679i	−0.0279013	−	0.00272648i
$739$	8.55700	−	8.55700i	0.314774	−	0.314774i	−0.531982	−	0.846756i	$-0.678552\pi$
$739$	8.55700	−	8.55700i	0.314774	−	0.314774i	0.846756	+	0.531982i	$0.178552\pi$
$740$	−2.06114	+	1.78126i	−0.0757689	+	0.0654803i
$741$	17.3625	+	17.3625i	0.637829	+	0.637829i
$742$	1.19011	−	0.978224i	0.0436904	−	0.0359117i
$743$	−20.9783	+	20.9783i	−0.769621	+	0.769621i	−0.978040	−	0.208419i	$-0.933168\pi$
$743$	−20.9783	+	20.9783i	−0.769621	+	0.769621i	0.208419	+	0.978040i	$0.433168\pi$
$744$	−4.59780	−	1.38321i	−0.168564	−	0.0507108i
$745$	35.4211	−	4.34677i	1.29773	−	0.159253i
$746$	−2.26705	+	23.1998i	−0.0830026	+	0.849404i
$747$	−6.88217			−0.251806
$748$	29.2582	+	5.77327i	1.06978	+	0.211091i
$749$	0.718670	+	0.718670i	0.0262596	+	0.0262596i
$750$	−13.7489	−	7.80812i	−0.502040	−	0.285112i
$751$			28.3484i			1.03445i	0.855850	+	0.517224i	$0.173034\pi$
$751$			28.3484i			1.03445i	−0.855850	+	0.517224i	$0.826966\pi$
$752$	25.3447	−	10.5892i	0.924227	−	0.386147i
$753$	2.45358	−	2.45358i	0.0894134	−	0.0894134i
$754$	−34.6587	−	42.1659i	−1.26220	−	1.53559i
$755$	−2.68779	−	2.10022i	−0.0978187	−	0.0764348i
$756$	0.251259	+	0.374793i	0.00913822	+	0.0136311i
$757$			18.6273i			0.677022i	0.940962	+	0.338511i	$0.109923\pi$
$757$			18.6273i			0.677022i	−0.940962	+	0.338511i	$0.890077\pi$
$758$	−15.0377	+	12.3604i	−0.546194	+	0.448950i
$759$		−	17.9772i		−	0.652531i
$760$	−6.02564	+	35.0773i	−0.218573	+	1.27239i
$761$		−	33.8880i		−	1.22844i	−0.789135	−	0.614220i	$-0.789471\pi$
$761$		−	33.8880i		−	1.22844i	0.789135	−	0.614220i	$-0.210529\pi$
$762$	−15.2751	−	18.5837i	−0.553358	−	0.673218i
$763$			0.259714i			0.00940227i
$764$	6.12334	−	31.0323i	0.221535	−	1.12271i
$765$	1.78521	+	14.5474i	0.0645444	+	0.525961i
$766$	−8.52027	+	7.00333i	−0.307850	+	0.253041i
$767$	25.2532	−	25.2532i	0.911842	−	0.911842i
$768$	−11.3828	−	11.2442i	−0.410740	−	0.405741i
$769$			4.73758i			0.170841i	0.996345	+	0.0854207i	$0.0272234\pi$
$769$			4.73758i			0.170841i	−0.996345	+	0.0854207i	$0.972777\pi$
$770$	1.11897	−	1.17565i	0.0403247	−	0.0423674i
$771$	4.52073	+	4.52073i	0.162810	+	0.162810i
$772$	3.62199	−	2.42817i	0.130358	−	0.0873916i
$773$	−1.05525			−0.0379546			−0.0189773	−	0.999820i	$-0.506041\pi$
$773$	−1.05525			−0.0379546			−0.0189773	+	0.999820i	$0.506041\pi$
$774$	−0.833610	−	0.0814592i	−0.0299635	−	0.00292799i
$775$	−8.23583	+	2.05226i	−0.295840	+	0.0737194i
$776$	33.9678	−	18.2566i	1.21937	−	0.655373i
$777$	0.0971776	−	0.0971776i	0.00348623	−	0.00348623i
$778$	−4.72813	−	5.75226i	−0.169512	−	0.206228i
$779$	2.14288	+	2.14288i	0.0767766	+	0.0767766i
$780$	−14.7640	+	12.7592i	−0.528635	+	0.456852i
