LMFDB - Embedded newform 945.2.cs.b.104.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.14
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27225 - 0.827033i) q^{2} +(1.72657 - 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(-1.34694 - 1.78487i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(-1.56879 - 2.13047i) q^{7} +(-2.23324 - 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +O(q^{10})$	\(q+(-2.27225 - 0.827033i) q^{2} +(1.72657 - 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(-1.34694 - 1.78487i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(-1.56879 - 2.13047i) q^{7} +(-2.23324 - 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +(1.58445 + 5.16963i) q^{10} +(-2.20675 + 0.389110i) q^{11} +(5.42865 + 3.86404i) q^{12} +(2.64817 - 0.963854i) q^{13} +(1.80272 + 6.13841i) q^{14} +(-2.57123 - 2.89634i) q^{15} +(0.539367 + 3.05890i) q^{16} +(-6.27053 - 3.62029i) q^{17} +(-7.12372 - 1.36994i) q^{18} +(3.30565 - 1.90852i) q^{19} +(0.444237 - 8.59094i) q^{20} +(-3.00183 - 3.46251i) q^{21} +(5.33610 + 0.940899i) q^{22} +(1.53289 + 1.28624i) q^{23} +(-4.38819 - 6.37121i) q^{24} +(-1.37150 + 4.80822i) q^{25} -6.81445 q^{26} +(5.04892 - 1.22816i) q^{27} +(0.645068 - 10.1581i) q^{28} +(0.483105 - 1.32732i) q^{29} +(3.44712 + 8.70771i) q^{30} +(-4.71738 + 5.62196i) q^{31} +(-0.246961 + 1.40059i) q^{32} +(-3.75657 + 0.975522i) q^{33} +(11.2541 + 13.4121i) q^{34} +(-1.68953 + 5.66970i) q^{35} +(9.90474 + 5.92445i) q^{36} +(-8.73664 - 5.04410i) q^{37} +(-9.08968 + 1.60276i) q^{38} +(4.43961 - 2.02861i) q^{39} +(-3.89598 + 9.19613i) q^{40} +(-4.34880 + 1.58283i) q^{41} +(3.95731 + 10.3503i) q^{42} +(2.57232 - 0.453569i) q^{43} +(-7.46566 - 4.31030i) q^{44} +(-4.83802 - 4.64689i) q^{45} +(-2.41934 - 4.19042i) q^{46} +(1.83180 + 2.18305i) q^{47} +(1.35223 + 5.20719i) q^{48} +(-2.07779 + 6.68452i) q^{49} +(7.09294 - 9.79123i) q^{50} +(-11.3248 - 5.38774i) q^{51} +(10.1878 + 3.70806i) q^{52} +0.692478 q^{53} +(-12.4882 - 1.38493i) q^{54} +(3.66687 + 3.41465i) q^{55} +(-4.73736 + 10.8261i) q^{56} +(5.44480 - 3.75012i) q^{57} +(-2.19548 + 2.61647i) q^{58} +(1.80747 - 10.2507i) q^{59} +(-0.415286 - 14.8940i) q^{60} +(0.0628143 + 0.0748592i) q^{61} +(15.3686 - 8.87309i) q^{62} +(-5.65940 - 5.56518i) q^{63} +(4.82558 - 8.35815i) q^{64} +(-5.28728 - 3.42837i) q^{65} +(9.34267 + 0.890173i) q^{66} +(0.870116 + 2.39062i) q^{67} +(-9.52710 - 26.1755i) q^{68} +(2.82366 + 2.00984i) q^{69} +(8.52807 - 11.4857i) q^{70} +(-10.4867 - 6.05448i) q^{71} +(-8.45335 - 10.3965i) q^{72} +(-0.469002 - 0.812335i) q^{73} +(15.6802 + 18.6870i) q^{74} +(-1.70628 + 8.49050i) q^{75} +(14.4615 + 2.54995i) q^{76} +(4.29092 + 4.09098i) q^{77} +(-11.7656 + 0.937811i) q^{78} +(-14.0479 - 5.11302i) q^{79} +(4.73324 - 5.08286i) q^{80} +(8.54832 - 2.81535i) q^{81} +11.1906 q^{82} +(0.0128448 - 0.0352908i) q^{83} +(-0.284204 - 17.6274i) q^{84} +(1.98430 + 16.0684i) q^{85} +(-6.22007 - 1.09677i) q^{86} +(0.651450 - 2.35820i) q^{87} +(6.43332 + 7.66694i) q^{88} +(-0.138079 - 0.239159i) q^{89} +(7.15008 + 14.5601i) q^{90} +(-6.20788 - 4.12975i) q^{91} +(1.33679 + 7.58129i) q^{92} +(-7.37122 + 10.3559i) q^{93} +(-2.35685 - 6.47540i) q^{94} +(-7.85896 - 3.32948i) q^{95} +(-0.233647 + 2.45220i) q^{96} +(1.49351 + 8.47013i) q^{97} +(10.2496 - 13.4705i) q^{98} +(-6.35175 + 2.20129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−2.27225	−	0.827033i	−1.60673	−	0.584800i	−0.625937	−	0.779873i	$-0.715283\pi$
$2$	−2.27225	−	0.827033i	−1.60673	−	0.584800i	−0.980789	+	0.195073i	$0.937506\pi$
$3$	1.72657	−	0.137621i	0.996838	−	0.0794555i
$3$	1.72657	−	0.137621i	0.996838	−	0.0794555i
$4$	2.94706	+	2.47288i	1.47353	+	1.23644i
$5$	−1.34694	−	1.78487i	−0.602371	−	0.798216i
$5$	−1.34694	−	1.78487i	−0.602371	−	0.798216i
$6$	−4.03703	−	1.11522i	−1.64811	−	0.455288i
$7$	−1.56879	−	2.13047i	−0.592947	−	0.805241i
$7$	−1.56879	−	2.13047i	−0.592947	−	0.805241i
$8$	−2.23324	−	3.86809i	−0.789571	−	1.36758i
$9$	2.96212	−	0.475226i	0.987374	−	0.158409i
$10$	1.58445	+	5.16963i	0.501047	+	1.63478i
$11$	−2.20675	+	0.389110i	−0.665360	+	0.117321i	−0.496120	−	0.868254i	$-0.665242\pi$
$11$	−2.20675	+	0.389110i	−0.665360	+	0.117321i	−0.169240	+	0.985575i	$0.554131\pi$
$12$	5.42865	+	3.86404i	1.56712	+	1.11545i
$13$	2.64817	−	0.963854i	0.734469	−	0.267325i	0.0524139	−	0.998625i	$-0.483308\pi$
$13$	2.64817	−	0.963854i	0.734469	−	0.267325i	0.682055	+	0.731300i	$0.261086\pi$
$14$	1.80272	+	6.13841i	0.481798	+	1.64056i
$15$	−2.57123	−	2.89634i	−0.663889	−	0.747831i
$16$	0.539367	+	3.05890i	0.134842	+	0.764725i
$17$	−6.27053	−	3.62029i	−1.52083	−	0.878049i	−0.999698	−	0.0245706i	$-0.992178\pi$
$17$	−6.27053	−	3.62029i	−1.52083	−	0.878049i	−0.521128	−	0.853479i	$-0.674489\pi$
$18$	−7.12372	−	1.36994i	−1.67908	−	0.322897i
$19$	3.30565	−	1.90852i	0.758368	−	0.437844i	−0.0703418	−	0.997523i	$-0.522409\pi$
$19$	3.30565	−	1.90852i	0.758368	−	0.437844i	0.828709	+	0.559679i	$0.189076\pi$
$20$	0.444237	−	8.59094i	0.0993344	−	1.92099i
