LMFDB - Embedded newform 275.2.l.d.31.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(31,275)] 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("275.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.l (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [100,2,-2] 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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$25$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	275.31
Dual form			275.2.l.d.71.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.47120 q^{2} +(-0.500346 + 1.53991i) q^{3} +0.164422 q^{4} +(-0.844616 - 2.07042i) q^{5} +(0.736108 - 2.26551i) q^{6} +(-1.36475 - 0.991546i) q^{7} +2.70050 q^{8} +(0.306083 + 0.222382i) q^{9} +(1.24260 + 3.04599i) q^{10} +(3.31662 - 0.00241943i) q^{11} +(-0.0822677 + 0.253194i) q^{12} +(0.766798 + 0.557111i) q^{13} +(2.00781 + 1.45876i) q^{14} +(3.61085 - 0.264706i) q^{15} -4.30181 q^{16} +(-2.10867 + 6.48983i) q^{17} +(-0.450308 - 0.327168i) q^{18} +1.90012 q^{19} +(-0.138873 - 0.340421i) q^{20} +(2.20973 - 1.60547i) q^{21} +(-4.87941 + 0.00355946i) q^{22} +(1.35181 + 4.16046i) q^{23} +(-1.35118 + 4.15852i) q^{24} +(-3.57325 + 3.49741i) q^{25} +(-1.12811 - 0.819620i) q^{26} +(-4.42537 + 3.21522i) q^{27} +(-0.224394 - 0.163032i) q^{28} +5.85159 q^{29} +(-5.31227 + 0.389434i) q^{30} +(7.43986 - 5.40537i) q^{31} +0.927814 q^{32} +(-1.65573 + 5.10850i) q^{33} +(3.10227 - 9.54782i) q^{34} +(-0.900226 + 3.66307i) q^{35} +(0.0503266 + 0.0365644i) q^{36} +(6.42888 - 4.67086i) q^{37} -2.79545 q^{38} +(-1.24156 + 0.902049i) q^{39} +(-2.28088 - 5.59115i) q^{40} +(3.14188 + 9.66970i) q^{41} +(-3.25095 + 2.36196i) q^{42} +8.15542 q^{43} +(0.545325 - 0.000397807i) q^{44} +(0.201901 - 0.821546i) q^{45} +(-1.98879 - 6.12085i) q^{46} +(1.63365 - 5.02786i) q^{47} +(2.15239 - 6.62439i) q^{48} +(-1.28375 - 3.95098i) q^{49} +(5.25695 - 5.14539i) q^{50} +(-8.93867 - 6.49432i) q^{51} +(0.126078 + 0.0916011i) q^{52} +(1.71350 + 5.27361i) q^{53} +(6.51059 - 4.73022i) q^{54} +(-2.80628 - 6.86475i) q^{55} +(-3.68549 - 2.67767i) q^{56} +(-0.950716 + 2.92600i) q^{57} -8.60885 q^{58} +(1.22275 - 0.888382i) q^{59} +(0.593702 - 0.0435234i) q^{60} +(-9.36574 + 6.80461i) q^{61} +(-10.9455 + 7.95237i) q^{62} +(-0.197223 - 0.606990i) q^{63} +7.23862 q^{64} +(0.505802 - 2.05814i) q^{65} +(2.43591 - 7.51562i) q^{66} +(-3.44013 - 2.49940i) q^{67} +(-0.346711 + 1.06707i) q^{68} -7.08309 q^{69} +(1.32441 - 5.38909i) q^{70} +(-0.393402 - 0.285823i) q^{71} +(0.826576 + 0.600543i) q^{72} +(-4.38877 + 13.5072i) q^{73} +(-9.45816 + 6.87175i) q^{74} +(-3.59783 - 7.25239i) q^{75} +0.312420 q^{76} +(-4.52875 - 3.28528i) q^{77} +(1.82658 - 1.32709i) q^{78} +(-2.91623 - 8.97522i) q^{79} +(3.63338 + 8.90653i) q^{80} +(-2.38618 - 7.34391i) q^{81} +(-4.62232 - 14.2260i) q^{82} +(2.05361 - 6.32036i) q^{83} +(0.363328 - 0.263973i) q^{84} +(15.2177 - 1.11558i) q^{85} -11.9982 q^{86} +(-2.92782 + 9.01091i) q^{87} +(8.95654 - 0.00653368i) q^{88} +(2.31611 + 7.12826i) q^{89} +(-0.297036 + 1.20866i) q^{90} +(-0.494083 - 1.52063i) q^{91} +(0.222268 + 0.684069i) q^{92} +(4.60127 + 14.1613i) q^{93} +(-2.40342 + 7.39698i) q^{94} +(-1.60487 - 3.93403i) q^{95} +(-0.464228 + 1.42875i) q^{96} +(-4.84973 - 14.9259i) q^{97} +(1.88865 + 5.81267i) q^{98} +(1.01570 + 0.736818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) $ 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.47120			−1.04029			−0.520147	−	0.854077i	$-0.674123\pi$
$2$	−1.47120			−1.04029			−0.520147	+	0.854077i	$0.674123\pi$
$3$	−0.500346	+	1.53991i	−0.288875	+	0.889066i	0.696335	+	0.717717i	$0.254813\pi$
$3$	−0.500346	+	1.53991i	−0.288875	+	0.889066i	−0.985210	+	0.171349i	$0.945187\pi$
$4$	0.164422			0.0822108
$5$	−0.844616	−	2.07042i	−0.377724	−	0.925918i
$5$	−0.844616	−	2.07042i	−0.377724	−	0.925918i
$6$	0.736108	−	2.26551i	0.300515	−	0.924890i
$7$	−1.36475	−	0.991546i	−0.515825	−	0.374769i	0.299204	−	0.954189i	$-0.403279\pi$
$7$	−1.36475	−	0.991546i	−0.515825	−	0.374769i	−0.815029	+	0.579420i	$0.803279\pi$
$8$	2.70050			0.954770
$9$	0.306083	+	0.222382i	0.102028	+	0.0741274i
$10$	1.24260	+	3.04599i	0.392944	+	0.963227i
$11$	3.31662	−	0.00241943i	1.00000	−	0.000729487i
$11$	3.31662	−	0.00241943i	1.00000	−	0.000729487i
$12$	−0.0822677	+	0.253194i	−0.0237487	+	0.0730908i
$13$	0.766798	+	0.557111i	0.212671	+	0.154515i	0.689022	−	0.724741i	$-0.258041\pi$
$13$	0.766798	+	0.557111i	0.212671	+	0.154515i	−0.476350	+	0.879256i	$0.658041\pi$
$14$	2.00781	+	1.45876i	0.536610	+	0.389870i
$15$	3.61085	−	0.264706i	0.932317	−	0.0683467i
$16$	−4.30181			−1.07545
$17$	−2.10867	+	6.48983i	−0.511428	+	1.57401i	0.278260	+	0.960506i	$0.410242\pi$
$17$	−2.10867	+	6.48983i	−0.511428	+	1.57401i	−0.789688	+	0.613509i	$0.789758\pi$
$18$	−0.450308	−	0.327168i	−0.106139	−	0.0771143i
$19$	1.90012			0.435916			0.217958	−	0.975958i	$-0.430060\pi$
$19$	1.90012			0.435916			0.217958	+	0.975958i	$0.430060\pi$
$20$	−0.138873	−	0.340421i	−0.0310530	−	0.0761205i
$21$	2.20973	−	1.60547i	0.482203	−	0.350341i
$22$	−4.87941	+	0.00355946i	−1.04029	+	0.000758880i
$23$	1.35181	+	4.16046i	0.281873	+	0.867515i	0.987319	+	0.158751i	$0.0507468\pi$
$23$	1.35181	+	4.16046i	0.281873	+	0.867515i	−0.705446	+	0.708764i	$0.749253\pi$
$24$	−1.35118	+	4.15852i	−0.275809	+	0.848854i
$25$	−3.57325	+	3.49741i	−0.714649	+	0.699483i
$26$	−1.12811	−	0.819620i	−0.221241	−	0.160741i
$27$	−4.42537	+	3.21522i	−0.851662	+	0.618769i
$28$	−0.224394	−	0.163032i	−0.0424064	−	0.0308101i
$29$	5.85159			1.08661			0.543307	−	0.839534i	$-0.317172\pi$
$29$	5.85159			1.08661			0.543307	+	0.839534i	$0.317172\pi$
$30$	−5.31227	+	0.389434i	−0.969884	+	0.0711007i
$31$	7.43986	−	5.40537i	1.33624	−	0.970834i	0.336665	−	0.941625i	$-0.390701\pi$
$31$	7.43986	−	5.40537i	1.33624	−	0.970834i	0.999573	−	0.0292091i	$-0.00929887\pi$
$32$	0.927814			0.164016
$33$	−1.65573	+	5.10850i	−0.288226	+	0.889276i
$34$	3.10227	−	9.54782i	0.532036	−	1.63744i
$35$	−0.900226	+	3.66307i	−0.152166	+	0.619171i
$36$	0.0503266	+	0.0365644i	0.00838777	+	0.00609407i
$37$	6.42888	−	4.67086i	1.05690	−	0.767884i	0.0833893	−	0.996517i	$-0.473425\pi$
$37$	6.42888	−	4.67086i	1.05690	−	0.767884i	0.973513	+	0.228633i	$0.0734255\pi$
$38$	−2.79545			−0.453481
$39$	−1.24156	+	0.902049i	−0.198809	+	0.144443i
$40$	−2.28088	−	5.59115i	−0.360640	−	0.884039i
$41$	3.14188	+	9.66970i	0.490679	+	1.51015i	0.823584	+	0.567194i	$0.191971\pi$
$41$	3.14188	+	9.66970i	0.490679	+	1.51015i	−0.332906	+	0.942960i	$0.608029\pi$
$42$	−3.25095	+	2.36196i	−0.501633	+	0.364458i
$43$	8.15542			1.24369			0.621845	−	0.783140i	$-0.286383\pi$
$43$	8.15542			1.24369			0.621845	+	0.783140i	$0.286383\pi$
$44$	0.545325		0.000397807i	0.0822108		5.99717e-5i
$45$	0.201901	−	0.821546i	0.0300976	−	0.122469i
$46$	−1.98879	−	6.12085i	−0.293230	−	0.902471i
$47$	1.63365	−	5.02786i	0.238293	−	0.733389i	−0.758375	−	0.651819i	$-0.774006\pi$
$47$	1.63365	−	5.02786i	0.238293	−	0.733389i	0.996668	−	0.0815707i	$-0.0259936\pi$
$48$	2.15239	−	6.62439i	0.310671	−	0.956148i
$49$	−1.28375	−	3.95098i	−0.183393	−	0.564426i
$50$	5.25695	−	5.14539i	0.743445	−	0.727668i
$51$	−8.93867	−	6.49432i	−1.25166	−	0.909387i
$52$	0.126078	+	0.0916011i	0.0174839	+	0.0127028i
$53$	1.71350	+	5.27361i	0.235367	+	0.724386i	0.997072	+	0.0764624i	$0.0243625\pi$
$53$	1.71350	+	5.27361i	0.235367	+	0.724386i	−0.761705	+	0.647924i	$0.775637\pi$
$54$	6.51059	−	4.73022i	0.885979	−	0.643701i
$55$	−2.80628	−	6.86475i	−0.378399	−	0.925642i
$56$	−3.68549	−	2.67767i	−0.492495	−	0.357818i
$57$	−0.950716	+	2.92600i	−0.125925	+	0.387558i
$58$	−8.60885			−1.13040
$59$	1.22275	−	0.888382i	0.159189	−	0.115657i	−0.505339	−	0.862921i	$-0.668633\pi$
$59$	1.22275	−	0.888382i	0.159189	−	0.115657i	0.664528	+	0.747263i	$0.268633\pi$
$60$	0.593702	−	0.0435234i	0.0766466	−	0.00561884i
$61$	−9.36574	+	6.80461i	−1.19916	+	0.871241i	−0.994202	−	0.107530i	$-0.965706\pi$
$61$	−9.36574	+	6.80461i	−1.19916	+	0.871241i	−0.204958	+	0.978771i	$0.565706\pi$
$62$	−10.9455	+	7.95237i	−1.39008	+	1.00995i
$63$	−0.197223	−	0.606990i	−0.0248478	−	0.0764736i
$64$	7.23862			0.904828
$65$	0.505802	−	2.05814i	0.0627370	−	0.255280i
$66$	2.43591	−	7.51562i	0.299840	−	0.925109i
$67$	−3.44013	−	2.49940i	−0.420278	−	0.305350i	0.357471	−	0.933924i	$-0.383639\pi$
$67$	−3.44013	−	2.49940i	−0.420278	−	0.305350i	−0.777750	+	0.628574i	$0.783639\pi$
$68$	−0.346711	+	1.06707i	−0.0420449	+	0.129401i
$69$	−7.08309			−0.852704
$70$	1.32441	−	5.38909i	0.158297	−	0.644120i
$71$	−0.393402	−	0.285823i	−0.0466882	−	0.0339210i	0.564196	−	0.825641i	$-0.309186\pi$
$71$	−0.393402	−	0.285823i	−0.0466882	−	0.0339210i	−0.610885	+	0.791720i	$0.709186\pi$
$72$	0.826576	+	0.600543i	0.0974129	+	0.0707746i
$73$	−4.38877	+	13.5072i	−0.513667	+	1.58090i	0.272028	+	0.962289i	$0.412306\pi$
$73$	−4.38877	+	13.5072i	−0.513667	+	1.58090i	−0.785695	+	0.618614i	$0.787694\pi$
$74$	−9.45816	+	6.87175i	−1.09949	+	0.798825i
