LMFDB - Embedded newform 693.2.l.c.562.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(529,693)] 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("693.529"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(693, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			562.27
Character	$\chi$	$=$	693.562
Dual form			693.2.l.c.529.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.09133 q^{2} +(1.64722 - 0.535401i) q^{3} -0.808990 q^{4} +(0.654559 + 1.13373i) q^{5} +(1.79767 - 0.584302i) q^{6} +(2.63808 - 0.201269i) q^{7} -3.06555 q^{8} +(2.42669 - 1.76385i) q^{9} +(0.714343 + 1.23728i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.33259 + 0.433134i) q^{12} +(0.0119048 - 0.0206197i) q^{13} +(2.87903 - 0.219651i) q^{14} +(1.68521 + 1.51705i) q^{15} -1.72756 q^{16} +(3.78216 + 6.55089i) q^{17} +(2.64833 - 1.92495i) q^{18} +(1.49917 - 2.59664i) q^{19} +(-0.529532 - 0.917176i) q^{20} +(4.23776 - 1.74397i) q^{21} +(0.545667 - 0.945123i) q^{22} +(-0.0456737 - 0.0791091i) q^{23} +(-5.04964 + 1.64130i) q^{24} +(1.64310 - 2.84594i) q^{25} +(0.0129921 - 0.0225030i) q^{26} +(3.05293 - 4.20471i) q^{27} +(-2.13418 + 0.162824i) q^{28} +(-3.22945 - 5.59358i) q^{29} +(1.83912 + 1.65561i) q^{30} -1.87652 q^{31} +4.24575 q^{32} +(0.359940 - 1.69424i) q^{33} +(4.12760 + 7.14921i) q^{34} +(1.95497 + 2.85913i) q^{35} +(-1.96317 + 1.42694i) q^{36} +(-5.14596 + 8.91306i) q^{37} +(1.63609 - 2.83380i) q^{38} +(0.00857003 - 0.0403391i) q^{39} +(-2.00658 - 3.47550i) q^{40} +(-3.54383 + 6.13809i) q^{41} +(4.62481 - 1.90325i) q^{42} +(-1.75851 - 3.04583i) q^{43} +(-0.404495 + 0.700606i) q^{44} +(3.58814 + 1.59667i) q^{45} +(-0.0498452 - 0.0863345i) q^{46} -11.2468 q^{47} +(-2.84567 + 0.924936i) q^{48} +(6.91898 - 1.06193i) q^{49} +(1.79318 - 3.10587i) q^{50} +(9.73742 + 8.76581i) q^{51} +(-0.00963085 + 0.0166811i) q^{52} +(-0.840812 - 1.45633i) q^{53} +(3.33177 - 4.58875i) q^{54} +1.30912 q^{55} +(-8.08717 + 0.616998i) q^{56} +(1.07922 - 5.07990i) q^{57} +(-3.52441 - 6.10446i) q^{58} +2.07003 q^{59} +(-1.36331 - 1.22728i) q^{60} -0.566786 q^{61} -2.04791 q^{62} +(6.04681 - 5.14161i) q^{63} +8.08865 q^{64} +0.0311696 q^{65} +(0.392815 - 1.84898i) q^{66} -7.34478 q^{67} +(-3.05973 - 5.29960i) q^{68} +(-0.117590 - 0.105857i) q^{69} +(2.13352 + 3.12027i) q^{70} +5.12434 q^{71} +(-7.43913 + 5.40717i) q^{72} +(-0.349760 - 0.605802i) q^{73} +(-5.61596 + 9.72713i) q^{74} +(1.18284 - 5.56762i) q^{75} +(-1.21281 + 2.10065i) q^{76} +(1.14474 - 2.38528i) q^{77} +(0.00935277 - 0.0440234i) q^{78} -6.97493 q^{79} +(-1.13079 - 1.95858i) q^{80} +(2.77765 - 8.56064i) q^{81} +(-3.86750 + 6.69871i) q^{82} +(-1.22162 - 2.11590i) q^{83} +(-3.42830 + 1.41085i) q^{84} +(-4.95129 + 8.57589i) q^{85} +(-1.91912 - 3.32402i) q^{86} +(-8.31444 - 7.48482i) q^{87} +(-1.53277 + 2.65484i) q^{88} +(-8.06879 + 13.9755i) q^{89} +(3.91586 + 1.74250i) q^{90} +(0.0272557 - 0.0567926i) q^{91} +(0.0369495 + 0.0639985i) q^{92} +(-3.09104 + 1.00469i) q^{93} -12.2740 q^{94} +3.92518 q^{95} +(6.99370 - 2.27318i) q^{96} +(1.05191 + 1.82196i) q^{97} +(7.55092 - 1.15892i) q^{98} +(-0.314195 - 2.98350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 80 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} - 4 q^{9} + 12 q^{10} + 40 q^{11} + 5 q^{12} + 21 q^{13} + 7 q^{14} - 5 q^{15} + 80 q^{16} - 3 q^{17} - 10 q^{18} + 18 q^{19} - 12 q^{20} - 33 q^{21} + 4 q^{23}+ \cdots - 2 q^{99}+O(q^{100}) $ 80 * q + 80 * q^4 - 4 * q^5 + 6 * q^6 - q^7 - 4 * q^9 + 12 * q^10 + 40 * q^11 + 5 * q^12 + 21 * q^13 + 7 * q^14 - 5 * q^15 + 80 * q^16 - 3 * q^17 - 10 * q^18 + 18 * q^19 - 12 * q^20 - 33 * q^21 + 4 * q^23 - 2 * q^24 - 40 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 14 * q^30 - 64 * q^31 - 70 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 - 23 * q^38 + 42 * q^39 + 51 * q^40 - 2 * q^41 + 25 * q^42 + 9 * q^43 + 40 * q^44 - 14 * q^45 - 6 * q^46 + 52 * q^47 - 28 * q^48 - q^49 + 2 * q^50 - 20 * q^51 + 44 * q^52 + 4 * q^53 - 2 * q^54 - 8 * q^55 + 6 * q^56 + 16 * q^57 - 16 * q^58 + 48 * q^59 - 70 * q^60 - 138 * q^61 + 12 * q^62 + 95 * q^63 + 44 * q^64 + 14 * q^65 + 3 * q^66 - 14 * q^67 - 17 * q^68 + 15 * q^69 - 40 * q^70 + 34 * q^71 - 19 * q^72 + 26 * q^73 - 4 * q^74 + 14 * q^75 + 52 * q^76 - 2 * q^77 - 60 * q^78 + 10 * q^79 - 47 * q^80 - 44 * q^81 + 60 * q^82 + 4 * q^83 - 205 * q^84 + 13 * q^85 + 82 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 44 * q^93 - 112 * q^94 + 40 * q^95 - 78 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.09133			0.771690			0.385845	−	0.922564i	$-0.373910\pi$
$2$	1.09133			0.771690			0.385845	+	0.922564i	$0.373910\pi$
$3$	1.64722	−	0.535401i	0.951025	−	0.309114i
$3$	1.64722	−	0.535401i	0.951025	−	0.309114i
$4$	−0.808990			−0.404495
$5$	0.654559	+	1.13373i	0.292728	+	0.507019i	0.974454	−	0.224588i	$-0.0721037\pi$
$5$	0.654559	+	1.13373i	0.292728	+	0.507019i	−0.681726	+	0.731608i	$0.738770\pi$
$6$	1.79767	−	0.584302i	0.733896	−	0.238540i
$7$	2.63808	−	0.201269i	0.997102	−	0.0760724i
$7$	2.63808	−	0.201269i	0.997102	−	0.0760724i
$8$	−3.06555			−1.08383
$9$	2.42669	−	1.76385i	0.808897	−	0.587951i
$10$	0.714343	+	1.23728i	0.225895	+	0.391262i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.33259	+	0.433134i	−0.384685	+	0.125035i
$13$	0.0119048	−	0.0206197i	0.00330179	−	0.00571888i	−0.864370	−	0.502857i	$-0.832282\pi$
$13$	0.0119048	−	0.0206197i	0.00330179	−	0.00571888i	0.867672	+	0.497138i	$0.165616\pi$
$14$	2.87903	−	0.219651i	0.769454	−	0.0587043i
$15$	1.68521	+	1.51705i	0.435118	+	0.391702i
$16$	−1.72756			−0.431889
$17$	3.78216	+	6.55089i	0.917308	+	1.58882i	0.803486	+	0.595323i	$0.202976\pi$
$17$	3.78216	+	6.55089i	0.917308	+	1.58882i	0.113822	+	0.993501i	$0.463691\pi$
$18$	2.64833	−	1.92495i	0.624217	−	0.453715i
$19$	1.49917	−	2.59664i	0.343933	−	0.595709i	−0.641227	−	0.767352i	$-0.721574\pi$
$19$	1.49917	−	2.59664i	0.343933	−	0.595709i	0.985159	+	0.171643i	$0.0549075\pi$
$20$	−0.529532	−	0.917176i	−0.118407	−	0.205087i
$21$	4.23776	−	1.74397i	0.924754	−	0.380565i
$22$	0.545667	−	0.945123i	0.116337	−	0.201501i
$23$	−0.0456737	−	0.0791091i	−0.00952362	−	0.0164954i	0.861224	−	0.508225i	$-0.169698\pi$
$23$	−0.0456737	−	0.0791091i	−0.00952362	−	0.0164954i	−0.870748	+	0.491730i	$0.836365\pi$
$24$	−5.04964	+	1.64130i	−1.03075	+	0.335029i
$25$	1.64310	−	2.84594i	0.328621	−	0.569188i
$26$	0.0129921	−	0.0225030i	0.00254796	−	0.00441320i
$27$	3.05293	−	4.20471i	0.587537	−	0.809197i
$28$	−2.13418	+	0.162824i	−0.403323	+	0.0307709i
$29$	−3.22945	−	5.59358i	−0.599695	−	1.03870i	−0.992866	−	0.119236i	$-0.961955\pi$
$29$	−3.22945	−	5.59358i	−0.599695	−	1.03870i	0.393171	−	0.919465i	$-0.371378\pi$
$30$	1.83912	+	1.65561i	0.335776	+	0.302272i
$31$	−1.87652			−0.337033			−0.168516	−	0.985699i	$-0.553898\pi$
$31$	−1.87652			−0.337033			−0.168516	+	0.985699i	$0.553898\pi$
$32$	4.24575			0.750550
$33$	0.359940	−	1.69424i	0.0626576	−	0.294929i
$34$	4.12760	+	7.14921i	0.707877	+	1.22608i
$35$	1.95497	+	2.85913i	0.330450	+	0.483282i
$36$	−1.96317	+	1.42694i	−0.327195	+	0.237823i
$37$	−5.14596	+	8.91306i	−0.845990	+	1.46530i	0.0387681	+	0.999248i	$0.487657\pi$
$37$	−5.14596	+	8.91306i	−0.845990	+	1.46530i	−0.884758	+	0.466050i	$0.845677\pi$
$38$	1.63609	−	2.83380i	0.265409	−	0.459703i
$39$	0.00857003	−	0.0403391i	0.00137230	−	0.00645943i
$40$	−2.00658	−	3.47550i	−0.317268	−	0.549525i
$41$	−3.54383	+	6.13809i	−0.553453	+	0.958609i	0.444569	+	0.895745i	$0.353357\pi$
$41$	−3.54383	+	6.13809i	−0.553453	+	0.958609i	−0.998022	+	0.0628644i	$0.979976\pi$
$42$	4.62481	−	1.90325i	0.713623	−	0.293678i
$43$	−1.75851	−	3.04583i	−0.268171	−	0.464485i	0.700219	−	0.713928i	$-0.253086\pi$
$43$	−1.75851	−	3.04583i	−0.268171	−	0.464485i	−0.968389	+	0.249443i	$0.919752\pi$
$44$	−0.404495	+	0.700606i	−0.0609799	+	0.105620i
$45$	3.58814	+	1.59667i	0.534889	+	0.238017i
$46$	−0.0498452	−	0.0863345i	−0.00734928	−	0.0127293i
$47$	−11.2468			−1.64051			−0.820256	−	0.571996i	$-0.806169\pi$
$47$	−11.2468			−1.64051			−0.820256	+	0.571996i	$0.806169\pi$
$48$	−2.84567	+	0.924936i	−0.410737	+	0.133503i
$49$	6.91898	−	1.06193i	0.988426	−	0.151704i
$50$	1.79318	−	3.10587i	0.253593	−	0.439237i
$51$	9.73742	+	8.76581i	1.36351	+	1.22746i
$52$	−0.00963085	+	0.0166811i	−0.00133556	+	0.00231326i
$53$	−0.840812	−	1.45633i	−0.115494	−	0.200042i	0.802483	−	0.596675i	$-0.203512\pi$
$53$	−0.840812	−	1.45633i	−0.115494	−	0.200042i	−0.917977	+	0.396633i	$0.870179\pi$
$54$	3.33177	−	4.58875i	0.453396	−	0.624449i
$55$	1.30912			0.176521
$56$	−8.08717	+	0.616998i	−1.08069	+	0.0824498i
$57$	1.07922	−	5.07990i	0.142947	−	0.672849i
$58$	−3.52441	−	6.10446i	−0.462778	−	0.801555i
$59$	2.07003			0.269495			0.134747	−	0.990880i	$-0.456978\pi$
$59$	2.07003			0.269495			0.134747	+	0.990880i	$0.456978\pi$
$60$	−1.36331	−	1.22728i	−0.176003	−	0.158441i
$61$	−0.566786			−0.0725695			−0.0362848	−	0.999341i	$-0.511552\pi$
$61$	−0.566786			−0.0725695			−0.0362848	+	0.999341i	$0.511552\pi$
$62$	−2.04791			−0.260085
$63$	6.04681	−	5.14161i	0.761826	−	0.647782i
$64$	8.08865			1.01108