$21$	−3.00183	−	3.46251i	−0.655053	−	0.755583i
$22$	5.33610	+	0.940899i	1.13766	+	0.200600i
$23$	1.53289	+	1.28624i	0.319629	+	0.268200i	0.788458	−	0.615088i	$-0.210880\pi$
$23$	1.53289	+	1.28624i	0.319629	+	0.268200i	−0.468829	+	0.883289i	$0.655324\pi$
$24$	−4.38819	−	6.37121i	−0.895736	−	1.30052i
$25$	−1.37150	+	4.80822i	−0.274299	+	0.961644i
$26$	−6.81445			−1.33642
$27$	5.04892	−	1.22816i	0.971666	−	0.236360i
$28$	0.645068	−	10.1581i	0.121906	−	1.91969i
$29$	0.483105	−	1.32732i	0.0897104	−	0.246477i	−0.886721	−	0.462305i	$-0.847023\pi$
$29$	0.483105	−	1.32732i	0.0897104	−	0.246477i	0.976432	+	0.215827i	$0.0692448\pi$
$30$	3.44712	+	8.70771i	0.629356	+	1.58980i
$31$	−4.71738	+	5.62196i	−0.847267	+	1.00973i	0.152503	+	0.988303i	$0.451267\pi$
$31$	−4.71738	+	5.62196i	−0.847267	+	1.00973i	−0.999770	+	0.0214306i	$0.993178\pi$
$32$	−0.246961	+	1.40059i	−0.0436570	+	0.247591i
$33$	−3.75657	+	0.975522i	−0.653935	+	0.169817i
$34$	11.2541	+	13.4121i	1.93007	+	2.30016i
$35$	−1.68953	+	5.66970i	−0.285583	+	0.958354i
$36$	9.90474	+	5.92445i	1.65079	+	0.987408i
$37$	−8.73664	−	5.04410i	−1.43630	−	0.829245i	−0.438705	−	0.898631i	$-0.644563\pi$
$37$	−8.73664	−	5.04410i	−1.43630	−	0.829245i	−0.997590	+	0.0693855i	$0.977896\pi$
$38$	−9.08968	+	1.60276i	−1.47454	+	0.260001i
$39$	4.43961	−	2.02861i	0.710907	−	0.324837i
$40$	−3.89598	+	9.19613i	−0.616008	+	1.45404i
$41$	−4.34880	+	1.58283i	−0.679168	+	0.247197i	−0.658490	−	0.752589i	$-0.728805\pi$
$41$	−4.34880	+	1.58283i	−0.679168	+	0.247197i	−0.0206777	+	0.999786i	$0.506582\pi$
$42$	3.95731	+	10.3503i	0.610626	+	1.59709i
$43$	2.57232	−	0.453569i	0.392274	−	0.0691686i	0.0259678	−	0.999663i	$-0.491733\pi$
$43$	2.57232	−	0.453569i	0.392274	−	0.0691686i	0.366307	+	0.930494i	$0.380622\pi$
$44$	−7.46566	−	4.31030i	−1.12549	−	0.649802i
$45$	−4.83802	−	4.64689i	−0.721209	−	0.692717i
$46$	−2.41934	−	4.19042i	−0.356712	−	0.617844i
$47$	1.83180	+	2.18305i	0.267195	+	0.318431i	0.882914	−	0.469535i	$-0.155579\pi$
$47$	1.83180	+	2.18305i	0.267195	+	0.318431i	−0.615719	+	0.787966i	$0.711134\pi$
$48$	1.35223	+	5.20719i	0.195177	+	0.751594i
$49$	−2.07779	+	6.68452i	−0.296828	+	0.954931i
$50$	7.09294	−	9.79123i	1.00309	−	1.38469i
$51$	−11.3248	−	5.38774i	−1.58578	−	0.754435i
$52$	10.1878	+	3.70806i	1.41280	+	0.514216i
$53$	0.692478			0.0951192			0.0475596	−	0.998868i	$-0.484856\pi$
$53$	0.692478			0.0951192			0.0475596	+	0.998868i	$0.484856\pi$
$54$	−12.4882	−	1.38493i	−1.69942	−	0.188465i
$55$	3.66687	+	3.41465i	0.494441	+	0.460431i
$56$	−4.73736	+	10.8261i	−0.633056	+	1.44670i
$57$	5.44480	−	3.75012i	0.721181	−	0.496716i
$58$	−2.19548	+	2.61647i	−0.288280	+	0.343559i
$59$	1.80747	−	10.2507i	0.235313	−	1.33453i	−0.606640	−	0.794977i	$-0.707483\pi$
$59$	1.80747	−	10.2507i	0.235313	−	1.33453i	0.841953	−	0.539551i	$-0.181406\pi$
$60$	−0.415286	−	14.8940i	−0.0536131	−	1.92281i
$61$	0.0628143	+	0.0748592i	0.00804255	+	0.00958474i	0.770051	−	0.637983i	$-0.220231\pi$
$61$	0.0628143	+	0.0748592i	0.00804255	+	0.00958474i	−0.762008	+	0.647567i	$0.775786\pi$
$62$	15.3686	−	8.87309i	1.95182	−	1.12688i
$63$	−5.65940	−	5.56518i	−0.713017	−	0.701146i
$64$	4.82558	−	8.35815i	0.603197	−	1.04477i
$65$	−5.28728	−	3.42837i	−0.655806	−	0.425237i
$66$	9.34267	+	0.890173i	1.15000	+	0.109573i
$67$	0.870116	+	2.39062i	0.106302	+	0.292061i	0.981427	−	0.191834i	$-0.0614437\pi$
$67$	0.870116	+	2.39062i	0.106302	+	0.292061i	−0.875126	+	0.483896i	$0.839221\pi$
$68$	−9.52710	−	26.1755i	−1.15533	−	3.17424i
$69$	2.82366	+	2.00984i	0.339928	+	0.241956i
$70$	8.52807	−	11.4857i	1.01930	−	1.37280i
$71$	−10.4867	−	6.05448i	−1.24454	−	0.718534i	−0.274523	−	0.961581i	$-0.588520\pi$
$71$	−10.4867	−	6.05448i	−1.24454	−	0.718534i	−0.970015	+	0.243046i	$0.921853\pi$
$72$	−8.45335	−	10.3965i	−0.996237	−	1.22523i
$73$	−0.469002	−	0.812335i	−0.0548925	−	0.0950766i	0.837273	−	0.546784i	$-0.184148\pi$
$73$	−0.469002	−	0.812335i	−0.0548925	−	0.0950766i	−0.892166	+	0.451708i	$0.850815\pi$
$74$	15.6802	+	18.6870i	1.82279	+	2.17232i
$75$	−1.70628	+	8.49050i	−0.197024	+	0.980399i
$76$	14.4615	+	2.54995i	1.65885	+	0.292499i
$77$	4.29092	+	4.09098i	0.488995	+	0.466211i
$78$	−11.7656	+	0.937811i	−1.33220	+	0.106186i
$79$	−14.0479	−	5.11302i	−1.58051	−	0.575259i	−0.605197	−	0.796076i	$-0.706906\pi$
$79$	−14.0479	−	5.11302i	−1.58051	−	0.575259i	−0.975315	+	0.220816i	$0.929128\pi$
$80$	4.73324	−	5.08286i	0.529192	−	0.568281i
$81$	8.54832	−	2.81535i	0.949813	−	0.312817i
$82$	11.1906			1.23580
$83$	0.0128448	−	0.0352908i	0.00140990	−	0.00387367i	−0.938986	−	0.343956i	$-0.888233\pi$
$83$	0.0128448	−	0.0352908i	0.00140990	−	0.00387367i	0.940396	+	0.340083i	$0.110455\pi$
$84$	−0.284204	−	17.6274i	−0.0310092	−	1.92331i
$85$	1.98430	+	16.0684i	0.215228	+	1.74286i
$86$	−6.22007	−	1.09677i	−0.670727	−	0.118267i
$87$	0.651450	−	2.35820i	0.0698428	−	0.252826i
$88$	6.43332	+	7.66694i	0.685794	+	0.817298i
$89$	−0.138079	−	0.239159i	−0.0146363	−	0.0253508i	0.858614	−	0.512622i	$-0.171326\pi$
$89$	−0.138079	−	0.239159i	−0.0146363	−	0.0253508i	−0.873251	+	0.487271i	$0.837992\pi$