$75$	−3.59783	−	7.25239i	−0.415442	−	0.837434i
$76$	0.312420			0.0358370
$77$	−4.52875	−	3.28528i	−0.516099	−	0.374393i
$78$	1.82658	−	1.32709i	0.206820	−	0.150264i
$79$	−2.91623	−	8.97522i	−0.328101	−	1.00979i	−0.970021	−	0.243020i	$-0.921862\pi$
$79$	−2.91623	−	8.97522i	−0.328101	−	1.00979i	0.641920	−	0.766771i	$-0.278138\pi$
$80$	3.63338	+	8.90653i	0.406224	+	0.995781i
$81$	−2.38618	−	7.34391i	−0.265131	−	0.815990i
$82$	−4.62232	−	14.2260i	−0.510450	−	1.57100i
$83$	2.05361	−	6.32036i	0.225413	−	0.693749i	−0.772837	−	0.634605i	$-0.781163\pi$
$83$	2.05361	−	6.32036i	0.225413	−	0.693749i	0.998249	−	0.0591443i	$-0.0188372\pi$
$84$	0.363328	−	0.263973i	0.0396423	−	0.0288018i
$85$	15.2177	−	1.11558i	1.65059	−	0.121002i
$86$	−11.9982			−1.29380
$87$	−2.92782	+	9.01091i	−0.313895	+	0.966071i
$88$	8.95654	−	0.00653368i	0.954770	−	0.000696492i
$89$	2.31611	+	7.12826i	0.245507	+	0.755594i	0.995553	+	0.0942076i	$0.0300317\pi$
$89$	2.31611	+	7.12826i	0.245507	+	0.755594i	−0.750045	+	0.661387i	$0.769968\pi$
$90$	−0.297036	+	1.20866i	−0.0313104	+	0.127404i
$91$	−0.494083	−	1.52063i	−0.0517939	−	0.159405i
$92$	0.222268	+	0.684069i	0.0231730	+	0.0713191i
$93$	4.60127	+	14.1613i	0.477129	+	1.46845i
$94$	−2.40342	+	7.39698i	−0.247894	+	0.762940i
$95$	−1.60487	−	3.93403i	−0.164656	−	0.403623i
$96$	−0.464228	+	1.42875i	−0.0473801	+	0.145821i
$97$	−4.84973	−	14.9259i	−0.492416	−	1.51550i	−0.820945	−	0.571007i	$-0.806553\pi$
$97$	−4.84973	−	14.9259i	−0.492416	−	1.51550i	0.328529	−	0.944494i	$-0.393447\pi$
$98$	1.88865	+	5.81267i	0.190783	+	0.587168i
$99$	1.01570	+	0.736818i	0.102082	+	0.0740529i
$100$	−0.587519	+	0.575051i	−0.0587519	+	0.0575051i
$101$	−2.96368	+	9.12126i	−0.294897	+	0.907599i	0.688359	+	0.725370i	$0.258331\pi$
$101$	−2.96368	+	9.12126i	−0.294897	+	0.907599i	−0.983256	+	0.182229i	$0.941669\pi$
$102$	13.1505	+	9.55443i	1.30210	+	0.946030i
$103$	2.14423			0.211277			0.105639	−	0.994405i	$-0.466311\pi$
$103$	2.14423			0.211277			0.105639	+	0.994405i	$0.466311\pi$
$104$	2.07074	+	1.50448i	0.203052	+	0.147526i
$105$	−5.19036	−	3.21907i	−0.506527	−	0.314149i
$106$	−2.52090	−	7.75852i	−0.244851	−	0.753574i
$107$	−3.53222	+	2.56630i	−0.341472	+	0.248094i	−0.745283	−	0.666749i	$-0.767685\pi$
$107$	−3.53222	+	2.56630i	−0.341472	+	0.248094i	0.403811	+	0.914843i	$0.367685\pi$
$108$	−0.727626	+	0.528651i	−0.0700158	+	0.0508695i
$109$	−0.114763	+	0.353206i	−0.0109923	+	0.0338310i	−0.956402	−	0.292053i	$-0.905662\pi$
$109$	−0.114763	+	0.353206i	−0.0109923	+	0.0338310i	0.945410	+	0.325884i	$0.105662\pi$
$110$	4.12860	+	10.0994i	0.393646	+	0.962940i
$111$	3.97602	+	12.2369i	0.377387	+	1.16148i
$112$	5.87088	+	4.26544i	0.554746	+	0.403046i
$113$	−3.46022	−	10.6495i	−0.325511	−	1.00182i	−0.971210	−	0.238226i	$-0.923434\pi$
$113$	−3.46022	−	10.6495i	−0.325511	−	1.00182i	0.645699	−	0.763592i	$-0.276566\pi$
$114$	1.39869	−	4.30473i	0.130999	−	0.403175i
$115$	7.47211	−	6.31281i	0.696778	−	0.588672i
$116$	0.962128			0.0893314
$117$	0.110812	+	0.341044i	0.0102446	+	0.0315295i
$118$	−1.79891	+	1.30699i	−0.165603	+	0.120318i
$119$	9.31276	−	6.76612i	0.853700	−	0.620249i
$120$	9.75109	−	0.714837i	0.890149	−	0.0652554i
$121$	11.0000	−	0.0160487i	0.999999	−	0.00145897i
$122$	13.7789	−	10.0109i	1.24748	−	0.906346i
$123$	−16.4625			−1.48437
$124$	1.22327	−	0.888760i	0.109853	−	0.0798130i
$125$	10.2591	+	4.44414i	0.917604	+	0.397496i
$126$	0.290154	+	0.893002i	0.0258490	+	0.0795550i
$127$	−2.90986	+	2.11413i	−0.258208	+	0.187599i	−0.709357	−	0.704850i	$-0.751014\pi$
$127$	−2.90986	+	2.11413i	−0.258208	+	0.187599i	0.451149	+	0.892449i	$0.351014\pi$
$128$	−12.5051			−1.10530
$129$	−4.08053	+	12.5586i	−0.359271	+	1.10572i
$130$	−0.744135	+	3.02792i	−0.0652649	+	0.265566i
$131$	−2.10461	−	1.52909i	−0.183881	−	0.133597i	0.492037	−	0.870574i	$-0.336252\pi$
$131$	−2.10461	−	1.52909i	−0.183881	−	0.133597i	−0.675918	+	0.736977i	$0.736252\pi$
$132$	−0.272239	+	0.839949i	−0.0236953	+	0.0731081i
$133$	−2.59317	−	1.88405i	−0.224857	−	0.163368i
$134$	5.06110	+	3.67711i	0.437213	+	0.317654i
$135$	10.3946	+	6.44672i	0.894622	+	0.554846i
$136$	−5.69447	+	17.5258i	−0.488297	+	1.50282i
$137$	10.5579			0.902019			0.451009	−	0.892519i	$-0.351064\pi$
$137$	10.5579			0.902019			0.451009	+	0.892519i	$0.351064\pi$
$138$	10.4206			0.887063
$139$	−3.19426	+	9.83094i	−0.270934	+	0.833849i	0.719333	+	0.694666i	$0.244448\pi$
$139$	−3.19426	+	9.83094i	−0.270934	+	0.833849i	−0.990267	+	0.139183i	$0.955552\pi$
$140$	−0.148017	+	0.602288i	−0.0125097	+	0.0509026i
$141$	6.92505	+	5.03134i	0.583195	+	0.423716i
$142$	0.578772	+	0.420503i	0.0485695	+	0.0352878i
$143$	2.54453	+	1.84587i	0.212784	+	0.154360i
$144$	−1.31671	−	0.956646i	−0.109726	−	0.0797205i
$145$	−4.94235	−	12.1152i	−0.410440	−	1.00612i
$146$	6.45675	−	19.8718i	0.534364	−	1.64460i
$147$	6.72646			0.554789
$148$	1.05705	−	0.767990i	0.0868888	−	0.0631284i
$149$	2.19784	+	6.76426i	0.180054	+	0.554150i	0.999828	−	0.0185374i	$-0.00590097\pi$
$149$	2.19784	+	6.76426i	0.180054	+	0.554150i	−0.819774	+	0.572687i	$0.805901\pi$
$150$	5.29312	+	10.6697i	0.432182	+	0.871177i
$151$	−6.93710	+	5.04010i	−0.564533	+	0.410157i	−0.833115	−	0.553099i	$-0.813445\pi$
$151$	−6.93710	+	5.04010i	−0.564533	+	0.410157i	0.268582	+	0.963257i	$0.413445\pi$
$152$	5.13126			0.416200
$153$	−2.08865	+	1.51749i	−0.168857	+	0.122682i
$154$	6.66268	+	4.83330i	0.536894	+	0.389478i
$155$	−17.4752	−	10.8381i	−1.40364	−	0.870540i
$156$	−0.204140	+	0.148316i	−0.0163443	+	0.0118748i
$157$	−2.88590	+	2.09673i	−0.230320	+	0.167337i	−0.696960	−	0.717110i	$-0.745464\pi$
$157$	−2.88590	+	2.09673i	−0.230320	+	0.167337i	0.466640	+	0.884447i	$0.345464\pi$
$158$	4.29034	+	13.2043i	0.341322	+	1.05048i
$159$	−8.97822			−0.712019
$160$	−0.783647	−	1.92096i	−0.0619527	−	0.151865i
$161$	2.28040	−	7.01835i	0.179721	−	0.553124i
$162$	3.51054	+	10.8043i	0.275814	+	0.848869i
$163$	−5.12307	−	3.72213i	−0.401270	−	0.291540i	0.368788	−	0.929514i	$-0.379773\pi$
$163$	−5.12307	−	3.72213i	−0.401270	−	0.291540i	−0.770058	+	0.637974i	$0.779773\pi$
$164$	0.516593	+	1.58991i	0.0403391	+	0.124151i
$165$	11.9752	−	0.886666i	0.932267	−	0.0690268i
$166$	−3.02126	+	9.29849i	−0.234496	+	0.721703i
$167$	9.30944	−	6.76371i	0.720386	−	0.523391i	−0.166121	−	0.986105i	$-0.553124\pi$
$167$	9.30944	−	6.76371i	0.720386	−	0.523391i	0.886508	+	0.462714i	$0.153124\pi$
$168$	5.96738	−	4.33556i	0.460394	−	0.334495i
$169$	−3.73962	−	11.5094i	−0.287663	−	0.885335i
$170$	−22.3882	+	1.64124i	−1.71710	+	0.125878i
$171$	0.581593	+	0.422552i	0.0444755	+	0.0323134i
$172$	1.34093			0.102245
$173$	6.32938	+	4.59856i	0.481214	+	0.349622i	0.801795	−	0.597599i	$-0.203878\pi$
$173$	6.32938	+	4.59856i	0.481214	+	0.349622i	−0.320582	+	0.947221i	$0.603878\pi$
$174$	4.30740	−	13.2568i	0.326543	−	1.00500i
$175$	8.34442	−	1.23004i	0.630779	−	0.0929825i
$176$	−14.2675	+	0.0104079i	−1.07545	+	0.000784528i
$177$	0.756226	+	2.32742i	0.0568414	+	0.174940i
$178$	−3.40746	−	10.4871i	−0.255400	−	0.786040i
$179$	−3.17769	+	9.77992i	−0.237512	+	0.730986i	0.759267	+	0.650780i	$0.225558\pi$
$179$	−3.17769	+	9.77992i	−0.237512	+	0.730986i	−0.996778	+	0.0802061i	$0.974442\pi$
$180$	0.0331969	−	0.135080i	0.00247435	−	0.0100683i
$181$	−4.79226	+	14.7491i	−0.356206	+	1.09629i	0.599101	+	0.800673i	$0.295525\pi$
$181$	−4.79226	+	14.7491i	−0.356206	+	1.09629i	−0.955307	+	0.295615i	$0.904475\pi$
$182$	0.726893	+	2.23715i	0.0538809	+	0.165828i
$183$	−5.79235	−	17.8270i	−0.428183	−	1.31781i
$184$	3.65057	+	11.2353i	0.269124	+	0.828278i
$185$	−15.1006	−	9.36538i	−1.11022	−	0.688557i
$186$	−6.76937	−	20.8340i	−0.496355	−	1.52762i
$187$	−6.97797	+	21.5294i	−0.510280	+	1.57439i
$188$	0.268608	−	0.826690i	0.0195902	−	0.0602925i
$189$	9.22753			0.671204
$190$	2.36108	+	5.78774i	0.171291	+	0.419886i
$191$	0.113012	−	0.0821078i	0.00817724	−	0.00594111i	−0.583689	−	0.811977i	$-0.698391\pi$
$191$	0.113012	−	0.0821078i	0.00817724	−	0.00594111i	0.591866	+	0.806036i	$0.298391\pi$
$192$	−3.62182	+	11.1468i	−0.261382	+	0.804451i
$193$	−5.37535	−	16.5436i	−0.386926	−	1.19084i	−0.935073	−	0.354455i	$-0.884666\pi$
$193$	−5.37535	−	16.5436i	−0.386926	−	1.19084i	0.548147	−	0.836382i	$-0.315334\pi$
$194$	7.13492	+	21.9590i	0.512257	+	1.57657i
$195$	2.91626	+	1.80867i	0.208838	+	0.129521i
$196$	−0.211076	−	0.649627i	−0.0150769	−	0.0464019i
$197$	−1.33488	+	0.969845i	−0.0951061	+	0.0690986i	−0.634322	−	0.773069i	$-0.718721\pi$
$197$	−1.33488	+	0.969845i	−0.0951061	+	0.0690986i	0.539216	+	0.842168i	$0.318721\pi$
$198$	−1.49429	−	1.08400i	−0.106195	−	0.0770368i
$199$	−6.02812			−0.427322			−0.213661	−	0.976908i	$-0.568539\pi$
$199$	−6.02812			−0.427322			−0.213661	+	0.976908i	$0.568539\pi$
$200$	−9.64955	+	9.44476i	−0.682326	+	0.667845i
$201$	5.57010	−	4.04691i	0.392884	−	0.285447i
$202$	4.36015	−	13.4192i	0.306779	−	0.944169i
$203$	−7.98593	−	5.80212i	−0.560503	−	0.407229i
