LMFDB - Embedded newform 693.2.k.c.67.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(67,693)] 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("693.67"); 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([2, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.k (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			67.14
Character	$\chi$	$=$	693.67
Dual form			693.2.k.c.331.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.545667 + 0.945123i) q^{2} +(-1.28728 - 1.15884i) q^{3} +(0.404495 + 0.700606i) q^{4} -1.30912 q^{5} +(1.79767 - 0.584302i) q^{6} +(-1.49335 + 2.18401i) q^{7} -3.06555 q^{8} +(0.314195 + 2.98350i) q^{9} +(0.714343 - 1.23728i) q^{10} -1.00000 q^{11} +(0.291188 - 1.37062i) q^{12} +(0.0119048 - 0.0206197i) q^{13} +(-1.24929 - 2.60314i) q^{14} +(1.68521 + 1.51705i) q^{15} +(0.863778 - 1.49611i) q^{16} +(3.78216 - 6.55089i) q^{17} +(-2.99122 - 1.33105i) q^{18} +(1.49917 + 2.59664i) q^{19} +(-0.529532 - 0.917176i) q^{20} +(4.45327 - 1.08090i) q^{21} +(0.545667 - 0.945123i) q^{22} +0.0913474 q^{23} +(3.94623 + 3.55247i) q^{24} -3.28621 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} +(-2.35336 + 0.764920i) q^{30} +(0.938259 + 1.62511i) q^{31} +(-2.12288 - 3.67693i) q^{32} +(1.28728 + 1.15884i) 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} -3.27219 q^{38} +(-0.0392197 + 0.0127477i) q^{39} +4.01316 q^{40} +(-3.54383 + 6.13809i) q^{41} +(-1.40842 + 4.79870i) q^{42} +(-1.75851 - 3.04583i) q^{43} +(-0.404495 - 0.700606i) q^{44} +(-0.411319 - 3.90576i) q^{45} +(-0.0498452 + 0.0863345i) q^{46} +(5.62339 - 9.74000i) q^{47} +(-2.84567 + 0.924936i) q^{48} +(-2.53984 - 6.52298i) q^{49} +(1.79318 - 3.10587i) q^{50} +(-12.4601 + 4.04995i) q^{51} +0.0192617 q^{52} +(-0.840812 + 1.45633i) q^{53} +(2.30809 + 5.17977i) q^{54} +1.30912 q^{55} +(4.57792 - 6.69520i) q^{56} +(1.07922 - 5.07990i) q^{57} +7.04883 q^{58} +(-1.03501 - 1.79270i) q^{59} +(-0.381200 + 1.79431i) q^{60} +(0.283393 - 0.490851i) q^{61} -2.04791 q^{62} +(-6.98521 - 3.76919i) q^{63} +8.08865 q^{64} +(-0.0155848 + 0.0269936i) q^{65} +(-1.79767 + 0.584302i) q^{66} +(3.67239 + 6.36077i) q^{67} +6.11945 q^{68} +(-0.117590 - 0.105857i) q^{69} +(1.63547 + 3.40782i) q^{70} +5.12434 q^{71} +(-0.963180 - 9.14606i) q^{72} +(-0.349760 + 0.605802i) q^{73} +11.2319 q^{74} +(4.23028 + 3.80818i) q^{75} +(-1.21281 + 2.10065i) q^{76} +(1.49335 - 2.18401i) q^{77} +(0.00935277 - 0.0440234i) q^{78} +(3.48747 - 6.04047i) q^{79} +(-1.13079 + 1.95858i) q^{80} +(-8.80256 + 1.87480i) q^{81} +(-3.86750 - 6.69871i) q^{82} +(-1.22162 - 2.11590i) q^{83} +(2.55861 + 2.68277i) q^{84} +(-4.95129 + 8.57589i) q^{85} +3.83825 q^{86} +(-2.32482 + 10.9429i) q^{87} +3.06555 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} +(0.675435 - 3.17927i) q^{93} +(6.13700 + 10.6296i) q^{94} +(-1.96259 - 3.39930i) q^{95} +(-1.52822 + 7.19331i) 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 - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9} + 12 q^{10} - 80 q^{11} - 10 q^{12} + 21 q^{13} - 8 q^{14} - 5 q^{15} - 40 q^{16} - 3 q^{17} + 32 q^{18} + 18 q^{19} - 12 q^{20} + 18 q^{21} - 8 q^{23}+ \cdots - 2 q^{99}+O(q^{100}) $ 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9 + 12 * q^10 - 80 * q^11 - 10 * q^12 + 21 * q^13 - 8 * q^14 - 5 * q^15 - 40 * q^16 - 3 * q^17 + 32 * q^18 + 18 * q^19 - 12 * q^20 + 18 * q^21 - 8 * q^23 - 14 * q^24 + 80 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 20 * q^30 + 32 * q^31 + 35 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 + 46 * q^38 - 48 * q^39 - 102 * q^40 - 2 * q^41 - 14 * q^42 + 9 * q^43 + 40 * q^44 - 5 * q^45 - 6 * q^46 - 26 * q^47 - 28 * q^48 - 19 * q^49 + 2 * q^50 + 22 * q^51 - 88 * q^52 + 4 * q^53 + 19 * q^54 - 8 * q^55 + 18 * q^56 + 16 * q^57 + 32 * q^58 - 24 * q^59 - 10 * q^60 + 69 * q^61 + 12 * q^62 + 20 * q^63 + 44 * q^64 - 7 * q^65 - 6 * q^66 + 7 * q^67 + 34 * q^68 + 15 * q^69 - 22 * q^70 + 34 * q^71 - 70 * q^72 + 26 * q^73 + 8 * q^74 - 64 * q^75 + 52 * q^76 + q^77 - 60 * q^78 - 5 * q^79 - 47 * q^80 + 46 * q^81 + 60 * q^82 + 4 * q^83 + 29 * q^84 + 13 * q^85 - 38 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 35 * q^93 + 56 * q^94 - 20 * q^95 + 15 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

Character values

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

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.545667	+	0.945123i	−0.385845	+	0.668303i	−0.991886	−	0.127130i	$-0.959423\pi$
$2$	−0.545667	+	0.945123i	−0.385845	+	0.668303i	0.606041	+	0.795433i	$0.292757\pi$
$3$	−1.28728	−	1.15884i	−0.743213	−	0.669055i
$3$	−1.28728	−	1.15884i	−0.743213	−	0.669055i
$4$	0.404495	+	0.700606i	0.202247	+	0.350303i
$5$	−1.30912			−0.585456			−0.292728	−	0.956196i	$-0.594563\pi$
$5$	−1.30912			−0.585456			−0.292728	+	0.956196i	$0.594563\pi$
$6$	1.79767	−	0.584302i	0.733896	−	0.238540i
$7$	−1.49335	+	2.18401i	−0.564432	+	0.825480i
$7$	−1.49335	+	2.18401i	−0.564432	+	0.825480i
$8$	−3.06555			−1.08383
$9$	0.314195	+	2.98350i	0.104732	+	0.994501i
$10$	0.714343	−	1.23728i	0.225895	−	0.391262i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.291188	−	1.37062i	0.0840588	−	0.395664i
$13$	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	$0.165616\pi$
$14$	−1.24929	−	2.60314i	−0.333887	−	0.695719i
$15$	1.68521	+	1.51705i	0.435118	+	0.391702i
$16$	0.863778	−	1.49611i	0.215945	−	0.374027i
$17$	3.78216	−	6.55089i	0.917308	−	1.58882i	0.113822	−	0.993501i	$-0.463691\pi$
$17$	3.78216	−	6.55089i	0.917308	−	1.58882i	0.803486	−	0.595323i	$-0.202976\pi$
$18$	−2.99122	−	1.33105i	−0.705038	−	0.313730i
$19$	1.49917	+	2.59664i	0.343933	+	0.595709i	0.985159	−	0.171643i	$-0.0549075\pi$
$19$	1.49917	+	2.59664i	0.343933	+	0.595709i	−0.641227	+	0.767352i	$0.721574\pi$
$20$	−0.529532	−	0.917176i	−0.118407	−	0.205087i
$21$	4.45327	−	1.08090i	0.971784	−	0.235872i
$22$	0.545667	−	0.945123i	0.116337	−	0.201501i
$23$	0.0913474			0.0190472			0.00952362	−	0.999955i	$-0.496968\pi$
$23$	0.0913474			0.0190472			0.00952362	+	0.999955i	$0.496968\pi$
$24$	3.94623	+	3.55247i	0.805520	+	0.725144i
$25$	−3.28621			−0.657242
$26$	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	$-0.371378\pi$
$30$	−2.35336	+	0.764920i	−0.429664	+	0.139655i
$31$	0.938259	+	1.62511i	0.168516	+	0.291879i	0.937898	−	0.346910i	$-0.112769\pi$
$31$	0.938259	+	1.62511i	0.168516	+	0.291879i	−0.769382	+	0.638789i	$0.779436\pi$
$32$	−2.12288	−	3.67693i	−0.375275	−	0.649995i
$33$	1.28728	+	1.15884i	0.224087	+	0.201728i
$34$	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	−0.884758	−	0.466050i	$-0.845677\pi$
$37$	−5.14596	−	8.91306i	−0.845990	−	1.46530i	0.0387681	−	0.999248i	$-0.487657\pi$
$38$	−3.27219			−0.530819
$39$	−0.0392197	+	0.0127477i	−0.00628018	+	0.00204126i
$40$	4.01316			0.634537
$41$	−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	$0.979976\pi$
$42$	−1.40842	+	4.79870i	−0.217324	+	0.740456i
$43$	−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
$45$	−0.411319	−	3.90576i	−0.0613158	−	0.582236i
$46$	−0.0498452	+	0.0863345i	−0.00734928	+	0.0127293i
$47$	5.62339	−	9.74000i	0.820256	−	1.42073i	−0.0852351	−	0.996361i	$-0.527164\pi$
$47$	5.62339	−	9.74000i	0.820256	−	1.42073i	0.905491	−	0.424365i	$-0.139503\pi$
$48$	−2.84567	+	0.924936i	−0.410737	+	0.133503i
$49$	−2.53984	−	6.52298i	−0.362834	−	0.931854i
$50$	1.79318	−	3.10587i	0.253593	−	0.439237i
$51$	−12.4601	+	4.04995i	−1.74477	+	0.567106i
$52$	0.0192617			0.00267112
$53$	−0.840812	+	1.45633i	−0.115494	+	0.200042i	−0.917977	−	0.396633i	$-0.870179\pi$
$53$	−0.840812	+	1.45633i	−0.115494	+	0.200042i	0.802483	+	0.596675i	$0.203512\pi$
$54$	2.30809	+	5.17977i	0.314091	+	0.704877i
$55$	1.30912			0.176521
$56$	4.57792	−	6.69520i	0.611751	−	0.894683i
$57$	1.07922	−	5.07990i	0.142947	−	0.672849i
$58$	7.04883			0.925556
$59$	−1.03501	−	1.79270i	−0.134747	−	0.233389i	0.790754	−	0.612135i	$-0.209689\pi$
$59$	−1.03501	−	1.79270i	−0.134747	−	0.233389i	−0.925501	+	0.378745i	$0.876356\pi$
