LMFDB - Embedded newform 150.2.h.a.139.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,2,Mod(19,150)] 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("150.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	150.139
Dual form			150.2.h.a.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.530249 - 2.17229i) q^{5} +(-0.309017 - 0.951057i) q^{6} -0.273457i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.06909 + 0.847859i) q^{10} +(3.87811 - 2.81761i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(-1.01869 + 1.40211i) q^{13} +(-0.221232 + 0.160734i) q^{14} +(1.17557 - 1.90211i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.79892 + 0.584503i) q^{17} -1.00000i q^{18} +(0.930333 + 2.86327i) q^{19} +(1.90211 + 1.17557i) q^{20} +(0.0845030 - 0.260074i) q^{21} +(-4.55899 - 1.48131i) q^{22} +(-2.73076 - 3.75856i) q^{23} +1.00000 q^{24} +(-4.43767 - 2.30371i) q^{25} +1.73311 q^{26} +(0.587785 + 0.809017i) q^{27} +(0.260074 + 0.0845030i) q^{28} +(-2.80808 + 8.64240i) q^{29} +(-2.22982 + 0.166977i) q^{30} +(1.18474 + 3.64625i) q^{31} +1.00000i q^{32} +(4.55899 - 1.48131i) q^{33} +(1.53025 + 1.11179i) q^{34} +(-0.594028 - 0.145000i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-5.29563 + 7.28881i) q^{37} +(1.76960 - 2.43564i) q^{38} +(-1.40211 + 1.01869i) q^{39} +(-0.166977 - 2.22982i) q^{40} +(6.13287 + 4.45579i) q^{41} +(-0.260074 + 0.0845030i) q^{42} +2.88963i q^{43} +(1.48131 + 4.55899i) q^{44} +(1.70582 - 1.44575i) q^{45} +(-1.43564 + 4.41846i) q^{46} +(-1.12991 - 0.367130i) q^{47} +(-0.587785 - 0.809017i) q^{48} +6.92522 q^{49} +(0.744661 + 4.94424i) q^{50} -1.89149 q^{51} +(-1.01869 - 1.40211i) q^{52} +(-11.0465 - 3.58924i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-4.06430 - 9.91840i) q^{55} +(-0.0845030 - 0.260074i) q^{56} +3.01062i q^{57} +(8.64240 - 2.80808i) q^{58} +(-11.5604 - 8.39915i) q^{59} +(1.44575 + 1.70582i) q^{60} +(4.16750 - 3.02786i) q^{61} +(2.25351 - 3.10169i) q^{62} +(0.160734 - 0.221232i) q^{63} +(0.809017 - 0.587785i) q^{64} +(2.50563 + 2.95637i) q^{65} +(-3.87811 - 2.81761i) q^{66} +(5.98215 - 1.94372i) q^{67} -1.89149i q^{68} +(-1.43564 - 4.41846i) q^{69} +(0.231853 + 0.565808i) q^{70} +(-0.433294 + 1.33354i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-1.04691 - 1.44095i) q^{73} +9.00947 q^{74} +(-3.50859 - 3.56227i) q^{75} -3.01062 q^{76} +(-0.770497 - 1.06050i) q^{77} +(1.64828 + 0.535560i) q^{78} +(4.96261 - 15.2733i) q^{79} +(-1.70582 + 1.44575i) q^{80} +(0.309017 + 0.951057i) q^{81} -7.58064i q^{82} +(14.3983 - 4.67828i) q^{83} +(0.221232 + 0.160734i) q^{84} +(0.315836 + 4.21769i) q^{85} +(2.33776 - 1.69848i) q^{86} +(-5.34129 + 7.35166i) q^{87} +(2.81761 - 3.87811i) q^{88} +(-11.9956 + 8.71529i) q^{89} +(-2.17229 - 0.530249i) q^{90} +(0.383418 + 0.278570i) q^{91} +(4.41846 - 1.43564i) q^{92} +3.83390i q^{93} +(0.367130 + 1.12991i) q^{94} +(6.71316 - 0.502706i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(5.59789 + 1.81886i) q^{97} +(-4.07054 - 5.60262i) q^{98} +4.79360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31}+ \cdots + 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.530249	−	2.17229i	0.237134	−	0.971477i
$5$	0.530249	−	2.17229i	0.237134	−	0.971477i
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$		−	0.273457i		−	0.103357i	−0.998664	−	0.0516786i	$-0.983543\pi$
$7$		−	0.273457i		−	0.103357i	0.998664	−	0.0516786i	$-0.0164571\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−2.06909	+	0.847859i	−0.654304	+	0.268116i
$11$	3.87811	−	2.81761i	1.16929	−	0.849541i	0.178369	−	0.983964i	$-0.442918\pi$
$11$	3.87811	−	2.81761i	1.16929	−	0.849541i	0.990924	+	0.134422i	$0.0429178\pi$
$12$	−0.587785	+	0.809017i	−0.169679	+	0.233543i
$13$	−1.01869	+	1.40211i	−0.282535	+	0.388876i	−0.926572	−	0.376119i	$-0.877259\pi$
$13$	−1.01869	+	1.40211i	−0.282535	+	0.388876i	0.644036	+	0.764995i	$0.277259\pi$
$14$	−0.221232	+	0.160734i	−0.0591267	+	0.0429580i
$15$	1.17557	−	1.90211i	0.303531	−	0.491123i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.79892	+	0.584503i	−0.436301	+	0.141763i	−0.518928	−	0.854818i	$-0.673669\pi$
$17$	−1.79892	+	0.584503i	−0.436301	+	0.141763i	0.0826274	+	0.996581i	$0.473669\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.930333	+	2.86327i	0.213433	+	0.656879i	0.999261	+	0.0384344i	$0.0122371\pi$
$19$	0.930333	+	2.86327i	0.213433	+	0.656879i	−0.785828	+	0.618445i	$0.787763\pi$
$20$	1.90211	+	1.17557i	0.425325	+	0.262866i
$21$	0.0845030	−	0.260074i	0.0184401	−	0.0567527i
$22$	−4.55899	−	1.48131i	−0.971980	−	0.315815i
$23$	−2.73076	−	3.75856i	−0.569402	−	0.783715i	0.423081	−	0.906092i	$-0.360948\pi$
$23$	−2.73076	−	3.75856i	−0.569402	−	0.783715i	−0.992484	+	0.122377i	$0.960948\pi$
$24$	1.00000			0.204124
$25$	−4.43767	−	2.30371i	−0.887535	−	0.460741i
$26$	1.73311			0.339890
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	0.260074	+	0.0845030i	0.0491493	+	0.0159696i
$29$	−2.80808	+	8.64240i	−0.521448	+	1.60485i	0.249786	+	0.968301i	$0.419640\pi$
$29$	−2.80808	+	8.64240i	−0.521448	+	1.60485i	−0.771234	+	0.636552i	$0.780360\pi$
$30$	−2.22982	+	0.166977i	−0.407108	+	0.0304858i
$31$	1.18474	+	3.64625i	0.212786	+	0.654887i	0.999303	+	0.0373190i	$0.0118818\pi$
$31$	1.18474	+	3.64625i	0.212786	+	0.654887i	−0.786518	+	0.617568i	$0.788118\pi$
$32$			1.00000i			0.176777i
$33$	4.55899	−	1.48131i	0.793618	−	0.257862i
$34$	1.53025	+	1.11179i	0.262435	+	0.190671i
$35$	−0.594028	−	0.145000i	−0.100409	−	0.0245096i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−5.29563	+	7.28881i	−0.870597	+	1.19827i	0.108341	+	0.994114i	$0.465446\pi$
$37$	−5.29563	+	7.28881i	−0.870597	+	1.19827i	−0.978938	+	0.204160i	$0.934554\pi$
$38$	1.76960	−	2.43564i	0.287067	−	0.395114i
$39$	−1.40211	+	1.01869i	−0.224518	+	0.163122i
$40$	−0.166977	−	2.22982i	−0.0264015	−	0.352566i
$41$	6.13287	+	4.45579i	0.957793	+	0.695878i	0.952637	−	0.304109i	$-0.0983587\pi$
$41$	6.13287	+	4.45579i	0.957793	+	0.695878i	0.00515619	+	0.999987i	$0.498359\pi$
$42$	−0.260074	+	0.0845030i	−0.0401302	+	0.0130391i
$43$			2.88963i			0.440664i	0.975425	+	0.220332i	$0.0707141\pi$
$43$			2.88963i			0.440664i	−0.975425	+	0.220332i	$0.929286\pi$
$44$	1.48131	+	4.55899i	0.223315	+	0.687293i
$45$	1.70582	−	1.44575i	0.254289	−	0.215519i
$46$	−1.43564	+	4.41846i	−0.211674	+	0.651466i
$47$	−1.12991	−	0.367130i	−0.164814	−	0.0535514i	0.225448	−	0.974255i	$-0.427616\pi$
$47$	−1.12991	−	0.367130i	−0.164814	−	0.0535514i	−0.390262	+	0.920704i	$0.627616\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	6.92522			0.989317
$50$	0.744661	+	4.94424i	0.105311	+	0.699221i
$51$	−1.89149			−0.264862
$52$	−1.01869	−	1.40211i	−0.141268	−	0.194438i
$53$	−11.0465	−	3.58924i	−1.51736	−	0.493020i	−0.572334	−	0.820020i	$-0.693962\pi$
$53$	−11.0465	−	3.58924i	−1.51736	−	0.493020i	−0.945024	+	0.327001i	$0.893962\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−4.06430	−	9.91840i	−0.548030	−	1.33740i
$56$	−0.0845030	−	0.260074i	−0.0112922	−	0.0347538i
$57$			3.01062i			0.398767i
$58$	8.64240	−	2.80808i	1.13480	−	0.368720i
$59$	−11.5604	−	8.39915i	−1.50504	−	1.09348i	−0.968319	−	0.249718i	$-0.919662\pi$
$59$	−11.5604	−	8.39915i	−1.50504	−	1.09348i	−0.536723	−	0.843759i	$-0.680338\pi$
$60$	1.44575	+	1.70582i	0.186645	+	0.220220i
$61$	4.16750	−	3.02786i	0.533593	−	0.387678i	−0.288107	−	0.957598i	$-0.593026\pi$
$61$	4.16750	−	3.02786i	0.533593	−	0.387678i	0.821700	+	0.569920i	$0.193026\pi$
$62$	2.25351	−	3.10169i	0.286196	−	0.393915i
$63$	0.160734	−	0.221232i	0.0202506	−	0.0278726i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	2.50563	+	2.95637i	0.310785	+	0.366692i
$66$	−3.87811	−	2.81761i	−0.477362	−	0.346824i
$67$	5.98215	−	1.94372i	0.730836	−	0.237463i	0.0801208	−	0.996785i	$-0.474469\pi$
$67$	5.98215	−	1.94372i	0.730836	−	0.237463i	0.650715	+	0.759322i	$0.274469\pi$
$68$		−	1.89149i		−	0.229377i
$69$	−1.43564	−	4.41846i	−0.172831	−	0.531920i
$70$	0.231853	+	0.565808i	0.0277118	+	0.0676270i
$71$	−0.433294	+	1.33354i	−0.0514226	+	0.158262i	−0.973470	−	0.228814i	$-0.926515\pi$
$71$	−0.433294	+	1.33354i	−0.0514226	+	0.158262i	0.922048	+	0.387077i	$0.126515\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	−1.04691	−	1.44095i	−0.122532	−	0.168651i	0.743344	−	0.668909i	$-0.233238\pi$
$73$	−1.04691	−	1.44095i	−0.122532	−	0.168651i	−0.865876	+	0.500258i	$0.833238\pi$
$74$	9.00947			1.04733
$75$	−3.50859	−	3.56227i	−0.405137	−	0.411336i
$76$	−3.01062			−0.345342
$77$	−0.770497	−	1.06050i	−0.0878062	−	0.120855i
$78$	1.64828	+	0.535560i	0.186631	+	0.0606402i
$79$	4.96261	−	15.2733i	0.558337	−	1.71839i	−0.128626	−	0.991693i	$-0.541057\pi$
$79$	4.96261	−	15.2733i	0.558337	−	1.71839i	0.686963	−	0.726692i	$-0.258943\pi$
$80$	−1.70582	+	1.44575i	−0.190716	+	0.161639i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	7.58064i		−	0.837142i
$83$	14.3983	−	4.67828i	1.58041	−	0.513508i	0.618250	−	0.785981i	$-0.287842\pi$
