LMFDB - Embedded newform 152.2.p.a.45.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(45,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.45"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.7
Character	$\chi$	$=$	152.45
Dual form			152.2.p.a.125.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.669488 + 1.24571i) q^{2} +(0.0638311 - 0.0368529i) q^{3} +(-1.10357 - 1.66797i) q^{4} +(-1.95840 + 1.13068i) q^{5} +(0.00317378 + 0.104187i) q^{6} -4.70260 q^{7} +(2.81663 - 0.258041i) q^{8} +(-1.49728 + 2.59337i) q^{9} +(-0.0973743 - 3.19656i) q^{10} +1.98019i q^{11} +(-0.131912 - 0.0657986i) q^{12} +(0.432449 + 0.249675i) q^{13} +(3.14833 - 5.85806i) q^{14} +(-0.0833377 + 0.144345i) q^{15} +(-1.56426 + 3.68145i) q^{16} +(0.371220 + 0.642972i) q^{17} +(-2.22817 - 3.60141i) q^{18} +(1.13983 - 4.20723i) q^{19} +(4.04717 + 2.01876i) q^{20} +(-0.300172 + 0.173304i) q^{21} +(-2.46674 - 1.32571i) q^{22} +(1.59672 - 2.76560i) q^{23} +(0.170279 - 0.120272i) q^{24} +(0.0568756 - 0.0985114i) q^{25} +(-0.600541 + 0.371551i) q^{26} +0.441834i q^{27} +(5.18966 + 7.84380i) q^{28} +(5.22471 + 3.01649i) q^{29} +(-0.124018 - 0.200452i) q^{30} -5.44101 q^{31} +(-3.53876 - 4.41329i) q^{32} +(0.0729758 + 0.126398i) q^{33} +(-1.04948 + 0.0319695i) q^{34} +(9.20955 - 5.31714i) q^{35} +(5.97803 - 0.364546i) q^{36} +10.3168i q^{37} +(4.47788 + 4.23658i) q^{38} +0.0368049 q^{39} +(-5.22432 + 3.69006i) q^{40} +(2.77027 + 4.79824i) q^{41} +(-0.0149250 - 0.489952i) q^{42} +(-6.56065 + 3.78779i) q^{43} +(3.30290 - 2.18528i) q^{44} -6.77180i q^{45} +(2.37615 + 3.84058i) q^{46} +(-0.782377 + 1.35512i) q^{47} +(0.0358240 + 0.292639i) q^{48} +15.1145 q^{49} +(0.0846389 + 0.136803i) q^{50} +(0.0473908 + 0.0273611i) q^{51} +(-0.0607887 - 0.996847i) q^{52} +(-10.0885 - 5.82458i) q^{53} +(-0.550396 - 0.295803i) q^{54} +(-2.23896 - 3.87800i) q^{55} +(-13.2455 + 1.21346i) q^{56} +(-0.0822924 - 0.310558i) q^{57} +(-7.25554 + 4.48896i) q^{58} +(4.10945 - 2.37259i) q^{59} +(0.332733 - 0.0202904i) q^{60} +(-1.51215 - 0.873042i) q^{61} +(3.64269 - 6.77790i) q^{62} +(7.04113 - 12.1956i) q^{63} +(7.86683 - 1.45361i) q^{64} -1.12921 q^{65} +(-0.206311 + 0.00628469i) q^{66} +(-9.42749 - 5.44296i) q^{67} +(0.662791 - 1.32875i) q^{68} -0.235375i q^{69} +(0.457913 + 15.0322i) q^{70} +(5.42083 + 9.38916i) q^{71} +(-3.54810 + 7.69093i) q^{72} +(-6.23576 - 10.8007i) q^{73} +(-12.8518 - 6.90701i) q^{74} -0.00838412i q^{75} +(-8.27542 + 2.74179i) q^{76} -9.31205i q^{77} +(-0.0246405 + 0.0458482i) q^{78} +(0.834855 + 1.44601i) q^{79} +(-1.09911 - 8.97842i) q^{80} +(-4.47557 - 7.75191i) q^{81} +(-7.83186 + 0.238576i) q^{82} +15.5733i q^{83} +(0.620329 + 0.309425i) q^{84} +(-1.45399 - 0.839462i) q^{85} +(-0.326205 - 10.7085i) q^{86} +0.444666 q^{87} +(0.510971 + 5.57747i) q^{88} +(-2.90236 + 5.02703i) q^{89} +(8.43567 + 4.53364i) q^{90} +(-2.03364 - 1.17412i) q^{91} +(-6.37504 + 0.388756i) q^{92} +(-0.347306 + 0.200517i) q^{93} +(-1.16429 - 1.88185i) q^{94} +(2.52480 + 9.52820i) q^{95} +(-0.388526 - 0.151292i) q^{96} +(-0.605380 - 1.04855i) q^{97} +(-10.1189 + 18.8282i) q^{98} +(-5.13537 - 2.96491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26}+ \cdots + 39 q^{98}+O(q^{100}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.669488	+	1.24571i	−0.473399	+	0.880848i
$2$	−0.669488	+	1.24571i	−0.473399	+	0.880848i
$3$	0.0638311	−	0.0368529i	0.0368529	−	0.0212770i	−0.481460	−	0.876468i	$-0.659893\pi$
$3$	0.0638311	−	0.0368529i	0.0368529	−	0.0212770i	0.518313	+	0.855191i	$0.326560\pi$
$4$	−1.10357	−	1.66797i	−0.551786	−	0.833986i
$5$	−1.95840	+	1.13068i	−0.875821	+	0.505656i	−0.869278	−	0.494323i	$-0.835416\pi$
$5$	−1.95840	+	1.13068i	−0.875821	+	0.505656i	−0.00654285	+	0.999979i	$0.502083\pi$
$6$	0.00317378	+	0.104187i	0.00129569	+	0.0425343i
$7$	−4.70260			−1.77742			−0.888708	−	0.458474i	$-0.848396\pi$
$7$	−4.70260			−1.77742			−0.888708	+	0.458474i	$0.848396\pi$
$8$	2.81663	−	0.258041i	0.995830	−	0.0912313i
$9$	−1.49728	+	2.59337i	−0.499095	+	0.864457i
$10$	−0.0973743	−	3.19656i	−0.0307925	−	1.01084i
$11$			1.98019i			0.597050i	0.954402	+	0.298525i	$0.0964947\pi$
$11$			1.98019i			0.597050i	−0.954402	+	0.298525i	$0.903505\pi$
$12$	−0.131912	−	0.0657986i	−0.0380797	−	0.0189944i
$13$	0.432449	+	0.249675i	0.119940	+	0.0692473i	0.558770	−	0.829323i	$-0.311274\pi$
$13$	0.432449	+	0.249675i	0.119940	+	0.0692473i	−0.438830	+	0.898570i	$0.644607\pi$
$14$	3.14833	−	5.85806i	0.841428	−	1.56563i
$15$	−0.0833377	+	0.144345i	−0.0215177	+	0.0372698i
$16$	−1.56426	+	3.68145i	−0.391064	+	0.920363i
$17$	0.371220	+	0.642972i	0.0900341	+	0.155944i	0.907525	−	0.419998i	$-0.137969\pi$
$17$	0.371220	+	0.642972i	0.0900341	+	0.155944i	−0.817491	+	0.575941i	$0.804636\pi$
$18$	−2.22817	−	3.60141i	−0.525184	−	0.848860i
$19$	1.13983	−	4.20723i	0.261494	−	0.965205i
$19$	1.13983	−	4.20723i	0.261494	−	0.965205i
$20$	4.04717	+	2.01876i	0.904975	+	0.451409i
$21$	−0.300172	+	0.173304i	−0.0655029	+	0.0378181i
$22$	−2.46674	−	1.32571i	−0.525911	−	0.282643i
$23$	1.59672	−	2.76560i	0.332939	−	0.576668i	−0.650147	−	0.759808i	$-0.725293\pi$
$23$	1.59672	−	2.76560i	0.332939	−	0.576668i	0.983087	+	0.183140i	$0.0586262\pi$
$24$	0.170279	−	0.120272i	0.0347581	−	0.0245504i
$25$	0.0568756	−	0.0985114i	0.0113751	−	0.0197023i
$26$	−0.600541	+	0.371551i	−0.117776	+	0.0728671i
$27$			0.441834i			0.0850311i
$28$	5.18966	+	7.84380i	0.980753	+	1.48234i
$29$	5.22471	+	3.01649i	0.970205	+	0.560148i	0.899299	−	0.437335i	$-0.144078\pi$
$29$	5.22471	+	3.01649i	0.970205	+	0.560148i	0.0709062	+	0.997483i	$0.477411\pi$
$30$	−0.124018	−	0.200452i	−0.0226425	−	0.0365973i
$31$	−5.44101			−0.977234			−0.488617	−	0.872498i	$-0.662498\pi$
$31$	−5.44101			−0.977234			−0.488617	+	0.872498i	$0.662498\pi$
$32$	−3.53876	−	4.41329i	−0.625571	−	0.780168i
$33$	0.0729758	+	0.126398i	0.0127035	+	0.0220030i
$34$	−1.04948	+	0.0319695i	−0.179985	+	0.00548273i
$35$	9.20955	−	5.31714i	1.55670	−	0.898760i
$36$	5.97803	−	0.364546i	0.996338	−	0.0607577i
$37$			10.3168i			1.69608i	0.529932	+	0.848040i	$0.322217\pi$
$37$			10.3168i			1.69608i	−0.529932	+	0.848040i	$0.677783\pi$
$38$	4.47788	+	4.23658i	0.726408	+	0.687264i
$39$	0.0368049			0.00589351
$40$	−5.22432	+	3.69006i	−0.826037	+	0.583449i
$41$	2.77027	+	4.79824i	0.432643	+	0.749359i	0.997100	−	0.0761031i	$-0.0242478\pi$
$41$	2.77027	+	4.79824i	0.432643	+	0.749359i	−0.564457	+	0.825462i	$0.690914\pi$
$42$	−0.0149250	−	0.489952i	−0.00230298	−	0.0756012i
$43$	−6.56065	+	3.78779i	−1.00049	+	0.577633i	−0.908393	−	0.418117i	$-0.862690\pi$
$43$	−6.56065	+	3.78779i	−1.00049	+	0.577633i	−0.0920962	+	0.995750i	$0.529357\pi$
$44$	3.30290	−	2.18528i	0.497932	−	0.329444i
$45$		−	6.77180i		−	1.00948i
$46$	2.37615	+	3.84058i	0.350344	+	0.566263i
$47$	−0.782377	+	1.35512i	−0.114121	+	0.197664i	−0.917428	−	0.397901i	$-0.869739\pi$
$47$	−0.782377	+	1.35512i	−0.114121	+	0.197664i	0.803307	+	0.595565i	$0.203072\pi$
$48$	0.0358240	+	0.292639i	0.00517075	+	0.0422387i
$49$	15.1145			2.15921
$50$	0.0846389	+	0.136803i	0.0119697	+	0.0193468i
$51$	0.0473908	+	0.0273611i	0.00663604	+	0.00383132i
$52$	−0.0607887	−	0.996847i	−0.00842987	−	0.138238i
$53$	−10.0885	−	5.82458i	−1.38576	−	0.800068i	−0.392925	−	0.919571i	$-0.628537\pi$
$53$	−10.0885	−	5.82458i	−1.38576	−	0.800068i	−0.992834	+	0.119503i	$0.961870\pi$
$54$	−0.550396	−	0.295803i	−0.0748994	−	0.0402537i
$55$	−2.23896	−	3.87800i	−0.301902	−	0.522909i
$56$	−13.2455	+	1.21346i	−1.77000	+	0.162156i
$57$	−0.0822924	−	0.310558i	−0.0108999	−	0.0411344i
$58$	−7.25554	+	4.48896i	−0.952700	+	0.589429i
$59$	4.10945	−	2.37259i	0.535005	−	0.308885i	−0.208047	−	0.978119i	$-0.566711\pi$
$59$	4.10945	−	2.37259i	0.535005	−	0.308885i	0.743052	+	0.669233i	$0.233377\pi$
$60$	0.332733	−	0.0202904i	0.0429556	−	0.00261947i
$61$	−1.51215	−	0.873042i	−0.193611	−	0.111782i	0.400061	−	0.916489i	$-0.368989\pi$
$61$	−1.51215	−	0.873042i	−0.193611	−	0.111782i	−0.593672	+	0.804707i	$0.702322\pi$
$62$	3.64269	−	6.77790i	0.462622	−	0.860794i
$63$	7.04113	−	12.1956i	0.887099	−	1.53650i
$64$	7.86683	−	1.45361i	0.983354	−	0.181702i
$65$	−1.12921			−0.140061
$66$	−0.206311	+	0.00628469i	−0.0253951	+	0.000773591i
$67$	−9.42749	−	5.44296i	−1.15175	−	0.664964i	−0.202438	−	0.979295i	$-0.564886\pi$
$67$	−9.42749	−	5.44296i	−1.15175	−	0.664964i	−0.949313	+	0.314332i	$0.898220\pi$
$68$	0.662791	−	1.32875i	0.0803752	−	0.161135i
$69$		−	0.235375i		−	0.0283359i
$70$	0.457913	+	15.0322i	0.0547310	+	1.79669i
$71$	5.42083	+	9.38916i	0.643335	+	1.11429i	0.984683	+	0.174352i	$0.0557829\pi$
$71$	5.42083	+	9.38916i	0.643335	+	1.11429i	−0.341349	+	0.939937i	$0.610884\pi$
$72$	−3.54810	+	7.69093i	−0.418148	+	0.906385i
$73$	−6.23576	−	10.8007i	−0.729841	−	1.26412i	−0.956950	−	0.290252i	$-0.906261\pi$
$73$	−6.23576	−	10.8007i	−0.729841	−	1.26412i	0.227109	−	0.973869i	$-0.427073\pi$
$74$	−12.8518	−	6.90701i	−1.49399	−	0.802923i
$75$		−	0.00838412i		−	0.000968115i
$76$	−8.27542	+	2.74179i	−0.949256	+	0.314505i