$60$	−0.381200	+	1.79431i	−0.0492127	+	0.231644i
$61$	0.283393	−	0.490851i	0.0362848	−	0.0628471i	−0.847313	−	0.531094i	$-0.821781\pi$
$61$	0.283393	−	0.490851i	0.0362848	−	0.0628471i	0.883597	+	0.468247i	$0.155114\pi$
$62$	−2.04791			−0.260085
$63$	−6.98521	−	3.76919i	−0.880054	−	0.474874i
$64$	8.08865			1.01108
$65$	−0.0155848	+	0.0269936i	−0.00193305	+	0.00334815i
$66$	−1.79767	+	0.584302i	−0.221278	+	0.0719226i
$67$	3.67239	+	6.36077i	0.448654	+	0.777091i	0.998299	−	0.0583071i	$-0.0185703\pi$
$67$	3.67239	+	6.36077i	0.448654	+	0.777091i	−0.549645	+	0.835398i	$0.685237\pi$
$68$	6.11945			0.742093
$69$	−0.117590	−	0.105857i	−0.0141562	−	0.0127436i
$70$	1.63547	+	3.40782i	0.195476	+	0.407312i
$71$	5.12434			0.608147			0.304074	−	0.952649i	$-0.401653\pi$
$71$	5.12434			0.608147			0.304074	+	0.952649i	$0.401653\pi$
$72$	−0.963180	−	9.14606i	−0.113512	−	1.07787i
$73$	−0.349760	+	0.605802i	−0.0409363	+	0.0709038i	−0.885768	−	0.464129i	$-0.846367\pi$
$73$	−0.349760	+	0.605802i	−0.0409363	+	0.0709038i	0.844831	+	0.535033i	$0.179701\pi$
$74$	11.2319			1.30568
$75$	4.23028	+	3.80818i	0.488471	+	0.439731i
$76$	−1.21281	+	2.10065i	−0.139119	+	0.240961i
$77$	1.49335	−	2.18401i	0.170183	−	0.248892i
$78$	0.00935277	−	0.0440234i	0.00105899	−	0.00498467i
$79$	3.48747	−	6.04047i	0.392371	−	0.679606i	−0.600391	−	0.799707i	$-0.704988\pi$
$79$	3.48747	−	6.04047i	0.392371	−	0.679606i	0.992762	+	0.120101i	$0.0383217\pi$
$80$	−1.13079	+	1.95858i	−0.126426	+	0.218976i
$81$	−8.80256	+	1.87480i	−0.978063	+	0.208312i
$82$	−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	$0.876144\pi$
$84$	2.55861	+	2.68277i	0.279167	+	0.292714i
$85$	−4.95129	+	8.57589i	−0.537043	+	0.930186i
$86$	3.83825			0.413889
$87$	−2.32482	+	10.9429i	−0.249247	+	1.17321i
$88$	3.06555			0.326788
$89$	−8.06879	−	13.9755i	−0.855290	−	1.48141i	−0.876376	−	0.481628i	$-0.840046\pi$
$89$	−8.06879	−	13.9755i	−0.855290	−	1.48141i	0.0210863	−	0.999778i	$-0.493288\pi$
$90$	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
$93$	0.675435	−	3.17927i	0.0700393	−	0.329675i
$94$	6.13700	+	10.6296i	0.632983	+	1.09636i
$95$	−1.96259	−	3.39930i	−0.201357	−	0.348761i
$96$	−1.52822	+	7.19331i	−0.155973	+	0.734165i
$97$	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
$101$	−15.4434			−1.53668			−0.768338	−	0.640045i	$-0.778916\pi$
$101$	−15.4434			−1.53668			−0.768338	+	0.640045i	$0.778916\pi$
$102$	2.97138	−	13.9863i	0.294210	−	1.38485i
$103$	19.0853			1.88053			0.940265	−	0.340442i	$-0.110577\pi$
$103$	19.0853			1.88053			0.940265	+	0.340442i	$0.110577\pi$
$104$	−0.0364947	+	0.0632107i	−0.00357860	+	0.00619831i
$105$	−5.82986	+	1.41503i	−0.568936	+	0.138092i
$106$	−0.917607	−	1.58934i	−0.0891259	−	0.154371i
$107$	−2.52063	−	4.36585i	−0.243678	−	0.422063i	0.718081	−	0.695960i	$-0.245021\pi$
$107$	−2.52063	−	4.36585i	−0.243678	−	0.422063i	−0.961759	+	0.273897i	$0.911687\pi$
$108$	4.18074	+	0.438118i	0.402292	+	0.0421579i
$109$	−8.82576	+	15.2867i	−0.845354	+	1.46420i	0.0399587	+	0.999201i	$0.487277\pi$
$109$	−8.82576	+	15.2867i	−0.845354	+	1.46420i	−0.885313	+	0.464995i	$0.846056\pi$
$110$	−0.714343	+	1.23728i	−0.0681099	+	0.117970i
$111$	−3.70448	+	17.4370i	−0.351613	+	1.65504i
$112$	1.97760	+	4.12071i	0.186866	+	0.389370i
$113$	−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	$0.921990\pi$
$114$	4.21223	+	3.79193i	0.394511	+	0.355147i
$115$	−0.119584			−0.0111513
$116$	2.61260	−	4.52515i	0.242573	−	0.420149i
$117$	0.0652593	+	0.0290393i	0.00603323	+	0.00268469i
$118$	2.25909			0.207966
$119$	8.65917	+	18.0430i	0.793784	+	1.65400i
$120$	−5.16608	−	4.65060i	−0.471596	−	0.424540i
$121$	1.00000			0.0909091
$122$	0.309277	+	0.535683i	0.0280006	+	0.0484984i
$123$	11.6750	−	3.79474i	1.05270	−	0.342160i
$124$	−0.759042	+	1.31470i	−0.0681640	+	0.118063i
$125$	10.8476			0.970241
$126$	7.37395	−	4.54516i	0.656924	−	0.404915i
$127$	−15.3710			−1.36395			−0.681976	−	0.731375i	$-0.738879\pi$
$127$	−15.3710			−1.36395			−0.681976	+	0.731375i	$0.738879\pi$
$128$	−0.167956	+	0.290909i	−0.0148454	+	0.0257129i
$129$	−1.26592	+	5.95867i	−0.111458	+	0.524632i
$130$	−0.0170082	−	0.0294591i	−0.00149172	−	0.00258373i
$131$	−7.24329			−0.632849			−0.316424	−	0.948618i	$-0.602482\pi$
$131$	−7.24329			−0.632849			−0.316424	+	0.948618i	$0.602482\pi$
$132$	−0.291188	+	1.37062i	−0.0253447	+	0.119297i
$133$	−7.90986	−	0.603471i	−0.685872	−	0.0523276i
$134$	−8.01561			−0.692443
$135$	−3.99665	+	5.50447i	−0.343977	+	0.473749i
$136$	−11.5944	+	20.0821i	−0.994210	+	1.72202i
$137$	10.6888			0.913204			0.456602	−	0.889671i	$-0.349066\pi$
$137$	10.6888			0.913204			0.456602	+	0.889671i	$0.349066\pi$
$138$	0.164213	−	0.0533744i	0.0139787	−	0.00454353i
$139$	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	$-0.0208064\pi$
$140$	2.79390	+	0.213156i	0.236128	+	0.0180150i
$141$	−18.5260	+	6.02155i	−1.56017	+	0.507106i
$142$	−2.79618	+	4.84313i	−0.234650	+	0.406427i
$143$	−0.0119048	+	0.0206197i	−0.000995529	+	0.00172431i
$144$	4.73503	+	2.10701i	0.394586	+	0.175584i
$145$	4.22774	+	7.32266i	0.351095	+	0.608114i
$146$	−0.381705	−	0.661133i	−0.0315901	−	0.0547157i
$147$	−4.28958	+	11.3402i	−0.353799	+	0.935322i
$148$	4.16303	−	7.21057i	0.342199	−	0.592706i
$149$	−13.9389			−1.14192			−0.570958	−	0.820979i	$-0.693428\pi$
$149$	−13.9389			−1.14192			−0.570958	+	0.820979i	$0.693428\pi$
$150$	−5.90752	+	1.92014i	−0.482347	+	0.156779i
$151$	6.11284			0.497456			0.248728	−	0.968573i	$-0.419988\pi$
$151$	6.11284			0.497456			0.248728	+	0.968573i	$0.419988\pi$
$152$	−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
$156$	−0.0247953	−	0.0223212i	−0.00198521	−	0.00178712i
$157$	−2.93140	−	5.07733i	−0.233951	−	0.405215i	0.725016	−	0.688732i	$-0.241832\pi$
$157$	−2.93140	−	5.07733i	−0.233951	−	0.405215i	−0.958967	+	0.283517i	$0.908499\pi$
$158$	3.80599	+	6.59217i	0.302788	+	0.524445i
$159$	2.77001	−	0.900344i	0.219676	−	0.0714019i
$160$	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	−0.999674	−	0.0255351i	$-0.991871\pi$
$163$	−6.66382	−	11.5421i	−0.521951	−	0.904046i	0.477723	−	0.878511i	$-0.341462\pi$
$164$	−5.73384			−0.447738
$165$	−1.68521	−	1.51705i	−0.131193	−	0.118103i
$166$	2.66638			0.206952
$167$	−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	$0.247941\pi$
$168$	−13.6517	+	3.31355i	−1.05325	+	0.255646i
$169$	6.49972	+	11.2578i	0.499978	+	0.865988i
$170$	−5.40351	−	9.35916i	−0.414431	−	0.717815i
$171$	−7.27603	+	5.28862i	−0.556412	+	0.404431i
$172$	1.42262	−	2.46405i	0.108474	−	0.187882i
$173$	−7.67906	+	13.3005i	−0.583828	+	1.01122i	0.411192	+	0.911549i	$0.365112\pi$
$173$	−7.67906	+	13.3005i	−0.583828	+	1.01122i	−0.995020	+	0.0996711i	$0.968221\pi$
$174$	−9.07384	−	8.16844i	−0.687886	−	0.619248i
$175$	4.90745	−	7.17713i	0.370968	−	0.542540i
$176$	−0.863778	+	1.49611i	−0.0651097	+	0.112773i
$177$	−0.745087	+	3.50712i	−0.0560042	+	0.263612i
$178$	17.6115			1.32004
$179$	2.08828	−	3.61702i	0.156086	−	0.270348i	−0.777368	−	0.629046i	$-0.783446\pi$
$179$	2.08828	−	3.61702i	0.156086	−	0.270348i	0.933454	+	0.358698i	$0.116779\pi$
$180$	2.57002	−	1.86803i	0.191558	−	0.139235i
$181$	1.58810			0.118042			0.0590212	−	0.998257i	$-0.481202\pi$
$181$	1.58810			0.118042			0.0590212	+	0.998257i	$0.481202\pi$
$182$	−0.0685485	−	0.00522980i	−0.00508116	−	0.000387659i
$183$	−0.933623	+	0.303458i	−0.0690154	+	0.0224323i
$184$	−0.280030			−0.0206441
$185$	6.73667	+	11.6683i	0.495290	+	0.857867i
$186$	2.63624	+	2.37319i	0.193298	+	0.174011i
$187$	−3.78216	+	6.55089i	−0.276579	+	0.479049i
$188$	9.09854			0.663579
$189$	4.62406	+	12.9467i	0.336351	+	0.941737i
$190$	4.28368			0.310771
$191$	−8.93912	+	15.4830i	−0.646812	+	1.12031i	0.337068	+	0.941480i	$0.390565\pi$
$191$	−8.93912	+	15.4830i	−0.646812	+	1.12031i	−0.983880	+	0.178831i	$0.942768\pi$
$192$	−10.4124	−	9.37342i	−0.751449	−	0.676468i
$193$	−1.53214	−	2.65375i	−0.110286	−	0.191021i	0.805600	−	0.592460i	$-0.201843\pi$
$193$	−1.53214	−	2.65375i	−0.110286	−	0.191021i	−0.915886	+	0.401440i	$0.868510\pi$
