LMFDB - Embedded newform 845.2.n.h.484.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] 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("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,16,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.18
Character	$\chi$	$=$	845.484
Dual form			845.2.n.h.529.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.18027 - 1.25878i) q^{2} +(-2.26868 + 1.30982i) q^{3} +(2.16905 - 3.75690i) q^{4} +(2.23296 + 0.117790i) q^{5} +(-3.29755 + 5.71153i) q^{6} +(1.06580 + 0.615337i) q^{7} -5.88628i q^{8} +(1.93127 - 3.34505i) q^{9} +(5.01673 - 2.55399i) q^{10} +(-1.47403 - 2.55309i) q^{11} +11.3643i q^{12} +3.09829 q^{14} +(-5.22016 + 2.65756i) q^{15} +(-3.07144 - 5.31988i) q^{16} +(5.08291 + 2.93462i) q^{17} -9.72414i q^{18} +(2.38180 - 4.12539i) q^{19} +(5.28593 - 8.13353i) q^{20} -3.22393 q^{21} +(-6.42754 - 3.71094i) q^{22} +(-1.46808 + 0.847597i) q^{23} +(7.70998 + 13.3541i) q^{24} +(4.97225 + 0.526042i) q^{25} +2.25952i q^{27} +(4.62352 - 2.66939i) q^{28} +(2.08553 + 3.61224i) q^{29} +(-8.03607 + 12.3652i) q^{30} +2.50193 q^{31} +(-3.19776 - 1.84623i) q^{32} +(6.68818 + 3.86142i) q^{33} +14.7762 q^{34} +(2.30740 + 1.49957i) q^{35} +(-8.37801 - 14.5111i) q^{36} +(-2.89391 + 1.67080i) q^{37} -11.9926i q^{38} +(0.693346 - 13.1439i) q^{40} +(-4.47978 - 7.75921i) q^{41} +(-7.02903 + 4.05821i) q^{42} +(-0.688986 - 0.397786i) q^{43} -12.7889 q^{44} +(4.70646 - 7.24189i) q^{45} +(-2.13387 + 3.69598i) q^{46} -10.0172i q^{47} +(13.9362 + 8.04606i) q^{48} +(-2.74272 - 4.75053i) q^{49} +(11.5030 - 5.11205i) q^{50} -15.3753 q^{51} +7.14496i q^{53} +(2.84424 + 4.92636i) q^{54} +(-2.99072 - 5.87457i) q^{55} +(3.62205 - 6.27357i) q^{56} +12.4789i q^{57} +(9.09402 + 5.25043i) q^{58} +(0.0174087 - 0.0301528i) q^{59} +(-1.33860 + 25.3760i) q^{60} +(-2.00703 + 3.47628i) q^{61} +(5.45489 - 3.14938i) q^{62} +(4.11667 - 2.37676i) q^{63} +2.98977 q^{64} +19.4427 q^{66} +(-6.25486 + 3.61124i) q^{67} +(22.0502 - 12.7307i) q^{68} +(2.22040 - 3.84585i) q^{69} +(6.91838 + 0.364948i) q^{70} +(-7.10807 + 12.3115i) q^{71} +(-19.6899 - 11.3680i) q^{72} +8.45275i q^{73} +(-4.20633 + 7.28557i) q^{74} +(-11.9695 + 5.31934i) q^{75} +(-10.3325 - 17.8963i) q^{76} -3.62809i q^{77} -7.06674 q^{79} +(-6.23177 - 12.2409i) q^{80} +(2.83423 + 4.90902i) q^{81} +(-19.5342 - 11.2781i) q^{82} +3.50072i q^{83} +(-6.99285 + 12.1120i) q^{84} +(11.0043 + 7.15162i) q^{85} -2.00290 q^{86} +(-9.46278 - 5.46334i) q^{87} +(-15.0282 + 8.67653i) q^{88} +(4.44516 + 7.69924i) q^{89} +(1.14541 - 21.7136i) q^{90} +7.35391i q^{92} +(-5.67608 + 3.27709i) q^{93} +(-12.6095 - 21.8402i) q^{94} +(5.80440 - 8.93130i) q^{95} +9.67292 q^{96} +(-9.26130 - 5.34701i) q^{97} +(-11.9597 - 6.90495i) q^{98} -11.3869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 16 q^{4} - 16 q^{6} + 18 q^{9} - 13 q^{10} - 22 q^{11} - 8 q^{14} - 8 q^{15} + 12 q^{16} + 28 q^{19} + 10 q^{20} + 52 q^{21} + 34 q^{24} - 16 q^{25} - 20 q^{29} - 31 q^{30} + 64 q^{31} - 36 q^{34}+ \cdots - 152 q^{99}+O(q^{100}) $ 36 * q + 16 * q^4 - 16 * q^6 + 18 * q^9 - 13 * q^10 - 22 * q^11 - 8 * q^14 - 8 * q^15 + 12 * q^16 + 28 * q^19 + 10 * q^20 + 52 * q^21 + 34 * q^24 - 16 * q^25 - 20 * q^29 - 31 * q^30 + 64 * q^31 - 36 * q^34 - 10 * q^35 - 32 * q^36 + 6 * q^40 - 52 * q^41 - 100 * q^44 - 5 * q^45 - 30 * q^46 + 44 * q^49 - 29 * q^50 - 80 * q^51 + 90 * q^54 + 20 * q^55 + 20 * q^56 + 76 * q^59 + 86 * q^60 - 8 * q^61 + 136 * q^64 + 16 * q^66 + 30 * q^69 + 92 * q^70 - 72 * q^71 + 30 * q^74 - 13 * q^75 - 4 * q^76 - 32 * q^79 - 73 * q^80 + 30 * q^81 + 78 * q^84 - 29 * q^85 - 60 * q^86 + 94 * q^89 - 140 * q^90 - 128 * q^94 - 41 * q^95 - 36 * q^96 - 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	2.18027	−	1.25878i	1.54168	−	0.890091i	0.542950	−	0.839765i	$-0.317307\pi$
$2$	2.18027	−	1.25878i	1.54168	−	0.890091i	0.998733	−	0.0503256i	$-0.0160259\pi$
$3$	−2.26868	+	1.30982i	−1.30982	+	0.756226i	−0.982066	−	0.188537i	$-0.939626\pi$
$3$	−2.26868	+	1.30982i	−1.30982	+	0.756226i	−0.327755	+	0.944763i	$0.606292\pi$
$4$	2.16905	−	3.75690i	1.08452	−	1.87845i
$5$	2.23296	+	0.117790i	0.998612	+	0.0526773i
$5$	2.23296	+	0.117790i	0.998612	+	0.0526773i
$6$	−3.29755	+	5.71153i	−1.34622	+	2.33172i
$7$	1.06580	+	0.615337i	0.402833	+	0.232576i	0.687706	−	0.725990i	$-0.258618\pi$
$7$	1.06580	+	0.615337i	0.402833	+	0.232576i	−0.284873	+	0.958565i	$0.591951\pi$
$8$		−	5.88628i		−	2.08112i
$9$	1.93127	−	3.34505i	0.643755	−	1.11502i
$10$	5.01673	−	2.55399i	1.58643	−	0.807643i
$11$	−1.47403	−	2.55309i	−0.444435	−	0.769785i	0.553577	−	0.832798i	$-0.313262\pi$
$11$	−1.47403	−	2.55309i	−0.444435	−	0.769785i	−0.998013	+	0.0630132i	$0.979929\pi$
$12$			11.3643i			3.28058i
$13$		0			0
$13$		0			0
$14$	3.09829			0.828054
$15$	−5.22016	+	2.65756i	−1.34784	+	0.686178i
$16$	−3.07144	−	5.31988i	−0.767859	−	1.32997i
$17$	5.08291	+	2.93462i	1.23279	+	0.711750i	0.967610	−	0.252450i	$-0.0812362\pi$
$17$	5.08291	+	2.93462i	1.23279	+	0.711750i	0.265177	+	0.964200i	$0.414570\pi$
$18$		−	9.72414i		−	2.29200i
$19$	2.38180	−	4.12539i	0.546422	−	0.946430i	−0.452094	−	0.891970i	$-0.649323\pi$
$19$	2.38180	−	4.12539i	0.546422	−	0.946430i	0.998516	−	0.0544601i	$-0.0173438\pi$
$20$	5.28593	−	8.13353i	1.18197	−	1.81871i
$21$	−3.22393			−0.703519
$22$	−6.42754	−	3.71094i	−1.37036	−	0.791176i
$23$	−1.46808	+	0.847597i	−0.306116	+	0.176736i	−0.645187	−	0.764025i	$-0.723221\pi$
$23$	−1.46808	+	0.847597i	−0.306116	+	0.176736i	0.339071	+	0.940761i	$0.389887\pi$
$24$	7.70998	+	13.3541i	1.57379	+	2.72589i
$25$	4.97225	+	0.526042i	0.994450	+	0.105208i
$26$		0			0
$27$			2.25952i			0.434845i
$28$	4.62352	−	2.66939i	0.873763	−	0.504467i
$29$	2.08553	+	3.61224i	0.387273	+	0.670776i	0.992082	−	0.125595i	$-0.0400838\pi$
$29$	2.08553	+	3.61224i	0.387273	+	0.670776i	−0.604809	+	0.796371i	$0.706751\pi$
$30$	−8.03607	+	12.3652i	−1.46718	+	2.25757i
$31$	2.50193			0.449360			0.224680	−	0.974433i	$-0.427866\pi$
$31$	2.50193			0.449360			0.224680	+	0.974433i	$0.427866\pi$
$32$	−3.19776	−	1.84623i	−0.565290	−	0.326370i
$33$	6.68818	+	3.86142i	1.16426	+	0.672187i
$34$	14.7762			2.53409
$35$	2.30740	+	1.49957i	0.390022	+	0.253473i
$36$	−8.37801	−	14.5111i	−1.39633	−	2.41852i
$37$	−2.89391	+	1.67080i	−0.475755	+	0.274677i	−0.718646	−	0.695376i	$-0.755238\pi$
$37$	−2.89391	+	1.67080i	−0.475755	+	0.274677i	0.242891	+	0.970054i	$0.421904\pi$
$38$		−	11.9926i		−	1.94546i
$39$		0			0
$40$	0.693346	−	13.1439i	0.109628	−	2.07823i
$41$	−4.47978	−	7.75921i	−0.699624	−	1.21178i	−0.968597	−	0.248637i	$-0.920017\pi$
$41$	−4.47978	−	7.75921i	−0.699624	−	1.21178i	0.268973	−	0.963148i	$-0.413316\pi$
$42$	−7.02903	+	4.05821i	−1.08460	+	0.626196i
$43$	−0.688986	−	0.397786i	−0.105069	−	0.0606619i	0.446544	−	0.894761i	$-0.352654\pi$
$43$	−0.688986	−	0.397786i	−0.105069	−	0.0606619i	−0.551614	+	0.834100i	$0.685988\pi$
$44$	−12.7889			−1.92800
$45$	4.70646	−	7.24189i	0.701597	−	1.07956i
$46$	−2.13387	+	3.69598i	−0.314623	+	0.544942i
$47$		−	10.0172i		−	1.46116i	−0.682827	−	0.730580i	$-0.739250\pi$
$47$		−	10.0172i		−	1.46116i	0.682827	−	0.730580i	$-0.260750\pi$
$48$	13.9362	+	8.04606i	2.01152	+	1.16135i
$49$	−2.74272	−	4.75053i	−0.391817	−	0.678647i
$50$	11.5030	−	5.11205i	1.62677	−	0.722953i
$51$	−15.3753			−2.15298
$52$		0			0
$53$			7.14496i			0.981436i	0.871318	+	0.490718i	$0.163265\pi$
$53$			7.14496i			0.981436i	−0.871318	+	0.490718i	$0.836735\pi$
$54$	2.84424	+	4.92636i	0.387052	+	0.670393i
$55$	−2.99072	−	5.87457i	−0.403268	−	0.792127i
$56$	3.62205	−	6.27357i	0.484017	−	0.838342i
$57$			12.4789i			1.65287i
$58$	9.09402	+	5.25043i	1.19410	+	0.689416i
$59$	0.0174087	−	0.0301528i	0.00226642	−	0.00392555i	−0.864890	−	0.501961i	$-0.832612\pi$
$59$	0.0174087	−	0.0301528i	0.00226642	−	0.00392555i	0.867156	+	0.498036i	$0.165945\pi$
$60$	−1.33860	+	25.3760i	−0.172812	+	3.27602i
$61$	−2.00703	+	3.47628i	−0.256974	+	0.445092i	−0.965430	−	0.260663i	$-0.916059\pi$
$61$	−2.00703	+	3.47628i	−0.256974	+	0.445092i	0.708456	+	0.705755i	$0.249392\pi$
$62$	5.45489	−	3.14938i	0.692771	−	0.399972i
$63$	4.11667	−	2.37676i	0.518651	−	0.299443i
$64$	2.98977			0.373721
$65$		0			0
$66$	19.4427			2.39323
$67$	−6.25486	+	3.61124i	−0.764152	+	0.441184i	−0.830785	−	0.556594i	$-0.812108\pi$
$67$	−6.25486	+	3.61124i	−0.764152	+	0.441184i	0.0666322	+	0.997778i	$0.478775\pi$
$68$	22.0502	−	12.7307i	2.67397	−	1.54382i
$69$	2.22040	−	3.84585i	0.267305	−	0.462986i
$70$	6.91838	+	0.364948i	0.826904	+	0.0436196i