$204$	−1.46971	−	1.06781i	−0.102900	−	0.0747615i
$205$	17.3666	−	14.6722i	1.21294	−	1.02475i
$206$	−3.15459			−0.219791
$207$	−0.511444	+	1.57406i	−0.0355478	+	0.109405i
$208$	−3.29862	−	2.39659i	−0.228718	−	0.166173i
$209$	6.30197	−	0.00459720i	0.435916	−	0.000317995i
$210$	7.63604	+	4.73588i	0.526937	+	0.326807i
$211$	20.7571			1.42898			0.714490	−	0.699646i	$-0.246659\pi$
$211$	20.7571			1.42898			0.714490	+	0.699646i	$0.246659\pi$
$212$	0.281737	+	0.867096i	0.0193497	+	0.0595524i
$213$	0.636979	−	0.462792i	0.0436451	−	0.0317100i
$214$	5.19659	−	3.77554i	0.355231	−	0.258091i
$215$	−6.88820	−	16.8851i	−0.469772	−	1.15156i
$216$	−11.9507	+	8.68269i	−0.813142	+	0.590782i
$217$	−15.5132			−1.05310
$218$	0.168840	−	0.519635i	0.0114353	−	0.0351941i
$219$	−18.6040	−	13.5166i	−1.25714	−	0.913367i
$220$	−0.461414	−	1.12871i	−0.0311085	−	0.0760978i
$221$	−5.23248	+	3.80162i	−0.351975	+	0.255725i
$222$	−5.84951	−	18.0029i	−0.392593	−	1.20828i
$223$	−4.55326	−	3.30814i	−0.304909	−	0.221529i	0.424800	−	0.905287i	$-0.360344\pi$
$223$	−4.55326	−	3.30814i	−0.304909	−	0.221529i	−0.729709	+	0.683758i	$0.760344\pi$
$224$	−1.26623	−	0.919970i	−0.0846035	−	0.0614681i
$225$	−1.87147	+	0.275872i	−0.124765	+	0.0183915i
$226$	5.09067	+	15.6675i	0.338627	+	1.04219i
$227$	4.72875	−	14.5536i	0.313858	−	0.965956i	−0.662364	−	0.749182i	$-0.730447\pi$
$227$	4.72875	−	14.5536i	0.313858	−	0.965956i	0.976222	−	0.216774i	$-0.0695534\pi$
$228$	−0.156318	+	0.481098i	−0.0103524	+	0.0318615i
$229$	−8.18392	−	25.1875i	−0.540809	−	1.66444i	−0.730752	−	0.682643i	$-0.760831\pi$
$229$	−8.18392	−	25.1875i	−0.540809	−	1.66444i	0.189944	−	0.981795i	$-0.439169\pi$
$230$	−10.9930	+	9.28739i	−0.724854	+	0.612392i
$231$	7.32497	−	5.33007i	0.481948	−	0.350693i
$232$	15.8022			1.03747
$233$	2.15521	−	1.56585i	0.141192	−	0.102582i	−0.514947	−	0.857222i	$-0.672188\pi$
$233$	2.15521	−	1.56585i	0.141192	−	0.102582i	0.656139	+	0.754640i	$0.272188\pi$
$234$	−0.163026	−	0.501743i	−0.0106574	−	0.0328000i
$235$	−11.7896	+	0.864276i	−0.769067	+	0.0563791i
$236$	0.201047	−	0.146069i	0.0130870	−	0.00950830i
$237$	15.2801			0.992551
$238$	−13.7009	+	9.95430i	−0.888098	+	0.645241i
$239$	−16.1993	−	11.7694i	−1.04784	−	0.761302i	−0.0760417	−	0.997105i	$-0.524228\pi$
$239$	−16.1993	−	11.7694i	−1.04784	−	0.761302i	−0.971801	+	0.235802i	$0.924228\pi$
$240$	−15.5332	+	1.13871i	−1.00266	+	0.0735037i
$241$	−3.53183	+	10.8699i	−0.227505	+	0.700189i	0.770522	+	0.637413i	$0.219995\pi$
$241$	−3.53183	+	10.8699i	−0.227505	+	0.700189i	−0.998028	+	0.0627763i	$0.980005\pi$
$242$	−16.1832	+	0.0236108i	−1.04029	+	0.00151776i
$243$	−3.90730			−0.250654
$244$	−1.53993	+	1.11882i	−0.0985839	+	0.0716254i
$245$	−7.09590	+	5.99496i	−0.453340	+	0.383004i
$246$	24.2195			1.54418
$247$	1.45700	+	1.05858i	0.0927069	+	0.0673555i
$248$	20.0913	−	14.5972i	1.27580	−	0.926923i
$249$	8.70525	+	6.32473i	0.551673	+	0.400814i
$250$	−15.0932	−	6.53820i	−0.954578	−	0.413512i
$251$	−2.47213	+	7.60844i	−0.156040	+	0.480241i	−0.998265	−	0.0588855i	$-0.981245\pi$
$251$	−2.47213	+	7.60844i	−0.156040	+	0.480241i	0.842225	+	0.539126i	$0.181245\pi$
$252$	−0.0324277	−	0.0998023i	−0.00204276	−	0.00628696i
$253$	4.49353	+	13.7954i	0.282506	+	0.867309i
$254$	4.28097	−	3.11031i	0.268612	−	0.195158i
$255$	−5.89621	+	23.9920i	−0.369235	+	1.50244i
$256$	3.92018			0.245011
$257$	22.6777	+	16.4763i	1.41460	+	1.02777i	0.992634	+	0.121153i	$0.0386592\pi$
$257$	22.6777	+	16.4763i	1.41460	+	1.02777i	0.421964	+	0.906613i	$0.361341\pi$
$258$	6.00327	−	18.4762i	0.373747	−	1.15028i
$259$	−13.4052			−0.832956
$260$	0.0831648	−	0.338402i	0.00515766	−	0.0209868i
$261$	1.79107	+	1.30129i	0.110865	+	0.0805478i
$262$	3.09630	+	2.24959i	0.191290	+	0.138980i
$263$	7.52907	−	23.1721i	0.464262	−	1.42885i	−0.395645	−	0.918403i	$-0.629479\pi$
$263$	7.52907	−	23.1721i	0.464262	−	1.42885i	0.859908	−	0.510449i	$-0.170521\pi$
$264$	−4.47131	+	13.7955i	−0.275190	+	0.849055i
$265$	9.47132	−	8.00184i	0.581819	−	0.491549i
$266$	3.81507	+	2.77181i	0.233917	+	0.169951i
$267$	−12.1357			−0.742694
$268$	−0.565631	−	0.410955i	−0.0345514	−	0.0251031i
$269$	0.610913	−	1.88020i	0.0372481	−	0.114638i	−0.930704	−	0.365774i	$-0.880804\pi$
$269$	0.610913	−	1.88020i	0.0372481	−	0.114638i	0.967952	+	0.251136i	$0.0808043\pi$
$270$	−15.2925	−	9.48440i	−0.930670	−	0.577202i
$271$	16.3939			0.995859			0.497929	−	0.867218i	$-0.334094\pi$
$271$	16.3939			0.995859			0.497929	+	0.867218i	$0.334094\pi$
$272$	9.07111	−	27.9180i	0.550017	−	1.69278i
$273$	2.58884			0.156684
$274$	−15.5327			−0.938364
$275$	−11.8427	+	11.6083i	−0.714139	+	0.700004i
$276$	−1.16461			−0.0701015
$277$	10.6781			0.641585			0.320793	−	0.947149i	$-0.396051\pi$
$277$	10.6781			0.641585			0.320793	+	0.947149i	$0.396051\pi$
$278$	4.69939	−	14.4632i	0.281851	−	0.867448i
$279$	3.47927			0.208299
$280$	−2.43106	+	9.89211i	−0.145284	+	0.591166i
$281$	0.330935	−	1.01851i	0.0197419	−	0.0607594i	−0.940700	−	0.339239i	$-0.889830\pi$
$281$	0.330935	−	1.01851i	0.0197419	−	0.0607594i	0.960442	+	0.278480i	$0.0898305\pi$
$282$	−10.1881	−	7.40210i	−0.606694	−	0.440789i
$283$	4.52737			0.269124			0.134562	−	0.990905i	$-0.457037\pi$
$283$	4.52737			0.269124			0.134562	+	0.990905i	$0.457037\pi$
$284$	−0.0646838	−	0.0469955i	−0.00383828	−	0.00278867i
$285$	6.86103	−	0.502972i	0.406412	−	0.0297935i
$286$	−3.74350	−	2.71564i	−0.221358	−	0.160579i
$287$	5.30009	−	16.3120i	0.312854	−	0.962867i
$288$	0.283988	+	0.206329i	0.0167341	+	0.0121581i
$289$	−23.9181	−	17.3775i	−1.40695	−	1.02221i
$290$	7.27117	+	17.8239i	0.426978	+	1.04666i
$291$	25.4111			1.48963
$292$	−0.721609	+	2.22088i	−0.0422290	+	0.129967i
$293$	−4.14516	−	3.01163i	−0.242163	−	0.175942i	0.460083	−	0.887876i	$-0.347819\pi$
$293$	−4.14516	−	3.01163i	−0.242163	−	0.175942i	−0.702246	+	0.711934i	$0.747819\pi$
$294$	−9.89595			−0.577144
$295$	−2.87208	−	1.78127i	−0.167219	−	0.103709i
$296$	17.3612	−	12.6136i	1.00910	−	0.733153i
$297$	−14.6695	+	10.6744i	−0.851210	+	0.619390i
$298$	−3.23346	−	9.95156i	−0.187309	−	0.576479i
$299$	−1.28127	+	3.94334i	−0.0740977	+	0.228049i
$300$	−0.591562	−	1.19245i	−0.0341538	−	0.0688461i
$301$	−11.1301	−	8.08648i	−0.641527	−	0.466097i
$302$	10.2058	−	7.41498i	0.587280	−	0.426684i
$303$	−12.5630	−	9.12757i	−0.721727	−	0.524365i
$304$	−8.17393			−0.468807
$305$	21.9988	+	13.6437i	1.25965	+	0.781236i
$306$	3.07282	−	2.23253i	0.175661	−	0.127625i
$307$	−22.2436			−1.26951			−0.634756	−	0.772713i	$-0.718899\pi$
$307$	−22.2436			−1.26951			−0.634756	+	0.772713i	$0.718899\pi$
$308$	−0.744624	−	0.540172i	−0.0424289	−	0.0307791i
$309$	−1.07286	+	3.30192i	−0.0610328	+	0.187840i
$310$	25.7095	+	15.9450i	1.46020	+	0.905617i
$311$	−16.2090	−	11.7765i	−0.919128	−	0.667785i	0.0241791	−	0.999708i	$-0.492303\pi$
$311$	−16.2090	−	11.7765i	−0.919128	−	0.667785i	−0.943307	+	0.331922i	$0.892303\pi$
$312$	−3.35284	+	2.43598i	−0.189817	+	0.137910i
$313$	13.3369			0.753845			0.376922	−	0.926245i	$-0.376982\pi$
$313$	13.3369			0.753845			0.376922	+	0.926245i	$0.376982\pi$
$314$	4.24573	−	3.08470i	0.239600	−	0.174080i
$315$	−1.09014	+	0.921008i	−0.0614227	+	0.0518929i
$316$	−0.479491	−	1.47572i	−0.0269735	−	0.0830158i
$317$	−23.5603	+	17.1176i	−1.32328	+	0.961420i	−0.323396	+	0.946264i	$0.604825\pi$
$317$	−23.5603	+	17.1176i	−1.32328	+	0.961420i	−0.999885	+	0.0151562i	$0.995175\pi$
$318$	13.2087			0.740709
$319$	19.4075	−	0.0141575i	1.08661	−	0.000792670i
$320$	−6.11386	−	14.9870i	−0.341775	−	0.837796i
$321$	−2.18454	−	6.72333i	−0.121929	−	0.375259i
$322$	−3.35492	+	10.3254i	−0.186962	+	0.575411i
$323$	−4.00672	+	12.3314i	−0.222940	+	0.686139i
$324$	−0.392340	−	1.20750i	−0.0217966	−	0.0670832i
$325$	−4.68840	+	0.691114i	−0.260066	+	0.0383361i
$326$	7.53705	+	5.47599i	0.417439	+	0.303287i
$327$	−0.486482	−	0.353450i	−0.0269025	−	0.0195458i
$328$	8.48463	+	26.1130i	0.468485	+	1.44185i
$329$	−7.21488	+	5.24191i	−0.397769	+	0.288996i
$330$	−17.6179	+	1.30446i	−0.969832	+	0.0718082i
$331$	26.0390	+	18.9184i	1.43123	+	1.03985i	0.989785	+	0.142565i	$0.0455351\pi$
$331$	26.0390	+	18.9184i	1.43123	+	1.03985i	0.441448	+	0.897287i	$0.354465\pi$
$332$	0.337658	−	1.03920i	0.0185314	−	0.0570337i
$333$	3.00649			0.164754
$334$	−13.6960	+	9.95074i	−0.749413	+	0.544481i
$335$	−2.26921	+	9.23353i	−0.123980	+	0.504481i
$336$	−9.50585	+	6.90641i	−0.518587	+	0.376775i
$337$	1.48106	−	1.07605i	0.0806782	−	0.0586161i	−0.546715	−	0.837319i	$-0.684122\pi$
$337$	1.48106	−	1.07605i	0.0806782	−	0.0586161i	0.627393	+	0.778703i	$0.284122\pi$
$338$	5.50171	+	16.9325i	0.299254	+	0.921008i
$339$	18.1305			0.984714
$340$	2.50211	−	0.183426i	0.135696	−	0.00994768i
$341$	24.6621	−	17.9456i	1.33553	−	0.971808i
$342$	−0.855638	−	0.621657i	−0.0462676	−	0.0336154i
$343$	−5.81459	+	17.8955i	−0.313958	+	0.966264i
$344$	22.0237			1.18744
$345$	5.98250	+	14.6650i	0.322087	+	0.789534i
$346$	−9.31177	−	6.76539i	−0.500604	−	0.363710i