$781$	11.0358	−	11.0358i	0.394891	−	0.394891i
$782$	−7.12407	+	72.9040i	−0.254756	+	2.60704i
$783$	6.25463	+	6.25463i	0.223522	+	0.223522i
$784$	10.5585	−	25.7130i	0.377091	−	0.918320i
$785$	−20.9152	−	16.3430i	−0.746496	−	0.583307i
$786$	20.4309	−	16.7934i	0.728746	−	0.599001i
$787$			0.792266i			0.0282412i	0.999900	+	0.0141206i	$0.00449488\pi$
$787$			0.792266i			0.0282412i	−0.999900	+	0.0141206i	$0.995505\pi$
$788$	2.31542	−	11.7343i	0.0824835	−	0.418016i
$789$	−16.0925	+	16.0925i	−0.572907	+	0.572907i
$790$	−15.5600	+	16.3482i	−0.553599	+	0.581642i
$791$	2.45494			0.0872875
$792$	−3.04620	−	5.66770i	−0.108242	−	0.201393i
$793$	−7.21994	−	7.21994i	−0.256387	−	0.256387i
$794$	−4.26094	+	43.6042i	−0.151215	+	1.54745i
$795$	−8.50736	−	6.64759i	−0.301725	−	0.235766i
$796$	4.86157	−	24.6378i	0.172314	−	0.873264i
$797$	5.92235			0.209780			0.104890	−	0.994484i	$-0.466551\pi$
$797$	5.92235			0.209780			0.104890	+	0.994484i	$0.466551\pi$
$798$	0.174622	−	1.78699i	0.00618156	−	0.0632588i
$799$	−45.0101			−1.59234
$800$	−27.4544	−	6.80106i	−0.970661	−	0.240454i
$801$	17.0238			0.601505
$802$	−0.0774458	+	0.792539i	−0.00273471	+	0.0279855i
$803$	−0.517945			−0.0182779
$804$	0.187898	−	0.952243i	0.00662665	−	0.0335830i
$805$	3.14130	+	2.45459i	0.110716	+	0.0865129i
$806$	−1.01874	+	10.4253i	−0.0358837	+	0.367215i
$807$	−8.32218	−	8.32218i	−0.292955	−	0.292955i
$808$	−14.1005	+	7.57853i	−0.496052	+	0.266612i
$809$	28.0382			0.985772			0.492886	−	0.870094i	$-0.335942\pi$
$809$	28.0382			0.985772			0.492886	+	0.870094i	$0.335942\pi$
$810$	2.18017	−	2.29061i	0.0766033	−	0.0804837i
$811$	−14.8696	+	14.8696i	−0.522141	+	0.522141i	−0.918217	−	0.396077i	$-0.870371\pi$
$811$	−14.8696	+	14.8696i	−0.522141	+	0.522141i	0.396077	+	0.918217i	$0.370371\pi$
$812$	−0.772657	+	3.91573i	−0.0271149	+	0.137415i
$813$			2.91266i			0.102152i
$814$	−1.51396	+	1.24442i	−0.0530643	+	0.0436168i
$815$	11.5842	+	9.05177i	0.405775	+	0.317070i
$816$	10.1074	+	24.1917i	0.353831	+	0.846880i
$817$	2.35672	+	2.35672i	0.0824511	+	0.0824511i
$818$	4.66953	−	47.7854i	0.163266	−	1.67078i
$819$	0.696085	−	0.696085i	0.0243232	−	0.0243232i
$820$	−1.82216	+	1.57473i	−0.0636328	+	0.0549921i
$821$	−33.9440	−	33.9440i	−1.18466	−	1.18466i	−0.978524	−	0.206131i	$-0.933913\pi$
$821$	−33.9440	−	33.9440i	−1.18466	−	1.18466i	−0.206131	−	0.978524i	$-0.566087\pi$
$822$	−6.19977	−	7.54266i	−0.216242	−	0.263080i
$823$	26.0121	−	26.0121i	0.906724	−	0.906724i	−0.0892823	−	0.996006i	$-0.528457\pi$
$823$	26.0121	−	26.0121i	0.906724	−	0.906724i	0.996006	+	0.0892823i	$0.0284573\pi$
$824$	15.2752	+	28.4207i	0.532137	+	0.990083i