$71$	−7.10807	+	12.3115i	−0.843572	+	1.46111i	0.0432827	+	0.999063i	$0.486218\pi$
$71$	−7.10807	+	12.3115i	−0.843572	+	1.46111i	−0.886855	+	0.462047i	$0.847115\pi$
$72$	−19.6899	−	11.3680i	−2.32048	−	1.33973i
$73$			8.45275i			0.989320i	0.869087	+	0.494660i	$0.164707\pi$
$73$			8.45275i			0.989320i	−0.869087	+	0.494660i	$0.835293\pi$
$74$	−4.20633	+	7.28557i	−0.488976	+	0.846931i
$75$	−11.9695	+	5.31934i	−1.38211	+	0.614225i
$76$	−10.3325	−	17.8963i	−1.18521	−	2.05285i
$77$		−	3.62809i		−	0.413459i
$78$		0			0
$79$	−7.06674			−0.795070			−0.397535	−	0.917587i	$-0.630134\pi$
$79$	−7.06674			−0.795070			−0.397535	+	0.917587i	$0.630134\pi$
$80$	−6.23177	−	12.2409i	−0.696733	−	1.36857i
$81$	2.83423	+	4.90902i	0.314914	+	0.545447i
$82$	−19.5342	−	11.2781i	−2.15720	−	1.24546i
$83$			3.50072i			0.384254i	0.981370	+	0.192127i	$0.0615385\pi$
$83$			3.50072i			0.384254i	−0.981370	+	0.192127i	$0.938462\pi$
$84$	−6.99285	+	12.1120i	−0.762983	+	1.32152i
$85$	11.0043	+	7.15162i	1.19358	+	0.775702i
$86$	−2.00290			−0.215978
$87$	−9.46278	−	5.46334i	−1.01452	−	0.585731i
$88$	−15.0282	+	8.67653i	−1.60201	+	0.924921i
$89$	4.44516	+	7.69924i	0.471186	+	0.816118i	0.999457	−	0.0329581i	$-0.0104928\pi$
$89$	4.44516	+	7.69924i	0.471186	+	0.816118i	−0.528271	+	0.849076i	$0.677159\pi$
$90$	1.14541	−	21.7136i	0.120736	−	2.28882i
$91$		0			0
$92$			7.35391i			0.766698i
$93$	−5.67608	+	3.27709i	−0.588582	+	0.339818i
$94$	−12.6095	−	21.8402i	−1.30057	−	2.25265i
$95$	5.80440	−	8.93130i	0.595519	−	0.916332i
$96$	9.67292			0.987238
$97$	−9.26130	−	5.34701i	−0.940342	−	0.542907i	−0.0502746	−	0.998735i	$-0.516010\pi$
$97$	−9.26130	−	5.34701i	−0.940342	−	0.542907i	−0.890068	+	0.455829i	$0.849343\pi$
$98$	−11.9597	−	6.90495i	−1.20812	−	0.697506i
$99$	−11.3869			−1.14443
$100$	12.7613	−	17.5392i	1.27613	−	1.75392i
$101$	6.45860	+	11.1866i	0.642655	+	1.11311i	0.984838	+	0.173478i	$0.0555005\pi$
$101$	6.45860	+	11.1866i	0.642655	+	1.11311i	−0.342183	+	0.939633i	$0.611166\pi$
$102$	−33.5223	+	19.3541i	−3.31920	+	1.91634i
$103$		−	5.67077i		−	0.558757i	−0.960181	−	0.279379i	$-0.909872\pi$
$103$		−	5.67077i		−	0.558757i	0.960181	−	0.279379i	$-0.0901285\pi$
$104$		0			0
$105$	−7.19891	−	0.379747i	−0.702542	−	0.0370595i
$106$	8.99392	+	15.5779i	0.873567	+	1.51306i
$107$	−9.05030	+	5.22519i	−0.874925	+	0.505138i	−0.868982	−	0.494844i	$-0.835225\pi$
$107$	−9.05030	+	5.22519i	−0.874925	+	0.505138i	−0.00594348	+	0.999982i	$0.501892\pi$
$108$	8.48879	+	4.90101i	0.816834	+	0.471600i
$109$	5.38402			0.515696			0.257848	−	0.966186i	$-0.416987\pi$
$109$	5.38402			0.515696			0.257848	+	0.966186i	$0.416987\pi$
$110$	−13.9154	−	9.04350i	−1.32678	−	0.862264i
$111$	4.37689	−	7.58100i	0.415436	−	0.719557i
$112$		−	7.55987i		−	0.714341i
$113$	−9.24179	−	5.33575i	−0.869395	−	0.501945i	−0.00224782	−	0.999997i	$-0.500716\pi$
$113$	−9.24179	−	5.33575i	−0.869395	−	0.501945i	−0.867147	+	0.498052i	$0.834049\pi$
$114$	15.7082	+	27.2074i	1.47121	+	2.54821i
$115$	−3.37801	+	1.71973i	−0.315001	+	0.160365i
$116$	18.0944			1.68003
$117$		0			0
$118$		−	0.0876548i		−	0.00806928i
$119$	3.61156	+	6.25541i	0.331071	+	0.573433i
$120$	15.6431	+	30.7273i	1.42802	+	2.80501i
$121$	1.15450	−	1.99965i	0.104954	−	0.181786i
$122$			10.1056i			0.914920i
$123$	20.3264	+	11.7354i	1.83277	+	1.05815i
$124$	5.42681	−	9.39951i	0.487342	−	0.844101i
$125$	11.0409	+	1.76031i	0.987527	+	0.157447i
$126$	5.98363	−	10.3639i	0.533064	−	0.923293i
$127$	−6.75006	+	3.89715i	−0.598971	+	0.345816i	−0.768637	−	0.639686i	$-0.779065\pi$
$127$	−6.75006	+	3.89715i	−0.598971	+	0.345816i	0.169666	+	0.985502i	$0.445731\pi$
$128$	12.9140	−	7.45591i	1.14145	−	0.659016i
$129$	2.08412			0.183496
$130$		0			0
$131$	−14.4962			−1.26654			−0.633270	−	0.773931i	$-0.718288\pi$
$131$	−14.4962			−1.26654			−0.633270	+	0.773931i	$0.718288\pi$
$132$	29.0139	−	16.7512i	2.52534	−	1.45801i
$133$	5.07702	−	2.93122i	0.440233	−	0.254169i
$134$	−9.09151	+	15.7470i	−0.785387	+	1.36033i
$135$	−0.266149	+	5.04543i	−0.0229065	+	0.434241i
$136$	17.2740	−	29.9195i	1.48123	−	2.56557i
$137$	−1.96342	−	1.13358i	−0.167747	−	0.0968486i	0.413776	−	0.910379i	$-0.364210\pi$
$137$	−1.96342	−	1.13358i	−0.167747	−	0.0968486i	−0.581523	+	0.813530i	$0.697543\pi$
$138$		−	11.1800i		−	0.951703i
$139$	−5.67890	+	9.83614i	−0.481678	+	0.834291i	−0.999779	−	0.0210287i	$-0.993306\pi$
$139$	−5.67890	+	9.83614i	−0.481678	+	0.834291i	0.518101	+	0.855320i	$0.326639\pi$
$140$	10.6386	−	5.41605i	0.899124	−	0.457740i
$141$	13.1208	+	22.7258i	1.10497	+	1.91386i
$142$			35.7899i			3.00342i
$143$		0			0
$144$	−23.7270			−1.97725
$145$	4.23142	+	8.31165i	0.351400	+	0.690245i
$146$	10.6401	+	18.4293i	0.880585	+	1.52522i
$147$	12.4447	+	7.18495i	1.02642	+	0.592605i
$148$			14.4962i			1.19158i
$149$	1.02850	−	1.78141i	0.0842577	−	0.145939i	−0.820817	−	0.571191i	$-0.806481\pi$
$149$	1.02850	−	1.78141i	0.0842577	−	0.145939i	0.905075	+	0.425253i	$0.139815\pi$
$150$	−19.4007	+	26.6645i	−1.58406	+	2.17715i
$151$	5.25169			0.427376			0.213688	−	0.976902i	$-0.431452\pi$
$151$	5.25169			0.427376			0.213688	+	0.976902i	$0.431452\pi$
$152$	−24.2832	−	14.0199i	−1.96963	−	1.13717i
$153$	19.6329	−	11.3351i	1.58723	−	0.916385i
$154$	−4.56696	−	7.91021i	−0.368016	−	0.637423i
$155$	5.58672	+	0.294703i	0.448737	+	0.0236711i
$156$		0			0
$157$			23.4521i			1.87168i	0.352419	+	0.935842i	$0.385359\pi$
$157$			23.4521i			1.87168i	−0.352419	+	0.935842i	$0.614641\pi$
$158$	−15.4074	+	8.89546i	−1.22575	+	0.707685i
$159$	−9.35862	−	16.2096i	−0.742187	−	1.28551i
$160$	−6.92302	−	4.49923i	−0.547313	−	0.355695i
$161$	−2.08623			−0.164418
$162$	12.3587	+	7.13533i	0.970995	+	0.560604i
$163$	−6.15397	−	3.55300i	−0.482016	−	0.278292i	0.239240	−	0.970960i	$-0.423102\pi$
$163$	−6.15397	−	3.55300i	−0.482016	−	0.278292i	−0.721256	+	0.692668i	$0.756435\pi$
$164$	−38.8674			−3.03503
$165$	14.4796	+	9.41021i	1.12724	+	0.732584i
$166$	4.40663	+	7.63250i	0.342021	+	0.592397i
$167$	17.7006	−	10.2194i	1.36971	−	0.790803i	0.378821	−	0.925470i	$-0.376330\pi$
$167$	17.7006	−	10.2194i	1.36971	−	0.790803i	0.990891	+	0.134667i	$0.0429963\pi$
$168$			18.9770i			1.46410i
$169$		0			0
$170$	32.9946	+	1.74048i	2.53057	+	0.133489i
$171$	−9.19976	−	15.9345i	−0.703524	−	1.21854i
$172$	−2.98889	+	1.72563i	−0.227901	+	0.131578i
$173$	−12.7662	−	7.37059i	−0.970599	−	0.560376i	−0.0711805	−	0.997463i	$-0.522677\pi$
$173$	−12.7662	−	7.37059i	−0.970599	−	0.560376i	−0.899419	+	0.437088i	$0.856010\pi$
$174$	−27.5085			−2.08542
$175$	4.97571	+	3.62026i	0.376128	+	0.273666i
$176$	−9.05475	+	15.6833i	−0.682527	+	1.18217i
$177$			0.0912092i			0.00685570i
$178$	19.3833	+	11.1909i	1.45284	+	0.838796i
$179$	−9.55046	−	16.5419i	−0.713835	−	1.23640i	−0.963407	−	0.268042i	$-0.913623\pi$
$179$	−9.55046	−	16.5419i	−0.713835	−	1.23640i	0.249572	−	0.968356i	$-0.419710\pi$
$180$	−16.9985	−	33.3897i	−1.26699	−	2.48872i
$181$	−12.2161			−0.908012			−0.454006	−	0.890999i	$-0.650006\pi$
$181$	−12.2161			−0.908012			−0.454006	+	0.890999i	$0.650006\pi$
$182$		0			0
$183$		−	10.5154i		−	0.777321i
$184$	4.98920	+	8.64155i	0.367809	+	0.637063i
$185$	−6.65879	+	3.38996i	−0.489564	+	0.249235i
$186$	−8.25025	+	14.2899i	−0.604938	+	1.04778i
$187$		−	17.3028i		−	1.26531i
$188$	−37.6337	−	21.7278i	−2.74472	−	1.58466i
$189$	−1.39037	+	2.40819i	−0.101134	+	0.175170i
$190$	1.41261	−	26.7791i	0.102482	−	1.94276i
$191$	−2.00589	+	3.47430i	−0.145141	+	0.251391i	−0.929426	−	0.369010i	$-0.879697\pi$
$191$	−2.00589	+	3.47430i	−0.145141	+	0.251391i	0.784285	+	0.620401i	$0.213030\pi$
$192$	−6.78282	+	3.91606i	−0.489508	+	0.282618i
$193$	−20.7784	+	11.9964i	−1.49566	+	0.863520i	−0.999988	−	0.00499022i	$-0.998412\pi$
$193$	−20.7784	+	11.9964i	−1.49566	+	0.863520i	−0.495672	+	0.868510i	$0.665078\pi$
$194$	−26.9228			−1.93295
$195$		0			0
$196$	−23.7964			−1.69974
$197$	6.00745	−	3.46840i	0.428013	−	0.247113i	−0.270487	−	0.962724i	$-0.587185\pi$
$197$	6.00745	−	3.46840i	0.428013	−	0.247113i	0.698500	+	0.715610i	$0.253851\pi$
$198$	−24.8266	+	14.3336i	−1.76435	+	1.01865i
$199$	2.89343	−	5.01157i	0.205110	−	0.355261i	−0.745058	−	0.667000i	$-0.767578\pi$
$199$	2.89343	−	5.01157i	0.205110	−	0.355261i	0.950168	+	0.311739i	$0.100911\pi$
$200$	3.09643	−	29.2681i	0.218951	−	2.06957i
$201$	9.46017	−	16.3855i	0.667269	−	1.15574i
$202$	28.1630	+	16.2599i	1.98154	+	1.14404i
$203$			5.13321i			0.360281i
$204$	−33.3498	+	57.7635i	−2.33495	+	4.04426i
$205$	−9.08923	−	17.8537i	−0.634819	−	1.24696i
$206$	−7.13824	−	12.3638i	−0.497345	−	0.861426i
$207$			6.54774i			0.455099i