$83$	14.3983	−	4.67828i	1.58041	−	0.513508i	0.962163	+	0.272474i	$0.0878417\pi$
$84$	0.221232	+	0.160734i	0.0241384	+	0.0175375i
$85$	0.315836	+	4.21769i	0.0342573	+	0.457473i
$86$	2.33776	−	1.69848i	0.252087	−	0.183152i
$87$	−5.34129	+	7.35166i	−0.572647	+	0.788181i
$88$	2.81761	−	3.87811i	0.300358	−	0.413408i
$89$	−11.9956	+	8.71529i	−1.27153	+	0.923819i	−0.999262	−	0.0384036i	$-0.987773\pi$
$89$	−11.9956	+	8.71529i	−1.27153	+	0.923819i	−0.272265	+	0.962222i	$0.587773\pi$
$90$	−2.17229	−	0.530249i	−0.228979	−	0.0558931i
$91$	0.383418	+	0.278570i	0.0401932	+	0.0292020i
$92$	4.41846	−	1.43564i	0.460656	−	0.149676i
$93$			3.83390i			0.397557i
$94$	0.367130	+	1.12991i	0.0378665	+	0.116541i
$95$	6.71316	−	0.502706i	0.688756	−	0.0515765i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	5.59789	+	1.81886i	0.568379	+	0.184678i	0.579088	−	0.815265i	$-0.303409\pi$
$97$	5.59789	+	1.81886i	0.568379	+	0.184678i	−0.0107087	+	0.999943i	$0.503409\pi$
$98$	−4.07054	−	5.60262i	−0.411187	−	0.565950i
$99$	4.79360			0.481775
$100$	3.56227	−	3.50859i	0.356227	−	0.350859i
$101$	4.83576			0.481176			0.240588	−	0.970627i	$-0.422660\pi$
$101$	4.83576			0.481176			0.240588	+	0.970627i	$0.422660\pi$
$102$	1.11179	+	1.53025i	0.110084	+	0.151517i
$103$	−0.0694118	−	0.0225533i	−0.00683935	−	0.00222224i	0.305595	−	0.952161i	$-0.401145\pi$
$103$	−0.0694118	−	0.0225533i	−0.00683935	−	0.00222224i	−0.312435	+	0.949939i	$0.601145\pi$
$104$	−0.535560	+	1.64828i	−0.0525159	+	0.161627i
$105$	−0.520147	−	0.321469i	−0.0507612	−	0.0313721i
$106$	3.58924	+	11.0465i	0.348618	+	1.07293i
$107$		−	5.84754i		−	0.565303i	−0.959223	−	0.282651i	$-0.908786\pi$
$107$		−	5.84754i		−	0.565303i	0.959223	−	0.282651i	$-0.0912140\pi$
$108$	−0.951057	+	0.309017i	−0.0915155	+	0.0297352i
$109$	−7.93329	−	5.76388i	−0.759872	−	0.552079i	0.138999	−	0.990292i	$-0.455611\pi$
$109$	−7.93329	−	5.76388i	−0.759872	−	0.552079i	−0.898871	+	0.438213i	$0.855611\pi$
$110$	−5.63522	+	9.11798i	−0.537297	+	0.869365i
$111$	−7.28881	+	5.29563i	−0.691824	+	0.502639i
$112$	−0.160734	+	0.221232i	−0.0151880	+	0.0209044i
$113$	−10.1858	+	14.0196i	−0.958201	+	1.31885i	−0.0104140	+	0.999946i	$0.503315\pi$
$113$	−10.1858	+	14.0196i	−0.958201	+	1.31885i	−0.947787	+	0.318905i	$0.896685\pi$
$114$	2.43564	−	1.76960i	0.228119	−	0.165738i
$115$	−9.61267	+	3.93902i	−0.896386	+	0.367315i
$116$	−7.35166	−	5.34129i	−0.682585	−	0.495927i
$117$	−1.64828	+	0.535560i	−0.152384	+	0.0495125i
$118$			14.2895i			1.31545i
$119$	0.159837	+	0.491927i	0.0146522	+	0.0450949i
$120$	0.530249	−	2.17229i	0.0484049	−	0.198302i
$121$	3.70160	−	11.3924i	0.336510	−	1.03567i
$122$	−4.89919	−	1.59184i	−0.443552	−	0.144119i
$123$	4.45579	+	6.13287i	0.401765	+	0.552982i
$124$	−3.83390			−0.344294
$125$	−7.35738	+	8.41837i	−0.658064	+	0.752962i
$126$	−0.273457			−0.0243615
$127$	10.7963	+	14.8598i	0.958013	+	1.31859i	0.947875	+	0.318643i	$0.103227\pi$
$127$	10.7963	+	14.8598i	0.958013	+	1.31859i	0.0101377	+	0.999949i	$0.496773\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−0.892944	+	2.74820i	−0.0786193	+	0.241965i
$130$	0.918978	−	3.76481i	0.0805997	−	0.330196i
$131$	−2.34036	−	7.20289i	−0.204478	−	0.629320i	−0.999734	−	0.0230460i	$-0.992664\pi$
$131$	−2.34036	−	7.20289i	−0.204478	−	0.629320i	0.795256	−	0.606274i	$-0.207336\pi$
$132$			4.79360i			0.417230i
$133$	0.782983	−	0.254407i	0.0678932	−	0.0220598i
$134$	−5.08872	−	3.69717i	−0.439598	−	0.319387i
$135$	2.06909	−	0.847859i	0.178079	−	0.0729721i
$136$	−1.53025	+	1.11179i	−0.131218	+	0.0953353i
$137$	11.5262	−	15.8644i	0.984747	−	1.35539i	0.0505148	−	0.998723i	$-0.483914\pi$
$137$	11.5262	−	15.8644i	0.984747	−	1.35539i	0.934232	−	0.356665i	$-0.116086\pi$
$138$	−2.73076	+	3.75856i	−0.232457	+	0.319950i
$139$	7.73836	−	5.62225i	0.656359	−	0.476873i	−0.209072	−	0.977900i	$-0.567044\pi$
$139$	7.73836	−	5.62225i	0.656359	−	0.476873i	0.865431	+	0.501027i	$0.167044\pi$
$140$	0.321469	−	0.520147i	0.0271691	−	0.0439604i
$141$	−0.961158	−	0.698322i	−0.0809441	−	0.0588093i
$142$	1.33354	−	0.433294i	0.111908	−	0.0363612i
$143$			8.30783i			0.694736i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	17.2848	+	10.6826i	1.43542	+	0.887141i
$146$	−0.550396	+	1.69394i	−0.0455511	+	0.140192i
$147$	6.58628	+	2.14001i	0.543227	+	0.176505i
$148$	−5.29563	−	7.28881i	−0.435298	−	0.599137i
$149$	4.64398			0.380449			0.190225	−	0.981741i	$-0.439078\pi$
$149$	4.64398			0.380449			0.190225	+	0.981741i	$0.439078\pi$
$150$	−0.819639	+	4.93236i	−0.0669232	+	0.402726i
$151$	−16.7881			−1.36619			−0.683097	−	0.730327i	$-0.739368\pi$
$151$	−16.7881			−1.36619			−0.683097	+	0.730327i	$0.739368\pi$
$152$	1.76960	+	2.43564i	0.143533	+	0.197557i
$153$	−1.79892	−	0.584503i	−0.145434	−	0.0472543i
$154$	−0.405074	+	1.24669i	−0.0326418	+	0.100461i
$155$	8.54892	−	0.640175i	0.686666	−	0.0514201i
$156$	−0.535560	−	1.64828i	−0.0428791	−	0.131968i
$157$		−	5.57763i		−	0.445143i	−0.974916	−	0.222572i	$-0.928555\pi$
$157$		−	5.57763i		−	0.445143i	0.974916	−	0.222572i	$-0.0714451\pi$
$158$	−15.2733	+	4.96261i	−1.21508	+	0.394804i
$159$	−9.39675	−	6.82714i	−0.745210	−	0.541427i
$160$	2.17229	+	0.530249i	0.171734	+	0.0419198i
$161$	−1.02781	+	0.746746i	−0.0810026	+	0.0588518i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	−10.8007	+	14.8659i	−0.845978	+	1.16439i	0.138757	+	0.990327i	$0.455689\pi$
$163$	−10.8007	+	14.8659i	−0.845978	+	1.16439i	−0.984735	+	0.174062i	$0.944311\pi$
$164$	−6.13287	+	4.45579i	−0.478897	+	0.347939i
$165$	−0.800424	−	10.6889i	−0.0623129	−	0.832130i
$166$	−12.2479	−	8.89861i	−0.950620	−	0.690666i
$167$	8.50651	−	2.76393i	0.658253	−	0.213879i	0.0392036	−	0.999231i	$-0.487518\pi$
$167$	8.50651	−	2.76393i	0.658253	−	0.213879i	0.619050	+	0.785352i	$0.287518\pi$
$168$		−	0.273457i		−	0.0210977i
$169$	3.08904	+	9.50708i	0.237618	+	0.731314i
$170$	3.22654	−	2.73462i	0.247465	−	0.209735i
$171$	−0.930333	+	2.86327i	−0.0711444	+	0.218960i
$172$	−2.74820	−	0.892944i	−0.209548	−	0.0680863i
$173$	−7.00354	−	9.63954i	−0.532469	−	0.732881i	0.455035	−	0.890473i	$-0.349627\pi$
$173$	−7.00354	−	9.63954i	−0.532469	−	0.732881i	−0.987504	+	0.157593i	$0.949627\pi$
$174$	9.08715			0.688895
$175$	−0.629966	+	1.21351i	−0.0476209	+	0.0917331i
$176$	−4.79360			−0.361332
$177$	−8.39915	−	11.5604i	−0.631319	−	0.868936i
$178$	14.1016	+	4.58190i	1.05696	+	0.343428i
$179$	1.16073	−	3.57237i	0.0867574	−	0.267012i	−0.898261	−	0.439463i	$-0.855169\pi$
$179$	1.16073	−	3.57237i	0.0867574	−	0.267012i	0.985018	+	0.172451i	$0.0551688\pi$
$180$	0.847859	+	2.06909i	0.0631957	+	0.154221i
$181$	−5.58164	−	17.1785i	−0.414880	−	1.27687i	−0.912358	−	0.409393i	$-0.865740\pi$
$181$	−5.58164	−	17.1785i	−0.414880	−	1.27687i	0.497478	−	0.867477i	$-0.334260\pi$
$182$		−	0.473931i		−	0.0351301i
$183$	4.89919	−	1.59184i	0.362158	−	0.117672i
$184$	−3.75856	−	2.73076i	−0.277085	−	0.201314i
$185$	13.0254	+	15.3685i	0.957647	+	1.12992i
$186$	3.10169	−	2.25351i	0.227427	−	0.165235i
$187$	−5.32949	+	7.33541i	−0.389731	+	0.536418i
$188$	0.698322	−	0.961158i	0.0509304	−	0.0700997i
$189$	0.221232	−	0.160734i	0.0160922	−	0.0116917i
$190$	−4.35259	−	5.13558i	−0.315770	−	0.372574i
$191$	13.4303	+	9.75767i	0.971781	+	0.706040i	0.955857	−	0.293833i	$-0.0949310\pi$
$191$	13.4303	+	9.75767i	0.971781	+	0.706040i	0.0159240	+	0.999873i	$0.494931\pi$
$192$	0.951057	−	0.309017i	0.0686366	−	0.0223014i
$193$			3.84858i			0.277027i	0.990361	+	0.138513i	$0.0442324\pi$
$193$			3.84858i			0.277027i	−0.990361	+	0.138513i	$0.955768\pi$
$194$	−1.81886	−	5.59789i	−0.130587	−	0.401905i
$195$	1.46943	+	3.58596i	0.105228	+	0.256796i
$196$	−2.14001	+	6.58628i	−0.152858	+	0.470448i
$197$	−10.2174	−	3.31984i	−0.727960	−	0.236529i	−0.0784892	−	0.996915i	$-0.525010\pi$
$197$	−10.2174	−	3.31984i	−0.727960	−	0.236529i	−0.649471	+	0.760386i	$0.725010\pi$
$198$	−2.81761	−	3.87811i	−0.200239	−	0.275605i
$199$	−2.49808			−0.177084			−0.0885421	−	0.996072i	$-0.528221\pi$
$199$	−2.49808			−0.177084			−0.0885421	+	0.996072i	$0.528221\pi$
$200$	−4.93236	−	0.819639i	−0.348771	−	0.0579572i
$201$	6.29000			0.443662
$202$	−2.84239	−	3.91221i	−0.199990	−	0.275262i
$203$	2.36333	+	0.767892i	0.165873	+	0.0538954i
$204$	0.584503	−	1.79892i	0.0409234	−	0.125949i
$205$	12.9312	−	10.9597i	0.903155	−	0.765458i
$206$	0.0225533	+	0.0694118i	0.00157136	+	0.00483615i
$207$		−	4.64584i		−	0.322908i
$208$	1.64828	−	0.535560i	0.114288	−	0.0371344i
$209$	11.6755	+	8.48276i	0.807612	+	0.586765i
$210$	0.0456612	+	0.609762i	0.00315092	+	0.0420776i
$211$	−19.6381	+	14.2679i	−1.35194	+	0.982245i	−0.353032	+	0.935611i	$0.614849\pi$
$211$	−19.6381	+	14.2679i	−1.35194	+	0.982245i	−0.998912	+	0.0466338i	$0.985151\pi$
$212$	6.82714	−	9.39675i	0.468890	−	0.645371i
$213$	−0.824175	+	1.13438i	−0.0564715	+	0.0777264i
$214$	−4.73076	+	3.43710i	−0.323388	+	0.234955i
$215$	6.27710	+	1.53222i	0.428095	+	0.104497i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	0.997095	−	0.323976i	0.0676872	−	0.0219929i