$347$	6.50128	+	4.72345i	0.349007	+	0.253568i	0.748452	−	0.663189i	$-0.230797\pi$
$347$	6.50128	+	4.72345i	0.349007	+	0.253568i	−0.399445	+	0.916757i	$0.630797\pi$
$348$	−0.481397	+	1.48159i	−0.0258056	+	0.0794215i
$349$	9.25683	−	6.72548i	0.495507	−	0.360007i	−0.311791	−	0.950151i	$-0.600929\pi$
$349$	9.25683	−	6.72548i	0.495507	−	0.360007i	0.807298	+	0.590144i	$0.200929\pi$
$350$	−12.2763	+	1.80964i	−0.656195	+	0.0967291i
$351$	−5.18459			−0.276733
$352$	3.07721	−	0.00224478i	0.164016	−	0.000119647i
$353$	−16.9363	+	12.3049i	−0.901426	+	0.654924i	−0.938832	−	0.344376i	$-0.888091\pi$
$353$	−16.9363	+	12.3049i	−0.901426	+	0.654924i	0.0374059	+	0.999300i	$0.488091\pi$
$354$	−1.11256	−	3.42410i	−0.0591318	−	0.181989i
$355$	−0.259499	+	1.05592i	−0.0137728	+	0.0560423i
$356$	0.380819	+	1.17204i	0.0201834	+	0.0621180i
$357$	5.75959	+	17.7262i	0.304830	+	0.938170i
$358$	4.67501	−	14.3882i	0.247082	−	0.760440i
$359$	−15.8311	+	11.5020i	−0.835535	+	0.607052i	−0.921120	−	0.389279i	$-0.872724\pi$
$359$	−15.8311	+	11.5020i	−0.835535	+	0.607052i	0.0855845	+	0.996331i	$0.472724\pi$
$360$	0.545234	−	2.21858i	0.0287363	−	0.116930i
$361$	−15.3896			−0.809977
$362$	7.05036	−	21.6988i	0.370559	−	1.14046i
$363$	−5.47909	+	16.9470i	−0.287578	+	0.889486i
$364$	−0.0812379	−	0.250024i	−0.00425802	−	0.0131048i
$365$	31.6725	−	2.32186i	1.65781	−	0.121532i
$366$	8.52170	+	26.2271i	0.445436	+	1.37091i
$367$	−6.12769	−	18.8591i	−0.319863	−	0.984437i	−0.973706	−	0.227807i	$-0.926844\pi$
$367$	−6.12769	−	18.8591i	−0.319863	−	0.984437i	0.653843	−	0.756630i	$-0.273156\pi$
$368$	−5.81525	−	17.8975i	−0.303141	−	0.932971i
$369$	−1.18870	+	3.65843i	−0.0618810	+	0.190450i
$370$	22.2159	+	13.7783i	1.15495	+	0.716301i
$371$	2.89054	−	8.89615i	0.150069	−	0.461865i
$372$	0.756548	+	2.32842i	0.0392252	+	0.120723i
$373$	5.03613	+	15.4996i	0.260761	+	0.802539i	0.992640	+	0.121104i	$0.0386436\pi$
$373$	5.03613	+	15.4996i	0.260761	+	0.802539i	−0.731879	+	0.681435i	$0.761356\pi$
$374$	10.2660	−	31.6740i	0.530841	−	1.63783i
$375$	−11.9767	+	13.5745i	−0.618473	+	0.700984i
$376$	4.41167	−	13.5777i	0.227515	−	0.700218i
$377$	4.48699	+	3.25999i	0.231092	+	0.167898i
$378$	−13.5755			−0.698249
$379$	−18.5572	−	13.4826i	−0.953221	−	0.692556i	−0.00165446	−	0.999999i	$-0.500527\pi$
$379$	−18.5572	−	13.4826i	−0.953221	−	0.692556i	−0.951566	+	0.307443i	$0.900527\pi$
$380$	−0.263875	−	0.646840i	−0.0135365	−	0.0331822i
$381$	−1.79964	−	5.53871i	−0.0921981	−	0.283757i
$382$	−0.166263	+	0.120797i	−0.00850673	+	0.00618050i
$383$	−2.43842	+	1.77162i	−0.124598	+	0.0905255i	−0.648339	−	0.761352i	$-0.724536\pi$
$383$	−2.43842	+	1.77162i	−0.124598	+	0.0905255i	0.523741	+	0.851877i	$0.324536\pi$
$384$	6.25686	−	19.2566i	0.319294	−	0.982686i
$385$	−2.97685	+	12.1512i	−0.151714	+	0.619282i
$386$	7.90821	+	24.3390i	0.402517	+	1.23882i
$387$	2.49623	+	1.81362i	0.126891	+	0.0921915i
$388$	−0.797401	−	2.45415i	−0.0404819	−	0.124591i
$389$	−4.73054	+	14.5591i	−0.239848	+	0.738175i	0.756594	+	0.653886i	$0.226862\pi$
$389$	−4.73054	+	14.5591i	−0.239848	+	0.738175i	−0.996441	+	0.0842900i	$0.973138\pi$
$390$	−4.29040	−	2.66091i	−0.217253	−	0.134740i
$391$	−29.8512			−1.50964
$392$	−3.46677	−	10.6696i	−0.175098	−	0.538897i
$393$	3.40769	−	2.47583i	0.171895	−	0.124889i
$394$	1.96387	−	1.42683i	0.0989382	−	0.0718828i
$395$	−16.1194	+	13.6184i	−0.811053	+	0.685217i
$396$	0.167003	+	0.121149i	0.00839222	+	0.00608795i
$397$	24.5452	−	17.8331i	1.23189	−	0.895017i	0.234856	−	0.972030i	$-0.424538\pi$
$397$	24.5452	−	17.8331i	1.23189	−	0.895017i	0.997030	+	0.0770128i	$0.0245382\pi$
$398$	8.86855			0.444540
$399$	4.19875	−	3.05057i	0.210200	−	0.152720i
$400$	15.3714	−	15.0452i	0.768571	−	0.752260i
$401$	−4.68511	−	14.4193i	−0.233963	−	0.720064i	−0.997257	−	0.0740133i	$-0.976419\pi$
$401$	−4.68511	−	14.4193i	−0.233963	−	0.720064i	0.763294	−	0.646051i	$-0.223581\pi$
$402$	−8.19471	+	5.95381i	−0.408715	+	0.296949i
$403$	8.71626			0.434188
$404$	−0.487292	+	1.49973i	−0.0242437	+	0.0746145i
$405$	−13.1895	+	11.1432i	−0.655394	+	0.553709i
$406$	11.7489	+	8.53607i	0.583087	+	0.423638i
$407$	21.3109	−	15.5070i	1.05634	−	0.768655i
$408$	−24.1389	−	17.5379i	−1.19505	−	0.868256i
$409$	−14.7145	−	10.6907i	−0.727585	−	0.528621i	0.161214	−	0.986920i	$-0.448459\pi$
$409$	−14.7145	−	10.6907i	−0.727585	−	0.528621i	−0.888798	+	0.458298i	$0.848459\pi$
$410$	−25.5497	+	21.5857i	−1.26181	+	1.06604i
$411$	−5.28258	+	16.2581i	−0.260571	+	0.801954i
$412$	0.352558			0.0173693
$413$	−2.54962			−0.125459
$414$	0.752436	−	2.31576i	0.0369802	−	0.113813i
$415$	−14.8203	+	1.08645i	−0.727499	+	0.0533318i
$416$	0.711445	+	0.516895i	0.0348815	+	0.0253429i
$417$	−13.5405	−	9.83774i	−0.663081	−	0.481756i
$418$	−9.27144	+	0.00676339i	−0.453481	+	0.000330808i
$419$	−9.32274	−	6.77337i	−0.455446	−	0.330901i	0.336296	−	0.941756i	$-0.390826\pi$
$419$	−9.32274	−	6.77337i	−0.455446	−	0.330901i	−0.791742	+	0.610856i	$0.790826\pi$
$420$	−0.853407	−	0.529284i	−0.0416420	−	0.0258264i
$421$	−1.14297	+	3.51770i	−0.0557050	+	0.171442i	−0.975038	−	0.222038i	$-0.928729\pi$
$421$	−1.14297	+	3.51770i	−0.0557050	+	0.171442i	0.919333	+	0.393480i	$0.128729\pi$
$422$	−30.5378			−1.48656
$423$	1.61814	−	1.17565i	0.0786767	−	0.0571619i
$424$	4.62730	+	14.2414i	0.224722	+	0.691623i
$425$	−15.1628	−	30.5647i	−0.735504	−	1.48260i
$426$	−0.937121	+	0.680858i	−0.0454037	+	0.0329877i
$427$	19.5289			0.945071
$428$	−0.580773	+	0.421956i	−0.0280727	+	0.0203960i
$429$	−4.11562	+	2.99476i	−0.198704	+	0.144588i
$430$	10.1339	+	24.8413i	0.488700	+	1.19796i
$431$	11.2102	−	8.14466i	0.539974	−	0.392314i	−0.284101	−	0.958794i	$-0.591695\pi$
$431$	11.2102	−	8.14466i	0.539974	−	0.392314i	0.824075	+	0.566480i	$0.191695\pi$
$432$	19.0371	−	13.8312i	0.915922	−	0.665456i
$433$	0.552333	+	1.69991i	0.0265434	+	0.0816923i	0.963451	−	0.267886i	$-0.0863250\pi$
$433$	0.552333	+	1.69991i	0.0265434	+	0.0816923i	−0.936907	+	0.349578i	$0.886325\pi$
$434$	22.8230			1.09554
$435$	21.1292	−	1.54895i	1.01307	−	0.0742665i
$436$	−0.0188696	+	0.0580746i	−0.000903689	+	0.00278127i
$437$	2.56860	+	7.90535i	0.122873	+	0.378164i
$438$	27.3702	+	19.8856i	1.30780	+	0.950170i
$439$	6.10768	+	18.7975i	0.291504	+	0.897156i	0.984373	+	0.176093i	$0.0563461\pi$
$439$	6.10768	+	18.7975i	0.291504	+	0.897156i	−0.692870	+	0.721063i	$0.743654\pi$
$440$	−7.57836	−	18.5382i	−0.361284	−	0.883776i
$441$	0.485693	−	1.49481i	0.0231283	−	0.0711815i
$442$	7.69801	−	5.59293i	0.366157	−	0.266029i
$443$	8.88881	−	6.45809i	0.422320	−	0.306833i	−0.356251	−	0.934390i	$-0.615945\pi$
$443$	8.88881	−	6.45809i	0.422320	−	0.306833i	0.778571	+	0.627557i	$0.215945\pi$
$444$	0.653744	+	2.01202i	0.0310253	+	0.0954861i
$445$	12.8022	−	10.8160i	0.606884	−	0.512726i
$446$	6.69875	+	4.86692i	0.317195	+	0.230456i
$447$	−11.5160			−0.544689
$448$	−9.87888	−	7.17742i	−0.466733	−	0.339101i
$449$	7.55361	−	23.2476i	0.356477	−	1.09712i	−0.598671	−	0.800995i	$-0.704304\pi$
$449$	7.55361	−	23.2476i	0.356477	−	1.09712i	0.955148	−	0.296128i	$-0.0956956\pi$
$450$	2.75330	−	0.405862i	0.129792	−	0.0191325i
$451$	10.4438	+	32.0632i	0.491780	+	1.50980i
$452$	−0.568936	−	1.75100i	−0.0267605	−	0.0823603i
$453$	−4.29033	−	13.2043i	−0.201577	−	0.620392i
$454$	−6.95693	+	21.4112i	−0.326505	+	1.00488i
$455$	−2.73103	+	2.30731i	−0.128032	+	0.108168i
$456$	−2.56741	+	7.90166i	−0.120230	+	0.370029i
$457$	3.38987	+	10.4329i	0.158571	+	0.488032i	0.998505	−	0.0546564i	$-0.0174064\pi$
$457$	3.38987	+	10.4329i	0.158571	+	0.488032i	−0.839934	+	0.542689i	$0.817406\pi$
$458$	12.0402	+	37.0558i	0.562600	+	1.73150i
$459$	−11.5346	−	35.4997i	−0.538387	−	1.65698i
$460$	1.22858	−	1.03796i	0.0572827	−	0.0483952i
$461$	−8.26893	−	25.4492i	−0.385123	−	1.18529i	−0.936391	−	0.350958i	$-0.885856\pi$
$461$	−8.26893	−	25.4492i	−0.385123	−	1.18529i	0.551269	−	0.834328i	$-0.314144\pi$
$462$	−10.7765	+	7.84159i	−0.501367	+	0.364824i
$463$	10.7977	−	33.2318i	0.501811	−	1.54441i	−0.304256	−	0.952590i	$-0.598408\pi$
$463$	10.7977	−	33.2318i	0.501811	−	1.54441i	0.806067	−	0.591824i	$-0.201592\pi$
$464$	−25.1724			−1.16860
$465$	25.4334	−	21.4874i	1.17944	−	0.996453i
$466$	−3.17073	+	2.30367i	−0.146881	+	0.106716i
$467$	−6.50571	+	20.0225i	−0.301048	+	0.926532i	0.680074	+	0.733144i	$0.261948\pi$
$467$	−6.50571	+	20.0225i	−0.301048	+	0.926532i	−0.981122	+	0.193388i	$0.938052\pi$
$468$	0.0182199	+	0.0560751i	0.000842215	+	0.00259207i
$469$	2.21663	+	6.82209i	0.102354	+	0.315015i
$470$	17.3448	−	1.27152i	0.800056	−	0.0586509i
$471$	−1.78482	−	5.49311i	−0.0822402	−	0.253109i
$472$	3.30204	−	2.39907i	0.151989	−	0.110426i
$473$	27.0485	−	0.0197315i	1.24369	−	0.000907256i
$474$	−22.4801			−1.03254
$475$	−6.78958	+	6.64549i	−0.311527	+	0.304916i
$476$	1.53122	−	1.11250i	0.0701834	−	0.0509912i
$477$	−0.648284	+	1.99521i	−0.0296829	+	0.0913546i
$478$	23.8323	+	17.3152i	1.09006	+	0.791978i
$479$	0.825903	+	0.600054i	0.0377365	+	0.0274172i	0.606494	−	0.795088i	$-0.292576\pi$