$194$	−2.29597			−0.164841
$195$	0.0513432	−	0.0166882i	0.00367677	−	0.00119507i
$196$	3.54268	−	4.41793i	0.253049	−	0.315567i
$197$	−14.5331			−1.03544			−0.517721	−	0.855550i	$-0.673219\pi$
$197$	−14.5331			−1.03544			−0.517721	+	0.855550i	$0.673219\pi$
$198$	2.99122	+	1.33105i	0.212577	+	0.0945933i
$199$	−1.55090	+	2.68624i	−0.109941	+	0.190423i	−0.915746	−	0.401758i	$-0.868399\pi$
$199$	−1.55090	+	2.68624i	−0.109941	+	0.190423i	0.805805	+	0.592180i	$0.201733\pi$
$200$	10.0740			0.712341
$201$	2.64368	−	12.4438i	0.186471	−	0.877719i
$202$	8.42695	−	14.5959i	0.592918	−	1.02696i
$203$	17.0391	+	1.29998i	1.19591	+	0.0912404i
$204$	−7.87747	−	7.09145i	−0.551533	−	0.496501i
$205$	4.63929	−	8.03549i	0.324022	−	0.561223i
$206$	−10.4142	+	18.0380i	−0.725593	+	1.25676i
$207$	0.0287009	+	0.272535i	0.00199485	+	0.0189425i
$208$	−0.0205662	−	0.0356217i	−0.00142601	−	0.00246992i
$209$	−1.49917	−	2.59664i	−0.103700	−	0.179613i
$210$	1.84379	−	6.28207i	0.127234	−	0.433504i
$211$	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	$-0.0200145\pi$
$212$	−1.36042			−0.0934338
$213$	−6.59647	−	5.93827i	−0.451983	−	0.406884i
$214$	5.50169			0.376088
$215$	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
$219$	1.15227	−	0.374524i	0.0778629	−	0.0253080i
$220$	0.529532	+	0.917176i	0.0357010	+	0.0618360i
$221$	−0.0900516	−	0.155974i	−0.00605753	−	0.0104919i
$222$	−14.4587	−	13.0160i	−0.970402	−	0.873574i
$223$	−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
$227$	−10.3280			−0.685492			−0.342746	−	0.939428i	$-0.611357\pi$
$227$	−10.3280			−0.685492			−0.342746	+	0.939428i	$0.611357\pi$
$228$	3.99554	−	1.29868i	0.264611	−	0.0860073i
$229$	−2.78377			−0.183957			−0.0919785	−	0.995761i	$-0.529319\pi$
$229$	−2.78377			−0.183957			−0.0919785	+	0.995761i	$0.529319\pi$
$230$	0.0652533	−	0.113022i	0.00430268	−	0.00745245i
$231$	−4.45327	+	1.08090i	−0.293004	+	0.0711180i
$232$	9.90004	+	17.1474i	0.649970	+	1.12578i
$233$	−3.16027	−	5.47375i	−0.207036	−	0.358598i	0.743743	−	0.668465i	$-0.233049\pi$
$233$	−3.16027	−	5.47375i	−0.207036	−	0.358598i	−0.950780	+	0.309868i	$0.899715\pi$
$234$	−0.0630556	+	0.0458323i	−0.00412208	+	0.00299615i
$235$	−7.36169	+	12.7508i	−0.480224	+	0.831772i
$236$	0.837316	−	1.45027i	0.0545047	−	0.0944048i
$237$	−11.4893	+	3.73439i	−0.746309	+	0.242575i
$238$	−21.7779	−	1.66151i	−1.41165	−	0.107700i
$239$	−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	$0.949337\pi$
$240$	3.72532	−	1.21085i	0.240468	−	0.0781601i
$241$	−22.9138			−1.47601			−0.738004	−	0.674796i	$-0.764231\pi$
$241$	−22.9138			−1.47601			−0.738004	+	0.674796i	$0.764231\pi$
$242$	−0.545667	+	0.945123i	−0.0350768	+	0.0607548i
$243$	13.5040	+	7.78733i	0.866281	+	0.499557i
$244$	0.458524			0.0293540
$245$	3.32494	+	8.53935i	0.212423	+	0.545559i
$246$	−2.78414	+	13.1049i	−0.177510	+	0.835540i
$247$	0.0713891			0.00454238
$248$	−2.87628	−	4.98186i	−0.182644	−	0.316348i
$249$	−0.879418	+	4.13942i	−0.0557309	+	0.262325i
$250$	−5.91919	+	10.2523i	−0.374363	+	0.648415i
$251$	0.493714			0.0311630			0.0155815	−	0.999879i	$-0.495040\pi$
$251$	0.493714			0.0311630			0.0155815	+	0.999879i	$0.495040\pi$
$252$	−0.184764	−	6.41850i	−0.0116390	−	0.404327i
$253$	−0.0913474			−0.00574296
$254$	8.38743	−	14.5274i	0.526274	−	0.911533i
$255$	16.3118	−	5.30186i	1.02148	−	0.332015i
$256$	7.90535	+	13.6925i	0.494084	+	0.855779i
$257$	18.6911			1.16592			0.582959	−	0.812501i	$-0.301895\pi$
$257$	18.6911			1.16592			0.582959	+	0.812501i	$0.301895\pi$
$258$	−4.94091	−	4.44790i	−0.307608	−	0.276914i
$259$	27.1509	+	2.07144i	1.68708	+	0.128713i
$260$	−0.0252159			−0.00156382
$261$	15.6738	−	11.3926i	0.970182	−	0.705182i
$262$	3.95242	−	6.84580i	0.244181	−	0.422935i
$263$	−14.8163			−0.913613			−0.456806	−	0.889566i	$-0.651007\pi$
$263$	−14.8163			−0.913613			−0.456806	+	0.889566i	$0.651007\pi$
$264$	−3.94623	−	3.55247i	−0.242873	−	0.218639i
$265$	1.10072	−	1.90651i	0.0676168	−	0.117116i
$266$	4.88651	−	7.14650i	0.299611	−	0.438180i
$267$	−5.80857	+	27.3409i	−0.355478	+	1.67324i
$268$	−2.97093	+	5.14579i	−0.181478	+	0.314329i
$269$	9.38483	−	16.2550i	0.572203	−	0.991085i	−0.424136	−	0.905598i	$-0.639422\pi$
$269$	9.38483	−	16.2550i	0.572203	−	0.991085i	0.996339	−	0.0854864i	$-0.0272444\pi$
$270$	−3.02156	−	6.78093i	−0.183886	−	0.412674i
$271$	3.40017	+	5.88927i	0.206546	+	0.357747i	0.950624	−	0.310345i	$-0.100444\pi$
$271$	3.40017	+	5.88927i	0.206546	+	0.357747i	−0.744078	+	0.668092i	$0.767111\pi$
$272$	−6.53389	−	11.3170i	−0.396175	−	0.686196i
$273$	0.0307275	−	0.104693i	0.00185971	−	0.00633631i
$274$	−5.83252	+	10.1022i	−0.352355	+	0.610297i
$275$	3.28621			0.198166
$276$	0.0265993	−	0.125203i	0.00160109	−	0.00753631i
$277$	−26.4680			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$277$	−26.4680			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$278$	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	$0.664353\pi$
$282$	4.41791	−	20.7951i	0.263083	−	1.23833i
$283$	−4.29852	−	7.44526i	−0.255521	−	0.442575i	0.709516	−	0.704689i	$-0.248914\pi$
$283$	−4.29852	−	7.44526i	−0.255521	−	0.442575i	−0.965037	+	0.262114i	$0.915580\pi$
$284$	2.07277	+	3.59014i	0.122996	+	0.213036i
$285$	−1.41283	+	6.65018i	−0.0836888	+	0.393923i
$286$	−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
$290$	−9.22775			−0.541872
$291$	0.757251	−	3.56438i	0.0443908	−	0.208947i
$292$	−0.565905			−0.0331171
$293$	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	$-0.0183036\pi$
$294$	−8.37718	−	10.2421i	−0.488567	−	0.597334i
$295$	1.35496	+	2.34685i	0.0788886	+	0.136639i
$296$	15.7752	+	27.3234i	0.916913	+	1.58814i
$297$	−3.05293	+	4.20471i	−0.177149	+	0.243982i
$298$	7.60598	−	13.1739i	0.440602	−	0.763146i
$299$	0.00108747	−	0.00188356i	6.28901e−5	−	0.000108929i
$300$	−0.956905	+	4.50415i	−0.0552469	+	0.260047i
$301$	9.27821	+	0.707866i	0.534787	+	0.0408007i
$302$	−3.33557	+	5.77738i	−0.191941	+	0.332451i
$303$	19.8800	+	17.8964i	1.14208	+	1.02812i
$304$	5.17979			0.297082
$305$	−0.370995	+	0.642582i	−0.0212431	+	0.0367942i
$306$	−20.0328	+	14.5609i	−1.14520	+	0.832394i
$307$	28.3664			1.61895			0.809477	−	0.587152i	$-0.199751\pi$
$307$	28.3664			1.61895			0.809477	+	0.587152i	$0.199751\pi$
$308$	2.13418	+	0.162824i	0.121606	+	0.00927777i
$309$	−24.5682	−	22.1167i	−1.39764	−	1.25818i
$310$	2.68095			0.152268
$311$	−12.8170	−	22.1996i	−0.726784	−	1.25883i	−0.958236	−	0.285980i	$-0.907681\pi$
$311$	−12.8170	−	22.1996i	−0.726784	−	1.25883i	0.231452	−	0.972846i	$-0.425652\pi$
$312$	0.120230	−	0.0390786i	0.00680667	−	0.00221239i
$313$	12.2638	−	21.2416i	0.693192	−	1.20064i	−0.277594	−	0.960698i	$-0.589537\pi$
$313$	12.2638	−	21.2416i	0.693192	−	1.20064i	0.970786	−	0.239945i	$-0.0771295\pi$
$314$	6.39827			0.361075
$315$	9.14447	+	4.93432i	0.515232	+	0.278017i
$316$	5.64265			0.317424
$317$	1.36272	−	2.36029i	0.0765377	−	0.132567i	−0.825216	−	0.564817i	$-0.808947\pi$
$317$	1.36272	−	2.36029i	0.0765377	−	0.132567i	0.901754	+	0.432250i	$0.142280\pi$
$318$	−0.660568	+	3.10929i	−0.0370428	+	0.174360i
$319$	3.22945	+	5.59358i	0.180815	+	0.313180i
$320$	−10.5890			−0.591943
$321$	−1.81455	+	8.54108i	−0.101278	+	0.476717i
$322$	−0.114120	−	0.237790i	−0.00635963	−	0.0132515i
$323$	22.6804			1.26197
$324$	−4.87409	−	5.40878i	−0.270783	−	0.300488i
$325$	−0.0391216	+	0.0677607i	−0.00217008	+	0.00375869i
$326$	14.5449			0.805568
$327$	29.0760	−	9.45065i	1.60791	−	0.522622i
$328$	10.8638	−	18.8166i	0.599852	−	1.03897i
$329$	12.8746	+	26.8268i	0.709801	+	1.47901i
$330$	2.35336	−	0.764920i	0.129548	−	0.0421075i
$331$	−3.56355	+	6.17226i	−0.195871	+	0.339258i	−0.947186	−	0.320686i	$-0.896087\pi$
$331$	−3.56355	+	6.17226i	−0.195871	+	0.339258i	0.751315	+	0.659944i	$0.229420\pi$
$332$	0.988275	−	1.71174i	0.0542387	−	0.0939441i
$333$	24.9753	−	18.1534i	1.36864	−	0.994801i
$334$	−3.56198	−	6.16953i	−0.194903	−	0.337582i
$335$	−4.80759	−	8.32700i	−0.262667	−	0.454952i
$336$	2.22950	−	7.59624i	0.121629	−	0.414409i