$218$			9.80609i			0.664152i
$219$	−0.550396	−	1.69394i	−0.0371923	−	0.114466i
$220$	10.6889	−	0.800424i	0.720645	−	0.0539646i
$221$	1.01301	−	3.11771i	0.0681422	−	0.209720i
$222$	8.56851	+	2.78408i	0.575081	+	0.186855i
$223$	−7.67291	−	10.5609i	−0.513816	−	0.707207i	0.470741	−	0.882271i	$-0.343987\pi$
$223$	−7.67291	−	10.5609i	−0.513816	−	0.707207i	−0.984557	+	0.175064i	$0.943987\pi$
$224$	0.273457			0.0182711
$225$	−2.23607	−	4.47214i	−0.149071	−	0.298142i
$226$	17.3291			1.15272
$227$	4.15067	+	5.71290i	0.275489	+	0.379179i	0.924233	−	0.381828i	$-0.124705\pi$
$227$	4.15067	+	5.71290i	0.275489	+	0.379179i	−0.648744	+	0.761007i	$0.724705\pi$
$228$	−2.86327	−	0.930333i	−0.189625	−	0.0616128i
$229$	3.88654	−	11.9615i	0.256830	−	0.790441i	−0.736634	−	0.676292i	$-0.763586\pi$
$229$	3.88654	−	11.9615i	0.256830	−	0.790441i	0.993464	−	0.114149i	$-0.0364143\pi$
$230$	8.83692	+	5.46151i	0.582689	+	0.360122i
$231$	−0.405074	−	1.24669i	−0.0266519	−	0.0820262i
$232$			9.08715i			0.596601i
$233$	9.32536	−	3.02999i	0.610925	−	0.198501i	0.0128179	−	0.999918i	$-0.495920\pi$
$233$	9.32536	−	3.02999i	0.610925	−	0.198501i	0.598107	+	0.801416i	$0.295920\pi$
$234$	1.40211	+	1.01869i	0.0916590	+	0.0665942i
$235$	−1.39664	+	2.25982i	−0.0911071	+	0.147414i
$236$	11.5604	−	8.39915i	0.752521	−	0.546738i
$237$	9.43945	−	12.9923i	0.613158	−	0.843939i
$238$	0.304027	−	0.418458i	0.0197072	−	0.0271246i
$239$	4.07768	−	2.96261i	0.263763	−	0.191635i	−0.448041	−	0.894013i	$-0.647878\pi$
$239$	4.07768	−	2.96261i	0.263763	−	0.191635i	0.711805	+	0.702378i	$0.247878\pi$
$240$	−2.06909	+	0.847859i	−0.133559	+	0.0547290i
$241$	−5.53446	−	4.02102i	−0.356506	−	0.259017i	0.395087	−	0.918644i	$-0.370714\pi$
$241$	−5.53446	−	4.02102i	−0.356506	−	0.259017i	−0.751593	+	0.659627i	$0.770714\pi$
$242$	−11.3924	+	3.70160i	−0.732329	+	0.237948i
$243$			1.00000i			0.0641500i
$244$	1.59184	+	4.89919i	0.101907	+	0.313638i
$245$	3.67209	−	15.0436i	0.234601	−	0.961099i
$246$	2.34255	−	7.20962i	0.149355	−	0.459669i
$247$	−4.96236	−	1.61237i	−0.315747	−	0.102592i
$248$	2.25351	+	3.10169i	0.143098	+	0.196957i
$249$	15.1392			0.959409
$250$	11.1352	+	1.00406i	0.704250	+	0.0635021i
$251$	−7.07549			−0.446601			−0.223301	−	0.974750i	$-0.571683\pi$
$251$	−7.07549			−0.446601			−0.223301	+	0.974750i	$0.571683\pi$
$252$	0.160734	+	0.221232i	0.0101253	+	0.0139363i
$253$	−21.1803	−	6.88191i	−1.33160	−	0.432662i
$254$	5.67593	−	17.4687i	0.356139	−	1.09608i
$255$	−1.00296	+	4.10886i	−0.0628079	+	0.257307i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	4.47318i		−	0.279029i	−0.990220	−	0.139515i	$-0.955446\pi$
$257$		−	4.47318i		−	0.279029i	0.990220	−	0.139515i	$-0.0445542\pi$
$258$	2.74820	−	0.892944i	0.171095	−	0.0555922i
$259$	1.99318	+	1.44813i	0.123850	+	0.0899824i
$260$	−3.58596	+	1.46943i	−0.222392	+	0.0911302i
$261$	−7.35166	+	5.34129i	−0.455056	+	0.330618i
$262$	−4.45163	+	6.12715i	−0.275023	+	0.378536i
$263$	1.47083	−	2.02442i	0.0906950	−	0.124831i	−0.761258	−	0.648449i	$-0.775418\pi$
$263$	1.47083	−	2.02442i	0.0906950	−	0.124831i	0.851953	+	0.523618i	$0.175418\pi$
$264$	3.87811	−	2.81761i	0.238681	−	0.173412i
$265$	−13.6543	+	22.0931i	−0.838775	+	1.35717i
$266$	−0.666045	−	0.483910i	−0.0408378	−	0.0296704i
$267$	−14.1016	+	4.58190i	−0.863006	+	0.280408i
$268$			6.29000i			0.384223i
$269$	−1.91241	−	5.88580i	−0.116602	−	0.358864i	0.875676	−	0.482899i	$-0.160416\pi$
$269$	−1.91241	−	5.88580i	−0.116602	−	0.358864i	−0.992278	+	0.124036i	$0.960416\pi$
$270$	−1.90211	−	1.17557i	−0.115759	−	0.0715429i
$271$	4.06941	−	12.5244i	0.247199	−	0.760801i	−0.748068	−	0.663622i	$-0.769018\pi$
$271$	4.06941	−	12.5244i	0.247199	−	0.760801i	0.995267	−	0.0971785i	$-0.0309818\pi$
$272$	1.79892	+	0.584503i	0.109075	+	0.0354407i
$273$	0.278570	+	0.383418i	0.0168598	+	0.0232055i
$274$	−19.6095			−1.18465
$275$	−23.7007	+	3.56961i	−1.42921	+	0.215256i
$276$	4.64584			0.279647
$277$	−3.03717	−	4.18031i	−0.182486	−	0.251170i	0.707967	−	0.706245i	$-0.249612\pi$
$277$	−3.03717	−	4.18031i	−0.182486	−	0.251170i	−0.890453	+	0.455075i	$0.849612\pi$
$278$	−9.09699	−	2.95579i	−0.545601	−	0.177277i
$279$	−1.18474	+	3.64625i	−0.0709285	+	0.218296i
$280$	−0.609762	+	0.0456612i	−0.0364403	+	0.00272878i
$281$	−0.0145149	−	0.0446724i	−0.000865889	−	0.00266493i	0.950623	−	0.310349i	$-0.100446\pi$
$281$	−0.0145149	−	0.0446724i	−0.000865889	−	0.00266493i	−0.951489	+	0.307684i	$0.900446\pi$
$282$			1.18806i			0.0707478i
$283$	20.8007	−	6.75856i	1.23647	−	0.401755i	0.383419	−	0.923575i	$-0.374747\pi$
$283$	20.8007	−	6.75856i	1.23647	−	0.401755i	0.853056	+	0.521820i	$0.174747\pi$
$284$	−1.13438	−	0.824175i	−0.0673130	−	0.0489058i
$285$	6.53994	+	1.59638i	0.387392	+	0.0945613i
$286$	6.72118	−	4.88322i	0.397431	−	0.288751i
$287$	1.21847	−	1.67708i	0.0719240	−	0.0989949i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−10.8588	+	7.88941i	−0.638755	+	0.464083i
$290$	−1.51735	−	20.2628i	−0.0891018	−	1.18987i
$291$	4.76185	+	3.45968i	0.279144	+	0.202810i
$292$	1.69394	−	0.550396i	0.0991306	−	0.0322095i
$293$			8.35289i			0.487981i	0.969778	+	0.243991i	$0.0784566\pi$
$293$			8.35289i			0.487981i	−0.969778	+	0.243991i	$0.921543\pi$
$294$	−2.14001	−	6.58628i	−0.124808	−	0.384119i
$295$	−24.3753	+	20.6590i	−1.41918	+	1.20281i
$296$	−2.78408	+	8.56851i	−0.161821	+	0.498035i
$297$	4.55899	+	1.48131i	0.264539	+	0.0859540i
$298$	−2.72966	−	3.75706i	−0.158125	−	0.217640i
$299$	8.05174			0.465644
$300$	4.47214	−	2.23607i	0.258199	−	0.129099i
$301$	0.790190			0.0455458
$302$	9.86779	+	13.5818i	0.567827	+	0.781547i
$303$	4.59908	+	1.49433i	0.264210	+	0.0858472i
$304$	0.930333	−	2.86327i	0.0533583	−	0.164220i
$305$	−4.36758	−	10.6585i	−0.250087	−	0.610305i
$306$	0.584503	+	1.79892i	0.0334138	+	0.102837i
$307$			2.28918i			0.130650i	0.997864	+	0.0653251i	$0.0208084\pi$
$307$			2.28918i			0.130650i	−0.997864	+	0.0653251i	$0.979192\pi$
$308$	1.24669	−	0.405074i	0.0710367	−	0.0230812i
$309$	−0.0590452	−	0.0428988i	−0.00335896	−	0.00244043i
$310$	−5.54284	−	6.53994i	−0.314812	−	0.371444i
$311$	−20.7653	+	15.0869i	−1.17749	+	0.855497i	−0.991886	−	0.127128i	$-0.959424\pi$
$311$	−20.7653	+	15.0869i	−1.17749	+	0.855497i	−0.185604	+	0.982625i	$0.559424\pi$
$312$	−1.01869	+	1.40211i	−0.0576722	+	0.0793790i
$313$	17.7576	−	24.4412i	1.00372	−	1.38150i	0.0807005	−	0.996738i	$-0.474284\pi$
$313$	17.7576	−	24.4412i	1.00372	−	1.38150i	0.923017	−	0.384760i	$-0.125716\pi$
$314$	−4.51240	+	3.27845i	−0.254649	+	0.185013i
$315$	−0.395350	−	0.466469i	−0.0222754	−	0.0262826i
$316$	12.9923	+	9.43945i	0.730873	+	0.531010i
$317$	−24.5955	+	7.99157i	−1.38142	+	0.448851i	−0.903137	−	0.429353i	$-0.858742\pi$
$317$	−24.5955	+	7.99157i	−1.38142	+	0.448851i	−0.478286	+	0.878204i	$0.658742\pi$
$318$			11.6150i			0.651338i
$319$	13.4608	+	41.4282i	0.753663	+	2.31954i
$320$	−0.847859	−	2.06909i	−0.0473967	−	0.115666i
$321$	1.80699	−	5.56134i	0.100856	−	0.310404i
$322$	1.20826	+	0.392588i	0.0673337	+	0.0218781i
$323$	−3.34718	−	4.60700i	−0.186242	−	0.256340i
$324$	−1.00000			−0.0555556
$325$	7.75069	−	3.87535i	0.429931	−	0.214965i
$326$	18.3753			1.01771
$327$	−5.76388	−	7.93329i	−0.318743	−	0.438712i
$328$	7.20962	+	2.34255i	0.398085	+	0.129346i
$329$	−0.100394	+	0.308982i	−0.00553492	+	0.0170347i
$330$	−8.17702	+	6.93033i	−0.450130	+	0.381502i
$331$	4.48366	+	13.7993i	0.246444	+	0.758477i	0.995396	+	0.0958519i	$0.0305575\pi$
$331$	4.48366	+	13.7993i	0.246444	+	0.758477i	−0.748952	+	0.662625i	$0.769442\pi$
$332$			15.1392i			0.830873i
$333$	−8.56851	+	2.78408i	−0.469552	+	0.152567i
$334$	−7.23607	−	5.25731i	−0.395940	−	0.287667i
$335$	−1.05029	−	14.0256i	−0.0573834	−	0.766300i
$336$	−0.221232	+	0.160734i	−0.0120692	+	0.00876877i
$337$	−6.50536	+	8.95385i	−0.354369	+	0.487747i	−0.948569	−	0.316570i	$-0.897469\pi$
$337$	−6.50536	+	8.95385i	−0.354369	+	0.487747i	0.594200	+	0.804317i	$0.297469\pi$
$338$	5.87570	−	8.08721i	0.319596	−	0.439886i
$339$	−14.0196	+	10.1858i	−0.761439	+	0.553217i
$340$	−4.10886	−	1.00296i	−0.222834	−	0.0543932i
$341$	14.8683	+	10.8024i	0.805162	+	0.584984i
$342$	2.86327	−	0.930333i	0.154828	−	0.0503067i
$343$		−	3.80796i		−	0.205610i
$344$	0.892944	+	2.74820i	0.0481443	+	0.148173i
$345$	−10.3594	+	0.775751i	−0.557732	+	0.0417650i
$346$	−3.68198	+	11.3320i	−0.197944	+	0.609210i
$347$	−0.961158	−	0.312299i	−0.0515977	−	0.0167651i	0.283104	−	0.959089i	$-0.408636\pi$
$347$	−0.961158	−	0.312299i	−0.0515977	−	0.0167651i	−0.334702	+	0.942324i	$0.608636\pi$
$348$	−5.34129	−	7.35166i	−0.286323	−	0.394090i
$349$	−30.4268			−1.62871			−0.814356	−	0.580366i	$-0.802910\pi$
$349$	−30.4268			−1.62871			−0.814356	+	0.580366i	$0.802910\pi$
$350$	1.35204	−	0.203633i	0.0722695	−	0.0108846i
$351$	−1.73311			−0.0925064
$352$	2.81761	+	3.87811i	0.150179	+	0.206704i
$353$	14.8932	+	4.83911i	0.792687	+	0.257560i	0.677248	−	0.735755i	$-0.263172\pi$