$825$	−9.74917	−	5.85966i	−0.339423	−	0.204007i
$826$	−2.59912	−	0.253982i	−0.0904349	−	0.00883717i
$827$	−14.1684			−0.492682			−0.246341	−	0.969183i	$-0.579228\pi$
$827$	−14.1684			−0.492682			−0.246341	+	0.969183i	$0.579228\pi$
$828$	13.1276	−	8.80070i	0.456217	−	0.305845i
$829$	19.7985	+	19.7985i	0.687630	+	0.687630i	0.961708	−	0.274077i	$-0.0883724\pi$
$829$	19.7985	+	19.7985i	0.687630	+	0.687630i	−0.274077	+	0.961708i	$0.588372\pi$
$830$	−15.0043	+	15.7643i	−0.520806	+	0.547188i
$831$			0.339665i			0.0117829i
$832$	−19.2596	+	29.1125i	−0.667705	+	1.00930i
$833$	−32.2076	+	32.2076i	−1.11593	+	1.11593i
$834$	−15.2441	+	12.5301i	−0.527861	+	0.433881i
$835$	7.01659	+	57.1770i	0.242819	+	1.97869i
$836$	−4.95664	+	25.1196i	−0.171429	+	0.868781i
$837$		−	1.69754i		−	0.0586754i
$838$	−15.2546	−	18.5588i	−0.526961	−	0.641103i
$839$		−	21.1013i		−	0.728499i	−0.931301	−	0.364250i	$-0.881326\pi$
$839$		−	21.1013i		−	0.728499i	0.931301	−	0.364250i	$-0.118674\pi$
$840$	1.40629	+	0.241575i	0.0485216	+	0.00833513i
$841$			49.2408i			1.69796i
$842$	7.82850	−	6.43472i	0.269788	−	0.221755i
$843$			20.9850i			0.722763i
$844$	28.9876	+	43.2395i	0.997793	+	1.48837i
$845$	10.6397	+	8.31380i	0.366018	+	0.286004i
$846$	6.16657	+	7.50227i	0.212011	+	0.257933i
$847$	−0.929224	+	0.929224i	−0.0319285	+	0.0319285i
$848$	−17.8659	−	7.33628i	−0.613516	−	0.251929i
$849$			15.6290i			0.536385i
$850$	37.2143	+	27.6264i	1.27644	+	0.947579i
$851$	−3.40377	−	3.40377i	−0.116680	−	0.116680i
$852$	13.4613	+	2.65620i	0.461176	+	0.0909999i
$853$	−0.282088			−0.00965852			−0.00482926	−	0.999988i	$-0.501537\pi$
$853$	−0.282088			−0.00965852			−0.00482926	+	0.999988i	$0.501537\pi$
$854$	−0.0726139	+	0.743091i	−0.00248480	+	0.0254281i
$855$	−12.4896	+	1.53269i	−0.427137	+	0.0524170i
$856$	3.67073	−	12.2016i	0.125463	−	0.417041i
$857$	−31.6316	+	31.6316i	−1.08051	+	1.08051i	−0.0840520	+	0.996461i	$0.526786\pi$
$857$	−31.6316	+	31.6316i	−1.08051	+	1.08051i	−0.996461	+	0.0840520i	$0.973214\pi$
$858$	−10.8446	+	8.91379i	−0.370227	+	0.304312i
$859$	−12.4550	−	12.4550i	−0.424958	−	0.424958i	0.461949	−	0.886907i	$-0.347150\pi$
$859$	−12.4550	−	12.4550i	−0.424958	−	0.424958i	−0.886907	+	0.461949i	$0.847150\pi$
$860$	−2.00400	+	1.73188i	−0.0683358	+	0.0590565i
$861$	0.0859106	−	0.0859106i	0.00292783	−	0.00292783i
$862$	−23.9550	−	2.34085i	−0.815912	−	0.0797298i
$863$	−28.8568	−	28.8568i	−0.982298	−	0.982298i	0.0175484	−	0.999846i	$-0.494414\pi$
$863$	−28.8568	−	28.8568i	−0.982298	−	0.982298i	−0.999846	+	0.0175484i	$0.994414\pi$
$864$	2.64751	−	4.99907i	0.0900701	−	0.170072i
$865$	−6.66785	+	8.53329i	−0.226714	+	0.290141i
$866$	31.2863	+	38.0630i	1.06315	+	1.29343i