$479$	0.825903	+	0.600054i	0.0377365	+	0.0274172i	−0.568757	+	0.822506i	$0.692576\pi$
$480$	3.35020	−	0.245598i	0.152915	−	0.0112099i
$481$	7.53184			0.343422
$482$	5.19602	−	15.9917i	0.236672	−	0.728402i
$483$	9.66662	+	7.02321i	0.439846	+	0.319567i
$484$	1.80864	−	0.00263875i	0.0822107	−	0.000119943i
$485$	−26.8068	+	22.6477i	−1.21723	+	1.02838i
$486$	5.74841			0.260753
$487$	9.37285	+	28.8467i	0.424724	+	1.30717i	0.903258	+	0.429098i	$0.141168\pi$
$487$	9.37285	+	28.8467i	0.424724	+	1.30717i	−0.478534	+	0.878069i	$0.658832\pi$
$488$	−25.2922	+	18.3758i	−1.14492	+	0.831835i
$489$	8.29505	−	6.02670i	0.375115	−	0.272537i
$490$	10.4395	−	8.81977i	0.471607	−	0.398437i
$491$	11.0415	−	8.02209i	0.498294	−	0.362032i	−0.310071	−	0.950713i	$-0.600353\pi$
$491$	11.0415	−	8.02209i	0.498294	−	0.362032i	0.808365	+	0.588682i	$0.200353\pi$
$492$	−2.70679			−0.122031
$493$	−12.3391	+	37.9758i	−0.555725	+	1.71035i
$494$	−2.14354	−	1.55737i	−0.0964424	−	0.0700695i
$495$	0.667643	−	2.72525i	0.0300083	−	0.122491i
$496$	−32.0048	+	23.2529i	−1.43706	+	1.04409i
$497$	0.253487	+	0.780152i	0.0113704	+	0.0349946i
$498$	−12.8071	−	9.30493i	−0.573902	−	0.416964i
$499$	25.4426	+	18.4851i	1.13897	+	0.827507i	0.986975	−	0.160875i	$-0.0514317\pi$
$499$	25.4426	+	18.4851i	1.13897	+	0.827507i	0.151990	+	0.988382i	$0.451432\pi$
$500$	1.68682	+	0.730712i	0.0754370	+	0.0326784i
$501$	5.75754	+	17.7199i	0.257228	+	0.791665i
$502$	3.63699	−	11.1935i	0.162327	−	0.499591i
$503$	12.1710	−	37.4586i	0.542680	−	1.67020i	−0.183762	−	0.982971i	$-0.558828\pi$
$503$	12.1710	−	37.4586i	0.542680	−	1.67020i	0.726442	−	0.687227i	$-0.241172\pi$
$504$	−0.532601	−	1.63918i	−0.0237239	−	0.0730147i
$505$	21.3880	−	1.56792i	0.951752	−	0.0697715i
$506$	−6.61086	−	20.2958i	−0.293889	−	0.902256i
$507$	19.5944			0.870220
$508$	−0.478443	+	0.347609i	−0.0212275	+	0.0154227i
$509$	3.99618	+	12.2990i	0.177127	+	0.545142i	0.999724	−	0.0234829i	$-0.00747553\pi$
$509$	3.99618	+	12.2990i	0.177127	+	0.545142i	−0.822597	+	0.568625i	$0.807476\pi$
$510$	8.67448	−	35.2969i	0.384113	−	1.56297i
$511$	19.3826	−	14.0823i	0.857436	−	0.622964i
$512$	19.2428			0.850419
$513$	−8.40871	+	6.10928i	−0.371253	+	0.269731i
$514$	−33.3634	−	24.2399i	−1.47160	−	1.06918i
$515$	−1.81105	−	4.43945i	−0.0798045	−	0.195626i
$516$	−0.670928	+	2.06490i	−0.0295360	+	0.0909024i
$517$	5.40604	−	16.6795i	0.237758	−	0.733563i
$518$	19.7216			0.866519
$519$	−10.2482	+	7.44578i	−0.449848	+	0.326834i
$520$	1.36592	−	5.55799i	0.0598994	−	0.243734i
$521$	−41.1616			−1.80332			−0.901662	−	0.432441i	$-0.857652\pi$
$521$	−41.1616			−1.80332			−0.901662	+	0.432441i	$0.857652\pi$
$522$	−2.63502	−	1.91445i	−0.115332	−	0.0837934i
$523$	1.31731	−	0.957085i	0.0576022	−	0.0418504i	−0.558612	−	0.829429i	$-0.688666\pi$
$523$	1.31731	−	0.957085i	0.0576022	−	0.0418504i	0.616214	+	0.787579i	$0.288666\pi$
$524$	−0.346043	−	0.251415i	−0.0151170	−	0.0109831i
$525$	−2.28095	+	13.4651i	−0.0995486	+	0.587664i
$526$	−11.0768	+	34.0907i	−0.482969	+	1.48643i
$527$	19.3917	+	59.6816i	0.844717	+	2.59977i
$528$	7.12265	−	21.9758i	0.309974	−	0.956374i
$529$	3.12539	−	2.27073i	0.135887	−	0.0987274i
$530$	−13.9342	+	11.7723i	−0.605262	+	0.511355i
$531$	0.571824			0.0248150
$532$	−0.426374	−	0.309779i	−0.0184857	−	0.0134306i
$533$	−2.97791	+	9.16508i	−0.128988	+	0.396984i
$534$	17.8540			0.772620
$535$	8.29669	+	5.14561i	0.358697	+	0.222464i
$536$	−9.29005	−	6.74962i	−0.401269	−	0.291539i
$537$	−13.4702	−	9.78669i	−0.581283	−	0.422327i
$538$	−0.898774	+	2.76614i	−0.0387489	+	0.119257i
$539$	−4.26728	−	13.1008i	−0.183805	−	0.564292i
$540$	1.70909	+	1.05998i	0.0735476	+	0.0456143i
$541$	2.05346	+	1.49193i	0.0882851	+	0.0641429i	0.631052	−	0.775740i	$-0.282623\pi$
$541$	2.05346	+	1.49193i	0.0882851	+	0.0641429i	−0.542767	+	0.839883i	$0.682623\pi$
$542$	−24.1187			−1.03599
$543$	−20.3144	−	14.7593i	−0.871774	−	0.633381i
$544$	−1.95646	+	6.02135i	−0.0838823	+	0.258163i
$545$	0.828213	−	0.0607150i	0.0354768	−	0.00260075i
$546$	−3.80870			−0.162997
$547$	4.20257	−	12.9342i	0.179689	−	0.553025i	−0.820128	−	0.572180i	$-0.806098\pi$
$547$	4.20257	−	12.9342i	0.179689	−	0.553025i	0.999817	+	0.0191553i	$0.00609770\pi$
$548$	1.73594			0.0741557
$549$	−4.37992			−0.186930
$550$	17.4229	−	17.0780i	0.742914	−	0.728210i
$551$	11.1187			0.473673
$552$	−19.1279			−0.814137
$553$	−4.91944	+	15.1405i	−0.209196	+	0.643838i
$554$	−15.7096			−0.667437
$555$	21.9773	−	18.5675i	0.932886	−	0.788148i
$556$	−0.525206	+	1.61642i	−0.0222737	+	0.0685514i
$557$	−20.7994	−	15.1117i	−0.881299	−	0.640301i	0.0522956	−	0.998632i	$-0.483346\pi$
$557$	−20.7994	−	15.1117i	−0.881299	−	0.640301i	−0.933595	+	0.358330i	$0.883346\pi$
$558$	−5.11870			−0.216692
$559$	6.25356	+	4.54348i	0.264497	+	0.192169i
$560$	3.87260	−	15.7578i	0.163647	−	0.665889i
$561$	−29.6619	−	21.5176i	−1.25233	−	0.908474i
$562$	−0.486870	+	1.49843i	−0.0205374	+	0.0632076i
$563$	−32.0544	−	23.2889i	−1.35093	−	0.981509i	−0.998965	−	0.0454958i	$-0.985513\pi$
$563$	−32.0544	−	23.2889i	−1.35093	−	0.981509i	−0.351966	−	0.936013i	$-0.614487\pi$
$564$	1.13863	+	0.827262i	0.0479449	+	0.0348340i
$565$	−19.1263	+	16.1588i	−0.804649	+	0.679807i
$566$	−6.66065			−0.279968
$567$	−4.02529	+	12.3886i	−0.169046	+	0.520271i
$568$	−1.06238	−	0.771865i	−0.0445765	−	0.0323867i
$569$	24.2874			1.01818			0.509090	−	0.860713i	$-0.329982\pi$
$569$	24.2874			1.01818			0.509090	+	0.860713i	$0.329982\pi$
$570$	−10.0939	+	0.739971i	−0.422788	+	0.0309940i
$571$	5.39394	−	3.91893i	0.225730	−	0.164002i	−0.469172	−	0.883107i	$-0.655448\pi$
$571$	5.39394	−	3.91893i	0.225730	−	0.164002i	0.694902	+	0.719104i	$0.255448\pi$
$572$	0.418375	+	0.303501i	0.0174931	+	0.0126900i
$573$	0.0698935	+	0.215110i	0.00291984	+	0.00898635i
$574$	−7.79748	+	23.9982i	−0.325460	+	1.00166i
$575$	−19.3812	−	10.1385i	−0.808252	−	0.422804i
$576$	2.21562	+	1.60974i	0.0923174	+	0.0670725i
$577$	−27.6032	+	20.0549i	−1.14914	+	0.834897i	−0.988366	−	0.152095i	$-0.951398\pi$
$577$	−27.6032	+	20.0549i	−1.14914	+	0.834897i	−0.160771	+	0.986992i	$0.551398\pi$
$578$	35.1882	+	25.5657i	1.46364	+	1.06339i
$579$	28.1652			1.17051
$580$	−0.812629	−	1.99201i	−0.0337426	−	0.0827136i
$581$	−9.06958	+	6.58943i	−0.376270	+	0.273376i
$582$	−37.3848			−1.54965
$583$	5.69580	+	17.4864i	0.235896	+	0.724214i
$584$	−11.8519	+	36.4763i	−0.490434	+	1.50940i
$585$	0.612510	−	0.517478i	0.0253242	−	0.0213951i
$586$	6.09835	+	4.43071i	0.251920	+	0.183031i
$587$	21.6515	−	15.7308i	0.893654	−	0.649278i	−0.0431741	−	0.999068i	$-0.513747\pi$
$587$	21.6515	−	15.7308i	0.893654	−	0.649278i	0.936828	+	0.349790i	$0.113747\pi$
$588$	1.10598			0.0456097
$589$	14.1366	−	10.2708i	0.582488	−	0.423202i
$590$	4.22539	+	2.62059i	0.173957	+	0.107888i
$591$	−0.825571	−	2.54085i	−0.0339594	−	0.104516i
$592$	−27.6558	+	20.0931i	−1.13665	+	0.825823i
$593$	−21.0759			−0.865482			−0.432741	−	0.901518i	$-0.642453\pi$
$593$	−21.0759			−0.865482			−0.432741	+	0.901518i	$0.642453\pi$
$594$	21.5817	−	15.7041i	0.885509	−	0.644347i
$595$	−21.8744	−	13.5665i	−0.896763	−	0.556173i
$596$	0.361373	+	1.11219i	0.0148024	+	0.0455571i
$597$	3.01614	−	9.28274i	0.123443	−	0.379917i
$598$	1.88500	−	5.80143i	0.0770833	−	0.237238i
$599$	5.25028	+	16.1587i	0.214521	+	0.660226i	0.999187	+	0.0403085i	$0.0128341\pi$
$599$	5.25028	+	16.1587i	0.214521	+	0.660226i	−0.784667	+	0.619918i	$0.787166\pi$
$600$	−9.71594	−	19.5851i	−0.396652	−	0.799557i
$601$	9.66176	+	7.01968i	0.394112	+	0.286339i	0.767138	−	0.641482i	$-0.221680\pi$
$601$	9.66176	+	7.01968i	0.394112	+	0.286339i	−0.373027	+	0.927821i	$0.621680\pi$
$602$	16.3745	+	11.8968i	0.667376	+	0.484877i
$603$	−0.497142	−	1.53005i	−0.0202452	−	0.0623083i
$604$	−1.14061	+	0.828701i	−0.0464108	+	0.0337194i
$605$	−9.32400	−	22.7610i	−0.379074	−	0.925366i
$606$	18.4827	+	13.4285i	0.750808	+	0.545494i
$607$	11.4655	−	35.2871i	0.465369	−	1.43226i	−0.393149	−	0.919475i	$-0.628614\pi$
$607$	11.4655	−	35.2871i	0.465369	−	1.43226i	0.858518	−	0.512783i	$-0.171386\pi$
$608$	1.76295			0.0714972
$609$	12.9305	−	9.39453i	0.523969	−	0.380686i
$610$	−32.3646	−	20.0726i	−1.31041	−	0.812715i
$611$	4.05376	−	2.94523i	0.163998	−	0.119151i
$612$	−0.343419	+	0.249509i	−0.0138819	+	0.0100858i
$613$	−1.44321	−	4.44174i	−0.0582907	−	0.179400i	0.917672	−	0.397340i	$-0.130066\pi$
$613$	−1.44321	−	4.44174i	−0.0582907	−	0.179400i	−0.975962	+	0.217939i	$0.930066\pi$
$614$	32.7248			1.32066
$615$	13.9045	+	34.0842i	0.560682	+	1.37441i
$616$	−12.2299	−	8.87190i	−0.492756	−	0.357459i
$617$	2.82287	+	2.05094i	0.113645	+	0.0825676i	0.643156	−	0.765735i	$-0.277625\pi$
$617$	2.82287	+	2.05094i	0.113645	+	0.0825676i	−0.529511	+	0.848303i	$0.677625\pi$
$618$	1.57839	−	4.85777i	0.0634920	−	0.195408i
$619$	−39.6013			−1.59171			−0.795856	−	0.605487i	$-0.792979\pi$
$619$	−39.6013			−1.59171			−0.795856	+	0.605487i	$0.792979\pi$
$620$	−2.87330	−	1.78202i	−0.115395	−	0.0715678i
