LMFDB - Embedded newform 924.2.bu.b.223.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [924,2,Mod(223,924)] 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("924.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(924, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	924.bu (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [192,2,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.37817714677$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			223.9
Character	$\chi$	$=$	924.223
Dual form			924.2.bu.b.895.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17589 + 0.785678i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.765420 - 1.84774i) q^{4} +(2.25375 - 3.10202i) q^{5} +(1.11059 + 0.875547i) q^{6} +(-2.63609 + 0.225872i) q^{7} +(0.551680 + 2.77410i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.212965 + 5.41835i) q^{10} +(-3.31662 + 0.00556485i) q^{11} +(-1.99383 - 0.156975i) q^{12} +(-0.615252 - 0.846822i) q^{13} +(2.92228 - 2.33672i) q^{14} +(-3.64665 - 1.18487i) q^{15} +(-2.82827 - 2.82859i) q^{16} +(-0.576270 + 0.793167i) q^{17} +(0.489502 - 1.32680i) q^{18} +(-0.320724 - 0.987087i) q^{19} +(-4.00666 - 6.53869i) q^{20} +(1.02941 + 2.43727i) q^{21} +(3.89560 - 2.61234i) q^{22} -3.08086i q^{23} +(2.46785 - 1.38192i) q^{24} +(-2.99807 - 9.22710i) q^{25} +(1.38880 + 0.512377i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.60037 + 5.04369i) q^{28} +(-1.67924 + 5.16817i) q^{29} +(5.21897 - 1.47182i) q^{30} +(-4.63060 + 3.36432i) q^{31} +(5.54808 + 1.10399i) q^{32} +(1.03018 + 3.15257i) q^{33} +(0.0544538 - 1.38544i) q^{34} +(-5.24044 + 8.68628i) q^{35} +(0.466835 + 1.94475i) q^{36} +(2.41682 - 7.43822i) q^{37} +(1.15267 + 0.908717i) q^{38} +(-0.615252 + 0.846822i) q^{39} +(9.84868 + 4.54082i) q^{40} +(-4.15240 + 1.34920i) q^{41} +(-3.12539 - 2.05717i) q^{42} +2.49393i q^{43} +(-2.52832 + 6.13250i) q^{44} +3.83431i q^{45} +(2.42056 + 3.62274i) q^{46} +(1.63680 + 5.03755i) q^{47} +(-1.81617 + 3.56392i) q^{48} +(6.89796 - 1.19084i) q^{49} +(10.7749 + 8.49451i) q^{50} +(0.932424 + 0.302963i) q^{51} +(-2.03563 + 0.488650i) q^{52} +(-9.90727 + 7.19806i) q^{53} +(-1.41312 - 0.0555419i) q^{54} +(-7.45758 + 10.3008i) q^{55} +(-2.08087 - 7.18818i) q^{56} +(-0.839666 + 0.610053i) q^{57} +(-2.08592 - 7.39653i) q^{58} +(-3.47678 + 10.7004i) q^{59} +(-4.98054 + 5.83113i) q^{60} +(3.73571 - 5.14176i) q^{61} +(2.80178 - 7.59422i) q^{62} +(1.99988 - 1.73219i) q^{63} +(-7.39130 + 3.06083i) q^{64} -4.01349 q^{65} +(-3.68829 - 2.89768i) q^{66} -1.32185i q^{67} +(1.02448 + 1.67190i) q^{68} +(-2.93007 + 0.952037i) q^{69} +(-0.662457 - 14.3314i) q^{70} +(6.89115 - 9.48485i) q^{71} +(-2.07690 - 1.92003i) q^{72} +(2.00435 + 0.651254i) q^{73} +(3.00213 + 10.6453i) q^{74} +(-7.84904 + 5.70266i) q^{75} +(-2.06937 - 0.162922i) q^{76} +(8.74166 - 0.763800i) q^{77} +(0.0581374 - 1.47916i) q^{78} +(-8.02725 - 11.0486i) q^{79} +(-15.1486 + 2.39841i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.82272 - 4.84895i) q^{82} +(-6.06266 - 4.40478i) q^{83} +(5.29138 - 0.0365489i) q^{84} +(1.16165 + 3.57521i) q^{85} +(-1.95942 - 2.93257i) q^{86} +5.43414 q^{87} +(-1.84515 - 9.19758i) q^{88} +14.7291i q^{89} +(-3.01254 - 4.50872i) q^{90} +(1.81314 + 2.09333i) q^{91} +(-5.69262 - 2.35815i) q^{92} +(4.63060 + 3.36432i) q^{93} +(-5.88259 - 4.63759i) q^{94} +(-3.78480 - 1.22976i) q^{95} +(-0.664491 - 5.61769i) q^{96} +(-9.97974 - 13.7359i) q^{97} +(-7.17561 + 6.81987i) q^{98} +(2.67993 - 1.95396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 2 q^{2} + 48 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 48 q^{9} + 2 q^{12} + 13 q^{14} + 6 q^{16} - 3 q^{18} + 6 q^{20} + 24 q^{22} + 3 q^{24} + 56 q^{25} - 18 q^{26} + 48 q^{27} + 16 q^{29} + 12 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) $ 192 * q + 2 * q^2 + 48 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 48 * q^9 + 2 * q^12 + 13 * q^14 + 6 * q^16 - 3 * q^18 + 6 * q^20 + 24 * q^22 + 3 * q^24 + 56 * q^25 - 18 * q^26 + 48 * q^27 + 16 * q^29 + 12 * q^31 - 8 * q^32 + 24 * q^34 + 14 * q^35 - 2 * q^36 - 24 * q^37 - 36 * q^38 - 36 * q^40 + 2 * q^42 + 29 * q^44 - 23 * q^46 + 8 * q^47 - 11 * q^48 + 16 * q^49 - 14 * q^50 - 40 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 + 7 * q^58 - 40 * q^59 - 6 * q^60 - 56 * q^64 - 16 * q^65 + 11 * q^66 - 78 * q^68 + 86 * q^70 - 3 * q^72 + 28 * q^74 - 36 * q^75 - 56 * q^76 + 28 * q^77 - 12 * q^78 + 6 * q^80 - 48 * q^81 + 8 * q^83 + 15 * q^84 - 60 * q^85 - 51 * q^86 - 16 * q^87 - 4 * q^88 + 8 * q^91 - 47 * q^92 - 12 * q^93 + 64 * q^94 - 2 * q^96 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/924\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$661$	$673$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.17589	+	0.785678i	−0.831478	+	0.555558i
$2$	−1.17589	+	0.785678i	−0.831478	+	0.555558i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.765420	−	1.84774i	0.382710	−	0.923869i
$5$	2.25375	−	3.10202i	1.00791	−	1.38727i	0.0875640	−	0.996159i	$-0.472092\pi$
$5$	2.25375	−	3.10202i	1.00791	−	1.38727i	0.920345	−	0.391108i	$-0.127908\pi$
$6$	1.11059	+	0.875547i	0.453398	+	0.357441i
$7$	−2.63609	+	0.225872i	−0.996349	+	0.0853714i
$7$	−2.63609	+	0.225872i	−0.996349	+	0.0853714i
$8$	0.551680	+	2.77410i	0.195048	+	0.980794i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.212965	+	5.41835i	−0.0673455	+	1.71343i
$11$	−3.31662	+	0.00556485i	−0.999999	+	0.00167787i
$11$	−3.31662	+	0.00556485i	−0.999999	+	0.00167787i
$12$	−1.99383	−	0.156975i	−0.575569	−	0.0453148i
$13$	−0.615252	−	0.846822i	−0.170640	−	0.234866i	0.715128	−	0.698993i	$-0.246368\pi$
$13$	−0.615252	−	0.846822i	−0.170640	−	0.234866i	−0.885769	+	0.464127i	$0.846368\pi$
$14$	2.92228	−	2.33672i	0.781013	−	0.624515i
$15$	−3.64665	−	1.18487i	−0.941560	−	0.305932i
$16$	−2.82827	−	2.82859i	−0.707066	−	0.707147i
$17$	−0.576270	+	0.793167i	−0.139766	+	0.192371i	−0.873162	−	0.487431i	$-0.837934\pi$
$17$	−0.576270	+	0.793167i	−0.139766	+	0.192371i	0.733396	+	0.679802i	$0.237934\pi$
$18$	0.489502	−	1.32680i	0.115377	−	0.312729i
$19$	−0.320724	−	0.987087i	−0.0735791	−	0.226453i	0.907503	−	0.420046i	$-0.137986\pi$
$19$	−0.320724	−	0.987087i	−0.0735791	−	0.226453i	−0.981082	+	0.193593i	$0.937986\pi$
$20$	−4.00666	−	6.53869i	−0.895916	−	1.46210i
$21$	1.02941	+	2.43727i	0.224637	+	0.531857i
$22$	3.89560	−	2.61234i	0.830544	−	0.556953i
$23$		−	3.08086i		−	0.642403i	−0.947011	−	0.321202i	$-0.895913\pi$
$23$		−	3.08086i		−	0.642403i	0.947011	−	0.321202i	$-0.104087\pi$
$24$	2.46785	−	1.38192i	0.503748	−	0.282084i
$25$	−2.99807	−	9.22710i	−0.599614	−	1.84542i
$26$	1.38880	+	0.512377i	0.272366	+	0.100485i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.60037	+	5.04369i	−0.302441	+	0.953168i
$29$	−1.67924	+	5.16817i	−0.311827	+	0.959706i	0.665213	+	0.746653i	$0.268341\pi$
$29$	−1.67924	+	5.16817i	−0.311827	+	0.959706i	−0.977041	+	0.213053i	$0.931659\pi$
$30$	5.21897	−	1.47182i	0.952849	−	0.268717i
$31$	−4.63060	+	3.36432i	−0.831680	+	0.604251i	−0.920034	−	0.391839i	$-0.871839\pi$
$31$	−4.63060	+	3.36432i	−0.831680	+	0.604251i	0.0883544	+	0.996089i	$0.471839\pi$
$32$	5.54808	+	1.10399i	0.980771	+	0.195160i
$33$	1.03018	+	3.15257i	0.179332	+	0.548793i
$34$	0.0544538	−	1.38544i	0.00933875	−	0.237601i
$35$	−5.24044	+	8.68628i	−0.885796	+	1.46825i
$36$	0.466835	+	1.94475i	0.0778059	+	0.324126i
$37$	2.41682	−	7.43822i	0.397323	−	1.22284i	−0.529814	−	0.848114i	$-0.677738\pi$
$37$	2.41682	−	7.43822i	0.397323	−	1.22284i	0.927137	−	0.374722i	$-0.122262\pi$
$38$	1.15267	+	0.908717i	0.186987	+	0.147413i
$39$	−0.615252	+	0.846822i	−0.0985192	+	0.135600i
$40$	9.84868	+	4.54082i	1.55721	+	0.717966i
$41$	−4.15240	+	1.34920i	−0.648496	+	0.210709i	−0.614751	−	0.788721i	$-0.710743\pi$
$41$	−4.15240	+	1.34920i	−0.648496	+	0.210709i	−0.0337452	+	0.999430i	$0.510743\pi$
$42$	−3.12539	−	2.05717i	−0.482258	−	0.317428i
$43$			2.49393i			0.380320i	0.981753	+	0.190160i	$0.0609007\pi$
$43$			2.49393i			0.380320i	−0.981753	+	0.190160i	$0.939099\pi$
$44$	−2.52832	+	6.13250i	−0.381159	+	0.924509i
$45$			3.83431i			0.571586i
$46$	2.42056	+	3.62274i	0.356892	+	0.534144i
$47$	1.63680	+	5.03755i	0.238752	+	0.734803i	0.996602	+	0.0823734i	$0.0262500\pi$
$47$	1.63680	+	5.03755i	0.238752	+	0.734803i	−0.757850	+	0.652429i	$0.773750\pi$
$48$	−1.81617	+	3.56392i	−0.262141	+	0.514408i
$49$	6.89796	−	1.19084i	0.985423	−	0.170120i
$50$	10.7749	+	8.49451i	1.52380	+	1.20131i
$51$	0.932424	+	0.302963i	0.130565	+	0.0424233i
$52$	−2.03563	+	0.488650i	−0.282291	+	0.0677636i
$53$	−9.90727	+	7.19806i	−1.36087	+	0.988729i	−0.362479	+	0.931992i	$0.618070\pi$
$53$	−9.90727	+	7.19806i	−1.36087	+	0.988729i	−0.998389	+	0.0567372i	$0.981930\pi$
$54$	−1.41312	−	0.0555419i	−0.192302	−	0.00755830i
$55$	−7.45758	+	10.3008i	−1.00558	+	1.38896i
$56$	−2.08087	−	7.18818i	−0.278068	−	0.960561i
$57$	−0.839666	+	0.610053i	−0.111217	+	0.0808035i
$58$	−2.08592	−	7.39653i	−0.273895	−	0.971212i
$59$	−3.47678	+	10.7004i	−0.452638	+	1.39308i	0.421248	+	0.906945i	$0.361592\pi$
$59$	−3.47678	+	10.7004i	−0.452638	+	1.39308i	−0.873886	+	0.486131i	$0.838408\pi$
$60$	−4.98054	+	5.83113i	−0.642985	+	0.752795i
$61$	3.73571	−	5.14176i	0.478308	−	0.658335i	−0.499870	−	0.866100i	$-0.666619\pi$
$61$	3.73571	−	5.14176i	0.478308	−	0.658335i	0.978179	+	0.207765i	$0.0666190\pi$
$62$	2.80178	−	7.59422i	0.355826	−	0.964467i
$63$	1.99988	−	1.73219i	0.251961	−	0.218235i