$867$		−	25.9625i		−	0.881733i
$868$	0.636225	−	0.426522i	0.0215949	−	0.0144771i
$869$	−11.4808	+	11.4808i	−0.389459	+	0.389459i
$870$	27.9630	−	0.690752i	0.948035	−	0.0234187i
$871$	−2.11753			−0.0717498
$872$	2.86797	−	1.54144i	0.0971219	−	0.0521998i
$873$	9.64079	+	9.64079i	0.326291	+	0.326291i
$874$	−62.5918	−	6.11638i	−2.11720	−	0.206890i
$875$	2.35505	−	0.903481i	0.0796152	−	0.0305432i
$876$	−0.253559	−	0.378223i	−0.00856697	−	0.0127790i
$877$	2.39445			0.0808547			0.0404273	−	0.999182i	$-0.487128\pi$
$877$	2.39445			0.0808547			0.0404273	+	0.999182i	$0.487128\pi$
$878$	−38.7082	−	3.78252i	−1.30634	−	0.127654i
$879$	−19.8819			−0.670599
$880$	−19.6237	−	5.37889i	−0.661515	−	0.181322i
$881$	−16.8589			−0.567991			−0.283996	−	0.958826i	$-0.591660\pi$
$881$	−16.8589			−0.567991			−0.283996	+	0.958826i	$0.591660\pi$
$882$	9.78092	+	0.955778i	0.329341	+	0.0321827i
$883$	32.1936			1.08340			0.541700	−	0.840572i	$-0.317781\pi$
$883$	32.1936			1.08340			0.541700	+	0.840572i	$0.317781\pi$
$884$	47.5109	−	31.8511i	1.59797	−	1.07127i
$885$	2.22925	+	18.1658i	0.0749355	+	0.610636i
$886$	−53.8602	−	5.26314i	−1.80947	−	0.176819i
$887$	−7.86611	−	7.86611i	−0.264118	−	0.264118i	0.562607	−	0.826725i	$-0.309799\pi$
$887$	−7.86611	−	7.86611i	−0.264118	−	0.264118i	−0.826725	+	0.562607i	$0.809799\pi$
$888$	−1.64988	−	0.496351i	−0.0553663	−	0.0166564i
$889$	3.83765			0.128711
$890$	37.1146	−	38.9947i	1.24408	−	1.30711i
$891$	1.60861	−	1.60861i	0.0538906	−	0.0538906i
$892$	−18.2934	−	27.2874i	−0.612507	−	0.913651i
$893$		−	38.6435i		−	1.29315i
$894$	14.3318	+	17.4361i	0.479327	+	0.583151i
$895$	−16.1497	+	1.98185i	−0.539827	+	0.0662460i
$896$	2.53883	−	0.263795i	0.0848163	−	0.00881277i
$897$	−24.3813	−	24.3813i	−0.814069	−	0.814069i
$898$	−27.8318	−	2.71969i	−0.928761	−	0.0907572i
$899$	10.6175	−	10.6175i	0.354112	−	0.354112i
$900$	−0.493746	−	9.98780i	−0.0164582	−	0.332927i
$901$	22.3784	+	22.3784i	0.745534	+	0.745534i
$902$	−1.33843	+	1.10014i	−0.0445649	+	0.0366305i
$903$	0.0944836	−	0.0944836i	0.00314422	−	0.00314422i
$904$	−14.5704	−	27.1094i	−0.484605	−	0.901647i
$905$	4.50278	+	36.6924i	0.149678	+	1.21970i
$906$	0.209811	−	2.14710i	0.00697052	−	0.0713326i
$907$	−50.7262			−1.68433			−0.842167	−	0.539217i	$-0.818720\pi$
$907$	−50.7262			−1.68433			−0.842167	+	0.539217i	$0.818720\pi$
$908$	−0.159301	+	0.807318i	−0.00528659	+	0.0267918i
$909$	−4.00201	−	4.00201i	−0.132738	−	0.132738i
$910$	−0.0768747	−	3.11204i	−0.00254837	−	0.103163i
$911$			1.86790i			0.0618862i	0.999521	+	0.0309431i	$0.00985106\pi$
$911$			1.86790i			0.0618862i	−0.999521	+	0.0309431i	$0.990149\pi$
$912$	−20.7698	+	8.67774i	−0.687758	+	0.287349i