$353$	14.8932	+	4.83911i	0.792687	+	0.257560i	0.115439	+	0.993315i	$0.463172\pi$
$354$	−4.41570	+	13.5901i	−0.234692	+	0.722306i
$355$	2.66708	+	1.64835i	0.141554	+	0.0874853i
$356$	−4.58190	−	14.1016i	−0.242840	−	0.747385i
$357$			0.517242i			0.0273754i
$358$	−3.57237	+	1.16073i	−0.188806	+	0.0613467i
$359$	3.53800	+	2.57051i	0.186729	+	0.135666i	0.677222	−	0.735778i	$-0.263184\pi$
$359$	3.53800	+	2.57051i	0.186729	+	0.135666i	−0.490494	+	0.871445i	$0.663184\pi$
$360$	1.17557	−	1.90211i	0.0619580	−	0.100250i
$361$	8.03852	−	5.84033i	0.423080	−	0.307386i
$362$	−10.6169	+	14.6129i	−0.558013	+	0.768039i
$363$	7.04087	−	9.69093i	0.369550	−	0.508642i
$364$	−0.383418	+	0.278570i	−0.0200966	+	0.0146010i
$365$	−3.68529	+	1.51014i	−0.192897	+	0.0790442i
$366$	−4.16750	−	3.02786i	−0.217839	−	0.158269i
$367$	20.7648	−	6.74689i	1.08391	−	0.352185i	0.288022	−	0.957624i	$-0.407003\pi$
$367$	20.7648	−	6.74689i	1.08391	−	0.352185i	0.795892	+	0.605439i	$0.207003\pi$
$368$			4.64584i			0.242181i
$369$	2.34255	+	7.20962i	0.121948	+	0.375318i
$370$	4.77726	−	19.5712i	0.248358	−	1.01746i
$371$	−0.981504	+	3.02076i	−0.0509571	+	0.156830i
$372$	−3.64625	−	1.18474i	−0.189049	−	0.0614259i
$373$	0.833899	+	1.14776i	0.0431776	+	0.0594289i	0.830060	−	0.557674i	$-0.188306\pi$
$373$	0.833899	+	1.14776i	0.0431776	+	0.0594289i	−0.786882	+	0.617103i	$0.788306\pi$
$374$	9.06706			0.468847
$375$	−9.59871	+	5.73279i	−0.495675	+	0.296040i
$376$	−1.18806			−0.0612694
$377$	−9.25703	−	12.7412i	−0.476762	−	0.656206i
$378$	−0.260074	−	0.0845030i	−0.0133767	−	0.00434637i
$379$	8.05934	−	24.8041i	0.413981	−	1.27410i	−0.499179	−	0.866499i	$-0.666365\pi$
$379$	8.05934	−	24.8041i	0.413981	−	1.27410i	0.913159	−	0.407603i	$-0.133635\pi$
$380$	−1.59638	+	6.53994i	−0.0818925	+	0.335492i
$381$	5.67593	+	17.4687i	0.290787	+	0.894949i
$382$		−	16.6007i		−	0.849367i
$383$	31.1609	−	10.1248i	1.59225	−	0.517353i	0.627074	−	0.778960i	$-0.284252\pi$
$383$	31.1609	−	10.1248i	1.59225	−	0.517353i	0.965175	+	0.261607i	$0.0842523\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	−2.71226	+	1.11141i	−0.138230	+	0.0566429i
$386$	3.11356	−	2.26214i	0.158476	−	0.115140i
$387$	−1.69848	+	2.33776i	−0.0863386	+	0.118835i
$388$	−3.45968	+	4.76185i	−0.175639	+	0.241746i
$389$	−3.60929	+	2.62231i	−0.182998	+	0.132956i	−0.675513	−	0.737348i	$-0.736078\pi$
$389$	−3.60929	+	2.62231i	−0.182998	+	0.132956i	0.492515	+	0.870304i	$0.336078\pi$
$390$	2.03739	−	3.29657i	0.103167	−	0.166928i
$391$	7.10929	+	5.16520i	0.359532	+	0.261216i
$392$	6.58628	−	2.14001i	0.332657	−	0.108087i
$393$		−	7.57357i		−	0.382036i
$394$	3.31984	+	10.2174i	0.167251	+	0.514746i
$395$	−30.5467	−	18.8789i	−1.53697	−	0.949900i
$396$	−1.48131	+	4.55899i	−0.0744384	+	0.229098i
$397$	2.01364	+	0.654271i	0.101062	+	0.0328369i	0.359111	−	0.933295i	$-0.383080\pi$
$397$	2.01364	+	0.654271i	0.101062	+	0.0328369i	−0.258050	+	0.966132i	$0.583080\pi$
$398$	1.46833	+	2.02099i	0.0736009	+	0.101303i
$399$	0.823277			0.0412154
$400$	2.23607	+	4.47214i	0.111803	+	0.223607i
$401$	−28.6530			−1.43086			−0.715431	−	0.698683i	$-0.753770\pi$
$401$	−28.6530			−1.43086			−0.715431	+	0.698683i	$0.753770\pi$
$402$	−3.69717	−	5.08872i	−0.184398	−	0.253802i
$403$	−6.31935	−	2.05328i	−0.314789	−	0.102281i
$404$	−1.49433	+	4.59908i	−0.0743458	+	0.228813i
$405$	2.22982	−	0.166977i	0.110801	−	0.00829718i
$406$	−0.767892	−	2.36333i	−0.0381098	−	0.117290i
$407$			43.1878i			2.14074i
$408$	−1.79892	+	0.584503i	−0.0890596	+	0.0289372i
$409$	31.8385	+	23.1320i	1.57431	+	1.14381i	0.922872	+	0.385107i	$0.125835\pi$
$409$	31.8385	+	23.1320i	1.57431	+	1.14381i	0.651442	+	0.758699i	$0.274165\pi$
$410$	−16.4673	−	4.01963i	−0.813264	−	0.198515i
$411$	15.8644	−	11.5262i	0.782534	−	0.568544i
$412$	0.0428988	−	0.0590452i	0.00211347	−	0.00290895i
$413$	−2.29681	+	3.16129i	−0.113019	+	0.155557i
$414$	−3.75856	+	2.73076i	−0.184723	+	0.134209i
$415$	−2.52791	−	33.7578i	−0.124090	−	1.65711i
$416$	−1.40211	−	1.01869i	−0.0687442	−	0.0499456i
$417$	9.09699	−	2.95579i	0.445481	−	0.144746i
$418$		−	14.4317i		−	0.705879i
$419$	−4.35926	−	13.4164i	−0.212964	−	0.655434i	−0.999292	−	0.0376256i	$-0.988021\pi$
$419$	−4.35926	−	13.4164i	−0.212964	−	0.655434i	0.786328	−	0.617809i	$-0.211979\pi$
$420$	0.466469	−	0.395350i	0.0227614	−	0.0192911i
$421$	5.03839	−	15.5066i	0.245556	−	0.755744i	−0.749988	−	0.661451i	$-0.769941\pi$
$421$	5.03839	−	15.5066i	0.245556	−	0.755744i	0.995545	−	0.0942928i	$-0.0300590\pi$
$422$	23.0860	+	7.50110i	1.12381	+	0.365148i
$423$	−0.698322	−	0.961158i	−0.0339536	−	0.0467331i
$424$	−11.6150			−0.564075
$425$	9.32952	+	1.55034i	0.452548	+	0.0752025i
$426$	1.40217			0.0679353
$427$	−0.827992	−	1.13963i	−0.0400693	−	0.0551507i
$428$	5.56134	+	1.80699i	0.268817	+	0.0873441i
$429$	−2.56726	+	7.90122i	−0.123949	+	0.381474i
$430$	−2.45000	−	5.97890i	−0.118149	−	0.288328i
$431$	−0.612525	−	1.88516i	−0.0295043	−	0.0908048i	0.935220	−	0.354067i	$-0.115202\pi$
$431$	−0.612525	−	1.88516i	−0.0295043	−	0.0908048i	−0.964724	+	0.263262i	$0.915202\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	4.26971	−	1.38731i	0.205189	−	0.0666699i	−0.204619	−	0.978842i	$-0.565596\pi$
$433$	4.26971	−	1.38731i	0.205189	−	0.0666699i	0.409808	+	0.912172i	$0.365596\pi$
$434$	−0.848180	−	0.616239i	−0.0407139	−	0.0295804i
$435$	13.1377	+	15.5010i	0.629905	+	0.743218i
$436$	7.93329	−	5.76388i	0.379936	−	0.276040i
$437$	8.22128	−	11.3156i	0.393277	−	0.541299i
$438$	−1.04691	+	1.44095i	−0.0500235	+	0.0688515i
$439$	20.8045	−	15.1154i	0.992946	−	0.721417i	0.0323816	−	0.999476i	$-0.489691\pi$
$439$	20.8045	−	15.1154i	0.992946	−	0.721417i	0.960564	+	0.278058i	$0.0896908\pi$
$440$	−6.93033	−	8.17702i	−0.330391	−	0.389824i
$441$	5.60262	+	4.07054i	0.266791	+	0.193835i
$442$	−3.11771	+	1.01301i	−0.148294	+	0.0481838i
$443$		−	29.1477i		−	1.38485i	−0.721491	−	0.692423i	$-0.756543\pi$
$443$		−	29.1477i		−	1.38485i	0.721491	−	0.692423i	$-0.243457\pi$
$444$	−2.78408	−	8.56851i	−0.132127	−	0.406644i
$445$	12.5715	+	30.6791i	0.595946	+	1.45433i
$446$	−4.03389	+	12.4150i	−0.191010	+	0.587869i
$447$	4.41668	+	1.43507i	0.208902	+	0.0678764i
$448$	−0.160734	−	0.221232i	−0.00759398	−	0.0104522i
$449$	5.14037			0.242589			0.121295	−	0.992617i	$-0.461295\pi$
$449$	5.14037			0.242589			0.121295	+	0.992617i	$0.461295\pi$
$450$	−2.30371	+	4.43767i	−0.108598	+	0.209194i
$451$	36.3386			1.71112
$452$	−10.1858	−	14.0196i	−0.479100	−	0.659425i
$453$	−15.9664	−	5.18780i	−0.750168	−	0.243744i
$454$	2.18213	−	6.71592i	0.102413	−	0.315194i
$455$	0.808441	−	0.685184i	0.0379003	−	0.0321219i
$456$	0.930333	+	2.86327i	0.0435668	+	0.134085i
$457$		−	20.8445i		−	0.975066i	−0.873105	−	0.487533i	$-0.837897\pi$
$457$		−	20.8445i		−	0.975066i	0.873105	−	0.487533i	$-0.162103\pi$
$458$	−11.9615	+	3.88654i	−0.558926	+	0.181606i
$459$	−1.53025	−	1.11179i	−0.0714259	−	0.0518939i
$460$	−0.775751	−	10.3594i	−0.0361696	−	0.483010i
$461$	4.02072	−	2.92123i	0.187264	−	0.136055i	−0.490204	−	0.871608i	$-0.663078\pi$
$461$	4.02072	−	2.92123i	0.187264	−	0.136055i	0.677467	+	0.735553i	$0.263078\pi$
$462$	−0.770497	+	1.06050i	−0.0358467	+	0.0493388i
$463$	4.17718	−	5.74940i	0.194130	−	0.267197i	−0.700845	−	0.713314i	$-0.747193\pi$
$463$	4.17718	−	5.74940i	0.194130	−	0.267197i	0.894975	+	0.446117i	$0.147193\pi$
$464$	7.35166	−	5.34129i	0.341292	−	0.247963i
$465$	8.32833	+	2.03292i	0.386217	+	0.0942744i
$466$	−7.93263	−	5.76339i	−0.367472	−	0.266984i
$467$	−28.7049	+	9.32679i	−1.32831	+	0.431592i	−0.885339	−	0.464946i	$-0.846074\pi$
$467$	−28.7049	+	9.32679i	−1.32831	+	0.431592i	−0.442966	+	0.896538i	$0.646074\pi$
$468$		−	1.73311i		−	0.0801129i
$469$	−0.531524	−	1.63586i	−0.0245435	−	0.0755371i
$470$	2.64916	−	0.198379i	0.122197	−	0.00915053i
$471$	1.72358	−	5.30464i	0.0794184	−	0.244425i
$472$	−13.5901	−	4.41570i	−0.625536	−	0.203249i
$473$	8.14184	+	11.2063i	0.374362	+	0.515265i
$474$	−16.0593			−0.737630
$475$	2.46762	−	14.8495i	0.113222	−	0.681341i
$476$	−0.517242			−0.0237078
$477$	−6.82714	−	9.39675i	−0.312593	−	0.430247i
$478$	−4.79360	−	1.55754i	−0.219254	−	0.0712401i
$479$	−8.60350	+	26.4788i	−0.393104	+	1.20985i	0.537325	+	0.843376i	$0.319435\pi$
$479$	−8.60350	+	26.4788i	−0.393104	+	1.20985i	−0.930428	+	0.366474i	$0.880565\pi$
$480$	1.90211	+	1.17557i	0.0868192	+	0.0536572i
$481$	−4.82511	−	14.8502i	−0.220006	−	0.677109i
$482$			6.84097i			0.311598i
$483$	−1.20826	+	0.392588i	−0.0549777	+	0.0178634i
$484$	9.69093	+	7.04087i	0.440497	+	0.320040i
$485$	6.91937	−	11.1958i	0.314192	−	0.508374i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	0.763835	−	1.05133i	0.0346127	−	0.0476402i	−0.791360	−	0.611351i	$-0.790627\pi$
$487$	0.763835	−	1.05133i	0.0346127	−	0.0476402i	0.825973	+	0.563710i	$0.190627\pi$
$488$	3.02786	−	4.16750i	0.137065	−	0.188654i
$489$	−14.8659	+	10.8007i	−0.672260	+	0.488426i
$490$	−14.3289	+	5.87161i	−0.647314	+	0.265252i
$491$	−15.5048	−	11.2649i	−0.699723	−	0.508379i	0.180119	−	0.983645i	$-0.442352\pi$