$90$	7.15008	+	14.5601i	0.753684	+	1.53477i
$91$	−6.20788	−	4.12975i	−0.650763	−	0.432916i
$92$	1.33679	+	7.58129i	0.139370	+	0.790404i
$93$	−7.37122	+	10.3559i	−0.764359	+	1.07386i
$94$	−2.35685	−	6.47540i	−0.243091	−	0.667887i
$95$	−7.85896	−	3.32948i	−0.806312	−	0.341597i
$96$	−0.233647	+	2.45220i	−0.0238465	+	0.250277i
$97$	1.49351	+	8.47013i	0.151643	+	0.860012i	0.961791	+	0.273786i	$0.0882758\pi$
$97$	1.49351	+	8.47013i	0.151643	+	0.860012i	−0.810148	+	0.586226i	$0.800613\pi$
$98$	10.2496	−	13.4705i	1.03536	−	1.36073i
$99$	−6.35175	+	2.20129i	−0.638375	+	0.221238i
$100$	−15.9320	+	10.7786i	−1.59320	+	1.07786i
$101$	4.97400	−	4.17368i	0.494931	−	0.415296i	−0.360858	−	0.932621i	$-0.617516\pi$
$101$	4.97400	−	4.17368i	0.494931	−	0.415296i	0.855790	+	0.517324i	$0.173072\pi$
$102$	21.2769	+	21.6083i	2.10673	+	2.13954i
$103$	−0.0111283	+	0.0631117i	−0.00109650	+	0.00621858i	−0.985351	−	0.170538i	$-0.945449\pi$
$103$	−0.0111283	+	0.0631117i	−0.00109650	+	0.00621858i	0.984255	+	0.176757i	$0.0565605\pi$
$104$	−9.64228	−	8.09083i	−0.945503	−	0.793371i
$105$	−2.13683	+	10.0217i	−0.208534	+	0.978015i
$106$	−1.57349	−	0.572702i	−0.152830	−	0.0556258i
$107$	−12.2726			−1.18644			−0.593218	−	0.805042i	$-0.702143\pi$
$107$	−12.2726			−1.18644			−0.593218	+	0.805042i	$0.702143\pi$
$108$	17.9166	+	8.86591i	1.72403	+	0.853122i
$109$	−10.4690			−1.00275			−0.501376	−	0.865229i	$-0.667173\pi$
$109$	−10.4690			−1.00275			−0.501376	+	0.865229i	$0.667173\pi$
$110$	−5.50804	−	10.7916i	−0.525171	−	1.02894i
$111$	−15.7786	−	7.50668i	−1.49764	−	0.712502i
$112$	5.67074	−	5.94788i	0.535835	−	0.562022i
$113$	−2.66088	+	15.0906i	−0.250315	+	1.41961i	0.557504	+	0.830174i	$0.311759\pi$
$113$	−2.66088	+	15.0906i	−0.250315	+	1.41961i	−0.807819	+	0.589431i	$0.799352\pi$
$114$	−15.4734	+	4.01821i	−1.44922	+	0.376340i
$115$	0.231065	−	4.46849i	0.0215470	−	0.416689i
$116$	4.70605	−	2.71704i	0.436946	−	0.252271i
$117$	7.38614	−	4.11353i	0.682849	−	0.380296i
$118$	−12.5847	+	21.7973i	−1.15852	+	2.00661i
$119$	2.12423	+	19.0386i	0.194728	+	1.74527i
$120$	−5.46111	+	16.4140i	−0.498529	+	1.49838i
$121$	−5.61828	+	2.04489i	−0.510752	+	0.185899i
$122$	−0.0808191	−	0.222049i	−0.00731701	−	0.0201033i
$123$	−7.29069	+	3.33136i	−0.657379	+	0.300379i
$124$	−27.8049	+	4.90275i	−2.49695	+	0.440280i
$125$	10.4294	−	4.02846i	0.932830	−	0.360316i
$126$	8.25701	+	17.3260i	0.735593	+	1.54352i
$127$	1.43824	−	0.830369i	0.127623	−	0.0736834i	−0.434829	−	0.900513i	$-0.643191\pi$
$127$	1.43824	−	0.830369i	0.127623	−	0.0736834i	0.562453	+	0.826830i	$0.309858\pi$
$128$	−15.6985	+	13.1726i	−1.38756	+	1.16430i
$129$	4.37887	−	1.13712i	0.385538	−	0.100118i
$130$	9.17866	+	12.1629i	0.805022	+	1.06675i
$131$	15.3991	+	12.9214i	1.34543	+	1.12895i	0.980196	+	0.198030i	$0.0634543\pi$
$131$	15.3991	+	12.9214i	1.34543	+	1.12895i	0.365231	+	0.930917i	$0.380990\pi$
$132$	−13.4832	−	6.41462i	−1.17356	−	0.558321i
$133$	−9.25190	−	4.04852i	−0.802242	−	0.351051i
$134$		−	6.15172i		−	0.531427i
$135$	−8.99271	−	7.35739i	−0.773969	−	0.633223i
$136$			32.3400i			2.77313i
$137$	−2.36264	−	0.859931i	−0.201854	−	0.0734689i	0.239115	−	0.970991i	$-0.423143\pi$
$137$	−2.36264	−	0.859931i	−0.201854	−	0.0734689i	−0.440969	+	0.897522i	$0.645365\pi$
$138$	−4.75386	−	6.90212i	−0.404676	−	0.587548i
$139$	5.79195	−	6.90258i	0.491267	−	0.585469i	−0.462272	−	0.886738i	$-0.652966\pi$
$139$	5.79195	−	6.90258i	0.491267	−	0.585469i	0.953539	+	0.301269i	$0.0974102\pi$
$140$	−18.9996	+	12.5310i	−1.60576	+	1.05906i
$141$	3.46317	+	3.51711i	0.291651	+	0.296194i
$142$	18.8211	+	22.4301i	1.57943	+	1.88229i
$143$	−5.46880	+	3.15741i	−0.457324	+	0.264036i
$144$	3.05134	+	8.80452i	0.254278	+	0.733710i
$145$	−3.01981	+	0.925546i	−0.250781	+	0.0768624i
$146$	0.393863	+	2.23371i	0.0325964	+	0.184863i
$147$	−2.66754	+	11.8273i	−0.220015	+	0.975497i
$148$	−13.2740	−	36.4700i	−1.09111	−	2.99781i
$149$	−5.73366	−	15.7531i	−0.469720	−	1.29054i	−0.917975	−	0.396639i	$-0.870177\pi$
$149$	−5.73366	−	15.7531i	−0.469720	−	1.29054i	0.448255	−	0.893906i	$-0.352046\pi$
$150$	10.8990	−	17.8814i	0.889901	−	1.46001i
$151$	−3.90149	−	22.1264i	−0.317499	−	1.80062i	−0.557854	−	0.829939i	$-0.688375\pi$
$151$	−3.90149	−	22.1264i	−0.317499	−	1.80062i	0.240355	−	0.970685i	$-0.422736\pi$
$152$	−14.7646	−	8.52436i	−1.19757	−	0.691417i
$153$	−20.2945	−	7.74382i	−1.64071	−	0.626051i
$154$	−6.36667	−	12.8445i	−0.513041	−	1.03504i
$155$	16.3885	+	0.847448i	1.31635	+	0.0680686i
$156$	18.1003	+	5.00019i	1.44919	+	0.400335i
$157$	−1.48339	+	8.41274i	−0.118388	+	0.671410i	0.866629	+	0.498952i	$0.166282\pi$
$157$	−1.48339	+	8.41274i	−0.118388	+	0.671410i	−0.985017	+	0.172457i	$0.944829\pi$
$158$	27.6918	+	23.2361i	2.20304	+	1.84857i
$159$	1.19562	−	0.0952996i	0.0948185	−	0.00755775i
$160$	2.83250	−	1.44572i	0.223929	−	0.114294i
$161$	0.335526	−	5.28361i	0.0264431	−	0.416407i
$162$	−21.7523	−	0.672544i	−1.70903	−	0.0528401i
$163$		−	9.23757i		−	0.723542i	−0.932267	−	0.361771i	$-0.882172\pi$