$77$		−	9.31205i		−	1.06121i
$78$	−0.0246405	+	0.0458482i	−0.00278998	+	0.00519128i
$79$	0.834855	+	1.44601i	0.0939285	+	0.162689i	0.909161	−	0.416445i	$-0.136724\pi$
$79$	0.834855	+	1.44601i	0.0939285	+	0.162689i	−0.815232	+	0.579134i	$0.803391\pi$
$80$	−1.09911	−	8.97842i	−0.122884	−	1.00382i
$81$	−4.47557	−	7.75191i	−0.497285	−	0.861324i
$82$	−7.83186	+	0.238576i	−0.864884	+	0.0263463i
$83$			15.5733i			1.70939i	0.519130	+	0.854695i	$0.326256\pi$
$83$			15.5733i			1.70939i	−0.519130	+	0.854695i	$0.673744\pi$
$84$	0.620329	+	0.309425i	0.0676834	+	0.0337610i
$85$	−1.45399	−	0.839462i	−0.157708	−	0.0910525i
$86$	−0.326205	−	10.7085i	−0.0351756	−	1.15473i
$87$	0.444666			0.0476732
$88$	0.510971	+	5.57747i	0.0544697	+	0.594561i
$89$	−2.90236	+	5.02703i	−0.307649	+	0.532864i	−0.977848	−	0.209318i	$-0.932876\pi$
$89$	−2.90236	+	5.02703i	−0.307649	+	0.532864i	0.670198	+	0.742182i	$0.266209\pi$
$90$	8.43567	+	4.53364i	0.889198	+	0.477887i
$91$	−2.03364	−	1.17412i	−0.213183	−	0.123081i
$92$	−6.37504	+	0.388756i	−0.664644	+	0.0405306i
$93$	−0.347306	+	0.200517i	−0.0360139	+	0.0207926i
$94$	−1.16429	−	1.88185i	−0.120087	−	0.194098i
$95$	2.52480	+	9.52820i	0.259040	+	0.977573i
$96$	−0.388526	−	0.151292i	−0.0396537	−	0.0154412i
$97$	−0.605380	−	1.04855i	−0.0614670	−	0.106464i	0.833654	−	0.552287i	$-0.186245\pi$
$97$	−0.605380	−	1.04855i	−0.0614670	−	0.106464i	−0.895121	+	0.445823i	$0.852911\pi$
$98$	−10.1189	+	18.8282i	−1.02217	+	1.90193i
$99$	−5.13537	−	2.96491i	−0.516124	−	0.297985i
$100$	−0.227081	+	0.0138476i	−0.0227081	+	0.00138476i
$101$	12.9353	+	7.46822i	1.28711	+	0.743115i	0.978138	−	0.207955i	$-0.0666807\pi$
$101$	12.9353	+	7.46822i	1.28711	+	0.743115i	0.308975	+	0.951070i	$0.400014\pi$
$102$	−0.0658114	+	0.0407171i	−0.00651630	+	0.00403159i
$103$	11.6211			1.14506			0.572530	−	0.819884i	$-0.305962\pi$
$103$	11.6211			1.14506			0.572530	+	0.819884i	$0.305962\pi$
$104$	1.28248	+	0.591652i	0.125757	+	0.0580163i
$105$	0.391904	−	0.678798i	0.0382459	−	0.0662439i
$106$	14.0098	−	8.66780i	1.36076	−	0.841891i
$107$		−	7.66606i		−	0.741106i	−0.928811	−	0.370553i	$-0.879168\pi$
$107$		−	7.66606i		−	0.741106i	0.928811	−	0.370553i	$-0.120832\pi$
$108$	0.736967	−	0.487596i	0.0709147	−	0.0469190i
$109$	2.28507	−	1.31929i	0.218870	−	0.126365i	−0.386557	−	0.922266i	$-0.626336\pi$
$109$	2.28507	−	1.31929i	0.218870	−	0.126365i	0.605427	+	0.795901i	$0.293002\pi$
$110$	6.32981	−	0.192820i	0.603524	−	0.0183847i
$111$	0.380206	+	0.658536i	0.0360875	+	0.0625055i
$112$	7.35608	−	17.3124i	0.695084	−	1.63587i
$113$	−8.94264			−0.841253			−0.420627	−	0.907234i	$-0.638190\pi$
$113$	−8.94264			−0.841253			−0.420627	+	0.907234i	$0.638190\pi$
$114$	0.441958	+	0.105403i	0.0413932	+	0.00987186i
$115$			7.22153i			0.673411i
$116$	−0.734429	−	12.0436i	−0.0681900	−	1.11822i
$117$	−1.29500	+	0.747668i	−0.119723	+	0.0691219i
$118$	0.204328	+	6.70760i	0.0188099	+	0.617484i
$119$	−1.74570	−	3.02364i	−0.160028	−	0.277177i
$120$	−0.197485	+	0.428072i	−0.0180278	+	0.0390774i
$121$	7.07884			0.643531
$122$	2.09992	−	1.29921i	0.190118	−	0.117625i
$123$	0.353658	+	0.204185i	0.0318883	+	0.0184107i
$124$	6.00454	+	9.07545i	0.539224	+	0.814999i
$125$		−	11.0496i		−	0.988304i
$126$	10.4782	+	16.9360i	0.933471	+	1.50878i
$127$	−2.38102	+	4.12405i	−0.211281	+	0.365950i	−0.952116	−	0.305738i	$-0.901097\pi$
$127$	−2.38102	+	4.12405i	−0.211281	+	0.365950i	0.740834	+	0.671688i	$0.234430\pi$
$128$	−3.45597	+	10.7729i	−0.305468	+	0.952202i
$129$	−0.279182	+	0.483558i	−0.0245806	+	0.0425749i
$130$	0.755992	−	1.40666i	0.0663048	−	0.123373i
$131$	−4.31780	+	2.49288i	−0.377248	+	0.217804i	−0.676620	−	0.736332i	$-0.736556\pi$
$131$	−4.31780	+	2.49288i	−0.377248	+	0.217804i	0.299372	+	0.954136i	$0.403223\pi$
$132$	0.130294	−	0.261211i	0.0113406	−	0.0227355i
$133$	−5.36014	+	19.7849i	−0.464783	+	1.71557i
$134$	13.0919	−	8.09989i	1.13097	−	0.699724i
$135$	−0.499573	−	0.865287i	−0.0429964	−	0.0744720i
$136$	1.21150	+	1.71523i	0.103886	+	0.147079i
$137$	−4.00007	+	6.92833i	−0.341749	+	0.591927i	−0.984758	−	0.173932i	$-0.944353\pi$
$137$	−4.00007	+	6.92833i	−0.341749	+	0.591927i	0.643008	+	0.765859i	$0.277686\pi$
$138$	0.293209	+	0.157581i	0.0249596	+	0.0134142i
$139$	6.90837	+	3.98855i	0.585960	+	0.338304i	0.763498	−	0.645810i	$-0.223480\pi$
$139$	6.90837	+	3.98855i	0.585960	+	0.338304i	−0.177538	+	0.984114i	$0.556813\pi$
$140$	−19.0322	−	9.49343i	−1.60852	−	0.802341i
$141$			0.115331i			0.00971266i
$142$	−15.3253	+	0.466843i	−1.28607	+	0.0391766i
$143$	−0.494404	+	0.856333i	−0.0413441	+	0.0716101i
$144$	−7.20524	−	9.56888i	−0.600437	−	0.797407i
$145$	−13.6427			−1.13297
$146$	17.6292	−	0.537025i	1.45901	−	0.0444445i
$147$	0.964772	−	0.557012i	0.0795731	−	0.0459415i
$148$	17.2082	−	11.3854i	1.41451	−	0.935873i
$149$	4.57651	−	2.64225i	0.374922	−	0.216462i	−0.300684	−	0.953724i	$-0.597215\pi$
$149$	4.57651	−	2.64225i	0.374922	−	0.216462i	0.675607	+	0.737262i	$0.263882\pi$
$150$	0.0104442	+	0.00561307i	0.000852762	+	0.000458305i
$151$	−3.63598			−0.295892			−0.147946	−	0.988995i	$-0.547266\pi$
$151$	−3.63598			−0.295892			−0.147946	+	0.988995i	$0.547266\pi$
$152$	2.12483	−	12.1443i	0.172346	−	0.985036i
$153$	−2.22329			−0.179742
$154$	11.6001	+	6.23431i	0.934762	+	0.502375i
$155$	10.6556	−	6.15204i	0.855882	−	0.494144i
$156$	−0.0406169	−	0.0613896i	−0.00325196	−	0.00491510i
$157$	16.5481	−	9.55404i	1.32068	−	0.762496i	0.336844	−	0.941561i	$-0.390641\pi$
$157$	16.5481	−	9.55404i	1.32068	−	0.762496i	0.983837	+	0.179065i	$0.0573073\pi$
$158$	−2.36023	+	0.0718978i	−0.187770	+	0.00571988i
$159$	−0.858611			−0.0680923
$160$	11.9203	+	4.64177i	0.942384	+	0.366964i
$161$	−7.50874	+	13.0055i	−0.591772	+	1.02498i
$162$	12.6529	−	0.385436i	0.994110	−	0.0302827i
$163$			9.73237i			0.762298i	0.924514	+	0.381149i	$0.124472\pi$
$163$			9.73237i			0.762298i	−0.924514	+	0.381149i	$0.875528\pi$
$164$	4.94614	−	9.91593i	0.386229	−	0.774304i
$165$	−0.285831	−	0.165025i	−0.0222519	−	0.0128472i
$166$	−19.3998	−	10.4261i	−1.50571	−	0.809225i
$167$	−9.40182	+	16.2844i	−0.727535	+	1.26013i	0.230387	+	0.973099i	$0.426001\pi$
$167$	−9.40182	+	16.2844i	−0.727535	+	1.26013i	−0.957922	+	0.287029i	$0.907333\pi$
$168$	−0.800755	+	0.565592i	−0.0617796	+	0.0436363i
$169$	−6.37533	−	11.0424i	−0.490410	−	0.849414i
$170$	2.01915	−	1.24924i	0.154862	−	0.0958122i
$171$	9.20427	+	9.25541i	0.703868	+	0.707779i
$172$	13.5581	+	6.76287i	1.03379	+	0.515664i
$173$	10.1721	−	5.87286i	0.773370	−	0.446505i	−0.0607055	−	0.998156i	$-0.519335\pi$
$173$	10.1721	−	5.87286i	0.773370	−	0.446505i	0.834075	+	0.551650i	$0.186002\pi$
$174$	−0.297698	+	0.553923i	−0.0225684	+	0.0419928i
$175$	−0.267463	+	0.463260i	−0.0202183	+	0.0350192i
$176$	−7.28999	−	3.09753i	−0.549503	−	0.233485i
$177$	0.174874	−	0.302890i	0.0131443	−	0.0227666i
$178$	−4.31912	−	6.98103i	−0.323731	−	0.523250i
$179$			11.1964i			0.836860i	0.908249	+	0.418430i	$0.137420\pi$
$179$			11.1964i			0.836860i	−0.908249	+	0.418430i	$0.862580\pi$
$180$	−11.2952	+	7.47317i	−0.841892	+	0.557017i
$181$	−10.2345	−	5.90892i	−0.760728	−	0.439206i	0.0688293	−	0.997628i	$-0.478074\pi$
$181$	−10.2345	−	5.90892i	−0.760728	−	0.439206i	−0.829557	+	0.558422i	$0.811407\pi$
$182$	2.82410	−	1.74726i	0.209337	−	0.129515i
$183$	−0.128697			−0.00951352
$184$	3.78374	−	8.20171i	0.278941	−	0.604638i
$185$	−11.6651	−	20.2045i	−0.857632	−	1.48546i
$186$	−0.0172685	−	0.566885i	−0.00126619	−	0.0415660i
$187$	−1.27321	+	0.735087i	−0.0931062	+	0.0537549i
$188$	3.12371	−	0.190487i	0.227820	−	0.0138927i
$189$		−	2.07777i		−	0.151136i
$190$	−13.5597	−	3.23385i	−0.983722	−	0.234608i
$191$	12.6474			0.915135			0.457568	−	0.889175i	$-0.348721\pi$
$191$	12.6474			0.915135			0.457568	+	0.889175i	$0.348721\pi$
$192$	0.448579	−	0.382701i	0.0323734	−	0.0276191i
$193$	−3.67277	−	6.36143i	−0.264372	−	0.457906i	0.703027	−	0.711163i	$-0.251831\pi$
$193$	−3.67277	−	6.36143i	−0.264372	−	0.457906i	−0.967399	+	0.253258i	$0.918498\pi$
$194$	1.71148	−	0.0521354i	0.122877	−	0.00374310i
$195$	−0.0720786	+	0.0416146i	−0.00516166	+	0.00298009i
$196$	−16.6799	−	25.2105i	−1.19142	−	1.80075i
$197$			12.1000i			0.862092i	0.902330	+	0.431046i	$0.141855\pi$
$197$			12.1000i			0.862092i	−0.902330	+	0.431046i	$0.858145\pi$
$198$	7.13148	−	4.41220i	0.506812	−	0.313561i
$199$	−3.73560	+	6.47025i	−0.264810	+	0.458664i	−0.967514	−	0.252819i	$-0.918642\pi$
$199$	−3.73560	+	6.47025i	−0.264810	+	0.458664i	0.702704	+	0.711482i	$0.251976\pi$
$200$	0.134778	−	0.292147i	0.00953022	−	0.0206579i
$201$	−0.802356			−0.0565938
$202$	−17.9633	+	11.1138i	−1.26389	+	0.781961i
$203$	−24.5697	−	14.1853i	−1.72446	−	0.995616i
$204$	−0.00666164	−	0.109241i	−0.000466408	−	0.00764843i
$205$	−10.8505	−	6.26457i	−0.757835	−	0.437536i
$206$	−7.78018	+	14.4765i	−0.542071	+	1.00862i
$207$	4.78149	+	8.28178i	0.332337	+	0.575624i
$208$	−1.59563	+	1.20149i	−0.110637	+	0.0833081i
$209$	8.33113	+	2.25707i	0.576276	+	0.156125i