$621$	−19.3590	−	14.0652i	−0.776852	−	0.564416i
$622$	23.8466	+	17.3256i	0.956163	+	0.694693i
$623$	3.90709	−	12.0248i	0.156534	−	0.481763i
$624$	5.34097	−	3.88044i	0.213810	−	0.155342i
$625$	0.536185	−	24.9942i	0.0214474	−	0.999770i
$626$	−19.6212			−0.784220
$627$	−3.14609	+	9.70675i	−0.125643	+	0.387650i
$628$	−0.474505	+	0.344748i	−0.0189348	+	0.0137569i
$629$	16.7567	+	51.5717i	0.668131	+	2.05630i
$630$	1.60382	−	1.35498i	0.0638976	−	0.0539839i
$631$	−12.0653	−	37.1333i	−0.480314	−	1.47825i	−0.838655	−	0.544663i	$-0.816658\pi$
$631$	−12.0653	−	37.1333i	−0.480314	−	1.47825i	0.358342	−	0.933591i	$-0.383342\pi$
$632$	−7.87526	−	24.2376i	−0.313261	−	0.964119i
$633$	−10.3858	+	31.9641i	−0.412797	+	1.27046i
$634$	34.6619	−	25.1834i	1.37660	−	1.00016i
$635$	6.83485	+	4.23898i	0.271233	+	0.168219i
$636$	−1.47621			−0.0585357
$637$	1.21676	−	3.74479i	0.0482097	−	0.148374i
$638$	−28.5523	+	0.0208285i	−1.13040	+	0.000824610i
$639$	−0.0568516	−	0.174971i	−0.00224901	−	0.00692175i
$640$	10.5620	+	25.8907i	0.417499	+	1.02342i
$641$	−10.0748	−	31.0070i	−0.397930	−	1.22470i	−0.926656	−	0.375911i	$-0.877330\pi$
$641$	−10.0748	−	31.0070i	−0.397930	−	1.22470i	0.528726	−	0.848793i	$-0.322670\pi$
$642$	3.21389	+	9.89134i	0.126842	+	0.390380i
$643$	−4.64111	−	14.2839i	−0.183028	−	0.563301i	0.816881	−	0.576806i	$-0.195701\pi$
$643$	−4.64111	−	14.2839i	−0.183028	−	0.563301i	−0.999909	+	0.0135050i	$0.995701\pi$
$644$	0.374947	−	1.15397i	0.0147750	−	0.0454727i
$645$	29.4480	−	2.15879i	1.15951	−	0.0850022i
$646$	5.89468	−	18.1420i	0.231923	−	0.713786i
$647$	5.04387	+	15.5234i	0.198295	+	0.610289i	0.999922	+	0.0124652i	$0.00396790\pi$
$647$	5.04387	+	15.5234i	0.198295	+	0.610289i	−0.801627	+	0.597824i	$0.796032\pi$
$648$	−6.44388	−	19.8322i	−0.253139	−	0.779083i
$649$	4.05326	−	2.94939i	0.159104	−	0.115774i
$650$	6.89757	−	1.01676i	0.270545	−	0.0398808i
$651$	7.76197	−	23.8889i	0.304215	−	0.936279i
$652$	−0.842344	−	0.611999i	−0.0329887	−	0.0239677i
$653$	25.8180			1.01034			0.505169	−	0.863020i	$-0.331430\pi$
$653$	25.8180			1.01034			0.505169	+	0.863020i	$0.331430\pi$
$654$	0.715711	+	0.519995i	0.0279865	+	0.0203334i
$655$	−1.38826	+	5.64891i	−0.0542439	+	0.220721i
$656$	−13.5158	−	41.5972i	−0.527702	−	1.62410i
$657$	−4.34710	+	3.15835i	−0.169596	+	0.123219i
$658$	10.6145	−	7.71189i	0.413797	−	0.300641i
$659$	−13.3566	+	41.1075i	−0.520301	+	1.60132i	0.253124	+	0.967434i	$0.418542\pi$
$659$	−13.3566	+	41.1075i	−0.520301	+	1.60132i	−0.773425	+	0.633888i	$0.781458\pi$
$660$	1.96898	−	0.145787i	0.0766425	−	0.00567475i
$661$	−7.91853	−	24.3707i	−0.307995	−	0.947912i	−0.978543	−	0.206045i	$-0.933941\pi$
$661$	−7.91853	−	24.3707i	−0.307995	−	0.947912i	0.670547	−	0.741867i	$-0.266059\pi$
$662$	−38.3085	−	27.8328i	−1.48890	−	1.08175i
$663$	−3.23609	−	9.95966i	−0.125679	−	0.386801i
$664$	5.54577	−	17.0681i	0.215217	−	0.662371i
$665$	−1.71053	+	6.96025i	−0.0663317	+	0.269907i
$666$	−4.42314			−0.171393
$667$	7.91027	+	24.3453i	0.306287	+	0.942654i
$668$	1.53067	−	1.11210i	0.0592235	−	0.0430284i
$669$	7.37243	−	5.35639i	0.285035	−	0.207090i
$670$	3.33845	−	13.5843i	0.128976	−	0.524809i
$671$	−31.0462	+	22.5910i	−1.19852	+	0.872115i
$672$	2.05022	−	1.48957i	0.0790890	−	0.0574615i
$673$	−44.1292			−1.70105			−0.850527	−	0.525931i	$-0.823717\pi$
$673$	−44.1292			−1.70105			−0.850527	+	0.525931i	$0.823717\pi$
$674$	−2.17892	+	1.58308i	−0.0839290	+	0.0609780i
$675$	4.56798	−	26.9661i	0.175822	−	1.03793i
$676$	−0.614874	−	1.89239i	−0.0236490	−	0.0727841i
$677$	−2.05829	+	1.49543i	−0.0791064	+	0.0574742i	−0.626636	−	0.779312i	$-0.715569\pi$
$677$	−2.05829	+	1.49543i	−0.0791064	+	0.0574742i	0.547529	+	0.836787i	$0.315569\pi$
$678$	−26.6736			−1.02439
$679$	−8.18111	+	25.1789i	−0.313962	+	0.966276i
$680$	41.0953	−	3.01263i	1.57593	−	0.115529i
$681$	20.0452	+	14.5637i	0.768133	+	0.558081i
$682$	−36.2829	+	26.4015i	−1.38934	+	1.01097i
$683$	−8.95495	−	6.50616i	−0.342652	−	0.248951i	0.403128	−	0.915144i	$-0.367923\pi$
$683$	−8.95495	−	6.50616i	−0.342652	−	0.248951i	−0.745780	+	0.666192i	$0.767923\pi$
$684$	0.0956264	+	0.0694767i	0.00365637	+	0.00265651i
$685$	−8.91734	−	21.8592i	−0.340714	−	0.835196i
$686$	8.55441	−	26.3278i	0.326609	−	1.00520i
$687$	42.8812			1.63602
$688$	−35.0831			−1.33753
$689$	−1.62408	+	4.99840i	−0.0618725	+	0.190424i
$690$	−8.80143	−	21.5750i	−0.335065	−	0.821348i
$691$	26.1608	+	19.0069i	0.995202	+	0.723057i	0.961054	−	0.276360i	$-0.0891282\pi$
$691$	26.1608	+	19.0069i	0.995202	+	0.723057i	0.0341481	+	0.999417i	$0.489128\pi$
$692$	1.04069	+	0.756103i	0.0395610	+	0.0287427i
$693$	−0.655583	−	2.01268i	−0.0249036	−	0.0764554i
$694$	−9.56466	−	6.94913i	−0.363069	−	0.263785i
$695$	23.0521	−	1.68991i	0.874414	−	0.0641020i
$696$	−7.90658	+	24.3339i	−0.299698	+	0.922376i
$697$	−69.3799			−2.62795
$698$	−13.6186	+	9.89451i	−0.515472	+	0.374513i
$699$	1.33291	+	4.10228i	0.0504154	+	0.155163i
$700$	1.37200	−	0.202246i	0.0518568	−	0.00764417i
$701$	−4.04814	+	2.94114i	−0.152896	+	0.111085i	−0.661603	−	0.749854i	$-0.730124\pi$
$701$	−4.04814	+	2.94114i	−0.152896	+	0.111085i	0.508707	+	0.860940i	$0.330124\pi$
$702$	7.62756			0.287884
$703$	12.2156	−	8.87517i	0.460721	−	0.334733i
$704$	24.0078	−	0.0175134i	0.904827	−	0.000660060i
$705$	4.56797	−	18.5873i	0.172040	−	0.700038i
$706$	24.9166	−	18.1030i	0.937748	−	0.681314i
$707$	13.0888	−	9.50958i	0.492255	−	0.357644i
$708$	0.124340	+	0.382679i	0.00467298	+	0.0143820i
$709$	11.4829			0.431248			0.215624	−	0.976476i	$-0.430821\pi$
$709$	11.4829			0.431248			0.215624	+	0.976476i	$0.430821\pi$
$710$	0.381775	−	1.55346i	0.0143278	−	0.0583004i
$711$	1.10332	−	3.39568i	0.0413778	−	0.127348i
$712$	6.25466	+	19.2499i	0.234403	+	0.721419i
$713$	32.5461	+	23.6461i	1.21886	+	0.885555i
$714$	−8.47349	−	26.0787i	−0.317113	−	0.975972i
$715$	1.67258	−	6.82728i	0.0625508	−	0.255326i
$716$	−0.522481	+	1.60803i	−0.0195260	+	0.0600949i
$717$	26.2291	−	19.0566i	0.979544	−	0.711680i
$718$	23.2907	−	16.9217i	0.869202	−	0.631512i
$719$	−1.44749	−	4.45492i	−0.0539823	−	0.166140i	0.920431	−	0.390906i	$-0.127838\pi$
$719$	−1.44749	−	4.45492i	−0.0539823	−	0.166140i	−0.974413	+	0.224766i	$0.927838\pi$
$720$	−0.868540	+	3.53414i	−0.0323686	+	0.131709i
$721$	−2.92633	−	2.12610i	−0.108982	−	0.0791802i
$722$	22.6411			0.842614
$723$	−14.9714	−	10.8774i	−0.556794	−	0.404534i
$724$	−0.787951	+	2.42506i	−0.0292840	+	0.0901268i
$725$	−20.9092	+	20.4654i	−0.776548	+	0.760067i
$726$	8.06082	−	24.9324i	0.299165	−	0.925327i
$727$	−0.492530	−	1.51585i	−0.0182669	−	0.0562198i	0.941508	−	0.336992i	$-0.109410\pi$
$727$	−0.492530	−	1.51585i	−0.0182669	−	0.0562198i	−0.959774	+	0.280772i	$0.909410\pi$
$728$	−1.33427	−	4.10646i	−0.0494513	−	0.152195i
$729$	9.11355	−	28.0486i	0.337539	−	1.03884i
$730$	−46.5964	+	3.41591i	−1.72461	+	0.126429i
$731$	−17.1971	+	52.9273i	−0.636059	+	1.95759i
$732$	−0.952388	−	2.93115i	−0.0352013	−	0.108338i
$733$	−2.42864	−	7.47460i	−0.0897040	−	0.276080i	0.896133	−	0.443785i	$-0.146365\pi$
$733$	−2.42864	−	7.47460i	−0.0897040	−	0.276080i	−0.985837	+	0.167704i	$0.946365\pi$
$734$	9.01505	+	27.7455i	0.332752	+	1.02410i
$735$	−5.68128	−	13.9266i	−0.209557	−	0.513690i
$736$	1.25423	+	3.86013i	0.0462316	+	0.142286i
$737$	−11.4157	−	8.28124i	−0.420501	−	0.305043i
$738$	1.74881	−	5.38227i	0.0643744	−	0.198124i
$739$	27.6826			1.01832			0.509161	−	0.860671i	$-0.329956\pi$
$739$	27.6826			1.01832			0.509161	+	0.860671i	$0.329956\pi$
$740$	−2.48286	−	1.53987i	−0.0912717	−	0.0566068i
$741$	−2.35911	+	1.71400i	−0.0866642	+	0.0629652i
$742$	−4.25255	+	13.0880i	−0.156116	+	0.480476i
$743$	−0.244413	−	0.752226i	−0.00896665	−	0.0275965i	0.946473	−	0.322783i	$-0.104618\pi$
$743$	−0.244413	−	0.752226i	−0.00896665	−	0.0275965i	−0.955440	+	0.295186i	$0.904618\pi$
$744$	12.4257	+	38.2424i	0.455549	+	1.40204i
$745$	12.1485	−	10.2637i	0.445087	−	0.376031i
$746$	−7.40913	−	22.8030i	−0.271268	−	0.834876i
$747$	2.03411	−	1.47787i	0.0744242	−	0.0540723i
$748$	−1.14733	+	3.53990i	−0.0419505	+	0.129432i
$749$	7.36519			0.269118
$750$	17.6200	−	19.9708i	0.643393	−	0.729229i
$751$	6.50352	−	4.72508i	0.237317	−	0.172421i	−0.462770	−	0.886478i	$-0.653145\pi$
$751$	6.50352	−	4.72508i	0.237317	−	0.172421i	0.700087	+	0.714058i	$0.253145\pi$
$752$	−7.02766	+	21.6289i	−0.256272	+	0.788725i
$753$	−10.4794	−	7.61371i	−0.381890	−	0.277459i
$754$	−6.60124	−	4.79608i	−0.240403	−	0.174663i
$755$	16.2943	+	10.1057i	0.593010	+	0.367785i
$756$	1.51721			0.0551803
$757$	−14.8507	+	45.7058i	−0.539758	+	1.66120i	0.193380	+	0.981124i	$0.438055\pi$
$757$	−14.8507	+	45.7058i	−0.539758	+	1.66120i	−0.733138	+	0.680080i	$0.761945\pi$
$758$	27.3013	+	19.8356i	0.991630	+	0.720461i
$759$	−23.4920	+	0.0171371i	−0.852704	+	0.000622036i
$760$	−4.33394	−	10.6238i	−0.157209	−	0.385367i
$761$	−11.0632			−0.401041			−0.200520	−	0.979690i	$-0.564263\pi$
$761$	−11.0632			−0.401041			−0.200520	+	0.979690i	$0.564263\pi$