$163$		−	9.23757i		−	0.723542i	0.932267	−	0.361771i	$-0.117828\pi$
$164$	−16.7303	−	6.08935i	−1.30642	−	0.475498i
$165$	6.80106	+	5.39100i	0.529462	+	0.419689i
$166$	−0.0583733	+	0.0695666i	−0.00453065	+	0.00539941i
$167$	18.3577	+	3.23697i	1.42056	+	0.250484i	0.830566	−	0.556920i	$-0.188017\pi$
$167$	18.3577	+	3.23697i	1.42056	+	0.250484i	0.589999	+	0.807404i	$0.299128\pi$
$168$	−6.68950	+	19.3440i	−0.516106	+	1.49242i
$169$	−3.87480	+	3.25135i	−0.298062	+	0.250104i
$170$	8.78023	−	38.1525i	0.673413	−	2.92616i
$171$	8.88475	−	7.22419i	0.679434	−	0.552447i
$172$	8.70240	+	5.02433i	0.663552	+	0.383102i
$173$	6.84061	−	1.20618i	0.520082	−	0.0917045i	0.0925558	−	0.995707i	$-0.470496\pi$
$173$	6.84061	−	1.20618i	0.520082	−	0.0917045i	0.427526	+	0.904003i	$0.359385\pi$
$174$	−3.43057	+	4.81967i	−0.260071	+	0.365378i
$175$	12.3954	−	4.62116i	0.937001	−	0.349327i
$176$	−2.38050	−	6.54036i	−0.179437	−	0.492998i
$177$	1.71003	−	17.9473i	0.128534	−	1.34901i
$178$	0.115957	+	0.657626i	0.00869136	+	0.0492911i
$179$	10.1633	+	5.86778i	0.759640	+	0.438578i	0.829167	−	0.559002i	$-0.188815\pi$
$179$	10.1633	+	5.86778i	0.759640	+	0.438578i	−0.0695264	+	0.997580i	$0.522149\pi$
$180$	−2.76675	−	25.6585i	−0.206222	−	1.91247i
$181$	12.2063	−	7.04731i	0.907287	−	0.523823i	0.0277301	−	0.999615i	$-0.491172\pi$
$181$	12.2063	−	7.04731i	0.907287	−	0.523823i	0.879557	+	0.475793i	$0.157839\pi$
$182$	10.6904	+	14.5180i	0.792428	+	1.07614i
$183$	0.118756	+	0.120605i	0.00877868	+	0.00891541i
$184$	1.55200	−	8.80184i	0.114415	−	0.648880i
$185$	2.76470	+	22.3879i	0.203265	+	1.64599i
$186$	25.3140	−	17.4351i	1.85611	−	1.27840i
$187$	15.2462	+	5.54915i	1.11491	+	0.405794i
$188$			10.9634i			0.799589i
$189$	−10.5373	−	8.82984i	−0.766473	−	0.642276i
$190$	15.1040	+	14.0650i	1.09576	+	1.02039i
$191$	−8.79796	+	24.1722i	−0.636598	+	1.74904i	0.0255583	+	0.999673i	$0.491864\pi$
$191$	−8.79796	+	24.1722i	−0.636598	+	1.74904i	−0.662156	+	0.749366i	$0.730359\pi$
$192$	7.18147	−	15.0951i	0.518278	−	1.08939i
$193$	10.7678	−	12.8326i	0.775083	−	0.923708i	−0.223617	−	0.974677i	$-0.571787\pi$
$193$	10.7678	−	12.8326i	0.775083	−	0.923708i	0.998700	+	0.0509692i	$0.0162310\pi$
$194$	3.61144	−	20.4815i	0.259286	−	1.47048i
$195$	−9.60069	−	5.19169i	−0.687520	−	0.371785i
$196$	−22.6534	+	14.5616i	−1.61810	+	1.04011i
$197$	−8.78625	−	15.2182i	−0.625995	−	1.08425i	−0.988348	−	0.152214i	$-0.951360\pi$
$197$	−8.78625	−	15.2182i	−0.625995	−	1.08425i	0.362353	−	0.932041i	$-0.381973\pi$
$198$	16.2533	+	0.251202i	1.15507	+	0.0178522i
$199$	−22.6896	−	13.0999i	−1.60843	−	0.928625i	−0.989723	−	0.143001i	$-0.954325\pi$
$199$	−22.6896	−	13.0999i	−1.60843	−	0.928625i	−0.618704	−	0.785624i	$-0.712342\pi$
$200$	21.6615	−	5.43286i	1.53170	−	0.384161i
$201$	1.83132	+	4.00784i	0.129171	+	0.282691i
$202$	−14.7539	+	5.37000i	−1.03808	+	0.377832i
$203$	−3.58571	+	1.05305i	−0.251667	+	0.0739095i
$204$	−20.0515	−	43.8828i	−1.40389	−	3.07241i
$205$	8.68272	+	5.63004i	0.606427	+	0.393219i
$206$	0.0774817	−	0.134202i	0.00539841	−	0.00935032i
$207$	5.15185	+	3.08154i	0.358078	+	0.214182i
$208$	4.37667	+	7.58061i	0.303467	+	0.525621i
$209$	−6.55212	+	5.49788i	−0.453219	+	0.380296i
$210$	13.1437	−	21.0046i	0.907000	−	1.44945i
$211$	0.656625	−	3.72391i	0.0452039	−	0.256364i	−0.953828	−	0.300353i	$-0.902895\pi$
$211$	0.656625	−	3.72391i	0.0452039	−	0.256364i	0.999032	+	0.0439888i	$0.0140066\pi$
$212$	2.04078	+	1.71242i	0.140161	+	0.117609i
$213$	−18.9392	−	9.01032i	−1.29769	−	0.617377i
$214$	27.8864	+	10.1498i	1.90628	+	0.693828i
$215$	−4.27432	−	3.98031i	−0.291506	−	0.271455i
$216$	−16.0261	−	16.7869i	−1.09044	−	1.14220i
$217$	19.3780	+	1.23056i	1.31546	+	0.0835360i
$218$	23.7883	+	8.65824i	1.61115	+	0.586410i
$219$	−0.921561	−	1.33801i	−0.0622733	−	0.0904145i
$220$	2.36250	+	19.1309i	0.159280	+	1.28981i
$221$	−20.0948	−	3.54326i	−1.35172	−	0.238345i
$222$	29.6448	+	30.1065i	1.98963	+	2.02062i
$223$	8.83262	−	7.41145i	0.591476	−	0.496307i	−0.297217	−	0.954810i	$-0.596059\pi$
$223$	8.83262	−	7.41145i	0.591476	−	0.496307i	0.888693	+	0.458503i	$0.151614\pi$
$224$	3.37133	−	1.67108i	0.225257	−	0.111654i
$225$	−1.77754	+	14.8943i	−0.118503	+	0.992954i
$226$	18.5266	−	32.0891i	1.23237	−	2.13453i
$227$	−25.7700	+	4.54395i	−1.71041	+	0.301592i	−0.941313	−	0.337534i	$-0.890407\pi$
$227$	−25.7700	+	4.54395i	−1.71041	+	0.301592i	−0.769102	+	0.639127i	$0.779296\pi$
$228$	25.3198	+	2.41248i	1.67684	+	0.159770i
$229$	−0.631040	−	1.73377i	−0.0417003	−	0.114571i	0.917095	−	0.398669i	$-0.130528\pi$
$229$	−0.631040	−	1.73377i	−0.0417003	−	0.114571i	−0.958795	+	0.284099i	$0.908306\pi$
$230$	−4.22063	+	9.96245i	−0.278300	+	0.656904i
$231$	7.97159	+	6.47287i	0.524492	+	0.425883i
$232$	−6.21309	+	1.09554i	−0.407909	+	0.0719254i
$233$	2.03500	−	3.52472i	0.133317	−	0.230912i	−0.791636	−	0.610993i	$-0.790770\pi$
$233$	2.03500	−	3.52472i	0.133317	−	0.230912i	0.924953	+	0.380081i	$0.124104\pi$
$234$	−20.1852	+	3.23840i	−1.31955	+	0.211701i
$235$	1.42913	−	6.20996i	0.0932262	−	0.405093i