$913$	−11.0708	+	11.0708i	−0.366389	+	0.366389i
$914$	4.81192	+	5.85420i	0.159164	+	0.193640i
$915$	5.19362	−	0.637346i	0.171696	−	0.0210700i
$916$	−26.3799	+	17.6850i	−0.871617	+	0.584328i
$917$			4.21911i			0.139327i
$918$	−7.16098	+	5.88604i	−0.236347	+	0.194268i
$919$			14.5671i			0.480525i	0.970708	+	0.240263i	$0.0772336\pi$
$919$			14.5671i			0.480525i	−0.970708	+	0.240263i	$0.922766\pi$
$920$	8.46149	−	49.2572i	0.278967	−	1.62396i
$921$		−	13.0401i		−	0.429686i
$922$	−4.22197	−	5.13647i	−0.139043	−	0.169161i
$923$		−	29.9342i		−	0.985297i
$924$	1.00708	+	0.198718i	0.0331304	+	0.00653734i
$925$	−2.95535	+	0.736436i	−0.0971714	+	0.0242139i
$926$	−13.1835	+	10.8363i	−0.433236	+	0.356103i
$927$	−8.06640	+	8.06640i	−0.264935	+	0.264935i
$928$	47.8265	−	14.7081i	1.56998	−	0.482818i
$929$			53.6486i			1.76015i	0.474831	+	0.880077i	$0.342509\pi$
$929$			53.6486i			1.76015i	−0.474831	+	0.880077i	$0.657491\pi$
$930$	−3.88838	−	3.70091i	−0.127505	−	0.121358i
$931$	−27.6519	−	27.6519i	−0.906253	−	0.906253i
$932$	−29.8755	−	44.5640i	−0.978605	−	1.45974i
$933$	−23.6036			−0.772746
$934$	−17.7705	−	1.73651i	−0.581470	−	0.0568204i
$935$	26.2728	+	20.5294i	0.859212	+	0.671382i
$936$	−11.8181	−	3.55537i	−0.386287	−	0.116211i
$937$	28.3937	−	28.3937i	0.927582	−	0.927582i	−0.0699675	−	0.997549i	$-0.522290\pi$
$937$	28.3937	−	28.3937i	0.927582	−	0.927582i	0.997549	+	0.0699675i	$0.0222896\pi$
$938$	0.0983220	+	0.119619i	0.00321033	+	0.00390570i
$939$	23.0604	+	23.0604i	0.752547	+	0.752547i
$940$	30.6289	+	2.23102i	0.999004	+	0.0727679i
$941$	37.0652	−	37.0652i	1.20829	−	1.20829i	0.236713	−	0.971580i	$-0.423930\pi$
$941$	37.0652	−	37.0652i	1.20829	−	1.20829i	0.971580	−	0.236713i	$-0.0760701\pi$
$942$	1.63266	−	16.7078i	0.0531950	−	0.544369i
$943$	−3.00913	−	3.00913i	−0.0979909	−	0.0979909i
$944$	12.6215	+	30.2090i	0.410795	+	0.983220i
$945$	0.0614476	+	0.500725i	0.00199889	+	0.0162886i
$946$	−1.47199	+	1.20992i	−0.0478586	+	0.0393379i
$947$			9.52796i			0.309617i	0.987944	+	0.154809i	$0.0494761\pi$
$947$			9.52796i			0.309617i	−0.987944	+	0.154809i	$0.950524\pi$
$948$	−14.0041	−	2.76331i	−0.454832	−	0.0897481i
$949$	−0.702456	+	0.702456i	−0.0228027	+	0.0228027i
$950$	−23.7187	+	31.9504i	−0.769537	+	1.03661i
$951$	−10.0772			−0.326775
$952$	−4.00531	−	1.20496i	−0.129813	−	0.0390530i
$953$	26.6687	+	26.6687i	0.863883	+	0.863883i	0.991787	−	0.127903i	$-0.0408248\pi$
$953$	26.6687	+	26.6687i	0.863883	+	0.863883i	−0.127903	+	0.991787i	$0.540825\pi$
$954$	0.664093	−	6.79597i	0.0215008	−	0.220028i
$955$	21.7742	−	27.8659i	0.704597	−	0.901720i
$956$	21.9947	+	4.34003i	0.711360	+	0.140366i