$210$	0.583208	+	0.942644i	0.0402452	+	0.0650486i
$211$	−5.04276	+	2.91144i	−0.347158	+	0.200432i	−0.663433	−	0.748236i	$-0.730901\pi$
$211$	−5.04276	+	2.91144i	−0.347158	+	0.200432i	0.316275	+	0.948668i	$0.397568\pi$
$212$	1.41812	+	23.2551i	0.0973969	+	1.59717i
$213$	0.692036	+	0.399547i	0.0474175	+	0.0273765i
$214$	9.54967	+	5.13234i	0.652802	+	0.350839i
$215$	8.56556	−	14.8360i	0.584166	−	1.01181i
$216$	0.114011	+	1.24448i	0.00775749	+	0.0846765i
$217$	25.5869			1.73695
$218$	0.113617	+	3.72978i	0.00769512	+	0.252612i
$219$	−0.796071	−	0.459612i	−0.0537935	−	0.0310577i
$220$	−3.99753	+	8.01418i	−0.269514	+	0.540316i
$221$			0.370737i			0.0249385i
$222$	−1.07489	+	0.0327434i	−0.0721416	+	0.00219759i
$223$	−3.54133	−	6.13377i	−0.237145	−	0.410748i	0.722749	−	0.691111i	$-0.242878\pi$
$223$	−3.54133	−	6.13377i	−0.237145	−	0.410748i	−0.959894	+	0.280363i	$0.909545\pi$
$224$	16.6414	+	20.7540i	1.11190	+	1.38668i
$225$	0.170318	+	0.294999i	0.0113545	+	0.0196666i
$226$	5.98699	−	11.1399i	0.398249	−	0.741016i
$227$			10.8506i			0.720179i	0.932918	+	0.360090i	$0.117254\pi$
$227$			10.8506i			0.720179i	−0.932918	+	0.360090i	$0.882746\pi$
$228$	−0.427186	+	0.479985i	−0.0282911	+	0.0317878i
$229$		−	5.71559i		−	0.377697i	−0.982006	−	0.188848i	$-0.939525\pi$
$229$		−	5.71559i		−	0.377697i	0.982006	−	0.188848i	$-0.0604755\pi$
$230$	−8.99591	−	4.83472i	−0.593173	−	0.318792i
$231$	−0.343176	−	0.594399i	−0.0225793	−	0.0391086i
$232$	15.4945	+	7.14815i	1.01726	+	0.469299i
$233$	11.6711	+	20.2149i	0.764598	+	1.32432i	0.940459	+	0.339908i	$0.110396\pi$
$233$	11.6711	+	20.2149i	0.764598	+	1.32432i	−0.175860	+	0.984415i	$0.556271\pi$
$234$	−0.0643892	−	2.11374i	−0.00420925	−	0.138180i
$235$		−	3.53847i		−	0.230825i
$236$	−8.49249	−	4.23612i	−0.552814	−	0.275748i
$237$	0.106579	+	0.0615336i	0.00692307	+	0.00399704i
$238$	4.93530	−	0.150340i	0.319908	−	0.00974509i
$239$	−10.4517			−0.676063			−0.338032	−	0.941135i	$-0.609761\pi$
$239$	−10.4517			−0.676063			−0.338032	+	0.941135i	$0.609761\pi$
$240$	−0.401038	−	0.532597i	−0.0258869	−	0.0343790i
$241$	−10.3416	+	17.9122i	−0.666160	+	1.15382i	0.312809	+	0.949816i	$0.398730\pi$
$241$	−10.3416	+	17.9122i	−0.666160	+	1.15382i	−0.978969	+	0.204007i	$0.934603\pi$
$242$	−4.73920	+	8.81816i	−0.304647	+	0.566853i
$243$	−1.71928	−	0.992627i	−0.110292	−	0.0636770i
$244$	0.212561	+	3.48569i	0.0136078	+	0.223149i
$245$	−29.6001	+	17.0896i	−1.89108	+	1.09182i
$246$	−0.491124	+	0.303855i	−0.0313129	+	0.0193731i
$247$	1.54336	−	1.53483i	0.0982014	−	0.0976588i
$248$	−15.3253	+	1.40400i	−0.973159	+	0.0891543i
$249$	0.573921	+	0.994060i	0.0363708	+	0.0629960i
$250$	13.7645	+	7.39755i	0.870545	+	0.467862i
$251$	0.147363	+	0.0850803i	0.00930149	+	0.00537022i	0.504644	−	0.863328i	$-0.331624\pi$
$251$	0.147363	+	0.0850803i	0.00930149	+	0.00537022i	−0.495342	+	0.868698i	$0.664957\pi$
$252$	−28.1123	+	1.71431i	−1.77091	+	0.107992i
$253$	5.47643	+	3.16182i	0.344300	+	0.198782i
$254$	−3.54329	−	5.72706i	−0.222326	−	0.359347i
$255$	−0.123747			−0.00774931
$256$	−11.1062	−	11.5175i	−0.694137	−	0.719843i
$257$	7.27034	−	12.5926i	0.453511	−	0.785504i	−0.545090	−	0.838378i	$-0.683505\pi$
$257$	7.27034	−	12.5926i	0.453511	−	0.785504i	0.998601	+	0.0528730i	$0.0168379\pi$
$258$	−0.415462	−	0.671515i	−0.0258655	−	0.0418067i
$259$		−	48.5160i		−	3.01464i
$260$	1.24616	+	1.88349i	0.0772838	+	0.116809i
$261$	−15.6458	+	9.03308i	−0.968448	+	0.559134i
$262$	−0.214687	−	7.04766i	−0.0132634	−	0.435406i
$263$	−7.54036	−	13.0603i	−0.464959	−	0.805332i	0.534241	−	0.845332i	$-0.320598\pi$
$263$	−7.54036	−	13.0603i	−0.464959	−	0.805332i	−0.999200	+	0.0400000i	$0.987264\pi$
$264$	0.238162	+	0.337185i	0.0146578	+	0.0207523i
$265$	26.3430			1.61824
$266$	−21.0577	−	19.9229i	−1.29113	−	1.22155i
$267$			0.427841i			0.0261835i
$268$	1.32521	+	21.7315i	0.0809499	+	1.32746i
$269$	6.34397	−	3.66269i	0.386799	−	0.223318i	−0.293973	−	0.955814i	$-0.594978\pi$
$269$	6.34397	−	3.66269i	0.386799	−	0.223318i	0.680772	+	0.732495i	$0.261644\pi$
$270$	1.41235	−	0.0430233i	0.0859530	−	0.00261832i
$271$	−4.12352	−	7.14215i	−0.250486	−	0.433855i	0.713174	−	0.700987i	$-0.247257\pi$
$271$	−4.12352	−	7.14215i	−0.250486	−	0.433855i	−0.963660	+	0.267133i	$0.913924\pi$
$272$	−2.94776	+	0.360856i	−0.178734	+	0.0218801i
$273$	−0.173079			−0.0104752
$274$	−5.95267	−	9.62135i	−0.359614	−	0.581247i
$275$	0.195072	+	0.112625i	0.0117633	+	0.00679152i
$276$	−0.392599	+	0.259754i	−0.0236317	+	0.0156353i
$277$			17.2973i			1.03929i	0.854382	+	0.519646i	$0.173936\pi$
$277$			17.2973i			1.03929i	−0.854382	+	0.519646i	$0.826064\pi$
$278$	−9.59363	+	5.93552i	−0.575388	+	0.355989i
$279$	8.14673	−	14.1106i	0.487732	−	0.844777i
$280$	24.5679	−	17.3529i	1.46821	−	1.03703i
$281$	−12.5105	+	21.6688i	−0.746312	+	1.29265i	0.203267	+	0.979123i	$0.434844\pi$
$281$	−12.5105	+	21.6688i	−0.746312	+	1.29265i	−0.949579	+	0.313527i	$0.898489\pi$
$282$	−0.143669	−	0.0772130i	−0.00855538	−	0.00459797i
$283$	16.0653	−	9.27531i	0.954984	−	0.551360i	0.0603582	−	0.998177i	$-0.480776\pi$
$283$	16.0653	−	9.27531i	0.954984	−	0.551360i	0.894626	+	0.446817i	$0.147442\pi$
$284$	9.67857	−	19.4034i	0.574317	−	1.15138i
$285$	0.512303	+	0.515149i	0.0303462	+	0.0305148i
$286$	−0.735742	−	1.18919i	−0.0435053	−	0.0703181i
$287$	−13.0275	−	22.5642i	−0.768986	−	1.33192i
$288$	16.7438	−	2.56937i	0.986640	−	0.151401i
$289$	8.22439	−	14.2451i	0.483788	−	0.837945i
$290$	9.13365	−	16.9949i	0.536346	−	0.997972i
$291$	−0.0772841	−	0.0446200i	−0.00453048	−	0.00261567i
$292$	−11.1336	+	22.3204i	−0.651543	+	1.30620i
$293$		−	1.02282i		−	0.0597535i	−0.999554	−	0.0298768i	$-0.990489\pi$
$293$		−	1.02282i		−	0.0597535i	0.999554	−	0.0298768i	$-0.00951149\pi$
$294$	0.0479699	+	1.57474i	0.00279766	+	0.0918405i
$295$	−5.36529	+	9.29295i	−0.312379	+	0.541057i
$296$	2.66217	+	29.0588i	0.154735	+	1.68901i
$297$	−0.874917			−0.0507678
$298$	0.227551	+	7.46995i	0.0131817	+	0.432722i
$299$	1.38100	−	0.797322i	0.0798654	−	0.0461103i
$300$	−0.0139845	+	0.00925248i	−0.000807394	+	0.000534192i
$301$	30.8521	−	17.8125i	1.77829	−	1.02669i
$302$	2.43424	−	4.52936i	0.140075	−	0.260636i
$303$	1.10090			0.0632451
$304$	13.7057	+	10.7774i	0.786079	+	0.618127i
$305$	3.94853			0.226092
$306$	1.48846	−	2.76956i	0.0850898	−	0.158325i
$307$	22.7524	−	13.1361i	1.29855	−	0.749717i	0.318395	−	0.947958i	$-0.396856\pi$
$307$	22.7524	−	13.1361i	1.29855	−	0.749717i	0.980153	+	0.198241i	$0.0635227\pi$
$308$	−15.5322	+	10.2765i	−0.885031	+	0.585559i
$309$	0.741787	−	0.428271i	0.0421988	−	0.0243635i
$310$	0.529814	+	17.3925i	0.0300914	+	0.987829i
$311$	24.2028			1.37241			0.686207	−	0.727407i	$-0.259275\pi$
$311$	24.2028			1.37241			0.686207	+	0.727407i	$0.259275\pi$
$312$	0.103666	−	0.00949718i	0.00586893	−	0.000537672i
$313$	14.3528	−	24.8598i	0.811270	−	1.40516i	−0.100706	−	0.994916i	$-0.532110\pi$
$313$	14.3528	−	24.8598i	0.811270	−	1.40516i	0.911976	−	0.410244i	$-0.134557\pi$
$314$	0.822795	+	27.0104i	0.0464330	+	1.52428i
$315$			31.8451i			1.79427i
$316$	1.49058	−	2.98829i	0.0838518	−	0.168104i
$317$	8.87555	+	5.12430i	0.498501	+	0.287809i	0.728094	−	0.685477i	$-0.240406\pi$
$317$	8.87555	+	5.12430i	0.498501	+	0.287809i	−0.229594	+	0.973287i	$0.573740\pi$
$318$	0.574830	−	1.06958i	0.0322348	−	0.0599790i
$319$	−5.97323	+	10.3459i	−0.334437	+	0.579261i
$320$	−13.7628	+	11.7416i	−0.769364	+	0.656376i
$321$	−0.282517	−	0.489333i	−0.0157685	−	0.0273119i
$322$	−11.1741	−	18.0607i	−0.622706	−	1.00649i
$323$	3.12826	−	0.828933i	0.174061	−	0.0461231i
$324$	−7.99085	+	16.0199i	−0.443936	+	0.889995i
$325$	0.0491916	−	0.0284008i	0.00272866	−	0.00157539i
$326$	−12.1237	−	6.51570i	−0.671469	−	0.360871i
$327$	0.0972391	−	0.168423i	0.00537733	−	0.00931381i
$328$	9.04096	+	12.8000i	0.499203	+	0.706764i
$329$	3.67921	−	6.37257i	0.202841	−	0.351331i
$330$	0.396933	−	0.245580i	0.0218504	−	0.0135187i
$331$		−	16.6930i		−	0.917528i	−0.888558	−	0.458764i	$-0.848292\pi$
$331$		−	16.6930i		−	0.917528i	0.888558	−	0.458764i	$-0.151708\pi$
$332$	25.9758	−	17.1863i	1.42561	−	0.943218i
$333$	−26.7554	−	15.4473i	−1.46619	−	0.846504i
$334$	−13.9912	−	22.6142i	−0.765566	−	1.23739i
$335$	24.6170			1.34497
$336$	−0.168466	−	1.37616i	−0.00919057	−	0.0750758i
$337$	14.1278	+	24.4701i	0.769591	+	1.33297i	0.937785	+	0.347216i	$0.112873\pi$
$337$	14.1278	+	24.4701i	0.769591	+	1.33297i	−0.168194	+	0.985754i	$0.553794\pi$
$338$	18.0238	−	0.549044i	0.980364	−	0.0298640i
$339$	−0.570819	+	0.329562i	−0.0310026	+	0.0178994i
$340$	0.204385	+	3.35162i	0.0110843	+	0.181767i
$341$		−	10.7742i		−	0.583458i
$342$	−17.6917	+	5.26944i	−0.956656	+	0.284939i
$343$	−38.1591			−2.06040
$344$	−17.5015	+	12.3617i	−0.943619	+	0.666500i
$345$	0.266134	+	0.460958i	0.0143282	+	0.0248171i
$346$	0.505771	+	16.6033i	0.0271904	+	0.892597i
$347$	−22.6793	+	13.0939i	−1.21749	+	0.702918i	−0.964380	−	0.264519i	$-0.914787\pi$
$347$	−22.6793	+	13.0939i	−1.21749	+	0.702918i	−0.253110	+	0.967438i	$0.581453\pi$