$236$	30.6755	−	25.7398i	1.99681	−	1.67552i
$237$	−24.9584	−	6.89472i	−1.62122	−	0.447860i
$238$	10.9188	−	45.0174i	0.707760	−	2.91805i
$239$	−1.54601	+	1.84246i	−0.100003	+	0.119179i	−0.813725	−	0.581250i	$-0.802564\pi$
$239$	−1.54601	+	1.84246i	−0.100003	+	0.119179i	0.713722	+	0.700429i	$0.247008\pi$
$240$	7.47278	−	9.42733i	0.482366	−	0.608532i
$241$	2.02357	−	5.55970i	0.130349	−	0.358132i	−0.857299	−	0.514819i	$-0.827859\pi$
$241$	2.02357	−	5.55970i	0.130349	−	0.358132i	0.987648	+	0.156687i	$0.0500814\pi$
$242$	14.4573			0.929353
$243$	14.3719	−	6.03735i	0.921955	−	0.387296i
$244$			0.375947i			0.0240675i
$245$	14.7296	−	5.29507i	0.941042	−	0.338290i
$246$	19.3214	−	1.54006i	1.23189	−	0.0981909i
$247$	6.91438	−	8.24023i	0.439951	−	0.524313i
$248$	32.2813	+	5.69207i	2.04987	+	0.361447i
$249$	0.0173208	−	0.0626999i	0.00109766	−	0.00397345i
$250$	−27.0298	+	0.528261i	−1.70952	+	0.0334102i
$251$	−4.80342	−	8.31977i	−0.303189	−	0.525139i	0.673667	−	0.739035i	$-0.264718\pi$
$251$	−4.80342	−	8.31977i	−0.303189	−	0.525139i	−0.976857	+	0.213895i	$0.931385\pi$
$252$	−2.91660	−	30.3960i	−0.183729	−	1.91477i
$253$	−3.88319	−	2.24196i	−0.244134	−	0.140951i
$254$	−3.95479	+	0.697337i	−0.248146	+	0.0437548i
$255$	5.63739	+	27.4702i	0.353027	+	1.72025i
$256$	28.4268	−	10.3465i	1.77668	−	0.646658i
$257$	5.68533	+	15.6203i	0.354641	+	0.974369i	0.980859	+	0.194721i	$0.0623800\pi$
$257$	5.68533	+	15.6203i	0.354641	+	0.974369i	−0.626217	+	0.779649i	$0.715398\pi$
$258$	−10.8904	−	1.03764i	−0.678004	−	0.0646004i
$259$	2.95966	+	26.5263i	0.183904	+	1.64826i
$260$	−7.10400	−	23.1784i	−0.440571	−	1.43747i
$261$	0.800239	−	4.16127i	0.0495336	−	0.257576i
$262$	−24.3043	−	42.0962i	−1.50152	−	2.60071i
$263$	21.4069	−	17.9625i	1.32000	−	1.10762i	0.333700	−	0.942679i	$-0.391703\pi$
$263$	21.4069	−	17.9625i	1.32000	−	1.10762i	0.986304	−	0.164936i	$-0.0527417\pi$
$264$	12.1627	+	12.3522i	0.748565	+	0.760224i
$265$	−0.932728	−	1.23598i	−0.0572970	−	0.0759257i
$266$	17.6744	+	16.8509i	1.08369	+	1.03319i
$267$	−0.271316	−	0.393924i	−0.0166043	−	0.0241077i
$268$	−3.34744	+	9.19701i	−0.204477	+	0.561797i
$269$	20.5343			1.25200			0.626001	−	0.779823i	$-0.284691\pi$
$269$	20.5343			1.25200			0.626001	+	0.779823i	$0.284691\pi$
$270$	14.3489	+	24.1551i	0.873248	+	1.47003i
$271$			6.10187i			0.370662i	0.982676	+	0.185331i	$0.0593358\pi$
$271$			6.10187i			0.370662i	−0.982676	+	0.185331i	$0.940664\pi$
$272$	7.69200	−	21.1336i	0.466396	−	1.28141i
$273$	−11.2867	−	6.27599i	−0.683103	−	0.379840i
$274$	4.65733	+	3.90796i	0.281359	+	0.236089i
$275$	1.15562	−	11.1442i	0.0696867	−	0.672021i
$276$	3.35141	+	12.9057i	0.201731	+	0.776831i
$277$	−9.70821	−	11.5698i	−0.583310	−	0.695162i	0.390996	−	0.920393i	$-0.372131\pi$
$277$	−9.70821	−	11.5698i	−0.583310	−	0.695162i	−0.974305	+	0.225231i	$0.927686\pi$
$278$	−18.8694	+	10.8943i	−1.13171	+	0.653395i
$279$	−11.3018	+	18.8947i	−0.676619	+	1.13120i
$280$	25.7040	−	6.12655i	1.53611	−	0.366132i
$281$	24.6540	−	4.34716i	1.47073	−	0.259330i	0.619864	−	0.784710i	$-0.287188\pi$
$281$	24.6540	−	4.34716i	1.47073	−	0.259330i	0.850868	+	0.525380i	$0.176077\pi$
$282$	−4.96044	−	10.8559i	−0.295390	−	0.646460i
$283$	15.9029	−	5.78818i	0.945329	−	0.344072i	0.177061	−	0.984200i	$-0.443341\pi$
$283$	15.9029	−	5.78818i	0.945329	−	0.344072i	0.768268	+	0.640128i	$0.221119\pi$
$284$	−15.9329	−	43.7752i	−0.945442	−	2.59758i
$285$	−14.0273	−	4.66704i	−0.830905	−	0.276451i
$286$	15.0378	−	2.65157i	0.889203	−	0.156790i
$287$	10.1945	+	6.78184i	0.601764	+	0.400319i
$288$	−0.0659339	+	4.26607i	−0.00388519	+	0.251380i
$289$	17.7130	+	30.6798i	1.04194	+	1.80469i
$290$	7.62722	+	0.394403i	0.447886	+	0.0231601i
$291$	3.74433	+	14.4188i	0.219496	+	0.845244i
$292$	0.626629	−	3.55379i	0.0366707	−	0.207970i
$293$	12.7809	−	15.2316i	0.746666	−	0.889842i	−0.250261	−	0.968178i	$-0.580517\pi$
$293$	12.7809	−	15.2316i	0.746666	−	0.889842i	0.996927	+	0.0783368i	$0.0249610\pi$
$294$	15.8429	−	24.6684i	0.923974	−	1.43869i
$295$	−20.7307	+	10.5810i	−1.20699	+	0.616049i
$296$			45.0588i			2.61899i
$297$	−10.6638	+	4.67483i	−0.618778	+	0.271261i
$298$			40.5370i			2.34824i
$299$	5.29909	+	1.92871i	0.306454	+	0.111540i
$300$	−26.0245	+	20.8026i	−1.50253	+	1.20104i
$301$	−5.00174	−	4.76868i	−0.288295	−	0.274862i
$302$	−9.43412	+	53.5035i	−0.542873	+	3.07878i
$303$	8.01359	−	7.89069i	0.460369	−	0.453309i
$304$	7.62092	+	9.08226i	0.437090	+	0.520903i
$305$	0.0490064	−	0.212946i	0.00280610	−	0.0121933i
$306$	39.7099	+	34.3801i	2.27006	+	1.96538i
$307$	15.4872	−	26.8246i	0.883899	−	1.53096i	0.0369295	−	0.999318i	$-0.488242\pi$
$307$	15.4872	−	26.8246i	0.883899	−	1.53096i	0.846970	−	0.531641i	$-0.178424\pi$
$308$	2.52909	+	22.6673i	0.144109	+	1.29159i
$309$	−0.0105283	+	0.110499i	−0.000598936	+	0.00628604i
$310$	−36.5379	−	15.4794i	−2.07521	−	0.879173i
$311$	21.1167	−	7.68586i	1.19742	−	0.435825i	0.335097	−	0.942184i	$-0.391231\pi$
$311$	21.1167	−	7.68586i	1.19742	−	0.435825i	0.862323	+	0.506358i	$0.169009\pi$
$312$	−17.7616	−	12.6424i	−1.00555	−	0.715737i