$208$		0			0
$209$	−14.0433			−0.971397
$210$	−16.1736	+	8.23389i	−1.11608	+	0.568192i
$211$	8.21288	+	14.2251i	0.565398	+	0.979298i	0.997013	+	0.0772399i	$0.0246107\pi$
$211$	8.21288	+	14.2251i	0.565398	+	0.979298i	−0.431615	+	0.902058i	$0.642056\pi$
$212$	26.8429	+	15.4978i	1.84358	+	1.06439i
$213$		−	37.2412i		−	2.55173i
$214$	−13.1547	+	22.7846i	−0.899238	+	1.55753i
$215$	−1.49163	−	0.969398i	−0.101728	−	0.0661124i
$216$	13.3002			0.904963
$217$	2.66655	+	1.53953i	0.181017	+	0.104510i
$218$	11.7386	−	6.77729i	0.795039	−	0.459016i
$219$	−11.0716	−	19.1766i	−0.748149	−	1.29583i
$220$	−28.5572	−	1.50641i	−1.92533	−	0.101562i
$221$		0			0
$222$		−	22.0382i		−	1.47910i
$223$	18.8452	−	10.8803i	1.26197	−	0.728596i	0.288511	−	0.957477i	$-0.406840\pi$
$223$	18.8452	−	10.8803i	1.26197	−	0.728596i	0.973454	+	0.228881i	$0.0735066\pi$
$224$	−2.27211	−	3.93540i	−0.151811	−	0.262945i
$225$	11.3624	−	15.6165i	0.757491	−	1.04110i
$226$	−26.8661			−1.78711
$227$	−13.9555	−	8.05723i	−0.926261	−	0.534777i	−0.0406338	−	0.999174i	$-0.512938\pi$
$227$	−13.9555	−	8.05723i	−0.926261	−	0.534777i	−0.885627	+	0.464397i	$0.846271\pi$
$228$	46.8820	+	27.0674i	3.10484	+	1.79258i
$229$	12.4251			0.821071			0.410536	−	0.911845i	$-0.365342\pi$
$229$	12.4251			0.821071			0.410536	+	0.911845i	$0.365342\pi$
$230$	−5.20021	+	8.00164i	−0.342892	+	0.527612i
$231$	4.75215	+	8.23097i	0.312669	+	0.541558i
$232$	21.2627	−	12.2760i	1.39596	−	0.805959i
$233$		−	9.05571i		−	0.593259i	−0.954993	−	0.296630i	$-0.904137\pi$
$233$		−	9.05571i		−	0.593259i	0.954993	−	0.296630i	$-0.0958626\pi$
$234$		0			0
$235$	1.17993	−	22.3681i	0.0769700	−	1.45913i
$236$	−0.0755206	−	0.130805i	−0.00491597	−	0.00851471i
$237$	16.0322	−	9.25617i	1.04140	−	0.601253i
$238$	15.7484	+	9.09232i	1.02081	+	0.589367i
$239$	21.4642			1.38841			0.694203	−	0.719779i	$-0.255757\pi$
$239$	21.4642			1.38841			0.694203	+	0.719779i	$0.255757\pi$
$240$	30.1713	+	19.6081i	1.94755	+	1.26570i
$241$	−4.53489	+	7.85466i	−0.292118	+	0.505963i	−0.974310	−	0.225210i	$-0.927693\pi$
$241$	−4.53489	+	7.85466i	−0.292118	+	0.505963i	0.682192	+	0.731173i	$0.261027\pi$
$242$		−	5.81304i		−	0.373676i
$243$	−18.7303	−	10.8139i	−1.20155	−	0.693715i
$244$	8.70668	+	15.0804i	0.557388	+	0.965425i
$245$	−5.56483	−	10.9308i	−0.355524	−	0.698345i
$246$	59.0892			3.76739
$247$		0			0
$248$		−	14.7271i		−	0.935171i
$249$	−4.58532	−	7.94200i	−0.290583	−	0.503304i
$250$	26.2880	−	10.0601i	1.66260	−	0.636255i
$251$	−12.7460	+	22.0767i	−0.804519	+	1.39347i	0.112096	+	0.993697i	$0.464244\pi$
$251$	−12.7460	+	22.0767i	−0.804519	+	1.39347i	−0.916615	+	0.399771i	$0.869090\pi$
$252$		−	20.6212i		−	1.29901i
$253$	4.32798	+	2.49876i	0.272098	+	0.157096i
$254$	−9.81129	+	16.9937i	−0.615615	+	1.06628i
$255$	−34.3325	−	1.81106i	−2.14999	−	0.113413i
$256$	15.7809	−	27.3334i	0.986308	−	1.70833i
$257$	21.5622	−	12.4489i	1.34501	−	0.776543i	0.357474	−	0.933923i	$-0.383638\pi$
$257$	21.5622	−	12.4489i	1.34501	−	0.776543i	0.987538	+	0.157380i	$0.0503049\pi$
$258$	4.54393	−	2.62344i	0.282893	−	0.163328i
$259$	−4.11242			−0.255533
$260$		0			0
$261$	16.1108			0.997235
$262$	−31.6057	+	18.2475i	−1.95260	+	1.12734i
$263$	−13.5456	+	7.82053i	−0.835255	+	0.482235i	−0.855648	−	0.517557i	$-0.826841\pi$
$263$	−13.5456	+	7.82053i	−0.835255	+	0.482235i	0.0203936	+	0.999792i	$0.493508\pi$
$264$	22.7294	−	39.3685i	1.39890	−	2.42296i
$265$	−0.841605	+	15.9544i	−0.0516994	+	0.980073i
$266$	7.37951	−	12.7817i	0.452467	−	0.783695i
$267$	−20.1693	−	11.6447i	−1.23434	−	0.712646i
$268$			31.3318i			1.91390i
$269$	11.7696	−	20.3855i	0.717603	−	1.24292i	−0.244344	−	0.969689i	$-0.578573\pi$
$269$	11.7696	−	20.3855i	0.717603	−	1.24292i	0.961947	−	0.273236i	$-0.0880939\pi$
$270$	5.77080	+	11.3354i	0.351200	+	0.689851i
$271$	1.40476	+	2.43312i	0.0853333	+	0.147802i	0.905533	−	0.424275i	$-0.139471\pi$
$271$	1.40476	+	2.43312i	0.0853333	+	0.147802i	−0.820200	+	0.572077i	$0.806138\pi$
$272$		−	36.0540i		−	2.18609i
$273$		0			0
$274$	−5.70772			−0.344816
$275$	−5.98619	−	13.4700i	−0.360981	−	0.812271i
$276$	−9.63231	−	16.6837i	−0.579797	−	1.00424i
$277$	−9.49116	−	5.47972i	−0.570268	−	0.329245i	0.186988	−	0.982362i	$-0.440127\pi$
$277$	−9.49116	−	5.47972i	−0.570268	−	0.329245i	−0.757257	+	0.653118i	$0.773461\pi$
$278$			28.5939i			1.71495i
$279$	4.83190	−	8.36909i	0.289278	−	0.501044i
$280$	8.82687	−	13.5820i	0.527506	−	0.811681i
$281$	5.44514			0.324830			0.162415	−	0.986723i	$-0.448072\pi$
$281$	5.44514			0.324830			0.162415	+	0.986723i	$0.448072\pi$
$282$	57.2136	+	33.0323i	3.40702	+	1.96704i
$283$	5.48229	−	3.16520i	0.325888	−	0.188152i	−0.328126	−	0.944634i	$-0.606417\pi$
$283$	5.48229	−	3.16520i	0.325888	−	0.188152i	0.654014	+	0.756482i	$0.273084\pi$
$284$	30.8355	+	53.4086i	1.82975	+	3.16922i
$285$	−1.46989	+	27.8650i	−0.0870689	+	1.65058i
$286$		0			0
$287$		−	11.0263i		−	0.650862i
$288$	−12.3515	+	7.13111i	−0.727816	+	0.420205i
$289$	8.72400	+	15.1104i	0.513176	+	0.888848i
$290$	19.6882	+	12.7952i	1.15613	+	0.751361i
$291$	28.0145			1.64224
$292$	31.7561	+	18.3344i	1.85839	+	1.07294i
$293$	−5.22629	−	3.01740i	−0.305323	−	0.176278i	0.339509	−	0.940603i	$-0.389739\pi$
$293$	−5.22629	−	3.01740i	−0.305323	−	0.176278i	−0.644832	+	0.764325i	$0.723073\pi$
$294$	36.1770			2.10989
$295$	0.0424247	−	0.0652794i	0.00247006	−	0.00380071i
$296$	9.83479	+	17.0344i	0.571636	+	0.990102i
$297$	5.76875	−	3.33059i	0.334737	−	0.193260i
$298$		−	5.17860i		−	0.299988i
$299$		0			0
$300$	−5.97807	+	56.5059i	−0.345144	+	3.26237i
$301$	−0.489546	−	0.847918i	−0.0282169	−	0.0488732i
$302$	11.4501	−	6.61071i	0.658879	−	0.380404i
$303$	−29.3050	−	16.9192i	−1.68353	−	0.971985i
$304$	−29.2621			−1.67830
$305$	−4.89109	+	7.52599i	−0.280063	+	0.430937i
$306$	28.5367	−	49.4270i	1.63133	−	2.82555i
$307$		−	7.24198i		−	0.413321i	−0.978413	−	0.206661i	$-0.933740\pi$
$307$		−	7.24198i		−	0.413321i	0.978413	−	0.206661i	$-0.0662596\pi$
$308$	−13.6304	−	7.86950i	−0.776662	−	0.448406i
$309$	7.42769	+	12.8651i	0.422547	+	0.731872i
$310$	12.5515	−	6.38992i	0.712879	−	0.362923i
$311$	7.01177			0.397601			0.198800	−	0.980040i	$-0.436295\pi$
$311$	7.01177			0.397601			0.198800	+	0.980040i	$0.436295\pi$
$312$		0			0
$313$		−	16.5018i		−	0.932739i	−0.884590	−	0.466369i	$-0.845562\pi$
$313$		−	16.5018i		−	0.932739i	0.884590	−	0.466369i	$-0.154438\pi$
$314$	29.5211	+	51.1320i	1.66597	+	2.88554i
$315$	9.47232	−	4.82231i	0.533705	−	0.271707i
$316$	−15.3281	+	26.5490i	−0.862273	+	1.49350i
$317$			11.6000i			0.651520i	0.945453	+	0.325760i	$0.105620\pi$
$317$			11.6000i			0.651520i	−0.945453	+	0.325760i	$0.894380\pi$
$318$	−40.8086	−	23.5609i	−2.28843	−	1.32123i
$319$	6.14824	−	10.6491i	0.344235	−	0.596233i
$320$	6.67604	+	0.352165i	0.373202	+	0.0196866i
$321$	13.6881	−	23.7086i	0.763997	−	1.32328i
$322$	−4.54855	+	2.62610i	−0.253481	+	0.146347i
$323$	24.2129	−	13.9793i	1.34724	−	0.777832i
$324$	24.5903			1.36613
$325$		0			0
$326$	−17.8897			−0.990821
$327$	−12.2146	+	7.05211i	−0.675469	+	0.389982i
$328$	−45.6729	+	26.3693i	−2.52186	+	1.45600i
$329$	6.16396	−	10.6763i	0.339830	−	0.588603i
$330$	43.4148	+	2.29016i	2.38991	+	0.126069i
$331$	−1.44641	+	2.50525i	−0.0795017	+	0.137701i	−0.903035	−	0.429567i	$-0.858666\pi$
$331$	−1.44641	+	2.50525i	−0.0795017	+	0.137701i	0.823533	+	0.567268i	$0.192000\pi$
$332$	13.1518	+	7.59322i	0.721801	+	0.416732i
$333$			12.9070i			0.707300i
$334$	25.7280	−	44.5622i	1.40777	−	2.43834i
$335$	−14.3922	+	7.32701i	−0.786332	+	0.400318i
$336$	9.90208	+	17.1509i	0.540203	+	0.935659i
$337$		−	24.6017i		−	1.34014i	−0.742297	−	0.670071i	$-0.766264\pi$
$337$		−	24.6017i		−	1.34014i	0.742297	−	0.670071i	$-0.233736\pi$
$338$		0			0
$339$	27.9555			1.51834
$340$	50.7367	−	25.8298i	2.75159	−	1.40082i
$341$	−3.68791	−	6.38765i	−0.199712	−	0.345911i
$342$	−40.1159	−	23.1609i	−2.16922	−	1.25240i
$343$		−	15.3655i		−	0.829660i
$344$	−2.34148	+	4.05557i	−0.126244	+	0.218662i
$345$	5.41108	−	8.32610i	0.291323	−	0.448262i
$346$	−37.1118			−1.99514
$347$	19.3114	+	11.1494i	1.03669	+	0.598532i	0.918894	−	0.394506i	$-0.129084\pi$
$347$	19.3114	+	11.1494i	1.03669	+	0.598532i	0.117795	+	0.993038i	$0.462417\pi$
$348$	−41.0504	+	23.7005i	−2.20053	+	1.27048i
$349$	0.422153	+	0.731191i	0.0225973	+	0.0391397i	0.877103	−	0.480302i	$-0.159473\pi$
$349$	0.422153	+	0.731191i	0.0225973	+	0.0391397i	−0.854506	+	0.519442i	$0.826140\pi$
$350$	15.4055	+	1.62983i	0.823458	+	0.0871181i
$351$		0			0
$352$			10.8855i			0.580202i