$491$	−15.5048	−	11.2649i	−0.699723	−	0.508379i	−0.879842	+	0.475266i	$0.842352\pi$
$492$	−7.20962	+	2.34255i	−0.325035	+	0.105610i
$493$		−	17.1883i		−	0.774121i
$494$	1.61237	+	4.96236i	0.0725438	+	0.223267i
$495$	2.54180	−	10.4131i	0.114246	−	0.468034i
$496$	1.18474	−	3.64625i	0.0531964	−	0.163722i
$497$	0.364667	+	0.118488i	0.0163576	+	0.00531489i
$498$	−8.89861	−	12.2479i	−0.398756	−	0.548841i
$499$	−6.41339			−0.287103			−0.143551	−	0.989643i	$-0.545852\pi$
$499$	−6.41339			−0.287103			−0.143551	+	0.989643i	$0.545852\pi$
$500$	−5.73279	−	9.59871i	−0.256378	−	0.429267i
$501$	8.94427			0.399601
$502$	4.15887	+	5.72419i	0.185619	+	0.255483i
$503$	34.0189	+	11.0534i	1.51683	+	0.492848i	0.944873	−	0.327436i	$-0.106185\pi$
$503$	34.0189	+	11.0534i	1.51683	+	0.492848i	0.571956	+	0.820284i	$0.306185\pi$
$504$	0.0845030	−	0.260074i	0.00376406	−	0.0115846i
$505$	2.56416	−	10.5047i	0.114104	−	0.467452i
$506$	6.88191	+	21.1803i	0.305938	+	0.941581i
$507$			9.99634i			0.443953i
$508$	−17.4687	+	5.67593i	−0.775049	+	0.251829i
$509$	9.75570	+	7.08793i	0.432414	+	0.314167i	0.782613	−	0.622508i	$-0.213886\pi$
$509$	9.75570	+	7.08793i	0.432414	+	0.314167i	−0.350200	+	0.936675i	$0.613886\pi$
$510$	3.91367	−	1.60372i	0.173300	−	0.0710138i
$511$	−0.394040	+	0.286287i	−0.0174313	+	0.0126646i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−1.76960	+	2.43564i	−0.0781297	+	0.107536i
$514$	−3.61888	+	2.62927i	−0.159622	+	0.115972i
$515$	−0.0857977	+	0.138824i	−0.00378070	+	0.00611730i
$516$	−2.33776	−	1.69848i	−0.102914	−	0.0747714i
$517$	−5.41634	+	1.75987i	−0.238210	+	0.0773992i
$518$		−	2.46371i		−	0.108249i
$519$	−3.68198	−	11.3320i	−0.161621	−	0.497418i
$520$	3.29657	+	2.03739i	0.144564	+	0.0893454i
$521$	1.08563	−	3.34124i	0.0475625	−	0.146382i	−0.924455	−	0.381292i	$-0.875479\pi$
$521$	1.08563	−	3.34124i	0.0475625	−	0.146382i	0.972017	+	0.234909i	$0.0754794\pi$
$522$	8.64240	+	2.80808i	0.378267	+	0.122907i
$523$	14.3695	+	19.7779i	0.628333	+	0.864826i	0.997926	−	0.0643677i	$-0.0205030\pi$
$523$	14.3695	+	19.7779i	0.628333	+	0.864826i	−0.369593	+	0.929194i	$0.620503\pi$
$524$	7.57357			0.330853
$525$	−0.974130	+	0.959451i	−0.0425145	+	0.0418739i
$526$	−2.50232			−0.109106
$527$	−4.26249	−	5.86682i	−0.185677	−	0.255563i
$528$	−4.55899	−	1.48131i	−0.198405	−	0.0644655i
$529$	0.437616	−	1.34684i	0.0190268	−	0.0585584i
$530$	25.8995	−	1.93945i	1.12500	−	0.0842442i
$531$	−4.41570	−	13.5901i	−0.191625	−	0.589761i
$532$			0.823277i			0.0356936i
$533$	−12.4950	+	4.05989i	−0.541220	+	0.175853i
$534$	11.9956	+	8.71529i	0.519099	+	0.377147i
$535$	−12.7025	−	3.10065i	−0.549179	−	0.134053i
$536$	5.08872	−	3.69717i	0.219799	−	0.159693i
$537$	2.20785	−	3.03884i	0.0952757	−	0.131136i
$538$	−3.63763	+	5.00676i	−0.156829	+	0.215857i
$539$	26.8568	−	19.5126i	1.15680	−	0.840466i
$540$	0.166977	+	2.22982i	0.00718557	+	0.0959564i
$541$	31.3407	+	22.7703i	1.34744	+	0.978974i	0.999135	+	0.0415933i	$0.0132434\pi$
$541$	31.3407	+	22.7703i	1.34744	+	0.978974i	0.348307	+	0.937380i	$0.386757\pi$
$542$	−12.5244	+	4.06941i	−0.537967	+	0.174796i
$543$		−	18.0626i		−	0.775139i
$544$	−0.584503	−	1.79892i	−0.0250604	−	0.0771279i
$545$	−16.7274	+	14.1771i	−0.716524	+	0.607281i
$546$	0.146453	−	0.450735i	0.00626760	−	0.0192897i
$547$	−28.8377	−	9.36994i	−1.23301	−	0.400630i	−0.381207	−	0.924490i	$-0.624491\pi$
$547$	−28.8377	−	9.36994i	−1.23301	−	0.400630i	−0.851804	+	0.523860i	$0.824491\pi$
$548$	11.5262	+	15.8644i	0.492374	+	0.677694i
$549$	5.15131			0.219853
$550$	16.8188	+	17.0761i	0.717156	+	0.728128i
$551$	−27.3580			−1.16549
$552$	−2.73076	−	3.75856i	−0.116229	−	0.159975i
$553$	−4.17661	−	1.35706i	−0.177608	−	0.0577082i
$554$	−1.59673	+	4.91424i	−0.0678387	+	0.208786i
$555$	7.63876	+	18.6414i	0.324247	+	0.791284i
$556$	2.95579	+	9.09699i	0.125353	+	0.385798i
$557$			25.7254i			1.09002i	0.838430	+	0.545010i	$0.183474\pi$
$557$			25.7254i			1.09002i	−0.838430	+	0.545010i	$0.816526\pi$
$558$	3.64625	−	1.18474i	0.154358	−	0.0501540i
$559$	−4.05158	−	2.94365i	−0.171364	−	0.124503i
$560$	0.395350	+	0.466469i	0.0167066	+	0.0197119i
$561$	−7.33541	+	5.32949i	−0.309701	+	0.225011i
$562$	−0.0276091	+	0.0380006i	−0.00116462	+	0.00160296i
$563$	−18.0058	+	24.7829i	−0.758854	+	1.04447i	0.238454	+	0.971154i	$0.423359\pi$
$563$	−18.0058	+	24.7829i	−0.758854	+	1.04447i	−0.997308	+	0.0733197i	$0.976641\pi$
$564$	0.961158	−	0.698322i	0.0404721	−	0.0294047i
$565$	25.0535	+	29.5604i	1.05401	+	1.24361i
$566$	−17.6942	−	12.8556i	−0.743741	−	0.540359i
$567$	0.260074	−	0.0845030i	0.0109221	−	0.00354879i
$568$			1.40217i			0.0588337i
$569$	−3.85826	−	11.8745i	−0.161747	−	0.497805i	0.837035	−	0.547149i	$-0.184287\pi$
$569$	−3.85826	−	11.8745i	−0.161747	−	0.497805i	−0.998782	+	0.0493440i	$0.984287\pi$
$570$	−2.55258	−	6.22925i	−0.106916	−	0.260915i
$571$	−7.52655	+	23.1644i	−0.314976	+	0.969398i	0.660788	+	0.750573i	$0.270222\pi$
$571$	−7.52655	+	23.1644i	−0.314976	+	0.969398i	−0.975764	+	0.218825i	$0.929778\pi$
$572$	−7.90122	−	2.56726i	−0.330366	−	0.107343i
$573$	9.75767	+	13.4303i	0.407632	+	0.561058i
$574$	−2.07298			−0.0865247
$575$	3.45958	+	22.9701i	0.144274	+	0.957921i
$576$	1.00000			0.0416667
$577$	−1.88827	−	2.59898i	−0.0786098	−	0.108197i	0.767901	−	0.640568i	$-0.221301\pi$
$577$	−1.88827	−	2.59898i	−0.0786098	−	0.108197i	−0.846511	+	0.532371i	$0.821301\pi$
$578$	12.7653	+	4.14771i	0.530968	+	0.172522i
$579$	−1.18928	+	3.66021i	−0.0494246	+	0.152113i
$580$	−15.5010	+	13.1377i	−0.643646	+	0.545514i
$581$	−1.27931	−	3.93731i	−0.0530747	−	0.163347i
$582$		−	5.88597i		−	0.243981i
$583$	−52.9527	+	17.2054i	−2.19308	+	0.712574i
$584$	−1.44095	−	1.04691i	−0.0596271	−	0.0433216i
$585$	0.289390	+	3.86452i	0.0119648	+	0.159778i
$586$	6.75763	−	4.90971i	0.279155	−	0.202818i
$587$	−8.92797	+	12.2883i	−0.368497	+	0.507192i	−0.952491	−	0.304565i	$-0.901489\pi$
$587$	−8.92797	+	12.2883i	−0.368497	+	0.507192i	0.583995	+	0.811757i	$0.301489\pi$
$588$	−4.07054	+	5.60262i	−0.167866	+	0.231048i
$589$	−9.33801	+	6.78446i	−0.384766	+	0.279549i
$590$	31.0409	+	7.57698i	1.27793	+	0.311940i
$591$	−8.69145	−	6.31471i	−0.357518	−	0.259752i
$592$	8.56851	−	2.78408i	0.352164	−	0.114425i
$593$			4.96989i			0.204089i	0.994780	+	0.102044i	$0.0325384\pi$
$593$			4.96989i			0.204089i	−0.994780	+	0.102044i	$0.967462\pi$
$594$	−1.48131	−	4.55899i	−0.0607787	−	0.187058i
$595$	1.15336	−	0.0863678i	0.0472832	−	0.00354074i
$596$	−1.43507	+	4.41668i	−0.0587827	+	0.180914i
$597$	−2.37581	−	0.771949i	−0.0972356	−	0.0315938i
$598$	−4.73269	−	6.51400i	−0.193534	−	0.266377i
$599$	3.23524			0.132188			0.0660942	−	0.997813i	$-0.478946\pi$
$599$	3.23524			0.132188			0.0660942	+	0.997813i	$0.478946\pi$
$600$	−4.43767	−	2.30371i	−0.181167	−	0.0940484i
$601$	−8.78152			−0.358205			−0.179103	−	0.983830i	$-0.557319\pi$
$601$	−8.78152			−0.358205			−0.179103	+	0.983830i	$0.557319\pi$
$602$	−0.464462	−	0.639277i	−0.0189301	−	0.0260550i
$603$	5.98215	+	1.94372i	0.243612	+	0.0791543i
$604$	5.18780	−	15.9664i	0.211089	−	0.649664i
$605$	−22.7847	−	14.0817i	−0.926331	−	0.572504i
$606$	−1.49433	−	4.59908i	−0.0607031	−	0.186825i
$607$		−	39.5692i		−	1.60606i	−0.595937	−	0.803031i	$-0.703219\pi$
$607$		−	39.5692i		−	1.60606i	0.595937	−	0.803031i	$-0.296781\pi$
$608$	−2.86327	+	0.930333i	−0.116121	+	0.0377300i
$609$	2.01037	+	1.46062i	0.0814642	+	0.0591872i
$610$	−6.05573	+	9.79837i	−0.245189	+	0.396725i
$611$	1.66579	−	1.21027i	0.0673907	−	0.0489622i
$612$	1.11179	−	1.53025i	0.0449415	−	0.0618566i
$613$	−27.5582	+	37.9307i	−1.11307	+	1.53201i	−0.296248	+	0.955111i	$0.595736\pi$
$613$	−27.5582	+	37.9307i	−1.11307	+	1.53201i	−0.816819	+	0.576894i	$0.804264\pi$
$614$	1.85198	−	1.34554i	0.0747399	−	0.0543017i
$615$	15.6850	−	6.42732i	0.632482	−	0.259174i
$616$	−1.06050	−	0.770497i	−0.0427287	−	0.0310442i
$617$	13.4594	−	4.37322i	0.541854	−	0.176059i	−0.0252863	−	0.999680i	$-0.508050\pi$
$617$	13.4594	−	4.37322i	0.541854	−	0.176059i	0.567140	+	0.823621i	$0.308050\pi$
$618$			0.0729839i			0.00293584i
$619$	2.02304	+	6.22627i	0.0813128	+	0.250255i	0.983446	−	0.181203i	$-0.0579992\pi$
$619$	2.02304	+	6.22627i	0.0813128	+	0.250255i	−0.902133	+	0.431458i	$0.857999\pi$
$620$	−2.03292	+	8.32833i	−0.0816440	+	0.334474i
$621$	1.43564	−	4.41846i	0.0576104	−	0.177307i
$622$	24.4110	+	7.93163i	0.978794	+	0.318029i
$623$	2.38326	+	3.28028i	0.0954833	+	0.131422i
$624$	1.73311			0.0693798
$625$	14.3859	+	20.4462i	0.575435	+	0.817848i
$626$	−30.2110			−1.20747
$627$	8.48276	+	11.6755i	0.338769	+	0.466275i
$628$	5.30464	+	1.72358i	0.211678	+	0.0687784i
$629$	5.26606	−	16.2073i	0.209972	−	0.646226i
$630$	−0.145000	+	0.594028i	−0.00577696	+	0.0236667i
$631$	1.86919	+	5.75279i	0.0744114	+	0.229015i	0.981344	−	0.192262i	$-0.0615822\pi$
$631$	1.86919	+	5.75279i	0.0744114	+	0.229015i	−0.906932	+	0.421276i	$0.861582\pi$
$632$		−	16.0593i		−	0.638806i
$633$	−23.0860	+	7.50110i	−0.917586	+	0.298142i