$65$	0.0311696			0.00386611
$66$	0.392815	−	1.84898i	0.0483522	−	0.227594i
$67$	−7.34478			−0.897308			−0.448654	−	0.893706i	$-0.648096\pi$
$67$	−7.34478			−0.897308			−0.448654	+	0.893706i	$0.648096\pi$
$68$	−3.05973	−	5.29960i	−0.371046	−	0.642671i
$69$	−0.117590	−	0.105857i	−0.0141562	−	0.0127436i
$70$	2.13352	+	3.12027i	0.255005	+	0.372944i
$71$	5.12434			0.608147			0.304074	−	0.952649i	$-0.401653\pi$
$71$	5.12434			0.608147			0.304074	+	0.952649i	$0.401653\pi$
$72$	−7.43913	+	5.40717i	−0.876710	+	0.637241i
$73$	−0.349760	−	0.605802i	−0.0409363	−	0.0709038i	0.844831	−	0.535033i	$-0.179701\pi$
$73$	−0.349760	−	0.605802i	−0.0409363	−	0.0709038i	−0.885768	+	0.464129i	$0.846367\pi$
$74$	−5.61596	+	9.72713i	−0.652842	+	1.13076i
$75$	1.18284	−	5.56762i	0.136583	−	0.642893i
$76$	−1.21281	+	2.10065i	−0.139119	+	0.240961i
$77$	1.14474	−	2.38528i	0.130455	−	0.271828i
$78$	0.00935277	−	0.0440234i	0.00105899	−	0.00498467i
$79$	−6.97493			−0.784741			−0.392371	−	0.919807i	$-0.628345\pi$
$79$	−6.97493			−0.784741			−0.392371	+	0.919807i	$0.628345\pi$
$80$	−1.13079	−	1.95858i	−0.126426	−	0.218976i
$81$	2.77765	−	8.56064i	0.308628	−	0.951183i
$82$	−3.86750	+	6.69871i	−0.427094	+	0.739749i
$83$	−1.22162	−	2.11590i	−0.134090	−	0.232250i	0.791160	−	0.611610i	$-0.209478\pi$
$83$	−1.22162	−	2.11590i	−0.134090	−	0.232250i	−0.925249	+	0.379359i	$0.876144\pi$
$84$	−3.42830	+	1.41085i	−0.374058	+	0.153937i
$85$	−4.95129	+	8.57589i	−0.537043	+	0.930186i
$86$	−1.91912	−	3.32402i	−0.206944	−	0.358438i
$87$	−8.31444	−	7.48482i	−0.891402	−	0.802457i
$88$	−1.53277	+	2.65484i	−0.163394	+	0.283007i
$89$	−8.06879	+	13.9755i	−0.855290	+	1.48141i	0.0210863	+	0.999778i	$0.493288\pi$
$89$	−8.06879	+	13.9755i	−0.855290	+	1.48141i	−0.876376	+	0.481628i	$0.840046\pi$
$90$	3.91586	+	1.74250i	0.412768	+	0.183675i
$91$	0.0272557	−	0.0567926i	0.00285718	−	0.00595348i
$92$	0.0369495	+	0.0639985i	0.00385226	+	0.00667230i
$93$	−3.09104	+	1.00469i	−0.320526	+	0.104182i
$94$	−12.2740			−1.26597
$95$	3.92518			0.402715
$96$	6.99370	−	2.27318i	0.713792	−	0.232006i
$97$	1.05191	+	1.82196i	0.106805	+	0.184992i	0.914474	−	0.404644i	$-0.132604\pi$
$97$	1.05191	+	1.82196i	0.106805	+	0.184992i	−0.807669	+	0.589636i	$0.799271\pi$
$98$	7.55092	−	1.15892i	0.762758	−	0.117068i
$99$	−0.314195	−	2.98350i	−0.0315778	−	0.299853i
$100$	−1.32925	+	2.30234i	−0.132925	+	0.230234i
$101$	7.72170	−	13.3744i	0.768338	−	1.33080i	−0.170126	−	0.985422i	$-0.554418\pi$
$101$	7.72170	−	13.3744i	0.768338	−	1.33080i	0.938464	−	0.345377i	$-0.112249\pi$
$102$	10.6268	+	9.56642i	1.05221	+	0.947217i
$103$	−9.54265	−	16.5284i	−0.940265	−	1.62859i	−0.764964	−	0.644073i	$-0.777243\pi$
$103$	−9.54265	−	16.5284i	−0.940265	−	1.62859i	−0.175301	−	0.984515i	$-0.556090\pi$
$104$	−0.0364947	+	0.0632107i	−0.00357860	+	0.00619831i
$105$	4.75105	+	3.66294i	0.463655	+	0.357466i
$106$	−0.917607	−	1.58934i	−0.0891259	−	0.154371i
$107$	−2.52063	+	4.36585i	−0.243678	+	0.422063i	−0.961759	−	0.273897i	$-0.911687\pi$
$107$	−2.52063	+	4.36585i	−0.243678	+	0.422063i	0.718081	+	0.695960i	$0.245021\pi$
$108$	−2.46979	+	3.40157i	−0.237656	+	0.327316i
$109$	−8.82576	−	15.2867i	−0.845354	−	1.46420i	−0.885313	−	0.464995i	$-0.846056\pi$
$109$	−8.82576	−	15.2867i	−0.845354	−	1.46420i	0.0399587	−	0.999201i	$-0.487277\pi$
$110$	1.42869			0.136220
$111$	−3.70448	+	17.4370i	−0.351613	+	1.65504i
$112$	−4.55744	+	0.347703i	−0.430638	+	0.0328548i
$113$	−7.38990	+	12.7997i	−0.695183	+	1.20409i	0.274935	+	0.961463i	$0.411344\pi$
$113$	−7.38990	+	12.7997i	−0.695183	+	1.20409i	−0.970119	+	0.242630i	$0.921990\pi$
$114$	1.17779	−	5.54386i	0.110310	−	0.519230i
$115$	0.0597922	−	0.103563i	0.00557566	−	0.00965732i
$116$	2.61260	+	4.52515i	0.242573	+	0.420149i
$117$	−0.00748086	−	0.0710359i	−0.000691606	−	0.00656727i
$118$	2.25909			0.207966
$119$	11.2961	+	16.5206i	1.03552	+	1.51444i
$120$	−5.16608	−	4.65060i	−0.471596	−	0.424540i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.618553			−0.0560012
$123$	−2.55114	+	12.0082i	−0.230028	+	1.08274i
$124$	1.51808			0.136328
$125$	10.8476			0.970241
$126$	6.59909	−	5.61121i	0.587893	−	0.499886i
$127$	−15.3710			−1.36395			−0.681976	−	0.731375i	$-0.738879\pi$
$127$	−15.3710			−1.36395			−0.681976	+	0.731375i	$0.738879\pi$
$128$	0.335912			0.0296907
$129$	−4.52740	−	4.07566i	−0.398616	−	0.358841i
$130$	0.0340164			0.00298344
$131$	3.62164	+	6.27287i	0.316424	+	0.548063i	0.979739	−	0.200277i	$-0.0641843\pi$
$131$	3.62164	+	6.27287i	0.316424	+	0.548063i	−0.663315	+	0.748340i	$0.730851\pi$
$132$	−0.291188	+	1.37062i	−0.0253447	+	0.119297i
$133$	3.43231	−	7.15188i	0.297619	−	0.620147i
$134$	−8.01561			−0.692443
$135$	6.76533	+	0.708968i	0.582267	+	0.0610182i
$136$	−11.5944	−	20.0821i	−0.994210	−	1.72202i
$137$	−5.34439	+	9.25676i	−0.456602	+	0.790858i	−0.998779	−	0.0494065i	$-0.984267\pi$
$137$	−5.34439	+	9.25676i	−0.456602	+	0.790858i	0.542177	+	0.840265i	$0.317600\pi$
$138$	−0.128330	−	0.115525i	−0.0109242	−	0.00983414i
$139$	6.54925	−	11.3436i	0.555500	−	0.962154i	−0.442365	−	0.896835i	$-0.645860\pi$
$139$	6.54925	−	11.3436i	0.555500	−	0.962154i	0.997864	−	0.0653186i	$-0.0208064\pi$
$140$	−1.58155	−	2.31301i	−0.133665	−	0.195485i
$141$	−18.5260	+	6.02155i	−1.56017	+	0.507106i
$142$	5.59237			0.469301
$143$	−0.0119048	−	0.0206197i	−0.000995529	−	0.00172431i
$144$	−4.19224	+	3.04715i	−0.349354	+	0.253929i
$145$	4.22774	−	7.32266i	0.351095	−	0.608114i
$146$	−0.381705	−	0.661133i	−0.0315901	−	0.0547157i
$147$	10.8286	−	5.45366i	0.893124	−	0.449811i
$148$	4.16303	−	7.21057i	0.342199	−	0.592706i
$149$	6.96943	+	12.0714i	0.570958	+	0.988928i	0.996468	+	0.0839744i	$0.0267614\pi$
$149$	6.96943	+	12.0714i	0.570958	+	0.988928i	−0.425510	+	0.904954i	$0.639905\pi$
$150$	1.29087	−	6.07614i	0.105399	−	0.496114i
$151$	−3.05642	+	5.29387i	−0.248728	+	0.430809i	−0.963173	−	0.268882i	$-0.913346\pi$
$151$	−3.05642	+	5.29387i	−0.248728	+	0.430809i	0.714445	+	0.699691i	$0.246679\pi$
$152$	−4.59577	+	7.96011i	−0.372766	+	0.645650i
$153$	20.7329	+	9.22582i	1.67616	+	0.745863i
$154$	1.24929	−	2.60314i	0.100671	−	0.209767i
$155$	−1.22829	−	2.12746i	−0.0986588	−	0.170882i
$156$	−0.00693307	+	0.0326339i	−0.000555090	+	0.00261280i
$157$	5.86280			0.467902			0.233951	−	0.972248i	$-0.424834\pi$
$157$	5.86280			0.467902			0.233951	+	0.972248i	$0.424834\pi$
$158$	−7.61198			−0.605577
$159$	−2.16473	−	1.94873i	−0.171674	−	0.154544i
$160$	2.77910	+	4.81354i	0.219707	+	0.380543i
$161$	−0.136413	−	0.199504i	−0.0107509	−	0.0157231i
$162$	3.03135	−	9.34252i	0.238165	−	0.734018i
$163$	−6.66382	+	11.5421i	−0.521951	+	0.904046i	0.477723	+	0.878511i	$0.341462\pi$
$163$	−6.66382	+	11.5421i	−0.521951	+	0.904046i	−0.999674	+	0.0255351i	$0.991871\pi$
$164$	2.86692	−	4.96565i	0.223869	−	0.387752i
$165$	2.15641	−	0.700904i	0.167876	−	0.0545653i
$166$	−1.33319	−	2.30916i	−0.103476	−	0.179225i
$167$	−3.26388	+	5.65320i	−0.252567	+	0.437458i	−0.964232	−	0.265061i	$-0.914608\pi$
$167$	−3.26388	+	5.65320i	−0.252567	+	0.437458i	0.711665	+	0.702519i	$0.247941\pi$
$168$	−12.9910	+	5.34622i	−1.00228	+	0.412470i
$169$	6.49972	+	11.2578i	0.499978	+	0.865988i
$170$	−5.40351	+	9.35916i	−0.414431	+	0.717815i
$171$	−0.942063	−	8.94554i	−0.0720413	−	0.684083i
$172$	1.42262	+	2.46405i	0.108474	+	0.187882i
$173$	15.3581			1.16766			0.583828	−	0.811877i	$-0.301554\pi$
$173$	15.3581			1.16766			0.583828	+	0.811877i	$0.301554\pi$
$174$	−9.07384	−	8.16844i	−0.687886	−	0.619248i
$175$	3.76185	−	7.83854i	0.284369	−	0.592538i
$176$	−0.863778	+	1.49611i	−0.0651097	+	0.112773i
$177$	3.40980	−	1.10830i	0.256296	−	0.0833047i
$178$	−8.80574	+	15.2520i	−0.660018	+	1.14319i
$179$	2.08828	+	3.61702i	0.156086	+	0.270348i	0.933454	−	0.358698i	$-0.116779\pi$
$179$	2.08828	+	3.61702i	0.156086	+	0.270348i	−0.777368	+	0.629046i	$0.783446\pi$
$180$	−2.90277	−	1.29169i	−0.216360	−	0.0962766i
$181$	1.58810			0.118042			0.0590212	−	0.998257i	$-0.481202\pi$
$181$	1.58810			0.118042			0.0590212	+	0.998257i	$0.481202\pi$
$182$	0.0297451	−	0.0619797i	0.00220486	−	0.00459424i
$183$	−0.933623	+	0.303458i	−0.0690154	+	0.0224323i
$184$	0.140015	+	0.242513i	0.0103220	+	0.0178783i
$185$	−13.4733			−0.990579
$186$	−3.37336	+	1.09645i	−0.247347	+	0.0803958i
$187$	7.56432			0.553158
$188$	9.09854			0.663579
$189$	7.20762	−	11.7068i	0.524277	−	0.851548i
$190$	4.28368			0.310771
$191$	17.8782			1.29362			0.646812	−	0.762649i	$-0.276102\pi$
$191$	17.8782			1.29362			0.646812	+	0.762649i	$0.276102\pi$
$192$	13.3238	−	4.33067i	0.961563	−	0.312539i
$193$	3.06428			0.220572			0.110286	−	0.993900i	$-0.464823\pi$
$193$	3.06428			0.220572			0.110286	+	0.993900i	$0.464823\pi$
$194$	1.14799	+	1.98837i	0.0824206	+	0.142757i
$195$	0.0513432	−	0.0166882i	0.00367677	−	0.00119507i
$196$	−5.59739	+	0.859088i	−0.399813	+	0.0613634i
$197$	−14.5331			−1.03544			−0.517721	−	0.855550i	$-0.673219\pi$
$197$	−14.5331			−1.03544			−0.517721	+	0.855550i	$0.673219\pi$
$198$	−0.342892	−	3.25600i	−0.0243683	−	0.231394i
$199$	−1.55090	−	2.68624i	−0.109941	−	0.190423i	0.805805	−	0.592180i	$-0.201733\pi$