$64$	−7.39130	+	3.06083i	−0.923912	+	0.382604i
$65$	−4.01349			−0.497812
$66$	−3.68829	−	2.89768i	−0.453997	−	0.356679i
$67$		−	1.32185i		−	0.161489i	−0.996735	−	0.0807446i	$-0.974270\pi$
$67$		−	1.32185i		−	0.161489i	0.996735	−	0.0807446i	$-0.0257298\pi$
$68$	1.02448	+	1.67190i	0.124236	+	0.202748i
$69$	−2.93007	+	0.952037i	−0.352739	+	0.114612i
$70$	−0.662457	−	14.3314i	−0.0791787	−	1.71293i
$71$	6.89115	−	9.48485i	0.817829	−	1.12565i	−0.172239	−	0.985055i	$-0.555100\pi$
$71$	6.89115	−	9.48485i	0.817829	−	1.12565i	0.990068	−	0.140590i	$-0.0448999\pi$
$72$	−2.07690	−	1.92003i	−0.244764	−	0.226277i
$73$	2.00435	+	0.651254i	0.234592	+	0.0762235i	0.423954	−	0.905684i	$-0.360642\pi$
$73$	2.00435	+	0.651254i	0.234592	+	0.0762235i	−0.189362	+	0.981907i	$0.560642\pi$
$74$	3.00213	+	10.6453i	0.348991	+	1.23750i
$75$	−7.84904	+	5.70266i	−0.906329	+	0.658487i
$76$	−2.06937	−	0.162922i	−0.237373	−	0.0186884i
$77$	8.74166	−	0.763800i	0.996205	−	0.0870431i
$78$	0.0581374	−	1.47916i	0.00658276	−	0.167482i
$79$	−8.02725	−	11.0486i	−0.903136	−	1.24306i	−0.969457	−	0.245261i	$-0.921126\pi$
$79$	−8.02725	−	11.0486i	−0.903136	−	1.24306i	0.0663212	−	0.997798i	$-0.478874\pi$
$80$	−15.1486	+	2.39841i	−1.69366	+	0.268150i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.82272	−	4.84895i	0.422149	−	0.535477i
$83$	−6.06266	−	4.40478i	−0.665464	−	0.483488i	0.203040	−	0.979170i	$-0.434918\pi$
$83$	−6.06266	−	4.40478i	−0.665464	−	0.483488i	−0.868504	+	0.495683i	$0.834918\pi$
$84$	5.29138	−	0.0365489i	0.577336	−	0.00398781i
$85$	1.16165	+	3.57521i	0.125999	+	0.387785i
$86$	−1.95942	−	2.93257i	−0.211290	−	0.316228i
$87$	5.43414			0.582601
$88$	−1.84515	−	9.19758i	−0.196694	−	0.980465i
$89$			14.7291i			1.56128i	0.624983	+	0.780638i	$0.285106\pi$
$89$			14.7291i			1.56128i	−0.624983	+	0.780638i	$0.714894\pi$
$90$	−3.01254	−	4.50872i	−0.317549	−	0.475261i
$91$	1.81314	+	2.09333i	0.190068	+	0.219441i
$92$	−5.69262	−	2.35815i	−0.593496	−	0.245854i
$93$	4.63060	+	3.36432i	0.480170	+	0.348864i
$94$	−5.88259	−	4.63759i	−0.606742	−	0.478331i
$95$	−3.78480	−	1.22976i	−0.388312	−	0.126170i
$96$	−0.664491	−	5.61769i	−0.0678194	−	0.573353i
$97$	−9.97974	−	13.7359i	−1.01329	−	1.39467i	−0.916804	−	0.399338i	$-0.869240\pi$
$97$	−9.97974	−	13.7359i	−1.01329	−	1.39467i	−0.0964854	−	0.995334i	$-0.530760\pi$
$98$	−7.17561	+	6.81987i	−0.724846	+	0.688911i
$99$	2.67993	−	1.95396i	0.269343	−	0.196381i
$100$	−19.3440	−	1.52296i	−1.93440	−	0.152296i
$101$	4.48112	+	6.16774i	0.445888	+	0.613713i	0.971508	−	0.237007i	$-0.0761664\pi$
$101$	4.48112	+	6.16774i	0.445888	+	0.613713i	−0.525620	+	0.850720i	$0.676166\pi$
$102$	−1.33446	+	0.376335i	−0.132131	+	0.0372627i
$103$	3.95624	−	12.1760i	0.389819	−	1.19974i	−0.543104	−	0.839666i	$-0.682751\pi$
$103$	3.95624	−	12.1760i	0.389819	−	1.19974i	0.932923	−	0.360075i	$-0.117249\pi$
$104$	2.00975	−	2.17395i	0.197072	−	0.213173i
$105$	9.88053	+	2.29975i	0.964241	+	0.224432i
$106$	5.99448	−	16.2480i	0.582235	−	1.57815i
$107$	0.953674	−	0.309867i	0.0921951	−	0.0299560i	−0.262556	−	0.964917i	$-0.584566\pi$
$107$	0.953674	−	0.309867i	0.0921951	−	0.0299560i	0.354751	+	0.934961i	$0.384566\pi$
$108$	1.70531	−	1.04495i	0.164094	−	0.100550i
$109$	−14.9248			−1.42954			−0.714768	−	0.699362i	$-0.753468\pi$
$109$	−14.9248			−1.42954			−0.714768	+	0.699362i	$0.753468\pi$
$110$	0.676172	−	17.9718i	0.0644705	−	1.71354i
$111$	−7.82100			−0.742337
$112$	8.09447	+	6.81760i	0.764855	+	0.644202i
$113$	−2.81337	−	8.65866i	−0.264659	−	0.814538i	−0.991772	−	0.128019i	$-0.959138\pi$
$113$	−2.81337	−	8.65866i	−0.264659	−	0.814538i	0.727112	−	0.686519i	$-0.240862\pi$
$114$	0.508047	−	1.37706i	0.0475830	−	0.128974i
$115$	−9.55689	−	6.94349i	−0.891185	−	0.647484i
$116$	8.26410	+	7.05862i	0.767303	+	0.655376i
$117$	0.995499	+	0.323457i	0.0920340	+	0.0299036i
$118$	−4.31879	−	15.3141i	−0.397577	−	1.40978i
$119$	1.33995	−	2.22103i	0.122833	−	0.203601i
$120$	1.27516	−	10.7698i	0.116406	−	0.983148i
$121$	10.9999	−	0.0369130i	0.999994	−	0.00335573i
$122$	−0.353000	+	8.98119i	−0.0319592	+	0.813119i
$123$	2.56632	+	3.53224i	0.231398	+	0.318492i
$124$	2.67204	+	11.1312i	0.239956	+	0.999615i
$125$	−17.1464	−	5.57119i	−1.53362	−	0.498302i
$126$	−0.990688	+	3.60812i	−0.0882575	+	0.321437i
$127$	2.17671	−	2.99599i	0.193152	−	0.265851i	−0.701446	−	0.712722i	$-0.747462\pi$
$127$	2.17671	−	2.99599i	0.193152	−	0.265851i	0.894598	+	0.446872i	$0.147462\pi$
$128$	6.28650	−	9.40638i	0.555653	−	0.831414i
$129$	2.37186	−	0.770666i	0.208831	−	0.0678533i
$130$	4.71941	−	3.15331i	0.413920	−	0.276564i
$131$	−11.1418			−0.973462			−0.486731	−	0.873552i	$-0.661811\pi$
$131$	−11.1418			−0.973462			−0.486731	+	0.873552i	$0.661811\pi$
$132$	6.61365	+	0.509531i	0.575644	+	0.0443490i
$133$	1.06841	+	2.52961i	0.0926431	+	0.219345i
$134$	1.03855	+	1.55434i	0.0897167	+	0.134275i
$135$	3.64665	−	1.18487i	0.313853	−	0.101977i
$136$	−2.51824	−	1.16106i	−0.215938	−	0.0995599i
$137$	−6.17098	−	4.48348i	−0.527223	−	0.383050i	0.292095	−	0.956389i	$-0.405648\pi$
$137$	−6.17098	−	4.48348i	−0.527223	−	0.383050i	−0.819318	+	0.573340i	$0.805648\pi$
$138$	2.69744	−	3.42158i	0.229621	−	0.291264i
$139$	−6.36407	+	19.5866i	−0.539793	+	1.66131i	0.193264	+	0.981147i	$0.438093\pi$
$139$	−6.36407	+	19.5866i	−0.539793	+	1.66131i	−0.733058	+	0.680167i	$0.761907\pi$
$140$	12.0388	+	16.3316i	1.01747	+	1.38027i
$141$	4.28520	−	3.11338i	0.360879	−	0.262194i
$142$	−0.651169	+	16.5673i	−0.0546449	+	1.39030i
$143$	2.04527	+	2.80516i	0.171034	+	0.234580i
$144$	3.95072	+	0.625963i	0.329226	+	0.0521636i
$145$	12.2472	+	16.8568i	1.01708	+	1.39988i
$146$	−2.86857	+	0.808976i	−0.237405	+	0.0669513i
$147$	−3.26414	−	6.19236i	−0.269222	−	0.510738i
$148$	−11.8940	−	10.1590i	−0.977680	−	0.835066i
$149$	2.33734	+	1.69818i	0.191482	+	0.139120i	0.679396	−	0.733772i	$-0.262242\pi$
$149$	2.33734	+	1.69818i	0.191482	+	0.139120i	−0.487914	+	0.872892i	$0.662242\pi$
$150$	4.74913	−	12.8725i	0.387765	−	1.05104i
$151$	0.343659	−	0.111662i	0.0279666	−	0.00908689i	−0.295000	−	0.955497i	$-0.595320\pi$
$151$	0.343659	−	0.111662i	0.0279666	−	0.00908689i	0.322967	+	0.946410i	$0.395320\pi$
$152$	2.56134	−	1.43428i	0.207752	−	0.116335i
$153$		−	0.980409i		−	0.0792614i
$154$	−9.67910	+	7.76627i	−0.779964	+	0.625824i
$155$			21.9466i			1.76279i
$156$	1.09378	+	1.78500i	0.0875724	+	0.142914i
$157$	−3.77832	+	1.22765i	−0.301543	+	0.0979772i	−0.455881	−	0.890041i	$-0.650676\pi$
$157$	−3.77832	+	1.22765i	−0.301543	+	0.0979772i	0.154338	+	0.988018i	$0.450676\pi$
$158$	18.1197	+	6.68502i	1.44153	+	0.531832i
$159$	9.90727	+	7.19806i	0.785698	+	0.570843i
$160$	15.9286	−	14.7222i	1.25927	−	1.16389i
$161$	0.695878	+	8.12142i	0.0548429	+	0.640058i
$162$	0.383855	+	1.36112i	0.0301585	+	0.106940i
$163$	−2.05535	−	2.82895i	−0.160988	−	0.221580i	0.720901	−	0.693038i	$-0.243728\pi$
$163$	−2.05535	−	2.82895i	−0.160988	−	0.221580i	−0.881889	+	0.471457i	$0.843728\pi$
$164$	−0.685368	+	8.70525i	−0.0535182	+	0.679766i
$165$	12.1011	+	3.90946i	0.942072	+	0.304351i
$166$	10.5897	+	0.416224i	0.821924	+	0.0323052i
$167$	17.0141	−	12.3615i	1.31659	−	0.956561i	0.316625	−	0.948551i	$-0.397450\pi$
$167$	17.0141	−	12.3615i	1.31659	−	0.956561i	0.999968	−	0.00800990i	$-0.00254966\pi$
$168$	−6.19334	+	4.20030i	−0.477827	+	0.324060i
$169$	3.67865	−	11.3217i	0.282973	−	0.870901i
$170$	−4.17494	−	3.29135i	−0.320203	−	0.252435i
$171$	0.839666	+	0.610053i	0.0642109	+	0.0466519i
$172$	4.60812	+	1.90890i	0.351366	+	0.145552i
$173$	23.4407	−	7.61635i	1.78216	−	0.579060i	0.783083	−	0.621917i	$-0.213646\pi$
$173$	23.4407	−	7.61635i	1.78216	−	0.579060i	0.999081	+	0.0428565i	$0.0136458\pi$
$174$	−6.38993	+	4.26949i	−0.484420	+	0.323669i
$175$	9.98732	+	23.6463i	0.754971	+	1.78749i
$176$	9.39602	+	9.36561i	0.708252	+	0.705960i
$177$	11.2511			0.845684
$178$	−11.5723	−	17.3197i	−0.867380	−	1.29817i
$179$	−10.5288	+	3.42101i	−0.786959	+	0.255698i	−0.674808	−	0.737993i	$-0.735774\pi$
$179$	−10.5288	+	3.42101i	−0.786959	+	0.255698i	−0.112150	+	0.993691i	$0.535774\pi$
$180$	7.08480	+	2.93486i	0.528070	+	0.218751i
$181$	−7.27090	+	10.0075i	−0.540442	+	0.743854i	−0.988677	−	0.150062i	$-0.952053\pi$
$181$	−7.27090	+	10.0075i	−0.540442	+	0.743854i	0.448235	+	0.893916i	$0.352053\pi$
$182$	−3.77673	−	1.03698i	−0.279950	−	0.0768663i
$183$	−6.04450	−	1.96398i	−0.446823	−	0.145181i
$184$	8.54662	−	1.69965i	0.630065	−	0.125300i
$185$	−17.6266	−	24.2609i	−1.29593	−	1.78370i
$186$	−8.08833	−	0.317907i	−0.593065	−	0.0233101i
$187$	1.90685	−	2.63384i	0.139443	−	0.192606i
$188$	10.5609	+	0.831465i	0.770234	+	0.0606408i
$189$	−2.26541	−	1.36672i	−0.164784	−	0.0994144i
$190$	5.41669	−	1.52758i	0.392968	−	0.110822i
$191$	−14.5274	−	4.72024i	−1.05117	−	0.341545i	−0.268041	−	0.963408i	$-0.586376\pi$
$191$	−14.5274	−	4.72024i	−1.05117	−	0.341545i	−0.783126	+	0.621863i	$0.786376\pi$
$192$	5.19506	+	6.08369i	0.374921	+	0.439053i
$193$	−3.93240	−	2.85706i	−0.283060	−	0.205655i	0.437191	−	0.899369i	$-0.355973\pi$
$193$	−3.93240	−	2.85706i	−0.283060	−	0.205655i	−0.720251	+	0.693713i	$0.755973\pi$
$194$	22.5271	+	8.31104i	1.61735	+	0.596698i
$195$	1.24024	+	3.81706i	0.0888152	+	0.273345i
$196$	3.07948	−	13.6571i	0.219963	−	0.975508i
$197$	−15.5656			−1.10900			−0.554502	−	0.832183i	$-0.687091\pi$
$197$	−15.5656			−1.10900			−0.554502	+	0.832183i	$0.687091\pi$
$198$	−1.61611	+	4.40320i	−0.114852	+	0.312922i
$199$	22.1789			1.57222			0.786111	−	0.618086i	$-0.212092\pi$