$348$	−0.490721	−	0.741689i	−0.0263054	−	0.0397587i
$349$		−	7.01947i		−	0.375743i	−0.982194	−	0.187872i	$-0.939841\pi$
$349$		−	7.01947i		−	0.375743i	0.982194	−	0.187872i	$-0.0601589\pi$
$350$	−0.398023	−	0.643328i	−0.0212752	−	0.0343873i
$351$	−0.110315	+	0.191071i	−0.00588817	+	0.0101986i
$352$	8.73917	−	7.00743i	0.465799	−	0.373497i
$353$	13.7525			0.731969			0.365985	−	0.930621i	$-0.380732\pi$
$353$	13.7525			0.731969			0.365985	+	0.930621i	$0.380732\pi$
$354$	0.260237	+	0.420623i	0.0138314	+	0.0223559i
$355$	−21.2323	−	12.2585i	−1.12689	−	0.650612i
$356$	11.5879	−	0.706642i	0.614158	−	0.0374519i
$357$	−0.222860	−	0.128668i	−0.0117950	−	0.00680984i
$358$	−13.9475	−	7.49587i	−0.737147	−	0.396169i
$359$	1.49285	+	2.58569i	0.0787895	+	0.136467i	0.902728	−	0.430212i	$-0.141561\pi$
$359$	1.49285	+	2.58569i	0.0787895	+	0.136467i	−0.823938	+	0.566679i	$0.808228\pi$
$360$	−1.74740	−	19.0737i	−0.0920961	−	1.00527i
$361$	−16.4016	−	9.59102i	−0.863242	−	0.504790i
$362$	14.2127	−	8.79329i	0.747002	−	0.462165i
$363$	0.451850	−	0.260876i	0.0237160	−	0.0136924i
$364$	0.285865	+	4.68777i	0.0149834	+	0.245706i
$365$	24.4242	+	14.1013i	1.27842	+	0.738096i
$366$	0.0861608	−	0.160318i	0.00450370	−	0.00837997i
$367$	−9.97261	+	17.2731i	−0.520566	+	0.901647i	0.479148	+	0.877734i	$0.340946\pi$
$367$	−9.97261	+	17.2731i	−0.520566	+	0.901647i	−0.999714	+	0.0239129i	$0.992388\pi$
$368$	7.68376	+	10.2044i	0.400543	+	0.531940i
$369$	−16.5915			−0.863719
$370$	32.9785	−	1.00460i	1.71447	−	0.0522265i
$371$	47.4421	+	27.3907i	2.46307	+	1.42205i
$372$	0.717733	+	0.358011i	0.0372127	+	0.0185620i
$373$			16.8878i			0.874416i	0.899360	+	0.437208i	$0.144033\pi$
$373$			16.8878i			0.874416i	−0.899360	+	0.437208i	$0.855967\pi$
$374$	−0.0633058	−	2.07818i	−0.00327346	−	0.107460i
$375$	−0.407209	−	0.705306i	−0.0210282	−	0.0364219i
$376$	−1.85399	+	4.01875i	−0.0956124	+	0.207251i
$377$	1.50628	+	2.60896i	0.0775775	+	0.134368i
$378$	2.58829	+	1.39104i	0.133127	+	0.0715475i
$379$			26.5474i			1.36365i	0.731517	+	0.681824i	$0.238813\pi$
$379$			26.5474i			1.36365i	−0.731517	+	0.681824i	$0.761187\pi$
$380$	13.1065	−	14.7264i	0.672347	−	0.755446i
$381$			0.350990i			0.0179818i
$382$	−8.46729	+	15.7550i	−0.433224	+	0.806095i
$383$	2.38085	+	4.12375i	0.121656	+	0.210714i	0.920421	−	0.390929i	$-0.127846\pi$
$383$	2.38085	+	4.12375i	0.121656	+	0.210714i	−0.798765	+	0.601643i	$0.794513\pi$
$384$	0.176416	+	0.815011i	0.00900268	+	0.0415909i
$385$	10.5290	+	18.2367i	0.536605	+	0.929428i
$386$	10.3834	−	0.316300i	0.528499	−	0.0160992i
$387$		−	22.6856i		−	1.15317i
$388$	−1.08087	+	2.16691i	−0.0548728	+	0.110008i
$389$	−17.0129	−	9.82241i	−0.862589	−	0.498016i	0.00228917	−	0.999997i	$-0.499271\pi$
$389$	−17.0129	−	9.82241i	−0.862589	−	0.498016i	−0.864879	+	0.501981i	$0.832605\pi$
$390$	−0.00358386	−	0.117649i	−0.000181476	−	0.00595741i
$391$	2.37094			0.119904
$392$	42.5719	−	3.90015i	2.15020	−	0.196987i
$393$	−0.183740	+	0.318247i	−0.00926845	+	0.0160534i
$394$	−15.0731	−	8.10083i	−0.759372	−	0.408114i
$395$	−3.26995	−	1.88791i	−0.164529	−	0.0949909i
$396$	0.721871	+	11.8376i	0.0362754	+	0.594864i
$397$	−22.1285	+	12.7759i	−1.11060	+	0.641203i	−0.938984	−	0.343962i	$-0.888231\pi$
$397$	−22.1285	+	12.7759i	−1.11060	+	0.641203i	−0.171612	+	0.985165i	$0.554898\pi$
$398$	−5.55909	−	8.98521i	−0.278652	−	0.450388i
$399$	0.386988	+	1.46043i	0.0193736	+	0.0731130i
$400$	0.273697	+	0.363482i	0.0136849	+	0.0181741i
$401$	4.14055	+	7.17165i	0.206769	+	0.358135i	0.950695	−	0.310127i	$-0.100372\pi$
$401$	4.14055	+	7.17165i	0.206769	+	0.358135i	−0.743926	+	0.668262i	$0.767038\pi$
$402$	0.537167	−	0.999500i	0.0267915	−	0.0498505i
$403$	−2.35296	−	1.35848i	−0.117209	−	0.0676708i
$404$	−1.81830	−	29.8175i	−0.0904637	−	1.48347i
$405$	17.5299	+	10.1209i	0.871066	+	0.502910i
$406$	34.1199	−	21.1098i	1.69334	−	1.04766i
$407$	−20.4293			−1.01265
$408$	0.140543	+	0.0648373i	0.00695790	+	0.00320993i
$409$	−8.00331	+	13.8621i	−0.395738	+	0.685439i	−0.993195	−	0.116462i	$-0.962845\pi$
$409$	−8.00331	+	13.8621i	−0.395738	+	0.685439i	0.597457	+	0.801901i	$0.296178\pi$
$410$	15.0681	−	9.32255i	0.744162	−	0.460408i
$411$			0.589657i			0.0290856i
$412$	−12.8247	−	19.3837i	−0.631828	−	0.954964i
$413$	−19.3251	+	11.1574i	−0.950927	+	0.549018i
$414$	−13.5178	+	0.411783i	−0.664365	+	0.0202380i
$415$	−17.6084	−	30.4987i	−0.864363	−	1.49712i
$416$	−0.428447	−	2.79206i	−0.0210063	−	0.136892i
$417$	0.587958			0.0287924
$418$	−8.38924	+	8.86706i	−0.410331	+	0.433702i
$419$		−	24.4736i		−	1.19562i	−0.801640	−	0.597808i	$-0.796039\pi$
$419$		−	24.4736i		−	1.19562i	0.801640	−	0.597808i	$-0.203961\pi$
$420$	−1.56471	+	0.0954174i	−0.0763500	+	0.00465589i
$421$	−10.0033	+	5.77541i	−0.487532	+	0.281476i	−0.723550	−	0.690272i	$-0.757491\pi$
$421$	−10.0033	+	5.77541i	−0.487532	+	0.281476i	0.236018	+	0.971749i	$0.424157\pi$
$422$	−0.250733	−	8.23098i	−0.0122055	−	0.400678i
$423$	−2.34288	−	4.05799i	−0.113915	−	0.197306i
$424$	−29.9185	−	13.8025i	−1.45297	−	0.670307i
$425$	0.0844535			0.00409659
$426$	−0.961028	+	0.594582i	−0.0465620	+	0.0288076i
$427$	7.11106	+	4.10557i	0.344128	+	0.198682i
$428$	−12.7868	+	8.46006i	−0.618072	+	0.408932i
$429$			0.0728809i			0.00351872i
$430$	12.7468	+	20.6027i	0.614703	+	0.993550i
$431$	6.07769	−	10.5269i	0.292752	−	0.507061i	−0.681707	−	0.731625i	$-0.738762\pi$
$431$	6.07769	−	10.5269i	0.292752	−	0.507061i	0.974459	+	0.224564i	$0.0720956\pi$
$432$	−1.62659	−	0.691143i	−0.0782595	−	0.0332526i
$433$	19.2219	−	33.2932i	0.923744	−	1.59997i	0.130174	−	0.991491i	$-0.458446\pi$
$433$	19.2219	−	33.2932i	0.923744	−	1.59997i	0.793570	−	0.608480i	$-0.208220\pi$
$434$	−17.1301	+	31.8738i	−0.822272	+	1.52999i
$435$	−0.870831	+	0.502775i	−0.0417532	+	0.0241062i
$436$	−4.72227	−	2.35551i	−0.226156	−	0.112808i
$437$	−9.81555	−	9.87008i	−0.469541	−	0.472150i
$438$	1.10550	−	0.683967i	0.0528229	−	0.0326812i
$439$	9.70327	+	16.8066i	0.463112	+	0.802133i	0.999114	−	0.0420834i	$-0.0133995\pi$
$439$	9.70327	+	16.8066i	0.463112	+	0.802133i	−0.536002	+	0.844217i	$0.680066\pi$
$440$	−7.30702	−	10.3452i	−0.348349	−	0.493186i
$441$	−22.6306	+	39.1974i	−1.07765	+	1.86654i
$442$	−0.461830	−	0.248204i	−0.0219670	−	0.0118059i
$443$	−16.3666	−	9.44924i	−0.777599	−	0.448947i	0.0579798	−	0.998318i	$-0.481534\pi$
$443$	−16.3666	−	9.44924i	−0.777599	−	0.448947i	−0.835579	+	0.549371i	$0.814867\pi$
$444$	0.678834	−	1.36091i	0.0322161	−	0.0645861i
$445$		−	13.1266i		−	0.622259i
$446$	10.0118	−	0.304980i	0.474071	−	0.0144412i
$447$	0.194749	−	0.337315i	0.00921132	−	0.0159545i
$448$	−36.9946	+	6.83576i	−1.74783	+	0.322959i
$449$	−25.1997			−1.18925			−0.594624	−	0.804004i	$-0.702699\pi$
$449$	−25.1997			−1.18925			−0.594624	+	0.804004i	$0.702699\pi$
$450$	−0.481508	+	0.0146678i	−0.0226985	+	0.000691446i
$451$	−9.50144	+	5.48566i	−0.447405	+	0.258310i
$452$	9.86885	+	14.9161i	0.464192	+	0.701593i
$453$	−0.232088	+	0.133996i	−0.0109045	+	0.00629570i
$454$	−13.5167	−	7.26434i	−0.634368	−	0.340932i
$455$	5.31022			0.248947
$456$	−0.311924	−	0.853493i	−0.0146072	−	0.0399685i
$457$	6.45543			0.301972			0.150986	−	0.988536i	$-0.451755\pi$
$457$	6.45543			0.301972			0.150986	+	0.988536i	$0.451755\pi$
$458$	7.11995	+	3.82652i	0.332694	+	0.178801i
$459$	−0.284087	+	0.164018i	−0.0132601	+	0.00765570i
$460$	12.0453	−	7.96948i	0.561615	−	0.371579i
$461$	−2.49112	+	1.43825i	−0.116023	+	0.0669858i	−0.556888	−	0.830587i	$-0.688005\pi$
$461$	−2.49112	+	1.43825i	−0.116023	+	0.0669858i	0.440866	+	0.897573i	$0.354672\pi$
$462$	0.970199	−	0.0295544i	0.0451377	−	0.00137499i
$463$	−29.6723			−1.37899			−0.689494	−	0.724292i	$-0.742167\pi$
$463$	−29.6723			−1.37899			−0.689494	+	0.724292i	$0.742167\pi$
$464$	−19.2779	+	14.5160i	−0.894952	+	0.673887i
$465$	0.453441	−	0.785383i	0.0210278	−	0.0364213i
$466$	−32.9955	+	1.00512i	−1.52849	+	0.0465611i
$467$			12.3400i			0.571026i	0.958375	+	0.285513i	$0.0921639\pi$
$467$			12.3400i			0.571026i	−0.958375	+	0.285513i	$0.907836\pi$
$468$	2.67621	+	1.33492i	0.123708	+	0.0617065i
$469$	44.3337	+	25.5961i	2.04714	+	1.18192i
$470$	4.40790	+	2.36897i	0.203321	+	0.109272i
$471$	0.704188	−	1.21969i	0.0324473	−	0.0562003i
$472$	10.9626	−	7.74313i	0.504594	−	0.356406i
$473$	−7.50055	−	12.9913i	−0.344876	−	0.597342i
$474$	−0.148006	+	0.0915707i	−0.00679816	+	0.00420598i
$475$	−0.349632	−	0.351575i	−0.0160422	−	0.0161314i
$476$	−3.11684	+	6.24858i	−0.142860	+	0.286403i
$477$	30.2106	−	17.4421i	1.38325	−	0.798619i
$478$	6.99727	−	13.0197i	0.320048	−	0.595509i
$479$	−3.99982	+	6.92789i	−0.182756	+	0.316543i	−0.942818	−	0.333307i	$-0.891835\pi$
$479$	−3.99982	+	6.92789i	−0.182756	+	0.316543i	0.760062	+	0.649851i	$0.225169\pi$
$480$	0.931950	−	0.143009i	0.0425375	−	0.00652744i
$481$	−2.57586	+	4.46151i	−0.117449	+	0.203428i
$482$	−15.3897	−	24.8746i	−0.700983	−	1.13301i
$483$			1.10688i			0.0503646i
$484$	−7.81201	−	11.8073i	−0.355091	−	0.536696i
$485$	2.37115	+	1.36898i	0.107668	+	0.0621623i
$486$	2.38756	−	1.47717i	0.108302	−	0.0670057i