$199$	−1.55090	−	2.68624i	−0.109941	−	0.190423i	−0.915746	+	0.401758i	$0.868399\pi$
$200$	−5.03701	+	8.72436i	−0.356171	+	0.616906i
$201$	−12.0985	+	3.93241i	−0.853362	+	0.277371i
$202$	8.42695	−	14.5959i	0.592918	−	1.02696i
$203$	−9.64539	−	14.1063i	−0.676973	−	0.990072i
$204$	−7.87747	−	7.09145i	−0.551533	−	0.496501i
$205$	−9.27858			−0.648044
$206$	−10.4142	−	18.0380i	−0.725593	−	1.25676i
$207$	−0.250373	−	0.111412i	−0.0174021	−	0.00774365i
$208$	−0.0205662	+	0.0356217i	−0.00142601	+	0.00246992i
$209$	−1.49917	−	2.59664i	−0.103700	−	0.179613i
$210$	5.18498	+	3.99749i	0.357798	+	0.275853i
$211$	8.03903	−	13.9240i	0.553429	−	0.958568i	−0.444594	−	0.895732i	$-0.646652\pi$
$211$	8.03903	−	13.9240i	0.553429	−	0.958568i	0.998024	−	0.0628360i	$-0.0200145\pi$
$212$	0.680208	+	1.17816i	0.0467169	+	0.0809160i
$213$	8.44093	−	2.74358i	0.578363	−	0.187987i
$214$	−2.75085	+	4.76460i	−0.188044	+	0.325702i
$215$	2.30210	−	3.98735i	0.157002	−	0.271935i
$216$	−9.35891	+	12.8897i	−0.636793	+	0.877036i
$217$	−4.95041	+	0.377684i	−0.336056	+	0.0256389i
$218$	−9.63185	−	16.6829i	−0.652351	−	1.12991i
$219$	−0.900480	−	0.810630i	−0.0608488	−	0.0547773i
$220$	−1.05906			−0.0714020
$221$	0.180103			0.0121151
$222$	−4.04282	+	19.0295i	−0.271336	+	1.27718i
$223$	−5.75019	−	9.95962i	−0.385061	−	0.666946i	0.606716	−	0.794918i	$-0.292486\pi$
$223$	−5.75019	−	9.95962i	−0.385061	−	0.666946i	−0.991778	+	0.127973i	$0.959153\pi$
$224$	11.2007	−	0.854536i	0.748375	−	0.0570961i
$225$	−1.03251	−	9.80441i	−0.0688341	−	0.653627i
$226$	−8.06485	+	13.9687i	−0.536466	+	0.929186i
$227$	5.16399	−	8.94429i	0.342746	−	0.593653i	−0.642196	−	0.766541i	$-0.721976\pi$
$227$	5.16399	−	8.94429i	0.342746	−	0.593653i	0.984942	+	0.172887i	$0.0553097\pi$
$228$	−0.873080	+	4.10958i	−0.0578211	+	0.272164i
$229$	1.39189	+	2.41082i	0.0919785	+	0.159311i	0.908344	−	0.418225i	$-0.137348\pi$
$229$	1.39189	+	2.41082i	0.0919785	+	0.159311i	−0.816365	+	0.577536i	$0.804014\pi$
$230$	0.0652533	−	0.113022i	0.00430268	−	0.00745245i
$231$	0.608557	−	4.54199i	0.0400401	−	0.298841i
$232$	9.90004	+	17.1474i	0.649970	+	1.12578i
$233$	−3.16027	+	5.47375i	−0.207036	+	0.358598i	−0.950780	−	0.309868i	$-0.899715\pi$
$233$	−3.16027	+	5.47375i	−0.207036	+	0.358598i	0.743743	+	0.668465i	$0.233049\pi$
$234$	−0.00816412	−	0.0775239i	−0.000533705	−	0.00506790i
$235$	−7.36169	−	12.7508i	−0.480224	−	0.831772i
$236$	−1.67463			−0.109009
$237$	−11.4893	+	3.73439i	−0.746309	+	0.242575i
$238$	12.3279	+	18.0295i	0.799097	+	1.16868i
$239$	−9.75405	+	16.8945i	−0.630937	+	1.09281i	0.356424	+	0.934324i	$0.383996\pi$
$239$	−9.75405	+	16.8945i	−0.630937	+	1.09281i	−0.987361	+	0.158490i	$0.949337\pi$
$240$	−2.91129	−	2.62080i	−0.187923	−	0.169172i
$241$	11.4569	−	19.8439i	0.738004	−	1.27826i	−0.215389	−	0.976528i	$-0.569102\pi$
$241$	11.4569	−	19.8439i	0.738004	−	1.27826i	0.953393	−	0.301732i	$-0.0975647\pi$
$242$	−0.545667	−	0.945123i	−0.0350768	−	0.0607548i
$243$	−0.00796591	−	15.5885i	−0.000511014	−	1.00000i
$244$	0.458524			0.0293540
$245$	5.73282	+	7.14916i	0.366257	+	0.456743i
$246$	−2.78414	+	13.1049i	−0.177510	+	0.835540i
$247$	−0.0356946	−	0.0618248i	−0.00227119	−	0.00393382i
$248$	5.75255			0.365288
$249$	−3.14513	−	2.83131i	−0.199315	−	0.179427i
$250$	11.8384			0.748725
$251$	0.493714			0.0311630			0.0155815	−	0.999879i	$-0.495040\pi$
$251$	0.493714			0.0311630			0.0155815	+	0.999879i	$0.495040\pi$
$252$	−4.89180	+	4.15951i	−0.308155	+	0.262024i
$253$	−0.0913474			−0.00574296
$254$	−16.7749			−1.05255
$255$	−3.56434	+	16.7773i	−0.223208	+	1.05064i
$256$	−15.8107			−0.988169
$257$	−9.34555	−	16.1870i	−0.582959	−	1.00972i	−0.995126	−	0.0986069i	$-0.968561\pi$
$257$	−9.34555	−	16.1870i	−0.582959	−	1.00972i	0.412167	−	0.911108i	$-0.364772\pi$
$258$	−4.94091	−	4.44790i	−0.307608	−	0.276914i
$259$	−11.7816	+	24.5491i	−0.732070	+	1.52541i
$260$	−0.0252159			−0.00156382
$261$	−17.7031	−	7.87761i	−1.09580	−	0.487612i
$262$	3.95242	+	6.84580i	0.244181	+	0.422935i
$263$	7.40815	−	12.8313i	0.456806	−	0.791212i	−0.541984	−	0.840389i	$-0.682327\pi$
$263$	7.40815	−	12.8313i	0.456806	−	0.791212i	0.998790	+	0.0491771i	$0.0156599\pi$
$264$	−1.10341	+	5.19377i	−0.0679104	+	0.319654i
$265$	1.10072	−	1.90651i	0.0676168	−	0.117116i
$266$	3.74580	−	7.80509i	0.229670	−	0.478561i
$267$	−5.80857	+	27.3409i	−0.355478	+	1.67324i
$268$	5.94185			0.362956
$269$	9.38483	+	16.2550i	0.572203	+	0.991085i	0.996339	+	0.0854864i	$0.0272444\pi$
$269$	9.38483	+	16.2550i	0.572203	+	0.991085i	−0.424136	+	0.905598i	$0.639422\pi$
$270$	7.38324	+	0.773721i	0.449330	+	0.0470872i
$271$	3.40017	−	5.88927i	0.206546	−	0.357747i	−0.744078	−	0.668092i	$-0.767111\pi$
$271$	3.40017	−	5.88927i	0.206546	−	0.357747i	0.950624	+	0.310345i	$0.100444\pi$
$272$	−6.53389	−	11.3170i	−0.396175	−	0.686196i
$273$	0.0144895	−	0.108143i	0.000876943	−	0.00654510i
$274$	−5.83252	+	10.1022i	−0.352355	+	0.610297i
$275$	−1.64310	−	2.84594i	−0.0990829	−	0.171617i
$276$	0.0951290	+	0.0856370i	0.00572609	+	0.00515474i
$277$	13.2340	−	22.9220i	0.795155	−	1.37725i	−0.127586	−	0.991828i	$-0.540723\pi$
$277$	13.2340	−	22.9220i	0.795155	−	1.37725i	0.922741	−	0.385421i	$-0.125944\pi$
$278$	7.14742	−	12.3797i	0.428674	−	0.742484i
$279$	−4.55373	+	3.30990i	−0.272625	+	0.198159i
$280$	−5.99304	−	8.76480i	−0.358153	−	0.523797i
$281$	8.48685	+	14.6996i	0.506283	+	0.876907i	0.999974	+	0.00726997i	$0.00231412\pi$
$281$	8.48685	+	14.6996i	0.506283	+	0.876907i	−0.493691	+	0.869638i	$0.664353\pi$
$282$	−20.2180	+	6.57152i	−1.20397	+	0.391328i
$283$	8.59705			0.511042			0.255521	−	0.966804i	$-0.417753\pi$
$283$	8.59705			0.511042			0.255521	+	0.966804i	$0.417753\pi$
$284$	−4.14554			−0.245992
$285$	6.46564	−	2.10155i	0.382992	−	0.124485i
$286$	−0.0129921	−	0.0225030i	−0.000768239	−	0.00133063i
$287$	−8.11352	+	16.9061i	−0.478926	+	0.997934i
$288$	10.3031	−	7.48888i	0.607118	−	0.441286i
$289$	−20.1094	+	34.8306i	−1.18291	+	2.04886i
$290$	4.61387	−	7.99147i	0.270936	−	0.469275i
$291$	2.70821	+	2.43799i	0.158758	+	0.142917i
$292$	0.282952	+	0.490088i	0.0165585	+	0.0286802i
$293$	9.39642	−	16.2751i	0.548945	−	0.950800i	−0.449402	−	0.893329i	$-0.648363\pi$
$293$	9.39642	−	16.2751i	0.548945	−	0.950800i	0.998347	−	0.0574708i	$-0.0183036\pi$
$294$	11.8176	−	5.95177i	0.689215	−	0.347114i
$295$	1.35496	+	2.34685i	0.0788886	+	0.136639i
$296$	15.7752	−	27.3234i	0.916913	−	1.58814i
$297$	−2.11492	−	4.74627i	−0.122720	−	0.275407i
$298$	7.60598	+	13.1739i	0.440602	+	0.763146i
$299$	−0.00217494			−0.000125780
$300$	−0.956905	+	4.50415i	−0.0552469	+	0.260047i
$301$	−5.25213	−	7.68123i	−0.302728	−	0.442739i
$302$	−3.33557	+	5.77738i	−0.191941	+	0.332451i
$303$	5.55870	−	26.1648i	0.319339	−	1.50313i
$304$	−2.58990	+	4.48583i	−0.148541	+	0.257280i
$305$	−0.370995	−	0.642582i	−0.0212431	−	0.0367942i
$306$	22.6266	+	10.0684i	1.29347	+	0.575575i
$307$	28.3664			1.61895			0.809477	−	0.587152i	$-0.199751\pi$
$307$	28.3664			1.61895			0.809477	+	0.587152i	$0.199751\pi$
$308$	−0.926082	+	1.92967i	−0.0527684	+	0.109953i
$309$	−24.5682	−	22.1167i	−1.39764	−	1.25818i
$310$	−1.34048	−	2.32177i	−0.0761340	−	0.131868i
$311$	25.6339			1.45357			0.726784	−	0.686866i	$-0.241014\pi$
$311$	25.6339			1.45357			0.726784	+	0.686866i	$0.241014\pi$
$312$	−0.0262718	+	0.123661i	−0.00148735	+	0.00700095i
$313$	−24.5276			−1.38638			−0.693192	−	0.720753i	$-0.743796\pi$
$313$	−24.5276			−1.38638			−0.693192	+	0.720753i	$0.743796\pi$
$314$	6.39827			0.361075
$315$	9.78719	+	3.48996i	0.551445	+	0.196637i
$316$	5.64265			0.317424
$317$	−2.72543			−0.153075			−0.0765377	−	0.997067i	$-0.524387\pi$
$317$	−2.72543			−0.153075			−0.0765377	+	0.997067i	$0.524387\pi$
$318$	−2.36244	−	2.12671i	−0.132479	−	0.119260i
$319$	−6.45891			−0.361629
$320$	5.29450	+	9.17034i	0.295971	+	0.512638i
$321$	−1.81455	+	8.54108i	−0.101278	+	0.476717i
$322$	−0.148872	−	0.217725i	−0.00829633	−	0.0121334i
$323$	22.6804			1.26197
$324$	−2.24709	+	6.92547i	−0.124839	+	0.384749i
$325$	−0.0391216	−	0.0677607i	−0.00217008	−	0.00375869i
$326$	−7.27246	+	12.5963i	−0.402784	+	0.697643i
$327$	−22.7225	−	20.4552i	−1.25656	−	1.13118i
$328$	10.8638	−	18.8166i	0.599852	−	1.03897i
$329$	−29.6700	+	2.26362i	−1.63576	+	0.124798i
$330$	2.35336	−	0.764920i	0.129548	−	0.0421075i
$331$	7.12711			0.391741			0.195871	−	0.980630i	$-0.437247\pi$
$331$	7.12711			0.391741			0.195871	+	0.980630i	$0.437247\pi$
$332$	0.988275	+	1.71174i	0.0542387	+	0.0939441i
$333$	3.23367	+	30.7059i	0.177204	+	1.68268i
$334$	−3.56198	+	6.16953i	−0.194903	+	0.337582i
$335$	−4.80759	−	8.32700i	−0.262667	−	0.454952i
$336$	−7.32096	+	3.01280i	−0.399391	+	0.164362i
$337$	15.0282	−	26.0295i	0.818636	−	1.41792i	−0.0880507	−	0.996116i	$-0.528064\pi$
$337$	15.0282	−	26.0295i	0.818636	−	1.41792i	0.906687	−	0.421804i	$-0.138603\pi$
$338$	7.09336	+	12.2861i	0.385828	+	0.668274i
$339$	−5.31985	+	25.0405i	−0.288935	+	1.36001i
$340$	4.00554	−	6.93781i	0.217231	−	0.376255i
$341$	−0.938259	+	1.62511i	−0.0508096	+	0.0880048i
$342$	−1.02811	−	9.76257i	−0.0555936	−	0.527900i
$343$	18.0391	−	4.19403i	0.974021	−	0.226456i