$337$	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	$-0.138603\pi$
$338$	−14.1867			−0.771656
$339$	24.3456	−	7.91313i	1.32227	−	0.429782i
$340$	−8.01109			−0.434462
$341$	−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
$345$	0.153939	+	0.138579i	0.00828780	+	0.00746084i
$346$	−8.38042	−	14.5153i	−0.450534	−	0.780348i
$347$	−13.2551	−	22.9586i	−0.711574	−	1.23248i	−0.964266	−	0.264935i	$-0.914649\pi$
$347$	−13.2551	−	22.9586i	−0.711574	−	1.23248i	0.252693	−	0.967547i	$-0.418684\pi$
$348$	−8.60706	+	2.79758i	−0.461387	+	0.149966i
$349$	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
$353$	−13.9621			−0.743127			−0.371563	−	0.928408i	$-0.621178\pi$
$353$	−13.9621			−0.743127			−0.371563	+	0.928408i	$0.621178\pi$
$354$	−2.90809	−	2.61792i	−0.154563	−	0.139141i
$355$	−6.70837			−0.356043
$356$	6.52757	−	11.3061i	0.345960	−	0.599221i
$357$	9.76213	−	33.2610i	0.516667	−	1.76036i
$358$	2.27902	+	3.94737i	0.120450	+	0.208625i
$359$	14.6388	+	25.3552i	0.772608	+	1.33820i	0.936129	+	0.351657i	$0.114382\pi$
$359$	14.6388	+	25.3552i	0.772608	+	1.33820i	−0.163521	+	0.986540i	$0.552285\pi$
$360$	1.26092	+	11.9733i	0.0664561	+	0.631047i
$361$	5.00499	−	8.66890i	0.263421	−	0.456258i
$362$	−0.866573	+	1.50095i	−0.0455461	+	0.0788881i
$363$	−1.28728	−	1.15884i	−0.0675648	−	0.0608232i
$364$	−0.0287644	+	0.0420678i	−0.00150766	+	0.00220495i
$365$	0.457877	−	0.793067i	0.0239664	−	0.0415110i
$366$	0.222642	−	1.04798i	0.0116377	−	0.0547786i
$367$	−18.6399			−0.972994			−0.486497	−	0.873682i	$-0.661726\pi$
$367$	−18.6399			−0.972994			−0.486497	+	0.873682i	$0.661726\pi$
$368$	0.0789038	−	0.136665i	0.00411315	−	0.00712418i
$369$	−19.4265	−	8.64446i	−1.01130	−	0.450013i
$370$	−14.7039			−0.764420
$371$	−1.92502	−	4.01115i	−0.0999421	−	0.208248i
$372$	2.50062	−	0.812784i	0.129651	−	0.0421409i
$373$	−17.2354			−0.892414			−0.446207	−	0.894930i	$-0.647225\pi$
$373$	−17.2354			−0.892414			−0.446207	+	0.894930i	$0.647225\pi$
$374$	−4.12760	−	7.14921i	−0.213433	−	0.369677i
$375$	−13.9640	−	12.5706i	−0.721096	−	0.649145i
$376$	−17.2388	+	29.8584i	−0.889022	+	1.53983i
$377$	−0.153784			−0.00792027
$378$	−14.7595	−	2.69430i	−0.759145	−	0.138580i
$379$	11.0945			0.569888			0.284944	−	0.958544i	$-0.408025\pi$
$379$	11.0945			0.569888			0.284944	+	0.958544i	$0.408025\pi$
$380$	1.58771	−	2.75000i	0.0814480	−	0.141072i
$381$	19.7868	+	17.8124i	1.01371	+	0.912558i
$382$	−9.75557	−	16.8971i	−0.499138	−	0.864533i
$383$	−0.461888			−0.0236014			−0.0118007	−	0.999930i	$-0.503756\pi$
$383$	−0.461888			−0.0236014			−0.0118007	+	0.999930i	$0.503756\pi$
$384$	0.553323	−	0.179848i	0.0282366	−	0.00917783i
$385$	−1.95497	+	2.85913i	−0.0996343	+	0.145715i
$386$	3.34416			0.170213
$387$	8.53473	−	6.20351i	0.433845	−	0.315342i
$388$	−0.850985	+	1.47395i	−0.0432022	+	0.0748285i
$389$	19.4521			0.986261			0.493130	−	0.869955i	$-0.335853\pi$
$389$	19.4521			0.986261			0.493130	+	0.869955i	$0.335853\pi$
$390$	−0.0122439	+	0.0576319i	−0.000619993	+	0.00291830i
$391$	0.345490	−	0.598406i	0.0174722	−	0.0302627i
$392$	7.78598	+	19.9965i	0.393252	+	1.00998i
$393$	9.32416	+	8.39378i	0.470342	+	0.423410i
$394$	7.93025	−	13.7356i	0.399520	−	0.691989i
$395$	−4.56551	+	7.90769i	−0.229716	+	0.397879i
$396$	1.96317	−	1.42694i	0.0986529	−	0.0717063i
$397$	−11.2575	−	19.4986i	−0.564999	−	0.978607i	−0.997050	−	0.0767579i	$-0.975543\pi$
$397$	−11.2575	−	19.4986i	−0.564999	−	0.978607i	0.432051	−	0.901849i	$-0.357790\pi$
$398$	−1.69255	−	2.93159i	−0.0848401	−	0.146947i
$399$	9.48291	+	9.94308i	0.474739	+	0.497777i
$400$	−2.83856	+	4.91652i	−0.141928	+	0.245826i
$401$	2.81074			0.140361			0.0701807	−	0.997534i	$-0.477642\pi$
$401$	2.81074			0.140361			0.0701807	+	0.997534i	$0.477642\pi$
$402$	10.3184	+	9.28878i	0.514633	+	0.463282i
$403$	0.0446791			0.00222563
$404$	−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
$408$	38.1971	−	12.4153i	1.89104	−	0.614649i
$409$	−1.78276	−	3.08782i	−0.0881516	−	0.152683i	0.818578	−	0.574395i	$-0.194763\pi$
$409$	−1.78276	−	3.08782i	−0.0881516	−	0.152683i	−0.906730	+	0.421712i	$0.861429\pi$
$410$	5.06302	+	8.76940i	0.250045	+	0.433090i
$411$	−13.7595	−	12.3866i	−0.678705	−	0.610984i
$412$	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
$416$	−0.101090			−0.00495632
$417$	−21.5761	+	7.01295i	−1.05659	+	0.343426i
$418$	3.27219			0.160048
$419$	−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	$0.181890\pi$
$420$	−3.34953	−	3.51206i	−0.163440	−	0.171371i
$421$	−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
$423$	30.8262	+	13.7171i	1.49882	+	0.666950i
$424$	2.57755	−	4.46444i	0.125177	−	0.216813i
$425$	−12.4290	+	21.5276i	−0.602893	+	1.04424i
$426$	9.21188	−	2.99416i	0.446317	−	0.145068i
$427$	0.648822	+	1.35195i	0.0313987	+	0.0654252i
$428$	2.03916	−	3.53193i	0.0985665	−	0.170722i
$429$	0.0392197	−	0.0127477i	0.00189355	−	0.000615464i
$430$	−5.02472			−0.242314
$431$	−18.4567	+	31.9680i	−0.889030	+	1.53985i	−0.0480063	+	0.998847i	$0.515287\pi$
$431$	−18.4567	+	31.9680i	−0.889030	+	1.53985i	−0.841024	+	0.540998i	$0.818047\pi$
$432$	−3.65364	−	8.19945i	−0.175786	−	0.394496i
$433$	−41.3779			−1.98849			−0.994247	−	0.107116i	$-0.965838\pi$
$433$	−41.3779			−1.98849			−0.994247	+	0.107116i	$0.965838\pi$
$434$	3.05824	−	4.47266i	0.146800	−	0.214695i
$435$	3.04347	−	14.3256i	0.145923	−	0.686859i
$436$	−14.2799			−0.683883
$437$	0.136945	+	0.237196i	0.00655097	+	0.0113466i
$438$	−0.274782	+	1.29340i	−0.0131296	+	0.0618010i
$439$	2.44011	−	4.22640i	0.116460	−	0.201715i	−0.801902	−	0.597455i	$-0.796179\pi$
$439$	2.44011	−	4.22640i	0.116460	−	0.201715i	0.918363	+	0.395740i	$0.129512\pi$
$440$	−4.01316			−0.191320
$441$	18.6633	−	9.62709i	0.888729	−	0.458433i
$442$	0.196553			0.00934906
$443$	−3.08430	+	5.34216i	−0.146539	+	0.253814i	−0.929946	−	0.367696i	$-0.880147\pi$
$443$	−3.08430	+	5.34216i	−0.146539	+	0.253814i	0.783407	+	0.621509i	$0.213480\pi$
$444$	−13.7149	+	4.45778i	−0.650879	+	0.211557i
$445$	10.5630	+	18.2956i	0.500734	+	0.867297i
$446$	12.5508			0.594296
$447$	17.9433	+	16.1529i	0.848687	+	0.764004i
$448$	−12.0791	+	17.6657i	−0.570686	+	0.834627i
$449$	14.9384			0.704988			0.352494	−	0.935814i	$-0.385334\pi$
$449$	14.9384			0.704988			0.352494	+	0.935814i	$0.385334\pi$
$450$	9.82978	+	4.37409i	0.463380	+	0.206197i
$451$	3.54383	−	6.13809i	0.166872	−	0.289032i
$452$	−11.9567			−0.562396
$453$	−7.86895	−	7.08378i	−0.369716	−	0.332825i
$454$	5.63564	−	9.76121i	0.264494	−	0.458116i
$455$	−0.0356810	−	0.0743482i	−0.00167275	−	0.00348550i
$456$	−3.30841	+	15.5727i	−0.154930	+	0.729256i
$457$	5.17503	−	8.96341i	0.242078	−	0.419291i	−0.719228	−	0.694774i	$-0.755504\pi$
$457$	5.17503	−	8.96341i	0.242078	−	0.419291i	0.961306	+	0.275483i	$0.0888378\pi$
$458$	1.51901	−	2.63101i	0.0709789	−	0.122939i
$459$	−15.9979	−	35.9023i	−0.746719	−	1.67578i
$460$	−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	$0.905693\pi$
$462$	1.40842	−	4.79870i	0.0655257	−	0.223256i
$463$	−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	$0.331269\pi$
$464$	−11.1581			−0.518003
$465$	−0.884224	+	4.16204i	−0.0410049	+	0.193010i
$466$	6.89783			0.319536
$467$	−20.1402	−	34.8839i	−0.931979	−	1.61423i	−0.779935	−	0.625861i	$-0.784748\pi$
$467$	−20.1402	−	34.8839i	−0.931979	−	1.61423i	−0.152044	−	0.988374i	$-0.548586\pi$
$468$	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
$471$	−2.11026	+	9.93298i	−0.0972356	+	0.457687i
$472$	3.17289	+	5.49560i	0.146044	+	0.252955i
$473$	1.75851	+	3.04583i	0.0808565	+	0.140047i
$474$	2.73986	−	12.8965i	0.125846	−	0.592356i
$475$	−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
$479$	0.858402			0.0392214			0.0196107	−	0.999808i	$-0.493757\pi$
$479$	0.858402			0.0392214			0.0196107	+	0.999808i	$0.493757\pi$
$480$	2.00062	−	9.41690i	0.0913153	−	0.429821i
$481$	−0.245046			−0.0111731
$482$	12.5033	−	21.6564i	0.569510	−	0.986420i
$483$	0.406795	−	0.0987374i	0.0185098	−	0.00449271i
$484$	0.404495	+	0.700606i	0.0183861	+	0.0318457i