$313$	−2.58539	−	14.6625i	−0.146135	−	0.828771i	−0.966449	−	0.256858i	$-0.917313\pi$
$313$	−2.58539	−	14.6625i	−0.146135	−	0.828771i	0.820314	−	0.571913i	$-0.193798\pi$
$314$	10.3283	−	17.8891i	0.582857	−	1.00954i
$315$	−2.31021	+	17.5972i	−0.130166	+	0.991492i
$316$	−28.7562	−	49.8072i	−1.61766	−	2.80187i
$317$	12.6104	−	10.5814i	0.708270	−	0.594309i	−0.215843	−	0.976428i	$-0.569250\pi$
$317$	12.6104	−	10.5814i	0.708270	−	0.594309i	0.924113	+	0.382119i	$0.124805\pi$
$318$	−2.79556	−	0.772268i	−0.156767	−	0.0433067i
$319$	−0.549620	+	3.11705i	−0.0307728	+	0.174521i
$320$	−21.4180	+	2.64493i	−1.19730	+	0.147856i
$321$	−21.1895	+	1.68896i	−1.18268	+	0.0942688i
$322$	−5.13212	+	11.7282i	−0.286002	+	0.653588i
$323$	−27.6375			−1.53779
$324$	32.1545	+	12.8420i	1.78636	+	0.713442i
$325$	1.00247	+	14.0549i	0.0556073	+	0.779625i
$326$	−7.63977	+	20.9901i	−0.423128	+	1.16253i
$327$	−18.0756	+	1.44076i	−0.999582	+	0.0796742i
$328$	15.8345	+	13.2867i	0.874312	+	0.733635i
$329$	1.77722	−	7.32734i	0.0979811	−	0.403969i
$330$	−10.9952	−	17.8744i	−0.605265	−	0.983955i
$331$	2.27096	−	1.90556i	0.124823	−	0.104739i	−0.578239	−	0.815867i	$-0.696260\pi$
$331$	2.27096	−	1.90556i	0.124823	−	0.104739i	0.703062	+	0.711128i	$0.251815\pi$
$332$	0.125124	−	0.0722406i	0.00686709	−	0.00396472i
$333$	−28.2761	−	10.7894i	−1.54952	−	0.591254i
$334$	−39.0364	−	22.5377i	−2.13598	−	1.23321i
$335$	3.09495	−	4.77307i	0.169095	−	0.260781i
$336$	8.97241	−	11.0499i	0.489485	−	0.602820i
$337$	1.39801	+	3.84099i	0.0761543	+	0.209232i	0.971928	−	0.235278i	$-0.0756000\pi$
$337$	1.39801	+	3.84099i	0.0761543	+	0.209232i	−0.895774	+	0.444510i	$0.853378\pi$
$338$	11.4935	−	4.18330i	0.625164	−	0.227541i
$339$	−2.51743	+	26.4213i	−0.136728	+	1.43501i
$340$	−33.8873	+	52.2615i	−1.83780	+	2.83428i
$341$	8.22253	−	14.2418i	0.445275	−	0.771239i
$342$	−26.1630	+	9.06720i	−1.41474	+	0.490298i
$343$	17.5008	−	6.05993i	0.944953	−	0.327206i
$344$	−7.49905	−	8.93702i	−0.404322	−	0.481852i
$345$	−0.216007	−	7.74699i	−0.0116294	−	0.417084i
$346$	−16.5412	−	2.91665i	−0.889258	−	0.156800i
$347$	−18.4741	−	15.5016i	−0.991743	−	0.832171i	−0.00592403	−	0.999982i	$-0.501886\pi$
$347$	−18.4741	−	15.5016i	−0.991743	−	0.832171i	−0.985819	+	0.167811i	$0.946330\pi$
$348$	7.75142	−	5.33882i	0.415520	−	0.286191i
$349$	−6.92074	+	19.0146i	−0.370459	+	1.01783i	0.604726	+	0.796434i	$0.293283\pi$
$349$	−6.92074	+	19.0146i	−0.370459	+	1.01783i	−0.975185	+	0.221393i	$0.928940\pi$
$350$	−31.9872	+	0.249095i	−1.70979	+	0.0133147i
$351$	12.1866	−	8.11880i	0.650474	−	0.433350i
$352$		−	3.18684i		−	0.169859i
$353$	5.81751	−	15.9835i	0.309635	−	0.850715i	−0.683093	−	0.730332i	$-0.739366\pi$
$353$	5.81751	−	15.9835i	0.309635	−	0.850715i	0.992728	−	0.120383i	$-0.0384123\pi$
$354$	−18.7287	+	39.3667i	−0.995417	+	2.09231i
$355$	3.31849	+	26.8723i	0.176127	+	1.42623i
$356$	0.184486	−	1.04627i	0.00977771	−	0.0554522i
$357$	6.28775	+	32.5793i	0.332783	+	1.72428i
$358$	−18.2407	−	21.7385i	−0.964053	−	1.14891i
$359$	22.0215	−	12.7141i	1.16225	−	0.671027i	0.210409	−	0.977613i	$-0.432520\pi$
$359$	22.0215	−	12.7141i	1.16225	−	0.671027i	0.951843	+	0.306587i	$0.0991869\pi$
$360$	−7.17011	+	29.0915i	−0.377898	+	1.53326i
$361$	−2.21513	+	3.83672i	−0.116586	+	0.201932i
$362$	−33.5642	+	5.91827i	−1.76409	+	0.311057i
$363$	−9.41896	+	4.30384i	−0.494367	+	0.225893i
$364$	−8.08264	−	27.5220i	−0.423645	−	1.44254i
$365$	−0.818191	+	1.93127i	−0.0428261	+	0.101087i
$366$	−0.170099	−	0.372261i	−0.00889120	−	0.0194584i
$367$	−3.94589	−	22.3783i	−0.205974	−	1.16814i	−0.895900	−	0.444256i	$-0.853468\pi$
$367$	−3.94589	−	22.3783i	−0.205974	−	1.16814i	0.689926	−	0.723880i	$-0.257643\pi$
$368$	−3.10771	+	5.38271i	−0.162000	+	0.280593i
$369$	−12.1295	+	6.75520i	−0.631434	+	0.351662i
$370$	12.2334	−	53.1574i	0.635984	−	2.76352i
$371$	−1.08635	−	1.47530i	−0.0564007	−	0.0765939i
$372$	−47.3325	+	12.2915i	−2.45407	+	0.637284i
$373$	10.0452	+	1.77125i	0.520122	+	0.0917116i	0.427545	−	0.903994i	$-0.359378\pi$
$373$	10.0452	+	1.77125i	0.520122	+	0.0917116i	0.0925771	+	0.995706i	$0.470490\pi$
$374$	−30.0538	−	25.2182i	−1.55405	−	1.30400i
$375$	17.4527	−	8.39074i	0.901252	−	0.433296i
$376$	4.35339	−	11.9608i	0.224509	−	0.616833i
$377$		−	3.98061i		−	0.205012i
$378$	16.6408	+	28.7783i	0.855909	+	1.48020i
$379$	20.7225			1.06444			0.532220	−	0.846606i	$-0.321358\pi$
$379$	20.7225			1.06444			0.532220	+	0.846606i	$0.321358\pi$
$380$	−14.9275	−	29.2465i	−0.765763	−	1.50031i
$381$	2.36896	−	1.63163i	0.121365	−	0.0835908i
$382$	39.9824	−	47.6492i	2.04568	−	2.43794i
$383$	−33.2623	−	5.86503i	−1.69962	−	0.299689i	−0.762060	−	0.647507i	$-0.775812\pi$
$383$	−33.2623	−	5.86503i	−1.69962	−	0.299689i	−0.937562	+	0.347818i	$0.886923\pi$
$384$	−25.2918	+	24.9039i	−1.29067	+	1.27087i
$385$	1.52224	−	13.1690i	0.0775806	−	0.671156i
$386$	−35.0801	+	20.2535i	−1.78553	+	1.03088i
$387$	7.40396	−	2.56596i	0.376364	−	0.130435i
$388$	−16.5441	+	28.6553i	−0.839902	+	1.45475i
$389$	23.9282	−	4.21918i	1.21321	−	0.213921i	0.469807	−	0.882769i	$-0.344323\pi$