$634$	20.9222	+	15.2009i	0.830927	+	0.603704i
$635$	38.0044	−	15.5732i	1.50816	−	0.618004i
$636$	9.39675	−	6.82714i	0.372605	−	0.270714i
$637$	−7.05469	+	9.70994i	−0.279517	+	0.384722i
$638$	25.6041	−	35.2410i	1.01367	−	1.39520i
$639$	−1.13438	+	0.824175i	−0.0448753	+	0.0326038i
$640$	−1.17557	+	1.90211i	−0.0464685	+	0.0751876i
$641$	−26.1185	−	18.9762i	−1.03162	−	0.749515i	−0.0629869	−	0.998014i	$-0.520063\pi$
$641$	−26.1185	−	18.9762i	−1.03162	−	0.749515i	−0.968632	+	0.248499i	$0.920063\pi$
$642$	−5.56134	+	1.80699i	−0.219489	+	0.0713161i
$643$		−	12.1187i		−	0.477914i	−0.971030	−	0.238957i	$-0.923194\pi$
$643$		−	12.1187i		−	0.477914i	0.971030	−	0.238957i	$-0.0768056\pi$
$644$	−0.392588	−	1.20826i	−0.0154701	−	0.0476121i
$645$	5.49640	+	3.39696i	0.216420	+	0.133755i
$646$	−1.75972	+	5.41585i	−0.0692352	+	0.213084i
$647$	19.2386	+	6.25100i	0.756348	+	0.245752i	0.661710	−	0.749760i	$-0.269831\pi$
$647$	19.2386	+	6.25100i	0.756348	+	0.245752i	0.0946373	+	0.995512i	$0.469831\pi$
$648$	0.587785	+	0.809017i	0.0230904	+	0.0317812i
$649$	−68.4982			−2.68879
$650$	−7.69096	−	3.99257i	−0.301664	−	0.156601i
$651$	1.04841			0.0410904
$652$	−10.8007	−	14.8659i	−0.422989	−	0.582194i
$653$	−31.7499	−	10.3162i	−1.24247	−	0.403702i	−0.387252	−	0.921974i	$-0.626576\pi$
$653$	−31.7499	−	10.3162i	−1.24247	−	0.403702i	−0.855216	+	0.518271i	$0.826576\pi$
$654$	−3.03025	+	9.32615i	−0.118492	+	0.364681i
$655$	−16.8877	+	1.26462i	−0.659858	+	0.0494126i
$656$	−2.34255	−	7.20962i	−0.0914611	−	0.281488i
$657$		−	1.78112i		−	0.0694880i
$658$	0.308982	−	0.100394i	0.0120454	−	0.00391378i
$659$	−24.5894	−	17.8653i	−0.957869	−	0.695932i	−0.00521401	−	0.999986i	$-0.501660\pi$
$659$	−24.5894	−	17.8653i	−0.957869	−	0.695932i	−0.952655	+	0.304054i	$0.901660\pi$
$660$	10.4131	+	2.54180i	0.405329	+	0.0989395i
$661$	−20.1744	+	14.6576i	−0.784694	+	0.570114i	−0.906384	−	0.422455i	$-0.861169\pi$
$661$	−20.1744	+	14.6576i	−0.784694	+	0.570114i	0.121690	+	0.992568i	$0.461169\pi$
$662$	8.52842	−	11.7384i	0.331466	−	0.456224i
$663$	1.92685	−	2.65208i	0.0748327	−	0.102998i
$664$	12.2479	−	8.89861i	0.475310	−	0.345333i
$665$	−0.137469	−	1.83576i	−0.00533081	−	0.0711879i
$666$	7.28881	+	5.29563i	0.282436	+	0.205202i
$667$	40.1512	−	13.0459i	1.55466	−	0.505140i
$668$			8.94427i			0.346064i
$669$	−4.03389	−	12.4150i	−0.155959	−	0.479993i
$670$	−10.7296	+	9.09374i	−0.414521	+	0.351322i
$671$	7.63066	−	23.4848i	0.294578	−	0.906619i
$672$	0.260074	+	0.0845030i	0.0100326	+	0.00325977i
$673$	27.0791	+	37.2711i	1.04382	+	1.43670i	0.894045	+	0.447977i	$0.147855\pi$
$673$	27.0791	+	37.2711i	1.04382	+	1.43670i	0.149777	+	0.988720i	$0.452145\pi$
$674$	11.0676			0.426307
$675$	−0.744661	−	4.94424i	−0.0286620	−	0.190304i
$676$	−9.99634			−0.384475
$677$	16.8060	+	23.1315i	0.645908	+	0.889016i	0.998913	−	0.0466053i	$-0.0148403\pi$
$677$	16.8060	+	23.1315i	0.645908	+	0.889016i	−0.353006	+	0.935621i	$0.614840\pi$
$678$	16.4810	+	5.35500i	0.632949	+	0.205658i
$679$	0.497382	−	1.53078i	0.0190878	−	0.0587461i
$680$	1.60372	+	3.91367i	0.0614998	+	0.150082i
$681$	2.18213	+	6.71592i	0.0836196	+	0.257355i
$682$		−	18.3782i		−	0.703737i
$683$	−8.49047	+	2.75872i	−0.324879	+	0.105560i	−0.466916	−	0.884302i	$-0.654635\pi$
$683$	−8.49047	+	2.75872i	−0.324879	+	0.105560i	0.142037	+	0.989861i	$0.454635\pi$
$684$	−2.43564	−	1.76960i	−0.0931292	−	0.0676623i
$685$	−28.3503	−	33.4502i	−1.08321	−	1.27807i
$686$	−3.08070	+	2.23826i	−0.117622	+	0.0854572i
$687$	7.39264	−	10.1751i	0.282047	−	0.388204i
$688$	1.69848	−	2.33776i	0.0647539	−	0.0891262i
$689$	16.2856	−	11.8322i	0.620431	−	0.450769i
$690$	6.71671	+	7.92497i	0.255701	+	0.301698i
$691$	1.06206	+	0.771634i	0.0404028	+	0.0293543i	0.607803	−	0.794088i	$-0.292051\pi$
$691$	1.06206	+	0.771634i	0.0404028	+	0.0293543i	−0.567401	+	0.823442i	$0.692051\pi$
$692$	11.3320	−	3.68198i	0.430777	−	0.139968i
$693$		−	1.31085i		−	0.0497950i
$694$	0.312299	+	0.961158i	0.0118547	+	0.0364851i
$695$	−8.10989	−	19.7911i	−0.307626	−	0.750721i
$696$	−2.80808	+	8.64240i	−0.106440	+	0.327589i
$697$	−13.6369	−	4.43091i	−0.516536	−	0.167833i
$698$	17.8845	+	24.6158i	0.676936	+	0.931723i
$699$	9.80527			0.370869
$700$	−0.959451	−	0.974130i	−0.0362638	−	0.0368186i
$701$	22.5267			0.850822			0.425411	−	0.905000i	$-0.360130\pi$
$701$	22.5267			0.850822			0.425411	+	0.905000i	$0.360130\pi$
$702$	1.01869	+	1.40211i	0.0384482	+	0.0529193i
$703$	−25.7966	−	8.38181i	−0.972935	−	0.316126i
$704$	1.48131	−	4.55899i	0.0558288	−	0.171823i
$705$	−2.02661	+	1.71763i	−0.0763266	+	0.0646896i
$706$	−4.83911	−	14.8932i	−0.182122	−	0.560515i
$707$		−	1.32238i		−	0.0497331i
$708$	13.5901	−	4.41570i	0.510748	−	0.165952i
$709$	−5.57914	−	4.05348i	−0.209529	−	0.152232i	0.478072	−	0.878321i	$-0.341336\pi$
$709$	−5.57914	−	4.05348i	−0.209529	−	0.152232i	−0.687600	+	0.726089i	$0.741336\pi$
$710$	−0.234131	−	3.12659i	−0.00878677	−	0.117339i
$711$	12.9923	−	9.43945i	0.487249	−	0.354007i
$712$	−8.71529	+	11.9956i	−0.326619	+	0.449553i
$713$	10.4694	−	14.4100i	0.392084	−	0.539657i
$714$	0.418458	−	0.304027i	0.0156604	−	0.0113779i
$715$	18.0470	+	4.40522i	0.674920	+	0.164746i
$716$	3.03884	+	2.20785i	0.113567	+	0.0825111i
$717$	4.79360	−	1.55754i	0.179020	−	0.0581673i
$718$		−	4.37321i		−	0.163207i
$719$	−8.75827	−	26.9552i	−0.326628	−	1.00526i	−0.970700	−	0.240293i	$-0.922756\pi$
$719$	−8.75827	−	26.9552i	−0.326628	−	1.00526i	0.644072	−	0.764965i	$-0.277244\pi$
$720$	−2.22982	+	0.166977i	−0.0831007	+	0.00622288i
$721$	−0.00616736	+	0.0189812i	−0.000229684	+	0.000706896i
$722$	−9.44985	−	3.07044i	−0.351687	−	0.114270i
$723$	−4.02102	−	5.53446i	−0.149543	−	0.205829i
$724$	18.0626			0.671290
$725$	32.3709	−	31.8831i	1.20223	−	1.18411i
$726$	−11.9786			−0.444569
$727$	10.0395	+	13.8182i	0.372344	+	0.512487i	0.953536	−	0.301279i	$-0.0974135\pi$
$727$	10.0395	+	13.8182i	0.372344	+	0.512487i	−0.581192	+	0.813766i	$0.697414\pi$
$728$	0.450735	+	0.146453i	0.0167054	+	0.00542790i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	3.38789	+	2.09383i	0.125391	+	0.0774961i
$731$	−1.68900	−	5.19819i	−0.0624698	−	0.192262i
$732$			5.15131i			0.190398i
$733$	11.3102	−	3.67491i	0.417753	−	0.135736i	−0.0925958	−	0.995704i	$-0.529516\pi$
$733$	11.3102	−	3.67491i	0.417753	−	0.135736i	0.510348	+	0.859968i	$0.329516\pi$
$734$	−17.6636	−	12.8333i	−0.651975	−	0.473687i
$735$	8.14109	−	13.1726i	0.300288	−	0.485877i
$736$	3.75856	−	2.73076i	0.138543	−	0.100657i
$737$	17.7228	−	24.3933i	0.652827	−	0.898539i
$738$	4.45579	−	6.13287i	0.164020	−	0.225754i
$739$	9.27173	−	6.73631i	0.341066	−	0.247799i	−0.404045	−	0.914739i	$-0.632396\pi$
$739$	9.27173	−	6.73631i	0.341066	−	0.247799i	0.745112	+	0.666940i	$0.232396\pi$
$740$	−18.6414	+	7.63876i	−0.685272	+	0.280806i
$741$	−4.22123	−	3.06690i	−0.155071	−	0.112666i
$742$	3.02076	−	0.981504i	0.110896	−	0.0360321i
$743$			8.64114i			0.317013i	0.987358	+	0.158506i	$0.0506678\pi$
$743$			8.64114i			0.317013i	−0.987358	+	0.158506i	$0.949332\pi$
$744$	1.18474	+	3.64625i	0.0434347	+	0.133678i
$745$	2.46246	−	10.0881i	0.0902177	−	0.369598i
$746$	0.438406	−	1.34928i	0.0160512	−	0.0494005i
$747$	14.3983	+	4.67828i	0.526805	+	0.171169i
$748$	−5.32949	−	7.33541i	−0.194865	−	0.268209i
$749$	−1.59905			−0.0584281
$750$	10.2799	+	4.39587i	0.375369	+	0.160514i
$751$	−8.45998			−0.308709			−0.154354	−	0.988016i	$-0.549330\pi$
$751$	−8.45998			−0.308709			−0.154354	+	0.988016i	$0.549330\pi$
$752$	0.698322	+	0.961158i	0.0254652	+	0.0350498i
$753$	−6.72919	−	2.18645i	−0.245225	−	0.0796786i
$754$	−4.86671	+	14.9782i	−0.177235	+	0.545474i
$755$	−8.90186	+	36.4685i	−0.323972	+	1.32723i
$756$	0.0845030	+	0.260074i	0.00307334	+	0.00945878i
$757$			53.6675i			1.95058i	0.220932	+	0.975289i	$0.429090\pi$
$757$			53.6675i			1.95058i	−0.220932	+	0.975289i	$0.570910\pi$
$758$	−24.8041	+	8.05934i	−0.900926	+	0.292729i
$759$	−18.0171	−	13.0902i	−0.653978	−	0.475143i
$760$	6.22925	−	2.55258i	0.225959	−	0.0925919i
$761$	−9.52327	+	6.91906i	−0.345218	+	0.250816i	−0.746860	−	0.664981i	$-0.768440\pi$
$761$	−9.52327	+	6.91906i	−0.345218	+	0.250816i	0.401642	+	0.915797i	$0.368440\pi$
$762$	10.7963	−	14.8598i	0.391107	−	0.538313i
$763$	−1.57617	+	2.16942i	−0.0570614	+	0.0785382i
$764$	−13.4303	+	9.75767i	−0.485890	+	0.353020i
$765$	−2.22358	+	3.59783i	−0.0803938	+	0.130080i
$766$	−26.5071	−	19.2585i	−0.957739	−	0.695838i
$767$	23.5531	−	7.65287i	0.850454	−	0.276329i
$768$			1.00000i			0.0360844i
$769$	−1.57472	−	4.84650i	−0.0567859	−	0.174769i	0.918641	−	0.395094i	$-0.129288\pi$
$769$	−1.57472	−	4.84650i	−0.0567859	−	0.174769i	−0.975426	+	0.220325i	$0.929288\pi$
$770$	2.49338	+	1.54099i	0.0898551	+	0.0555335i
$771$	1.38229	−	4.25424i	0.0497819	−	0.153213i
$772$	−3.66021	−	1.18928i	−0.131734	−	0.0428030i
$773$	7.41916	+	10.2116i	0.266849	+	0.367285i	0.921323	−	0.388799i	$-0.127110\pi$
$773$	7.41916	+	10.2116i	0.266849	+	0.367285i	−0.654474	+	0.756084i	$0.727110\pi$