$485$	−1.37708	−	2.38517i	−0.0625298	−	0.108305i
$486$	−14.7287	+	8.51364i	−0.668106	+	0.386186i
$487$	9.70921	−	16.8168i	0.439966	−	0.762044i	−0.557720	−	0.830029i	$-0.688324\pi$
$487$	9.70921	−	16.8168i	0.439966	−	0.762044i	0.997686	+	0.0679853i	$0.0216571\pi$
$488$	−0.868755	+	1.50473i	−0.0393267	+	0.0681158i
$489$	−4.79716	+	22.5802i	−0.216935	+	1.02111i
$490$	−9.88505	−	1.51716i	−0.446561	−	0.0685383i
$491$	−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	$0.314960\pi$
$492$	7.38108	+	6.64459i	0.332765	+	0.299561i
$493$	−48.8572			−2.20042
$494$	−0.0389547	+	0.0674715i	−0.00175265	+	0.00303569i
$495$	0.411319	+	3.90576i	0.0184874	+	0.175551i
$496$	3.24179			0.145561
$497$	−7.65241	+	11.1916i	−0.343258	+	0.502013i
$498$	−3.43239	−	3.08990i	−0.153809	−	0.138462i
$499$	−15.9982			−0.716177			−0.358088	−	0.933688i	$-0.616571\pi$
$499$	−15.9982			−0.716177			−0.358088	+	0.933688i	$0.616571\pi$
$500$	4.38781	+	7.59991i	0.196229	+	0.339878i
$501$	10.7527	−	3.49497i	0.480394	−	0.156144i
$502$	−0.269404	+	0.466621i	−0.0120241	+	0.0208263i
$503$	−18.1995			−0.811474			−0.405737	−	0.913990i	$-0.632985\pi$
$503$	−18.1995			−0.811474			−0.405737	+	0.913990i	$0.632985\pi$
$504$	21.4135	+	11.5546i	0.953833	+	0.514684i
$505$	20.2172			0.899655
$506$	0.0498452	−	0.0863345i	0.00221589	−	0.00383804i
$507$	4.67902	−	22.0241i	0.207803	−	0.978126i
$508$	−6.21747	−	10.7690i	−0.275856	−	0.477796i
$509$	8.47276			0.375548			0.187774	−	0.982212i	$-0.439873\pi$
$509$	8.47276			0.375548			0.187774	+	0.982212i	$0.439873\pi$
$510$	−3.88989	+	18.3097i	−0.172247	+	0.810766i
$511$	−0.800768	−	1.66855i	−0.0354239	−	0.0738124i
$512$	−17.9266			−0.792250
$513$	15.4950	+	1.62378i	0.684119	+	0.0716918i
$514$	−10.1991	+	17.6654i	−0.449864	+	0.779187i
$515$	−24.9849			−1.10097
$516$	−4.68674	+	1.52334i	−0.206322	+	0.0670615i
$517$	−5.62339	+	9.74000i	−0.247317	+	0.428365i
$518$	−16.7731	+	24.5307i	−0.736970	+	1.07782i
$519$	25.2982	−	8.22276i	1.11047	−	0.360939i
$520$	0.0477759	−	0.0827502i	0.00209511	−	0.00362884i
$521$	2.92490	−	5.06608i	0.128142	−	0.221949i	−0.794815	−	0.606852i	$-0.792432\pi$
$521$	2.92490	−	5.06608i	0.128142	−	0.221949i	0.922957	+	0.384903i	$0.125765\pi$
$522$	2.21471	+	21.0302i	0.0969351	+	0.920466i
$523$	8.51772	+	14.7531i	0.372454	+	0.645109i	0.989942	−	0.141471i	$-0.0451832\pi$
$523$	8.51772	+	14.7531i	0.372454	+	0.645109i	−0.617489	+	0.786580i	$0.711850\pi$
$524$	−2.92987	−	5.07469i	−0.127992	−	0.221689i
$525$	−14.6344	+	3.55206i	−0.638697	+	0.155025i
$526$	8.08477	−	14.0032i	0.352513	−	0.610570i
$527$	14.1946			0.618325
$528$	2.84567	−	0.924936i	0.123842	−	0.0402527i
$529$	−22.9917			−0.999637
$530$	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
$534$	−22.6710	−	20.4088i	−0.981069	−	0.883177i
$535$	3.29980	+	5.71542i	0.142663	+	0.247099i
$536$	−11.2579	−	19.4992i	−0.486266	−	0.842238i
$537$	−6.87974	+	2.23614i	−0.296883	+	0.0964966i
$538$	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	−0.910665	−	0.413145i	$-0.864430\pi$
$541$	−18.9128	−	32.7580i	−0.813126	−	1.40838i	0.0975390	−	0.995232i	$-0.468903\pi$
$542$	−7.42144			−0.318778
$543$	−2.04433	−	1.84035i	−0.0877307	−	0.0789768i
$544$	−32.1162			−1.37697
$545$	11.5540	−	20.0121i	0.494917	−	0.857222i
$546$	0.0821809	+	0.0861688i	0.00351702	+	0.00368768i
$547$	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
$549$	1.55350	+	0.691280i	0.0663016	+	0.0295031i
$550$	−1.79318	+	3.10587i	−0.0764613	+	0.132435i
$551$	9.68299	−	16.7714i	0.412509	−	0.714487i
$552$	0.360477	+	0.324509i	0.0153429	+	0.0138120i
$553$	7.98448	+	16.6372i	0.339534	+	0.707485i
$554$	14.4427	−	25.0156i	0.613613	−	1.06281i
$555$	4.84960	−	22.8270i	0.205854	−	0.968954i
$556$	10.5965			0.449394
$557$	−8.50893	+	14.7379i	−0.360535	+	0.624465i	−0.988049	−	0.154141i	$-0.950739\pi$
$557$	−8.50893	+	14.7379i	−0.360535	+	0.624465i	0.627514	+	0.778605i	$0.284072\pi$
$558$	−0.643443	−	6.10994i	−0.0272391	−	0.258654i
$559$	−0.0837389			−0.00354178
$560$	−2.58891	−	5.39450i	−0.109402	−	0.227959i
$561$	12.4601	−	4.04995i	0.526067	−	0.170989i
$562$	−18.5240			−0.781386
$563$	3.49365	+	6.05119i	0.147240	+	0.255027i	0.930206	−	0.367037i	$-0.119628\pi$
$563$	3.49365	+	6.05119i	0.147240	+	0.255027i	−0.782966	+	0.622064i	$0.786294\pi$
$564$	−11.7124	−	10.5437i	−0.493181	−	0.443971i
$565$	9.67426	−	16.7563i	0.406999	−	0.704943i
$566$	9.38225			0.394366
$567$	9.05067	−	22.0247i	0.380093	−	0.924948i
$568$	−15.7089			−0.659131
$569$	15.5126	−	26.8686i	0.650322	−	1.12639i	−0.332722	−	0.943025i	$-0.607967\pi$
$569$	15.5126	−	26.8686i	0.650322	−	1.12639i	0.983045	−	0.183367i	$-0.0586995\pi$
$570$	−5.51431	−	4.96408i	−0.230969	−	0.207923i
$571$	−8.72601	−	15.1139i	−0.365172	−	0.632496i	0.623632	−	0.781718i	$-0.285656\pi$
$571$	−8.72601	−	15.1139i	−0.365172	−	0.632496i	−0.988804	+	0.149222i	$0.952323\pi$
$572$	−0.0192617			−0.000805372
$573$	29.4495	−	9.57204i	1.23027	−	0.399878i
$574$	20.4056	+	1.55681i	0.851713	+	0.0649801i
$575$	−0.300187			−0.0125186
$576$	2.54141	+	24.1325i	0.105892	+	1.00552i
$577$	−0.967738	+	1.67617i	−0.0402875	+	0.0697799i	−0.885466	−	0.464704i	$-0.846161\pi$
$577$	−0.967738	+	1.67617i	−0.0402875	+	0.0697799i	0.845179	+	0.534484i	$0.179494\pi$
$578$	43.8922			1.82568
$579$	−1.10296	+	5.19162i	−0.0458374	+	0.215757i
$580$	−3.42020	+	5.92395i	−0.142016	+	0.245979i
$581$	6.44546	+	0.491746i	0.267403	+	0.0204011i
$582$	2.95557	+	2.66066i	0.122512	+	0.110288i
$583$	0.840812	−	1.45633i	0.0348229	−	0.0603150i
$584$	1.07221	−	1.85711i	0.0443682	−	0.0768480i
$585$	−0.0854322	−	0.0380159i	−0.00353219	−	0.00157177i
$586$	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	$0.625089\pi$
$588$	−9.68010	+	1.58174i	−0.399201	+	0.0652298i
$589$	−2.81322	+	4.87263i	−0.115917	+	0.200773i
$590$	−2.95742			−0.121755
$591$	18.7082	+	16.8415i	0.769554	+	0.692767i
$592$	−17.7799			−0.730748
$593$	8.56745	+	14.8393i	0.351823	+	0.609375i	0.986569	−	0.163346i	$-0.0522286\pi$
$593$	8.56745	+	14.8393i	0.351823	+	0.609375i	−0.634746	+	0.772721i	$0.718895\pi$
$594$	−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
$597$	5.10937	−	1.66071i	0.209113	−	0.0679684i
$598$	0.00118679	+	0.00205559i	4.85316e−5	+	8.40593e-5i
$599$	7.36316	+	12.7534i	0.300851	+	0.521089i	0.976329	−	0.216291i	$-0.0693961\pi$
$599$	7.36316	+	12.7534i	0.300851	+	0.521089i	−0.675478	+	0.737380i	$0.736063\pi$
$600$	−12.9681	−	11.6742i	−0.529421	−	0.476595i
$601$	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
$605$	−1.30912			−0.0532232
$606$	−27.7621	+	9.02360i	−1.12776	+	0.366559i
$607$	−34.3883			−1.39578			−0.697889	−	0.716206i	$-0.745877\pi$
$607$	−34.3883			−1.39578			−0.697889	+	0.716206i	$0.745877\pi$
$608$	6.36510	−	11.0247i	0.258139	−	0.447109i
$609$	−20.4277	−	21.4190i	−0.827774	−	0.867943i
$610$	−0.404880	−	0.701272i	−0.0163931	−	0.0283937i
$611$	−0.133891	−	0.231905i	−0.00541664	−	0.00938189i
$612$	1.92270	+	18.2574i	0.0777207	+	0.738012i
$613$	−12.7087	+	22.0122i	−0.513301	+	0.889063i	0.486580	+	0.873636i	$0.338244\pi$
$613$	−12.7087	+	22.0122i	−0.513301	+	0.889063i	−0.999881	+	0.0154273i	$0.995089\pi$
$614$	−15.4786	+	26.8097i	−0.624665	+	1.08195i
$615$	−15.2839	+	4.96777i	−0.616306	+	0.200320i
$616$	−4.57792	+	6.69520i	−0.184450	+	0.269757i
$617$	−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	$0.209516\pi$
$618$	34.3091	−	11.1516i	1.38011	−	0.448582i
$619$	35.4401			1.42446			0.712229	−	0.701947i	$-0.247686\pi$
$619$	35.4401			1.42446			0.712229	+	0.701947i	$0.247686\pi$
$620$	0.993676	−	1.72110i	0.0399070	−	0.0691209i
$621$	0.278877	−	0.384089i	0.0111910	−	0.0154130i
$622$	27.9752			1.12170
$623$	42.5723	+	3.24799i	1.70562	+	0.130128i
$624$	−0.0148052	+	0.0696881i	−0.000592683	+	0.00278976i
$625$	2.23022			0.0892087
$626$	13.3839	+	23.1816i	0.534929	+	0.926524i
$627$	−1.07922	+	5.07990i	−0.0431000	+	0.202871i
$628$	2.37147	−	4.10751i	0.0946320	−	0.163907i
$629$	−77.8513			−3.10413
$630$	−9.65338	+	5.95015i	−0.384600	+	0.237060i