$353$	31.4852	−	18.1780i	1.67579	−	0.967517i	0.711491	−	0.702695i	$-0.248020\pi$
$353$	31.4852	−	18.1780i	1.67579	−	0.967517i	0.964297	−	0.264822i	$-0.0853131\pi$
$354$	0.114812	+	0.198860i	0.00610220	+	0.0105693i
$355$	−17.3222	+	26.6539i	−0.919369	+	1.41464i
$356$	38.5670			2.04405
$357$	−16.3869	−	9.46101i	−0.867289	−	0.500730i
$358$	−41.6451	−	24.0438i	−2.20101	−	1.27076i
$359$	−13.7611			−0.726281			−0.363140	−	0.931734i	$-0.618295\pi$
$359$	−13.7611			−0.726281			−0.363140	+	0.931734i	$0.618295\pi$
$360$	−42.6278	−	27.7035i	−2.24668	−	1.46011i
$361$	−1.84592	−	3.19722i	−0.0971536	−	0.168275i
$362$	−26.6343	+	15.3773i	−1.39987	+	0.808213i
$363$			6.04875i			0.317477i
$364$		0			0
$365$	−0.995650	+	18.8747i	−0.0521147	+	0.987946i
$366$	−13.2366	−	22.9264i	−0.691886	−	1.19838i
$367$	10.6419	−	6.14410i	0.555503	−	0.320720i	−0.195836	−	0.980637i	$-0.562742\pi$
$367$	10.6419	−	6.14410i	0.555503	−	0.320720i	0.751338	+	0.659917i	$0.229409\pi$
$368$	9.01823	+	5.20668i	0.470108	+	0.271417i
$369$	−34.6066			−1.80155
$370$	−10.2507	+	15.7730i	−0.532911	+	0.819997i
$371$	−4.39656	+	7.61507i	−0.228258	+	0.395355i
$372$			28.4326i			1.47416i
$373$	−15.8742	−	9.16497i	−0.821934	−	0.474544i	0.0291487	−	0.999575i	$-0.490720\pi$
$373$	−15.8742	−	9.16497i	−0.821934	−	0.474544i	−0.851083	+	0.525031i	$0.824054\pi$
$374$	−21.7804	−	37.7248i	−1.12624	−	1.95070i
$375$	−27.3539	+	10.4680i	−1.41255	+	0.540566i
$376$	−58.9642			−3.04084
$377$		0			0
$378$			7.00066i			0.360075i
$379$	−11.6509	−	20.1800i	−0.598469	−	1.03658i	−0.993047	−	0.117716i	$-0.962443\pi$
$379$	−11.6509	−	20.1800i	−0.598469	−	1.03658i	0.394579	−	0.918862i	$-0.370891\pi$
$380$	−20.9640	−	41.1789i	−1.07543	−	2.11244i
$381$	10.2091	−	17.6827i	0.523030	−	0.905914i
$382$			10.0999i			0.516754i
$383$	14.9523	+	8.63272i	0.764028	+	0.441112i	0.830740	−	0.556661i	$-0.187918\pi$
$383$	14.9523	+	8.63272i	0.764028	+	0.441112i	−0.0667122	+	0.997772i	$0.521251\pi$
$384$	−19.5318	+	33.8301i	−0.996730	+	1.72639i
$385$	0.427353	−	8.10139i	0.0217799	−	0.412885i
$386$	−30.2016	+	52.3107i	−1.53722	+	2.66255i
$387$	−2.66123	+	1.53646i	−0.135278	+	0.0781028i
$388$	−40.1764	+	23.1958i	−2.03965	+	1.17759i
$389$	−1.50480			−0.0762963			−0.0381482	−	0.999272i	$-0.512146\pi$
$389$	−1.50480			−0.0762963			−0.0381482	+	0.999272i	$0.512146\pi$
$390$		0			0
$391$	−9.94951			−0.503168
$392$	−27.9630	+	16.1444i	−1.41234	+	0.815417i
$393$	32.8872	−	18.9875i	1.65894	−	0.957791i
$394$	8.73190	−	15.1241i	0.439907	−	0.761941i
$395$	−15.7798	−	0.832392i	−0.793967	−	0.0418822i
$396$	−24.6988	+	42.7796i	−1.24116	+	2.14975i
$397$	−4.93431	−	2.84882i	−0.247646	−	0.142978i	0.371040	−	0.928617i	$-0.379001\pi$
$397$	−4.93431	−	2.84882i	−0.247646	−	0.142978i	−0.618686	+	0.785638i	$0.712335\pi$
$398$		−	14.5688i		−	0.730266i
$399$	−7.67874	+	13.3000i	−0.384418	+	0.665831i
$400$	−12.4735	−	28.0675i	−0.623673	−	1.40337i
$401$	−5.90462	−	10.2271i	−0.294863	−	0.510717i	0.680090	−	0.733128i	$-0.261941\pi$
$401$	−5.90462	−	10.2271i	−0.294863	−	0.510717i	−0.974953	+	0.222411i	$0.928607\pi$
$402$		−	47.6330i		−	2.37572i
$403$		0			0
$404$	56.0361			2.78790
$405$	5.75049	+	11.2955i	0.285744	+	0.561279i
$406$	6.46158	+	11.1918i	0.320683	+	0.555439i
$407$	8.53138	+	4.92560i	0.422885	+	0.244153i
$408$			90.5035i			4.48059i
$409$	−3.77414	+	6.53699i	−0.186619	+	0.323234i	−0.944121	−	0.329599i	$-0.893086\pi$
$409$	−3.77414	+	6.53699i	−0.186619	+	0.323234i	0.757502	+	0.652833i	$0.226420\pi$
$410$	−42.2908	−	27.4845i	−2.08859	−	1.35736i
$411$	5.93917			0.292958
$412$	−21.3045	−	12.3002i	−1.04960	−	0.605985i
$413$	0.0371082	−	0.0214244i	0.00182598	−	0.00105423i
$414$	8.24215	+	14.2758i	0.405080	+	0.701619i
$415$	−0.412350	+	7.81697i	−0.0202414	+	0.383720i
$416$		0			0
$417$		−	29.7534i		−	1.45703i
$418$	−30.6182	+	17.6774i	−1.49759	+	0.864631i
$419$	2.02723	+	3.51127i	0.0990367	+	0.171537i	0.911286	−	0.411774i	$-0.135091\pi$
$419$	2.02723	+	3.51127i	0.0990367	+	0.171537i	−0.812249	+	0.583310i	$0.801757\pi$
$420$	−17.0414	+	26.2219i	−0.831538	+	1.27950i
$421$	−2.77948			−0.135464			−0.0677318	−	0.997704i	$-0.521576\pi$
$421$	−2.77948			−0.135464			−0.0677318	+	0.997704i	$0.521576\pi$
$422$	35.8126	+	20.6764i	1.74333	+	1.00651i
$423$	−33.5081	−	19.3459i	−1.62922	−	0.940629i
$424$	42.0573			2.04248
$425$	23.7298	+	17.2655i	1.15106	+	0.837500i
$426$	−46.8784	−	81.1958i	−2.27127	−	3.93395i
$427$	−4.27817	+	2.47000i	−0.207035	+	0.119532i
$428$			45.3347i			2.19134i
$429$		0			0
$430$	−4.47240	−	0.235922i	−0.215678	−	0.0113772i
$431$	16.1767	+	28.0189i	0.779206	+	1.34962i	0.932400	+	0.361428i	$0.117711\pi$
$431$	16.1767	+	28.0189i	0.779206	+	1.34962i	−0.153194	+	0.988196i	$0.548956\pi$
$432$	12.0204	−	6.93997i	0.578331	−	0.333900i
$433$	15.2806	+	8.82226i	0.734339	+	0.423971i	0.820007	−	0.572353i	$-0.193969\pi$
$433$	15.2806	+	8.82226i	0.734339	+	0.423971i	−0.0856687	+	0.996324i	$0.527303\pi$
$434$	7.75172			0.372095
$435$	−20.4865	−	13.3141i	−0.982253	−	0.638360i
$436$	11.6782	−	20.2272i	0.559284	−	0.968708i
$437$			8.07522i			0.386290i
$438$	−48.2781	−	27.8734i	−2.30682	−	1.33184i
$439$	10.1663	+	17.6085i	0.485209	+	0.840407i	0.999856	−	0.0169957i	$-0.00541015\pi$
$439$	10.1663	+	17.6085i	0.485209	+	0.840407i	−0.514646	+	0.857402i	$0.672077\pi$
$440$	−34.5794	+	17.6042i	−1.64851	+	0.839248i
$441$	−21.1877			−1.00894
$442$		0			0
$443$			20.4297i			0.970647i	0.874335	+	0.485323i	$0.161298\pi$
$443$			20.4297i			0.970647i	−0.874335	+	0.485323i	$0.838702\pi$
$444$	−18.9874	−	32.8871i	−0.901101	−	1.56075i
$445$	9.01898	+	17.7157i	0.427541	+	0.839805i
$446$	27.3917	−	47.4438i	1.29703	−	2.24653i
$447$			5.38859i			0.254871i
$448$	3.18648	+	1.83972i	0.150547	+	0.0869184i
$449$	−7.84291	+	13.5843i	−0.370130	+	0.641084i	−0.989585	−	0.143948i	$-0.954020\pi$
$449$	−7.84291	+	13.5843i	−0.370130	+	0.641084i	0.619455	+	0.785032i	$0.287354\pi$
$450$	5.11530	−	48.3509i	0.241138	−	2.27928i
$451$	−13.2066	+	22.8745i	−0.621875	+	1.07712i
$452$	−40.0918	+	23.1470i	−1.88576	+	1.08874i
$453$	−11.9144	+	6.87877i	−0.559787	+	0.323193i
$454$	−40.5691			−1.90400
$455$		0			0
$456$	73.4545			3.43982
$457$	22.8294	−	13.1806i	1.06791	−	0.616561i	0.140304	−	0.990109i	$-0.455192\pi$
$457$	22.8294	−	13.1806i	1.06791	−	0.616561i	0.927611	+	0.373548i	$0.121859\pi$
$458$	27.0900	−	15.6404i	1.26583	−	0.730828i
$459$	−6.63084	+	11.4849i	−0.309501	+	0.536071i
$460$	−0.866218	+	16.4210i	−0.0403876	+	0.765634i
$461$	7.66740	−	13.2803i	0.357107	−	0.618527i	−0.630370	−	0.776295i	$-0.717097\pi$
$461$	7.66740	−	13.2803i	0.357107	−	0.618527i	0.987476	+	0.157768i	$0.0504300\pi$
$462$	20.7219	+	11.9638i	0.964071	+	0.556607i
$463$			14.3752i			0.668074i	0.942560	+	0.334037i	$0.108411\pi$
$463$			14.3752i			0.668074i	−0.942560	+	0.334037i	$0.891589\pi$
$464$	12.8111	−	22.1895i	0.594742	−	1.03012i
$465$	−13.0605	+	6.64903i	−0.605665	+	0.308341i
$466$	−11.3991	−	19.7439i	−0.528054	−	0.914617i
$467$		−	7.66475i		−	0.354683i	−0.984149	−	0.177341i	$-0.943250\pi$
$467$		−	7.66475i		−	0.354683i	0.984149	−	0.177341i	$-0.0567496\pi$
$468$		0			0
$469$	−8.88853			−0.410434
$470$	−25.5839	−	50.2537i	−1.18010	−	2.31803i
$471$	−30.7181	−	53.2053i	−1.41542	−	2.45157i
$472$	−0.177488	−	0.102473i	−0.00816953	−	0.00471668i
$473$			2.34539i			0.107841i
$474$	23.3029	−	40.3619i	1.07034	−	1.85388i
$475$	14.0130	−	19.2596i	0.642962	−	0.883690i
$476$	31.3346			1.43622
$477$	23.9002	+	13.7988i	1.09432	+	0.631804i
$478$	46.7978	−	27.0187i	2.14048	−	1.23581i
$479$	12.1587	+	21.0595i	0.555545	+	0.962233i	0.997861	+	0.0653733i	$0.0208238\pi$
$479$	12.1587	+	21.0595i	0.555545	+	0.962233i	−0.442315	+	0.896860i	$0.645843\pi$
$480$	21.5993	+	1.13937i	0.985868	+	0.0520050i
$481$		0			0
$482$			22.8337i			1.04005i
$483$	4.73299	−	2.73259i	0.215358	−	0.124337i
$484$	−5.00833	−	8.67468i	−0.227651	−	0.394303i
$485$	−20.0503	−	13.0306i	−0.910438	−	0.591688i
$486$	−54.4494			−2.46988
$487$	−24.5743	−	14.1880i	−1.11357	−	0.642918i	−0.173815	−	0.984778i	$-0.555610\pi$
$487$	−24.5743	−	14.1880i	−1.11357	−	0.642918i	−0.939751	+	0.341861i	$0.888943\pi$
$488$	20.4624	+	11.8139i	0.926287	+	0.534792i
$489$	18.6152			0.841807
$490$	−25.8923	−	16.8272i	−1.16970	−	0.760178i
$491$	0.718069	+	1.24373i	0.0324060	+	0.0561289i	0.881774	−	0.471673i	$-0.156350\pi$
$491$	0.718069	+	1.24373i	0.0324060	+	0.0561289i	−0.849368	+	0.527802i	$0.823016\pi$
$492$	88.1776	−	50.9094i	3.97535	−	2.29517i
$493$			24.4809i			1.10257i
$494$		0			0
$495$	−25.4266	−	1.34127i	−1.14284	−	0.0602855i
$496$	−7.68452	−	13.3100i	−0.345045	−	0.597636i