$957$	20.1226			0.650470
$958$	−3.30520	+	33.8236i	−0.106786	+	1.09279i
$959$	1.55760			0.0502977
$960$	−5.67888	−	16.9632i	−0.183285	−	0.547485i
$961$	28.1184			0.907044
$962$	−0.365567	+	3.74102i	−0.0117864	+	0.120615i
$963$	4.50489			0.145168
$964$	−0.101834	−	0.0200941i	−0.00327987	−	0.000647188i
$965$	4.83900	−	0.593828i	0.155773	−	0.0191160i
$966$	−0.245213	+	2.50938i	−0.00788960	+	0.0807380i
$967$	6.91802	+	6.91802i	0.222468	+	0.222468i	0.809537	−	0.587069i	$-0.199718\pi$
$967$	6.91802	+	6.91802i	0.222468	+	0.222468i	−0.587069	+	0.809537i	$0.699718\pi$
$968$	15.7763	+	4.74617i	0.507071	+	0.152548i
$969$	36.8855			1.18493
$970$	43.1018	−	1.06471i	1.38391	−	0.0341859i
$971$	−21.6040	+	21.6040i	−0.693305	+	0.693305i	−0.962958	−	0.269652i	$-0.913091\pi$
$971$	−21.6040	+	21.6040i	−0.693305	+	0.693305i	0.269652	+	0.962958i	$0.413091\pi$
$972$	1.96217	+	0.387177i	0.0629365	+	0.0124187i
$973$		−	3.14800i		−	0.100920i
$974$	−37.9231	+	31.1713i	−1.21513	+	0.998792i
$975$	−21.1693	+	5.27511i	−0.677959	+	0.168939i
$976$	8.63680	−	3.60850i	0.276457	−	0.115505i
$977$	1.13074	+	1.13074i	0.0361757	+	0.0361757i	0.724963	−	0.688788i	$-0.241857\pi$
$977$	1.13074	+	1.13074i	0.0361757	+	0.0361757i	−0.688788	+	0.724963i	$0.741857\pi$
$978$	−0.904271	+	9.25382i	−0.0289154	+	0.295905i
$979$	27.3846	−	27.3846i	0.875217	−	0.875217i
$980$	23.5134	−	20.3205i	0.751107	−	0.649114i
$981$	0.813992	+	0.813992i	0.0259888	+	0.0259888i
$982$	21.1396	+	25.7185i	0.674591	+	0.820709i
$983$	−24.3146	+	24.3146i	−0.775517	+	0.775517i	−0.979065	−	0.203548i	$-0.934753\pi$
$983$	−24.3146	+	24.3146i	−0.775517	+	0.775517i	0.203548	+	0.979065i	$0.434753\pi$
$984$	−1.45859	−	0.438803i	−0.0464981	−	0.0139885i
$985$	8.23349	−	10.5369i	0.262341	−	0.335735i
$986$	−81.6042	−	7.97425i	−2.59881	−	0.253952i
$987$	−1.54926			−0.0493136
$988$	27.3458	+	40.7906i	0.869986	+	1.29772i
$989$	−3.30942	−	3.30942i	−0.105233	−	0.105233i
$990$	−0.177653	−	7.19175i	−0.00564618	−	0.228569i
$991$			21.3602i			0.678529i	0.940691	+	0.339264i	$0.110178\pi$
$991$			21.3602i			0.678529i	−0.940691	+	0.339264i	$0.889822\pi$
$992$	−8.48610	−	4.49424i	−0.269434	−	0.142692i
$993$	−6.16029	+	6.16029i	−0.195491	+	0.195491i
$994$	−1.69098	+	1.38992i	−0.0536346	+	0.0440855i
$995$	17.2874	−	22.1239i	0.548048	−	0.701374i
$996$	−13.5040	−	2.66462i	−0.427889	−	0.0844318i
$997$		−	32.6767i		−	1.03488i	−0.855719	−	0.517442i	$-0.826885\pi$
$997$		−	32.6767i		−	1.03488i	0.855719	−	0.517442i	$-0.173115\pi$
$998$	−23.9910	−	29.1875i	−0.759421	−	0.923914i
$999$		−	0.609145i		−	0.0192725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.f.187.5	yes	20
3.2	odd	2		720.2.z.h.667.6		20