$631$	28.5499			1.13656			0.568278	−	0.822837i	$-0.307610\pi$
$631$	28.5499			1.13656			0.568278	+	0.822837i	$0.307610\pi$
$632$	−10.6910	+	18.5173i	−0.425265	+	0.736580i
$633$	−26.4842	+	8.60821i	−1.05265	+	0.342146i
$634$	1.48718	+	2.57587i	0.0590634	+	0.102301i
$635$	20.1224			0.798533
$636$	1.75124	+	1.57650i	0.0694412	+	0.0625123i
$637$	−0.164738	−	0.0252840i	−0.00652716	−	0.00100179i
$638$	−7.04883			−0.279066
$639$	1.61004	+	15.2885i	0.0636923	+	0.604803i
$640$	0.219874	−	0.380834i	0.00869130	−	0.0150538i
$641$	43.9290			1.73509			0.867546	−	0.497357i	$-0.165696\pi$
$641$	43.9290			1.73509			0.867546	+	0.497357i	$0.165696\pi$
$642$	−7.08223	−	6.37556i	−0.279513	−	0.251623i
$643$	−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	$0.276450\pi$
$644$	−0.194952	−	0.0148736i	−0.00768219	−	0.000586100i
$645$	1.65724	−	7.80061i	0.0652537	−	0.307149i
$646$	−12.3759	+	21.4357i	−0.486924	+	0.843378i
$647$	−15.9422	+	27.6128i	−0.626754	+	1.08557i	0.361445	+	0.932393i	$0.382284\pi$
$647$	−15.9422	+	27.6128i	−0.626754	+	1.08557i	−0.988199	+	0.153176i	$0.951050\pi$
$648$	26.9847	−	5.74730i	1.06006	−	0.225775i
$649$	1.03501	+	1.79270i	0.0406279	+	0.0703696i
$650$	−0.0426948	−	0.0739495i	−0.00167463	−	0.00290054i
$651$	5.93491	+	6.22291i	0.232607	+	0.243895i
$652$	5.39097	−	9.33743i	0.211126	−	0.365682i
$653$	−27.8094			−1.08826			−0.544132	−	0.838999i	$-0.683141\pi$
$653$	−27.8094			−1.08826			−0.544132	+	0.838999i	$0.683141\pi$
$654$	−6.93379	+	32.6373i	−0.271133	+	1.27622i
$655$	9.48232			0.370505
$656$	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	$0.898286\pi$
$660$	0.381200	−	1.79431i	0.0148382	−	0.0698432i
$661$	9.54256	+	16.5282i	0.371162	+	0.642872i	0.989745	−	0.142848i	$-0.0456260\pi$
$661$	9.54256	+	16.5282i	0.371162	+	0.642872i	−0.618582	+	0.785720i	$0.712293\pi$
$662$	−3.88903	−	6.73599i	−0.151151	−	0.261802i
$663$	−0.0648264	+	0.305138i	−0.00251765	+	0.0118506i
$664$	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
$668$	−5.28089			−0.204324
$669$	−4.13945	+	19.4844i	−0.160041	+	0.753310i
$670$	10.4934			0.405395
$671$	−0.283393	+	0.490851i	−0.0109403	+	0.0189491i
$672$	−13.4281	−	14.0798i	−0.518002	−	0.543138i
$673$	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
$675$	−10.0326	+	13.8176i	−0.386154	+	0.531838i
$676$	−5.25820	+	9.10748i	−0.202239	+	0.350288i
$677$	24.1609	−	41.8480i	0.928580	−	1.60835i	0.142880	−	0.989740i	$-0.454364\pi$
$677$	24.1609	−	41.8480i	0.928580	−	1.60835i	0.785700	−	0.618608i	$-0.212303\pi$
$678$	−5.80573	+	27.3276i	−0.222968	+	1.04951i
$679$	−5.55006	−	0.423433i	−0.212992	−	0.0162499i
$680$	15.1784	−	26.2898i	0.582066	−	1.00817i
$681$	13.2950	+	11.9684i	0.509467	+	0.458632i
$682$	2.04791			0.0784185
$683$	11.7227	−	20.3042i	0.448555	−	0.776920i	−0.549737	−	0.835338i	$-0.685272\pi$
$683$	11.7227	−	20.3042i	0.448555	−	0.776920i	0.998292	+	0.0584178i	$0.0186056\pi$
$684$	−6.64836	−	2.95841i	−0.254206	−	0.113118i
$685$	−13.9929			−0.534640
$686$	−13.8072	+	14.7607i	−0.527163	+	0.563564i
$687$	3.58351	+	3.22594i	0.136719	+	0.123077i
$688$	−6.07586			−0.231640
$689$	0.0200194	+	0.0346746i	0.000762678	+	0.00132100i
$690$	−0.214974	+	0.0698735i	−0.00818391	+	0.00266004i
$691$	−12.5956	+	21.8163i	−0.479160	+	0.829930i	−0.999714	−	0.0238989i	$-0.992392\pi$
$691$	−12.5956	+	21.8163i	−0.479160	+	0.829930i	0.520554	+	0.853829i	$0.325725\pi$
$692$	−12.4246			−0.472311
$693$	6.98521	+	3.76919i	0.265346	+	0.143180i
$694$	28.9316			1.09823
$695$	−8.57374	+	14.8501i	−0.325220	+	0.563298i
$696$	7.12685	−	33.5461i	0.270143	−	1.27156i
$697$	26.8066	+	46.4305i	1.01537	+	1.75868i
$698$	−25.8878			−0.979866
$699$	−2.27502	+	10.7085i	−0.0860492	+	0.405033i
$700$	7.01337	+	0.535074i	0.265081	+	0.0202239i
$701$	−18.6401			−0.704028			−0.352014	−	0.935995i	$-0.614503\pi$
$701$	−18.6401			−0.704028			−0.352014	+	0.935995i	$0.614503\pi$
$702$	0.134283	+	0.0140720i	0.00506817	+	0.000531115i
$703$	15.4293	−	26.7244i	0.581927	−	1.00793i
$704$	−8.08865			−0.304852
$705$	24.2527	−	7.88292i	0.913409	−	0.296888i
$706$	7.61865	−	13.1959i	0.286732	−	0.496634i
$707$	23.0623	−	33.7286i	0.867348	−	1.26849i
$708$	−2.75849	+	0.896601i	−0.103671	+	0.0336963i
$709$	−6.94034	+	12.0210i	−0.260650	+	0.451459i	−0.966415	−	0.256987i	$-0.917270\pi$
$709$	−6.94034	+	12.0210i	−0.260650	+	0.451459i	0.705765	+	0.708446i	$0.250603\pi$
$710$	3.66053	−	6.34023i	0.137377	−	0.237945i
$711$	19.1175	+	8.50698i	0.716962	+	0.319037i
$712$	24.7352	+	42.8427i	0.926992	+	1.60560i
$713$	0.0857075	+	0.148450i	0.00320977	+	0.00555949i
$714$	26.1089	+	27.3759i	0.977101	+	1.02452i
$715$	0.0155848	−	0.0269936i	0.000582838	−	0.00100950i
$716$	3.37880			0.126272
$717$	32.1342	−	10.4447i	1.20007	−	0.390063i
$718$	−31.9517			−1.19243
$719$	13.3033	+	23.0420i	0.496129	+	0.859320i	0.999990	−	0.00446437i	$-0.00142106\pi$
$719$	13.3033	+	23.0420i	0.496129	+	0.859320i	−0.503861	+	0.863785i	$0.668088\pi$
$720$	−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
$723$	29.4965	+	26.5534i	1.09699	+	0.987530i
$724$	0.642378	+	1.11263i	0.0238738	+	0.0413506i
$725$	10.6127	+	18.3817i	0.394144	+	0.682678i
$726$	1.79767	−	0.584302i	0.0667178	−	0.0216855i
$727$	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
$731$	−26.6039			−0.983980
$732$	−0.590250	−	0.531355i	−0.0218163	−	0.0196394i
$733$	27.5981			1.01936			0.509680	−	0.860364i	$-0.329764\pi$
$733$	27.5981			1.01936			0.509680	+	0.860364i	$0.329764\pi$
$734$	10.1712	−	17.6170i	0.375425	−	0.650255i
$735$	5.61557	−	14.8456i	0.207133	−	0.547589i
$736$	−0.193919	−	0.335878i	−0.00714795	−	0.0123806i
$737$	−3.67239	−	6.36077i	−0.135274	−	0.234302i
$738$	18.7705	−	13.6434i	0.690950	−	0.502221i
$739$	10.8358	−	18.7682i	0.398602	−	0.690400i	−0.594951	−	0.803762i	$-0.702829\pi$
$739$	10.8358	−	18.7682i	0.398602	−	0.690400i	0.993554	+	0.113362i	$0.0361620\pi$
$740$	−5.44990	+	9.43950i	−0.200342	+	0.347003i
$741$	−0.0918980	−	0.0827283i	−0.00337596	−	0.00303910i
$742$	4.84145	+	0.369371i	0.177735	+	0.0135600i
$743$	−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	$0.233285\pi$
$744$	−2.07058	+	9.74620i	−0.0759110	+	0.357313i
$745$	18.2476			0.668541
$746$	9.40478	−	16.2896i	0.344333	−	0.596403i
$747$	5.92897	−	4.30950i	0.216930	−	0.157676i
$748$	−6.11945			−0.223749
$749$	13.2993	+	1.01465i	0.485944	+	0.0370743i
$750$	19.5005	−	6.33829i	0.712056	−	0.231442i
$751$	23.5302			0.858630			0.429315	−	0.903155i	$-0.358755\pi$
$751$	23.5302			0.858630			0.429315	+	0.903155i	$0.358755\pi$
$752$	−9.71473	−	16.8264i	−0.354260	−	0.613596i
$753$	−0.635550	−	0.572134i	−0.0231607	−	0.0208497i
$754$	0.0839148	−	0.145345i	0.00305600	−	0.00529314i
$755$	−8.00243			−0.291238
$756$	−7.20015	+	8.47654i	−0.261867	+	0.308289i
$757$	−34.9128			−1.26893			−0.634463	−	0.772953i	$-0.718779\pi$
$757$	−34.9128			−1.26893			−0.634463	+	0.772953i	$0.718779\pi$
$758$	−6.05392	+	10.4857i	−0.219888	+	0.380858i
$759$	0.117590	+	0.105857i	0.00426824	+	0.00384235i
$760$	6.01641	+	10.4207i	0.218238	+	0.377999i
$761$	−4.68298			−0.169758			−0.0848790	−	0.996391i	$-0.527050\pi$
$761$	−4.68298			−0.169758			−0.0848790	+	0.996391i	$0.527050\pi$
$762$	−27.6319	+	8.98128i	−1.00100	+	0.325357i
$763$	−20.2064	−	42.1039i	−0.731520	−	1.52426i
$764$	−14.4633			−0.523264
$765$	−27.1419	−	12.0777i	−0.981316	−	0.436670i
$766$	0.252037	−	0.436541i	0.00910646	−	0.0157729i
$767$	−0.0492865			−0.00177963
$768$	5.69091	−	26.7871i	0.205353	−	0.966596i
$769$	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	$-0.170541\pi$
$770$	−1.63547	−	3.40782i	−0.0589383	−	0.122809i
$771$	−24.0607	−	21.6599i	−0.866526	−	0.780063i
$772$	1.23949	−	2.14685i	0.0446101	−	0.0772669i
$773$	−2.72867	+	4.72620i	−0.0981435	+	0.169990i	−0.910916	−	0.412591i	$-0.864624\pi$
$773$	−2.72867	+	4.72620i	−0.0981435	+	0.169990i	0.812773	+	0.582581i	$0.197957\pi$
$774$	1.20596	+	11.4514i	0.0433473	+	0.411613i
$775$	−3.08332	−	5.34046i	−0.110756	−	0.191835i
$776$	−3.22468	−	5.58531i	−0.115759	−	0.200501i
$777$	−32.5505	−	34.1300i	−1.16774	−	1.22441i