$199$	22.1789			1.57222			0.786111	+	0.618086i	$0.212092\pi$
$200$	23.9430	−	13.4074i	1.69302	−	0.948043i
$201$	−1.25715	+	0.408473i	−0.0886725	+	0.0288115i
$202$	−10.1152	−	3.73184i	−0.711699	−	0.262571i
$203$	3.25929	−	14.0031i	0.228757	−	0.982823i
$204$	1.27349	−	1.49098i	0.0891623	−	0.104390i
$205$	−5.17324	+	15.9216i	−0.361315	+	1.11201i
$206$	4.91436	+	17.4260i	0.342400	+	1.21413i
$207$	1.81088	+	2.49247i	0.125865	+	0.173238i
$208$	−0.655215	+	4.13533i	−0.0454310	+	0.286734i
$209$	1.06921	+	3.27201i	0.0739590	+	0.226329i
$210$	−13.4252	+	5.05867i	−0.926430	+	0.349082i
$211$	−7.39886	−	10.1837i	−0.509358	−	0.701071i	0.474453	−	0.880281i	$-0.342646\pi$
$211$	−7.39886	−	10.1837i	−0.509358	−	0.701071i	−0.983811	+	0.179210i	$0.942646\pi$
$212$	5.71689	+	23.8156i	0.392638	+	1.63566i
$213$	−11.1501	−	3.62289i	−0.763993	−	0.248236i
$214$	−0.877956	+	1.11365i	−0.0600159	+	0.0761275i
$215$	7.73622	+	5.62069i	0.527606	+	0.383328i
$216$	−1.18426	+	2.56857i	−0.0805786	+	0.174769i
$217$	11.4468	−	9.91459i	0.777058	−	0.673046i
$218$	17.5499	−	11.7261i	1.18863	−	0.794190i
$219$		−	2.10750i		−	0.142412i
$220$	13.3250	+	21.6641i	0.898368	+	1.46059i
$221$	1.02622			0.0690313
$222$	9.19662	−	6.14479i	0.617236	−	0.412411i
$223$	0.512079	+	1.57602i	0.0342913	+	0.105538i	0.966737	−	0.255772i	$-0.0823297\pi$
$223$	0.512079	+	1.57602i	0.0342913	+	0.105538i	−0.932446	+	0.361310i	$0.882330\pi$
$224$	−14.8746	−	1.65707i	−0.993852	−	0.110718i
$225$	7.84904	+	5.70266i	0.523270	+	0.380178i
$226$	10.1111	+	7.97120i	0.672582	+	0.530236i
$227$	4.24174	−	13.0547i	0.281534	−	0.866472i	−0.705882	−	0.708329i	$-0.749449\pi$
$227$	4.24174	−	13.0547i	0.281534	−	0.866472i	0.987416	−	0.158143i	$-0.0505507\pi$
$228$	0.484521	+	2.01843i	0.0320882	+	0.133674i
$229$	3.49297	+	4.80766i	0.230822	+	0.317699i	0.908680	−	0.417494i	$-0.137091\pi$
$229$	3.49297	+	4.80766i	0.230822	+	0.317699i	−0.677858	+	0.735193i	$0.737091\pi$
$230$	16.6932	+	0.656115i	1.10072	+	0.0432629i
$231$	−3.42774	−	8.07779i	−0.225529	−	0.531479i
$232$	−15.2635	−	1.80721i	−1.00209	−	0.118649i
$233$	−2.72204	+	1.97768i	−0.178327	+	0.129562i	−0.673368	−	0.739307i	$-0.735153\pi$
$233$	−2.72204	+	1.97768i	−0.178327	+	0.129562i	0.495041	+	0.868870i	$0.335153\pi$
$234$	−1.42473	+	0.401793i	−0.0931374	+	0.0262660i
$235$	19.3155	+	6.27600i	1.26001	+	0.409401i
$236$	17.1104	+	14.6145i	1.11379	+	0.951322i
$237$	−8.02725	+	11.0486i	−0.521426	+	0.717681i
$238$	0.169386	+	3.66444i	0.0109797	+	0.237530i
$239$	−21.5558	+	7.00390i	−1.39433	+	0.453045i	−0.907353	−	0.420370i	$-0.861900\pi$
$239$	−21.5558	+	7.00390i	−1.39433	+	0.453045i	−0.486976	+	0.873415i	$0.661900\pi$
$240$	6.96219	+	13.6660i	0.449407	+	0.882136i
$241$		−	9.68373i		−	0.623784i	−0.950118	−	0.311892i	$-0.899037\pi$
$241$		−	9.68373i		−	0.623784i	0.950118	−	0.311892i	$-0.100963\pi$
$242$	−12.9057	+	8.68582i	−0.829609	+	0.558345i
$243$	−1.00000			−0.0641500
$244$	−6.64124	−	10.8382i	−0.425162	−	0.693846i
$245$	11.8523	−	24.0815i	0.757216	−	1.53851i
$246$	−5.79291	−	2.13721i	−0.369343	−	0.136264i
$247$	−0.638561	+	0.878904i	−0.0406307	+	0.0559233i
$248$	−11.8876	−	10.9897i	−0.754863	−	0.697848i
$249$	−2.31573	+	7.12709i	−0.146754	+	0.451661i
$250$	24.5393	−	6.92043i	1.55200	−	0.437687i
$251$	22.1932	−	16.1243i	1.40082	−	1.01776i	0.406246	−	0.913764i	$-0.366838\pi$
$251$	22.1932	−	16.1243i	1.40082	−	1.01776i	0.994578	−	0.103994i	$-0.0331623\pi$
$252$	−1.66989	−	5.02110i	−0.105193	−	0.316300i
$253$	0.0171445	+	10.2180i	0.00107787	+	0.642402i
$254$	−0.205685	+	5.23314i	−0.0129058	+	0.328356i
$255$	3.04125	−	2.20960i	0.190451	−	0.138370i
$256$	−0.00182582	+	16.0000i	−0.000114114	+	1.00000i
$257$	−13.8081	−	4.48653i	−0.861326	−	0.279862i	−0.155144	−	0.987892i	$-0.549584\pi$
$257$	−13.8081	−	4.48653i	−0.861326	−	0.279862i	−0.706182	+	0.708030i	$0.749584\pi$
$258$	−2.18355	+	2.76974i	−0.135942	+	0.172436i
$259$	−4.69089	+	20.1537i	−0.291478	+	1.25229i
$260$	−3.07200	+	7.41587i	−0.190518	+	0.459913i
$261$	−1.67924	−	5.16817i	−0.103942	−	0.319902i
$262$	13.1015	−	8.75386i	0.809412	−	0.540815i
$263$		−	23.0878i		−	1.42366i	−0.702354	−	0.711828i	$-0.747868\pi$
$263$		−	23.0878i		−	1.42366i	0.702354	−	0.711828i	$-0.252132\pi$
$264$	−8.17723	+	4.59705i	−0.503274	+	0.282929i
$265$			46.9552i			2.88444i
$266$	−3.24379	−	2.13511i	−0.198890	−	0.130912i
$267$	14.0082	−	4.55153i	0.857286	−	0.278549i
$268$	−2.44242	−	1.01177i	−0.149195	−	0.0618035i
$269$	13.3642	−	18.3942i	0.814827	−	1.12151i	−0.175734	−	0.984438i	$-0.556230\pi$
$269$	13.3642	−	18.3942i	0.814827	−	1.12151i	0.990561	−	0.137075i	$-0.0437702\pi$
$270$	−3.35712	+	4.25836i	−0.204308	+	0.259156i
$271$	0.422692	−	1.30091i	0.0256767	−	0.0790249i	−0.937397	−	0.348263i	$-0.886772\pi$
$271$	0.422692	−	1.30091i	0.0256767	−	0.0790249i	0.963074	+	0.269238i	$0.0867717\pi$
$272$	3.87339	−	0.613258i	0.234859	−	0.0371842i
$273$	1.43059	−	2.37127i	0.0865832	−	0.143516i
$274$	10.7790	+	0.423660i	0.651180	+	0.0255942i
$275$	9.99480	+	30.5861i	0.602709	+	1.84441i
$276$	−0.483618	+	6.14271i	−0.0291104	+	0.369748i
$277$	−3.21370	+	2.33489i	−0.193093	+	0.140290i	−0.680131	−	0.733091i	$-0.738077\pi$
$277$	−3.21370	+	2.33489i	−0.193093	+	0.140290i	0.487038	+	0.873381i	$0.338077\pi$
$278$	−7.90533	−	28.0317i	−0.474130	−	1.68123i
$279$	1.76873	−	5.44359i	0.105891	−	0.325899i
$280$	−26.9877	−	9.74547i	−1.61282	−	0.582403i
$281$	−12.0392	−	8.74700i	−0.718199	−	0.521802i	0.167609	−	0.985853i	$-0.446395\pi$
$281$	−12.0392	−	8.74700i	−0.718199	−	0.521802i	−0.885808	+	0.464051i	$0.846395\pi$
$282$	−2.59279	+	7.02777i	−0.154399	+	0.418497i
$283$	−5.05675	−	15.5631i	−0.300592	−	0.925128i	−0.981285	−	0.192559i	$-0.938321\pi$
$283$	−5.05675	−	15.5631i	−0.300592	−	0.925128i	0.680693	−	0.732569i	$-0.261679\pi$
$284$	−12.2509	−	19.9929i	−0.726957	−	1.18636i
$285$			3.97957i			0.235730i
$286$	−4.60896	−	1.69163i	−0.272534	−	0.100028i
$287$	10.6414	−	4.49452i	0.628140	−	0.265303i
$288$	−5.13740	+	2.36793i	−0.302724	+	0.139532i
$289$	4.95626	+	15.2538i	0.291545	+	0.897283i
$290$	−27.6454	−	10.1994i	−1.62339	−	0.598927i
$291$	−9.97974	+	13.7359i	−0.585023	+	0.805215i
$292$	2.73752	−	3.20504i	0.160201	−	0.187561i
$293$	−17.8367	−	5.79551i	−1.04203	−	0.338577i	−0.262497	−	0.964933i	$-0.584546\pi$
$293$	−17.8367	−	5.79551i	−1.04203	−	0.338577i	−0.779538	+	0.626356i	$0.784546\pi$
$294$	8.70347	+	4.71696i	0.507596	+	0.275098i
$295$	25.3572	+	34.9011i	1.47635	+	2.03202i
$296$	21.9677	+	2.60100i	1.27685	+	0.151180i
$297$	−2.68647	−	1.94496i	−0.155885	−	0.112858i
$298$	−4.08267	−	0.160467i	−0.236503	−	0.00929559i
$299$	−2.60894	+	1.89551i	−0.150879	+	0.109620i
$300$	4.52921	+	18.8679i	0.261494	+	1.08934i
$301$	−0.563307	−	6.57422i	−0.0324685	−	0.378932i
$302$	−0.316374	+	0.401307i	−0.0182053	+	0.0230926i
$303$	4.48112	−	6.16774i	0.257434	−	0.354327i
$304$	−1.88497	+	3.69894i	−0.108110	+	0.212149i
$305$	−7.53051	−	23.1765i	−0.431196	−	1.32708i
$306$	0.770286	+	1.15285i	0.0440343	+	0.0659040i
$307$	25.7087			1.46727			0.733636	−	0.679543i	$-0.237822\pi$
$307$	25.7087			1.46727			0.733636	+	0.679543i	$0.237822\pi$
$308$	5.27974	−	16.7369i	0.300841	−	0.953674i
$309$	−12.8026			−0.728317
$310$	−17.2429	−	25.8067i	−0.979333	−	1.46572i
$311$	6.75984	+	20.8046i	0.383315	+	1.17972i	0.937695	+	0.347459i	$0.112955\pi$
$311$	6.75984	+	20.8046i	0.383315	+	1.17972i	−0.554380	+	0.832264i	$0.687045\pi$
$312$	−2.68860	−	1.23960i	−0.152212	−	0.0701785i
$313$	7.05603	−	9.71179i	0.398830	−	0.548943i	−0.561620	−	0.827396i	$-0.689822\pi$
$313$	7.05603	−	9.71179i	0.398830	−	0.548943i	0.960450	+	0.278453i	$0.0898215\pi$
$314$	3.47834	−	4.41212i	0.196294	−	0.248991i
$315$	−0.866062	−	10.1076i	−0.0487971	−	0.569499i
$316$	−26.5590	+	6.37546i	−1.49406	+	0.358648i
$317$	11.8719	−	8.62545i	0.666793	−	0.484454i	−0.202157	−	0.979353i	$-0.564795\pi$
$317$	11.8719	−	8.62545i	0.666793	−	0.484454i	0.868950	+	0.494899i	$0.164795\pi$
$318$	−17.3052	−	0.680170i	−0.970427	−	0.0381420i
$319$	5.54065	−	17.1502i	0.310217	−	0.960228i
$320$	−7.16337	+	29.8263i	−0.400445	+	1.66734i
$321$	−0.589403	−	0.811243i	−0.0328973	−	0.0452792i
$322$	−7.19910	−	9.00314i	−0.401190	−	0.501725i
$323$	0.967749	+	0.314441i	0.0538470	+	0.0174959i
$324$	−1.52077	−	1.29894i	−0.0844875	−	0.0721633i
$325$	−5.96915	+	8.21583i	−0.331109	+	0.455732i
$326$	4.63951	+	1.71168i	0.256958	+	0.0948012i
$327$	4.61201	+	14.1943i	0.255045	+	0.784947i
$328$	−6.03361	−	10.7749i	−0.333150	−	0.594942i
$329$	−5.45260	−	12.9097i	−0.300611	−	0.711737i
$330$	−17.3011	+	4.91051i	−0.952397	+	0.270315i
$331$		−	31.0738i		−	1.70797i	−0.520296	−	0.853986i	$-0.674178\pi$
$331$		−	31.0738i		−	1.70797i	0.520296	−	0.853986i	$-0.325822\pi$
$332$	−12.7794	+	7.83070i	−0.701359	+	0.429766i
$333$	2.41682	+	7.43822i	0.132441	+	0.407612i
$334$	−10.2945	+	27.9033i	−0.563292	+	1.52680i
$335$	−4.10040	−	2.97911i	−0.224029	−	0.162766i
$336$	3.98259	−	9.80505i	0.217268	−	0.534909i
$337$	−0.583205	+	1.79492i	−0.0317692	+	0.0977755i	−0.965684	−	0.259721i	$-0.916369\pi$
$337$	−0.583205	+	1.79492i	−0.0317692	+	0.0977755i	0.933915	+	0.357496i	$0.116369\pi$
$338$	4.56955	+	16.2033i	0.248551	+	0.881343i
$339$	−7.36550	+	5.35135i	−0.400039	+	0.290645i
$340$	7.49519	+	0.590100i	0.406484	+	0.0320026i
$341$	15.3392	−	11.1840i	0.830665	−	0.605645i
$342$	−1.46666	−	0.0576461i	−0.0793078	−	0.00311714i
$343$	−17.9147	+	4.69721i	−0.967302	+	0.253625i
$344$	−6.91841	+	1.37585i	−0.373016	+	0.0741808i