$389$	23.9282	−	4.21918i	1.21321	−	0.213921i	0.743399	+	0.668848i	$0.233212\pi$
$390$	17.5215	+	19.7369i	0.887236	+	0.999419i
$391$	−4.95542	−	13.6149i	−0.250607	−	0.688536i
$392$	30.4965	−	6.89106i	1.54031	−	0.348051i
$393$	28.3660	+	20.1905i	1.43087	+	1.01848i
$394$	7.37862	+	41.8462i	0.371729	+	2.10818i
$395$	9.79565	+	31.9606i	0.492873	+	1.60811i
$396$	−24.1626	−	9.21976i	−1.21421	−	0.463310i
$397$	11.6362	+	20.1546i	0.584006	+	1.01153i	0.994998	+	0.0998899i	$0.0318491\pi$
$397$	11.6362	+	20.1546i	0.584006	+	1.01153i	−0.410992	+	0.911639i	$0.634818\pi$
$398$	40.7226	+	48.5313i	2.04124	+	2.43265i
$399$	−16.5313	−	5.71681i	−0.827598	−	0.286198i
$400$	−15.4476	−	1.60187i	−0.772381	−	0.0800937i
$401$	−20.6667	+	24.6297i	−1.03205	+	1.22995i	−0.0592613	+	0.998243i	$0.518875\pi$
$401$	−20.6667	+	24.6297i	−1.03205	+	1.22995i	−0.972786	+	0.231704i	$0.925570\pi$
$402$	−0.846605	−	10.6214i	−0.0422248	−	0.529747i
$403$	−7.07367	+	19.4348i	−0.352365	+	0.968114i
$404$	24.9797			1.24279
$405$	−16.5391	−	11.4655i	−0.821835	−	0.569725i
$406$	9.01854	+	0.572705i	0.447583	+	0.0284229i
$407$	21.2423	+	7.73157i	1.05294	+	0.383239i
$408$	4.45066	+	55.8373i	0.220340	+	2.76436i
$409$	−6.69644	+	7.98051i	−0.331118	+	0.394611i	−0.905758	−	0.423795i	$-0.860698\pi$
$409$	−6.69644	+	7.98051i	−0.331118	+	0.394611i	0.574640	+	0.818406i	$0.305142\pi$
$410$	−15.0731	−	19.9738i	−0.744408	−	0.986434i
$411$	−4.19762	−	1.15959i	−0.207053	−	0.0571982i
$412$	−0.188863	+	0.158475i	−0.00930464	+	0.00780752i
$413$	−24.6743	+	12.2304i	−1.21414	+	0.601820i
$414$	−9.15777	−	11.2628i	−0.450080	−	0.553536i
$415$	−0.0802906	+	0.0246084i	−0.00394131	+	0.00120798i
$416$	0.695966	+	3.94702i	0.0341225	+	0.193519i
$417$	9.05030	−	12.7149i	0.443195	−	0.622652i
$418$	19.4350	−	7.07376i	0.950597	−	0.345989i
$419$	−10.4036	+	3.78661i	−0.508250	+	0.184988i	−0.583401	−	0.812184i	$-0.698278\pi$
$419$	−10.4036	+	3.78661i	−0.508250	+	0.184988i	0.0751511	+	0.997172i	$0.476056\pi$
$420$	−31.0798	+	24.2504i	−1.51654	+	1.18330i
$421$	−5.19292	−	29.4505i	−0.253088	−	1.43533i	−0.800934	−	0.598752i	$-0.795663\pi$
$421$	−5.19292	−	29.4505i	−0.253088	−	1.43533i	0.547847	−	0.836579i	$-0.315448\pi$
$422$	−4.57181	+	7.91861i	−0.222552	+	0.385472i
$423$	6.46345	+	5.59594i	0.314264	+	0.272084i
$424$	−1.54647	−	2.67857i	−0.0751033	−	0.130083i
$425$	26.0072	−	25.1849i	1.26153	−	1.22165i
$426$	35.5829	+	36.1371i	1.72400	+	1.75085i
$427$	0.0609426	−	0.251262i	0.00294922	−	0.0121594i
$428$	−36.1681	−	30.3486i	−1.74825	−	1.46696i
$429$	−9.00776	+	6.20413i	−0.434899	+	0.299538i
$430$	6.42049	+	12.5793i	0.309624	+	0.606626i
$431$			17.0669i			0.822086i	0.911616	+	0.411043i	$0.134835\pi$
$431$			17.0669i			0.822086i	−0.911616	+	0.411043i	$0.865165\pi$
$432$	6.48005	+	14.7817i	0.311772	+	0.711186i
$433$	29.4009			1.41292			0.706458	−	0.707755i	$-0.250292\pi$
$433$	29.4009			1.41292			0.706458	+	0.707755i	$0.250292\pi$
$434$	−43.0140	−	18.8224i	−2.06474	−	0.903503i
$435$	−5.08655	+	2.01361i	−0.243881	+	0.0965453i
$436$	−30.8529	−	25.8887i	−1.47759	−	1.23984i
$437$	7.52200	+	1.32633i	0.359826	+	0.0634470i
$438$	0.987440	+	3.80246i	0.0471817	+	0.181689i
$439$	17.3607	+	20.6897i	0.828582	+	0.987465i	0.999997	+	0.00226640i	$0.000721417\pi$
$439$	17.3607	+	20.6897i	0.828582	+	0.987465i	−0.171416	+	0.985199i	$0.554834\pi$
$440$	5.01914	−	21.8095i	0.239278	−	1.03973i
$441$	−2.97802	+	20.7878i	−0.141810	+	0.989894i
$442$	42.7302	+	24.6703i	2.03247	+	1.17344i
$443$	2.82708	+	16.0332i	0.134318	+	0.761758i	0.975332	+	0.220744i	$0.0708484\pi$
$443$	2.82708	+	16.0332i	0.134318	+	0.761758i	−0.841013	+	0.541014i	$0.818040\pi$
$444$	−27.9376	−	61.1414i	−1.32586	−	2.90164i
$445$	−0.240883	+	0.568585i	−0.0114190	+	0.0269535i
$446$	−26.1995	+	9.53582i	−1.24058	+	0.451534i
$447$	−12.0676	−	26.4098i	−0.570776	−	1.24914i
$448$	−25.3771	+	2.83144i	−1.19895	+	0.133773i
$449$	9.39365	+	5.42343i	0.443314	+	0.255947i	0.705002	−	0.709205i	$-0.250946\pi$
$449$	9.39365	+	5.42343i	0.443314	+	0.255947i	−0.261688	+	0.965152i	$0.584279\pi$
$450$	16.3571	−	32.3736i	0.771081	−	1.52610i
$451$	8.98081	−	5.18507i	0.422890	−	0.244156i
$452$	−45.1591	+	37.8930i	−2.12410	+	1.78234i
$453$	−9.78127	−	37.6660i	−0.459564	−	1.76970i
$454$	62.3140	+	10.9876i	2.92454	+	0.515675i
$455$	0.990598	+	16.6428i	0.0464399	+	0.780225i
$456$	−26.6654	−	12.6860i	−1.24872	−	0.594078i
$457$	−3.26660	+	8.97492i	−0.152805	+	0.419829i	−0.992349	−	0.123463i	$-0.960600\pi$
$457$	−3.26660	+	8.97492i	−0.152805	+	0.419829i	0.839544	+	0.543292i	$0.182822\pi$
$458$			4.46145i			0.208470i
$459$	−36.1057	−	10.5773i	−1.68527	−	0.493708i
$460$	11.7310	−	12.5975i	0.546961	−	0.587363i
$461$	−8.78579	−	3.19777i	−0.409195	−	0.148935i	0.129217	−	0.991616i	$-0.458754\pi$
$461$	−8.78579	−	3.19777i	−0.409195	−	0.148935i	−0.538412	+	0.842681i	$0.680976\pi$
$462$	−12.7602	−	21.3008i	−0.593658	−	0.991001i
$463$	2.45863	−	2.93008i	0.114262	−	0.136172i	−0.705882	−	0.708330i	$-0.749449\pi$