$497$	−15.1515	+	8.74772i	−0.679637	+	0.392389i
$498$	−19.9944	−	11.5438i	−0.895972	−	0.517290i
$499$	−16.7094			−0.748017			−0.374008	−	0.927425i	$-0.622017\pi$
$499$	−16.7094			−0.748017			−0.374008	+	0.927425i	$0.622017\pi$
$500$	30.5615	−	37.6613i	1.36675	−	1.68427i
$501$	−26.7713	+	46.3692i	−1.19605	+	2.07162i
$502$			64.1775i			2.86438i
$503$	27.9180	+	16.1184i	1.24480	+	0.718686i	0.970068	−	0.242835i	$-0.0780774\pi$
$503$	27.9180	+	16.1184i	1.24480	+	0.718686i	0.274732	+	0.961521i	$0.411411\pi$
$504$	−13.9903	−	24.2319i	−0.623176	−	1.07937i
$505$	13.1042	+	25.7401i	0.583127	+	1.14542i
$506$	12.5815			0.559318
$507$		0			0
$508$			33.8124i			1.50018i
$509$	−4.08199	−	7.07022i	−0.180931	−	0.313382i	0.761267	−	0.648439i	$-0.224578\pi$
$509$	−4.08199	−	7.07022i	−0.180931	−	0.313382i	−0.942198	+	0.335057i	$0.891244\pi$
$510$	−77.1338	+	39.2684i	−3.41554	+	1.73884i
$511$	−5.20129	+	9.00891i	−0.230092	+	0.398531i
$512$		−	49.6351i		−	2.19358i
$513$	9.32141	+	5.38172i	0.411550	+	0.237609i
$514$	31.3409	−	54.2840i	1.38239	−	2.39437i
$515$	0.667960	−	12.6626i	0.0294338	−	0.557982i
$516$	4.52055	−	7.82982i	0.199006	−	0.344689i
$517$	−25.5748	+	14.7656i	−1.12478	+	0.649391i
$518$	−8.96617	+	5.17662i	−0.393951	+	0.227448i
$519$	38.6167			1.69508
$520$		0			0
$521$	35.3357			1.54808			0.774042	−	0.633135i	$-0.218232\pi$
$521$	35.3357			1.54808			0.774042	+	0.633135i	$0.218232\pi$
$522$	35.1259	−	20.2800i	1.53742	−	0.887630i
$523$	−26.1104	+	15.0749i	−1.14173	+	0.659177i	−0.946858	−	0.321652i	$-0.895762\pi$
$523$	−26.1104	+	15.0749i	−1.14173	+	0.659177i	−0.194870	+	0.980829i	$0.562429\pi$
$524$	−31.4430	+	54.4608i	−1.37359	+	2.37913i
$525$	−16.0302	−	1.69592i	−0.699614	−	0.0740160i
$526$	−19.6886	+	34.1017i	−0.858465	+	1.48691i
$527$	12.7171	+	7.34222i	0.553966	+	0.319832i
$528$		−	47.4404i		−	2.06458i
$529$	−10.0632	+	17.4299i	−0.437529	+	0.757822i
$530$	18.2482	+	35.8444i	0.792650	+	1.55698i
$531$	−0.0672416	−	0.116466i	−0.00291804	−	0.00505419i
$532$		−	25.4318i		−	1.10261i
$533$		0			0
$534$	−58.6325			−2.53728
$535$	−20.8245	+	10.6016i	−0.900320	+	0.458348i
$536$	21.2568	+	36.8179i	0.918154	+	1.59029i
$537$	43.3338	+	25.0188i	1.86999	+	1.07964i
$538$		−	59.2611i		−	2.55493i
$539$	−8.08568	+	14.0048i	−0.348275	+	0.603230i
$540$	18.3779	+	11.9437i	0.790858	+	0.513973i
$541$	17.5295			0.753650			0.376825	−	0.926284i	$-0.377016\pi$
$541$	17.5295			0.753650			0.376825	+	0.926284i	$0.377016\pi$
$542$	6.12552	+	3.53657i	0.263114	+	0.151909i
$543$	27.7143	−	16.0008i	1.18933	−	0.686662i
$544$	−10.8360	−	18.7684i	−0.464588	−	0.804690i
$545$	12.0223	+	0.634184i	0.514980	+	0.0271655i
$546$		0			0
$547$		−	19.5537i		−	0.836055i	−0.908434	−	0.418028i	$-0.862722\pi$
$547$		−	19.5537i		−	0.836055i	0.908434	−	0.418028i	$-0.137278\pi$
$548$	−8.51752	+	4.91759i	−0.363850	+	0.210069i
$549$	7.75221	+	13.4272i	0.330856	+	0.573060i
$550$	−30.0072	−	21.8329i	−1.27951	−	0.930958i
$551$	19.8692			0.846457
$552$	−22.6378	−	13.0699i	−0.963527	−	0.556293i
$553$	−7.53170	−	4.34843i	−0.320280	−	0.184914i
$554$	−27.5910			−1.17223
$555$	10.6664	−	16.4125i	0.452764	−	0.696674i
$556$	24.6356	+	42.6701i	1.04478	+	1.80962i
$557$	18.6075	−	10.7430i	0.788424	−	0.455197i	−0.0509836	−	0.998699i	$-0.516236\pi$
$557$	18.6075	−	10.7430i	0.788424	−	0.455197i	0.839407	+	0.543503i	$0.182902\pi$
$558$		−	24.3291i		−	1.02993i
$559$		0			0
$560$	0.890478	−	16.8809i	0.0376295	−	0.713349i
$561$	22.6636	+	39.2545i	0.956858	+	1.65733i
$562$	11.8719	−	6.85422i	0.500784	−	0.289128i
$563$	−20.1323	−	11.6234i	−0.848477	−	0.489869i	0.0116595	−	0.999932i	$-0.496289\pi$
$563$	−20.1323	−	11.6234i	−0.848477	−	0.489869i	−0.860137	+	0.510063i	$0.829622\pi$
$564$	113.838			4.79345
$565$	−20.0081	−	13.0031i	−0.841747	−	0.547046i
$566$	7.96857	−	13.8020i	0.334944	−	0.580140i
$567$			6.97602i			0.292965i
$568$	72.4692	+	41.8401i	3.04074	+	1.75557i
$569$	−6.96608	−	12.0656i	−0.292033	−	0.505817i	0.682257	−	0.731112i	$-0.260998\pi$
$569$	−6.96608	−	12.0656i	−0.292033	−	0.505817i	−0.974290	+	0.225296i	$0.927665\pi$
$570$	31.8711	+	62.6034i	1.33493	+	2.62217i
$571$	8.49820			0.355639			0.177819	−	0.984063i	$-0.443096\pi$
$571$	8.49820			0.355639			0.177819	+	0.984063i	$0.443096\pi$
$572$		0			0
$573$		−	10.5094i		−	0.439037i
$574$	−13.8797	−	24.0403i	−0.579326	−	1.00342i
$575$	−7.74554	+	3.44219i	−0.323011	+	0.143549i
$576$	5.77404	−	10.0009i	0.240585	−	0.416705i
$577$			2.02248i			0.0841967i	0.999113	+	0.0420984i	$0.0134043\pi$
$577$			2.02248i			0.0841967i	−0.999113	+	0.0420984i	$0.986596\pi$
$578$	38.0413	+	21.9632i	1.58231	+	0.913547i
$579$	31.4263	−	54.4319i	1.30603	−	2.26211i
$580$	40.4042	+	2.13134i	1.67769	+	0.0884992i
$581$	−2.15412	+	3.73105i	−0.0893680	+	0.154790i
$582$	61.0792	−	35.2641i	2.53181	−	1.46174i
$583$	18.2417	−	10.5319i	0.755494	−	0.436185i
$584$	49.7553			2.05889
$585$		0			0
$586$	−15.1929			−0.627615
$587$	−5.34158	+	3.08396i	−0.220471	+	0.127289i	−0.606168	−	0.795336i	$-0.707294\pi$
$587$	−5.34158	+	3.08396i	−0.220471	+	0.127289i	0.385697	+	0.922625i	$0.373961\pi$
$588$	53.9863	−	31.1690i	2.22636	−	1.28539i
$589$	5.95910	−	10.3215i	0.245540	−	0.425288i
$590$	0.0103249	−	0.195730i	0.000425068	−	0.00805807i
$591$	−9.08597	+	15.7374i	−0.373747	+	0.647349i
$592$	17.7769	+	10.2635i	0.730626	+	0.421827i
$593$		−	16.6286i		−	0.682857i	−0.939908	−	0.341428i	$-0.889089\pi$
$593$		−	16.6286i		−	0.682857i	0.939908	−	0.341428i	$-0.110911\pi$
$594$	8.38495	−	14.5232i	0.344039	−	0.595893i
$595$	7.32766	+	14.3935i	0.300405	+	0.590076i
$596$	−4.46171	−	7.72792i	−0.182759	−	0.316548i
$597$			15.1595i			0.620438i
$598$		0			0
$599$	−26.1127			−1.06694			−0.533468	−	0.845820i	$-0.679112\pi$
$599$	−26.1127			−1.06694			−0.533468	+	0.845820i	$0.679112\pi$
$600$	31.3112	+	70.4556i	1.27827	+	2.87634i
$601$	−12.5282	−	21.6995i	−0.511036	−	0.885140i	−0.999918	−	0.0127903i	$-0.995929\pi$
$601$	−12.5282	−	21.6995i	−0.511036	−	0.885140i	0.488882	−	0.872350i	$-0.337405\pi$
$602$	−2.13468	−	1.23246i	−0.0870031	−	0.0502313i
$603$			27.8971i			1.13606i
$604$	11.3912	−	19.7301i	0.463500	−	0.802805i
$605$	2.81349	−	4.32916i	0.114385	−	0.176005i
$606$	−85.1903			−3.46062
$607$	−1.98746	−	1.14746i	−0.0806685	−	0.0465740i	0.459123	−	0.888373i	$-0.348164\pi$
$607$	−1.98746	−	1.14746i	−0.0806685	−	0.0465740i	−0.539792	+	0.841799i	$0.681497\pi$
$608$	−15.2328	+	8.79468i	−0.617773	+	0.356672i
$609$	−6.72359	−	11.6456i	−0.272454	−	0.471904i
$610$	−1.19034	+	22.5655i	−0.0481955	+	0.913650i
$611$		0			0
$612$		−	98.3451i		−	3.97537i
$613$	−39.8628	+	23.0148i	−1.61004	+	0.929559i	−0.620685	+	0.784060i	$0.713145\pi$
$613$	−39.8628	+	23.0148i	−1.61004	+	0.929559i	−0.989358	+	0.145499i	$0.953521\pi$
$614$	−9.11605	−	15.7895i	−0.367894	−	0.637211i
$615$	44.0057	+	28.5990i	1.77448	+	1.15322i
$616$	−21.3560			−0.860457
$617$	23.4839	+	13.5584i	0.945424	+	0.545841i	0.891657	−	0.452712i	$-0.149544\pi$
$617$	23.4839	+	13.5584i	0.945424	+	0.545841i	0.0537678	+	0.998553i	$0.482877\pi$
$618$	32.3887	+	18.6996i	1.30287	+	0.752210i
$619$	−12.8016			−0.514539			−0.257270	−	0.966340i	$-0.582823\pi$
$619$	−12.8016			−0.514539			−0.257270	+	0.966340i	$0.582823\pi$
$620$	13.2250	−	20.3495i	0.531130	−	0.817257i
$621$	−1.91516	−	3.31716i	−0.0768529	−	0.133113i
$622$	15.2875	−	8.82627i	0.612975	−	0.353901i
$623$			10.9411i			0.438345i
$624$		0			0
$625$	24.4466	+	5.23122i	0.977862	+	0.209249i
$626$	−20.7722	−	35.9784i	−0.830222	−	1.43799i
$627$	31.8598	−	18.3942i	1.27236	−	0.734595i
$628$	88.1073	+	50.8688i	3.51587	+	2.02989i
$629$	−19.6126			−0.782007
$630$	14.5820	−	22.4375i	0.580960	−	0.893931i
$631$	−13.6975	+	23.7248i	−0.545290	+	0.944470i	0.453299	+	0.891359i	$0.350247\pi$
$631$	−13.6975	+	23.7248i	−0.545290	+	0.944470i	−0.998589	+	0.0531111i	$0.983086\pi$
$632$			41.5968i			1.65463i
$633$	−37.2648	−	21.5148i	−1.48114	−	0.855137i
$634$	14.6018	+	25.2911i	0.579912	+	1.00444i
$635$	−15.5317	+	7.90710i	−0.616356	+	0.313784i
$636$	−81.1972			−3.21968
$637$		0			0
$638$		−	30.9571i		−	1.22560i
$639$	27.4551	+	47.5537i	1.08611	+	1.88119i
$640$	29.7148	−	15.1276i	1.17458	−	0.597972i
$641$	14.1300	−	24.4739i	0.558102	−	0.966661i	−0.439553	−	0.898217i	$-0.644863\pi$
$641$	14.1300	−	24.4739i	0.558102	−	0.966661i	0.997655	−	0.0684446i	$-0.0218037\pi$
$642$		−	68.9213i		−	2.72011i
$643$	3.35454	+	1.93674i	0.132290	+	0.0763776i	0.564684	−	0.825307i	$-0.308998\pi$
$643$	3.35454	+	1.93674i	0.132290	+	0.0763776i	−0.432395	+	0.901685i	$0.642331\pi$