$345$	−3.65041	+	11.2348i	−0.196531	+	0.604861i
$346$	−21.5796	+	27.3728i	−1.16013	+	1.47157i
$347$	10.2679	−	14.1326i	0.551211	−	0.758676i	−0.438965	−	0.898504i	$-0.644655\pi$
$347$	10.2679	−	14.1326i	0.551211	−	0.758676i	0.990176	+	0.139828i	$0.0446549\pi$
$348$	4.15940	−	10.0409i	0.222967	−	0.538247i
$349$	−18.0476	+	5.86402i	−0.966067	+	0.313894i	−0.749227	−	0.662313i	$-0.769575\pi$
$349$	−18.0476	+	5.86402i	−0.966067	+	0.313894i	−0.216839	+	0.976207i	$0.569575\pi$
$350$	−30.3224	−	19.9586i	−1.62080	−	1.06683i
$351$		−	1.04673i		−	0.0558703i
$352$	−18.4070	−	3.63065i	−0.981097	−	0.193514i
$353$			24.8773i			1.32408i	0.749467	+	0.662042i	$0.230310\pi$
$353$			24.8773i			1.32408i	−0.749467	+	0.662042i	$0.769690\pi$
$354$	−13.2300	+	8.83973i	−0.703167	+	0.469827i
$355$	−13.8913	−	42.7530i	−0.737274	−	2.26909i
$356$	27.2154	+	11.2739i	1.44241	+	0.597516i
$357$	−2.52639	−	0.588030i	−0.133711	−	0.0311219i
$358$	9.69285	−	12.2950i	0.512283	−	0.649809i
$359$	35.9684	+	11.6868i	1.89834	+	0.616807i	0.968629	+	0.248513i	$0.0799419\pi$
$359$	35.9684	+	11.6868i	1.89834	+	0.616807i	0.929709	+	0.368294i	$0.120058\pi$
$360$	−10.6368	+	2.11531i	−0.560607	+	0.111487i
$361$	14.4998	−	10.5348i	0.763150	−	0.554461i
$362$	0.687053	−	17.4803i	0.0361107	−	0.918745i
$363$	−3.43427	−	10.4502i	−0.180253	−	0.548491i
$364$	5.25574	−	1.74792i	0.275476	−	0.0916159i
$365$	6.53752	−	4.74979i	0.342190	−	0.248615i
$366$	8.65071	−	2.43962i	0.452180	−	0.127521i
$367$	2.69170	−	8.28420i	0.140506	−	0.432432i	−0.855900	−	0.517141i	$-0.826996\pi$
$367$	2.69170	−	8.28420i	0.140506	−	0.432432i	0.996406	+	0.0847094i	$0.0269962\pi$
$368$	−8.71448	+	8.71348i	−0.454274	+	0.454222i
$369$	2.56632	−	3.53224i	0.133598	−	0.183881i
$370$	39.7882	+	14.6793i	2.06849	+	0.763140i
$371$	24.4906	−	21.2125i	1.27149	−	1.10130i
$372$	9.76074	−	5.98100i	0.506071	−	0.310101i
$373$	5.44874			0.282125			0.141063	−	0.990001i	$-0.454948\pi$
$373$	5.44874			0.282125			0.141063	+	0.990001i	$0.454948\pi$
$374$	−0.172893	+	4.59527i	−0.00894007	+	0.237616i
$375$			18.0287i			0.931001i
$376$	−13.0717	+	7.31977i	−0.674121	+	0.377488i
$377$	5.40968	−	1.75771i	0.278613	−	0.0905268i
$378$	3.73767	−	0.172771i	0.192245	−	0.00888636i
$379$	20.0326	−	27.5725i	1.02900	−	1.41630i	0.123310	−	0.992368i	$-0.460649\pi$
$379$	20.0326	−	27.5725i	1.02900	−	1.41630i	0.905693	−	0.423934i	$-0.139351\pi$
$380$	−5.16923	+	6.05204i	−0.265176	+	0.310463i
$381$	−3.52199	−	1.14437i	−0.180437	−	0.0586276i
$382$	20.7912	−	5.86340i	1.06377	−	0.299998i
$383$	6.19940	−	4.50413i	0.316774	−	0.230150i	−0.418023	−	0.908436i	$-0.637277\pi$
$383$	6.19940	−	4.50413i	0.316774	−	0.230150i	0.734798	+	0.678286i	$0.237277\pi$
$384$	−10.8886	−	3.07209i	−0.555658	−	0.156772i
$385$	17.3322	−	28.8383i	0.883331	−	1.46973i
$386$	6.86879	+	0.269974i	0.349612	+	0.0137413i
$387$	−1.46589	−	2.01763i	−0.0745155	−	0.102562i
$388$	−33.0191	+	7.92618i	−1.67629	+	0.402391i
$389$	−1.90927	+	5.87614i	−0.0968040	+	0.297932i	−0.987720	−	0.156237i	$-0.950064\pi$
$389$	−1.90927	+	5.87614i	−0.0968040	+	0.297932i	0.890916	+	0.454169i	$0.150064\pi$
$390$	−4.45736	−	3.51400i	−0.225707	−	0.177938i
$391$	2.44364	+	1.77541i	0.123580	+	0.0897861i
$392$	7.10897	+	18.4787i	0.359057	+	0.933315i
$393$	3.44300	+	10.5965i	0.173676	+	0.534521i
$394$	18.3034	−	12.2296i	0.922111	−	0.616116i
$395$	−52.3643			−2.63473
$396$	−1.55914	−	6.44741i	−0.0783496	−	0.323995i
$397$			23.4255i			1.17569i	0.808973	+	0.587846i	$0.200024\pi$
$397$			23.4255i			1.17569i	−0.808973	+	0.587846i	$0.799976\pi$
$398$	−26.0799	+	17.4255i	−1.30727	+	0.873461i
$399$	2.07564	−	1.79781i	0.103912	−	0.0900032i
$400$	−17.6203	+	34.5770i	−0.881017	+	1.72885i
$401$	2.51411	+	1.82661i	0.125549	+	0.0912164i	0.648787	−	0.760970i	$-0.275276\pi$
$401$	2.51411	+	1.82661i	0.125549	+	0.0912164i	−0.523239	+	0.852186i	$0.675276\pi$
$402$	1.15734	−	1.46803i	0.0577228	−	0.0732188i
$403$	5.69797	+	1.85138i	0.283836	+	0.0922240i
$404$	14.8263	−	3.55903i	0.737636	−	0.177068i
$405$	−2.25375	−	3.10202i	−0.111990	−	0.154141i
$406$	7.16935	+	19.0268i	0.355809	+	0.944284i
$407$	−7.97429	+	24.6832i	−0.395271	+	1.22350i
$408$	−0.326051	+	2.75378i	−0.0161419	+	0.136332i
$409$	−12.5029	−	17.2087i	−0.618228	−	0.850918i	0.378994	−	0.925399i	$-0.376270\pi$
$409$	−12.5029	−	17.2087i	−0.618228	−	0.850918i	−0.997222	+	0.0744811i	$0.976270\pi$
$410$	−6.42611	−	22.7865i	−0.317363	−	1.12535i
$411$	−2.35711	+	7.25443i	−0.116267	+	0.357834i
$412$	−19.4699	−	16.6299i	−0.959215	−	0.819294i
$413$	6.74818	−	28.9926i	0.332056	−	1.42663i
$414$	−4.08767	−	1.50809i	−0.200898	−	0.0741184i
$415$	−27.3275	+	8.87924i	−1.34145	+	0.435865i
$416$	−2.47858	−	5.37747i	−0.121523	−	0.263652i
$417$	20.5946			1.00852
$418$	−3.82802	−	3.00745i	−0.187234	−	0.147099i
$419$	−20.7894			−1.01563			−0.507813	−	0.861467i	$-0.669546\pi$
$419$	−20.7894			−1.01563			−0.507813	+	0.861467i	$0.669546\pi$
$420$	11.8121	−	16.4963i	0.576370	−	0.804939i
$421$	−0.0534072	−	0.164370i	−0.00260291	−	0.00801092i	0.949747	−	0.313020i	$-0.101341\pi$
$421$	−0.0534072	−	0.164370i	−0.00260291	−	0.00801092i	−0.952350	+	0.305009i	$0.901341\pi$
$422$	16.7013	+	6.16170i	0.813006	+	0.299947i
$423$	−4.28520	−	3.11338i	−0.208353	−	0.151378i
$424$	−25.4338	−	23.5128i	−1.23517	−	1.14188i
$425$	9.04633	+	2.93933i	0.438812	+	0.142579i
$426$	15.9577	−	4.50029i	0.773153	−	0.218040i
$427$	−8.68629	+	14.3979i	−0.420359	+	0.696766i
$428$	0.157407	−	1.99932i	0.00760856	−	0.0966406i
$429$	2.03585	−	2.81201i	0.0982916	−	0.135765i
$430$	−13.5130	−	0.531119i	−0.651653	−	0.0256128i
$431$	7.72768	+	10.6362i	0.372229	+	0.512330i	0.953505	−	0.301377i	$-0.0974463\pi$
$431$	7.72768	+	10.6362i	0.372229	+	0.512330i	−0.581276	+	0.813707i	$0.697446\pi$
$432$	−0.625512	−	3.95079i	−0.0300950	−	0.190082i
$433$	−16.6058	−	5.39556i	−0.798025	−	0.259294i	−0.118507	−	0.992953i	$-0.537811\pi$
$433$	−16.6058	−	5.39556i	−0.798025	−	0.259294i	−0.679518	+	0.733659i	$0.737811\pi$
$434$	−5.67043	+	20.6519i	−0.272189	+	0.991324i
$435$	12.2472	−	16.8568i	0.587209	−	0.808223i
$436$	−11.4237	+	27.5771i	−0.547097	+	1.32070i
$437$	−3.04107	+	0.988105i	−0.145474	+	0.0472675i
$438$	1.65582	+	2.47818i	0.0791181	+	0.118412i
$439$	6.53113			0.311714			0.155857	−	0.987780i	$-0.450186\pi$
$439$	6.53113			0.311714			0.155857	+	0.987780i	$0.450186\pi$
$440$	−32.6896	−	15.0054i	−1.55842	−	0.715352i
$441$	−4.88061	+	5.01793i	−0.232410	+	0.238949i
$442$	−1.20672	+	0.806281i	−0.0573979	+	0.0383509i
$443$	7.65145	−	2.48611i	0.363531	−	0.118118i	−0.121555	−	0.992585i	$-0.538788\pi$
$443$	7.65145	−	2.48611i	0.363531	−	0.118118i	0.485086	+	0.874466i	$0.338788\pi$
$444$	−5.98635	+	14.4512i	−0.284100	+	0.685822i
$445$	45.6899	+	33.1956i	2.16591	+	1.57362i
$446$	−1.84039	−	1.45089i	−0.0871449	−	0.0687015i
$447$	0.892785	−	2.74771i	0.0422273	−	0.129962i
$448$	18.7928	−	9.73813i	0.887876	−	0.460083i
$449$	2.89688	−	2.10471i	0.136712	−	0.0993273i	−0.517327	−	0.855788i	$-0.673073\pi$
$449$	2.89688	−	2.10471i	0.136712	−	0.0993273i	0.654040	+	0.756460i	$0.273073\pi$
$450$	−13.7100	−	0.538865i	−0.646298	−	0.0254023i
$451$	13.7644	−	4.49788i	0.648142	−	0.211797i
$452$	−18.1523	−	1.42914i	−0.853814	−	0.0672211i
$453$	−0.212393	−	0.292334i	−0.00997910	−	0.0137350i
$454$	5.26901	+	18.6835i	0.247287	+	0.876861i
$455$	10.5799	−	0.906533i	0.495995	−	0.0424989i
$456$	−2.15558	−	1.99277i	−0.100944	−	0.0933199i
$457$	−18.6365	−	13.5402i	−0.871780	−	0.633385i	0.0592842	−	0.998241i	$-0.481118\pi$
$457$	−18.6365	−	13.5402i	−0.871780	−	0.633385i	−0.931064	+	0.364856i	$0.881118\pi$
$458$	−7.88461	−	2.90891i	−0.368424	−	0.135925i
$459$	−0.932424	+	0.302963i	−0.0435218	+	0.0141411i
$460$	−20.1448	+	12.3439i	−0.939255	+	0.575539i
$461$			24.0276i			1.11908i	0.828805	+	0.559538i	$0.189021\pi$
$461$			24.0276i			1.11908i	−0.828805	+	0.559538i	$0.810979\pi$
$462$	10.3772	+	6.80546i	0.482790	+	0.316619i
$463$			21.6362i			1.00552i	0.864426	+	0.502761i	$0.167682\pi$
$463$			21.6362i			1.00552i	−0.864426	+	0.502761i	$0.832318\pi$
$464$	19.3680	−	9.86709i	0.899136	−	0.458068i
$465$	20.8724	−	6.78186i	0.967936	−	0.314501i
$466$	1.64699	−	4.46418i	0.0762955	−	0.206799i
$467$	22.2181	+	16.1424i	1.02813	+	0.746981i	0.967934	−	0.251206i	$-0.0808270\pi$
$467$	22.2181	+	16.1424i	1.02813	+	0.746981i	0.0601973	+	0.998186i	$0.480827\pi$
$468$	1.35964	−	1.59184i	0.0628493	−	0.0735829i
$469$	0.298567	+	3.48451i	0.0137866	+	0.160900i
$470$	−27.6438	+	7.79594i	−1.27511	+	0.359600i
$471$	2.33513	+	3.21403i	0.107597	+	0.148095i
$472$	−31.6021	−	3.74173i	−1.45461	−	0.172227i
$473$	−0.0138783	−	8.27141i	−0.000638126	−	0.380320i
$474$	0.758523	−	19.2987i	0.0348401	−	0.886418i
$475$	−8.14640	+	5.91871i	−0.373783	+	0.271569i
$476$	−3.07825	−	4.17589i	−0.141091	−	0.191401i
$477$	3.78424	−	11.6467i	0.173269	−	0.533266i
$478$	19.8444	−	25.1717i	0.907660	−	1.15133i
$479$	12.5188	+	9.09546i	0.572000	+	0.415582i	0.835831	−	0.548987i	$-0.184986\pi$
$479$	12.5188	+	9.09546i	0.572000	+	0.415582i	−0.263831	+	0.964569i	$0.584986\pi$
$480$	−18.9238	−	10.5996i	−0.863750	−	0.483804i
$481$	−7.78581	+	2.52976i	−0.355002	+	0.115347i
$482$	7.60830	+	11.3870i	0.346549	+	0.518663i
$483$	7.50890	−	3.17148i	0.341667	−	0.144307i
$484$	8.35136	−	20.3532i	0.379607	−	0.925148i
$485$	−65.1011			−2.95609
$486$	1.17589	−	0.785678i	0.0533393	−	0.0356391i
$487$	−4.98867	+	1.62092i	−0.226058	+	0.0734507i	−0.419856	−	0.907591i	$-0.637919\pi$