$778$	−10.6144	+	18.3846i	−0.380544	+	0.659121i
$779$	−21.2512			−0.761403
$780$	0.0324599	+	0.0292211i	0.00116225	+	0.00104628i
$781$	−5.12434			−0.183363
$782$	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
$786$	−13.0210	+	4.23227i	−0.464445	+	0.150960i
$787$	−2.64946	−	4.58899i	−0.0944429	−	0.163580i	0.814933	−	0.579555i	$-0.196774\pi$
$787$	−2.64946	−	4.58899i	−0.0944429	−	0.163580i	−0.909376	+	0.415975i	$0.863440\pi$
$788$	−5.87857	−	10.1820i	−0.209415	−	0.362718i
$789$	19.0728	+	17.1697i	0.679009	+	0.611257i
$790$	−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
$794$	24.5715			0.872008
$795$	−3.62627	+	1.17866i	−0.128611	+	0.0418026i
$796$	−2.50933			−0.0889409
$797$	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	$0.138448\pi$
$798$	−14.5719	+	3.53691i	−0.515841	+	0.125205i
$799$	−42.5371	−	73.6765i	−1.50486	−	2.60649i
$800$	6.97621	+	12.0832i	0.246646	+	0.427204i
$801$	39.1609	−	28.4643i	1.38368	−	1.00574i
$802$	−1.53373	+	2.65649i	−0.0541577	+	0.0938039i
$803$	0.349760	−	0.605802i	0.0123428	−	0.0213783i
$804$	9.78756	−	3.18128i	0.345181	−	0.112195i
$805$	0.178581	−	0.261174i	0.00629415	−	0.00920518i
$806$	−0.0243799	+	0.0422273i	−0.000858746	+	0.00148739i
$807$	−30.9178	+	10.0493i	−1.08836	+	0.353752i
$808$	47.3424			1.66550
$809$	−2.55209	+	4.42036i	−0.0897269	+	0.155411i	−0.907396	−	0.420277i	$-0.861933\pi$
$809$	−2.55209	+	4.42036i	−0.0897269	+	0.155411i	0.817669	+	0.575689i	$0.195266\pi$
$810$	−3.96839	+	12.2305i	−0.139435	+	0.429735i
$811$	26.8877			0.944154			0.472077	−	0.881557i	$-0.343504\pi$
$811$	26.8877			0.944154			0.472077	+	0.881557i	$0.343504\pi$
$812$	5.98148	+	12.4636i	0.209909	+	0.437385i
$813$	2.44772	−	11.5214i	0.0858452	−	0.404073i
$814$	−11.2319			−0.393679
$815$	8.72373	+	15.1100i	0.305579	+	0.529278i
$816$	−4.70362	+	22.1399i	−0.164660	+	0.775053i
$817$	5.27261	−	9.13243i	0.184465	−	0.319503i
$818$	3.89116			0.136051
$819$	−0.160877	+	0.0991615i	−0.00562150	+	0.00346498i
$820$	7.50628			0.262131
$821$	−3.03975	+	5.26499i	−0.106088	+	0.183750i	−0.914182	−	0.405304i	$-0.867166\pi$
$821$	−3.03975	+	5.26499i	−0.106088	+	0.183750i	0.808094	+	0.589053i	$0.200499\pi$
$822$	19.2149	−	6.24548i	0.670197	−	0.217836i
$823$	8.35378	+	14.4692i	0.291195	+	0.504364i	0.974092	−	0.226150i	$-0.0726140\pi$
$823$	8.35378	+	14.4692i	0.291195	+	0.504364i	−0.682898	+	0.730514i	$0.739281\pi$
$824$	−58.5069			−2.03818
$825$	−4.23028	−	3.80818i	−0.147279	−	0.132584i
$826$	−3.37361	+	4.93389i	−0.117383	+	0.171672i
$827$	−6.98944			−0.243047			−0.121523	−	0.992589i	$-0.538778\pi$
$827$	−6.98944			−0.243047			−0.121523	+	0.992589i	$0.538778\pi$
$828$	−0.179330	+	0.130347i	−0.00623215	+	0.00452987i
$829$	25.0777	−	43.4358i	0.870984	−	1.50859i	0.0100031	−	0.999950i	$-0.496816\pi$
$829$	25.0777	−	43.4358i	0.870984	−	1.50859i	0.860981	−	0.508638i	$-0.169851\pi$
$830$	−3.49061			−0.121161
$831$	34.0719	+	30.6721i	1.18194	+	1.06400i
$832$	0.0962936	−	0.166785i	0.00333838	−	0.00578225i
$833$	−52.3374	−	8.03275i	−1.81338	−	0.278318i
$834$	5.14529	−	24.2188i	0.178167	−	0.838630i
$835$	4.27280	−	7.40071i	0.147866	−	0.256112i
$836$	1.21281	−	2.10065i	0.0419460	−	0.0726525i
$837$	9.69757	+	1.01625i	0.335197	+	0.0351267i
$838$	−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	$0.863253\pi$
$840$	17.8717	−	4.33783i	0.616633	−	0.149669i
$841$	−6.35875	+	11.0137i	−0.219267	+	0.379782i
$842$	30.6162			1.05510
$843$	6.10952	−	28.7575i	0.210423	−	0.990460i
$844$	13.0070			0.447719
$845$	−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
$849$	−3.09443	+	14.5654i	−0.106200	+	0.499885i
$850$	−13.5642	−	23.4938i	−0.465247	−	0.805831i
$851$	−0.470070	−	0.814185i	−0.0161138	−	0.0279099i
$852$	1.49215	−	7.02353i	0.0511201	−	0.240622i
$853$	−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
$857$	19.8625			0.678491			0.339246	−	0.940698i	$-0.389828\pi$
$857$	19.8625			0.678491			0.339246	+	0.940698i	$0.389828\pi$
$858$	−0.00935277	+	0.0440234i	−0.000319298	+	0.00150294i
$859$	22.7152			0.775031			0.387515	−	0.921863i	$-0.373333\pi$
$859$	22.7152			0.775031			0.387515	+	0.921863i	$0.373333\pi$
$860$	−1.86238	+	3.22573i	−0.0635065	+	0.109996i
$861$	−9.14698	+	31.1651i	−0.311728	+	1.06211i
$862$	−20.1425	−	34.8878i	−0.686055	−	1.18828i
$863$	14.3526	+	24.8594i	0.488568	+	0.846225i	0.999914	−	0.0131506i	$-0.00418610\pi$
$863$	14.3526	+	24.8594i	0.488568	+	0.846225i	−0.511346	+	0.859375i	$0.670853\pi$
$864$	−21.9414	−	2.29934i	−0.746462	−	0.0782250i
$865$	10.0528	−	17.4120i	0.341805	−	0.592024i
$866$	22.5785	−	39.1072i	0.767250	−	1.32892i
$867$	−14.4764	+	68.1404i	−0.491644	+	2.31417i
$868$	−1.73781	−	3.62106i	−0.0589851	−	0.122907i
$869$	−3.48747	+	6.04047i	−0.118304	+	0.204909i
$870$	11.8787	+	10.6935i	0.402727	+	0.362542i
$871$	0.174876			0.00592545
$872$	27.0558	−	46.8620i	0.916224	−	1.58695i
$873$	−5.10533	+	3.71083i	−0.172789	+	0.125593i
$874$	−0.298906			−0.0101106
$875$	−16.1993	+	23.6914i	−0.547635	+	0.800915i
$876$	0.728479	+	0.655791i	0.0246130	+	0.0221571i
$877$	26.7028			0.901690			0.450845	−	0.892602i	$-0.351123\pi$
$877$	26.7028			0.901690			0.450845	+	0.892602i	$0.351123\pi$
$878$	2.66298	+	4.61241i	0.0898712	+	0.155661i
$879$	−30.9560	+	10.0617i	−1.04412	+	0.339373i
$880$	1.13079	−	1.95858i	0.0381188	−	0.0660238i
$881$	−47.6686			−1.60600			−0.802999	−	0.595981i	$-0.796763\pi$
$881$	−47.6686			−1.60600			−0.802999	+	0.595981i	$0.796763\pi$
$882$	−1.08517	+	22.8923i	−0.0365395	+	0.770824i
$883$	11.2441			0.378395			0.189198	−	0.981939i	$-0.439411\pi$
$883$	11.2441			0.378395			0.189198	+	0.981939i	$0.439411\pi$
$884$	0.0728508	−	0.126181i	0.00245024	−	0.00424394i
$885$	0.975408	−	4.59124i	0.0327880	−	0.154333i
$886$	−3.36600	−	5.83008i	−0.113083	−	0.195866i
$887$	17.0695			0.573136			0.286568	−	0.958060i	$-0.407486\pi$
$887$	17.0695			0.573136			0.286568	+	0.958060i	$0.407486\pi$
$888$	11.3562	−	53.4538i	0.381091	−	1.79379i
$889$	22.9542	−	33.5704i	0.769858	−	1.12591i
$890$	−23.0555			−0.772823
$891$	8.80256	−	1.87480i	0.294897	−	0.0628083i
$892$	4.65185	−	8.05723i	0.155755	−	0.269776i
$893$	33.7216			1.12845
$894$	−25.0575	+	8.14450i	−0.838048	+	0.272393i
$895$	−2.73381	+	4.73510i	−0.0913813	+	0.158277i
$896$	−0.384532	−	0.801246i	−0.0128463	−	0.0267677i
$897$	−0.00358262	+	0.00116447i	−0.000119620	+	3.88804e-5i
$898$	−8.15141	+	14.1187i	−0.272016	+	0.471146i
$899$	6.06013	−	10.4965i	0.202117	−	0.350076i
$900$	6.45138	−	4.68922i	0.215046	−	0.156307i
$901$	6.36017	+	11.0161i	0.211888	+	0.367001i
$902$	3.86750	+	6.69871i	0.128774	+	0.223043i
$903$	−11.1234	−	11.6631i	−0.370163	−	0.388125i
$904$	22.6541	−	39.2380i	0.753464	−	1.30504i
$905$	−2.07901			−0.0691086
$906$	10.9889	−	3.57174i	0.365081	−	0.118663i
$907$	−17.0496			−0.566123			−0.283061	−	0.959102i	$-0.591350\pi$
$907$	−17.0496			−0.566123			−0.283061	+	0.959102i	$0.591350\pi$
$908$	−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	$0.886026\pi$
$912$	−6.66786	−	6.00253i	−0.220795	−	0.198764i
$913$	1.22162	+	2.11590i	0.0404296	+	0.0700261i
$914$	5.64769	+	9.78208i	0.186809	+	0.323562i
$915$	1.22222	−	0.397263i	0.0404055	−	0.0131331i
$916$	−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	0.998407	+	0.0564248i	$0.0179701\pi$
$919$	16.6147	+	28.7775i	0.548069	+	0.949283i	−0.450338	+	0.892858i	$0.648697\pi$
$920$	0.366592			0.0120862
$921$	−36.5155	−	32.8720i	−1.20323	−	1.08317i
$922$	10.5618			0.347835
$923$	0.0610042	−	0.105662i	0.00200798	−	0.00347792i
$924$	−2.55861	−	2.68277i	−0.0841721	−	0.0882567i
$925$	16.9107	+	29.2902i	0.556020	+	0.963055i
$926$	−11.6092	−	20.1078i	−0.381503	−	0.660782i
$927$	5.99651	+	56.9410i	0.196951	+	1.87019i
$928$	−13.7115	+	23.7489i	−0.450101	+	0.779597i
$929$	10.3969	−	18.0080i	0.341111	−	0.590822i	−0.643528	−	0.765423i	$-0.722530\pi$
$929$	10.3969	−	18.0080i	0.341111	−	0.590822i	0.984639	+	0.174600i	$0.0558633\pi$
$930$	−3.45115	−	3.10679i	−0.113168	−	0.101876i
$931$	13.1302	−	16.3741i	0.430323	−	0.536638i