$644$	−4.52514	+	7.83777i	−0.178315	+	0.308851i
$645$	4.65376	+	0.245488i	0.183242	+	0.00966609i
$646$	35.1938	−	60.9574i	1.38468	−	2.39834i
$647$	−1.00160	+	0.578277i	−0.0393771	+	0.0227344i	−0.519559	−	0.854434i	$-0.673904\pi$
$647$	−1.00160	+	0.578277i	−0.0393771	+	0.0227344i	0.480182	+	0.877169i	$0.340571\pi$
$648$	28.8959	−	16.6831i	1.13514	−	0.655373i
$649$	−0.102643			−0.00402911
$650$		0			0
$651$	−8.06605			−0.316133
$652$	−26.6965	+	15.4132i	−1.04552	+	0.603629i
$653$	−12.5337	+	7.23634i	−0.490482	+	0.283180i	−0.724774	−	0.688986i	$-0.758056\pi$
$653$	−12.5337	+	7.23634i	−0.490482	+	0.283180i	0.234292	+	0.972166i	$0.424723\pi$
$654$	−17.7541	+	30.7510i	−0.694239	+	1.20246i
$655$	−32.3695	−	1.70751i	−1.26478	−	0.0667179i
$656$	−27.5187	+	47.6638i	−1.07442	+	1.86096i
$657$	28.2749	+	16.3245i	1.10311	+	0.636880i
$658$		−	31.0363i		−	1.20992i
$659$	4.59452	−	7.95793i	0.178977	−	0.309997i	−0.762553	−	0.646925i	$-0.776055\pi$
$659$	4.59452	−	7.95793i	0.178977	−	0.309997i	0.941530	+	0.336928i	$0.109388\pi$
$660$	66.7602	−	33.9873i	2.59864	−	1.32295i
$661$	−10.3254	−	17.8840i	−0.401610	−	0.695608i	0.592311	−	0.805710i	$-0.298216\pi$
$661$	−10.3254	−	17.8840i	−0.401610	−	0.695608i	−0.993920	+	0.110101i	$0.964882\pi$
$662$			7.28282i			0.283055i
$663$		0			0
$664$	20.6062			0.799676
$665$	11.6821	−	5.94728i	0.453011	−	0.230626i
$666$	16.2471	+	28.1407i	0.629561	+	1.09043i
$667$	−6.12345	−	3.53537i	−0.237101	−	0.136890i
$668$		−	88.6657i		−	3.43058i
$669$	−28.5024	+	49.3676i	−1.10197	+	1.90866i
$670$	−22.1558	+	34.0915i	−0.855955	+	1.31707i
$671$	11.8336			0.456833
$672$	10.3094	+	5.95211i	0.397692	+	0.229608i
$673$	−29.0787	+	16.7886i	−1.12090	+	0.647153i	−0.941631	−	0.336647i	$-0.890707\pi$
$673$	−29.0787	+	16.7886i	−1.12090	+	0.647153i	−0.179270	+	0.983800i	$0.557374\pi$
$674$	−30.9681	−	53.6384i	−1.19285	−	2.06607i
$675$	−1.18860	+	11.2349i	−0.0457493	+	0.432432i
$676$		0			0
$677$			26.9980i			1.03762i	0.854890	+	0.518809i	$0.173625\pi$
$677$			26.9980i			1.03762i	−0.854890	+	0.518809i	$0.826375\pi$
$678$	60.9506	−	35.1898i	2.34079	−	1.35146i
$679$	−6.58043	−	11.3976i	−0.252534	−	0.437401i
$680$	42.0965	−	64.7744i	1.61433	−	2.48398i
$681$	42.2141			1.61765
$682$	−16.0813	−	9.28453i	−0.615784	−	0.355523i
$683$	41.1641	+	23.7661i	1.57510	+	0.909385i	0.995528	+	0.0944635i	$0.0301136\pi$
$683$	41.1641	+	23.7661i	1.57510	+	0.909385i	0.579572	+	0.814921i	$0.303220\pi$
$684$	−79.8189			−3.05195
$685$	−4.25073	−	2.76252i	−0.162412	−	0.105551i
$686$	−19.3418	−	33.5009i	−0.738472	−	1.27907i
$687$	−28.1885	+	16.2746i	−1.07546	+	0.620915i
$688$			4.88710i			0.186319i
$689$		0			0
$690$	1.31689	−	24.9645i	0.0501331	−	0.950382i
$691$	1.82941	+	3.16863i	0.0695941	+	0.120540i	0.898723	−	0.438517i	$-0.144496\pi$
$691$	1.82941	+	3.16863i	0.0695941	+	0.120540i	−0.829129	+	0.559058i	$0.811163\pi$
$692$	−55.3812	+	31.9743i	−2.10528	+	1.21548i
$693$	−12.1361	−	7.00680i	−0.461014	−	0.266166i
$694$	56.1386			2.13099
$695$	−13.8394	+	21.2948i	−0.524957	+	0.807759i
$696$	−32.1588	+	55.7006i	−1.21897	+	2.11133i
$697$		−	52.5858i		−	1.99183i
$698$	1.84081	+	1.06279i	0.0696759	+	0.0402274i
$699$	11.8614	+	20.5445i	0.448638	+	0.777063i
$700$	24.3935	−	10.8407i	0.921988	−	0.409741i
$701$	22.4645			0.848471			0.424235	−	0.905552i	$-0.360543\pi$
$701$	22.4645			0.848471			0.424235	+	0.905552i	$0.360543\pi$
$702$		0			0
$703$			15.9180i			0.600359i
$704$	−4.40699	−	7.63314i	−0.166095	−	0.287685i
$705$	26.6213	+	52.2914i	1.00262	+	1.96941i
$706$	45.7641	−	79.2658i	1.72236	−	2.98321i
$707$			15.8969i			0.597864i
$708$	0.342664	+	0.197837i	0.0128781	+	0.00743517i
$709$	−14.5011	+	25.1167i	−0.544602	+	0.943278i	0.454030	+	0.890986i	$0.349986\pi$
$709$	−14.5011	+	25.1167i	−0.544602	+	0.943278i	−0.998632	+	0.0522917i	$0.983347\pi$
$710$	−4.21570	+	79.9176i	−0.158212	+	2.99925i
$711$	−13.6477	+	23.6386i	−0.511831	+	0.886517i
$712$	45.3199	−	26.1655i	1.69844	−	0.980592i
$713$	−3.67304	+	2.12063i	−0.137556	+	0.0794183i
$714$	−47.6372			−1.78278
$715$		0			0
$716$	−82.8616			−3.09668
$717$	−48.6954	+	28.1143i	−1.81856	+	1.04995i
$718$	−30.0028	+	17.3221i	−1.11969	+	0.646456i
$719$	−21.0782	+	36.5086i	−0.786086	+	1.36154i	0.142263	+	0.989829i	$0.454562\pi$
$719$	−21.0782	+	36.5086i	−0.786086	+	1.36154i	−0.928348	+	0.371711i	$0.878771\pi$
$720$	−52.9816	−	2.79481i	−1.97451	−	0.104156i
$721$	3.48943	−	6.04388i	0.129953	−	0.225086i
$722$	−8.04919	−	4.64720i	−0.299560	−	0.172951i
$723$		−	23.7596i		−	0.883629i
$724$	−26.4972	+	45.8945i	−0.984760	+	1.70565i
$725$	8.46958	+	19.0580i	0.314552	+	0.707798i
$726$	7.61404	+	13.1879i	0.282584	+	0.489449i
$727$		−	22.1957i		−	0.823192i	−0.911366	−	0.411596i	$-0.864971\pi$
$727$		−	22.1957i		−	0.823192i	0.911366	−	0.411596i	$-0.135029\pi$
$728$		0			0
$729$	39.6520			1.46859
$730$	21.5883	+	42.4052i	0.799018	+	1.56949i
$731$	−2.33470	−	4.04383i	−0.0863522	−	0.149566i
$732$	−39.5053	−	22.8084i	−1.46016	−	0.843023i
$733$		−	46.0958i		−	1.70259i	−0.524690	−	0.851293i	$-0.675819\pi$
$733$		−	46.0958i		−	1.70259i	0.524690	−	0.851293i	$-0.324181\pi$
$734$	15.4681	−	26.7916i	0.570939	−	0.988895i
$735$	26.9422	+	17.5096i	0.993779	+	0.645851i
$736$	6.25943			0.230726
$737$	18.4396	+	10.6461i	0.679233	+	0.392155i
$738$	−75.4516	+	43.5620i	−2.77741	+	1.60354i
$739$	−20.8277	−	36.0746i	−0.766158	−	1.32702i	−0.939632	−	0.342186i	$-0.888833\pi$
$739$	−20.8277	−	36.0746i	−0.766158	−	1.32702i	0.173474	−	0.984838i	$-0.444501\pi$
$740$	−1.70750	+	32.3694i	−0.0627690	+	1.18992i
$741$		0			0
$742$			22.1372i			0.812682i
$743$	32.6259	−	18.8366i	1.19693	−	0.691046i	0.237058	−	0.971495i	$-0.423817\pi$
$743$	32.6259	−	18.8366i	1.19693	−	0.691046i	0.959869	+	0.280449i	$0.0904834\pi$
$744$	19.2899	+	33.4110i	0.707201	+	1.22491i
$745$	2.50643	−	3.85667i	0.0918284	−	0.141298i
$746$	−46.1467			−1.68955
$747$	11.7101	+	6.76081i	0.428449	+	0.247365i
$748$	−65.0050	−	37.5306i	−2.37682	−	1.37226i
$749$	−12.8610			−0.469931
$750$	−46.4620	+	57.2556i	−1.69655	+	2.09068i
$751$	−10.2668	−	17.7826i	−0.374641	−	0.648897i	0.615632	−	0.788034i	$-0.288901\pi$
$751$	−10.2668	−	17.7826i	−0.374641	−	0.648897i	−0.990273	+	0.139136i	$0.955567\pi$
$752$	−53.2904	+	30.7672i	−1.94330	+	1.12196i
$753$		−	66.7799i		−	2.43359i
$754$		0			0
$755$	11.7268	+	0.618597i	0.426783	+	0.0225130i
$756$	6.03154	+	10.4469i	0.219365	+	0.379952i
$757$	−27.3727	+	15.8037i	−0.994879	+	0.574394i	−0.906729	−	0.421713i	$-0.861429\pi$
$757$	−27.3727	+	15.8037i	−0.994879	+	0.574394i	−0.0881502	+	0.996107i	$0.528096\pi$
$758$	−50.8043	−	29.3319i	−1.84530	−	1.06538i
$759$	−13.0917			−0.475199
$760$	−52.5722	−	34.1663i	−1.90699	−	1.23934i
$761$	−2.54460	+	4.40738i	−0.0922417	+	0.159767i	−0.908454	−	0.417985i	$-0.862737\pi$
$761$	−2.54460	+	4.40738i	−0.0922417	+	0.159767i	0.816212	+	0.577752i	$0.196070\pi$
$762$		−	51.4042i		−	1.86218i
$763$	5.73826	+	3.31299i	0.207739	+	0.119938i
$764$	8.70173	+	15.0718i	0.314817	+	0.545280i
$765$	45.1747	−	22.9982i	1.63329	−	0.831502i
$766$	43.4668			1.57052
$767$		0			0
$768$			82.6808i			2.98348i
$769$	−13.7791	−	23.8662i	−0.496888	−	0.860636i	0.503105	−	0.864225i	$-0.332191\pi$
$769$	−13.7791	−	23.8662i	−0.496888	−	0.860636i	−0.999994	+	0.00358943i	$0.998857\pi$
$770$	−9.26612	−	18.2012i	−0.333928	−	0.655924i
$771$	−32.6117	+	56.4852i	−1.17448	+	2.03427i
$772$			104.083i			3.74603i
$773$	−13.9102	−	8.03108i	−0.500316	−	0.288858i	0.228528	−	0.973537i	$-0.426609\pi$
$773$	−13.9102	−	8.03108i	−0.500316	−	0.288858i	−0.728844	+	0.684680i	$0.759942\pi$
$774$	−3.86813	+	6.69980i	−0.139037	+	0.240819i
$775$	12.4402	+	1.31612i	0.446867	+	0.0472765i
$776$	−31.4740	+	54.5146i	−1.12985	+	1.95696i
$777$	9.32974	−	5.38653i	0.334703	−	0.193241i
$778$	−3.28086	+	1.89421i	−0.117625	+	0.0679107i
$779$	−42.6797			−1.52916
$780$		0			0
$781$	41.9099			1.49965
$782$	−21.6926	+	12.5242i	−0.775726	+	0.447865i
$783$	−8.16193	+	4.71229i	−0.291684	+	0.168404i
$784$	−16.8482	+	29.1819i	−0.601721	+	1.04221i
$785$	−2.76243	+	52.3678i	−0.0985953	+	1.86909i
$786$	47.8020	−	82.7955i	1.70504	−	2.95322i
$787$	19.6503	+	11.3451i	0.700459	+	0.404410i	0.807518	−	0.589842i	$-0.200810\pi$
$787$	19.6503	+	11.3451i	0.700459	+	0.404410i	−0.107059	+	0.994253i	$0.534143\pi$
$788$		−	30.0925i		−	1.07200i
$789$	20.4870	−	35.4845i	0.729357	−	1.26328i
$790$	−35.4519	+	18.0484i	−1.26132	+	0.642133i
$791$	−6.56657	−	11.3736i	−0.233481	−	0.404400i
$792$			67.0267i			2.38169i
$793$		0			0
$794$	−14.3442			−0.509055
$795$	−18.9881	−	37.2978i	−0.673440	−	1.32282i