$487$	−4.98867	+	1.62092i	−0.226058	+	0.0734507i	0.193798	+	0.981041i	$0.437919\pi$
$488$	16.3247	+	7.52663i	0.738984	+	0.340715i
$489$	−2.05535	+	2.82895i	−0.0929463	+	0.127930i
$490$	4.98335	+	37.6292i	0.225125	+	1.69991i
$491$	−12.3709	−	4.01955i	−0.558291	−	0.181400i	0.0162611	−	0.999868i	$-0.494824\pi$
$491$	−12.3709	−	4.01955i	−0.558291	−	0.181400i	−0.574552	+	0.818468i	$0.694824\pi$
$492$	8.49097	−	2.03825i	0.382803	−	0.0918912i
$493$	−3.13153	−	4.31018i	−0.141037	−	0.194121i
$494$	0.0603399	−	1.53520i	0.00271482	−	0.0690717i
$495$	−0.0213374	−	12.7170i	−0.000959043	−	0.571585i
$496$	22.6128	+	3.58285i	1.01535	+	0.160875i
$497$	−16.0233	+	26.5595i	−0.718745	+	1.19135i
$498$	−2.87656	−	10.2001i	−0.128902	−	0.457076i
$499$	−42.3172	−	13.7497i	−1.89438	−	0.615520i	−0.975031	−	0.222069i	$-0.928719\pi$
$499$	−42.3172	−	13.7497i	−1.89438	−	0.615520i	−0.919346	−	0.393451i	$-0.871281\pi$
$500$	−23.4183	+	27.4177i	−1.04730	+	1.22616i
$501$	−17.0141	−	12.3615i	−0.760135	−	0.552271i
$502$	−13.4282	+	36.3971i	−0.599329	+	1.62448i
$503$	−8.03639	−	24.7335i	−0.358325	−	1.10281i	−0.954056	−	0.299627i	$-0.903138\pi$
$503$	−8.03639	−	24.7335i	−0.358325	−	1.10281i	0.595732	−	0.803184i	$-0.296862\pi$
$504$	5.90857	+	4.59226i	0.263189	+	0.204555i
$505$	29.2318			1.30080
$506$	−8.04825	−	12.0018i	−0.357788	−	0.533544i
$507$	−11.9044			−0.528691
$508$	−3.86970	−	6.31518i	−0.171690	−	0.280191i
$509$	−16.1164	+	5.23655i	−0.714349	+	0.232106i	−0.643571	−	0.765386i	$-0.722548\pi$
$509$	−16.1164	+	5.23655i	−0.714349	+	0.232106i	−0.0707776	+	0.997492i	$0.522548\pi$
$510$	−1.84013	+	4.98768i	−0.0814825	+	0.220858i
$511$	−5.43076	−	1.26404i	−0.240243	−	0.0559178i
$512$	−12.5687	−	18.8156i	−0.555463	−	0.831541i
$513$	0.320724	−	0.987087i	0.0141603	−	0.0435810i
$514$	19.7617	−	5.57308i	0.871653	−	0.245818i
$515$	−28.8540	−	39.7141i	−1.27146	−	1.75001i
$516$	0.391484	−	4.97247i	0.0172341	−	0.218901i
$517$	−5.45668	−	16.6985i	−0.239984	−	0.734401i
$518$	−10.3184	−	27.3840i	−0.453364	−	1.20318i
$519$	−14.4872	−	19.9399i	−0.635916	−	0.875263i
$520$	−2.21416	−	11.1338i	−0.0970974	−	0.488251i
$521$	−18.2343	−	5.92467i	−0.798858	−	0.259565i	−0.118986	−	0.992896i	$-0.537964\pi$
$521$	−18.2343	−	5.92467i	−0.798858	−	0.259565i	−0.679872	+	0.733331i	$0.737964\pi$
$522$	6.03512	+	4.75784i	0.264150	+	0.208245i
$523$	−33.3205	−	24.2087i	−1.45700	−	1.05857i	−0.984131	−	0.177443i	$-0.943218\pi$
$523$	−33.3205	−	24.2087i	−1.45700	−	1.05857i	−0.472871	−	0.881131i	$-0.656782\pi$
$524$	−8.52814	+	20.5871i	−0.372554	+	0.899351i
$525$	19.4027	−	16.8056i	0.846805	−	0.733458i
$526$	18.1396	+	27.1487i	0.790924	+	1.18374i
$527$		−	5.61160i		−	0.244445i
$528$	6.00370	−	11.8303i	0.261277	−	0.514847i
$529$	13.5083			0.587318
$530$	−36.8917	−	55.2140i	−1.60247	−	2.39834i
$531$	−3.47678	−	10.7004i	−0.150879	−	0.464359i
$532$	5.49184	−	0.0379335i	0.238101	−	0.00164463i
$533$	3.69731	+	2.68625i	0.160148	+	0.116354i
$534$	−12.8960	+	16.3580i	−0.558063	+	0.707879i
$535$	1.18813	−	3.65668i	0.0513673	−	0.158092i
$536$	3.66694	−	0.729236i	0.158388	−	0.0314982i
$537$	6.50715	+	8.95632i	0.280804	+	0.386494i
$538$	−1.26283	+	32.1294i	−0.0544443	+	1.38520i
$539$	−22.8713	+	3.98794i	−0.985137	+	0.171773i
$540$	0.601891	−	7.64497i	0.0259013	−	0.328987i
$541$	16.8106	−	12.2136i	0.722743	−	0.525103i	−0.164517	−	0.986374i	$-0.552606\pi$
$541$	16.8106	−	12.2136i	0.722743	−	0.525103i	0.887259	+	0.461271i	$0.152606\pi$
$542$	0.525061	+	1.86183i	0.0225533	+	0.0799723i
$543$	11.7646	+	3.82254i	0.504866	+	0.164041i
$544$	−4.07284	+	3.76436i	−0.174622	+	0.161396i
$545$	−33.6368	+	46.2970i	−1.44084	+	1.98315i
$546$	0.180844	+	3.91233i	0.00773942	+	0.167432i
$547$	−24.8523	+	8.07500i	−1.06261	+	0.345262i	−0.787605	−	0.616181i	$-0.788679\pi$
$547$	−24.8523	+	8.07500i	−1.06261	+	0.345262i	−0.275003	+	0.961443i	$0.588679\pi$
$548$	−13.0077	+	7.97061i	−0.555661	+	0.340488i
$549$			6.35557i			0.271249i
$550$	−35.7836	−	28.1131i	−1.52582	−	1.19875i
$551$	5.64001			0.240273
$552$	−4.25751	−	7.60310i	−0.181212	−	0.323609i
$553$	23.6561	+	27.3119i	1.00596	+	1.16142i
$554$	1.94448	−	5.27050i	0.0826129	−	0.223922i
$555$	−17.6266	+	24.2609i	−0.748208	+	1.02982i
$556$	31.3197	+	26.7511i	1.32825	+	1.13450i
$557$	−2.79288	+	8.59559i	−0.118338	+	0.364207i	−0.992629	−	0.121196i	$-0.961327\pi$
$557$	−2.79288	+	8.59559i	−0.118338	+	0.364207i	0.874291	+	0.485403i	$0.161327\pi$
$558$	2.19708	+	7.79070i	0.0930100	+	0.329807i
$559$	2.11191	−	1.53439i	0.0893244	−	0.0648980i
$560$	39.3913	−	9.74406i	1.66458	−	0.411762i
$561$	−3.09418	−	0.999624i	−0.130636	−	0.0422042i
$562$	21.0291	+	0.826535i	0.887058	+	0.0348653i
$563$	33.6492	−	24.4476i	1.41814	−	1.03034i	0.426070	−	0.904690i	$-0.359898\pi$
$563$	33.6492	−	24.4476i	1.41814	−	1.03034i	0.992074	−	0.125653i	$-0.0401024\pi$
$564$	−2.47273	−	10.3010i	−0.104121	−	0.433749i
$565$	−33.2000	−	10.7873i	−1.39673	−	0.453827i
$566$	18.1737	+	14.3274i	0.763898	+	0.602227i
$567$	−0.599781	+	2.57687i	−0.0251884	+	0.108218i
$568$	30.1137	+	13.8842i	1.26354	+	0.582566i
$569$	−0.537536	−	1.65436i	−0.0225347	−	0.0693546i	0.939157	−	0.343489i	$-0.111609\pi$
$569$	−0.537536	−	1.65436i	−0.0225347	−	0.0693546i	−0.961691	+	0.274134i	$0.911609\pi$
$570$	−3.12666	−	4.67953i	−0.130962	−	0.196004i
$571$		−	8.89550i		−	0.372265i	−0.982525	−	0.186133i	$-0.940405\pi$
$571$		−	8.89550i		−	0.372265i	0.982525	−	0.186133i	$-0.0595954\pi$
$572$	6.74870	−	1.63200i	0.282177	−	0.0682372i
$573$			15.2750i			0.638124i
$574$	−8.98180	+	13.6457i	−0.374893	+	0.569562i
$575$	−28.4274	+	9.23662i	−1.18550	+	0.385194i
$576$	4.18057	−	6.82076i	0.174191	−	0.284198i
$577$	7.95794	−	10.9532i	0.331293	−	0.455986i	−0.610580	−	0.791955i	$-0.709064\pi$
$577$	7.95794	−	10.9532i	0.331293	−	0.455986i	0.941873	+	0.335969i	$0.109064\pi$
$578$	−17.8126	−	14.0427i	−0.740906	−	0.584100i
$579$	−1.50204	+	4.62282i	−0.0624228	+	0.192118i
$580$	40.5212	−	9.72707i	1.68255	−	0.403895i
$581$	16.9767	+	10.2420i	0.704310	+	0.424911i
$582$	0.943021	−	23.9928i	0.0390895	−	0.994532i
$583$	32.8186	−	23.9283i	1.35921	−	0.991011i
$584$	−0.700884	+	5.91957i	−0.0290028	+	0.244954i
$585$	3.24698	−	2.35907i	0.134246	−	0.0975355i
$586$	25.5274	−	7.19908i	1.05453	−	0.297391i
$587$	−9.95510	+	30.6387i	−0.410891	+	1.26459i	0.504984	+	0.863129i	$0.331498\pi$
$587$	−9.95510	+	30.6387i	−0.410891	+	1.26459i	−0.915875	+	0.401464i	$0.868502\pi$
$588$	−13.9403	+	1.29152i	−0.574888	+	0.0532613i
$589$	4.80602	+	3.49178i	0.198029	+	0.143876i
$590$	−57.2382	−	21.1172i	−2.35646	−	0.869382i
$591$	4.81004	+	14.8038i	0.197858	+	0.608946i
$592$	−27.8751	+	14.2011i	−1.14566	+	0.583660i
$593$			7.69817i			0.316126i	0.987429	+	0.158063i	$0.0505249\pi$
$593$			7.69817i			0.316126i	−0.987429	+	0.158063i	$0.949475\pi$
$594$	4.68710	+	0.176348i	0.192314	+	0.00723563i
$595$	−3.86977	−	9.16219i	−0.158645	−	0.375613i
$596$	4.92683	−	3.01897i	0.201811	−	0.123662i
$597$	−6.85366	−	21.0934i	−0.280502	−	0.863295i
$598$	1.57856	−	4.27869i	0.0645521	−	0.174968i
$599$	−13.5827	+	18.6950i	−0.554974	+	0.763856i	−0.990677	−	0.136235i	$-0.956500\pi$
$599$	−13.5827	+	18.6950i	−0.554974	+	0.763856i	0.435703	+	0.900091i	$0.356500\pi$
$600$	−20.1499	−	18.6280i	−0.822618	−	0.760485i
$601$	14.9615	+	4.86129i	0.610292	+	0.198296i	0.597826	−	0.801626i	$-0.296032\pi$
$601$	14.9615	+	4.86129i	0.610292	+	0.198296i	0.0124669	+	0.999922i	$0.496032\pi$
$602$	5.82761	+	7.28796i	0.237515	+	0.297035i
$603$	0.776962	+	1.06940i	0.0316403	+	0.0435492i
$604$	0.0567221	−	0.720460i	0.00230799	−	0.0293151i
$605$	24.6766	−	34.2053i	1.00325	−	1.39064i
$606$	−0.423437	+	10.7733i	−0.0172010	+	0.437635i
$607$	16.2376	−	11.7973i	0.659065	−	0.478839i	−0.207282	−	0.978281i	$-0.566462\pi$
$607$	16.2376	−	11.7973i	0.659065	−	0.478839i	0.866347	+	0.499442i	$0.166462\pi$
$608$	−0.689665	−	5.83051i	−0.0279696	−	0.236459i
$609$	−14.3249	+	1.22742i	−0.580474	+	0.0497375i
$610$	27.0643	+	21.3364i	1.09580	+	0.863886i
$611$	3.25887	−	4.48545i	0.131840	−	0.181462i
$612$	−1.81154	−	0.750424i	−0.0732271	−	0.0303341i
$613$	12.0999	+	37.2398i	0.488712	+	1.50410i	0.826531	+	0.562891i	$0.190311\pi$
$613$	12.0999	+	37.2398i	0.488712	+	1.50410i	−0.337819	+	0.941211i	$0.609689\pi$
$614$	−30.2305	+	20.1987i	−1.22000	+	0.815155i
$615$	16.7410			0.675061
$616$	6.94146	+	23.8289i	0.279679	+	0.960093i
$617$	11.0516			0.444921			0.222461	−	0.974942i	$-0.428591\pi$
$617$	11.0516			0.444921			0.222461	+	0.974942i	$0.428591\pi$
$618$	15.0545	−	10.0588i	0.605579	−	0.404623i
$619$	8.32442	+	25.6199i	0.334587	+	1.02975i	0.966925	+	0.255060i	$0.0820952\pi$
$619$	8.32442	+	25.6199i	0.334587	+	1.02975i	−0.632338	+	0.774692i	$0.717905\pi$
$620$	40.5515	+	16.7983i	1.62859	+	0.674637i
$621$	1.81088	−	2.49247i	0.0726682	−	0.100019i
$622$	−24.2945	−	19.1528i	−0.974123	−	0.767959i
$623$	−3.32688	−	38.8271i	−0.133288	−	1.55558i
$624$	4.13541	−	0.654743i	0.165549	−	0.0262107i
$625$	−16.6804	+	12.1190i	−0.667216	+	0.484761i
$626$	−0.666749	+	16.9637i	−0.0266487	+	0.678007i
$627$	2.78146	−	2.02799i	0.111081	−	0.0809900i
$628$	−0.623625	+	7.92102i	−0.0248853	+	0.316083i
$629$	4.50701	+	6.20337i	0.179706	+	0.247344i
$630$	8.95971	+	11.2049i	0.356963	+	0.446416i
$631$	25.3368	+	8.23242i	1.00864	+	0.327728i	0.766313	−	0.642467i	$-0.222089\pi$
$631$	25.3368	+	8.23242i	1.00864	+	0.327728i	0.242328	+	0.970194i	$0.422089\pi$
$632$	26.2214	−	28.3637i	1.04303	−	1.12825i
$633$	−7.39886	+	10.1837i	−0.294078	+	0.404764i