$344$	5.39080	+	9.33714i	0.290652	+	0.503425i
$345$	0.0430433	−	0.202605i	0.00231737	−	0.0109079i
$346$	16.7608			0.901068
$347$	26.5103			1.42315			0.711574	−	0.702612i	$-0.247983\pi$
$347$	26.5103			1.42315			0.711574	+	0.702612i	$0.247983\pi$
$348$	6.72630	+	6.05514i	0.360568	+	0.324590i
$349$	11.8606	+	20.5432i	0.634883	+	1.09965i	0.986540	+	0.163521i	$0.0522852\pi$
$349$	11.8606	+	20.5432i	0.634883	+	1.09965i	−0.351656	+	0.936129i	$0.614381\pi$
$350$	4.10544	−	8.55446i	0.219445	−	0.457255i
$351$	−0.0503554	−	0.113007i	−0.00268777	−	0.00603186i
$352$	2.12288	−	3.67693i	0.113150	−	0.195981i
$353$	6.98104	−	12.0915i	0.371563	−	0.643567i	−0.618243	−	0.785987i	$-0.712155\pi$
$353$	6.98104	−	12.0915i	0.371563	−	0.643567i	0.989806	+	0.142420i	$0.0454885\pi$
$354$	3.72123	−	1.20952i	0.197781	−	0.0642854i
$355$	3.35418	+	5.80962i	0.178022	+	0.308342i
$356$	6.52757	−	11.3061i	0.345960	−	0.599221i
$357$	27.4524	+	21.1651i	1.45294	+	1.12018i
$358$	2.27902	+	3.94737i	0.120450	+	0.208625i
$359$	14.6388	−	25.3552i	0.772608	−	1.33820i	−0.163521	−	0.986540i	$-0.552285\pi$
$359$	14.6388	−	25.3552i	0.772608	−	1.33820i	0.936129	−	0.351657i	$-0.114382\pi$
$360$	−10.9996	−	4.89465i	−0.579731	−	0.257971i
$361$	5.00499	+	8.66890i	0.263421	+	0.456258i
$362$	1.73315			0.0910921
$363$	−1.28728	−	1.15884i	−0.0675648	−	0.0608232i
$364$	−0.0220496	+	0.0459446i	−0.00115571	+	0.00240815i
$365$	0.457877	−	0.793067i	0.0239664	−	0.0415110i
$366$	−1.01890	+	0.331174i	−0.0532585	+	0.0173108i
$367$	9.31994	−	16.1426i	0.486497	−	0.842637i	−0.513383	−	0.858160i	$-0.671608\pi$
$367$	9.31994	−	16.1426i	0.486497	−	0.842637i	0.999880	+	0.0155224i	$0.00494114\pi$
$368$	0.0789038	+	0.136665i	0.00411315	+	0.00712418i
$369$	2.22691	+	21.1460i	0.115928	+	1.10082i
$370$	−14.7039			−0.764420
$371$	−2.51125	−	3.67269i	−0.130377	−	0.190677i
$372$	2.50062	−	0.812784i	0.129651	−	0.0421409i
$373$	8.61769	+	14.9263i	0.446207	+	0.772853i	0.998135	−	0.0610383i	$-0.0194412\pi$
$373$	8.61769	+	14.9263i	0.446207	+	0.772853i	−0.551928	+	0.833891i	$0.686108\pi$
$374$	8.25520			0.426866
$375$	17.8685	−	5.80784i	0.922724	−	0.299915i
$376$	34.4775			1.77804
$377$	−0.153784			−0.00792027
$378$	7.86592	−	12.7761i	0.404579	−	0.657131i
$379$	11.0945			0.569888			0.284944	−	0.958544i	$-0.408025\pi$
$379$	11.0945			0.569888			0.284944	+	0.958544i	$0.408025\pi$
$380$	−3.17543			−0.162896
$381$	−25.3194	+	8.22963i	−1.29715	+	0.421617i
$382$	19.5111			0.998277
$383$	0.230944	+	0.400006i	0.0118007	+	0.0204394i	0.871865	−	0.489745i	$-0.162910\pi$
$383$	0.230944	+	0.400006i	0.0118007	+	0.0204394i	−0.860065	+	0.510185i	$0.829577\pi$
$384$	0.553323	−	0.179848i	0.0282366	−	0.00917783i
$385$	3.45357	−	0.263484i	0.176010	−	0.0134284i
$386$	3.34416			0.170213
$387$	−9.63976	−	4.28954i	−0.490016	−	0.218049i
$388$	−0.850985	−	1.47395i	−0.0432022	−	0.0748285i
$389$	−9.72605	+	16.8460i	−0.493130	+	0.854127i	−0.999969	−	0.00791427i	$-0.997481\pi$
$389$	−9.72605	+	16.8460i	−0.493130	+	0.854127i	0.506838	+	0.862041i	$0.330814\pi$
$390$	0.0560326	−	0.0182124i	0.00283732	−	0.000922222i
$391$	0.345490	−	0.598406i	0.0174722	−	0.0302627i
$392$	−21.2105	+	3.25539i	−1.07129	+	0.164422i
$393$	9.32416	+	8.39378i	0.470342	+	0.423410i
$394$	−15.8605			−0.799040
$395$	−4.56551	−	7.90769i	−0.229716	−	0.397879i
$396$	0.254181	+	2.41362i	0.0127731	+	0.121289i
$397$	−11.2575	+	19.4986i	−0.564999	+	0.978607i	0.432051	+	0.901849i	$0.357790\pi$
$397$	−11.2575	+	19.4986i	−0.564999	+	0.978607i	−0.997050	+	0.0767579i	$0.975543\pi$
$398$	−1.69255	−	2.93159i	−0.0848401	−	0.146947i
$399$	1.82466	−	13.6184i	0.0913471	−	0.681773i
$400$	−2.83856	+	4.91652i	−0.141928	+	0.245826i
$401$	−1.40537	−	2.43417i	−0.0701807	−	0.121557i	0.828800	−	0.559545i	$-0.189024\pi$
$401$	−1.40537	−	2.43417i	−0.0701807	−	0.121557i	−0.898980	+	0.437989i	$0.855691\pi$
$402$	−13.2035	+	4.29157i	−0.658531	+	0.214044i
$403$	−0.0223396	+	0.0386932i	−0.00111281	+	0.00192745i
$404$	−6.24677	+	10.8197i	−0.310789	+	0.538302i
$405$	11.5236	−	2.45434i	0.572612	−	0.121957i
$406$	−10.5263	−	15.3947i	−0.522413	−	0.764028i
$407$	5.14596	+	8.91306i	0.255076	+	0.441804i
$408$	−29.8505	−	26.8720i	−1.47782	−	1.33036i
$409$	3.56551			0.176303			0.0881516	−	0.996107i	$-0.471904\pi$
$409$	3.56551			0.176303			0.0881516	+	0.996107i	$0.471904\pi$
$410$	−10.1260			−0.500089
$411$	−3.84732	+	18.1093i	−0.189775	+	0.893268i
$412$	7.71991	+	13.3713i	0.380333	+	0.658755i
$413$	5.46091	−	0.416632i	0.268714	−	0.0205011i
$414$	−0.273240	−	0.121587i	−0.0134290	−	0.00597570i
$415$	1.59924	−	2.76997i	0.0785036	−	0.135972i
$416$	0.0505448	−	0.0875461i	0.00247816	−	0.00429230i
$417$	4.71468	−	22.1920i	0.230879	−	1.08675i
$418$	−1.63609	−	2.83380i	−0.0800239	−	0.138606i
$419$	−0.978608	+	1.69500i	−0.0478082	+	0.0828062i	−0.888939	−	0.458025i	$-0.848557\pi$
$419$	−0.978608	+	1.69500i	−0.0478082	+	0.0828062i	0.841131	+	0.540831i	$0.181890\pi$
$420$	−3.84355	−	2.96328i	−0.187546	−	0.144593i
$421$	−14.0269	−	24.2954i	−0.683631	−	1.18408i	−0.973865	−	0.227128i	$-0.927066\pi$
$421$	−14.0269	−	24.2954i	−0.683631	−	1.18408i	0.290234	−	0.956956i	$-0.406267\pi$
$422$	8.77327	−	15.1957i	0.427076	−	0.739717i
$423$	−27.2925	+	19.8377i	−1.32701	+	0.964540i
$424$	2.57755	+	4.46444i	0.125177	+	0.216813i
$425$	24.8579			1.20579
$426$	9.21188	−	2.99416i	0.446317	−	0.145068i
$427$	−1.49523	+	0.114076i	−0.0723592	+	0.00552054i
$428$	2.03916	−	3.53193i	0.0985665	−	0.170722i
$429$	−0.0306497	−	0.0275914i	−0.00147978	−	0.00133213i
$430$	2.51236	−	4.35154i	0.121157	−	0.209850i
$431$	−18.4567	−	31.9680i	−0.889030	−	1.53985i	−0.841024	−	0.540998i	$-0.818047\pi$
$431$	−18.4567	−	31.9680i	−0.889030	−	1.53985i	−0.0480063	−	0.998847i	$-0.515287\pi$
$432$	−5.27411	+	7.26388i	−0.253751	+	0.349483i
$433$	−41.3779			−1.98849			−0.994247	−	0.107116i	$-0.965838\pi$
$433$	−41.3779			−1.98849			−0.994247	+	0.107116i	$0.965838\pi$
$434$	−5.40256	+	0.412180i	−0.259331	+	0.0197853i
$435$	3.04347	−	14.3256i	0.145923	−	0.686859i
$436$	7.13995	+	12.3668i	0.341942	+	0.592260i
$437$	−0.273890			−0.0131019
$438$	−0.982725	−	0.884668i	−0.0469564	−	0.0422711i
$439$	−4.88023			−0.232920			−0.116460	−	0.993195i	$-0.537155\pi$
$439$	−4.88023			−0.232920			−0.116460	+	0.993195i	$0.537155\pi$
$440$	−4.01316			−0.191320
$441$	14.9171	−	14.7810i	0.710340	−	0.703858i
$442$	0.196553			0.00934906
$443$	6.16860			0.293079			0.146539	−	0.989205i	$-0.453186\pi$
$443$	6.16860			0.293079			0.146539	+	0.989205i	$0.453186\pi$
$444$	2.99688	−	14.1063i	0.142226	−	0.669456i
$445$	−21.1260			−1.00147
$446$	−6.27538	−	10.8693i	−0.297148	−	0.514675i
$447$	17.9433	+	16.1529i	0.848687	+	0.764004i
$448$	21.3385	−	1.62799i	1.00815	−	0.0769153i
$449$	14.9384			0.704988			0.352494	−	0.935814i	$-0.385334\pi$
$449$	14.9384			0.704988			0.352494	+	0.935814i	$0.385334\pi$
$450$	−1.12681	−	10.6999i	−0.0531186	−	0.504398i
$451$	3.54383	+	6.13809i	0.166872	+	0.289032i
$452$	5.97835	−	10.3548i	0.281198	−	0.487049i
$453$	−2.20026	+	10.3566i	−0.103377	+	0.486596i
$454$	5.63564	−	9.76121i	0.264494	−	0.458116i
$455$	0.0822279	−	0.00627345i	0.00385491	−	0.000294104i
$456$	−3.30841	+	15.5727i	−0.154930	+	0.729256i
$457$	−10.3501			−0.484155			−0.242078	−	0.970257i	$-0.577829\pi$
$457$	−10.3501			−0.484155			−0.242078	+	0.970257i	$0.577829\pi$
$458$	1.51901	+	2.63101i	0.0709789	+	0.122939i
$459$	39.0913	+	4.09654i	1.82462	+	0.191210i
$460$	−0.0483713	+	0.0837816i	−0.00225532	+	0.00390634i
$461$	−4.83894	−	8.38129i	−0.225372	−	0.390356i	0.731059	−	0.682314i	$-0.239026\pi$
$461$	−4.83894	−	8.38129i	−0.225372	−	0.390356i	−0.956431	+	0.291959i	$0.905693\pi$
$462$	0.664139	−	4.95683i	0.0308985	−	0.230612i
$463$	−10.6376	+	18.4249i	−0.494373	+	0.856280i	−0.999979	−	0.00648488i	$-0.997936\pi$
$463$	−10.6376	+	18.4249i	−0.494373	+	0.856280i	0.505606	+	0.862765i	$0.331269\pi$
$464$	5.57906	+	9.66322i	0.259002	+	0.448604i
$465$	−3.16232	−	2.84678i	−0.146649	−	0.132016i
$466$	−3.44891	+	5.97369i	−0.159768	+	0.276726i
$467$	−20.1402	+	34.8839i	−0.931979	+	1.61423i	−0.152044	+	0.988374i	$0.548586\pi$
$467$	−20.1402	+	34.8839i	−0.931979	+	1.61423i	−0.779935	+	0.625861i	$0.784748\pi$
$468$	0.00605194	+	0.0574673i	0.000279751	+	0.00265643i
$469$	−19.3762	+	1.47827i	−0.894708	+	0.0682603i
$470$	−8.03406	−	13.9154i	−0.370584	−	0.641870i
$471$	9.65734	−	3.13895i	0.444987	−	0.144635i
$472$	−6.34577			−0.292088
$473$	−3.51702			−0.161713
$474$	−12.5386	+	4.07547i	−0.575919	+	0.187192i
$475$	−4.92658	−	8.53309i	−0.226047	−	0.391525i
$476$	−9.13846	−	13.3650i	−0.418861	−	0.612583i
$477$	−4.60914	−	2.05099i	−0.211038	−	0.0939085i
$478$	−10.6449	+	18.4376i	−0.486888	+	0.843314i
$479$	−0.429201	+	0.743398i	−0.0196107	+	0.0339667i	−0.875664	−	0.482920i	$-0.839576\pi$
$479$	−0.429201	+	0.743398i	−0.0196107	+	0.0339667i	0.856054	+	0.516887i	$0.172909\pi$
$480$	7.15497	+	6.44104i	0.326578	+	0.293992i
$481$	0.122523	+	0.212216i	0.00558657	+	0.00967623i
$482$	12.5033	−	21.6564i	0.569510	−	0.986420i
$483$	−0.331518	−	0.255592i	−0.0150846	−	0.0116298i
$484$	0.404495	+	0.700606i	0.0183861	+	0.0318457i