$487$	11.3433			0.514013			0.257007	−	0.966410i	$-0.417264\pi$
$487$	11.3433			0.514013			0.257007	+	0.966410i	$0.417264\pi$
$488$	−4.48446	−	2.06884i	−0.203002	−	0.0936520i
$489$	0.358666	+	0.621228i	0.0162194	+	0.0280929i
$490$	−1.47176	−	48.3143i	−0.0664873	−	2.18262i
$491$	20.0056	−	11.5502i	0.902840	−	0.521255i	0.0247197	−	0.999694i	$-0.492131\pi$
$491$	20.0056	−	11.5502i	0.902840	−	0.521255i	0.878121	+	0.478439i	$0.158797\pi$
$492$	−0.0497131	−	0.815224i	−0.00224124	−	0.0367531i
$493$			4.47913i			0.201730i
$494$	0.878689	+	2.95012i	0.0395341	+	0.132732i
$495$	13.4095			0.602710
$496$	8.51114	−	20.0308i	0.382161	−	0.899410i
$497$	−25.4920	−	44.1535i	−1.14347	−	1.98055i
$498$	−1.62254	+	0.0494261i	−0.0727078	+	0.00221484i
$499$	−17.4946	+	10.1005i	−0.783166	+	0.452161i	−0.837551	−	0.546359i	$-0.816014\pi$
$499$	−17.4946	+	10.1005i	−0.783166	+	0.452161i	0.0543850	+	0.998520i	$0.482680\pi$
$500$	−18.4304	+	12.1940i	−0.824231	+	0.545332i
$501$			1.38594i			0.0619191i
$502$	−0.204643	+	0.126611i	−0.00913367	+	0.00565094i
$503$	−2.59755	+	4.49909i	−0.115819	+	0.200604i	−0.918107	−	0.396333i	$-0.870283\pi$
$503$	−2.59755	+	4.49909i	−0.115819	+	0.200604i	0.802288	+	0.596937i	$0.203616\pi$
$504$	16.6853	−	36.1674i	0.743222	−	1.61102i
$505$	−33.7767			−1.50304
$506$	−7.60510	+	4.70522i	−0.338088	+	0.209173i
$507$	−0.813888	−	0.469898i	−0.0361460	−	0.0208689i
$508$	9.50643	−	0.579711i	0.421779	−	0.0257205i
$509$	−26.5099	−	15.3055i	−1.17503	−	0.678404i	−0.220171	−	0.975461i	$-0.570662\pi$
$509$	−26.5099	−	15.3055i	−1.17503	−	0.678404i	−0.954860	+	0.297057i	$0.903995\pi$
$510$	0.0828468	−	0.154152i	0.00366852	−	0.00682596i
$511$	29.3243	+	50.7912i	1.29723	+	2.24687i
$512$	21.7829	−	6.12426i	0.962676	−	0.270656i
$513$	1.85890	+	0.503614i	0.0820724	+	0.0222351i
$514$	10.8193	+	17.4873i	0.477218	+	0.771332i
$515$	−22.7587	+	13.1397i	−1.00287	+	0.579006i
$516$	1.11466	−	0.0679729i	0.0490701	−	0.00299234i
$517$	−2.68339	−	1.54926i	−0.118015	−	0.0681363i
$518$	60.4368	+	32.4809i	2.65544	+	1.42713i
$519$	0.432864	−	0.749742i	0.0190006	−	0.0329100i
$520$	−3.18057	+	0.291382i	−0.139477	+	0.0127780i
$521$	−24.6215			−1.07869			−0.539343	−	0.842086i	$-0.681327\pi$
$521$	−24.6215			−1.07869			−0.539343	+	0.842086i	$0.681327\pi$
$522$	−0.777930	−	25.5376i	−0.0340491	−	1.11775i
$523$	−28.6708	−	16.5531i	−1.25369	−	0.723816i	−0.281847	−	0.959459i	$-0.590947\pi$
$523$	−28.6708	−	16.5531i	−1.25369	−	0.723816i	−0.971840	+	0.235643i	$0.924280\pi$
$524$	8.92305	+	4.45089i	0.389805	+	0.194438i
$525$			0.0394272i			0.00172074i
$526$	21.3175	−	0.649377i	0.929486	−	0.0283142i
$527$	−2.01981	−	3.49842i	−0.0879844	−	0.152393i
$528$	−0.579481	+	0.0709384i	−0.0252187	+	0.00308720i
$529$	6.40096	+	11.0868i	0.278303	+	0.482034i
$530$	−17.6363	+	32.8156i	−0.766072	+	1.42542i
$531$			14.2098i			0.616652i
$532$	38.9160	−	12.8935i	1.68722	−	0.559006i
$533$			2.76666i			0.119837i
$534$	−0.532965	−	0.286435i	−0.0230637	−	0.0123952i
$535$	8.66787	+	15.0132i	0.374745	+	0.649077i
$536$	−27.9583	−	12.8981i	−1.20761	−	0.557115i
$537$	0.412621	+	0.714680i	0.0178059	+	0.0308407i
$538$	0.315432	+	10.3549i	0.0135992	+	0.446430i
$539$			29.9295i			1.28916i
$540$	−0.891958	+	1.78818i	−0.0383838	+	0.0769510i
$541$	−15.7964	−	9.12004i	−0.679139	−	0.392101i	0.120391	−	0.992727i	$-0.461585\pi$
$541$	−15.7964	−	9.12004i	−0.679139	−	0.392101i	−0.799531	+	0.600625i	$0.794918\pi$
$542$	11.6577	−	0.355118i	0.500740	−	0.0152536i
$543$	−0.871043			−0.0373800
$544$	1.52397	−	3.91363i	0.0653395	−	0.167795i
$545$	−2.98338	+	5.16737i	−0.127794	+	0.221346i
$546$	0.115874	−	0.215606i	0.00495896	−	0.00922707i
$547$	18.9714	+	10.9532i	0.811160	+	0.468323i	0.847358	−	0.531021i	$-0.178192\pi$
$547$	18.9714	+	10.9532i	0.811160	+	0.468323i	−0.0361988	+	0.999345i	$0.511525\pi$
$548$	15.9706	−	0.973904i	0.682231	−	0.0416031i
$549$	4.52825	−	2.61438i	0.193261	−	0.111579i
$550$	−0.270895	+	0.167601i	−0.0115510	+	0.00714654i
$551$	18.6463	−	18.5433i	0.794360	−	0.789971i
$552$	−0.0607365	−	0.662966i	−0.00258512	−	0.0282177i
$553$	−3.92599	−	6.80001i	−0.166950	−	0.289166i
$554$	−21.5473	−	11.5803i	−0.915458	−	0.492000i
$555$	−1.48919	−	0.859782i	−0.0632125	−	0.0364957i
$556$	−0.971098	−	15.9246i	−0.0411837	−	0.675354i
$557$	24.5414	+	14.1690i	1.03985	+	0.600359i	0.919791	−	0.392408i	$-0.128358\pi$
$557$	24.5414	+	14.1690i	1.03985	+	0.600359i	0.120061	+	0.992767i	$0.461691\pi$
$558$	12.1235	+	19.5953i	0.513228	+	0.829535i
$559$	−3.78286			−0.159998
$560$	5.16869	+	42.2219i	0.218417	+	1.78420i
$561$	−0.0541802	+	0.0938428i	−0.00228749	+	0.00396205i
$562$	−18.6173	−	30.0914i	−0.785325	−	1.26933i
$563$			5.98383i			0.252188i	0.992018	+	0.126094i	$0.0402442\pi$
$563$			5.98383i			0.252188i	−0.992018	+	0.126094i	$0.959756\pi$
$564$	0.192370	−	0.127277i	0.00810022	−	0.00535931i
$565$	17.5132	−	10.1113i	0.736787	−	0.425384i
$566$	0.798791	+	26.2224i	0.0335757	+	1.10221i
$567$	21.0468	+	36.4541i	0.883883	+	1.53093i
$568$	17.6913	+	25.0470i	0.742310	+	1.05095i
$569$	26.0900			1.09375			0.546875	−	0.837214i	$-0.315817\pi$
$569$	26.0900			1.09375			0.546875	+	0.837214i	$0.315817\pi$
$570$	−0.984706	+	0.293293i	−0.0412448	+	0.0122847i
$571$			17.5053i			0.732573i	0.930502	+	0.366287i	$0.119371\pi$
$571$			17.5053i			0.732573i	−0.930502	+	0.366287i	$0.880629\pi$
$572$	1.97395	−	0.120373i	0.0825349	−	0.00503306i
$573$	0.807299	−	0.466094i	0.0337254	−	0.0194714i
$574$	36.8301	−	1.12193i	1.53726	−	0.0468283i
$575$	−0.181629	−	0.314591i	−0.00757445	−	0.0131193i
$576$	−8.00912	+	22.5781i	−0.333713	+	0.940753i
$577$	−4.31463			−0.179621			−0.0898103	−	0.995959i	$-0.528626\pi$
$577$	−4.31463			−0.179621			−0.0898103	+	0.995959i	$0.528626\pi$
$578$	12.2390	+	19.7821i	0.509077	+	0.822826i
$579$	−0.468874	−	0.270705i	−0.0194858	−	0.0112501i
$580$	15.0557	+	22.7557i	0.625156	+	0.944879i
$581$		−	73.2350i		−	3.03830i
$582$	0.107324	−	0.0664008i	0.00444873	−	0.00275240i
$583$	11.5338	−	19.9771i	0.477681	−	0.827368i
$584$	−20.3509	−	28.8124i	−0.842125	−	1.19227i
$585$	1.69075	−	2.92846i	0.0699037	−	0.121077i
$586$	1.27413	+	0.684763i	0.0526338	+	0.0282873i
$587$	22.3055	−	12.8781i	0.920645	−	0.531535i	0.0368044	−	0.999322i	$-0.488282\pi$
$587$	22.3055	−	12.8781i	0.920645	−	0.531535i	0.883841	+	0.467788i	$0.154949\pi$
$588$	−1.99378	−	0.994510i	−0.0822219	−	0.0410129i
$589$	−6.20180	+	22.8916i	−0.255541	+	0.943231i
$590$	−7.98430	−	12.9051i	−0.328708	−	0.531294i
$591$	0.445922	+	0.772359i	0.0183428	+	0.0317706i
$592$	−37.9810	−	16.1382i	−1.56101	−	0.663276i
$593$	18.0229	−	31.2166i	0.740112	−	1.28191i	−0.212331	−	0.977198i	$-0.568106\pi$
$593$	18.0229	−	31.2166i	0.740112	−	1.28191i	0.952444	−	0.304714i	$-0.0985610\pi$
$594$	0.585746	−	1.08989i	0.0240335	−	0.0447187i
$595$	6.83754	+	3.94766i	0.280312	+	0.161838i
$596$	−9.45771	−	4.71758i	−0.387403	−	0.193239i
$597$			0.550671i			0.0225374i
$598$	0.0686654	+	2.25412i	0.00280794	+	0.0921779i
$599$	−6.14336	+	10.6406i	−0.251011	+	0.434763i	−0.963804	−	0.266610i	$-0.914096\pi$
$599$	−6.14336	+	10.6406i	−0.251011	+	0.434763i	0.712794	+	0.701374i	$0.247430\pi$
$600$	−0.00216345	−	0.0236150i	−8.83224e−5	−	0.000964078i
$601$	−9.74846			−0.397648			−0.198824	−	0.980035i	$-0.563712\pi$
$601$	−9.74846			−0.397648			−0.198824	+	0.980035i	$0.563712\pi$
$602$	1.53401	+	50.3579i	0.0625217	+	2.05244i
$603$	28.2312	−	16.2993i	1.14967	−	0.663760i
$604$	4.01256	+	6.06471i	0.163269	+	0.246769i
$605$	−13.8632	+	8.00390i	−0.563618	+	0.325405i
$606$	−0.737040	+	1.37140i	−0.0299402	+	0.0557094i
$607$	28.3299			1.14988			0.574938	−	0.818197i	$-0.305026\pi$
$607$	28.3299			1.14988			0.574938	+	0.818197i	$0.305026\pi$
$608$	−22.6013	+	9.85800i	−0.916605	+	0.399795i
$609$	−2.09108			−0.0847350
$610$	−2.64349	+	4.91871i	−0.107032	+	0.199153i
$611$	−0.676677	+	0.390680i	−0.0273754	+	0.0158052i
$612$	2.45356	+	3.70838i	0.0991792	+	0.149902i
$613$	17.4855	−	10.0952i	0.706232	−	0.407743i	−0.103433	−	0.994636i	$-0.532983\pi$
$613$	17.4855	−	10.0952i	0.706232	−	0.407743i	0.809664	+	0.586893i	$0.199649\pi$
$614$	1.13128	+	37.1373i	0.0456549	+	1.49874i
$615$	−0.923470			−0.0372379
$616$	−2.40289	−	26.2286i	−0.0968153	−	1.05678i
$617$	6.87561	−	11.9089i	0.276801	−	0.479434i	−0.693787	−	0.720181i	$-0.744059\pi$
$617$	6.87561	−	11.9089i	0.276801	−	0.479434i	0.970588	+	0.240746i	$0.0773922\pi$
$618$	0.0368828	+	1.21077i	0.00148364	+	0.0487044i
$619$			4.39271i			0.176558i	0.996096	+	0.0882791i	$0.0281367\pi$
$619$			4.39271i			0.176558i	−0.996096	+	0.0882791i	$0.971863\pi$
$620$	−22.0207	−	10.9841i	−0.884373	−	0.441132i
$621$	1.22194	+	0.705487i	0.0490347	+	0.0283102i
$622$	−16.2035	+	30.1496i	−0.649699	+	1.20889i
$623$	13.6486	−	23.6401i	0.546821	−	0.947122i
$624$	−0.0575724	+	0.135496i	−0.00230474	+	0.00542417i
$625$	12.7779	+	22.1320i	0.511116	+	0.885279i
$626$	21.3590	+	34.5228i	0.853678	+	1.37981i
$627$	0.614965	−	0.162955i	0.0245593	−	0.00650779i
$628$	−34.1979	−	17.0582i	−1.36464	−	0.680695i