$634$	−7.18320	+	19.4701i	−0.285281	+	0.773255i
$635$	−4.38785	−	13.5044i	−0.174127	−	0.535907i
$636$	20.8833	−	12.7965i	0.828078	−	0.507414i
$637$	−5.25242	−	5.10869i	−0.208108	−	0.202413i
$638$	6.95938	+	24.5199i	0.275524	+	0.970751i
$639$			11.7239i			0.463791i
$640$	−15.0106	−	40.7005i	−0.593346	−	1.60883i
$641$	8.55779	+	26.3382i	0.338012	+	1.04030i	0.965219	+	0.261442i	$0.0841981\pi$
$641$	8.55779	+	26.3382i	0.338012	+	1.04030i	−0.627207	+	0.778853i	$0.715802\pi$
$642$	1.33045	+	0.490849i	0.0525086	+	0.0193723i
$643$	−0.636300	−	0.462299i	−0.0250932	−	0.0182313i	0.575168	−	0.818035i	$-0.304937\pi$
$643$	−0.636300	−	0.462299i	−0.0250932	−	0.0182313i	−0.600261	+	0.799804i	$0.704937\pi$
$644$	15.5389	+	4.93050i	0.612318	+	0.194289i
$645$	2.95497	−	9.09447i	0.116352	−	0.358094i
$646$	−1.38501	+	0.390592i	−0.0544926	+	0.0153677i
$647$	11.1368	−	8.09134i	0.437832	−	0.318103i	−0.346941	−	0.937887i	$-0.612780\pi$
$647$	11.1368	−	8.09134i	0.437832	−	0.318103i	0.784773	+	0.619784i	$0.212780\pi$
$648$	2.80881	+	0.332566i	0.110340	+	0.0130644i
$649$	11.4716	−	35.5086i	0.450300	−	1.39383i
$650$	0.564046	−	14.3507i	0.0221237	−	0.562881i
$651$	−12.9666	−	7.82275i	−0.508200	−	0.306598i
$652$	−6.80036	+	1.63242i	−0.266323	+	0.0639304i
$653$	11.7995	−	36.3152i	0.461751	−	1.42112i	−0.401272	−	0.915959i	$-0.631432\pi$
$653$	11.7995	−	36.3152i	0.461751	−	1.42112i	0.863023	−	0.505165i	$-0.168568\pi$
$654$	−16.5754	−	13.0673i	−0.648148	−	0.510974i
$655$	−25.1108	+	34.5621i	−0.981161	+	1.35045i
$656$	15.5604	+	7.92955i	0.607532	+	0.309597i
$657$	−2.00435	+	0.651254i	−0.0781973	+	0.0254078i
$658$	16.5545	+	10.8964i	0.645363	+	0.424786i
$659$			1.93783i			0.0754872i	0.999287	+	0.0377436i	$0.0120170\pi$
$659$			1.93783i			0.0754872i	−0.999287	+	0.0377436i	$0.987983\pi$
$660$	16.4861	−	19.3673i	0.641721	−	0.753873i
$661$		−	11.0804i		−	0.430976i	−0.976506	−	0.215488i	$-0.930866\pi$
$661$		−	11.0804i		−	0.430976i	0.976506	−	0.215488i	$-0.0691343\pi$
$662$	24.4140	+	36.5393i	0.948878	+	1.42014i
$663$	−0.317120	−	0.975996i	−0.0123159	−	0.0379046i
$664$	8.87467	−	19.2485i	0.344404	−	0.746986i
$665$	10.2548	+	2.38687i	0.397666	+	0.0925589i
$666$	−8.68596	−	6.84766i	−0.336574	−	0.265341i
$667$	15.9224	+	5.17350i	0.616518	+	0.200319i
$668$	−9.81783	−	40.8994i	−0.379863	−	1.58244i
$669$	1.34064	−	0.974031i	0.0518321	−	0.0376582i
$670$	7.16223	+	0.281507i	0.276701	+	0.0108756i
$671$	−12.3613	+	17.0741i	−0.477203	+	0.659137i
$672$	3.02054	+	14.6587i	0.116520	+	0.565470i
$673$	−23.9616	+	17.4091i	−0.923652	+	0.671072i	−0.944430	−	0.328712i	$-0.893386\pi$
$673$	−23.9616	+	17.4091i	−0.923652	+	0.671072i	0.0207784	+	0.999784i	$0.493386\pi$
$674$	−0.724446	−	2.56883i	−0.0279046	−	0.0989477i
$675$	2.99807	−	9.22710i	0.115396	−	0.355151i
$676$	−18.1038	−	15.4630i	−0.696302	−	0.594732i
$677$	−21.7970	+	30.0010i	−0.837728	+	1.15303i	0.148707	+	0.988881i	$0.452489\pi$
$677$	−21.7970	+	30.0010i	−0.837728	+	1.15303i	−0.986435	+	0.164152i	$0.947511\pi$
$678$	4.45655	−	12.0795i	0.171153	−	0.463910i
$679$	29.4101	+	33.9550i	1.12865	+	1.30308i
$680$	−9.27713	+	5.19492i	−0.355762	+	0.199216i
$681$	−13.7265			−0.526002
$682$	−9.25018	+	25.2027i	−0.354208	+	0.965063i
$683$		−	23.7433i		−	0.908511i	−0.890872	−	0.454255i	$-0.849905\pi$
$683$		−	23.7433i		−	0.908511i	0.890872	−	0.454255i	$-0.150095\pi$
$684$	1.76992	−	1.08454i	0.0676744	−	0.0414683i
$685$	−27.8157	+	9.03788i	−1.06278	+	0.345320i
$686$	17.3752	−	19.5986i	0.663387	−	0.748277i
$687$	3.49297	−	4.80766i	0.133265	−	0.183424i
$688$	7.05429	−	7.05349i	0.268942	−	0.268912i
$689$	12.1909	+	3.96108i	0.464438	+	0.150905i
$690$	−4.53447	−	16.0789i	−0.172624	−	0.612113i
$691$	−15.7314	+	11.4295i	−0.598449	+	0.434799i	−0.845328	−	0.534247i	$-0.820595\pi$
$691$	−15.7314	+	11.4295i	−0.598449	+	0.434799i	0.246879	+	0.969046i	$0.420595\pi$
$692$	3.86897	−	49.1420i	0.147076	−	1.86810i
$693$	−6.62320	+	5.75615i	−0.251595	+	0.218658i
$694$	−0.970252	+	24.6856i	−0.0368303	+	0.937052i
$695$	46.4151	+	63.8848i	1.76062	+	2.42329i
$696$	2.99791	+	15.0749i	0.113635	+	0.571411i
$697$	1.32276	−	4.07105i	0.0501033	−	0.154202i
$698$	16.6147	−	21.0750i	0.628876	−	0.797702i
$699$	2.72204	+	1.97768i	0.102957	+	0.0748027i
$700$	51.3367	−	0.354595i	1.94034	−	0.0134024i
$701$	10.0107	+	30.8096i	0.378097	+	1.16366i	0.941365	+	0.337389i	$0.109544\pi$
$701$	10.0107	+	30.8096i	0.378097	+	1.16366i	−0.563268	+	0.826274i	$0.690456\pi$
$702$	0.822393	+	1.23084i	0.0310392	+	0.0464549i
$703$	−8.11730			−0.306150
$704$	24.4971	−	10.1928i	0.923269	−	0.384154i
$705$		−	20.3096i		−	0.764903i
$706$	−19.5455	−	29.2529i	−0.735606	−	1.10095i
$707$	−13.2058	−	15.2466i	−0.496654	−	0.573406i
$708$	8.61180	−	20.7891i	0.323651	−	0.781301i
$709$	−37.5951	−	27.3144i	−1.41191	−	1.02581i	−0.993041	−	0.117769i	$-0.962426\pi$
$709$	−37.5951	−	27.3144i	−1.41191	−	1.02581i	−0.418871	−	0.908046i	$-0.637574\pi$
$710$	49.9247	+	39.3586i	1.87364	+	1.47710i
$711$	12.9884	+	4.22017i	0.487101	+	0.158269i
$712$	−40.8599	+	8.12572i	−1.53129	+	0.304524i
$713$	10.3650	+	14.2662i	0.388173	+	0.534274i
$714$	3.43275	−	1.29347i	0.128467	−	0.0484069i
$715$	13.3112	−	0.0223345i	0.497811	−	0.000835262i
$716$	−1.73781	+	22.0729i	−0.0649451	+	0.824905i
$717$	13.3222	+	18.3365i	0.497527	+	0.684788i
$718$	−51.4768	+	14.5172i	−1.92110	+	0.541776i
$719$	−7.23269	+	22.2599i	−0.269734	+	0.830155i	0.720831	+	0.693111i	$0.243760\pi$
$719$	−7.23269	+	22.2599i	−0.269734	+	0.830155i	−0.990565	+	0.137045i	$0.956240\pi$
$720$	10.8457	−	10.8445i	0.404195	−	0.404149i
$721$	−7.67878	+	32.9908i	−0.285973	+	1.22864i
$722$	−8.77325	+	23.7799i	−0.326507	+	0.884996i
$723$	−9.20978	+	2.99244i	−0.342515	+	0.111290i
$724$	12.9260	+	21.0947i	0.480391	+	0.783977i
$725$	52.7218			1.95804
$726$	12.2488	+	9.58997i	0.454595	+	0.355917i
$727$	2.01439			0.0747098			0.0373549	−	0.999302i	$-0.488107\pi$
$727$	2.01439			0.0747098			0.0373549	+	0.999302i	$0.488107\pi$
$728$	−4.80685	+	6.18468i	−0.178154	+	0.229219i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.95558	+	10.7216i	−0.146403	+	0.396824i
$731$	−1.97810	−	1.43717i	−0.0731627	−	0.0531558i
$732$	−8.25550	+	9.66539i	−0.305132	+	0.357243i
$733$	−39.2053	−	12.7386i	−1.44808	−	0.470509i	−0.523673	−	0.851919i	$-0.675439\pi$
$733$	−39.2053	−	12.7386i	−1.44808	−	0.470509i	−0.924406	+	0.381410i	$0.875439\pi$
$734$	3.34358	+	11.8561i	0.123414	+	0.437616i
$735$	−26.5654	−	3.83061i	−0.979881	−	0.141294i
$736$	3.40125	−	17.0928i	0.125372	−	0.630051i
$737$	0.00735587	+	4.38406i	0.000270957	+	0.161489i
$738$	−0.242501	+	6.16982i	−0.00892659	+	0.227114i
$739$	13.6338	+	18.7654i	0.501529	+	0.690295i	0.982462	−	0.186462i	$-0.0597022\pi$
$739$	13.6338	+	18.7654i	0.501529	+	0.690295i	−0.480933	+	0.876757i	$0.659702\pi$
$740$	−58.3196	+	13.9995i	−2.14387	+	0.514633i
$741$	1.03321	+	0.335711i	0.0379560	+	0.0123327i
$742$	−12.1320	+	44.1853i	−0.445381	+	1.62209i
$743$	20.5162	−	28.2381i	0.752666	−	1.03596i	−0.245123	−	0.969492i	$-0.578828\pi$
$743$	20.5162	−	28.2381i	0.752666	−	1.03596i	0.997789	−	0.0664638i	$-0.0211717\pi$
$744$	−6.77838	+	14.7018i	−0.248507	+	0.538993i
$745$	10.5356	−	3.42322i	0.385994	−	0.125417i
$746$	−6.40710	+	4.28096i	−0.234581	+	0.156737i
$747$	7.49386			0.274186
$748$	−3.40710	−	5.53936i	−0.124576	−	0.202539i
$749$	−2.44398	+	1.03225i	−0.0893011	+	0.0377175i
$750$	−14.1648	−	21.1998i	−0.517225	−	0.774106i
$751$	−0.882113	+	0.286616i	−0.0321888	+	0.0104588i	−0.325067	−	0.945691i	$-0.605387\pi$
$751$	−0.882113	+	0.286616i	−0.0321888	+	0.0104588i	0.292878	+	0.956150i	$0.405387\pi$
$752$	9.61986	−	18.8774i	0.350800	−	0.688387i
$753$	−22.1932	−	16.1243i	−0.808766	−	0.587603i
$754$	−4.98018	+	6.31714i	−0.181367	+	0.230057i
$755$	0.428146	−	1.31770i	0.0155818	−	0.0479559i
$756$	−4.25933	+	3.13976i	−0.154910	+	0.114192i
$757$	33.8072	−	24.5624i	1.22874	−	0.892735i	0.231949	−	0.972728i	$-0.425490\pi$
$757$	33.8072	−	24.5624i	1.22874	−	0.892735i	0.996795	+	0.0799933i	$0.0254899\pi$
$758$	−1.89295	+	48.1612i	−0.0687550	+	1.74929i
$759$	9.71263	−	3.17385i	0.352546	−	0.115204i
$760$	1.32347	−	11.1779i	0.0480074	−	0.405463i
$761$	−18.8182	−	25.9011i	−0.682160	−	0.938913i	0.317797	−	0.948159i	$-0.397057\pi$
$761$	−18.8182	−	25.9011i	−0.682160	−	0.938913i	−0.999957	+	0.00924613i	$0.997057\pi$
$762$	5.04057	−	1.42151i	0.182601	−	0.0514959i
$763$	39.3431	−	3.37109i	1.42432	−	0.122041i
$764$	−19.8413	+	23.2299i	−0.717835	+	0.840428i
$765$	−3.04125	−	2.20960i	−0.109957	−	0.0798882i
$766$	−3.75100	+	10.1671i	−0.135529	+	0.367351i
$767$	11.2005	−	3.63925i	0.404425	−	0.131406i
$768$	15.2175	−	4.94254i	0.549113	−	0.178348i
$769$		−	0.459165i		−	0.0165579i	−0.999966	−	0.00827896i	$-0.997365\pi$
$769$		−	0.459165i		−	0.0165579i	0.999966	−	0.00827896i	$-0.00263530\pi$
$770$	2.27687	+	47.5281i	0.0820527	+	1.71279i
$771$			14.5187i			0.522878i
$772$	−8.28903	+	5.07920i	−0.298329	+	0.182804i
$773$	16.4448	−	5.34323i	0.591478	−	0.192183i	0.00204176	−	0.999998i	$-0.499350\pi$
$773$	16.4448	−	5.34323i	0.591478	−	0.192183i	0.589436	+	0.807815i	$0.299350\pi$
$774$	3.30893	+	1.22078i	0.118937	+	0.0438801i
$775$	44.9258	+	32.6405i	1.61378	+	1.17248i
$776$	32.5993	−	35.2627i	1.17025	−	1.26586i
$777$	20.6169	−	1.76654i	0.739627	−	0.0633744i
$778$	−2.37166	−	8.40975i	−0.0850283	−	0.301504i
$779$	2.66355	+	3.66606i	0.0954316	+	0.131350i
$780$	8.00222	+	0.630018i	0.286525	+	0.0225583i