$485$	−1.37708	+	2.38517i	−0.0625298	+	0.108305i
$486$	−0.00869347	−	17.0122i	−0.000394344	−	0.771690i
$487$	9.70921	+	16.8168i	0.439966	+	0.762044i	0.997686	−	0.0679853i	$-0.0216571\pi$
$487$	9.70921	+	16.8168i	0.439966	+	0.762044i	−0.557720	+	0.830029i	$0.688324\pi$
$488$	1.73751			0.0786533
$489$	−4.79716	+	22.5802i	−0.216935	+	1.02111i
$490$	6.25642	+	7.80212i	0.282636	+	0.352464i
$491$	−9.95373	+	17.2404i	−0.449206	+	0.778047i	−0.998335	−	0.0576906i	$-0.981626\pi$
$491$	−9.95373	+	17.2404i	−0.449206	+	0.778047i	0.549129	+	0.835738i	$0.314960\pi$
$492$	2.06384	−	9.71450i	0.0930452	−	0.437963i
$493$	24.4286	−	42.3116i	1.10021	−	1.90562i
$494$	−0.0389547	−	0.0674715i	−0.00175265	−	0.00303569i
$495$	3.17682	−	2.30909i	0.142788	−	0.103786i
$496$	3.24179			0.145561
$497$	13.5184	−	1.03137i	0.606385	−	0.0462632i
$498$	−3.43239	−	3.08990i	−0.153809	−	0.138462i
$499$	7.99909	+	13.8548i	0.358088	+	0.620227i	0.987641	−	0.156730i	$-0.0500953\pi$
$499$	7.99909	+	13.8548i	0.358088	+	0.620227i	−0.629553	+	0.776958i	$0.716762\pi$
$500$	−8.77562			−0.392458
$501$	−2.34960	+	11.0596i	−0.104973	+	0.494105i
$502$	0.538807			0.0240481
$503$	−18.1995			−0.811474			−0.405737	−	0.913990i	$-0.632985\pi$
$503$	−18.1995			−0.811474			−0.405737	+	0.913990i	$0.632985\pi$
$504$	−18.5368	+	15.7618i	−0.825693	+	0.702088i
$505$	20.2172			0.899655
$506$	−0.0996905			−0.00443178
$507$	16.7339	+	15.0642i	0.743181	+	0.669025i
$508$	12.4349			0.551712
$509$	−4.23638	−	7.33763i	−0.187774	−	0.325235i	0.756734	−	0.653723i	$-0.226794\pi$
$509$	−4.23638	−	7.33763i	−0.187774	−	0.325235i	−0.944508	+	0.328489i	$0.893461\pi$
$510$	−3.88989	+	18.3097i	−0.172247	+	0.810766i
$511$	−1.04463	−	1.52776i	−0.0462115	−	0.0675842i
$512$	−17.9266			−0.792250
$513$	−6.34124	−	14.2309i	−0.279973	−	0.628311i
$514$	−10.1991	−	17.6654i	−0.449864	−	0.779187i
$515$	12.4925	−	21.6376i	0.550484	−	0.953465i
$516$	3.66262	+	3.29716i	0.161238	+	0.145150i
$517$	−5.62339	+	9.74000i	−0.247317	+	0.428365i
$518$	−12.8576	+	26.7913i	−0.564931	+	1.17714i
$519$	25.2982	−	8.22276i	1.11047	−	0.360939i
$520$	−0.0955517			−0.00419022
$521$	2.92490	+	5.06608i	0.128142	+	0.221949i	0.922957	−	0.384903i	$-0.125765\pi$
$521$	2.92490	+	5.06608i	0.128142	+	0.221949i	−0.794815	+	0.606852i	$0.792432\pi$
$522$	−19.3200	−	8.59710i	−0.845615	−	0.376285i
$523$	8.51772	−	14.7531i	0.372454	−	0.645109i	−0.617489	−	0.786580i	$-0.711850\pi$
$523$	8.51772	−	14.7531i	0.372454	−	0.645109i	0.989942	+	0.141471i	$0.0451832\pi$
$524$	−2.92987	−	5.07469i	−0.127992	−	0.221689i
$525$	1.99984	−	14.9259i	0.0872804	−	0.651421i
$526$	8.08477	−	14.0032i	0.352513	−	0.610570i
$527$	−7.09729	−	12.2929i	−0.309163	−	0.535486i
$528$	−0.621817	+	2.92689i	−0.0270611	+	0.127377i
$529$	11.4958	−	19.9114i	0.499819	−	0.865711i
$530$	1.20126	−	2.08064i	0.0521792	−	0.0903771i
$531$	5.02332	−	3.65123i	0.217994	−	0.158450i
$532$	−2.77670	+	5.78580i	−0.120385	+	0.250846i
$533$	0.0843771	+	0.146145i	0.00365478	+	0.00633026i
$534$	−6.33909	+	29.8381i	−0.274319	+	1.29122i
$535$	−6.59960			−0.285325
$536$	22.5158			0.972533
$537$	5.37643	+	4.83996i	0.232010	+	0.208860i
$538$	10.2420	+	17.7396i	0.441563	+	0.764810i
$539$	2.53984	−	6.52298i	0.109398	−	0.280965i
$540$	−5.47308	−	0.573548i	−0.235524	−	0.0246816i
$541$	−18.9128	+	32.7580i	−0.813126	+	1.40838i	0.0975390	+	0.995232i	$0.468903\pi$
$541$	−18.9128	+	32.7580i	−0.813126	+	1.40838i	−0.910665	+	0.413145i	$0.864430\pi$
$542$	3.71072	−	6.42716i	0.159389	−	0.276070i
$543$	2.61595	−	0.850270i	0.112261	−	0.0364886i
$544$	16.0581	+	27.8135i	0.688486	+	1.19249i
$545$	11.5540	−	20.0121i	0.494917	−	0.857222i
$546$	0.0158129	−	0.118020i	0.000676728	−	0.00505079i
$547$	8.58223	+	14.8649i	0.366950	+	0.635575i	0.989087	−	0.147333i	$-0.0470688\pi$
$547$	8.58223	+	14.8649i	0.366950	+	0.635575i	−0.622137	+	0.782908i	$0.713735\pi$
$548$	4.32356	−	7.48862i	0.184693	−	0.319898i
$549$	−1.37541	+	0.999727i	−0.0587013	+	0.0426673i
$550$	−1.79318	−	3.10587i	−0.0764613	−	0.132435i
$551$	−19.3660			−0.825018
$552$	0.360477	+	0.324509i	0.0153429	+	0.0138120i
$553$	−18.4005	+	1.40383i	−0.782467	+	0.0596971i
$554$	14.4427	−	25.0156i	0.613613	−	1.06281i
$555$	−22.1936	+	7.21364i	−0.942066	+	0.306202i
$556$	−5.29827	+	9.17688i	−0.224697	+	0.389186i
$557$	−8.50893	−	14.7379i	−0.360535	−	0.624465i	0.627514	−	0.778605i	$-0.284072\pi$
$557$	−8.50893	−	14.7379i	−0.360535	−	0.624465i	−0.988049	+	0.154141i	$0.950739\pi$
$558$	−4.96964	+	3.61221i	−0.210382	+	0.152917i
$559$	−0.0837389			−0.00354178
$560$	−3.37731	−	4.93931i	−0.142718	−	0.208724i
$561$	12.4601	−	4.04995i	0.526067	−	0.170989i
$562$	9.26198	+	16.0422i	0.390693	+	0.676701i
$563$	−6.98731			−0.294480			−0.147240	−	0.989101i	$-0.547039\pi$
$563$	−6.98731			−0.294480			−0.147240	+	0.989101i	$0.547039\pi$
$564$	14.9873	−	4.87137i	0.631080	−	0.205122i
$565$	−19.3485			−0.813998
$566$	9.38225			0.394366
$567$	5.60470	−	23.1428i	0.235375	−	0.971905i
$568$	−15.7089			−0.659131
$569$	−31.0252			−1.30064			−0.650322	−	0.759658i	$-0.725366\pi$
$569$	−31.0252			−1.30064			−0.650322	+	0.759658i	$0.725366\pi$
$570$	7.05618	−	2.29349i	0.295551	−	0.0960637i
$571$	17.4520			0.730344			0.365172	−	0.930940i	$-0.381010\pi$
$571$	17.4520			0.730344			0.365172	+	0.930940i	$0.381010\pi$
$572$	0.00963085	+	0.0166811i	0.000402686	+	0.000697473i
$573$	29.4495	−	9.57204i	1.23027	−	0.399878i
$574$	−8.85456	+	18.4502i	−0.369582	+	0.770095i
$575$	−0.300187			−0.0125186
$576$	19.6286	−	14.2672i	0.817860	−	0.594466i
$577$	−0.967738	−	1.67617i	−0.0402875	−	0.0697799i	0.845179	−	0.534484i	$-0.179494\pi$
$577$	−0.967738	−	1.67617i	−0.0402875	−	0.0697799i	−0.885466	+	0.464704i	$0.846161\pi$
$578$	−21.9461	+	38.0118i	−0.912838	+	1.58108i
$579$	5.04756	−	1.64062i	0.209769	−	0.0681819i
$580$	−3.42020	+	5.92395i	−0.142016	+	0.245979i
$581$	−3.64859	−	5.33606i	−0.151369	−	0.221377i
$582$	2.95557	+	2.66066i	0.122512	+	0.110288i
$583$	−1.68162			−0.0696458
$584$	1.07221	+	1.85711i	0.0443682	+	0.0768480i
$585$	0.0756389	−	0.0549785i	0.00312728	−	0.00227308i
$586$	10.2546	−	17.7615i	0.423615	−	0.733723i
$587$	14.7437	+	25.5369i	0.608538	+	1.05402i	0.991482	+	0.130248i	$0.0415772\pi$
$587$	14.7437	+	25.5369i	0.608538	+	1.05402i	−0.382943	+	0.923772i	$0.625089\pi$
$588$	−8.76019	+	4.41196i	−0.361264	+	0.181946i
$589$	−2.81322	+	4.87263i	−0.115917	+	0.200773i
$590$	1.47871	+	2.56120i	0.0608776	+	0.105443i
$591$	−23.9393	+	7.78105i	−0.984731	+	0.320070i
$592$	8.88993	−	15.3978i	0.365374	−	0.632846i
$593$	8.56745	−	14.8393i	0.351823	−	0.609375i	−0.634746	−	0.772721i	$-0.718895\pi$
$593$	8.56745	−	14.8393i	0.351823	−	0.609375i	0.986569	+	0.163346i	$0.0522286\pi$
$594$	−2.30809	−	5.17977i	−0.0947019	−	0.212529i
$595$	−11.3359	+	23.6205i	−0.464725	+	0.968345i
$596$	−5.63820	−	9.76564i	−0.230950	−	0.400016i
$597$	−3.99290	−	3.59449i	−0.163419	−	0.147113i
$598$	−0.00237359			−9.70633e−5
$599$	−14.7263			−0.601701			−0.300851	−	0.953671i	$-0.597271\pi$
$599$	−14.7263			−0.601701			−0.300851	+	0.953671i	$0.597271\pi$
$600$	−3.62605	+	17.0678i	−0.148033	+	0.696790i
$601$	13.1998	+	22.8627i	0.538431	+	0.932589i	0.998989	+	0.0449598i	$0.0143160\pi$
$601$	13.1998	+	22.8627i	0.538431	+	0.932589i	−0.460558	+	0.887630i	$0.652351\pi$
$602$	−5.73183	−	8.38279i	−0.233612	−	0.341657i
$603$	−17.8235	+	12.9551i	−0.725829	+	0.527573i
$604$	2.47261	−	4.28269i	0.100609	−	0.174260i
$605$	0.654559	−	1.13373i	0.0266116	−	0.0460927i
$606$	6.06640	−	28.5545i	0.246431	−	1.15995i
$607$	17.1942	+	29.7812i	0.697889	+	1.20878i	0.969197	+	0.246287i	$0.0792106\pi$
$607$	17.1942	+	29.7812i	0.697889	+	1.20878i	−0.271308	+	0.962493i	$0.587456\pi$
$608$	6.36510	−	11.0247i	0.258139	−	0.447109i
$609$	−23.4407	−	18.0722i	−0.949864	−	0.732321i
$610$	−0.404880	−	0.701272i	−0.0163931	−	0.0283937i
$611$	−0.133891	+	0.231905i	−0.00541664	+	0.00938189i
$612$	−16.7727	−	7.46359i	−0.677997	−	0.301698i
$613$	−12.7087	−	22.0122i	−0.513301	−	0.889063i	−0.999881	−	0.0154273i	$-0.995089\pi$
$613$	−12.7087	−	22.0122i	−0.513301	−	0.889063i	0.486580	−	0.873636i	$-0.338244\pi$
$614$	30.9572			1.24933
$615$	−15.2839	+	4.96777i	−0.616306	+	0.200320i
$616$	−3.50925	+	7.31219i	−0.141392	+	0.294617i
$617$	−3.33367	+	5.77409i	−0.134209	+	0.232456i	−0.925295	−	0.379249i	$-0.876183\pi$
$617$	−3.33367	+	5.77409i	−0.134209	+	0.232456i	0.791086	+	0.611705i	$0.209516\pi$
$618$	−26.8121	−	24.1368i	−1.07854	−	0.970923i
$619$	−17.7201	+	30.6920i	−0.712229	+	1.23362i	0.251789	+	0.967782i	$0.418981\pi$
$619$	−17.7201	+	30.6920i	−0.712229	+	1.23362i	−0.964018	+	0.265835i	$0.914352\pi$
$620$	0.993676	+	1.72110i	0.0399070	+	0.0691209i
$621$	−0.472070	−	0.0494702i	−0.0189435	−	0.00198517i
$622$	27.9752			1.12170
$623$	−18.4733	+	38.4927i	−0.740117	+	1.54218i
$624$	−0.0148052	+	0.0696881i	−0.000592683	+	0.00278976i
$625$	−1.11511	−	1.93142i	−0.0446043	−	0.0772570i
$626$	−26.7678			−1.06986
$627$	−3.85971	−	3.47458i	−0.154142	−	0.138761i
$628$	−4.74294			−0.189264
$629$	−77.8513			−3.10413
$630$	10.6811	+	3.80871i	0.425545	+	0.151743i