$629$	−6.63345	+	3.82982i	−0.264493	+	0.152705i
$630$	−39.6696	−	21.3199i	−1.58048	−	0.849404i
$631$	13.8673	−	24.0188i	0.552047	−	0.956173i	−0.446080	−	0.894993i	$-0.647180\pi$
$631$	13.8673	−	24.0188i	0.552047	−	0.956173i	0.998127	−	0.0611800i	$-0.0194864\pi$
$632$	2.72461	+	3.85745i	0.108379	+	0.153441i
$633$	−0.214590	+	0.371681i	−0.00852919	+	0.0147730i
$634$	−12.3255	+	7.62568i	−0.489506	+	0.302854i
$635$		−	10.7687i		−	0.427343i
$636$	0.947539	+	1.43214i	0.0375724	+	0.0567880i
$637$	6.53623	+	3.77370i	0.258975	+	0.149519i
$638$	−8.88900	−	14.3674i	−0.351919	−	0.568810i
$639$	−32.4661			−1.28434
$640$	−5.41259	−	25.0053i	−0.213952	−	0.988420i
$641$	2.60078	+	4.50468i	0.102725	+	0.177924i	0.912806	−	0.408393i	$-0.133911\pi$
$641$	2.60078	+	4.50468i	0.102725	+	0.177924i	−0.810082	+	0.586317i	$0.800577\pi$
$642$	0.798707	−	0.0243304i	0.0315225	−	0.000960243i
$643$	−9.12347	+	5.26744i	−0.359794	+	0.207727i	−0.668991	−	0.743271i	$-0.733273\pi$
$643$	−9.12347	+	5.26744i	−0.359794	+	0.207727i	0.309196	+	0.950998i	$0.399940\pi$
$644$	29.9793	−	1.82817i	1.18135	−	0.0720398i
$645$		−	1.26266i		−	0.0497173i
$646$	−1.06172	+	4.45185i	−0.0417729	+	0.175156i
$647$	−29.5690			−1.16248			−0.581239	−	0.813733i	$-0.697432\pi$
$647$	−29.5690			−1.16248			−0.581239	+	0.813733i	$0.697432\pi$
$648$	−14.6063	−	20.6794i	−0.573791	−	0.812364i
$649$	4.69819	+	8.13750i	0.184420	+	0.319425i
$650$	0.00244588	+	0.0802923i	9.59353e−5	+	0.00314932i
$651$	1.63324	−	0.942951i	0.0640117	−	0.0369572i
$652$	16.2333	−	10.7404i	0.635746	−	0.420625i
$653$		−	5.92429i		−	0.231835i	−0.993259	−	0.115918i	$-0.963019\pi$
$653$		−	5.92429i		−	0.231835i	0.993259	−	0.115918i	$-0.0369809\pi$
$654$	0.144705	+	0.233889i	0.00565843	+	0.00914577i
$655$	5.63730	−	9.76410i	0.220268	−	0.381515i
$656$	−21.9979	+	2.69292i	−0.858874	+	0.105141i
$657$	37.3468			1.45704
$658$	5.47518	+	8.84958i	0.213445	+	0.344992i
$659$	−13.1894	−	7.61488i	−0.513785	−	0.296634i	0.220603	−	0.975364i	$-0.429197\pi$
$659$	−13.1894	−	7.61488i	−0.513785	−	0.296634i	−0.734388	+	0.678730i	$0.762531\pi$
$660$	0.0401788	+	0.658875i	0.00156396	+	0.0256467i
$661$	−7.12782	−	4.11525i	−0.277240	−	0.160065i	0.354933	−	0.934892i	$-0.384504\pi$
$661$	−7.12782	−	4.11525i	−0.277240	−	0.160065i	−0.632173	+	0.774827i	$0.717837\pi$
$662$	20.7945	+	11.1757i	0.808202	+	0.434357i
$663$	0.0136627	+	0.0236645i	0.000530617	+	0.000919055i
$664$	4.01855	+	43.8642i	0.155950	+	1.70226i
$665$	−11.8731	−	44.8073i	−0.460421	−	1.73755i
$666$	37.1552	−	22.9877i	1.43973	−	0.890754i
$667$	16.6848	−	9.63299i	0.646039	−	0.372991i
$668$	37.5376	−	2.28908i	1.45237	−	0.0885670i
$669$	−0.452094	−	0.261017i	−0.0174790	−	0.0100915i
$670$	−16.4808	+	30.6656i	−0.636708	+	1.18471i
$671$	1.72879	−	2.99435i	0.0667393	−	0.115596i
$672$	1.82708	+	0.711465i	0.0704812	+	0.0274454i
$673$	−5.85922			−0.225856			−0.112928	−	0.993603i	$-0.536023\pi$
$673$	−5.85922			−0.225856			−0.112928	+	0.993603i	$0.536023\pi$
$674$	−39.9409	+	1.21669i	−1.53847	+	0.0468651i
$675$	0.0435257	+	0.0251296i	0.00167531	+	0.000967239i
$676$	−11.3828	+	22.8199i	−0.437798	+	0.877690i
$677$		−	2.54790i		−	0.0979236i	−0.998801	−	0.0489618i	$-0.984409\pi$
$677$		−	2.54790i		−	0.0979236i	0.998801	−	0.0489618i	$-0.0155913\pi$
$678$	−0.0283819	−	0.931711i	−0.00109000	−	0.0357821i
$679$	2.84686	+	4.93091i	0.109252	+	0.189231i
$680$	−4.31197	−	1.98927i	−0.165357	−	0.0762849i
$681$	0.399876	+	0.692605i	0.0153233	+	0.0265407i
$682$	13.4215	+	7.21322i	0.513938	+	0.276209i
$683$		−	24.9303i		−	0.953930i	−0.878922	−	0.476965i	$-0.841737\pi$
$683$		−	24.9303i		−	0.953930i	0.878922	−	0.476965i	$-0.158263\pi$
$684$	5.28018	−	25.5665i	0.201893	−	0.977559i
$685$		−	18.0912i		−	0.691230i
$686$	25.5470	−	47.5350i	0.975390	−	1.81489i
$687$	−0.210636	−	0.364832i	−0.00803627	−	0.0139192i
$688$	−3.68204	−	30.0778i	−0.140376	−	1.14671i
$689$	−2.90850	−	5.03767i	−0.110805	−	0.191920i
$690$	−0.752392	+	0.0229195i	−0.0286431	+	0.000872531i
$691$			51.3756i			1.95442i	0.212277	+	0.977209i	$0.431912\pi$
$691$			51.3756i			1.95442i	−0.212277	+	0.977209i	$0.568088\pi$
$692$	−21.0214	−	10.4856i	−0.799114	−	0.398604i
$693$	24.1496	+	13.9428i	0.917368	+	0.529643i
$694$	−1.12765	−	37.0180i	−0.0428050	−	1.40519i
$695$	−18.0391			−0.684262
$696$	1.25246	−	0.114742i	0.0474743	−	0.00434928i
$697$	−2.05676	+	3.56241i	−0.0779052	+	0.134936i
$698$	8.74420	+	4.69945i	0.330973	+	0.177877i
$699$	1.48996	+	0.860227i	0.0563553	+	0.0325368i
$700$	1.06787	−	0.0651197i	0.0403617	−	0.00246129i
$701$	−10.9994	+	6.35049i	−0.415441	+	0.239855i	−0.693125	−	0.720818i	$-0.743766\pi$
$701$	−10.9994	+	6.35049i	−0.415441	+	0.239855i	0.277684	+	0.960672i	$0.410433\pi$
$702$	−0.164164	−	0.265340i	−0.00619597	−	0.0100146i
$703$	43.4054	+	11.7594i	1.63706	+	0.443514i
$704$	2.87843	+	15.5778i	0.108485	+	0.587112i
$705$	−0.130403	−	0.225865i	−0.00491126	−	0.00850656i
$706$	−9.20710	+	17.1315i	−0.346514	+	0.644754i
$707$	−60.8297	−	35.1200i	−2.28774	−	1.32082i
$708$	−0.698199	+	0.0425768i	−0.0262399	+	0.00160013i
$709$	−10.6515	−	6.14967i	−0.400027	−	0.230956i	0.286469	−	0.958090i	$-0.407519\pi$
$709$	−10.6515	−	6.14967i	−0.400027	−	0.230956i	−0.686496	+	0.727134i	$0.740852\pi$
$710$	29.4852	−	18.2423i	1.10656	−	0.684622i
$711$	−5.00006			−0.187517
$712$	−6.87770	+	14.9082i	−0.257753	+	0.558710i
$713$	−8.68778	+	15.0477i	−0.325360	+	0.563540i
$714$	0.309485	−	0.191476i	0.0115822	−	0.00716582i
$715$		−	2.23605i		−	0.0836235i
$716$	18.6753	−	12.3561i	0.697930	−	0.461768i
$717$	−0.667142	+	0.385175i	−0.0249149	+	0.0143846i
$718$	−4.22045	+	0.128564i	−0.157506	+	0.00479797i
$719$	17.5424	+	30.3843i	0.654222	+	1.13314i	0.982088	+	0.188421i	$0.0603369\pi$
$719$	17.5424	+	30.3843i	0.654222	+	1.13314i	−0.327867	+	0.944724i	$0.606330\pi$
$720$	24.9301	+	10.5928i	0.929088	+	0.394772i
$721$	−54.6494			−2.03525
$722$	22.9283	−	14.0105i	0.853302	−	0.521417i
$723$			1.52447i			0.0566957i
$724$	1.43865	+	23.5918i	0.0534671	+	0.876784i
$725$	0.594317	−	0.343129i	0.0220724	−	0.0127435i
$726$	0.0224666	+	0.737526i	0.000833816	+	0.0273722i
$727$	−12.3695	−	21.4246i	−0.458759	−	0.794593i	0.540137	−	0.841577i	$-0.318372\pi$
$727$	−12.3695	−	21.4246i	−0.458759	−	0.794593i	−0.998896	+	0.0469839i	$0.985039\pi$
$728$	−6.03098	−	2.78230i	−0.223523	−	0.103119i
$729$	26.7071			0.989151
$730$	−33.9178	+	20.9847i	−1.25535	+	0.776679i
$731$	−4.87089	−	2.81221i	−0.180156	−	0.104013i
$732$	0.142026	+	0.214662i	0.00524943	+	0.00793414i
$733$		−	20.0808i		−	0.741701i	−0.928693	−	0.370851i	$-0.879066\pi$
$733$		−	20.0808i		−	0.741701i	0.928693	−	0.370851i	$-0.120934\pi$
$734$	−14.8406	−	23.9871i	−0.547778	−	0.885379i
$735$	−1.25960	+	2.18170i	−0.0464612	+	0.0804731i
$736$	−17.8558	+	2.74001i	−0.658175	+	0.100998i
$737$	10.7781	−	18.6682i	0.397017	−	0.687653i
$738$	11.1078	−	20.6681i	0.408884	−	0.760805i
$739$	−1.16064	+	0.670093i	−0.0426947	+	0.0246498i	−0.521195	−	0.853437i	$-0.674514\pi$
$739$	−1.16064	+	0.670093i	−0.0426947	+	0.0246498i	0.478501	+	0.878087i	$0.341180\pi$
$740$	−20.8273	+	41.7541i	−0.765625	+	1.53491i
$741$	0.0419512	−	0.154847i	0.00154112	−	0.00568844i
$742$	−65.8827	+	40.7612i	−2.41863	+	1.49639i
$743$	5.99092	+	10.3766i	0.219786	+	0.380680i	0.954742	−	0.297434i	$-0.0961309\pi$
$743$	5.99092	+	10.3766i	0.219786	+	0.380680i	−0.734957	+	0.678114i	$0.762798\pi$
$744$	−0.926490	+	0.654401i	−0.0339668	+	0.0239915i
$745$	−5.97508	+	10.3491i	−0.218910	+	0.379163i
$746$	−21.0372	−	11.3062i	−0.770227	−	0.413948i
$747$	−40.3873	−	23.3176i	−1.47770	−	0.853148i
$748$	2.63118	+	1.31245i	0.0962055	+	0.0479880i
$749$			36.0504i			1.31725i
$750$	1.15123	−	0.0350689i	0.0420368	−	0.00128053i
$751$	9.58183	−	16.5962i	0.349646	−	0.605605i	−0.636541	−	0.771243i	$-0.719635\pi$
$751$	9.58183	−	16.5962i	0.349646	−	0.605605i	0.986187	+	0.165639i	$0.0529686\pi$
$752$	−3.76496	−	5.00004i	−0.137294	−	0.182333i
$753$	0.0125418			0.000457049
$754$	−4.25843	+	0.129721i	−0.155083	+	0.00472417i
$755$	7.12068	−	4.11113i	0.259148	−	0.149619i
$756$	−3.46566	+	2.29297i	−0.126045	+	0.0833945i
$757$	−35.7919	+	20.6645i	−1.30088	+	0.751062i	−0.980555	−	0.196246i	$-0.937125\pi$
$757$	−35.7919	+	20.6645i	−1.30088	+	0.751062i	−0.320324	+	0.947308i	$0.603792\pi$
$758$	−33.0703	−	17.7731i	−1.20117	−	0.645550i
$759$	0.466088			0.0169179
$760$	9.57011	+	26.1859i	0.347144	+	0.949864i
$761$	30.3361			1.09968			0.549841	−	0.835269i	$-0.314688\pi$
$761$	30.3361			1.09968			0.549841	+	0.835269i	$0.314688\pi$
$762$	−0.437231	−	0.234984i	−0.0158392	−	0.00851256i
$763$	−10.7458	+	6.20408i	−0.389023	+	0.224603i
$764$	−13.9573	−	21.0955i	−0.504959	−	0.763210i
$765$	4.35408	−	2.51383i	0.157422	−	0.0908876i
$766$	−6.73093	+	0.205039i	−0.243198	+	0.00740835i
$767$	2.36951			0.0855579
$768$	−1.13337	−	0.325878i	−0.0408971	−	0.0117591i
$769$	7.68635	−	13.3131i	0.277177	−	0.480084i	−0.693505	−	0.720452i	$-0.743935\pi$
$769$	7.68635	−	13.3131i	0.277177	−	0.480084i	0.970682	+	0.240367i	$0.0772679\pi$