$781$	−22.8025	+	31.4960i	−0.815939	+	1.12702i
$782$	−4.26834	−	0.167764i	−0.152635	−	0.00599924i
$783$	−4.39631	+	3.19411i	−0.157111	+	0.114148i
$784$	−22.8777	−	16.1435i	−0.817059	−	0.576554i
$785$	−4.70720	+	14.4873i	−0.168007	+	0.517073i
$786$	−12.3740	−	9.75516i	−0.441366	−	0.347955i
$787$	−7.61640	−	5.53364i	−0.271496	−	0.197253i	0.443704	−	0.896173i	$-0.353664\pi$
$787$	−7.61640	−	5.53364i	−0.271496	−	0.197253i	−0.715199	+	0.698920i	$0.753664\pi$
$788$	−11.9142	+	28.7611i	−0.424426	+	1.02457i
$789$	−21.9578	+	7.13453i	−0.781719	+	0.253996i
$790$	61.5745	−	41.1415i	2.19072	−	1.46375i
$791$	9.37204	+	22.1896i	0.333232	+	0.788970i
$792$	6.89896	+	6.35644i	0.245144	+	0.225866i
$793$	−6.65256			−0.236239
$794$	−18.4049	−	27.5457i	−0.653166	−	0.977562i
$795$	44.6571	−	14.5100i	1.58382	−	0.514615i
$796$	16.9762	−	40.9808i	0.601705	−	1.45253i
$797$	19.8306	−	27.2945i	0.702436	−	0.966821i	−0.297491	−	0.954725i	$-0.596150\pi$
$797$	19.8306	−	27.2945i	0.702436	−	0.966821i	0.999927	−	0.0120959i	$-0.00385033\pi$
$798$	−1.02822	+	3.74481i	−0.0363986	+	0.132565i
$799$	−4.93886	−	1.60473i	−0.174724	−	0.0567714i
$800$	−6.44686	−	54.5026i	−0.227931	−	1.92696i
$801$	−8.65752	−	11.9161i	−0.305898	−	0.421033i
$802$	−4.39143	−	0.172603i	−0.155067	−	0.00609481i
$803$	−6.65131	−	2.14881i	−0.234719	−	0.0758298i
$804$	−0.207497	+	2.63554i	−0.00731785	+	0.0929482i
$805$	26.7612	+	16.1450i	0.943208	+	0.569038i
$806$	−8.15476	+	2.29975i	−0.287239	+	0.0810054i
$807$	−21.6237	−	7.02595i	−0.761189	−	0.247325i
$808$	−14.6378	+	15.8337i	−0.514956	+	0.557028i
$809$	−10.7288	−	7.79492i	−0.377204	−	0.274055i	0.382988	−	0.923753i	$-0.374895\pi$
$809$	−10.7288	−	7.79492i	−0.377204	−	0.274055i	−0.760192	+	0.649699i	$0.774895\pi$
$810$	5.08735	+	1.87690i	0.178751	+	0.0659477i
$811$	−1.17442	−	3.61451i	−0.0412396	−	0.126922i	0.928317	−	0.371790i	$-0.121256\pi$
$811$	−1.17442	−	3.61451i	−0.0412396	−	0.126922i	−0.969557	+	0.244867i	$0.921256\pi$
$812$	−23.3793	−	16.7405i	−0.820452	−	0.587478i
$813$	−1.36786			−0.0479730
$814$	−10.0162	−	35.2899i	−0.351067	−	1.23691i
$815$	−13.4077			−0.469652
$816$	−1.78019	−	3.49430i	−0.0623190	−	0.122325i
$817$	2.46172	−	0.799862i	0.0861247	−	0.0279836i
$818$	28.2225	+	10.4123i	0.986777	+	0.364057i
$819$	−2.69729	−	0.627808i	−0.0942509	−	0.0219374i
$820$	25.4592	+	21.7455i	0.889075	+	0.759386i
$821$	6.36034	−	19.5751i	0.221978	−	0.683177i	−0.776607	−	0.629986i	$-0.783061\pi$
$821$	6.36034	−	19.5751i	0.221978	−	0.683177i	0.998584	−	0.0531910i	$-0.0169392\pi$
$822$	−2.92795	−	10.3823i	−0.102124	−	0.362125i
$823$	10.2494	+	14.1071i	0.357272	+	0.491742i	0.949386	−	0.314112i	$-0.101707\pi$
$823$	10.2494	+	14.1071i	0.357272	+	0.491742i	−0.592114	+	0.805854i	$0.701707\pi$
$824$	35.9602	+	4.25773i	1.25273	+	0.148325i
$825$	26.0006	−	18.9572i	0.905223	−	0.660007i
$826$	14.8438	+	39.3939i	0.516480	+	1.37069i
$827$	−14.4050	−	19.8267i	−0.500910	−	0.689443i	0.481444	−	0.876477i	$-0.340113\pi$
$827$	−14.4050	−	19.8267i	−0.500910	−	0.689443i	−0.982353	+	0.187034i	$0.940113\pi$
$828$	5.99151	−	1.43825i	0.208219	−	0.0499827i
$829$	32.9485	+	10.7056i	1.14435	+	0.371822i	0.819012	−	0.573776i	$-0.194522\pi$
$829$	32.9485	+	10.7056i	1.14435	+	0.371822i	0.325338	+	0.945598i	$0.394522\pi$
$830$	25.1578	−	31.9116i	0.873240	−	1.10767i
$831$	3.21370	+	2.33489i	0.111482	+	0.0809965i
$832$	7.13950	+	4.37593i	0.247518	+	0.151708i
$833$	−3.03056	+	6.15748i	−0.105003	+	0.213344i
$834$	−24.2169	+	16.1807i	−0.838562	+	0.560292i
$835$		−	80.6380i		−	2.79059i
$836$	6.86421	+	0.528835i	0.237404	+	0.0182901i
$837$	−5.72373			−0.197841
$838$	24.4459	−	16.3337i	0.844471	−	0.564240i
$839$	17.1298	+	52.7200i	0.591386	+	1.82010i	0.571952	+	0.820287i	$0.306186\pi$
$839$	17.1298	+	52.7200i	0.591386	+	1.82010i	0.0194334	+	0.999811i	$0.493814\pi$
$840$	−0.928844	+	28.6783i	−0.0320481	+	0.989496i
$841$	−0.428681	−	0.311455i	−0.0147821	−	0.0107398i
$842$	0.191943	+	0.151320i	0.00661479	+	0.00521484i
$843$	−4.59857	+	14.1529i	−0.158383	+	0.487453i
$844$	−24.4799	+	5.87637i	−0.842634	+	0.202273i
$845$	−26.8295	−	36.9276i	−0.922962	−	1.27035i
$846$	7.48502	+	0.294194i	0.257340	+	0.0101146i
$847$	−28.9885	+	2.58188i	−0.996057	+	0.0887144i
$848$	48.3807	+	7.66559i	1.66140	+	0.263237i
$849$	−13.2387	+	9.61850i	−0.454352	+	0.330106i
$850$	−12.9468	+	3.65119i	−0.444073	+	0.125235i
$851$	−22.9161	−	7.44589i	−0.785553	−	0.255242i
$852$	−15.2287	+	17.8294i	−0.521726	+	0.610827i
$853$	−15.1406	+	20.8393i	−0.518406	+	0.713524i	−0.985308	−	0.170785i	$-0.945370\pi$
$853$	−15.1406	+	20.8393i	−0.518406	+	0.713524i	0.466903	+	0.884309i	$0.345370\pi$
$854$	−1.09806	−	23.7550i	−0.0375747	−	0.812879i
$855$	3.78480	−	1.22976i	0.129437	−	0.0420568i
$856$	1.38573	+	2.47464i	0.0473632	+	0.0845815i
$857$		−	35.5272i		−	1.21359i	−0.794859	−	0.606794i	$-0.792455\pi$
$857$		−	35.5272i		−	1.21359i	0.794859	−	0.606794i	$-0.207545\pi$
$858$	−0.184588	+	4.90613i	−0.00630174	+	0.167492i
$859$	26.7738			0.913512			0.456756	−	0.889592i	$-0.349011\pi$
$859$	26.7738			0.913512			0.456756	+	0.889592i	$0.349011\pi$
$860$	16.3070	−	9.99231i	0.556065	−	0.340735i
$861$	−7.56290	−	8.73166i	−0.257743	−	0.297574i
$862$	−17.4435	−	6.43554i	−0.594129	−	0.219195i
$863$	−18.1647	+	25.0016i	−0.618335	+	0.851065i	−0.997230	−	0.0743747i	$-0.976304\pi$
$863$	−18.1647	+	25.0016i	−0.618335	+	0.851065i	0.378896	+	0.925439i	$0.376304\pi$
$864$	3.83958	+	4.15423i	0.130625	+	0.141330i
$865$	29.2035	−	89.8790i	0.992948	−	3.05598i
$866$	23.7658	−	6.70227i	0.807593	−	0.227752i
$867$	12.9757	−	9.42737i	0.440677	−	0.320170i
$868$	−9.55797	−	28.7394i	−0.324419	−	0.975480i
$869$	26.6848	+	36.5992i	0.905220	+	1.24154i
$870$	−1.15728	+	29.4441i	−0.0392355	+	0.998248i
$871$	−1.11937	+	0.813269i	−0.0379284	+	0.0275566i
$872$	−8.23371	−	41.4029i	−0.278828	−	1.40208i
$873$	16.1476	+	5.24666i	0.546512	+	0.177573i
$874$	2.79963	−	3.55121i	0.0946988	−	0.120121i
$875$	46.4578	+	10.8133i	1.57056	+	0.365556i
$876$	−3.89411	−	1.61312i	−0.131570	−	0.0545024i
$877$	7.50709	+	23.1045i	0.253497	+	0.780182i	0.994122	+	0.108264i	$0.0345293\pi$
$877$	7.50709	+	23.1045i	0.253497	+	0.780182i	−0.740626	+	0.671918i	$0.765471\pi$
$878$	−7.67986	+	5.13136i	−0.259183	+	0.173175i
$879$			18.7547i			0.632579i
$880$	50.2287	−	8.03891i	1.69321	−	0.270992i
$881$		−	18.1236i		−	0.610598i	−0.952257	−	0.305299i	$-0.901244\pi$
$881$		−	18.1236i		−	0.610598i	0.952257	−	0.305299i	$-0.0987564\pi$
$882$	1.79657	−	9.73511i	0.0604937	−	0.327798i
$883$	−13.9366	+	4.52829i	−0.469005	+	0.152389i	−0.533979	−	0.845498i	$-0.679304\pi$
$883$	−13.9366	+	4.52829i	−0.469005	+	0.152389i	0.0649735	+	0.997887i	$0.479304\pi$
$884$	0.785491	−	1.89619i	0.0264189	−	0.0637758i
$885$	25.3572	−	34.9011i	0.852372	−	1.17319i
$886$	−7.04396	+	8.93496i	−0.236646	+	0.300176i
$887$	−10.2712	+	31.6116i	−0.344875	+	1.06142i	0.616776	+	0.787139i	$0.288438\pi$
$887$	−10.2712	+	31.6116i	−0.344875	+	1.06142i	−0.961651	+	0.274277i	$0.911562\pi$
$888$	−4.31469	−	21.6963i	−0.144792	−	0.728079i
$889$	−5.06130	+	8.38936i	−0.169751	+	0.281370i
$890$	−79.8072	−	3.13677i	−2.67514	−	0.105145i
$891$	−1.01960	+	3.15601i	−0.0341579	+	0.105730i
$892$	3.30402	+	0.260127i	0.110627	+	0.00870968i
$893$	4.44754	−	3.23133i	0.148831	−	0.108132i
$894$	1.10900	+	3.93244i	0.0370905	+	0.131520i
$895$	−13.1172	+	40.3707i	−0.438460	+	1.34944i
$896$	−14.4472	+	26.2160i	−0.482646	+	0.875816i
$897$	2.60894	+	1.89551i	0.0871099	+	0.0632891i
$898$	−1.75278	+	4.75092i	−0.0584911	+	0.158540i
$899$	−9.61153	−	29.5812i	−0.320562	−	0.986590i
$900$	16.5448	−	10.1380i	0.551495	−	0.337935i
$901$		−	12.0061i		−	0.399983i
$902$	−12.6515	+	16.1034i	−0.421250	+	0.536185i
$903$	−6.07838	+	2.56728i	−0.202276	+	0.0854338i
$904$	22.4679	−	12.5814i	0.747272	−	0.418451i
$905$	14.6568	+	45.1090i	0.487209	+	1.49947i
$906$	0.479431	+	0.176879i	0.0159280	+	0.00587641i
$907$	−18.1712	+	25.0106i	−0.603366	+	0.830462i	−0.996011	−	0.0892279i	$-0.971560\pi$
$907$	−18.1712	+	25.0106i	−0.603366	+	0.830462i	0.392645	+	0.919690i	$0.371560\pi$
$908$	−20.8750	−	17.8300i	−0.692761	−	0.591708i
$909$	−7.25061	−	2.35587i	−0.240488	−	0.0781391i
$910$	−11.7286	+	9.37840i	−0.388798	+	0.310891i
$911$	−12.3584	−	17.0099i	−0.409454	−	0.563565i	0.553631	−	0.832762i	$-0.313242\pi$
$911$	−12.3584	−	17.0099i	−0.409454	−	0.563565i	−0.963085	+	0.269197i	$0.913242\pi$
$912$	4.10039	+	0.649678i	0.135777	+	0.0215130i
$913$	20.1321	+	14.5753i	0.666274	+	0.482370i
$914$	32.5527	+	1.27946i	1.07675	+	0.0423209i
$915$	−19.7151	+	14.3239i	−0.651762	+	0.473533i
$916$	11.5569	−	2.77421i	0.381850	−	0.0916626i
$917$	29.3708	−	2.51661i	0.969908	−	0.0831059i
$918$	0.858394	−	1.08884i	0.0283312	−	0.0359369i
$919$	−14.2523	+	19.6166i	−0.470140	+	0.647092i	−0.976573	−	0.215187i	$-0.930964\pi$
$919$	−14.2523	+	19.6166i	−0.470140	+	0.647092i	0.506433	+	0.862279i	$0.330964\pi$
$920$	13.9896	−	30.3424i	0.461224	−	1.00036i
$921$	−7.94442	−	24.4504i	−0.261777	−	0.805668i
$922$	−18.8779	−	28.2537i	−0.621711	−	0.930486i
$923$	−12.2718			−0.403931
$924$	−17.5493	+	0.150664i	−0.577329	+	0.00495650i
$925$	−75.8790			−2.49489
$926$	−16.9991	−	25.4418i	−0.558626	−	0.836068i
$927$	3.95624	+	12.1760i	0.129940	+	0.399914i
$928$	−15.0222	+	26.8196i	−0.493128	+	0.880396i
$929$	−2.59010	+	3.56496i	−0.0849784	+	0.116963i	−0.849390	−	0.527766i	$-0.823030\pi$
$929$	−2.59010	+	3.56496i	−0.0849784	+	0.116963i	0.764411	+	0.644729i	$0.223030\pi$