$796$	−12.5520	−	21.7407i	−0.444893	−	0.770577i
$797$	−41.9519	−	24.2209i	−1.48601	−	0.857950i	−0.486139	−	0.873881i	$-0.661595\pi$
$797$	−41.9519	−	24.2209i	−1.48601	−	0.857950i	−0.999873	+	0.0159318i	$0.994929\pi$
$798$			38.6633i			1.36867i
$799$	29.3967	−	50.9166i	1.03998	−	1.80130i
$800$	−14.9289	−	10.8621i	−0.527816	−	0.384032i
$801$	34.3391			1.21331
$802$	−25.7473	−	14.8652i	−0.909170	−	0.524909i
$803$	21.5806	−	12.4596i	0.761563	−	0.439689i
$804$	−41.0391	−	71.0818i	−1.44734	−	2.50686i
$805$	−4.65848	−	0.245737i	−0.164190	−	0.00866110i
$806$		0			0
$807$			61.6641i			2.17068i
$808$	65.8477	−	38.0172i	2.31651	−	1.33744i
$809$	6.74402	+	11.6810i	0.237107	+	0.410681i	0.959883	−	0.280401i	$-0.0904675\pi$
$809$	6.74402	+	11.6810i	0.237107	+	0.410681i	−0.722776	+	0.691082i	$0.757134\pi$
$810$	26.7562	+	17.3887i	0.940116	+	0.610975i
$811$	8.29712			0.291351			0.145676	−	0.989332i	$-0.453464\pi$
$811$	8.29712			0.291351			0.145676	+	0.989332i	$0.453464\pi$
$812$	19.2850	+	11.1342i	0.676769	+	0.390733i
$813$	−6.37391	−	3.67998i	−0.223543	−	0.129062i
$814$	24.8009			0.869272
$815$	−13.3231	−	8.65859i	−0.466687	−	0.303297i
$816$	47.2243	+	81.7949i	1.65318	+	2.86339i
$817$	−3.28205	+	1.89489i	−0.114824	+	0.0662939i
$818$			19.0032i			0.664431i
$819$		0			0
$820$	−86.7895	−	4.57819i	−3.03082	−	0.159877i
$821$	−2.77763	−	4.81100i	−0.0969401	−	0.167905i	0.813477	−	0.581598i	$-0.197572\pi$
$821$	−2.77763	−	4.81100i	−0.0969401	−	0.167905i	−0.910417	+	0.413693i	$0.864239\pi$
$822$	12.9490	−	7.47610i	0.451648	−	0.260759i
$823$	31.3171	+	18.0809i	1.09164	+	0.630261i	0.934014	−	0.357237i	$-0.116281\pi$
$823$	31.3171	+	18.0809i	1.09164	+	0.630261i	0.157630	+	0.987498i	$0.449615\pi$
$824$	−33.3798			−1.16284
$825$	31.2240	+	22.7182i	1.08708	+	0.790946i
$826$	0.0539373	−	0.0934221i	0.00187672	−	0.00325057i
$827$			44.8578i			1.55986i	0.625867	+	0.779930i	$0.284745\pi$
$827$			44.8578i			1.55986i	−0.625867	+	0.779930i	$0.715255\pi$
$828$	24.5992	+	14.2024i	0.854881	+	0.493566i
$829$	−21.9853	−	38.0796i	−0.763581	−	1.32256i	−0.940994	−	0.338424i	$-0.890106\pi$
$829$	−21.9853	−	38.0796i	−0.763581	−	1.32256i	0.177413	−	0.984137i	$-0.443227\pi$
$830$	8.94081	+	17.5622i	0.310340	+	0.609591i
$831$	28.7098			0.995933
$832$		0			0
$833$		−	32.1954i		−	1.11550i
$834$	−37.4529	−	64.8704i	−1.29689	−	2.24628i
$835$	40.7285	−	20.7347i	1.40947	−	0.717553i
$836$	−30.4606	+	52.7593i	−1.05350	+	1.82472i
$837$			5.65317i			0.195402i
$838$	8.83981	+	5.10367i	0.305366	+	0.176303i
$839$	22.4928	−	38.9587i	0.776539	−	1.34501i	−0.157386	−	0.987537i	$-0.550307\pi$
$839$	22.4928	−	38.9587i	0.776539	−	1.34501i	0.933925	−	0.357468i	$-0.116360\pi$
$840$	−2.23530	+	42.3748i	−0.0771250	+	1.46207i
$841$	5.80115	−	10.0479i	0.200040	−	0.346479i
$842$	−6.06002	+	3.49875i	−0.208842	+	0.120575i
$843$	−12.3533	+	7.13216i	−0.425469	+	0.245645i
$844$	71.2565			2.45275
$845$		0			0
$846$	−97.4088			−3.34898
$847$	2.46092	−	1.42081i	0.0845582	−	0.0488197i
$848$	38.0103	−	21.9453i	1.30528	−	0.753604i
$849$	−8.29170	+	14.3616i	−0.284570	+	0.492890i
$850$	73.4707	+	7.77287i	2.52003	+	0.266607i
$851$	2.83233	−	4.90573i	0.0970909	−	0.168166i
$852$	−139.911	−	80.7779i	−4.79329	−	2.76741i
$853$			22.7812i			0.780012i	0.920812	+	0.390006i	$0.127527\pi$
$853$			22.7812i			0.780012i	−0.920812	+	0.390006i	$0.872473\pi$
$854$	−6.21837	+	10.7705i	−0.212788	+	0.368560i
$855$	−18.6658	−	36.6647i	−0.638357	−	1.25391i
$856$	30.7570	+	53.2726i	1.05125	+	1.82082i
$857$			47.5063i			1.62278i	0.584503	+	0.811391i	$0.301289\pi$
$857$			47.5063i			1.62278i	−0.584503	+	0.811391i	$0.698711\pi$
$858$		0			0
$859$	1.32832			0.0453215			0.0226608	−	0.999743i	$-0.492786\pi$
$859$	1.32832			0.0453215			0.0226608	+	0.999743i	$0.492786\pi$
$860$	−6.87734	+	3.50122i	−0.234515	+	0.119391i
$861$	14.4425	+	25.0151i	0.492199	+	0.852513i
$862$	70.5392	+	40.7258i	2.40258	+	1.38713i
$863$			32.7971i			1.11643i	0.829698	+	0.558213i	$0.188513\pi$
$863$			32.7971i			1.11643i	−0.829698	+	0.558213i	$0.811487\pi$
$864$	4.17159	−	7.22541i	0.141920	−	0.245813i
$865$	−27.6384	−	17.9620i	−0.939733	−	0.610726i
$866$	44.4211			1.50949
$867$	−39.5839	−	22.8538i	−1.34434	−	0.776154i
$868$	11.5677	−	6.67864i	0.392635	−	0.226688i
$869$	10.4166	+	18.0420i	0.353357	+	0.612033i
$870$	−61.4255	−	3.24023i	−2.08252	−	0.109854i
$871$		0			0
$872$		−	31.6919i		−	1.07322i
$873$	−35.7720	+	20.6530i	−1.21070	+	0.698998i
$874$	10.1649	+	17.6061i	0.343833	+	0.595537i
$875$	10.6841	+	8.67001i	0.361190	+	0.293100i
$876$	−96.0593			−3.24554
$877$	10.0505	+	5.80267i	0.339382	+	0.195942i	0.659999	−	0.751267i	$-0.270557\pi$
$877$	10.0505	+	5.80267i	0.339382	+	0.195942i	−0.320617	+	0.947209i	$0.603890\pi$
$878$	44.3304	+	25.5941i	1.49608	+	0.863760i
$879$	15.8090			0.533225
$880$	−22.0662	+	33.9536i	−0.743853	+	1.14458i
$881$	27.4949	+	47.6225i	0.926326	+	1.60444i	0.789415	+	0.613860i	$0.210384\pi$
$881$	27.4949	+	47.6225i	0.926326	+	1.60444i	0.136912	+	0.990583i	$0.456282\pi$
$882$	−46.1948	+	26.6706i	−1.55546	+	0.898046i
$883$		−	37.4501i		−	1.26030i	−0.776475	−	0.630148i	$-0.782994\pi$
$883$		−	37.4501i		−	1.26030i	0.776475	−	0.630148i	$-0.217006\pi$
$884$		0			0
$885$	−0.0107435	+	0.203667i	−0.000361140	+	0.00684618i
$886$	25.7165	+	44.5423i	0.863964	+	1.49643i
$887$	−8.21017	+	4.74014i	−0.275670	+	0.159158i	−0.631462	−	0.775407i	$-0.717545\pi$
$887$	−8.21017	+	4.74014i	−0.275670	+	0.159158i	0.355791	+	0.934565i	$0.384211\pi$
$888$	−44.6239	−	25.7636i	−1.49748	−	0.864571i
$889$	−9.59224			−0.321713
$890$	41.9640	+	27.2721i	1.40664	+	0.914163i
$891$	8.35544	−	14.4720i	0.279918	−	0.484832i
$892$		−	94.3992i		−	3.16072i
$893$	−41.3249	−	23.8590i	−1.38289	−	0.798410i
$894$	6.78304	+	11.7486i	0.226859	+	0.392931i
$895$	−19.3774	−	38.0624i	−0.647714	−	1.27229i
$896$	18.3516			0.613084
$897$		0			0
$898$			39.4900i			1.31780i
$899$	5.21785	+	9.03758i	0.174025	+	0.301420i
$900$	−34.0241	−	76.5602i	−1.13414	−	2.55201i
$901$	−20.9678	+	36.3172i	−0.698537	+	1.20990i
$902$			66.4968i			2.21410i
$903$	2.22124	+	1.28243i	0.0739183	+	0.0426768i
$904$	−31.4078	+	54.3998i	−1.04461	+	1.80931i
$905$	−27.2780	−	1.43893i	−0.906751	−	0.0478316i
$906$	−17.3177	+	29.9952i	−0.575342	+	0.996522i
$907$	−17.1958	+	9.92800i	−0.570977	+	0.329654i	−0.757540	−	0.652789i	$-0.773599\pi$
$907$	−17.1958	+	9.92800i	−0.570977	+	0.329654i	0.186562	+	0.982443i	$0.440265\pi$
$908$	−60.5404	+	34.9530i	−2.00910	+	1.15996i
$909$	49.8931			1.65485
$910$		0			0
$911$	34.4106			1.14007			0.570037	−	0.821619i	$-0.306929\pi$
$911$	34.4106			1.14007			0.570037	+	0.821619i	$0.306929\pi$
$912$	66.3864	−	38.3282i	2.19827	−	1.26917i
$913$	8.93763	−	5.16015i	0.295793	−	0.170776i
$914$	33.1828	−	57.4743i	1.09759	−	1.90108i
$915$	1.23861	−	23.4805i	0.0409472	−	0.776242i
$916$	26.9505	−	46.6797i	0.890471	−	1.54234i
$917$	−15.4500	−	8.92006i	−0.510204	−	0.294566i
$918$			33.3870i			1.10194i
$919$	−6.56666	+	11.3738i	−0.216614	+	0.375187i	−0.953771	−	0.300535i	$-0.902835\pi$
$919$	−6.56666	+	11.3738i	−0.216614	+	0.375187i	0.737157	+	0.675722i	$0.236168\pi$
$920$	10.1228	+	19.8839i	0.333739	+	0.655554i
$921$	9.48570	+	16.4297i	0.312564	+	0.541377i
$922$		−	38.6063i		−	1.27143i
$923$		0			0
$924$	41.2306			1.35639
$925$	−15.2681	+	6.78531i	−0.502013	+	0.223100i
$926$	18.0952	+	31.3419i	0.594647	+	1.02996i
$927$	−18.9690	−	10.9518i	−0.623024	−	0.359703i
$928$		−	15.4014i		−	0.505577i
$929$	16.3707	−	28.3550i	0.537107	−	0.930296i	−0.461951	−	0.886905i	$-0.652851\pi$
$929$	16.3707	−	28.3550i	0.537107	−	0.930296i	0.999058	−	0.0433910i	$-0.0138161\pi$
$930$	−20.1057	+	30.9369i	−0.659292	+	1.01446i
$931$	−26.1304			−0.856390
$932$	−34.0214	−	19.6423i	−1.11441	−	0.643403i
$933$	−15.9074	+	9.18417i	−0.520786	+	0.300676i
$934$	−9.64823	−	16.7112i	−0.315700	−	0.546808i
$935$	2.03810	−	38.6366i	0.0666530	−	1.26355i
$936$		0			0
$937$		−	38.4788i		−	1.25705i	−0.777790	−	0.628524i	$-0.783659\pi$
$937$		−	38.4788i		−	1.25705i	0.777790	−	0.628524i	$-0.216341\pi$
$938$	−19.3794	+	11.1887i	−0.632759	+	0.365324i
$939$	21.6145	+	37.4373i	0.705361	+	1.22172i
$940$	−81.4753	−	52.9503i	−2.65743	−	1.72705i
$941$	−2.78860			−0.0909057			−0.0454528	−	0.998966i	$-0.514473\pi$
$941$	−2.78860			−0.0909057			−0.0454528	+	0.998966i	$0.514473\pi$
$942$	−133.947	−	77.3346i	−4.36425	−	2.51970i
$943$	13.1534	+	7.59410i	0.428332	+	0.247298i
$944$	−0.213879			−0.00696116
$945$	−3.38830	+	5.21362i	−0.110221	+	0.169599i
$946$	2.95233	+	5.11358i	0.0959884	+	0.166257i