$631$	28.5499			1.13656			0.568278	−	0.822837i	$-0.307610\pi$
$631$	28.5499			1.13656			0.568278	+	0.822837i	$0.307610\pi$
$632$	21.3820			0.850530
$633$	5.78714	−	27.2401i	0.230018	−	1.08269i
$634$	−2.97436			−0.118127
$635$	−10.0612	−	17.4265i	−0.399267	−	0.691550i
$636$	1.75124	+	1.57650i	0.0694412	+	0.0625123i
$637$	0.0604724	−	0.155309i	0.00239600	−	0.00615358i
$638$	−7.04883			−0.279066
$639$	12.4352	−	9.03857i	0.491928	−	0.357560i
$640$	0.219874	+	0.380834i	0.00869130	+	0.0150538i
$641$	−21.9645	+	38.0436i	−0.867546	+	1.50263i	−0.00304868	+	0.999995i	$0.500970\pi$
$641$	−21.9645	+	38.0436i	−0.867546	+	1.50263i	−0.864497	+	0.502638i	$0.832363\pi$
$642$	−1.98028	+	9.32117i	−0.0781555	+	0.367877i
$643$	−8.57325	+	14.8493i	−0.338096	+	0.585599i	−0.984075	−	0.177756i	$-0.943116\pi$
$643$	−8.57325	+	14.8493i	−0.338096	+	0.585599i	0.645979	+	0.763356i	$0.276450\pi$
$644$	0.110357	+	0.161397i	0.00434867	+	0.00635992i
$645$	1.65724	−	7.80061i	0.0652537	−	0.307149i
$646$	24.7519			0.973849
$647$	−15.9422	−	27.6128i	−0.626754	−	1.08557i	−0.988199	−	0.153176i	$-0.951050\pi$
$647$	−15.9422	−	27.6128i	−0.626754	−	1.08557i	0.361445	−	0.932393i	$-0.382284\pi$
$648$	−8.51503	+	26.2431i	−0.334502	+	1.03092i
$649$	1.03501	−	1.79270i	0.0406279	−	0.0703696i
$650$	−0.0426948	−	0.0739495i	−0.00167463	−	0.00290054i
$651$	−7.95223	+	3.27259i	−0.311672	+	0.128263i
$652$	5.39097	−	9.33743i	0.211126	−	0.365682i
$653$	13.9047	+	24.0836i	0.544132	+	0.942465i	0.998661	+	0.0517328i	$0.0164744\pi$
$653$	13.9047	+	24.0836i	0.544132	+	0.942465i	−0.454529	+	0.890732i	$0.650192\pi$
$654$	−24.7978	−	22.3235i	−0.969672	−	0.872917i
$655$	−4.74116	+	8.21193i	−0.185252	+	0.320867i
$656$	6.12216	−	10.6039i	0.239030	−	0.414013i
$657$	−1.91730	−	0.853169i	−0.0748012	−	0.0332853i
$658$	−32.3799	+	2.47037i	−1.26230	+	0.0963051i
$659$	−5.20201	−	9.01015i	−0.202642	−	0.350986i	0.746737	−	0.665119i	$-0.231619\pi$
$659$	−5.20201	−	9.01015i	−0.202642	−	0.350986i	−0.949379	+	0.314134i	$0.898286\pi$
$660$	−1.74451	+	0.567024i	−0.0679051	+	0.0220714i
$661$	−19.0851			−0.742325			−0.371162	−	0.928568i	$-0.621041\pi$
$661$	−19.0851			−0.742325			−0.371162	+	0.928568i	$0.621041\pi$
$662$	7.77806			0.302303
$663$	0.296670	−	0.0964275i	0.0115217	−	0.00374493i
$664$	3.74492	+	6.48640i	0.145331	+	0.251721i
$665$	10.3549	−	0.790015i	0.401548	−	0.0306355i
$666$	3.52902	+	33.5104i	0.136747	+	1.29850i
$667$	−0.295002	+	0.510959i	−0.0114225	+	0.0197844i
$668$	2.64044	−	4.57338i	0.102162	−	0.176950i
$669$	−14.8042	−	13.3271i	−0.572365	−	0.515254i
$670$	−5.24669	−	9.08754i	−0.202697	−	0.351082i
$671$	−0.283393	+	0.490851i	−0.0109403	+	0.0189491i
$672$	17.9925	−	7.40446i	0.694074	−	0.285633i
$673$	8.81714	+	15.2717i	0.339876	+	0.588682i	0.984409	−	0.175894i	$-0.0562816\pi$
$673$	8.81714	+	15.2717i	0.339876	+	0.588682i	−0.644533	+	0.764576i	$0.722948\pi$
$674$	16.4008	−	28.4069i	0.631733	−	1.09419i
$675$	−6.95007	−	15.5972i	−0.267508	−	0.600338i
$676$	−5.25820	−	9.10748i	−0.202239	−	0.350288i
$677$	−48.3219			−1.85716			−0.928580	−	0.371132i	$-0.878970\pi$
$677$	−48.3219			−1.85716			−0.928580	+	0.371132i	$0.878970\pi$
$678$	−5.80573	+	27.3276i	−0.222968	+	1.04951i
$679$	3.14173	+	4.59478i	0.120569	+	0.176331i
$680$	15.1784	−	26.2898i	0.582066	−	1.00817i
$681$	3.71746	−	17.4981i	0.142453	−	0.670527i
$682$	−1.02395	+	1.77354i	−0.0392092	+	0.0679124i
$683$	11.7227	+	20.3042i	0.448555	+	0.776920i	0.998292	−	0.0584178i	$-0.0186056\pi$
$683$	11.7227	+	20.3042i	0.448555	+	0.776920i	−0.549737	+	0.835338i	$0.685272\pi$
$684$	0.762119	+	7.23685i	0.0291404	+	0.276708i
$685$	−13.9929			−0.534640
$686$	19.6867	−	4.57709i	0.751642	−	0.174754i
$687$	3.58351	+	3.22594i	0.136719	+	0.123077i
$688$	3.03793	+	5.26184i	0.115820	+	0.200606i
$689$	−0.0400388			−0.00152536
$690$	0.0469746	−	0.221109i	0.00178829	−	0.00841749i
$691$	25.1913			0.958320			0.479160	−	0.877727i	$-0.340941\pi$
$691$	25.1913			0.958320			0.479160	+	0.877727i	$0.340941\pi$
$692$	−12.4246			−0.472311
$693$	−1.42936	−	7.80749i	−0.0542968	−	0.296582i
$694$	28.9316			1.09823
$695$	17.1475			0.650441
$696$	25.4883	+	22.9451i	0.966132	+	0.869730i
$697$	−53.6133			−2.03075
$698$	12.9439	+	22.4195i	0.489933	+	0.848589i
$699$	−2.27502	+	10.7085i	−0.0860492	+	0.405033i
$700$	−3.04330	+	6.34130i	−0.115026	+	0.239678i
$701$	−18.6401			−0.704028			−0.352014	−	0.935995i	$-0.614503\pi$
$701$	−18.6401			−0.704028			−0.352014	+	0.935995i	$0.614503\pi$
$702$	−0.0549546	−	0.123328i	−0.00207413	−	0.00465472i
$703$	15.4293	+	26.7244i	0.581927	+	1.00793i
$704$	4.04432	−	7.00497i	0.152426	−	0.264010i
$705$	−18.9532	−	17.0620i	−0.713817	−	0.642592i
$706$	7.61865	−	13.1959i	0.286732	−	0.496634i
$707$	17.6786	−	36.8369i	0.664874	−	1.38539i
$708$	−2.75849	+	0.896601i	−0.103671	+	0.0336963i
$709$	13.8807			0.521300			0.260650	−	0.965433i	$-0.416063\pi$
$709$	13.8807			0.521300			0.260650	+	0.965433i	$0.416063\pi$
$710$	3.66053	+	6.34023i	0.137377	+	0.237945i
$711$	−16.9260	+	12.3027i	−0.634775	+	0.461389i
$712$	24.7352	−	42.8427i	0.926992	−	1.60560i
$713$	0.0857075	+	0.148450i	0.00320977	+	0.00555949i
$714$	29.9598	+	23.0982i	1.12122	+	0.864429i
$715$	0.0155848	−	0.0269936i	0.000582838	−	0.00100950i
$716$	−1.68940	−	2.92613i	−0.0631359	−	0.109355i
$717$	−7.02175	+	33.0514i	−0.262232	+	1.23433i
$718$	15.9759	−	27.6710i	0.596214	−	1.03267i
$719$	13.3033	−	23.0420i	0.496129	−	0.859320i	−0.503861	−	0.863785i	$-0.668088\pi$
$719$	13.3033	−	23.0420i	0.496129	−	0.859320i	0.999990	+	0.00446437i	$0.00142106\pi$
$720$	−6.19872	−	2.75833i	−0.231013	−	0.102797i
$721$	−28.5010	−	41.6826i	−1.06143	−	1.55234i
$722$	5.46212	+	9.46066i	0.203279	+	0.352089i
$723$	8.24760	−	38.8214i	0.306732	−	1.44378i
$724$	−1.28476			−0.0477475
$725$	−21.2253			−0.788289
$726$	−1.40486	−	1.26468i	−0.0521391	−	0.0469366i
$727$	26.8251	+	46.4624i	0.994887	+	1.72319i	0.584910	+	0.811098i	$0.301130\pi$
$727$	26.8251	+	46.4624i	0.994887	+	1.72319i	0.409977	+	0.912096i	$0.365537\pi$
$728$	−0.0835538	+	0.174100i	−0.00309671	+	0.00645259i
$729$	−8.35920	−	25.6734i	−0.309600	−	0.950867i
$730$	0.499697	−	0.865501i	0.0184946	−	0.0320336i
$731$	13.3019	−	23.0396i	0.491990	−	0.852152i
$732$	0.755292	−	0.245495i	0.0279164	−	0.00907374i
$733$	−13.7991	−	23.9007i	−0.509680	−	0.882792i	−0.999937	−	0.0112140i	$-0.996430\pi$
$733$	−13.7991	−	23.9007i	−0.509680	−	0.882792i	0.490257	−	0.871578i	$-0.336903\pi$
$734$	10.1712	−	17.6170i	0.375425	−	0.650255i
$735$	13.2709	+	8.70691i	0.489505	+	0.321159i
$736$	−0.193919	−	0.335878i	−0.00714795	−	0.0123806i
$737$	−3.67239	+	6.36077i	−0.135274	+	0.234302i
$738$	2.43030	+	23.0774i	0.0894606	+	0.849491i
$739$	10.8358	+	18.7682i	0.398602	+	0.690400i	0.993554	−	0.113362i	$-0.0361620\pi$
$739$	10.8358	+	18.7682i	0.398602	+	0.690400i	−0.594951	+	0.803762i	$0.702829\pi$
$740$	10.8998			0.400684
$741$	−0.0918980	−	0.0827283i	−0.00337596	−	0.00303910i
$742$	−2.74061	−	4.00813i	−0.100611	−	0.147143i
$743$	−5.66321	+	9.80897i	−0.207763	+	0.359856i	−0.951010	−	0.309161i	$-0.899952\pi$
$743$	−5.66321	+	9.80897i	−0.207763	+	0.359856i	0.743246	+	0.669018i	$0.233285\pi$
$744$	9.47574	−	3.07993i	0.347398	−	0.112916i
$745$	−9.12381	+	15.8029i	−0.334270	+	0.578973i
$746$	9.40478	+	16.2896i	0.344333	+	0.596403i
$747$	−6.69662	−	2.97989i	−0.245017	−	0.109028i
$748$	−6.11945			−0.223749
$749$	−5.77092	+	12.0248i	−0.210865	+	0.439377i
$750$	19.5005	−	6.33829i	0.712056	−	0.231442i
$751$	−11.7651	−	20.3778i	−0.429315	−	0.743595i	0.567498	−	0.823375i	$-0.307912\pi$
$751$	−11.7651	−	20.3778i	−0.429315	−	0.743595i	−0.996813	+	0.0797798i	$0.974578\pi$
$752$	19.4295			0.708519
$753$	0.813257	−	0.264335i	0.0296367	−	0.00963291i
$754$	−0.167830			−0.00611200
$755$	−8.00243			−0.291238
$756$	−5.83089	+	9.47072i	−0.212067	+	0.344447i
$757$	−34.9128			−1.26893			−0.634463	−	0.772953i	$-0.718779\pi$
$757$	−34.9128			−1.26893			−0.634463	+	0.772953i	$0.718779\pi$
$758$	12.1078			0.439777
$759$	−0.150470	+	0.0489075i	−0.00546170	+	0.00177523i
$760$	−12.0328			−0.436476
$761$	2.34149	+	4.05558i	0.0848790	+	0.147015i	0.905340	−	0.424688i	$-0.139616\pi$
$761$	2.34149	+	4.05558i	0.0848790	+	0.147015i	−0.820461	+	0.571703i	$0.806283\pi$
$762$	−27.6319	+	8.98128i	−1.00100	+	0.325357i
$763$	−26.3598	−	38.5512i	−0.954290	−	1.39565i
$764$	−14.4633			−0.523264
$765$	3.11135	+	29.5444i	0.112491	+	1.06818i
$766$	0.252037	+	0.436541i	0.00910646	+	0.0157729i
$767$	0.0246433	−	0.0426834i	0.000889817	−	0.00154121i
$768$	−26.0438	+	8.46507i	−0.939773	+	0.305457i
$769$	24.1826	−	41.8855i	0.872047	−	1.51043i	0.0121710	−	0.999926i	$-0.496126\pi$
$769$	24.1826	−	41.8855i	0.872047	−	1.51043i	0.859876	−	0.510503i	$-0.170541\pi$
$770$	3.76899	−	0.287549i	0.135825	−	0.0103626i
$771$	−24.0607	−	21.6599i	−0.866526	−	0.780063i
$772$	−2.47897			−0.0892202
$773$	−2.72867	−	4.72620i	−0.0981435	−	0.169990i	0.812773	−	0.582581i	$-0.197957\pi$
$773$	−2.72867	−	4.72620i	−0.0981435	−	0.169990i	−0.910916	+	0.412591i	$0.864624\pi$
$774$	−10.5202	−	4.68132i	−0.378141	−	0.168266i
$775$	−3.08332	+	5.34046i	−0.110756	+	0.191835i