$762$	2.64762	+	8.14853i	0.0959131	+	0.295190i
$763$	0.506842	−	0.368242i	0.0183489	−	0.0133313i
$764$	0.0185816	−	0.0135003i	0.000672258	−	0.000488424i
$765$	4.90595	+	3.04268i	0.177375	+	0.110008i
$766$	3.58740	−	2.60640i	0.129618	−	0.0941731i
$767$	1.43253			0.0517257
$768$	−1.96145	+	6.03671i	−0.0707776	+	0.217831i
$769$	12.3494	+	8.97233i	0.445329	+	0.323551i	0.787749	−	0.615997i	$-0.211246\pi$
$769$	12.3494	+	8.97233i	0.445329	+	0.323551i	−0.342420	+	0.939547i	$0.611246\pi$
$770$	4.37953	−	17.8768i	0.157827	−	0.644235i
$771$	−36.7187	+	26.6777i	−1.32239	+	0.960775i
$772$	−0.883825	−	2.72013i	−0.0318095	−	0.0978997i
$773$	21.7663	+	15.8141i	0.782878	+	0.568794i	0.905841	−	0.423617i	$-0.139240\pi$
$773$	21.7663	+	15.8141i	0.782878	+	0.568794i	−0.122964	+	0.992411i	$0.539240\pi$
$774$	−3.67245	−	2.66819i	−0.132004	−	0.0959063i
$775$	−7.67962	+	45.3350i	−0.275860	+	1.62848i
$776$	−13.0967	−	40.3075i	−0.470144	−	1.44695i
$777$	6.70722	−	20.6427i	0.240620	−	0.740553i
$778$	6.95955	−	21.4193i	0.249512	−	0.767919i
$779$	5.96993	+	18.3736i	0.213895	+	0.658301i
$780$	0.479496	+	0.297384i	0.0171687	+	0.0106481i
$781$	−1.30546	−	0.947017i	−0.0467130	−	0.0338869i
$782$	43.9170			1.57047
$783$	−25.8954	+	18.8141i	−0.925427	+	0.672362i
$784$	5.52245	+	16.9964i	0.197230	+	0.607013i
$785$	6.77859	+	4.20409i	0.241938	+	0.150050i
$786$	−5.01338	+	3.64243i	−0.178821	+	0.129921i
$787$	−21.8474			−0.778774			−0.389387	−	0.921074i	$-0.627313\pi$
$787$	−21.8474			−0.778774			−0.389387	+	0.921074i	$0.627313\pi$
$788$	−0.219483	+	0.159464i	−0.00781875	+	0.00568065i
$789$	31.9157	+	23.1881i	1.13623	+	0.825520i
$790$	23.7148	−	20.0354i	0.843733	−	0.712827i
$791$	−5.83712	+	17.9648i	−0.207544	+	0.638755i
$792$	2.74289	+	1.98977i	0.0974645	+	0.0707036i
$793$	−10.9725			−0.389647
$794$	−36.1108	+	26.2360i	−1.28152	+	0.931081i
$795$	7.58315	+	18.5886i	0.268947	+	0.659271i
$796$	−0.991153			−0.0351305
$797$	−0.864770	−	0.628292i	−0.0306317	−	0.0222552i	0.572364	−	0.820000i	$-0.306026\pi$
$797$	−0.864770	−	0.628292i	−0.0306317	−	0.0222552i	−0.602996	+	0.797744i	$0.706026\pi$
$798$	−6.17719	+	4.48799i	−0.218670	+	0.158873i
$799$	29.1851	+	21.2042i	1.03250	+	0.750152i
$800$	−3.31531	+	3.24495i	−0.117214	+	0.114726i
$801$	−0.876276	+	2.69690i	−0.0309617	+	0.0952903i
$802$	6.89272	+	21.2136i	0.243390	+	0.749078i
$803$	−14.5232	+	44.8091i	−0.512513	+	1.58128i
$804$	0.915844	−	0.665400i	0.0322993	−	0.0234668i
$805$	−16.4570	+	1.20644i	−0.580032	+	0.0425213i
$806$	−12.8233			−0.451683
$807$	2.58966	+	1.88150i	0.0911605	+	0.0662319i
$808$	−8.00340	+	24.6319i	−0.281559	+	0.866548i
$809$	0.736212			0.0258838			0.0129419	−	0.999916i	$-0.495880\pi$
$809$	0.736212			0.0258838			0.0129419	+	0.999916i	$0.495880\pi$
$810$	19.4044	−	16.3938i	0.681802	−	0.576020i
$811$	15.0638	+	10.9445i	0.528963	+	0.384314i	0.819970	−	0.572407i	$-0.193990\pi$
$811$	15.0638	+	10.9445i	0.528963	+	0.384314i	−0.291007	+	0.956721i	$0.593990\pi$
$812$	−1.31306	−	0.953994i	−0.0460794	−	0.0334786i
$813$	−8.20263	+	25.2451i	−0.287679	+	0.885384i
$814$	−31.3525	+	22.8139i	−1.09891	+	0.799627i
$815$	−3.37933	+	13.7507i	−0.118373	+	0.481665i
$816$	38.4524	+	27.9373i	1.34610	+	0.978002i
$817$	15.4962			0.542145
$818$	21.6479	+	15.7281i	0.756902	+	0.549921i
$819$	0.186931	−	0.575314i	0.00653189	−	0.0201031i
$820$	2.85545	−	2.41242i	0.0997166	−	0.0842455i
$821$	−0.210293			−0.00733926			−0.00366963	−	0.999993i	$-0.501168\pi$
$821$	−0.210293			−0.00733926			−0.00366963	+	0.999993i	$0.501168\pi$
$822$	7.77172	−	23.9189i	0.271070	−	0.834268i
$823$	21.9389			0.764741			0.382370	−	0.924009i	$-0.375108\pi$
$823$	21.9389			0.764741			0.382370	+	0.924009i	$0.375108\pi$
$824$	5.79049			0.201721
$825$	−11.9502	−	24.0447i	−0.416053	−	0.837130i
$826$	3.75099			0.130514
$827$	−33.8781			−1.17806			−0.589029	−	0.808112i	$-0.700490\pi$
$827$	−33.8781			−1.17806			−0.589029	+	0.808112i	$0.700490\pi$
$828$	−0.0840925	+	0.258810i	−0.00292242	+	0.00899427i
$829$	35.4855			1.23246			0.616231	−	0.787565i	$-0.288659\pi$
$829$	35.4855			1.23246			0.616231	+	0.787565i	$0.288659\pi$
$830$	21.8036	−	1.59839i	0.756813	−	0.0554808i
$831$	−5.34275	+	16.4433i	−0.185338	+	0.570412i
$832$	5.55056	+	4.03272i	0.192431	+	0.139809i
$833$	28.3482			0.982207
$834$	19.9207	+	14.4733i	0.689799	+	0.501168i
$835$	−21.8666	−	13.5617i	−0.756725	−	0.469321i
$836$	1.03618		0.000755880i	0.0358370		2.61427e-5i
$837$	−15.5446	+	47.8415i	−0.537302	+	1.65364i
$838$	13.7156	+	9.96496i	0.473797	+	0.344234i
$839$	−44.2447	−	32.1456i	−1.52750	−	1.10979i	−0.957610	−	0.288067i	$-0.906987\pi$
$839$	−44.2447	−	32.1456i	−1.52750	−	1.10979i	−0.569886	−	0.821724i	$-0.693013\pi$
$840$	−14.0166	−	8.69308i	−0.483617	−	0.299940i
$841$	5.24113			0.180729
$842$	1.68154	−	5.17524i	0.0579496	−	0.178350i
$843$	1.40283	+	1.01922i	0.0483161	+	0.0351037i
$844$	3.41292			0.117478
$845$	−20.6706	+	17.4635i	−0.711091	+	0.600764i
$846$	−2.38060	+	1.72961i	−0.0818468	+	0.0594652i
$847$	−15.0281	−	10.8851i	−0.516372	−	0.374016i
$848$	−7.37115	−	22.6861i	−0.253126	−	0.779043i
$849$	−2.26525	+	6.97173i	−0.0777432	+	0.239269i
$850$	22.3075	+	44.9667i	0.765140	+	1.54234i
$851$	28.1236	+	20.4330i	0.964063	+	0.700433i
$852$	0.104733	−	0.0760930i	0.00358810	−	0.00260690i
$853$	9.47489	+	6.88391i	0.324414	+	0.235700i	0.738057	−	0.674739i	$-0.235744\pi$
$853$	9.47489	+	6.88391i	0.324414	+	0.235700i	−0.413643	+	0.910439i	$0.635744\pi$
$854$	−28.7309			−0.983152
$855$	0.383636	−	1.56103i	0.0131201	−	0.0533862i
$856$	−9.53874	+	6.93030i	−0.326027	+	0.236873i
$857$	19.0515			0.650787			0.325393	−	0.945579i	$-0.394503\pi$
$857$	19.0515			0.650787			0.325393	+	0.945579i	$0.394503\pi$
$858$	6.05488	−	4.40588i	0.206710	−	0.150414i
$859$	14.1164	−	43.4458i	0.481645	−	1.48235i	−0.355136	−	0.934815i	$-0.615565\pi$
$859$	14.1164	−	43.4458i	0.481645	−	1.48235i	0.836781	−	0.547537i	$-0.184435\pi$
$860$	−1.13257	−	2.77628i	−0.0386203	−	0.0946703i
$861$	22.4671	+	16.3233i	0.765676	+	0.556296i
$862$	−16.4924	+	11.9824i	−0.561732	+	0.408122i
$863$	36.9522			1.25787			0.628934	−	0.777459i	$-0.283491\pi$
$863$	36.9522			1.25787			0.628934	+	0.777459i	$0.283491\pi$
$864$	−4.10591	+	2.98312i	−0.139686	+	0.101488i
$865$	4.17504	−	16.9885i	0.141956	−	0.577625i
$866$	−0.812591	−	2.50090i	−0.0276130	−	0.0849839i
$867$	38.7271	−	28.1369i	1.31524	−	0.955578i
$868$	−2.55070			−0.0865765
$869$	−9.69374	−	29.7604i	−0.328838	−	1.00955i
$870$	−31.0853	+	2.27881i	−1.05389	+	0.0772589i
$871$	−1.24544	−	3.83306i	−0.0422001	−	0.129878i
$872$	−0.309918	+	0.953831i	−0.0104952	+	0.0323008i
$873$	1.83484	−	5.64707i	0.0621001	−	0.191124i
$874$	−3.77892	−	11.6303i	−0.127824	−	0.393402i
$875$	−9.59453	−	16.2375i	−0.324354	−	0.548928i
$876$	−3.05890	−	2.22242i	−0.103351	−	0.0750887i
$877$	−37.2290	−	27.0484i	−1.25713	−	0.913360i	−0.258519	−	0.966006i	$-0.583235\pi$
$877$	−37.2290	−	27.0484i	−1.25713	−	0.913360i	−0.998613	+	0.0526459i	$0.983235\pi$
$878$	−8.98560	−	27.6548i	−0.303249	−	0.933306i
$879$	6.71165	−	4.87630i	0.226378	−	0.164474i
$880$	12.0721	+	29.5308i	0.406950	+	0.995484i
$881$	44.8551	+	32.5892i	1.51121	+	1.09796i	0.965638	+	0.259892i	$0.0836869\pi$
$881$	44.8551	+	32.5892i	1.51121	+	1.09796i	0.545570	+	0.838065i	$0.316313\pi$
$882$	−0.714551	+	2.19916i	−0.0240602	+	0.0740496i
$883$	24.3065			0.817978			0.408989	−	0.912539i	$-0.365881\pi$
$883$	24.3065			0.817978			0.408989	+	0.912539i	$0.365881\pi$
$884$	−0.860333	+	0.625069i	−0.0289361	+	0.0210233i
$885$	4.18002	−	3.53148i	0.140510	−	0.118710i
$886$	−13.0772	+	9.50113i	−0.439337	+	0.319197i
$887$	−27.9263	+	20.2897i	−0.937674	+	0.681260i	−0.947860	−	0.318688i	$-0.896758\pi$
$887$	−27.9263	+	20.2897i	−0.937674	+	0.681260i	0.0101854	+	0.999948i	$0.496758\pi$
$888$	10.7372	+	33.0458i	0.360318	+	1.10894i
$889$	6.06747			0.203497
$890$	−18.8346	+	15.9124i	−0.631338	+	0.533385i
$891$	−7.93183	−	24.3512i	−0.265726	−	0.815796i
$892$	−0.748655	−	0.543929i	−0.0250668	−	0.0182121i
$893$	3.10413	−	9.55352i	0.103876	−	0.319696i
$894$	16.9423			0.566636
$895$	22.9324	−	1.68114i	0.766547	−	0.0561944i
$896$	17.0662	+	12.3993i	0.570143	+	0.414233i
$897$	−5.43130	−	3.94607i	−0.181346	−	0.131755i
$898$	−11.1129	+	34.2018i	−0.370841	+	1.14133i
$899$	43.5350	−	31.6300i	1.45197	−	1.05492i
$900$	−0.307711	+	0.0453593i	−0.0102570	+	0.00151198i
$901$	−37.8381			−1.26057
$902$	−15.3649	−	47.1712i	−0.511596	−	1.57063i
$903$	18.0213	−	13.0933i	0.599712	−	0.435716i
$904$	−9.34433	−	28.7589i	−0.310788	−	0.956506i
$905$	34.5843	−	2.53532i	1.14962	−	0.0842770i
$906$	6.31193	+	19.4261i	0.209700	+	0.645389i
$907$	−7.98686	−	24.5810i	−0.265199	−	0.816199i	−0.991647	−	0.128978i	$-0.958830\pi$
$907$	−7.98686	−	24.5810i	−0.265199	−	0.816199i	0.726448	−	0.687221i	$-0.241170\pi$
$908$	0.777509	−	2.39293i	0.0258025	−	0.0794121i
$909$	−2.93554	+	2.13279i	−0.0973656	+	0.0707402i
$910$	4.01788	−	3.39450i	0.133191	−	0.112527i