$932$	2.55663	−	4.42821i	0.0837452	−	0.145051i
$933$	−9.22669	+	43.4300i	−0.302068	+	1.42183i
$934$	43.9595			1.43840
$935$	4.95129	−	8.57589i	0.161925	−	0.280462i
$936$	−0.200056	−	0.0890215i	−0.00653902	−	0.00290976i
$937$	−23.5779			−0.770255			−0.385128	−	0.922863i	$-0.625843\pi$
$937$	−23.5779			−0.770255			−0.385128	+	0.922863i	$0.625843\pi$
$938$	11.9701	−	17.5062i	0.390837	−	0.571598i
$939$	−40.4025	+	13.1321i	−1.31849	+	0.428551i
$940$	−11.9111			−0.388496
$941$	−3.90372	−	6.76143i	−0.127257	−	0.220416i	0.795356	−	0.606143i	$-0.207284\pi$
$941$	−3.90372	−	6.76143i	−0.127257	−	0.220416i	−0.922613	+	0.385727i	$0.873951\pi$
$942$	−8.23639	−	7.41455i	−0.268356	−	0.241579i
$943$	−0.323719	+	0.560699i	−0.0105418	+	0.0182589i
$944$	−3.57609			−0.116392
$945$	−6.05345	−	16.9488i	−0.196919	−	0.551345i
$946$	−3.83825			−0.124792
$947$	−14.6959	+	25.4540i	−0.477552	+	0.827144i	−0.999669	−	0.0257296i	$-0.991809\pi$
$947$	−14.6959	+	25.4540i	−0.477552	+	0.827144i	0.522117	+	0.852874i	$0.325142\pi$
$948$	−7.26369	−	6.53891i	−0.235914	−	0.212374i
$949$	0.00832764	+	0.0144239i	0.000270327	+	0.000468219i
$950$	10.7531			0.348876
$951$	−4.48939	+	1.45920i	−0.145579	+	0.0473178i
$952$	−26.5451	−	55.3118i	−0.860331	−	1.79266i
$953$	56.1149			1.81774			0.908870	−	0.417079i	$-0.136946\pi$
$953$	56.1149			1.81774			0.908870	+	0.417079i	$0.136946\pi$
$954$	4.45350	−	3.23705i	0.144187	−	0.104803i
$955$	11.7024	−	20.2691i	0.378680	−	0.655893i
$956$	−15.7819			−0.510422
$957$	2.32482	−	10.9429i	0.0751508	−	0.353735i
$958$	−0.468402	+	0.811296i	−0.0151334	+	0.0262118i
$959$	−15.9620	+	23.3444i	−0.515441	+	0.753832i
$960$	13.6310	+	12.2709i	0.439940	+	0.396042i
$961$	13.7393	−	23.7972i	0.443205	−	0.767653i
$962$	0.133714	−	0.231599i	0.00431110	−	0.00746705i
$963$	12.2336	−	8.89202i	0.394221	−	0.286541i
$964$	−9.26852	−	16.0535i	−0.298519	−	0.517050i
$965$	2.00575	+	3.47407i	0.0645675	+	0.111834i
$966$	−0.128656	+	0.438349i	−0.00413943	+	0.0141036i
$967$	−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	$0.949302\pi$
$968$	−3.06555			−0.0985304
$969$	−29.1960	−	26.2828i	−0.937912	−	0.844326i
$970$	3.00570			0.0965072
$971$	30.6870	+	53.1514i	0.984791	+	1.70571i	0.642860	+	0.765984i	$0.277748\pi$
$971$	30.6870	+	53.1514i	0.984791	+	1.70571i	0.341931	+	0.939725i	$0.388919\pi$
$972$	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
$975$	0.128884	−	0.0418916i	0.00412760	−	0.00134160i
$976$	−0.489577	−	0.847973i	−0.0156710	−	0.0271430i
$977$	9.44690	+	16.3625i	0.302233	+	0.523483i	0.976641	−	0.214875i	$-0.0689345\pi$
$977$	9.44690	+	16.3625i	0.302233	+	0.523483i	−0.674408	+	0.738359i	$0.735601\pi$
$978$	−18.7234	−	16.8552i	−0.598709	−	0.538969i
$979$	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
$983$	−25.6844			−0.819204			−0.409602	−	0.912264i	$-0.634332\pi$
$983$	−25.6844			−0.819204			−0.409602	+	0.912264i	$0.634332\pi$
$984$	−35.7901	+	11.6330i	−1.14095	+	0.370845i
$985$	19.0256			0.606205
$986$	26.6598	−	46.1761i	0.849020	−	1.47055i
$987$	14.5145	−	49.4532i	0.462003	−	1.57411i
$988$	0.0288765	+	0.0500156i	0.000918685	+	0.00159121i
$989$	−0.160635	−	0.278229i	−0.00510791	−	0.00884716i
$990$	−3.91586	−	1.74250i	−0.124454	−	0.0553802i
$991$	−17.4129	+	30.1600i	−0.553139	+	0.958065i	0.444907	+	0.895577i	$0.353237\pi$
$991$	−17.4129	+	30.1600i	−0.553139	+	0.958065i	−0.998046	+	0.0624880i	$0.980096\pi$
$992$	3.98362	−	6.89982i	0.126480	−	0.219070i
$993$	11.7399	−	3.81586i	0.372556	−	0.121093i
$994$	−6.40180	−	13.3394i	−0.203053	−	0.423099i
$995$	2.03032	−	3.51661i	0.0643654	−	0.111484i
$996$	−3.25582	+	1.05825i	−0.103165	+	0.0335319i
$997$	8.48823			0.268825			0.134413	−	0.990925i	$-0.457085\pi$
$997$	8.48823			0.268825			0.134413	+	0.990925i	$0.457085\pi$
$998$	8.72968	−	15.1203i	0.276333	−	0.478623i
$999$	−53.1871	−	5.57370i	−1.68277	−	0.176344i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.k.c.67.14	✓	80	1.1	even	1	trivial
693.2.k.c.331.14	yes	80	63.16	even	3	inner
693.2.l.c.529.27	yes	80	9.7	even	3
693.2.l.c.562.27	yes	80	7.2	even	3

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.545667 + 0.945123i) q^{2} +(-1.28728 - 1.15884i) q^{3} +(0.404495 + 0.700606i) q^{4} -1.30912 q^{5} +(1.79767 - 0.584302i) q^{6} +(-1.49335 + 2.18401i) q^{7} -3.06555 q^{8} +(0.314195 + 2.98350i) q^{9} +(0.714343 - 1.23728i) q^{10} -1.00000 q^{11} +(0.291188 - 1.37062i) q^{12} +(0.0119048 - 0.0206197i) q^{13} +(-1.24929 - 2.60314i) q^{14} +(1.68521 + 1.51705i) q^{15} +(0.863778 - 1.49611i) q^{16} +(3.78216 - 6.55089i) q^{17} +(-2.99122 - 1.33105i) q^{18} +(1.49917 + 2.59664i) q^{19} +(-0.529532 - 0.917176i) q^{20} +(4.45327 - 1.08090i) q^{21} +(0.545667 - 0.945123i) q^{22} +0.0913474 q^{23} +(3.94623 + 3.55247i) q^{24} -3.28621 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} +(-2.35336 + 0.764920i) q^{30} +(0.938259 + 1.62511i) q^{31} +(-2.12288 - 3.67693i) q^{32} +(1.28728 + 1.15884i) 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} -3.27219 q^{38} +(-0.0392197 + 0.0127477i) q^{39} +4.01316 q^{40} +(-3.54383 + 6.13809i) q^{41} +(-1.40842 + 4.79870i) q^{42} +(-1.75851 - 3.04583i) q^{43} +(-0.404495 - 0.700606i) q^{44} +(-0.411319 - 3.90576i) q^{45} +(-0.0498452 + 0.0863345i) q^{46} +(5.62339 - 9.74000i) q^{47} +(-2.84567 + 0.924936i) q^{48} +(-2.53984 - 6.52298i) q^{49} +(1.79318 - 3.10587i) q^{50} +(-12.4601 + 4.04995i) q^{51} +0.0192617 q^{52} +(-0.840812 + 1.45633i) q^{53} +(2.30809 + 5.17977i) q^{54} +1.30912 q^{55} +(4.57792 - 6.69520i) q^{56} +(1.07922 - 5.07990i) q^{57} +7.04883 q^{58} +(-1.03501 - 1.79270i) q^{59} +(-0.381200 + 1.79431i) q^{60} +(0.283393 - 0.490851i) q^{61} -2.04791 q^{62} +(-6.98521 - 3.76919i) q^{63} +8.08865 q^{64} +(-0.0155848 + 0.0269936i) q^{65} +(-1.79767 + 0.584302i) q^{66} +(3.67239 + 6.36077i) q^{67} +6.11945 q^{68} +(-0.117590 - 0.105857i) q^{69} +(1.63547 + 3.40782i) q^{70} +5.12434 q^{71} +(-0.963180 - 9.14606i) q^{72} +(-0.349760 + 0.605802i) q^{73} +11.2319 q^{74} +(4.23028 + 3.80818i) q^{75} +(-1.21281 + 2.10065i) q^{76} +(1.49335 - 2.18401i) q^{77} +(0.00935277 - 0.0440234i) q^{78} +(3.48747 - 6.04047i) q^{79} +(-1.13079 + 1.95858i) q^{80} +(-8.80256 + 1.87480i) q^{81} +(-3.86750 - 6.69871i) q^{82} +(-1.22162 - 2.11590i) q^{83} +(2.55861 + 2.68277i) q^{84} +(-4.95129 + 8.57589i) q^{85} +3.83825 q^{86} +(-2.32482 + 10.9429i) q^{87} +3.06555 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} +(0.675435 - 3.17927i) q^{93} +(6.13700 + 10.6296i) q^{94} +(-1.96259 - 3.39930i) q^{95} +(-1.52822 + 7.19331i) q^{96} +(1.05191 + 1.82196i) q^{97} +(7.55092 + 1.15892i) q^{98} +(-0.314195 - 2.98350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9} + 12 q^{10} - 80 q^{11} - 10 q^{12} + 21 q^{13} - 8 q^{14} - 5 q^{15} - 40 q^{16} - 3 q^{17} + 32 q^{18} + 18 q^{19} - 12 q^{20} + 18 q^{21} - 8 q^{23}+ \cdots - 2 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9 + 12 * q^10 - 80 * q^11 - 10 * q^12 + 21 * q^13 - 8 * q^14 - 5 * q^15 - 40 * q^16 - 3 * q^17 + 32 * q^18 + 18 * q^19 - 12 * q^20 + 18 * q^21 - 8 * q^23 - 14 * q^24 + 80 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 20 * q^30 + 32 * q^31 + 35 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 + 46 * q^38 - 48 * q^39 - 102 * q^40 - 2 * q^41 - 14 * q^42 + 9 * q^43 + 40 * q^44 - 5 * q^45 - 6 * q^46 - 26 * q^47 - 28 * q^48 - 19 * q^49 + 2 * q^50 + 22 * q^51 - 88 * q^52 + 4 * q^53 + 19 * q^54 - 8 * q^55 + 18 * q^56 + 16 * q^57 + 32 * q^58 - 24 * q^59 - 10 * q^60 + 69 * q^61 + 12 * q^62 + 20 * q^63 + 44 * q^64 - 7 * q^65 - 6 * q^66 + 7 * q^67 + 34 * q^68 + 15 * q^69 - 22 * q^70 + 34 * q^71 - 70 * q^72 + 26 * q^73 + 8 * q^74 - 64 * q^75 + 52 * q^76 + q^77 - 60 * q^78 - 5 * q^79 - 47 * q^80 + 46 * q^81 + 60 * q^82 + 4 * q^83 + 29 * q^84 + 13 * q^85 - 38 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 35 * q^93 + 56 * q^94 - 20 * q^95 + 15 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

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