$770$	−29.7666	+	0.906755i	−1.07271	+	0.0326772i
$771$		−	1.07173i		−	0.0385975i
$772$	−6.55751	+	13.1464i	−0.236010	+	0.473149i
$773$	−14.3035	−	8.25814i	−0.514462	−	0.297025i	0.220204	−	0.975454i	$-0.429328\pi$
$773$	−14.3035	−	8.25814i	−0.514462	−	0.297025i	−0.734666	+	0.678429i	$0.762661\pi$
$774$	28.2596	+	15.1877i	1.01577	+	0.545912i
$775$	−0.309461	+	0.536001i	−0.0111162	+	0.0192537i
$776$	−1.97570	−	2.79716i	−0.0709235	−	0.100412i
$777$	−1.78796	−	3.09683i	−0.0641426	−	0.111098i
$778$	23.6258	−	14.6171i	0.847026	−	0.524049i
$779$	23.3449	−	6.18599i	0.836419	−	0.221636i
$780$	0.148956	+	0.0743004i	0.00533348	+	0.00266038i
$781$	−18.5923	+	10.7343i	−0.665286	+	0.384103i
$782$	−1.58732	+	2.95350i	−0.0567623	+	0.105617i
$783$	−1.33279	+	2.30846i	−0.0476300	+	0.0824976i
$784$	−23.6429	+	55.6432i	−0.844389	+	1.98726i
$785$	−21.6051	+	37.4212i	−0.771120	+	1.33562i
$786$	−0.273431	−	0.441948i	−0.00975295	−	0.0157638i
$787$			45.6546i			1.62741i	0.581277	+	0.813705i	$0.302553\pi$
$787$			45.6546i			1.62741i	−0.581277	+	0.813705i	$0.697447\pi$
$788$	20.1825	−	13.3533i	0.718973	−	0.475691i
$789$	−0.962620	−	0.555769i	−0.0342702	−	0.0197859i
$790$	4.54097	−	2.80947i	0.161561	−	0.0999565i
$791$	42.0537			1.49526
$792$	−15.2295	−	7.02592i	−0.541158	−	0.249655i
$793$	−0.435953	−	0.755093i	−0.0154811	−	0.0268141i
$794$	−1.10026	−	36.1189i	−0.0390468	−	1.28181i
$795$	1.68150	−	0.970815i	0.0596367	−	0.0344312i
$796$	14.9147	−	0.909512i	0.528637	−	0.0322368i
$797$			21.7112i			0.769052i	0.923114	+	0.384526i	$0.125635\pi$
$797$			21.7112i			0.769052i	−0.923114	+	0.384526i	$0.874365\pi$
$798$	−2.07835	−	0.495667i	−0.0735729	−	0.0175464i
$799$	−1.16174			−0.0410993
$800$	−0.636029	+	0.0975996i	−0.0224870	+	0.00345067i
$801$	−8.69131	−	15.0538i	−0.307092	−	0.531900i
$802$	−11.7058	+	0.356585i	−0.413347	+	0.0125914i
$803$	21.3874	−	12.3480i	0.754744	−	0.435752i
$804$	0.885457	+	1.33831i	0.0312277	+	0.0471984i
$805$		−	33.9600i		−	1.19693i
$806$	3.26755	−	2.02161i	0.115094	−	0.0712082i
$807$	0.269962	−	0.467588i	0.00950310	−	0.0164599i
$808$	38.3612	+	17.6974i	1.34954	+	0.622591i
$809$	4.74208			0.166723			0.0833613	−	0.996519i	$-0.473434\pi$
$809$	4.74208			0.166723			0.0833613	+	0.996519i	$0.473434\pi$
$810$	−24.3437	+	15.0613i	−0.855350	+	0.529199i
$811$	−17.1243	−	9.88671i	−0.601315	−	0.347169i	0.168244	−	0.985745i	$-0.446190\pi$
$811$	−17.1243	−	9.88671i	−0.601315	−	0.347169i	−0.769559	+	0.638576i	$0.779524\pi$
$812$	3.45373	+	56.6362i	0.121202	+	1.98754i
$813$	−0.526418	−	0.303928i	−0.0184623	−	0.0106592i
$814$	13.6772	−	25.4490i	0.479386	−	0.891986i
$815$	−11.0042	−	19.0598i	−0.385460	−	0.667637i
$816$	−0.174860	+	0.131667i	−0.00612132	+	0.00460927i
$817$	8.45812	+	31.9196i	0.295912	+	1.11672i
$818$	−11.9100	−	19.2503i	−0.416425	−	0.673072i
$819$	6.08986	−	3.51598i	0.212797	−	0.122858i
$820$	1.52524	+	25.0118i	0.0532638	+	0.873450i
$821$	4.45174	+	2.57021i	0.155367	+	0.0897011i	0.575668	−	0.817684i	$-0.304742\pi$
$821$	4.45174	+	2.57021i	0.155367	+	0.0897011i	−0.420301	+	0.907385i	$0.638075\pi$
$822$	−0.734540	−	0.394768i	−0.0256200	−	0.0137691i
$823$	−11.4962	+	19.9120i	−0.400731	+	0.694087i	−0.993814	−	0.111054i	$-0.964577\pi$
$823$	−11.4962	+	19.9120i	−0.400731	+	0.694087i	0.593083	+	0.805141i	$0.297911\pi$
$824$	32.7323	−	2.99872i	1.14029	−	0.104465i
$825$	0.0166022			0.000578014
$826$	−0.960873	−	31.5431i	−0.0334330	−	1.09753i
$827$	−12.7107	−	7.33853i	−0.441994	−	0.255186i	0.262449	−	0.964946i	$-0.415470\pi$
$827$	−12.7107	−	7.33853i	−0.441994	−	0.255186i	−0.704443	+	0.709760i	$0.748803\pi$
$828$	8.53706	−	17.1149i	0.296683	−	0.594785i
$829$			41.7030i			1.44840i	0.689588	+	0.724202i	$0.257792\pi$
$829$			41.7030i			1.44840i	−0.689588	+	0.724202i	$0.742208\pi$
$830$	49.7810	−	1.51644i	1.72792	−	0.0526363i
$831$	0.637454	+	1.10410i	0.0221130	+	0.0383009i
$832$	3.76493	+	1.33553i	0.130526	+	0.0463013i
$833$	5.61079	+	9.71817i	0.194402	+	0.336715i
$834$	−0.393631	+	0.732424i	−0.0136303	+	0.0253618i
$835$		−	42.5218i		−	1.47153i
$836$	−5.42927	−	16.3869i	−0.187775	−	0.566754i
$837$		−	2.40402i		−	0.0830952i
$838$	30.4870	+	16.3848i	1.05316	+	0.566003i
$839$	−21.9878	−	38.0839i	−0.759102	−	1.31480i	−0.943309	−	0.331915i	$-0.892305\pi$
$839$	−21.9878	−	38.0839i	−0.759102	−	1.31480i	0.184208	−	0.982887i	$-0.441028\pi$
$840$	0.928692	−	2.01305i	0.0320429	−	0.0694568i
$841$	3.69842	+	6.40585i	0.127532	+	0.220891i
$842$	−0.497379	−	16.3278i	−0.0171408	−	0.562692i
$843$			1.84419i			0.0635172i
$844$	10.4212	+	5.19820i	0.358714	+	0.178929i
$845$	24.9708	+	14.4169i	0.859022	+	0.495957i
$846$	6.62360	−	0.201769i	0.227724	−	0.00693697i
$847$	−33.2890			−1.14382
$848$	37.2239	−	28.0291i	1.27827	−	0.962523i
$849$	0.683644	−	1.18411i	0.0234626	−	0.0406384i
$850$	−0.0565406	+	0.105204i	−0.00193933	+	0.00360848i
$851$	28.5323	+	16.4731i	0.978075	+	0.564692i
$852$	−0.0972783	−	1.59522i	−0.00333270	−	0.0546515i
$853$	35.8544	−	20.7005i	1.22763	−	0.708773i	0.261097	−	0.965313i	$-0.415916\pi$
$853$	35.8544	−	20.7005i	1.22763	−	0.708773i	0.966534	+	0.256540i	$0.0825826\pi$
$854$	−9.87510	+	6.10966i	−0.337919	+	0.209068i
$855$	−28.4905	−	7.71867i	−0.974355	−	0.263973i
$856$	−1.97816	−	21.5925i	−0.0676121	−	0.738016i
$857$	11.4143	+	19.7701i	0.389903	+	0.675333i	0.992436	−	0.122762i	$-0.0391750\pi$
$857$	11.4143	+	19.7701i	0.389903	+	0.675333i	−0.602533	+	0.798094i	$0.705842\pi$
$858$	−0.0907882	−	0.0487929i	−0.00309946	−	0.00166576i
$859$	41.9571	+	24.2239i	1.43156	+	0.826509i	0.997240	−	0.0742508i	$-0.0236565\pi$
$859$	41.9571	+	24.2239i	1.43156	+	0.826509i	0.434317	+	0.900760i	$0.356990\pi$
$860$	−34.1987	+	2.08547i	−1.16617	+	0.0711139i
$861$	−1.66311	−	0.960199i	−0.0566787	−	0.0327235i
$862$	9.04445	+	14.6186i	0.308055	+	0.497912i
$863$	−54.0511			−1.83992			−0.919960	−	0.392013i	$-0.871779\pi$
$863$	−54.0511			−1.83992			−0.919960	+	0.392013i	$0.871779\pi$
$864$	1.94995	−	1.56355i	0.0663385	−	0.0531929i
$865$	−13.2807	+	23.0028i	−0.451556	+	0.782118i
$866$	28.6048	+	46.2342i	0.972031	+	1.57110i
$867$		−	1.21237i		−	0.0411743i
$868$	−28.2370	−	42.6782i	−0.958425	−	1.44859i
$869$	−2.86338	+	1.65317i	−0.0971335	+	0.0560800i
$870$	−0.0432990	−	1.42140i	−0.00146797	−	0.0481900i
$871$	−2.71794	−	4.70761i	−0.0920939	−	0.159511i
$872$	6.09577	−	4.30559i	0.206429	−	0.145806i
$873$	3.62570			0.122711
$874$	18.8666	−	5.61940i	0.638173	−	0.190079i
$875$			51.9617i			1.75663i
$876$	0.111902	+	1.83504i	0.00378083	+	0.0620002i
$877$	−21.3846	+	12.3464i	−0.722106	+	0.416908i	−0.815527	−	0.578718i	$-0.803553\pi$
$877$	−21.3846	+	12.3464i	−0.722106	+	0.416908i	0.0934212	+	0.995627i	$0.470220\pi$
$878$	−27.4323	+	0.835647i	−0.925794	+	0.0282017i
$879$	−0.0376937	−	0.0652875i	−0.00127138	−	0.00220209i
$880$	17.7790	−	2.17645i	0.599330	−	0.0733682i
$881$	22.1718			0.746988			0.373494	−	0.927633i	$-0.378160\pi$
$881$	22.1718			0.746988			0.373494	+	0.927633i	$0.378160\pi$
$882$	−33.6775	−	54.4333i	−1.13398	−	1.83287i
$883$	37.4154	+	21.6018i	1.25913	+	0.726959i	0.972905	−	0.231204i	$-0.0742664\pi$
$883$	37.4154	+	21.6018i	1.25913	+	0.726959i	0.286224	+	0.958163i	$0.407600\pi$
$884$	0.618379	−	0.409135i	0.0207983	−	0.0137607i
$885$			0.790906i			0.0265860i
$886$	22.7282	−	14.0618i	0.763569	−	0.472415i
$887$	−15.8289	+	27.4165i	−0.531483	+	0.920556i	0.467841	+	0.883812i	$0.345032\pi$
$887$	−15.8289	+	27.4165i	−0.531483	+	0.920556i	−0.999325	+	0.0367436i	$0.988302\pi$
$888$	1.24083	+	1.75674i	0.0416395	+	0.0589525i
$889$	11.1970	−	19.3938i	0.375535	−	0.650446i
$890$	16.3518	+	8.78807i	0.548115	+	0.294577i
$891$	15.3503	−	8.86249i	0.514254	−	0.296904i
$892$	−6.32284	+	12.6759i	−0.211704	+	0.424421i
$893$	4.80952	+	4.83624i	0.160944	+	0.161839i
$894$	0.289814	+	0.468429i	0.00969283	+	0.0156666i
$895$	−12.6596	−	21.9270i	−0.423163	−	0.732940i
$896$	16.2521	−	50.6608i	0.542943	−	1.69246i
$897$	0.0587673	−	0.101788i	0.00196218	−	0.00339860i
$898$	16.8709	−	31.3914i	0.562989	−	1.04755i
$899$	−28.4277	−	16.4127i	−0.948117	−	0.547396i
$900$	0.304092	−	0.609638i	0.0101364	−	0.0203213i
$901$		−	8.64881i		−	0.288134i
$902$	−0.472425	−	15.5086i	−0.0157300	−	0.516379i
$903$	1.31288	−	2.27398i	0.0436900	−	0.0756733i
$904$	−25.1881	+	2.30757i	−0.837745	+	0.0767486i
$905$	26.7244			0.888348
$906$	−0.0115398	−	0.378823i	−0.000383383	−	0.0125856i
$907$	24.1186	−	13.9249i	0.800847	−	0.462369i	−0.0429205	−	0.999078i	$-0.513666\pi$
$907$	24.1186	−	13.9249i	0.800847	−	0.462369i	0.843767	+	0.536709i	$0.180333\pi$
$908$	18.0985	−	11.9744i	0.600619	−	0.397385i
$909$	−38.7357	+	22.3641i	−1.28478	+	0.741770i
$910$	−3.55513	+	6.61498i	−0.117851	+	0.219284i
$911$	−45.6102			−1.51113			−0.755567	−	0.655071i	$-0.772639\pi$
$911$	−45.6102			−1.51113			−0.755567	+	0.655071i	$0.772639\pi$
$912$	1.27203	+	0.182837i	0.0421212	+	0.00605434i
$913$	−30.8381			−1.02059
$914$	−4.32183	+	8.04157i	−0.142953	+	0.265992i
$915$	0.252039	−	0.145515i	0.00833215	−	0.00481057i