$911$	17.1442			0.568013			0.284007	−	0.958822i	$-0.408336\pi$
$911$	17.1442			0.568013			0.284007	+	0.958822i	$0.408336\pi$
$912$	4.08980	−	12.5871i	0.135427	−	0.416801i
$913$	6.79576	−	20.9672i	0.224907	−	0.693914i
$914$	−4.98716	−	15.3489i	−0.164961	−	0.507697i
$915$	−32.0171	+	27.0496i	−1.05845	+	0.894232i
$916$	−1.34561	−	4.14137i	−0.0444603	−	0.136835i
$917$	1.35610	+	4.17363i	0.0447822	+	0.137826i
$918$	16.9696	+	52.2271i	0.560080	+	1.72375i
$919$	14.3776	−	44.2497i	0.474273	−	1.45966i	−0.372663	−	0.927967i	$-0.621555\pi$
$919$	14.3776	−	44.2497i	0.474273	−	1.45966i	0.846936	−	0.531695i	$-0.178445\pi$
$920$	20.1784	−	17.0477i	0.665263	−	0.562047i
$921$	11.1295	−	34.2531i	0.366730	−	1.12868i
$922$	12.1652	+	37.4407i	0.400641	+	1.23305i
$923$	−0.142424	−	0.438337i	−0.00468796	−	0.0144280i
$924$	1.20438	−	0.876379i	0.0396213	−	0.0288308i
$925$	−6.63606	+	39.1746i	−0.218192	+	1.28805i
$926$	−15.8855	+	48.8906i	−0.522031	+	1.60664i
$927$	0.656313	+	0.476839i	0.0215561	+	0.0156614i
$928$	5.42919			0.178222
$929$	−0.992734	−	0.721264i	−0.0325706	−	0.0236639i	0.571381	−	0.820685i	$-0.306408\pi$
$929$	−0.992734	−	0.721264i	−0.0325706	−	0.0236639i	−0.603951	+	0.797021i	$0.706408\pi$
$930$	−37.4175	+	31.6122i	−1.22697	+	1.03660i
$931$	−2.43928	−	7.50732i	−0.0799440	−	0.246042i
$932$	0.354362	−	0.257459i	0.0116075	−	0.00843336i
$933$	26.2449	−	19.0680i	0.859218	−	0.624258i
$934$	9.57118	−	29.4571i	0.313179	−	0.963865i
$935$	50.4686	−	3.73679i	1.65050	−	0.122206i
$936$	0.299248	+	0.920989i	0.00978121	+	0.0301035i
$937$	−2.00063	−	1.45355i	−0.0653579	−	0.0474853i	0.554627	−	0.832099i	$-0.312861\pi$
$937$	−2.00063	−	1.45355i	−0.0653579	−	0.0474853i	−0.619984	+	0.784614i	$0.712861\pi$
$938$	−3.26110	−	10.0366i	−0.106479	−	0.327708i
$939$	−6.67306	+	20.5376i	−0.217767	+	0.670218i
$940$	−1.93846	+	0.142106i	−0.0632257	+	0.00463498i
$941$	−45.4041			−1.48013			−0.740065	−	0.672535i	$-0.765205\pi$
$941$	−45.4041			−1.48013			−0.740065	+	0.672535i	$0.765205\pi$
$942$	2.62582	+	8.08145i	0.0855539	+	0.263308i
$943$	−35.9831	+	26.1433i	−1.17177	+	0.851343i
$944$	−5.26005	+	3.82165i	−0.171200	+	0.124384i
$945$	−7.79372	−	19.1048i	−0.253530	−	0.621480i
$946$	−39.7936	+	0.0290289i	−1.29380	+	0.000943812i
$947$	0.772748	−	0.561435i	0.0251109	−	0.0182442i	−0.575159	−	0.818042i	$-0.695060\pi$
$947$	0.772748	−	0.561435i	0.0251109	−	0.0182442i	0.600270	+	0.799797i	$0.295060\pi$
$948$	2.51238			0.0815985
$949$	−10.8903	+	7.91229i	−0.353515	+	0.256844i
$950$	9.98882	−	9.77683i	0.324080	−	0.317202i
$951$	−14.5712	−	44.8455i	−0.472503	−	1.45421i
$952$	25.1491	−	18.2719i	0.815087	−	0.592195i
$953$	2.37842			0.0770446			0.0385223	−	0.999258i	$-0.487735\pi$
$953$	2.37842			0.0770446			0.0385223	+	0.999258i	$0.487735\pi$
$954$	0.953754	−	2.93535i	0.0308789	−	0.0950356i
$955$	−0.265449	−	0.164632i	−0.00858973	−	0.00532736i
$956$	−2.66351	−	1.93515i	−0.0861440	−	0.0625873i
$957$	−9.68868	+	29.8929i	−0.313191	+	0.966300i
$958$	−1.21507	−	0.882798i	−0.0392570	−	0.0285219i
$959$	−14.4088	−	10.4686i	−0.465284	−	0.338049i
$960$	26.1376	−	1.91610i	0.843586	−	0.0618420i
$961$	16.5539	−	50.9477i	0.533997	−	1.64347i
$962$	−11.0808			−0.357260
$963$	−1.65185			−0.0532302
$964$	−0.580710	+	1.78724i	−0.0187034	+	0.0575631i
$965$	−29.7121	+	25.1022i	−0.956467	+	0.808070i
$966$	−14.2215	−	10.3325i	−0.457569	−	0.332444i
$967$	11.2498	+	8.17345i	0.361769	+	0.262840i	0.753789	−	0.657116i	$-0.228224\pi$
$967$	11.2498	+	8.17345i	0.361769	+	0.262840i	−0.392021	+	0.919956i	$0.628224\pi$
$968$	29.7054	−	0.0433395i	0.954769	−	0.00139298i
$969$	−16.9845	−	12.3400i	−0.545621	−	0.396417i
$970$	39.4380	−	33.3192i	1.26628	−	1.06981i
$971$	−3.30825	+	10.1817i	−0.106167	+	0.326747i	−0.990002	−	0.141050i	$-0.954952\pi$
$971$	−3.30825	+	10.1817i	−0.106167	+	0.326747i	0.883836	+	0.467797i	$0.154952\pi$
$972$	−0.642445			−0.0206064
$973$	14.1072	−	10.2495i	0.452256	−	0.328583i
$974$	−13.7893	−	42.4391i	−0.441838	−	1.35984i
$975$	1.28157	−	7.56550i	0.0410432	−	0.242290i
$976$	40.2896	−	29.2721i	1.28964	−	0.936978i
$977$	16.4012			0.524721			0.262360	−	0.964970i	$-0.415499\pi$
$977$	16.4012			0.524721			0.262360	+	0.964970i	$0.415499\pi$
$978$	−12.2037	+	8.86647i	−0.390230	+	0.283519i
$979$	7.69892	+	23.6362i	0.246059	+	0.755415i
$980$	−1.16672	+	0.985701i	−0.0372695	+	0.0314871i
$981$	−0.113674	+	0.0825888i	−0.00362932	+	0.00263686i
$982$	−16.2442	+	11.8021i	−0.518372	+	0.376619i
$983$	0.729830	+	2.24618i	0.0232780	+	0.0716422i	0.962021	−	0.272977i	$-0.0880082\pi$
$983$	0.729830	+	2.24618i	0.0232780	+	0.0716422i	−0.938743	+	0.344619i	$0.888008\pi$
$984$	−44.4569			−1.41723
$985$	3.13544	+	1.94460i	0.0999035	+	0.0619602i
$986$	18.1532	−	55.8699i	0.578117	−	1.77926i
$987$	−4.46213	−	13.7330i	−0.142031	−	0.437127i
$988$	0.239563	+	0.174053i	0.00762151	+	0.00553735i
$989$	11.0246	+	33.9303i	0.350562	+	1.07892i
$990$	−0.982234	+	4.00938i	−0.0312174	+	0.127426i
$991$	14.1088	−	43.4223i	0.448179	−	1.37935i	−0.430780	−	0.902457i	$-0.641762\pi$
$991$	14.1088	−	43.4223i	0.448179	−	1.37935i	0.878959	−	0.476897i	$-0.158238\pi$
$992$	6.90280	−	5.01518i	0.219164	−	0.159232i
$993$	−42.1612	+	30.6319i	−1.33794	+	0.972074i
$994$	−0.372929	−	1.14776i	−0.0118286	−	0.0364047i
$995$	5.09144	+	12.4807i	0.161410	+	0.395665i
$996$	1.43133	+	1.03992i	0.0453535	+	0.0329512i
$997$	−16.3999			−0.519390			−0.259695	−	0.965691i	$-0.583622\pi$
$997$	−16.3999			−0.519390			−0.259695	+	0.965691i	$0.583622\pi$
$998$	−37.4310	−	27.1952i	−1.18486	−	0.860850i
$999$	−13.4323	+	41.3405i	−0.424981	+	1.30796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.l.d.31.8	yes	100
11.5	even	5		275.2.k.d.181.18	✓	100
25.21	even	5		275.2.k.d.196.18	yes	100
275.71	even	5	inner	275.2.l.d.71.8	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.k.d.181.18	✓	100	11.5	even	5
275.2.k.d.196.18	yes	100	25.21	even	5
275.2.l.d.31.8	yes	100	1.1	even	1	trivial
275.2.l.d.71.8	yes	100	275.71	even	5	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.47120 q^{2} +(-0.500346 + 1.53991i) q^{3} +0.164422 q^{4} +(-0.844616 - 2.07042i) q^{5} +(0.736108 - 2.26551i) q^{6} +(-1.36475 - 0.991546i) q^{7} +2.70050 q^{8} +(0.306083 + 0.222382i) q^{9} +(1.24260 + 3.04599i) q^{10} +(3.31662 - 0.00241943i) q^{11} +(-0.0822677 + 0.253194i) q^{12} +(0.766798 + 0.557111i) q^{13} +(2.00781 + 1.45876i) q^{14} +(3.61085 - 0.264706i) q^{15} -4.30181 q^{16} +(-2.10867 + 6.48983i) q^{17} +(-0.450308 - 0.327168i) q^{18} +1.90012 q^{19} +(-0.138873 - 0.340421i) q^{20} +(2.20973 - 1.60547i) q^{21} +(-4.87941 + 0.00355946i) q^{22} +(1.35181 + 4.16046i) q^{23} +(-1.35118 + 4.15852i) q^{24} +(-3.57325 + 3.49741i) q^{25} +(-1.12811 - 0.819620i) q^{26} +(-4.42537 + 3.21522i) q^{27} +(-0.224394 - 0.163032i) q^{28} +5.85159 q^{29} +(-5.31227 + 0.389434i) q^{30} +(7.43986 - 5.40537i) q^{31} +0.927814 q^{32} +(-1.65573 + 5.10850i) q^{33} +(3.10227 - 9.54782i) q^{34} +(-0.900226 + 3.66307i) q^{35} +(0.0503266 + 0.0365644i) q^{36} +(6.42888 - 4.67086i) q^{37} -2.79545 q^{38} +(-1.24156 + 0.902049i) q^{39} +(-2.28088 - 5.59115i) q^{40} +(3.14188 + 9.66970i) q^{41} +(-3.25095 + 2.36196i) q^{42} +8.15542 q^{43} +(0.545325 - 0.000397807i) q^{44} +(0.201901 - 0.821546i) q^{45} +(-1.98879 - 6.12085i) q^{46} +(1.63365 - 5.02786i) q^{47} +(2.15239 - 6.62439i) q^{48} +(-1.28375 - 3.95098i) q^{49} +(5.25695 - 5.14539i) q^{50} +(-8.93867 - 6.49432i) q^{51} +(0.126078 + 0.0916011i) q^{52} +(1.71350 + 5.27361i) q^{53} +(6.51059 - 4.73022i) q^{54} +(-2.80628 - 6.86475i) q^{55} +(-3.68549 - 2.67767i) q^{56} +(-0.950716 + 2.92600i) q^{57} -8.60885 q^{58} +(1.22275 - 0.888382i) q^{59} +(0.593702 - 0.0435234i) q^{60} +(-9.36574 + 6.80461i) q^{61} +(-10.9455 + 7.95237i) q^{62} +(-0.197223 - 0.606990i) q^{63} +7.23862 q^{64} +(0.505802 - 2.05814i) q^{65} +(2.43591 - 7.51562i) q^{66} +(-3.44013 - 2.49940i) q^{67} +(-0.346711 + 1.06707i) q^{68} -7.08309 q^{69} +(1.32441 - 5.38909i) q^{70} +(-0.393402 - 0.285823i) q^{71} +(0.826576 + 0.600543i) q^{72} +(-4.38877 + 13.5072i) q^{73} +(-9.45816 + 6.87175i) q^{74} +(-3.59783 - 7.25239i) q^{75} +0.312420 q^{76} +(-4.52875 - 3.28528i) q^{77} +(1.82658 - 1.32709i) q^{78} +(-2.91623 - 8.97522i) q^{79} +(3.63338 + 8.90653i) q^{80} +(-2.38618 - 7.34391i) q^{81} +(-4.62232 - 14.2260i) q^{82} +(2.05361 - 6.32036i) q^{83} +(0.363328 - 0.263973i) q^{84} +(15.2177 - 1.11558i) q^{85} -11.9982 q^{86} +(-2.92782 + 9.01091i) q^{87} +(8.95654 - 0.00653368i) q^{88} +(2.31611 + 7.12826i) q^{89} +(-0.297036 + 1.20866i) q^{90} +(-0.494083 - 1.52063i) q^{91} +(0.222268 + 0.684069i) q^{92} +(4.60127 + 14.1613i) q^{93} +(-2.40342 + 7.39698i) q^{94} +(-1.60487 - 3.93403i) q^{95} +(-0.464228 + 1.42875i) q^{96} +(-4.84973 - 14.9259i) q^{97} +(1.88865 + 5.81267i) q^{98} +(1.01570 + 0.736818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

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