$776$	−3.22468	−	5.58531i	−0.115759	−	0.200501i
$777$	−6.26321	+	46.7458i	−0.224692	+	1.67699i
$778$	−10.6144	+	18.3846i	−0.380544	+	0.659121i
$779$	10.6256	+	18.4041i	0.380701	+	0.659394i
$780$	−0.0415361	+	0.0135006i	−0.00148723	+	0.000483399i
$781$	2.56217	−	4.43781i	0.0916816	−	0.158797i
$782$	0.377045	−	0.653061i	0.0134831	−	0.0233534i
$783$	−33.3787	−	3.49790i	−1.19286	−	0.125005i
$784$	−11.9529	+	1.83454i	−0.426890	+	0.0655192i
$785$	3.83755	+	6.64683i	0.136968	+	0.237235i
$786$	10.1758	+	9.16042i	0.362958	+	0.326741i
$787$	5.29891			0.188886			0.0944429	−	0.995530i	$-0.469893\pi$
$787$	5.29891			0.188886			0.0944429	+	0.995530i	$0.469893\pi$
$788$	11.7571			0.418831
$789$	5.33299	−	25.1024i	0.189859	−	0.893668i
$790$	−4.98249	−	8.62993i	−0.177269	−	0.307039i
$791$	−16.9190	+	35.2540i	−0.601571	+	1.25349i
$792$	0.963180	+	9.14606i	0.0342251	+	0.324991i
$793$	−0.00674747	+	0.0116870i	−0.000239610	+	0.000415016i
$794$	−12.2857	+	21.2795i	−0.436004	+	0.755181i
$795$	0.792389	−	3.72977i	0.0281031	−	0.132281i
$796$	1.25467	+	2.17314i	0.0444704	+	0.0770251i
$797$	2.49948	−	4.32923i	0.0885362	−	0.153349i	−0.818356	−	0.574711i	$-0.805114\pi$
$797$	2.49948	−	4.32923i	0.0885362	−	0.153349i	0.906893	+	0.421362i	$0.138448\pi$
$798$	1.99131	−	14.8622i	0.0704916	−	0.526117i
$799$	−42.5371	−	73.6765i	−1.50486	−	2.60649i
$800$	6.97621	−	12.0832i	0.246646	−	0.427204i
$801$	5.07035	+	48.1465i	0.179152	+	1.70117i
$802$	−1.53373	−	2.65649i	−0.0541577	−	0.0938039i
$803$	−0.699520			−0.0246855
$804$	9.78756	−	3.18128i	0.345181	−	0.112195i
$805$	0.136893	−	0.285243i	0.00482484	−	0.0100535i
$806$	−0.0243799	+	0.0422273i	−0.000858746	+	0.00148739i
$807$	24.1619	+	21.7510i	0.850538	+	0.765670i
$808$	−23.6712	+	40.9998i	−0.832751	+	1.44237i
$809$	−2.55209	−	4.42036i	−0.0897269	−	0.155411i	0.817669	−	0.575689i	$-0.195266\pi$
$809$	−2.55209	−	4.42036i	−0.0897269	−	0.155411i	−0.907396	+	0.420277i	$0.861933\pi$
$810$	12.5761	−	2.67851i	0.441879	−	0.0941131i
$811$	26.8877			0.944154			0.472077	−	0.881557i	$-0.343504\pi$
$811$	26.8877			0.944154			0.472077	+	0.881557i	$0.343504\pi$
$812$	7.80302	+	11.4119i	0.273832	+	0.400479i
$813$	2.44772	−	11.5214i	0.0858452	−	0.404073i
$814$	5.61596	+	9.72713i	0.196839	+	0.340936i
$815$	−17.4475			−0.611158
$816$	−16.8219	−	15.1434i	−0.588885	−	0.530126i
$817$	−10.5452			−0.368930
$818$	3.89116			0.136051
$819$	−0.0340324	−	0.185893i	−0.00118919	−	0.00649563i
$820$	7.50628			0.262131
$821$	6.07949			0.212176			0.106088	−	0.994357i	$-0.466168\pi$
$821$	6.07949			0.212176			0.106088	+	0.994357i	$0.466168\pi$
$822$	−4.19872	+	19.7633i	−0.146447	+	0.689326i
$823$	−16.7076			−0.582389			−0.291195	−	0.956664i	$-0.594053\pi$
$823$	−16.7076			−0.582389			−0.291195	+	0.956664i	$0.594053\pi$
$824$	29.2534	+	50.6684i	1.01909	+	1.76512i
$825$	−4.23028	−	3.80818i	−0.147279	−	0.132584i
$826$	5.95968	−	0.454685i	0.207364	−	0.0158205i
$827$	−6.98944			−0.243047			−0.121523	−	0.992589i	$-0.538778\pi$
$827$	−6.98944			−0.243047			−0.121523	+	0.992589i	$0.538778\pi$
$828$	0.202549	+	0.0901310i	0.00703906	+	0.00313227i
$829$	25.0777	+	43.4358i	0.870984	+	1.50859i	0.860981	+	0.508638i	$0.169851\pi$
$829$	25.0777	+	43.4358i	0.870984	+	1.50859i	0.0100031	+	0.999950i	$0.496816\pi$
$830$	1.74531	−	3.02296i	0.0605805	−	0.104928i
$831$	9.52692	−	44.8432i	0.330485	−	1.55559i
$832$	0.0962936	−	0.166785i	0.00333838	−	0.00578225i
$833$	33.1253	+	41.3091i	1.14772	+	1.43128i
$834$	5.14529	−	24.2188i	0.178167	−	0.838630i
$835$	−8.54561			−0.295733
$836$	1.21281	+	2.10065i	0.0419460	+	0.0726525i
$837$	−5.72888	+	7.89022i	−0.198019	+	0.272726i
$838$	−1.06799	+	1.84981i	−0.0368931	+	0.0639007i
$839$	−2.71859	−	4.70874i	−0.0938563	−	0.162564i	0.815274	−	0.579075i	$-0.196586\pi$
$839$	−2.71859	−	4.70874i	−0.0938563	−	0.162564i	−0.909131	+	0.416511i	$0.863253\pi$
$840$	−14.5646	−	11.2289i	−0.502525	−	0.387434i
$841$	−6.35875	+	11.0137i	−0.219267	+	0.379782i
$842$	−15.3081	−	26.5144i	−0.527551	−	0.913745i
$843$	21.8499	+	19.6697i	0.752552	+	0.677462i
$844$	−6.50349	+	11.2644i	−0.223859	+	0.387736i
$845$	−8.50890	+	14.7378i	−0.292715	+	0.506997i
$846$	−29.7852	+	21.6495i	−1.02404	+	0.744326i
$847$	−1.49335	−	2.18401i	−0.0513120	−	0.0750436i
$848$	1.45255	+	2.51589i	0.0498808	+	0.0863960i
$849$	14.1613	−	4.60287i	0.486013	−	0.157970i
$850$	27.1283			0.930493
$851$	0.940139			0.0322276
$852$	−6.82863	+	2.21953i	−0.233945	+	0.0760397i
$853$	−23.4512	−	40.6187i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869926\pi$
$853$	−23.4512	−	40.6187i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$854$	−1.63180	+	0.124495i	−0.0558389	+	0.00426014i
$855$	9.52519	−	6.92343i	0.325755	−	0.236776i
$856$	7.72710	−	13.3837i	0.264107	−	0.457446i
$857$	−9.93127	+	17.2015i	−0.339246	+	0.587591i	−0.984291	−	0.176553i	$-0.943505\pi$
$857$	−9.93127	+	17.2015i	−0.339246	+	0.587591i	0.645045	+	0.764144i	$0.276838\pi$
$858$	−0.0334490	−	0.0301115i	−0.00114193	−	0.00102799i
$859$	−11.3576	−	19.6719i	−0.387515	−	0.671197i	0.604599	−	0.796530i	$-0.293333\pi$
$859$	−11.3576	−	19.6719i	−0.387515	−	0.671197i	−0.992115	+	0.125333i	$0.960000\pi$
$860$	−1.86238	+	3.22573i	−0.0635065	+	0.109996i
$861$	−4.31324	+	32.1921i	−0.146995	+	1.09710i
$862$	−20.1425	−	34.8878i	−0.686055	−	1.18828i
$863$	14.3526	−	24.8594i	0.488568	−	0.846225i	−0.511346	−	0.859375i	$-0.670853\pi$
$863$	14.3526	−	24.8594i	0.488568	−	0.846225i	0.999914	+	0.0131506i	$0.00418610\pi$
$864$	12.9620	−	17.8522i	0.440976	−	0.607343i
$865$	10.0528	+	17.4120i	0.341805	+	0.592024i
$866$	−45.1571			−1.53450
$867$	−14.4764	+	68.1404i	−0.491644	+	2.31417i
$868$	4.00483	−	0.305543i	0.135933	−	0.0103708i
$869$	−3.48747	+	6.04047i	−0.118304	+	0.204909i
$870$	3.32144	−	15.6340i	0.112607	−	0.530042i
$871$	−0.0874381	+	0.151447i	−0.00296273	+	0.00513159i
$872$	27.0558	+	46.8620i	0.916224	+	1.58695i
$873$	5.76634	+	2.56593i	0.195161	+	0.0868434i
$874$	−0.298906			−0.0101106
$875$	28.6170	−	2.18329i	0.967430	−	0.0738086i
$876$	0.728479	+	0.655791i	0.0246130	+	0.0221571i
$877$	−13.3514	−	23.1253i	−0.450845	−	0.780887i	0.547594	−	0.836744i	$-0.315544\pi$
$877$	−13.3514	−	23.1253i	−0.450845	−	0.780887i	−0.998439	+	0.0558578i	$0.982211\pi$
$878$	−5.32596			−0.179742
$879$	6.76430	−	31.8395i	0.228154	−	1.07392i
$880$	−2.26158			−0.0762377
$881$	−47.6686			−1.60600			−0.802999	−	0.595981i	$-0.796763\pi$
$881$	−47.6686			−1.60600			−0.802999	+	0.595981i	$0.796763\pi$
$882$	16.2796	−	16.1310i	0.548162	−	0.543160i
$883$	11.2441			0.378395			0.189198	−	0.981939i	$-0.439411\pi$
$883$	11.2441			0.378395			0.189198	+	0.981939i	$0.439411\pi$
$884$	−0.145702			−0.00490048
$885$	3.48843	+	3.14035i	0.117262	+	0.105562i
$886$	6.73200			0.226166
$887$	−8.53473	−	14.7826i	−0.286568	−	0.496350i	0.686420	−	0.727205i	$-0.259181\pi$
$887$	−8.53473	−	14.7826i	−0.286568	−	0.496350i	−0.972988	+	0.230855i	$0.925848\pi$
$888$	11.3562	−	53.4538i	0.381091	−	1.79379i
$889$	−40.5499	+	3.09369i	−1.36000	+	0.103759i
$890$	−23.0555			−0.772823
$891$	−6.02491	−	6.68584i	−0.201842	−	0.223984i
$892$	4.65185	+	8.05723i	0.155755	+	0.269776i
$893$	−16.8608	+	29.2038i	−0.564226	+	0.977268i
$894$	19.5821	+	17.6282i	0.654923	+	0.589574i
$895$	−2.73381	+	4.73510i	−0.0913813	+	0.158277i
$896$	0.886165	−	0.0676086i	0.0296047	−	0.00225864i
$897$	−0.00358262	+	0.00116447i	−0.000119620	+	3.88804e-5i
$898$	16.3028			0.544032
$899$	6.06013	+	10.4965i	0.202117	+	0.350076i
$900$	0.835291	+	7.93167i	0.0278430	+	0.264389i
$901$	6.36017	−	11.0161i	0.211888	−	0.367001i
$902$	3.86750	+	6.69871i	0.128774	+	0.223043i
$903$	−12.7640	−	9.84070i	−0.424759	−	0.327478i
$904$	22.6541	−	39.2380i	0.753464	−	1.30504i
$905$	1.03950	+	1.80047i	0.0345543	+	0.0598498i
$906$	−2.40122	+	11.3025i	−0.0797750	+	0.375501i
$907$	8.52480	−	14.7654i	0.283061	−	0.490277i	−0.689076	−	0.724689i	$-0.741983\pi$
$907$	8.52480	−	14.7654i	0.283061	−	0.490277i	0.972137	+	0.234413i	$0.0753167\pi$
$908$	−4.17761	+	7.23584i	−0.138639	+	0.240130i
$909$	−4.85224	−	46.0754i	−0.160939	−	1.52822i
$910$	0.0897382	−	0.00684643i	0.00297479	−	0.000226957i
$911$	−4.97367	−	8.61466i	−0.164785	−	0.285416i	0.771794	−	0.635873i	$-0.219360\pi$
$911$	−4.97367	−	8.61466i	−0.164785	−	0.285416i	−0.936579	+	0.350457i	$0.886026\pi$
$912$	−1.86442	+	8.77580i	−0.0617370	+	0.290596i
$913$	−2.44323			−0.0808592
$914$	−11.2954			−0.373618
$915$	−0.955151	−	0.859845i	−0.0315763	−	0.0284256i
$916$	−1.12602	−	1.95033i	−0.0372048	−	0.0644406i
$917$	10.8167	+	15.8194i	0.357200	+	0.522404i
$918$	42.6616	+	4.47070i	1.40804	+	0.147555i
$919$	16.6147	−	28.7775i	0.548069	−	0.949283i	−0.450338	−	0.892858i	$-0.648697\pi$
$919$	16.6147	−	28.7775i	0.548069	−	0.949283i	0.998407	−	0.0564248i	$-0.0179701\pi$
$920$	−0.183296	+	0.317478i	−0.00604309	+	0.0104669i
$921$	46.7257	−	15.1874i	1.53967	−	0.500442i
$922$	−5.28090	−	9.14679i	−0.173917	−	0.301234i
$923$	0.0610042	−	0.105662i	0.00200798	−	0.00347792i
$924$	−0.492316	+	3.67442i	−0.0161960	+	0.120880i
$925$	16.9107	+	29.2902i	0.556020	+	0.963055i
$926$	−11.6092	+	20.1078i	−0.381503	+	0.660782i