$930$	−19.2153	+	24.3737i	−0.630093	+	0.799246i
$931$	−3.38780	−	6.42696i	−0.111031	−	0.210635i
$932$	1.57073	+	6.54338i	0.0514509	+	0.214335i
$933$	17.6975	−	12.8580i	0.579389	−	0.420951i
$934$	−38.8087	−	1.52535i	−1.26986	−	0.0499111i
$935$	−3.87266	−	11.8511i	−0.126650	−	0.387574i
$936$	−0.348107	+	2.94006i	−0.0113782	+	0.0960990i
$937$	20.4623	+	28.1639i	0.668473	+	0.920074i	0.999725	−	0.0234686i	$-0.00747097\pi$
$937$	20.4623	+	28.1639i	0.668473	+	0.920074i	−0.331252	+	0.943542i	$0.607471\pi$
$938$	−3.08878	−	3.86281i	−0.100852	−	0.126125i
$939$	−11.4169	−	3.70957i	−0.372576	−	0.121057i
$940$	26.3809	−	30.8863i	0.860450	−	1.00740i
$941$	−12.9155	+	17.7766i	−0.421032	+	0.579501i	−0.965866	−	0.259043i	$-0.916593\pi$
$941$	−12.9155	+	17.7766i	−0.421032	+	0.579501i	0.544834	+	0.838544i	$0.316593\pi$
$942$	−5.27105	−	1.94468i	−0.171740	−	0.0633610i
$943$	4.15668	+	12.7930i	0.135360	+	0.416596i
$944$	40.1003	−	20.4293i	1.30515	−	0.664916i
$945$	−9.34527	+	3.94709i	−0.304002	+	0.128399i
$946$	6.51498	+	9.71533i	0.211820	+	0.315873i
$947$			44.6050i			1.44947i	0.689029	+	0.724734i	$0.258037\pi$
$947$			44.6050i			1.44947i	−0.689029	+	0.724734i	$0.741963\pi$
$948$	14.2706	+	23.2890i	0.463488	+	0.756392i
$949$	−0.681687	−	2.09802i	−0.0221285	−	0.0681045i
$950$	4.92905	−	13.3602i	0.159919	−	0.433461i
$951$	−11.8719	−	8.62545i	−0.384973	−	0.279699i
$952$	6.90058	+	2.49185i	0.223649	+	0.0807615i
$953$	13.9513	−	42.9377i	0.451927	−	1.39089i	−0.422778	−	0.906233i	$-0.638945\pi$
$953$	13.9513	−	42.9377i	0.451927	−	1.39089i	0.874705	−	0.484656i	$-0.161055\pi$
$954$	4.70072	+	16.6684i	0.152191	+	0.539659i
$955$	−47.3835	+	34.4261i	−1.53329	+	1.11400i
$956$	−3.55786	+	45.1904i	−0.115069	+	1.46156i
$957$	−18.0230	+	0.0302402i	−0.582600	+	0.000977526i
$958$	−21.8668	−	0.859462i	−0.706485	−	0.0277680i
$959$	17.2800	+	10.4250i	0.557999	+	0.336642i
$960$	30.5801	−	2.40408i	0.986970	−	0.0775912i
$961$	0.544210	−	1.67491i	0.0175552	−	0.0540293i
$962$	7.16765	−	9.09185i	0.231094	−	0.293133i
$963$	−0.589403	+	0.811243i	−0.0189932	+	0.0261420i
$964$	−17.8930	−	7.41212i	−0.576295	−	0.238728i
$965$	−17.7253	+	5.75931i	−0.570598	+	0.185399i
$966$	−6.33785	+	9.62887i	−0.203917	+	0.309804i
$967$			22.2308i			0.714894i	0.933933	+	0.357447i	$0.116353\pi$
$967$			22.2308i			0.714894i	−0.933933	+	0.357447i	$0.883647\pi$
$968$	6.17085	+	30.4946i	0.198339	+	0.980134i
$969$		−	1.01755i		−	0.0326885i
$970$	76.5515	−	51.1485i	2.45792	−	1.64228i
$971$	−9.84233	−	30.2916i	−0.315855	−	0.972103i	−0.975401	−	0.220438i	$-0.929251\pi$
$971$	−9.84233	−	30.2916i	−0.315855	−	0.972103i	0.659545	−	0.751665i	$-0.270749\pi$
$972$	−0.765420	+	1.84774i	−0.0245508	+	0.0592662i
$973$	12.3522	−	53.0695i	0.395994	−	1.70133i
$974$	4.59259	−	5.82550i	0.147156	−	0.186661i
$975$	9.65829	+	3.13817i	0.309313	+	0.100502i
$976$	−25.1095	+	3.97549i	−0.803736	+	0.127252i
$977$	−18.6180	+	13.5268i	−0.595644	+	0.432761i	−0.844330	−	0.535823i	$-0.820001\pi$
$977$	−18.6180	+	13.5268i	−0.595644	+	0.432761i	0.248686	+	0.968584i	$0.420001\pi$
$978$	0.194218	−	4.94137i	0.00621039	−	0.158008i
$979$	−0.0819650	−	48.8507i	−0.00261961	−	1.56127i
$980$	−35.4243	−	40.3324i	−1.13159	−	1.28837i
$981$	12.0744	−	8.77257i	0.385506	−	0.280087i
$982$	17.7048	−	4.99301i	0.564984	−	0.159333i
$983$	7.68760	−	23.6600i	0.245196	−	0.754637i	−0.750408	−	0.660975i	$-0.770143\pi$
$983$	7.68760	−	23.6600i	0.245196	−	0.754637i	0.995604	−	0.0936616i	$-0.0298572\pi$
$984$	−8.38302	+	9.06792i	−0.267241	+	0.289075i
$985$	−35.0810	+	48.2849i	−1.11777	+	1.53848i
$986$	7.06874	+	2.60791i	0.225115	+	0.0830528i
$987$	−10.5930	+	9.17506i	−0.337177	+	0.292045i
$988$	1.13522	+	1.85262i	0.0361160	+	0.0589398i
$989$	7.68343			0.244319
$990$	10.0165	+	14.9369i	0.318346	+	0.474727i
$991$		−	47.3699i		−	1.50475i	−0.658733	−	0.752377i	$-0.728907\pi$
$991$		−	47.3699i		−	1.50475i	0.658733	−	0.752377i	$-0.271093\pi$
$992$	−29.4051	+	13.5534i	−0.933613	+	0.430321i
$993$	−29.5530	+	9.60234i	−0.937835	+	0.304721i
$994$	−2.02555	−	43.8201i	−0.0642465	−	1.38989i
$995$	49.9858	−	68.7995i	1.58466	−	2.18109i
$996$	11.3965	+	9.73408i	0.361111	+	0.308436i
$997$	15.1267	+	4.91496i	0.479067	+	0.155658i	0.538589	−	0.842569i	$-0.318958\pi$
$997$	15.1267	+	4.91496i	0.479067	+	0.155658i	−0.0595218	+	0.998227i	$0.518958\pi$
$998$	60.5630	−	17.0796i	1.91709	−	0.540645i
$999$	6.32733	−	4.59707i	0.200188	−	0.145445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	924.2.bu.b.223.9	yes	192
4.3	odd	2		924.2.bu.a.223.11	yes	192
7.6	odd	2		924.2.bu.a.223.9	✓	192
11.4	even	5	inner	924.2.bu.b.895.11	yes	192
28.27	even	2	inner	924.2.bu.b.223.11	yes	192
44.15	odd	10		924.2.bu.a.895.9	yes	192
77.48	odd	10		924.2.bu.a.895.11	yes	192
308.279	even	10	inner	924.2.bu.b.895.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
924.2.bu.a.223.9	✓	192	7.6	odd	2
924.2.bu.a.223.11	yes	192	4.3	odd	2
924.2.bu.a.895.9	yes	192	44.15	odd	10
924.2.bu.a.895.11	yes	192	77.48	odd	10
924.2.bu.b.223.9	yes	192	1.1	even	1	trivial
924.2.bu.b.223.11	yes	192	28.27	even	2	inner
924.2.bu.b.895.9	yes	192	308.279	even	10	inner
924.2.bu.b.895.11	yes	192	11.4	even	5	inner

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:	\( N \)	\(=\)	\( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	924.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17589 + 0.785678i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.765420 - 1.84774i) q^{4} +(2.25375 - 3.10202i) q^{5} +(1.11059 + 0.875547i) q^{6} +(-2.63609 + 0.225872i) q^{7} +(0.551680 + 2.77410i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.212965 + 5.41835i) q^{10} +(-3.31662 + 0.00556485i) q^{11} +(-1.99383 - 0.156975i) q^{12} +(-0.615252 - 0.846822i) q^{13} +(2.92228 - 2.33672i) q^{14} +(-3.64665 - 1.18487i) q^{15} +(-2.82827 - 2.82859i) q^{16} +(-0.576270 + 0.793167i) q^{17} +(0.489502 - 1.32680i) q^{18} +(-0.320724 - 0.987087i) q^{19} +(-4.00666 - 6.53869i) q^{20} +(1.02941 + 2.43727i) q^{21} +(3.89560 - 2.61234i) q^{22} -3.08086i q^{23} +(2.46785 - 1.38192i) q^{24} +(-2.99807 - 9.22710i) q^{25} +(1.38880 + 0.512377i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.60037 + 5.04369i) q^{28} +(-1.67924 + 5.16817i) q^{29} +(5.21897 - 1.47182i) q^{30} +(-4.63060 + 3.36432i) q^{31} +(5.54808 + 1.10399i) q^{32} +(1.03018 + 3.15257i) q^{33} +(0.0544538 - 1.38544i) q^{34} +(-5.24044 + 8.68628i) q^{35} +(0.466835 + 1.94475i) q^{36} +(2.41682 - 7.43822i) q^{37} +(1.15267 + 0.908717i) q^{38} +(-0.615252 + 0.846822i) q^{39} +(9.84868 + 4.54082i) q^{40} +(-4.15240 + 1.34920i) q^{41} +(-3.12539 - 2.05717i) q^{42} +2.49393i q^{43} +(-2.52832 + 6.13250i) q^{44} +3.83431i q^{45} +(2.42056 + 3.62274i) q^{46} +(1.63680 + 5.03755i) q^{47} +(-1.81617 + 3.56392i) q^{48} +(6.89796 - 1.19084i) q^{49} +(10.7749 + 8.49451i) q^{50} +(0.932424 + 0.302963i) q^{51} +(-2.03563 + 0.488650i) q^{52} +(-9.90727 + 7.19806i) q^{53} +(-1.41312 - 0.0555419i) q^{54} +(-7.45758 + 10.3008i) q^{55} +(-2.08087 - 7.18818i) q^{56} +(-0.839666 + 0.610053i) q^{57} +(-2.08592 - 7.39653i) q^{58} +(-3.47678 + 10.7004i) q^{59} +(-4.98054 + 5.83113i) q^{60} +(3.73571 - 5.14176i) q^{61} +(2.80178 - 7.59422i) q^{62} +(1.99988 - 1.73219i) q^{63} +(-7.39130 + 3.06083i) q^{64} -4.01349 q^{65} +(-3.68829 - 2.89768i) q^{66} -1.32185i q^{67} +(1.02448 + 1.67190i) q^{68} +(-2.93007 + 0.952037i) q^{69} +(-0.662457 - 14.3314i) q^{70} +(6.89115 - 9.48485i) q^{71} +(-2.07690 - 1.92003i) q^{72} +(2.00435 + 0.651254i) q^{73} +(3.00213 + 10.6453i) q^{74} +(-7.84904 + 5.70266i) q^{75} +(-2.06937 - 0.162922i) q^{76} +(8.74166 - 0.763800i) q^{77} +(0.0581374 - 1.47916i) q^{78} +(-8.02725 - 11.0486i) q^{79} +(-15.1486 + 2.39841i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.82272 - 4.84895i) q^{82} +(-6.06266 - 4.40478i) q^{83} +(5.29138 - 0.0365489i) q^{84} +(1.16165 + 3.57521i) q^{85} +(-1.95942 - 2.93257i) q^{86} +5.43414 q^{87} +(-1.84515 - 9.19758i) q^{88} +14.7291i q^{89} +(-3.01254 - 4.50872i) q^{90} +(1.81314 + 2.09333i) q^{91} +(-5.69262 - 2.35815i) q^{92} +(4.63060 + 3.36432i) q^{93} +(-5.88259 - 4.63759i) q^{94} +(-3.78480 - 1.22976i) q^{95} +(-0.664491 - 5.61769i) q^{96} +(-9.97974 - 13.7359i) q^{97} +(-7.17561 + 6.81987i) q^{98} +(2.67993 - 1.95396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 2 q^{2} + 48 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 48 q^{9} + 2 q^{12} + 13 q^{14} + 6 q^{16} - 3 q^{18} + 6 q^{20} + 24 q^{22} + 3 q^{24} + 56 q^{25} - 18 q^{26} + 48 q^{27} + 16 q^{29} + 12 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) \) 192 * q + 2 * q^2 + 48 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 48 * q^9 + 2 * q^12 + 13 * q^14 + 6 * q^16 - 3 * q^18 + 6 * q^20 + 24 * q^22 + 3 * q^24 + 56 * q^25 - 18 * q^26 + 48 * q^27 + 16 * q^29 + 12 * q^31 - 8 * q^32 + 24 * q^34 + 14 * q^35 - 2 * q^36 - 24 * q^37 - 36 * q^38 - 36 * q^40 + 2 * q^42 + 29 * q^44 - 23 * q^46 + 8 * q^47 - 11 * q^48 + 16 * q^49 - 14 * q^50 - 40 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 + 7 * q^58 - 40 * q^59 - 6 * q^60 - 56 * q^64 - 16 * q^65 + 11 * q^66 - 78 * q^68 + 86 * q^70 - 3 * q^72 + 28 * q^74 - 36 * q^75 - 56 * q^76 + 28 * q^77 - 12 * q^78 + 6 * q^80 - 48 * q^81 + 8 * q^83 + 15 * q^84 - 60 * q^85 - 51 * q^86 - 16 * q^87 - 4 * q^88 + 8 * q^91 - 47 * q^92 - 12 * q^93 + 64 * q^94 - 2 * q^96 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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