$916$	−9.53344	+	6.30757i	−0.314994	+	0.208408i
$917$	20.3049	−	11.7230i	0.670526	−	0.387128i
$918$	−0.0141252	−	0.463697i	−0.000466202	−	0.0153043i
$919$	−41.3141			−1.36283			−0.681413	−	0.731899i	$-0.738634\pi$
$919$	−41.3141			−1.36283			−0.681413	+	0.731899i	$0.738634\pi$
$920$	1.86345	+	20.3404i	0.0614361	+	0.670603i
$921$	0.968208	−	1.67698i	0.0319035	−	0.0552585i
$922$	−0.123862	−	4.06609i	−0.00407918	−	0.133910i
$923$			5.41378i			0.178197i
$924$	−0.612720	+	1.22837i	−0.0201570	+	0.0404104i
$925$	1.01633	+	0.586777i	0.0334166	+	0.0192931i
$926$	19.8652	−	36.9630i	0.652812	−	1.21468i
$927$	−17.4001	+	30.1378i	−0.571494	+	0.989856i
$928$	−5.17636	−	33.7328i	−0.169922	−	1.10733i
$929$	3.58663	+	6.21223i	0.117674	+	0.203817i	0.918845	−	0.394618i	$-0.129123\pi$
$929$	3.58663	+	6.21223i	0.117674	+	0.203817i	−0.801172	+	0.598435i	$0.795790\pi$
$930$	0.674784	+	1.09066i	0.0221270	+	0.0357641i
$931$	17.2278	−	63.5900i	0.564620	−	2.08408i
$932$	20.8380	−	41.7757i	0.682572	−	1.36841i
$933$	1.54489	−	0.891942i	0.0505774	−	0.0292009i
$934$	−15.3720	−	8.26146i	−0.502987	−	0.270323i
$935$	1.66230	−	2.87918i	0.0543629	−	0.0941593i
$936$	−3.45460	+	2.44007i	−0.112917	+	0.0797561i
$937$	−10.0009	+	17.3221i	−0.326716	+	0.565889i	−0.981858	−	0.189616i	$-0.939276\pi$
$937$	−10.0009	+	17.3221i	−0.326716	+	0.565889i	0.655142	+	0.755506i	$0.272609\pi$
$938$	−61.5661	+	38.0906i	−2.01020	+	1.24370i
$939$		−	2.11577i		−	0.0690457i
$940$	−5.90207	+	3.90496i	−0.192504	+	0.127366i
$941$	31.3632	+	18.1076i	1.02241	+	0.590289i	0.914801	−	0.403904i	$-0.132347\pi$
$941$	31.3632	+	18.1076i	1.02241	+	0.590289i	0.107610	+	0.994193i	$0.465680\pi$
$942$	1.04793	+	1.69378i	0.0341434	+	0.0551863i
$943$	17.6934			0.576175
$944$	2.30635	+	18.8401i	0.0750653	+	0.613193i
$945$	2.34929	+	4.06910i	0.0764226	+	0.132368i
$946$	21.2049	−	0.645949i	0.689432	−	0.0210016i
$947$	29.1318	−	16.8192i	0.946656	−	0.546552i	0.0546155	−	0.998507i	$-0.482607\pi$
$947$	29.1318	−	16.8192i	0.946656	−	0.546552i	0.892041	+	0.451955i	$0.149273\pi$
$948$	−0.0149817	−	0.245678i	−0.000486583	−	0.00797925i
$949$		−	6.22765i		−	0.202158i
$950$	0.672033	−	0.200164i	0.0218036	−	0.00649419i
$951$	0.755381			0.0244949
$952$	−5.69722	−	8.06602i	−0.184648	−	0.261421i
$953$	19.7258	+	34.1662i	0.638983	+	1.10675i	0.985656	+	0.168765i	$0.0539777\pi$
$953$	19.7258	+	34.1662i	0.638983	+	1.10675i	−0.346674	+	0.937986i	$0.612689\pi$
$954$	1.50212	+	49.3109i	0.0486328	+	1.59650i
$955$	−24.7687	+	14.3002i	−0.801495	+	0.462743i
$956$	11.5342	+	17.4331i	0.373042	+	0.563827i
$957$			0.880523i			0.0284633i
$958$	−5.95229	−	9.62074i	−0.192310	−	0.310832i
$959$	18.8107	−	32.5812i	0.607431	−	1.05210i
$960$	−0.445782	+	1.25668i	−0.0143875	+	0.0405591i
$961$	−1.39543			−0.0450140
$962$	−3.83323	−	6.19569i	−0.123588	−	0.199757i
$963$	19.8810	+	11.4783i	0.640655	+	0.369882i
$964$	41.2897	−	2.51788i	1.32985	−	0.0810955i
$965$	14.3855	+	8.30546i	0.463085	+	0.267362i
$966$	−1.37884	−	0.741040i	−0.0443636	−	0.0238426i
$967$	−6.05042	−	10.4796i	−0.194568	−	0.337002i	0.752191	−	0.658946i	$-0.228997\pi$
$967$	−6.05042	−	10.4796i	−0.194568	−	0.337002i	−0.946759	+	0.321943i	$0.895664\pi$
$968$	19.9385	−	1.82663i	0.640847	−	0.0587101i
$969$	0.169132	−	0.168197i	0.00543329	−	0.00540327i
$970$	−3.29280	+	2.03724i	−0.105726	+	0.0654117i
$971$	−24.1496	+	13.9428i	−0.774997	+	0.447445i	−0.834654	−	0.550774i	$-0.814333\pi$
$971$	−24.1496	+	13.9428i	−0.774997	+	0.447445i	0.0596571	+	0.998219i	$0.480999\pi$
$972$	0.241676	+	3.96315i	0.00775177	+	0.127118i
$973$	−32.4873	−	18.7565i	−1.04149	−	0.601307i
$974$	−7.59419	+	14.1304i	−0.243333	+	0.452767i
$975$	0.00209330	−	0.00362571i	6.70394e−5	−	0.000116116i
$976$	5.57946	−	4.20126i	0.178594	−	0.134479i
$977$	6.91747			0.221310			0.110655	−	0.993859i	$-0.464705\pi$
$977$	6.91747			0.221310			0.110655	+	0.993859i	$0.464705\pi$
$978$	−1.01399	+	0.0308884i	−0.0324238	+	0.000987701i
$979$	−9.95449	−	5.74723i	−0.318147	−	0.183682i
$980$	61.1708	+	30.5125i	1.95403	+	0.974685i
$981$			7.90138i			0.252272i
$982$	0.994708	+	32.6539i	0.0317424	+	1.04203i
$983$	20.4691	+	35.4536i	0.652864	+	1.13079i	0.982425	+	0.186660i	$0.0597661\pi$
$983$	20.4691	+	35.4536i	0.652864	+	1.13079i	−0.329560	+	0.944135i	$0.606901\pi$
$984$	1.04881	+	0.483855i	0.0334349	+	0.0154247i
$985$	−13.6813	−	23.6967i	−0.435922	−	0.755039i
$986$	−5.57968	−	2.99872i	−0.177693	−	0.0954987i
$987$		−	0.542358i		−	0.0172634i
$988$	−4.26325	−	0.880479i	−0.135632	−	0.0280118i
$989$			24.1922i			0.769267i
$990$	−8.97747	+	16.7043i	−0.285323	+	0.530896i
$991$	−0.898204	−	1.55573i	−0.0285324	−	0.0494195i	0.851407	−	0.524506i	$-0.175750\pi$
$991$	−0.898204	−	1.55573i	−0.0285324	−	0.0494195i	−0.879939	+	0.475087i	$0.842417\pi$
$992$	19.2544	+	24.0128i	0.611329	+	0.762406i
$993$	−0.615184	−	1.06553i	−0.0195223	−	0.0338136i
$994$	72.0689	−	2.19538i	2.28589	−	0.0696331i
$995$		−	16.8951i		−	0.535610i
$996$	1.02470	−	2.05430i	0.0324689	−	0.0650930i
$997$	1.49295	+	0.861952i	0.0472821	+	0.0272983i	0.523455	−	0.852054i	$-0.324643\pi$
$997$	1.49295	+	0.861952i	0.0472821	+	0.0272983i	−0.476173	+	0.879352i	$0.657976\pi$
$998$	−0.869858	−	28.5553i	−0.0275349	−	0.903903i
$999$	−4.55834			−0.144219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.p.a.45.7	✓	36
4.3	odd	2		608.2.t.a.273.9		36
8.3	odd	2		608.2.t.a.273.10		36
8.5	even	2	inner	152.2.p.a.45.18	yes	36
19.11	even	3	inner	152.2.p.a.125.18	yes	36
76.11	odd	6		608.2.t.a.49.10		36
152.11	odd	6		608.2.t.a.49.9		36
152.125	even	6	inner	152.2.p.a.125.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.p.a.45.7	✓	36	1.1	even	1	trivial
152.2.p.a.45.18	yes	36	8.5	even	2	inner
152.2.p.a.125.7	yes	36	152.125	even	6	inner
152.2.p.a.125.18	yes	36	19.11	even	3	inner
608.2.t.a.49.9		36	152.11	odd	6
608.2.t.a.49.10		36	76.11	odd	6
608.2.t.a.273.9		36	4.3	odd	2
608.2.t.a.273.10		36	8.3	odd	2

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669488 + 1.24571i) q^{2} +(0.0638311 - 0.0368529i) q^{3} +(-1.10357 - 1.66797i) q^{4} +(-1.95840 + 1.13068i) q^{5} +(0.00317378 + 0.104187i) q^{6} -4.70260 q^{7} +(2.81663 - 0.258041i) q^{8} +(-1.49728 + 2.59337i) q^{9} +(-0.0973743 - 3.19656i) q^{10} +1.98019i q^{11} +(-0.131912 - 0.0657986i) q^{12} +(0.432449 + 0.249675i) q^{13} +(3.14833 - 5.85806i) q^{14} +(-0.0833377 + 0.144345i) q^{15} +(-1.56426 + 3.68145i) q^{16} +(0.371220 + 0.642972i) q^{17} +(-2.22817 - 3.60141i) q^{18} +(1.13983 - 4.20723i) q^{19} +(4.04717 + 2.01876i) q^{20} +(-0.300172 + 0.173304i) q^{21} +(-2.46674 - 1.32571i) q^{22} +(1.59672 - 2.76560i) q^{23} +(0.170279 - 0.120272i) q^{24} +(0.0568756 - 0.0985114i) q^{25} +(-0.600541 + 0.371551i) q^{26} +0.441834i q^{27} +(5.18966 + 7.84380i) q^{28} +(5.22471 + 3.01649i) q^{29} +(-0.124018 - 0.200452i) q^{30} -5.44101 q^{31} +(-3.53876 - 4.41329i) q^{32} +(0.0729758 + 0.126398i) q^{33} +(-1.04948 + 0.0319695i) q^{34} +(9.20955 - 5.31714i) q^{35} +(5.97803 - 0.364546i) q^{36} +10.3168i q^{37} +(4.47788 + 4.23658i) q^{38} +0.0368049 q^{39} +(-5.22432 + 3.69006i) q^{40} +(2.77027 + 4.79824i) q^{41} +(-0.0149250 - 0.489952i) q^{42} +(-6.56065 + 3.78779i) q^{43} +(3.30290 - 2.18528i) q^{44} -6.77180i q^{45} +(2.37615 + 3.84058i) q^{46} +(-0.782377 + 1.35512i) q^{47} +(0.0358240 + 0.292639i) q^{48} +15.1145 q^{49} +(0.0846389 + 0.136803i) q^{50} +(0.0473908 + 0.0273611i) q^{51} +(-0.0607887 - 0.996847i) q^{52} +(-10.0885 - 5.82458i) q^{53} +(-0.550396 - 0.295803i) q^{54} +(-2.23896 - 3.87800i) q^{55} +(-13.2455 + 1.21346i) q^{56} +(-0.0822924 - 0.310558i) q^{57} +(-7.25554 + 4.48896i) q^{58} +(4.10945 - 2.37259i) q^{59} +(0.332733 - 0.0202904i) q^{60} +(-1.51215 - 0.873042i) q^{61} +(3.64269 - 6.77790i) q^{62} +(7.04113 - 12.1956i) q^{63} +(7.86683 - 1.45361i) q^{64} -1.12921 q^{65} +(-0.206311 + 0.00628469i) q^{66} +(-9.42749 - 5.44296i) q^{67} +(0.662791 - 1.32875i) q^{68} -0.235375i q^{69} +(0.457913 + 15.0322i) q^{70} +(5.42083 + 9.38916i) q^{71} +(-3.54810 + 7.69093i) q^{72} +(-6.23576 - 10.8007i) q^{73} +(-12.8518 - 6.90701i) q^{74} -0.00838412i q^{75} +(-8.27542 + 2.74179i) q^{76} -9.31205i q^{77} +(-0.0246405 + 0.0458482i) q^{78} +(0.834855 + 1.44601i) q^{79} +(-1.09911 - 8.97842i) q^{80} +(-4.47557 - 7.75191i) q^{81} +(-7.83186 + 0.238576i) q^{82} +15.5733i q^{83} +(0.620329 + 0.309425i) q^{84} +(-1.45399 - 0.839462i) q^{85} +(-0.326205 - 10.7085i) q^{86} +0.444666 q^{87} +(0.510971 + 5.57747i) q^{88} +(-2.90236 + 5.02703i) q^{89} +(8.43567 + 4.53364i) q^{90} +(-2.03364 - 1.17412i) q^{91} +(-6.37504 + 0.388756i) q^{92} +(-0.347306 + 0.200517i) q^{93} +(-1.16429 - 1.88185i) q^{94} +(2.52480 + 9.52820i) q^{95} +(-0.388526 - 0.151292i) q^{96} +(-0.605380 - 1.04855i) q^{97} +(-10.1189 + 18.8282i) q^{98} +(-5.13537 - 2.96491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26}+ \cdots + 39 q^{98}+O(q^{100}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

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