$927$	−52.3106	−	23.2774i	−1.71811	−	0.764530i
$928$	−13.7115	−	23.7489i	−0.450101	−	0.779597i
$929$	−20.7938			−0.682223			−0.341111	−	0.940023i	$-0.610803\pi$
$929$	−20.7938			−0.682223			−0.341111	+	0.940023i	$0.610803\pi$
$930$	−3.45115	−	3.10679i	−0.113168	−	0.101876i
$931$	7.61528	−	19.5581i	0.249581	−	0.640990i
$932$	2.55663	−	4.42821i	0.0837452	−	0.145051i
$933$	42.2248	−	13.7244i	1.38238	−	0.449318i
$934$	−21.9797	+	38.0700i	−0.719199	+	1.24569i
$935$	4.95129	+	8.57589i	0.161925	+	0.280462i
$936$	0.0229329	+	0.217764i	0.000749586	+	0.00711784i
$937$	−23.5779			−0.770255			−0.385128	−	0.922863i	$-0.625843\pi$
$937$	−23.5779			−0.770255			−0.385128	+	0.922863i	$0.625843\pi$
$938$	−21.1459	+	1.61329i	−0.690437	+	0.0526758i
$939$	−40.4025	+	13.1321i	−1.31849	+	0.428551i
$940$	5.95553	+	10.3153i	0.194248	+	0.336447i
$941$	7.80743			0.254515			0.127257	−	0.991870i	$-0.459383\pi$
$941$	7.80743			0.254515			0.127257	+	0.991870i	$0.459383\pi$
$942$	10.5394	−	3.42564i	0.343392	−	0.111614i
$943$	0.647439			0.0210835
$944$	−3.57609			−0.116392
$945$	17.9902	+	0.508669i	0.585222	+	0.0165470i
$946$	−3.83825			−0.124792
$947$	29.3918			0.955104			0.477552	−	0.878604i	$-0.341524\pi$
$947$	29.3918			0.955104			0.477552	+	0.878604i	$0.341524\pi$
$948$	9.29471	−	3.02108i	0.301878	−	0.0981202i
$949$	−0.0166553			−0.000540653
$950$	−5.37654	−	9.31245i	−0.174438	−	0.302136i
$951$	−4.48939	+	1.45920i	−0.145579	+	0.0473178i
$952$	−34.6288	−	50.6446i	−1.12233	−	1.64140i
$953$	56.1149			1.81774			0.908870	−	0.417079i	$-0.136946\pi$
$953$	56.1149			1.81774			0.908870	+	0.417079i	$0.136946\pi$
$954$	−5.03011	−	2.23832i	−0.162856	−	0.0724682i
$955$	11.7024	+	20.2691i	0.378680	+	0.655893i
$956$	7.89093	−	13.6675i	0.255211	−	0.442038i
$957$	−10.6393	+	3.45811i	−0.343919	+	0.111785i
$958$	−0.468402	+	0.811296i	−0.0151334	+	0.0262118i
$959$	−12.2359	+	25.4958i	−0.395117	+	0.823301i
$960$	13.6310	+	12.2709i	0.439940	+	0.396042i
$961$	−27.4787			−0.886409
$962$	0.133714	+	0.231599i	0.00431110	+	0.00746705i
$963$	1.58394	+	15.0406i	0.0510417	+	0.484676i
$964$	−9.26852	+	16.0535i	−0.298519	+	0.517050i
$965$	2.00575	+	3.47407i	0.0645675	+	0.111834i
$966$	−0.361797	−	0.278936i	−0.0116406	−	0.00897462i
$967$	−19.6227	+	33.9875i	−0.631024	+	1.09296i	0.356319	+	0.934364i	$0.384032\pi$
$967$	−19.6227	+	33.9875i	−0.631024	+	1.09296i	−0.987343	+	0.158601i	$0.949302\pi$
$968$	1.53277	+	2.65484i	0.0492652	+	0.0853298i
$969$	37.3596	−	12.1431i	1.20016	−	0.390093i
$970$	−1.50285	+	2.60301i	−0.0482536	+	0.0835777i
$971$	30.6870	−	53.1514i	0.984791	−	1.70571i	0.341931	−	0.939725i	$-0.388919\pi$
$971$	30.6870	−	53.1514i	0.984791	−	1.70571i	0.642860	−	0.765984i	$-0.277748\pi$
$972$	0.00644434	+	12.6109i	0.000206702	+	0.404495i
$973$	14.9944	−	31.2436i	0.480697	−	1.00162i
$974$	10.5960	+	18.3528i	0.339517	+	0.588061i
$975$	−0.100721	−	0.0906712i	−0.00322566	−	0.00290380i
$976$	0.979155			0.0313420
$977$	−18.8938			−0.604467			−0.302233	−	0.953234i	$-0.597732\pi$
$977$	−18.8938			−0.604467			−0.302233	+	0.953234i	$0.597732\pi$
$978$	−5.23530	+	24.6426i	−0.167407	+	0.787982i
$979$	8.06879	+	13.9755i	0.257880	+	0.446660i
$980$	−4.63779	−	5.78360i	−0.148149	−	0.184750i
$981$	−48.3808	−	21.5287i	−1.54468	−	0.687357i
$982$	−10.8628	+	18.8150i	−0.346647	+	0.600411i
$983$	12.8422	−	22.2433i	0.409602	−	0.709452i	−0.585243	−	0.810858i	$-0.699001\pi$
$983$	12.8422	−	22.2433i	0.409602	−	0.709452i	0.994845	+	0.101406i	$0.0323342\pi$
$984$	7.82062	−	36.8116i	0.249312	−	1.17351i
$985$	−9.51279	−	16.4766i	−0.303103	−	0.524989i
$986$	26.6598	−	46.1761i	0.849020	−	1.47055i
$987$	−47.6611	+	19.6140i	−1.51707	+	0.624322i
$988$	0.0288765	+	0.0500156i	0.000918685	+	0.00159121i
$989$	−0.160635	+	0.278229i	−0.00510791	+	0.00884716i
$990$	3.46698	−	2.51999i	0.110188	−	0.0800905i
$991$	−17.4129	−	30.1600i	−0.553139	−	0.958065i	−0.998046	−	0.0624880i	$-0.980096\pi$
$991$	−17.4129	−	30.1600i	−0.553139	−	0.958065i	0.444907	−	0.895577i	$-0.353237\pi$
$992$	−7.96723			−0.252960
$993$	11.7399	−	3.81586i	0.372556	−	0.121093i
$994$	14.7531	−	1.12557i	0.467941	−	0.0357008i
$995$	2.03032	−	3.51661i	0.0643654	−	0.111484i
$996$	2.54438	+	2.29050i	0.0806218	+	0.0725772i
$997$	−4.24412	+	7.35103i	−0.134413	+	0.232809i	−0.925373	−	0.379058i	$-0.876248\pi$
$997$	−4.24412	+	7.35103i	−0.134413	+	0.232809i	0.790960	+	0.611867i	$0.209581\pi$
$998$	8.72968	+	15.1203i	0.276333	+	0.478623i
$999$	21.7666	+	48.8482i	0.688664	+	1.54549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.l.c.562.27	yes	80
7.4	even	3		693.2.k.c.67.14	✓	80
9.7	even	3		693.2.k.c.331.14	yes	80
63.25	even	3	inner	693.2.l.c.529.27	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.k.c.67.14	✓	80	7.4	even	3
693.2.k.c.331.14	yes	80	9.7	even	3
693.2.l.c.529.27	yes	80	63.25	even	3	inner
693.2.l.c.562.27	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.09133 q^{2} +(1.64722 - 0.535401i) q^{3} -0.808990 q^{4} +(0.654559 + 1.13373i) q^{5} +(1.79767 - 0.584302i) q^{6} +(2.63808 - 0.201269i) q^{7} -3.06555 q^{8} +(2.42669 - 1.76385i) q^{9} +(0.714343 + 1.23728i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.33259 + 0.433134i) q^{12} +(0.0119048 - 0.0206197i) q^{13} +(2.87903 - 0.219651i) q^{14} +(1.68521 + 1.51705i) q^{15} -1.72756 q^{16} +(3.78216 + 6.55089i) q^{17} +(2.64833 - 1.92495i) q^{18} +(1.49917 - 2.59664i) q^{19} +(-0.529532 - 0.917176i) q^{20} +(4.23776 - 1.74397i) q^{21} +(0.545667 - 0.945123i) q^{22} +(-0.0456737 - 0.0791091i) q^{23} +(-5.04964 + 1.64130i) q^{24} +(1.64310 - 2.84594i) q^{25} +(0.0129921 - 0.0225030i) q^{26} +(3.05293 - 4.20471i) q^{27} +(-2.13418 + 0.162824i) q^{28} +(-3.22945 - 5.59358i) q^{29} +(1.83912 + 1.65561i) q^{30} -1.87652 q^{31} +4.24575 q^{32} +(0.359940 - 1.69424i) q^{33} +(4.12760 + 7.14921i) q^{34} +(1.95497 + 2.85913i) q^{35} +(-1.96317 + 1.42694i) q^{36} +(-5.14596 + 8.91306i) q^{37} +(1.63609 - 2.83380i) q^{38} +(0.00857003 - 0.0403391i) q^{39} +(-2.00658 - 3.47550i) q^{40} +(-3.54383 + 6.13809i) q^{41} +(4.62481 - 1.90325i) q^{42} +(-1.75851 - 3.04583i) q^{43} +(-0.404495 + 0.700606i) q^{44} +(3.58814 + 1.59667i) q^{45} +(-0.0498452 - 0.0863345i) q^{46} -11.2468 q^{47} +(-2.84567 + 0.924936i) q^{48} +(6.91898 - 1.06193i) q^{49} +(1.79318 - 3.10587i) q^{50} +(9.73742 + 8.76581i) q^{51} +(-0.00963085 + 0.0166811i) q^{52} +(-0.840812 - 1.45633i) q^{53} +(3.33177 - 4.58875i) q^{54} +1.30912 q^{55} +(-8.08717 + 0.616998i) q^{56} +(1.07922 - 5.07990i) q^{57} +(-3.52441 - 6.10446i) q^{58} +2.07003 q^{59} +(-1.36331 - 1.22728i) q^{60} -0.566786 q^{61} -2.04791 q^{62} +(6.04681 - 5.14161i) q^{63} +8.08865 q^{64} +0.0311696 q^{65} +(0.392815 - 1.84898i) q^{66} -7.34478 q^{67} +(-3.05973 - 5.29960i) q^{68} +(-0.117590 - 0.105857i) q^{69} +(2.13352 + 3.12027i) q^{70} +5.12434 q^{71} +(-7.43913 + 5.40717i) q^{72} +(-0.349760 - 0.605802i) q^{73} +(-5.61596 + 9.72713i) q^{74} +(1.18284 - 5.56762i) q^{75} +(-1.21281 + 2.10065i) q^{76} +(1.14474 - 2.38528i) q^{77} +(0.00935277 - 0.0440234i) q^{78} -6.97493 q^{79} +(-1.13079 - 1.95858i) q^{80} +(2.77765 - 8.56064i) q^{81} +(-3.86750 + 6.69871i) q^{82} +(-1.22162 - 2.11590i) q^{83} +(-3.42830 + 1.41085i) q^{84} +(-4.95129 + 8.57589i) q^{85} +(-1.91912 - 3.32402i) q^{86} +(-8.31444 - 7.48482i) q^{87} +(-1.53277 + 2.65484i) q^{88} +(-8.06879 + 13.9755i) q^{89} +(3.91586 + 1.74250i) q^{90} +(0.0272557 - 0.0567926i) q^{91} +(0.0369495 + 0.0639985i) q^{92} +(-3.09104 + 1.00469i) q^{93} -12.2740 q^{94} +3.92518 q^{95} +(6.99370 - 2.27318i) q^{96} +(1.05191 + 1.82196i) q^{97} +(7.55092 - 1.15892i) q^{98} +(-0.314195 - 2.98350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 80 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} - 4 q^{9} + 12 q^{10} + 40 q^{11} + 5 q^{12} + 21 q^{13} + 7 q^{14} - 5 q^{15} + 80 q^{16} - 3 q^{17} - 10 q^{18} + 18 q^{19} - 12 q^{20} - 33 q^{21} + 4 q^{23}+ \cdots - 2 q^{99}+O(q^{100}) \) 80 * q + 80 * q^4 - 4 * q^5 + 6 * q^6 - q^7 - 4 * q^9 + 12 * q^10 + 40 * q^11 + 5 * q^12 + 21 * q^13 + 7 * q^14 - 5 * q^15 + 80 * q^16 - 3 * q^17 - 10 * q^18 + 18 * q^19 - 12 * q^20 - 33 * q^21 + 4 * q^23 - 2 * q^24 - 40 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 14 * q^30 - 64 * q^31 - 70 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 - 23 * q^38 + 42 * q^39 + 51 * q^40 - 2 * q^41 + 25 * q^42 + 9 * q^43 + 40 * q^44 - 14 * q^45 - 6 * q^46 + 52 * q^47 - 28 * q^48 - q^49 + 2 * q^50 - 20 * q^51 + 44 * q^52 + 4 * q^53 - 2 * q^54 - 8 * q^55 + 6 * q^56 + 16 * q^57 - 16 * q^58 + 48 * q^59 - 70 * q^60 - 138 * q^61 + 12 * q^62 + 95 * q^63 + 44 * q^64 + 14 * q^65 + 3 * q^66 - 14 * q^67 - 17 * q^68 + 15 * q^69 - 40 * q^70 + 34 * q^71 - 19 * q^72 + 26 * q^73 - 4 * q^74 + 14 * q^75 + 52 * q^76 - 2 * q^77 - 60 * q^78 + 10 * q^79 - 47 * q^80 - 44 * q^81 + 60 * q^82 + 4 * q^83 - 205 * q^84 + 13 * q^85 + 82 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 44 * q^93 - 112 * q^94 + 40 * q^95 - 78 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

Introduction

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