4.3	odd	2		960.2.y.f.847.3		20
5.3	odd	4		240.2.bc.f.43.10	yes	20
8.3	odd	2		1920.2.y.k.1567.8		20
8.5	even	2		1920.2.y.l.1567.8		20
15.8	even	4		720.2.bd.h.523.1		20
16.3	odd	4		240.2.bc.f.67.10	yes	20
16.5	even	4		1920.2.bc.l.607.9		20
16.11	odd	4		1920.2.bc.k.607.9		20
16.13	even	4		960.2.bc.f.367.2		20
20.3	even	4		960.2.bc.f.463.2		20
40.3	even	4		1920.2.bc.l.1183.9		20
40.13	odd	4		1920.2.bc.k.1183.9		20
48.35	even	4		720.2.bd.h.307.1		20
80.3	even	4	inner	240.2.y.f.163.5	✓	20
80.13	odd	4		960.2.y.f.943.3		20
80.43	even	4		1920.2.y.l.223.8		20
80.53	odd	4		1920.2.y.k.223.8		20
240.83	odd	4		720.2.z.h.163.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.5	✓	20	80.3	even	4	inner
240.2.y.f.187.5	yes	20	1.1	even	1	trivial
240.2.bc.f.43.10	yes	20	5.3	odd	4
240.2.bc.f.67.10	yes	20	16.3	odd	4
720.2.z.h.163.6		20	240.83	odd	4
720.2.z.h.667.6		20	3.2	odd	2
720.2.bd.h.307.1		20	48.35	even	4
720.2.bd.h.523.1		20	15.8	even	4
960.2.y.f.847.3		20	4.3	odd	2
960.2.y.f.943.3		20	80.13	odd	4
960.2.bc.f.367.2		20	16.13	even	4
960.2.bc.f.463.2		20	20.3	even	4
1920.2.y.k.223.8		20	80.53	odd	4
1920.2.y.k.1567.8		20	8.3	odd	2
1920.2.y.l.223.8		20	80.43	even	4
1920.2.y.l.1567.8		20	8.5	even	2
1920.2.bc.k.607.9		20	16.11	odd	4
1920.2.bc.k.1183.9		20	40.13	odd	4
1920.2.bc.l.607.9		20	16.5	even	4
1920.2.bc.l.1183.9		20	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.137540 + 1.40751i) q^{2} -1.00000 q^{3} +(-1.96217 - 0.387177i) q^{4} +(-1.76195 - 1.37678i) q^{5} +(0.137540 - 1.40751i) q^{6} +(0.159531 + 0.159531i) q^{7} +(0.814832 - 2.70851i) q^{8} +1.00000 q^{9} +(2.18017 - 2.29061i) q^{10} +(1.60861 - 1.60861i) q^{11} +(1.96217 + 0.387177i) q^{12} -4.36332i q^{13} +(-0.246483 + 0.202600i) q^{14} +(1.76195 + 1.37678i) q^{15} +(3.70019 + 1.51941i) q^{16} +(-4.63479 - 4.63479i) q^{17} +(-0.137540 + 1.40751i) q^{18} +(3.97920 - 3.97920i) q^{19} +(2.92419 + 3.38365i) q^{20} +(-0.159531 - 0.159531i) q^{21} +(2.04289 + 2.48539i) q^{22} +(-5.58779 + 5.58779i) q^{23} +(-0.814832 + 2.70851i) q^{24} +(1.20897 + 4.85164i) q^{25} +(6.14142 + 0.600131i) q^{26} -1.00000 q^{27} +(-0.251259 - 0.374793i) q^{28} +(-6.25463 - 6.25463i) q^{29} +(-2.18017 + 2.29061i) q^{30} +1.69754i q^{31} +(-2.64751 + 4.99907i) q^{32} +(-1.60861 + 1.60861i) q^{33} +(7.16098 - 5.88604i) q^{34} +(-0.0614476 - 0.500725i) q^{35} +(-1.96217 - 0.387177i) q^{36} +0.609145i q^{37} +(5.05346 + 6.14806i) q^{38} +4.36332i q^{39} +(-5.16472 + 3.65044i) q^{40} +0.538520i q^{41} +(0.246483 - 0.202600i) q^{42} +0.592259i q^{43} +(-3.77919 + 2.53355i) q^{44} +(-1.76195 - 1.37678i) q^{45} +(-7.09632 - 8.63341i) q^{46} +(4.85568 - 4.85568i) q^{47} +(-3.70019 - 1.51941i) q^{48} -6.94910i q^{49} +(-6.99501 + 1.03434i) q^{50} +(4.63479 + 4.63479i) q^{51} +(-1.68938 + 8.56156i) q^{52} -4.82837 q^{53} +(0.137540 - 1.40751i) q^{54} +(-5.04901 + 0.619600i) q^{55} +(0.562083 - 0.302101i) q^{56} +(-3.97920 + 3.97920i) q^{57} +(9.66371 - 7.94319i) q^{58} +(5.78762 + 5.78762i) q^{59} +(-2.92419 - 3.38365i) q^{60} +(1.65469 - 1.65469i) q^{61} +(-2.38930 - 0.233479i) q^{62} +(0.159531 + 0.159531i) q^{63} +(-6.67210 - 4.41397i) q^{64} +(-6.00733 + 7.68798i) q^{65} +(-2.04289 - 2.48539i) q^{66} -0.485302i q^{67} +(7.29974 + 10.8887i) q^{68} +(5.58779 - 5.58779i) q^{69} +(0.713227 - 0.0176184i) q^{70} +6.86042 q^{71} +(0.814832 - 2.70851i) q^{72} +(-0.160991 - 0.160991i) q^{73} +(-0.857378 - 0.0837818i) q^{74} +(-1.20897 - 4.85164i) q^{75} +(-9.34851 + 6.26719i) q^{76} +0.513248 q^{77} +(-6.14142 - 0.600131i) q^{78} -7.13706 q^{79} +(-4.42767 - 7.77147i) q^{80} +1.00000 q^{81} +(-0.757972 - 0.0740679i) q^{82} -6.88217 q^{83} +(0.251259 + 0.374793i) q^{84} +(1.78521 + 14.5474i) q^{85} +(-0.833610 - 0.0814592i) q^{86} +(6.25463 + 6.25463i) q^{87} +(-3.04620 - 5.66770i) q^{88} +17.0238 q^{89} +(2.18017 - 2.29061i) q^{90} +(0.696085 - 0.696085i) q^{91} +(13.1276 - 8.80070i) q^{92} -1.69754i q^{93} +(6.16657 + 7.50227i) q^{94} +(-12.4896 + 1.53269i) q^{95} +(2.64751 - 4.99907i) q^{96} +(9.64079 + 9.64079i) q^{97} +(9.78092 + 0.955778i) q^{98} +(1.60861 - 1.60861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 20 q^{9} + 8 q^{10} + 8 q^{11} - 2 q^{12} + 10 q^{14} + 26 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 4 q^{21} - 10 q^{22} - 16 q^{23} - 6 q^{24} + 4 q^{25}+ \cdots + 8 q^{99}+O(q^{100}) \) 20 * q - 20 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 20 * q^9 + 8 * q^10 + 8 * q^11 - 2 * q^12 + 10 * q^14 + 26 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 4 * q^21 - 10 * q^22 - 16 * q^23 - 6 * q^24 + 4 * q^25 - 20 * q^26 - 20 * q^27 + 6 * q^28 - 8 * q^30 - 10 * q^32 - 8 * q^33 + 6 * q^34 - 28 * q^35 + 2 * q^36 - 2 * q^38 + 6 * q^40 - 10 * q^42 + 22 * q^44 - 18 * q^46 - 26 * q^48 - 52 * q^50 - 12 * q^51 + 8 * q^53 - 4 * q^55 - 26 * q^56 - 16 * q^57 - 22 * q^58 - 16 * q^59 + 10 * q^60 - 12 * q^61 + 4 * q^62 - 4 * q^63 + 26 * q^64 + 4 * q^65 + 10 * q^66 + 2 * q^68 + 16 * q^69 - 10 * q^70 + 6 * q^72 - 20 * q^73 - 8 * q^74 - 4 * q^75 + 26 * q^76 + 20 * q^78 + 48 * q^79 - 54 * q^80 + 20 * q^81 - 8 * q^82 - 24 * q^83 - 6 * q^84 + 4 * q^85 + 4 * q^86 + 34 * q^88 + 40 * q^89 + 8 * q^90 - 24 * q^91 + 82 * q^92 + 58 * q^94 - 72 * q^95 + 10 * q^96 - 28 * q^97 + 70 * q^98 + 8 * q^99

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