$774$	2.88963			0.103865
$775$	3.14241	−	18.9102i	0.112879	−	0.679274i
$776$	5.88597			0.211294
$777$	1.44813	+	1.99318i	0.0519514	+	0.0715050i
$778$	4.24298	+	1.37863i	0.152118	+	0.0494262i
$779$	−7.05253	+	21.7054i	−0.252683	+	0.777678i
$780$	−3.86452	+	0.289390i	−0.138372	+	0.0103618i
$781$	2.07704	+	6.39247i	0.0743224	+	0.228741i
$782$		−	8.78757i		−	0.314243i
$783$	−8.64240	+	2.80808i	−0.308854	+	0.100353i
$784$	−5.60262	−	4.07054i	−0.200094	−	0.145377i
$785$	−12.1162	−	2.95753i	−0.432446	−	0.105559i
$786$	−6.12715	+	4.45163i	−0.218548	+	0.158784i
$787$	25.9859	−	35.7665i	0.926296	−	1.27494i	−0.0349910	−	0.999388i	$-0.511140\pi$
$787$	25.9859	−	35.7665i	0.926296	−	1.27494i	0.961287	−	0.275549i	$-0.0888597\pi$
$788$	6.31471	−	8.69145i	0.224952	−	0.309620i
$789$	2.02442	−	1.47083i	0.0720712	−	0.0523628i
$790$	2.68155	+	35.8095i	0.0954052	+	1.27405i
$791$	3.83376	+	2.78539i	0.136313	+	0.0990370i
$792$	4.55899	−	1.48131i	0.161997	−	0.0526359i
$793$			8.92777i			0.317034i
$794$	−0.654271	−	2.01364i	−0.0232192	−	0.0714614i
$795$	−19.8131	+	16.7924i	−0.702699	+	0.595564i
$796$	0.771949	−	2.37581i	0.0273610	−	0.0842085i
$797$	44.0719	+	14.3198i	1.56111	+	0.507235i	0.957103	−	0.289746i	$-0.0935710\pi$
$797$	44.0719	+	14.3198i	1.56111	+	0.507235i	0.604004	+	0.796981i	$0.293571\pi$
$798$	−0.483910	−	0.666045i	−0.0171302	−	0.0235777i
$799$	2.24720			0.0795002
$800$	2.30371	−	4.43767i	0.0814483	−	0.156895i
$801$	−14.8273			−0.523898
$802$	16.8418	+	23.1808i	0.594705	+	0.818541i
$803$	−8.12010	−	2.63838i	−0.286552	−	0.0931064i
$804$	−1.94372	+	5.98215i	−0.0685496	+	0.210974i
$805$	1.07715	+	2.62866i	0.0379647	+	0.0926479i
$806$	2.05328	+	6.31935i	0.0723237	+	0.222590i
$807$		−	6.18870i		−	0.217853i
$808$	4.59908	−	1.49433i	0.161795	−	0.0525705i
$809$	40.0393	+	29.0902i	1.40771	+	1.02276i	0.993651	+	0.112507i	$0.0358881\pi$
$809$	40.0393	+	29.0902i	1.40771	+	1.02276i	0.414056	+	0.910252i	$0.364112\pi$
$810$	−1.44575	−	1.70582i	−0.0507983	−	0.0599364i
$811$	2.27136	−	1.65024i	0.0797583	−	0.0579478i	−0.547192	−	0.837007i	$-0.684303\pi$
$811$	2.27136	−	1.65024i	0.0797583	−	0.0579478i	0.626950	+	0.779060i	$0.284303\pi$
$812$	−1.46062	+	2.01037i	−0.0512576	+	0.0705500i
$813$	7.74048	−	10.6539i	0.271471	−	0.373647i
$814$	34.9397	−	25.3852i	1.22464	−	0.889750i
$815$	26.5660	+	31.3449i	0.930566	+	1.09796i
$816$	1.53025	+	1.11179i	0.0535694	+	0.0389205i
$817$	−8.27378	+	2.68832i	−0.289463	+	0.0940523i
$818$		−	39.3546i		−	1.37600i
$819$	0.146453	+	0.450735i	0.00511747	+	0.0157500i
$820$	6.42732	+	15.6850i	0.224452	+	0.547745i
$821$	−11.5462	+	35.5356i	−0.402965	+	1.24020i	0.519617	+	0.854399i	$0.326075\pi$
$821$	−11.5462	+	35.5356i	−0.402965	+	1.24020i	−0.922582	+	0.385800i	$0.873925\pi$
$822$	−18.6497	−	6.05967i	−0.650484	−	0.211355i
$823$	13.4238	+	18.4763i	0.467925	+	0.644044i	0.976129	−	0.217193i	$-0.0696902\pi$
$823$	13.4238	+	18.4763i	0.467925	+	0.644044i	−0.508203	+	0.861237i	$0.669690\pi$
$824$	−0.0729839			−0.00254251
$825$	−23.6438	−	3.92902i	−0.823171	−	0.136791i
$826$	3.90757			0.135962
$827$	6.29560	+	8.66515i	0.218919	+	0.301317i	0.904325	−	0.426845i	$-0.140375\pi$
$827$	6.29560	+	8.66515i	0.218919	+	0.301317i	−0.685405	+	0.728162i	$0.740375\pi$
$828$	4.41846	+	1.43564i	0.153552	+	0.0498921i
$829$	8.52760	−	26.2453i	0.296176	−	0.911536i	−0.686648	−	0.726990i	$-0.740919\pi$
$829$	8.52760	−	26.2453i	0.296176	−	0.911536i	0.982824	−	0.184546i	$-0.0590814\pi$
$830$	−25.8248	+	21.8875i	−0.896391	+	0.759725i
$831$	−1.59673	−	4.91424i	−0.0553901	−	0.170473i
$832$			1.73311i			0.0600847i
$833$	−12.4579	+	4.04781i	−0.431640	+	0.140248i
$834$	−7.73836	−	5.62225i	−0.267958	−	0.194683i
$835$	−1.49349	−	19.9442i	−0.0516844	−	0.690196i
$836$	−11.6755	+	8.48276i	−0.403806	+	0.293382i
$837$	−2.25351	+	3.10169i	−0.0778927	+	0.107210i
$838$	−8.29180	+	11.4127i	−0.286435	+	0.394244i
$839$	−8.03884	+	5.84056i	−0.277532	+	0.201639i	−0.717840	−	0.696208i	$-0.754869\pi$
$839$	−8.03884	+	5.84056i	−0.277532	+	0.201639i	0.440308	+	0.897847i	$0.354869\pi$
$840$	−0.594028	−	0.145000i	−0.0204959	−	0.00500299i
$841$	−43.3442	−	31.4914i	−1.49463	−	1.08591i
$842$	−15.5066	+	5.03839i	−0.534392	+	0.173634i
$843$		−	0.0469714i		−	0.00161778i
$844$	−7.50110	−	23.0860i	−0.258198	−	0.794653i
$845$	22.2901	−	1.66916i	0.766802	−	0.0574210i
$846$	−0.367130	+	1.12991i	−0.0126222	+	0.0388471i
$847$	−3.11533	−	1.01223i	−0.107044	−	0.0347807i
$848$	6.82714	+	9.39675i	0.234445	+	0.322686i
$849$	21.8712			0.750617
$850$	−4.22950	−	8.45901i	−0.145071	−	0.290142i
$851$	41.8566			1.43482
$852$	−0.824175	−	1.13438i	−0.0282358	−	0.0388632i
$853$	42.8052	+	13.9083i	1.46562	+	0.476210i	0.929782	−	0.368110i	$-0.119995\pi$
$853$	42.8052	+	13.9083i	1.46562	+	0.476210i	0.535840	+	0.844319i	$0.319995\pi$
$854$	−0.435301	+	1.33972i	−0.0148957	+	0.0458442i
$855$	5.72654	+	3.53920i	0.195844	+	0.121038i
$856$	−1.80699	−	5.56134i	−0.0617616	−	0.190083i
$857$		−	24.6986i		−	0.843686i	−0.906669	−	0.421843i	$-0.861383\pi$
$857$		−	24.6986i		−	0.843686i	0.906669	−	0.421843i	$-0.138617\pi$
$858$	7.90122	−	2.56726i	0.269743	−	0.0876448i
$859$	−14.0283	−	10.1922i	−0.478641	−	0.347753i	0.322159	−	0.946686i	$-0.395592\pi$
$859$	−14.0283	−	10.1922i	−0.478641	−	0.347753i	−0.800799	+	0.598933i	$0.795592\pi$
$860$	−3.39696	+	5.49640i	−0.115835	+	0.187426i
$861$	1.67708	−	1.21847i	0.0571547	−	0.0415253i
$862$	−1.16509	+	1.60361i	−0.0396832	+	0.0546192i
$863$	−15.2158	+	20.9428i	−0.517954	+	0.712902i	−0.985235	−	0.171207i	$-0.945233\pi$
$863$	−15.2158	+	20.9428i	−0.517954	+	0.712902i	0.467282	+	0.884109i	$0.345233\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−24.6535	+	10.1023i	−0.838243	+	0.343490i
$866$	−3.63203	−	2.63882i	−0.123421	−	0.0896709i
$867$	−12.7653	+	4.14771i	−0.433533	+	0.140863i
$868$			1.04841i			0.0355853i
$869$	−23.7888	−	73.2144i	−0.806979	−	2.48363i
$870$	4.81845	−	19.7399i	0.163361	−	0.669246i
$871$	−3.36867	+	10.3677i	−0.114143	+	0.351296i
$872$	−9.32615	−	3.03025i	−0.315823	−	0.102617i
$873$	3.45968	+	4.76185i	0.117093	+	0.161164i
$874$	−13.9869			−0.473113
$875$	2.30207	+	2.01193i	0.0778240	+	0.0680157i
$876$	1.78112			0.0601784
$877$	11.8673	+	16.3339i	0.400729	+	0.551557i	0.960927	−	0.276802i	$-0.0892748\pi$
$877$	11.8673	+	16.3339i	0.400729	+	0.551557i	−0.560198	+	0.828359i	$0.689275\pi$
$878$	−24.4572	−	7.94662i	−0.825390	−	0.268185i
$879$	−2.58119	+	7.94407i	−0.0870612	+	0.267947i
$880$	−2.54180	+	10.4131i	−0.0856842	+	0.351025i
$881$	7.34633	+	22.6097i	0.247504	+	0.761739i	0.995215	+	0.0977143i	$0.0311531\pi$
$881$	7.34633	+	22.6097i	0.247504	+	0.761739i	−0.747710	+	0.664025i	$0.768847\pi$
$882$		−	6.92522i		−	0.233184i
$883$	−30.9842	+	10.0674i	−1.04270	+	0.338794i	−0.779800	−	0.626029i	$-0.784679\pi$
$883$	−30.9842	+	10.0674i	−1.04270	+	0.338794i	−0.262900	+	0.964823i	$0.584679\pi$
$884$	2.65208	+	1.92685i	0.0891993	+	0.0648071i
$885$	−29.5663	+	12.1155i	−0.993859	+	0.407257i
$886$	−23.5809	+	17.1326i	−0.792217	+	0.575580i
$887$	−33.1027	+	45.5619i	−1.11148	+	1.52982i	−0.292261	+	0.956339i	$0.594408\pi$
$887$	−33.1027	+	45.5619i	−1.11148	+	1.52982i	−0.819218	+	0.573482i	$0.805592\pi$
$888$	−5.29563	+	7.28881i	−0.177710	+	0.244597i
$889$	4.06351	−	2.95232i	0.136286	−	0.0990175i
$890$	17.4306	−	28.2033i	0.584274	−	0.945376i
$891$	3.87811	+	2.81761i	0.129921	+	0.0943935i
$892$	12.4150	−	4.03389i	0.415686	−	0.135065i
$893$		−	3.57679i		−	0.119693i
$894$	−1.43507	−	4.41668i	−0.0479958	−	0.147716i
$895$	−7.14475	−	4.41570i	−0.238823	−	0.147600i
$896$	−0.0845030	+	0.260074i	−0.00282305	+	0.00868845i
$897$	7.65766	+	2.48812i	0.255682	+	0.0830761i
$898$	−3.02144	−	4.15865i	−0.100827	−	0.138776i
$899$	−34.8392			−1.16195
$900$	4.94424	−	0.744661i	0.164808	−	0.0248220i
$901$	21.9697			0.731917
$902$	−21.3593	−	29.3986i	−0.711187	−	0.978865i
$903$	0.751515	+	0.244182i	0.0250089	+	0.00812587i
$904$	−5.35500	+	16.4810i	−0.178105	+	0.548150i
$905$	−40.2764	+	3.01604i	−1.33883	+	0.100257i
$906$	5.18780	+	15.9664i	0.172353	+	0.530449i
$907$		−	46.7617i		−	1.55270i	−0.630304	−	0.776349i	$-0.717070\pi$
$907$		−	46.7617i		−	1.55270i	0.630304	−	0.776349i	$-0.282930\pi$
$908$	−6.71592	+	2.18213i	−0.222876	+	0.0724167i
$909$	3.91221	+	2.84239i	0.129760	+	0.0942761i
$910$	−1.02951	−	0.251301i	−0.0341281	−	0.00833056i
$911$	13.5487	−	9.84374i	0.448890	−	0.326138i	−0.340268	−	0.940329i	$-0.610518\pi$
$911$	13.5487	−	9.84374i	0.448890	−	0.326138i	0.789157	+	0.614191i	$0.210518\pi$
$912$	1.76960	−	2.43564i	0.0585973	−	0.0806522i
$913$	42.6564	−	58.7115i	1.41172	−	1.94307i
$914$	−16.8636	+	12.2521i	−0.557797	+	0.405263i
$915$	−0.860153	−	11.4865i	−0.0284358	−	0.379733i
$916$	10.1751	+	7.39264i	0.336195	+	0.244260i
$917$	−1.96968	+	0.639989i	−0.0650447	+	0.0211343i
$918$			1.89149i			0.0624285i
$919$	1.58373	+	4.87423i	0.0522426	+	0.160786i	0.973774	−	0.227518i	$-0.0730610\pi$
$919$	1.58373	+	4.87423i	0.0522426	+	0.160786i	−0.921531	+	0.388304i	$0.873061\pi$