$947$	−20.5751	+	11.8790i	−0.668601	+	0.386017i	−0.795547	−	0.605893i	$-0.792816\pi$
$947$	−20.5751	+	11.8790i	−0.668601	+	0.386017i	0.126945	+	0.991910i	$0.459483\pi$
$948$		−	80.3083i		−	2.60829i
$949$		0			0
$950$	6.30862	−	59.6303i	0.204679	−	1.93466i
$951$	−15.1939	−	26.3166i	−0.492696	−	0.853374i
$952$	36.8211	−	21.2587i	1.19338	−	0.688998i
$953$	18.9402	+	10.9351i	0.613532	+	0.354223i	0.774347	−	0.632762i	$-0.218079\pi$
$953$	18.9402	+	10.9351i	0.613532	+	0.354223i	−0.160815	+	0.986985i	$0.551412\pi$
$954$	69.4786			2.24945
$955$	−4.88831	+	7.52171i	−0.158182	+	0.243397i
$956$	46.5569	−	80.6390i	1.50576	−	2.60805i
$957$			32.2124i			1.04128i
$958$	53.0185	+	30.6102i	1.71295	+	0.988972i
$959$	−1.39507	−	2.41634i	−0.0450492	−	0.0780275i
$960$	−15.6071	+	7.94548i	−0.503716	+	0.256439i
$961$	−24.7403			−0.798075
$962$		0			0
$963$			40.3649i			1.30074i
$964$	19.6728	+	34.0743i	0.633618	+	1.09746i
$965$	−47.8104	+	24.3400i	−1.53907	+	0.783533i
$966$	6.87946	−	11.9156i	0.221343	−	0.383377i
$967$		−	19.4851i		−	0.626600i	−0.949654	−	0.313300i	$-0.898566\pi$
$967$		−	19.4851i		−	0.626600i	0.949654	−	0.313300i	$-0.101434\pi$
$968$	−11.7705	−	6.79571i	−0.378319	−	0.218422i
$969$	−36.6209	+	63.4292i	−1.17643	+	2.03764i
$970$	−60.1177	−	3.17124i	−1.93026	−	0.101822i
$971$	27.6035	−	47.8107i	0.885839	−	1.53432i	0.0410894	−	0.999155i	$-0.486917\pi$
$971$	27.6035	−	47.8107i	0.885839	−	1.53432i	0.844749	−	0.535162i	$-0.179750\pi$
$972$	−81.2538	+	46.9119i	−2.60622	+	1.50470i
$973$	−12.1051	+	6.98888i	−0.388071	+	0.224053i
$974$	−71.4380			−2.28902
$975$		0			0
$976$	24.6578			0.789278
$977$	9.59188	−	5.53787i	0.306871	−	0.177172i	−0.338654	−	0.940911i	$-0.609972\pi$
$977$	9.59188	−	5.53787i	0.306871	−	0.177172i	0.645526	+	0.763739i	$0.276638\pi$
$978$	40.5861	−	23.4324i	1.29780	−	0.749284i
$979$	13.1046	−	22.6977i	0.418823	−	0.725423i
$980$	−53.1364	−	2.80297i	−1.69738	−	0.0895377i
$981$	10.3980	−	18.0098i	0.331982	−	0.575009i
$982$	3.13117	+	1.80778i	0.0999196	+	0.0576886i
$983$			17.0548i			0.543965i	0.962302	+	0.271982i	$0.0876792\pi$
$983$			17.0548i			0.543965i	−0.962302	+	0.271982i	$0.912321\pi$
$984$	69.0781	−	119.647i	2.20213	−	3.81420i
$985$	13.8230	−	7.03719i	0.440436	−	0.224224i
$986$	30.8161	+	53.3750i	0.981384	+	1.69981i
$987$			32.2948i			1.02795i
$988$		0			0
$989$	1.34865			0.0428846
$990$	−57.1252	+	29.0821i	−1.81556	+	0.924291i
$991$	−28.3003	−	49.0175i	−0.898987	−	1.55709i	−0.828791	−	0.559559i	$-0.810971\pi$
$991$	−28.3003	−	49.0175i	−0.898987	−	1.55709i	−0.0701965	−	0.997533i	$-0.522363\pi$
$992$	−8.00059	−	4.61914i	−0.254019	−	0.146658i
$993$		−	7.57814i		−	0.240485i
$994$	−22.0229	+	38.1447i	−0.698523	+	1.20988i
$995$	7.05124	−	10.8498i	0.223539	−	0.343963i
$996$	−39.7831			−1.26057
$997$	−47.8459	−	27.6238i	−1.51529	−	0.874855i	−0.999839	−	0.0179387i	$-0.994290\pi$
$997$	−47.8459	−	27.6238i	−1.51529	−	0.874855i	−0.515455	−	0.856917i	$-0.672377\pi$
$998$	−36.4310	+	21.0335i	−1.15320	+	0.665803i
$999$	−3.77520	−	6.53884i	−0.119442	−	0.206880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.h.484.18		36
5.4	even	2	inner	845.2.n.h.484.1		36
13.2	odd	12		845.2.d.e.844.35		36
13.3	even	3		845.2.b.h.339.18	yes	18
13.4	even	6		845.2.n.i.529.18		36
13.5	odd	4		845.2.l.g.699.1		72
13.6	odd	12		845.2.l.g.654.2		72
13.7	odd	12		845.2.l.g.654.36		72
13.8	odd	4		845.2.l.g.699.35		72
13.9	even	3	inner	845.2.n.h.529.1		36
13.10	even	6		845.2.b.g.339.1	✓	18
13.11	odd	12		845.2.d.e.844.1		36
13.12	even	2		845.2.n.i.484.1		36
65.3	odd	12		4225.2.a.cb.1.18		18
65.4	even	6		845.2.n.i.529.1		36
65.9	even	6	inner	845.2.n.h.529.18		36
65.19	odd	12		845.2.l.g.654.35		72
65.23	odd	12		4225.2.a.ca.1.1		18
65.24	odd	12		845.2.d.e.844.36		36
65.29	even	6		845.2.b.h.339.1	yes	18
65.34	odd	4		845.2.l.g.699.2		72
65.42	odd	12		4225.2.a.cb.1.1		18
65.44	odd	4		845.2.l.g.699.36		72
65.49	even	6		845.2.b.g.339.18	yes	18
65.54	odd	12		845.2.d.e.844.2		36
65.59	odd	12		845.2.l.g.654.1		72
65.62	odd	12		4225.2.a.ca.1.18		18
65.64	even	2		845.2.n.i.484.18		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.b.g.339.1	✓	18	13.10	even	6
845.2.b.g.339.18	yes	18	65.49	even	6
845.2.b.h.339.1	yes	18	65.29	even	6
845.2.b.h.339.18	yes	18	13.3	even	3
845.2.d.e.844.1		36	13.11	odd	12
845.2.d.e.844.2		36	65.54	odd	12
845.2.d.e.844.35		36	13.2	odd	12
845.2.d.e.844.36		36	65.24	odd	12
845.2.l.g.654.1		72	65.59	odd	12
845.2.l.g.654.2		72	13.6	odd	12
845.2.l.g.654.35		72	65.19	odd	12
845.2.l.g.654.36		72	13.7	odd	12
845.2.l.g.699.1		72	13.5	odd	4
845.2.l.g.699.2		72	65.34	odd	4
845.2.l.g.699.35		72	13.8	odd	4
845.2.l.g.699.36		72	65.44	odd	4
845.2.n.h.484.1		36	5.4	even	2	inner
845.2.n.h.484.18		36	1.1	even	1	trivial
845.2.n.h.529.1		36	13.9	even	3	inner
845.2.n.h.529.18		36	65.9	even	6	inner
845.2.n.i.484.1		36	13.12	even	2
845.2.n.i.484.18		36	65.64	even	2
845.2.n.i.529.1		36	65.4	even	6
845.2.n.i.529.18		36	13.4	even	6
4225.2.a.ca.1.1		18	65.23	odd	12
4225.2.a.ca.1.18		18	65.62	odd	12
4225.2.a.cb.1.1		18	65.42	odd	12
4225.2.a.cb.1.18		18	65.3	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18027 - 1.25878i) q^{2} +(-2.26868 + 1.30982i) q^{3} +(2.16905 - 3.75690i) q^{4} +(2.23296 + 0.117790i) q^{5} +(-3.29755 + 5.71153i) q^{6} +(1.06580 + 0.615337i) q^{7} -5.88628i q^{8} +(1.93127 - 3.34505i) q^{9} +(5.01673 - 2.55399i) q^{10} +(-1.47403 - 2.55309i) q^{11} +11.3643i q^{12} +3.09829 q^{14} +(-5.22016 + 2.65756i) q^{15} +(-3.07144 - 5.31988i) q^{16} +(5.08291 + 2.93462i) q^{17} -9.72414i q^{18} +(2.38180 - 4.12539i) q^{19} +(5.28593 - 8.13353i) q^{20} -3.22393 q^{21} +(-6.42754 - 3.71094i) q^{22} +(-1.46808 + 0.847597i) q^{23} +(7.70998 + 13.3541i) q^{24} +(4.97225 + 0.526042i) q^{25} +2.25952i q^{27} +(4.62352 - 2.66939i) q^{28} +(2.08553 + 3.61224i) q^{29} +(-8.03607 + 12.3652i) q^{30} +2.50193 q^{31} +(-3.19776 - 1.84623i) q^{32} +(6.68818 + 3.86142i) q^{33} +14.7762 q^{34} +(2.30740 + 1.49957i) q^{35} +(-8.37801 - 14.5111i) q^{36} +(-2.89391 + 1.67080i) q^{37} -11.9926i q^{38} +(0.693346 - 13.1439i) q^{40} +(-4.47978 - 7.75921i) q^{41} +(-7.02903 + 4.05821i) q^{42} +(-0.688986 - 0.397786i) q^{43} -12.7889 q^{44} +(4.70646 - 7.24189i) q^{45} +(-2.13387 + 3.69598i) q^{46} -10.0172i q^{47} +(13.9362 + 8.04606i) q^{48} +(-2.74272 - 4.75053i) q^{49} +(11.5030 - 5.11205i) q^{50} -15.3753 q^{51} +7.14496i q^{53} +(2.84424 + 4.92636i) q^{54} +(-2.99072 - 5.87457i) q^{55} +(3.62205 - 6.27357i) q^{56} +12.4789i q^{57} +(9.09402 + 5.25043i) q^{58} +(0.0174087 - 0.0301528i) q^{59} +(-1.33860 + 25.3760i) q^{60} +(-2.00703 + 3.47628i) q^{61} +(5.45489 - 3.14938i) q^{62} +(4.11667 - 2.37676i) q^{63} +2.98977 q^{64} +19.4427 q^{66} +(-6.25486 + 3.61124i) q^{67} +(22.0502 - 12.7307i) q^{68} +(2.22040 - 3.84585i) q^{69} +(6.91838 + 0.364948i) q^{70} +(-7.10807 + 12.3115i) q^{71} +(-19.6899 - 11.3680i) q^{72} +8.45275i q^{73} +(-4.20633 + 7.28557i) q^{74} +(-11.9695 + 5.31934i) q^{75} +(-10.3325 - 17.8963i) q^{76} -3.62809i q^{77} -7.06674 q^{79} +(-6.23177 - 12.2409i) q^{80} +(2.83423 + 4.90902i) q^{81} +(-19.5342 - 11.2781i) q^{82} +3.50072i q^{83} +(-6.99285 + 12.1120i) q^{84} +(11.0043 + 7.15162i) q^{85} -2.00290 q^{86} +(-9.46278 - 5.46334i) q^{87} +(-15.0282 + 8.67653i) q^{88} +(4.44516 + 7.69924i) q^{89} +(1.14541 - 21.7136i) q^{90} +7.35391i q^{92} +(-5.67608 + 3.27709i) q^{93} +(-12.6095 - 21.8402i) q^{94} +(5.80440 - 8.93130i) q^{95} +9.67292 q^{96} +(-9.26130 - 5.34701i) q^{97} +(-11.9597 - 6.90495i) q^{98} -11.3869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 16 q^{4} - 16 q^{6} + 18 q^{9} - 13 q^{10} - 22 q^{11} - 8 q^{14} - 8 q^{15} + 12 q^{16} + 28 q^{19} + 10 q^{20} + 52 q^{21} + 34 q^{24} - 16 q^{25} - 20 q^{29} - 31 q^{30} + 64 q^{31} - 36 q^{34}+ \cdots - 152 q^{99}+O(q^{100}) \) 36 * q + 16 * q^4 - 16 * q^6 + 18 * q^9 - 13 * q^10 - 22 * q^11 - 8 * q^14 - 8 * q^15 + 12 * q^16 + 28 * q^19 + 10 * q^20 + 52 * q^21 + 34 * q^24 - 16 * q^25 - 20 * q^29 - 31 * q^30 + 64 * q^31 - 36 * q^34 - 10 * q^35 - 32 * q^36 + 6 * q^40 - 52 * q^41 - 100 * q^44 - 5 * q^45 - 30 * q^46 + 44 * q^49 - 29 * q^50 - 80 * q^51 + 90 * q^54 + 20 * q^55 + 20 * q^56 + 76 * q^59 + 86 * q^60 - 8 * q^61 + 136 * q^64 + 16 * q^66 + 30 * q^69 + 92 * q^70 - 72 * q^71 + 30 * q^74 - 13 * q^75 - 4 * q^76 - 32 * q^79 - 73 * q^80 + 30 * q^81 + 78 * q^84 - 29 * q^85 - 60 * q^86 + 94 * q^89 - 140 * q^90 - 128 * q^94 - 41 * q^95 - 36 * q^96 - 152 * q^99

Introduction

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