$920$	−7.92497	+	6.71671i	−0.261278	+	0.221443i
$921$	−0.707394	+	2.17714i	−0.0233094	+	0.0717391i
$922$	−4.72664	−	1.53578i	−0.155664	−	0.0505782i
$923$	−1.42838	−	1.96600i	−0.0470158	−	0.0647117i
$924$	1.31085			0.0431237
$925$	40.2916	−	20.1458i	1.32478	−	0.662389i
$926$	−7.10664			−0.233539
$927$	−0.0428988	−	0.0590452i	−0.00140898	−	0.00193930i
$928$	−8.64240	−	2.80808i	−0.283701	−	0.0921799i
$929$	−14.0119	+	43.1241i	−0.459715	+	1.41486i	0.405795	+	0.913964i	$0.366995\pi$
$929$	−14.0119	+	43.1241i	−0.459715	+	1.41486i	−0.865510	+	0.500892i	$0.833005\pi$
$930$	−3.25060	−	7.93268i	−0.106592	−	0.260123i
$931$	6.44276	+	19.8288i	0.211153	+	0.649862i
$932$			9.80527i			0.321182i
$933$	−24.4110	+	7.93163i	−0.799182	+	0.259670i
$934$	24.4179	+	17.7406i	0.798977	+	0.580491i
$935$	13.1087	+	15.4668i	0.428699	+	0.505817i
$936$	−1.40211	+	1.01869i	−0.0458295	+	0.0332971i
$937$	−18.2283	+	25.0891i	−0.595493	+	0.819626i	−0.995286	−	0.0969794i	$-0.969082\pi$
$937$	−18.2283	+	25.0891i	−0.595493	+	0.819626i	0.399793	+	0.916605i	$0.369082\pi$
$938$	−1.01102	+	1.39155i	−0.0330109	+	0.0454356i
$939$	24.4412	−	17.7576i	0.797608	−	0.579496i
$940$	−1.71763	−	2.02661i	−0.0560229	−	0.0661007i
$941$	39.0847	+	28.3967i	1.27412	+	0.925705i	0.999359	−	0.0358067i	$-0.0114001\pi$
$941$	39.0847	+	28.3967i	1.27412	+	0.925705i	0.274765	+	0.961512i	$0.411400\pi$
$942$	−5.30464	+	1.72358i	−0.172834	+	0.0561573i
$943$		−	35.2185i		−	1.14687i
$944$	4.41570	+	13.5901i	0.143719	+	0.442321i
$945$	−0.231853	−	0.565808i	−0.00754219	−	0.0184057i
$946$	4.28042	−	13.1738i	0.139168	−	0.428316i
$947$	−31.7532	−	10.3172i	−1.03184	−	0.335265i	−0.256322	−	0.966591i	$-0.582511\pi$
$947$	−31.7532	−	10.3172i	−1.03184	−	0.335265i	−0.775517	+	0.631327i	$0.782511\pi$
$948$	9.43945	+	12.9923i	0.306579	+	0.421970i
$949$	3.08687			0.100204
$950$	−13.4639	+	6.73195i	−0.436827	+	0.218413i
$951$	−25.8613			−0.838609
$952$	0.304027	+	0.418458i	0.00985359	+	0.0135623i
$953$	20.7830	+	6.75280i	0.673226	+	0.218745i	0.625627	−	0.780122i	$-0.284843\pi$
$953$	20.7830	+	6.75280i	0.673226	+	0.218745i	0.0475990	+	0.998867i	$0.484843\pi$
$954$	−3.58924	+	11.0465i	−0.116206	+	0.357645i
$955$	28.3179	−	24.0004i	0.916344	−	0.776636i
$956$	1.55754	+	4.79360i	0.0503743	+	0.155036i
$957$			43.5602i			1.40810i
$958$	26.4788	−	8.60350i	0.855493	−	0.277966i
$959$	−4.33824	−	3.15192i	−0.140089	−	0.101781i
$960$	−0.166977	−	2.22982i	−0.00538917	−	0.0719673i
$961$	13.1880	−	9.58162i	0.425418	−	0.309084i
$962$	−9.17790	+	12.6323i	−0.295907	+	0.407282i
$963$	3.43710	−	4.73076i	0.110759	−	0.152447i
$964$	5.53446	−	4.02102i	0.178253	−	0.129508i
$965$	8.36022	+	2.04070i	0.269125	+	0.0656926i
$966$	1.02781	+	0.746746i	0.0330692	+	0.0240262i
$967$	−30.6435	+	9.95669i	−0.985430	+	0.320186i	−0.757029	−	0.653382i	$-0.773350\pi$
$967$	−30.6435	+	9.95669i	−0.985430	+	0.320186i	−0.228401	+	0.973567i	$0.573350\pi$
$968$		−	11.9786i		−	0.385008i
$969$	−1.75972	−	5.41585i	−0.0565303	−	0.173982i
$970$	−13.1247	+	0.982824i	−0.421408	+	0.0315566i
$971$	11.0045	−	33.8684i	0.353152	−	1.08689i	−0.603922	−	0.797044i	$-0.706396\pi$
$971$	11.0045	−	33.8684i	0.353152	−	1.08689i	0.957073	−	0.289845i	$-0.0936039\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	−1.53745	−	2.11611i	−0.0492883	−	0.0678395i
$974$	−1.29951			−0.0416391
$975$	8.56889	−	1.29058i	0.274424	−	0.0413315i
$976$	−5.15131			−0.164889
$977$	−5.79486	−	7.97594i	−0.185394	−	0.255173i	0.706196	−	0.708016i	$-0.250410\pi$
$977$	−5.79486	−	7.97594i	−0.185394	−	0.255173i	−0.891590	+	0.452843i	$0.850410\pi$
$978$	17.4759	+	5.67828i	0.558819	+	0.181571i
$979$	−21.9638	+	67.5976i	−0.701966	+	2.16043i
$980$	13.1726	+	8.14109i	0.420782	+	0.260057i
$981$	−3.03025	−	9.32615i	−0.0967484	−	0.297761i
$982$			19.1650i			0.611580i
$983$	−28.9244	+	9.39810i	−0.922544	+	0.299753i	−0.731510	−	0.681831i	$-0.761184\pi$
$983$	−28.9244	+	9.39810i	−0.922544	+	0.299753i	−0.191034	+	0.981583i	$0.561184\pi$
$984$	6.13287	+	4.45579i	0.195509	+	0.142045i
$985$	−12.6294	+	20.4348i	−0.402406	+	0.651107i
$986$	−13.9056	+	10.1030i	−0.442845	+	0.321745i
$987$	−0.190961	+	0.262836i	−0.00607837	+	0.00836616i
$988$	3.06690	−	4.22123i	0.0975712	−	0.134295i
$989$	10.8608	−	7.89087i	0.345355	−	0.250915i
$990$	−9.91840	+	4.06430i	−0.315227	+	0.129172i
$991$	33.1759	+	24.1037i	1.05387	+	0.765680i	0.972944	−	0.231040i	$-0.0742128\pi$
$991$	33.1759	+	24.1037i	1.05387	+	0.765680i	0.0809242	+	0.996720i	$0.474213\pi$
$992$	−3.64625	+	1.18474i	−0.115769	+	0.0376155i
$993$			14.5094i			0.460442i
$994$	−0.118488	−	0.364667i	−0.00375820	−	0.0115665i
$995$	−1.32460	+	5.42655i	−0.0419927	+	0.172033i
$996$	−4.67828	+	14.3983i	−0.148237	+	0.456226i
$997$	−7.61617	−	2.47464i	−0.241206	−	0.0783727i	0.185919	−	0.982565i	$-0.440474\pi$
$997$	−7.61617	−	2.47464i	−0.241206	−	0.0783727i	−0.427126	+	0.904192i	$0.640474\pi$
$998$	3.76970	+	5.18854i	0.119328	+	0.164240i
$999$	−9.00947			−0.285047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.a.139.1	yes	8
3.2	odd	2		450.2.l.a.289.2		8
5.2	odd	4		750.2.g.e.301.1		8
5.3	odd	4		750.2.g.c.301.2		8
5.4	even	2		750.2.h.c.199.2		8
25.3	odd	20		3750.2.a.o.1.3		4
25.4	even	10		3750.2.c.e.1249.2		8
25.9	even	10	inner	150.2.h.a.109.1	✓	8
25.12	odd	20		750.2.g.e.451.1		8
25.13	odd	20		750.2.g.c.451.2		8
25.16	even	5		750.2.h.c.49.2		8
25.21	even	5		3750.2.c.e.1249.7		8
25.22	odd	20		3750.2.a.m.1.2		4
75.59	odd	10		450.2.l.a.109.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.109.1	✓	8	25.9	even	10	inner
150.2.h.a.139.1	yes	8	1.1	even	1	trivial
450.2.l.a.109.2		8	75.59	odd	10
450.2.l.a.289.2		8	3.2	odd	2
750.2.g.c.301.2		8	5.3	odd	4
750.2.g.c.451.2		8	25.13	odd	20
750.2.g.e.301.1		8	5.2	odd	4
750.2.g.e.451.1		8	25.12	odd	20
750.2.h.c.49.2		8	25.16	even	5
750.2.h.c.199.2		8	5.4	even	2
3750.2.a.m.1.2		4	25.22	odd	20
3750.2.a.o.1.3		4	25.3	odd	20
3750.2.c.e.1249.2		8	25.4	even	10
3750.2.c.e.1249.7		8	25.21	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.530249 - 2.17229i) q^{5} +(-0.309017 - 0.951057i) q^{6} -0.273457i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-2.06909 + 0.847859i) q^{10} +(3.87811 - 2.81761i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(-1.01869 + 1.40211i) q^{13} +(-0.221232 + 0.160734i) q^{14} +(1.17557 - 1.90211i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.79892 + 0.584503i) q^{17} -1.00000i q^{18} +(0.930333 + 2.86327i) q^{19} +(1.90211 + 1.17557i) q^{20} +(0.0845030 - 0.260074i) q^{21} +(-4.55899 - 1.48131i) q^{22} +(-2.73076 - 3.75856i) q^{23} +1.00000 q^{24} +(-4.43767 - 2.30371i) q^{25} +1.73311 q^{26} +(0.587785 + 0.809017i) q^{27} +(0.260074 + 0.0845030i) q^{28} +(-2.80808 + 8.64240i) q^{29} +(-2.22982 + 0.166977i) q^{30} +(1.18474 + 3.64625i) q^{31} +1.00000i q^{32} +(4.55899 - 1.48131i) q^{33} +(1.53025 + 1.11179i) q^{34} +(-0.594028 - 0.145000i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-5.29563 + 7.28881i) q^{37} +(1.76960 - 2.43564i) q^{38} +(-1.40211 + 1.01869i) q^{39} +(-0.166977 - 2.22982i) q^{40} +(6.13287 + 4.45579i) q^{41} +(-0.260074 + 0.0845030i) q^{42} +2.88963i q^{43} +(1.48131 + 4.55899i) q^{44} +(1.70582 - 1.44575i) q^{45} +(-1.43564 + 4.41846i) q^{46} +(-1.12991 - 0.367130i) q^{47} +(-0.587785 - 0.809017i) q^{48} +6.92522 q^{49} +(0.744661 + 4.94424i) q^{50} -1.89149 q^{51} +(-1.01869 - 1.40211i) q^{52} +(-11.0465 - 3.58924i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-4.06430 - 9.91840i) q^{55} +(-0.0845030 - 0.260074i) q^{56} +3.01062i q^{57} +(8.64240 - 2.80808i) q^{58} +(-11.5604 - 8.39915i) q^{59} +(1.44575 + 1.70582i) q^{60} +(4.16750 - 3.02786i) q^{61} +(2.25351 - 3.10169i) q^{62} +(0.160734 - 0.221232i) q^{63} +(0.809017 - 0.587785i) q^{64} +(2.50563 + 2.95637i) q^{65} +(-3.87811 - 2.81761i) q^{66} +(5.98215 - 1.94372i) q^{67} -1.89149i q^{68} +(-1.43564 - 4.41846i) q^{69} +(0.231853 + 0.565808i) q^{70} +(-0.433294 + 1.33354i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-1.04691 - 1.44095i) q^{73} +9.00947 q^{74} +(-3.50859 - 3.56227i) q^{75} -3.01062 q^{76} +(-0.770497 - 1.06050i) q^{77} +(1.64828 + 0.535560i) q^{78} +(4.96261 - 15.2733i) q^{79} +(-1.70582 + 1.44575i) q^{80} +(0.309017 + 0.951057i) q^{81} -7.58064i q^{82} +(14.3983 - 4.67828i) q^{83} +(0.221232 + 0.160734i) q^{84} +(0.315836 + 4.21769i) q^{85} +(2.33776 - 1.69848i) q^{86} +(-5.34129 + 7.35166i) q^{87} +(2.81761 - 3.87811i) q^{88} +(-11.9956 + 8.71529i) q^{89} +(-2.17229 - 0.530249i) q^{90} +(0.383418 + 0.278570i) q^{91} +(4.41846 - 1.43564i) q^{92} +3.83390i q^{93} +(0.367130 + 1.12991i) q^{94} +(6.71316 - 0.502706i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(5.59789 + 1.81886i) q^{97} +(-4.07054 - 5.60262i) q^{98} +4.79360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31}+ \cdots + 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

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