$463$	2.45863	−	2.93008i	0.114262	−	0.136172i	0.820144	+	0.572157i	$0.193893\pi$
$464$	4.32072	+	0.761859i	0.200584	+	0.0353684i
$465$	28.4126	−	0.792218i	1.31760	−	0.0367382i
$466$	−7.53909	+	6.32605i	−0.349242	+	0.293049i
$467$	−8.41520	+	4.85852i	−0.389409	+	0.224825i	−0.681904	−	0.731442i	$-0.738848\pi$
$467$	−8.41520	+	4.85852i	−0.389409	+	0.224825i	0.292495	+	0.956267i	$0.405515\pi$
$468$	31.9397	+	6.14221i	1.47641	+	0.283924i
$469$	3.72812	−	5.60414i	0.172149	−	0.258775i
$470$	−8.38318	+	12.9287i	−0.386687	+	0.596355i
$471$	−1.40342	+	14.7294i	−0.0646661	+	0.678693i
$472$	−43.6872	+	15.9008i	−2.01086	+	0.731895i
$473$	−5.49997	+	2.00183i	−0.252889	+	0.0920440i
$474$	51.0097	+	36.3080i	2.34295	+	1.66768i
$475$	4.64289	+	18.5118i	0.213030	+	0.849380i
$476$	−40.8200	+	61.3610i	−1.87098	+	2.81248i
$477$	2.05120	−	0.329084i	0.0939182	−	0.0150677i
$478$	5.03670	−	2.90794i	0.230373	−	0.133006i
$479$	22.1281	−	18.5676i	1.01106	−	0.848377i	0.0225793	−	0.999745i	$-0.492812\pi$
$479$	22.1281	−	18.5676i	1.01106	−	0.848377i	0.988478	+	0.151368i	$0.0483677\pi$
$480$	4.69156	−	2.88595i	0.214140	−	0.131725i
$481$	−27.9979	−	4.93678i	−1.27659	−	0.225098i
$482$	−9.19611	+	10.9595i	−0.418871	+	0.499192i
$483$	−0.147826	−	9.16873i	−0.00672631	−	0.417192i
$484$	−21.6142	−	7.86692i	−0.982463	−	0.357587i
$485$	13.1064	−	14.0745i	0.595130	−	0.639090i
$486$	−37.6496	+	1.83238i	−1.70782	+	0.0831185i
$487$		−	20.5657i		−	0.931919i	−0.884806	−	0.465959i	$-0.845709\pi$
$487$		−	20.5657i		−	0.931919i	0.884806	−	0.465959i	$-0.154291\pi$
$488$	0.149282	−	0.410150i	0.00675770	−	0.0185666i
$489$	−1.27128	−	15.9493i	−0.0574894	−	0.721254i
$490$	−37.8487	−	0.150141i	−1.70983	−	0.00678269i
$491$	−5.15684	−	0.909291i	−0.232725	−	0.0410357i	0.0560692	−	0.998427i	$-0.482143\pi$
$491$	−5.15684	−	0.909291i	−0.232725	−	0.0410357i	−0.288794	+	0.957391i	$0.593254\pi$
$492$	−29.7242	−	8.21126i	−1.34007	−	0.370192i
$493$	−7.83461	+	6.57402i	−0.352853	+	0.296079i
$494$	−22.5262	+	13.0055i	−1.01350	+	0.585144i
$495$	12.4845	+	8.37200i	0.561134	+	0.376294i
$496$	−19.7414	−	11.3977i	−0.886416	−	0.511773i
$497$	3.55250	+	31.8397i	0.159351	+	1.42821i
$498$	−0.0912120	+	0.128145i	−0.00408731	+	0.00574233i
$499$	−20.9190	+	7.61388i	−0.936462	+	0.340844i	−0.764768	−	0.644306i	$-0.777146\pi$
$499$	−20.9190	+	7.61388i	−0.936462	+	0.340844i	−0.171694	+	0.985150i	$0.554924\pi$
$500$	40.6979	+	13.9184i	1.82007	+	0.622451i
$501$	32.1415	+	3.06245i	1.43598	+	0.136820i
$502$	4.03387	+	22.8772i	0.180041	+	1.02106i
$503$	−18.7162	−	10.8058i	−0.834513	−	0.481806i	0.0208823	−	0.999782i	$-0.493352\pi$
$503$	−18.7162	−	10.8058i	−0.834513	−	0.481806i	−0.855395	+	0.517976i	$0.826686\pi$
$504$	−8.88779	+	34.3195i	−0.395893	+	1.52871i
$505$	−14.1491	−	3.25622i	−0.629628	−	0.144900i
$506$	6.96941	+	8.30582i	0.309828	+	0.369239i
$507$	−6.24269	+	6.14695i	−0.277247	+	0.272996i
$508$	6.29200	+	1.10945i	0.279162	+	0.0492238i
$509$	−13.7735	−	11.5574i	−0.610501	−	0.512272i	0.284300	−	0.958735i	$-0.408239\pi$
$509$	−13.7735	−	11.5574i	−0.610501	−	0.512272i	−0.894802	+	0.446464i	$0.852683\pi$
$510$	9.90915	−	67.0815i	0.438784	−	2.97042i
$511$	−0.994888	+	2.27358i	−0.0440113	+	0.100577i
$512$	−32.1641			−1.42146
$513$	14.3460	−	13.6958i	0.633391	−	0.604685i
$514$		−	40.1953i		−	1.77294i
$515$	0.127635	−	0.0651453i	0.00562427	−	0.00287064i
$516$	15.7168	+	7.47725i	0.691893	+	0.329168i
$517$	−4.89177	−	4.10468i	−0.215140	−	0.180524i
$518$	15.2130	−	62.7222i	0.668421	−	2.75585i
$519$	11.6448	−	3.02398i	0.511151	−	0.132738i
$520$	−1.45347	+	28.1080i	−0.0637387	+	1.23262i
$521$	−3.34304	−	5.79031i	−0.146461	−	0.253678i	0.783456	−	0.621447i	$-0.213455\pi$
$521$	−3.34304	−	5.79031i	−0.146461	−	0.253678i	−0.929917	+	0.367769i	$0.880122\pi$
$522$	−5.25985	+	8.79364i	−0.230217	+	0.384887i
$523$	−10.1124	+	17.5152i	−0.442185	+	0.765887i	−0.997851	−	0.0655187i	$-0.979130\pi$
$523$	−10.1124	+	17.5152i	−0.442185	+	0.765887i	0.555667	+	0.831405i	$0.312463\pi$
$524$	13.4291	+	76.1603i	0.586654	+	3.32708i
$525$	20.7655	−	9.68465i	0.906282	−	0.422673i
$526$	−63.4974	+	23.1112i	−2.76862	+	1.00769i
$527$	49.9336	−	18.1743i	2.17514	−	0.791687i
$528$	−5.01020	−	10.9648i	−0.218041	−	0.477182i
$529$	−3.29859	−	18.7072i	−0.143417	−	0.813359i
$530$	1.09720	+	3.57986i	0.0476592	+	0.155499i
$531$	0.482561	−	31.2228i	0.0209414	−	1.35495i
$532$	−17.2545	−	34.8101i	−0.748076	−	1.50921i
$533$	−9.99072	+	8.38321i	−0.432746	+	0.363117i
$534$	0.290712	+	1.11948i	0.0125803	+	0.0484447i
$535$	16.5305	+	21.9049i	0.714674	+	0.947032i
$536$	7.30397	−	8.70453i	0.315483	−	0.375978i
$537$	18.3552	+	8.73248i	0.792086	+	0.376834i
$538$	−46.6592	−	16.9826i	−2.01162	−	0.732171i
$539$	1.98416	−	15.5596i	0.0854639	−	0.670197i
$540$	−8.30816	−	43.9206i	−0.357526	−	1.89004i
$541$	33.6954			1.44868			0.724339	−	0.689444i	$-0.242145\pi$
$541$	33.6954			1.44868			0.724339	+	0.689444i	$0.242145\pi$
$542$	5.04645	−	13.8650i	0.216764	−	0.595553i
$543$	20.1052	−	13.8476i	0.862798	−	0.594256i
$544$	6.61910	−	7.88834i	0.283792	−	0.338210i
$545$	14.1012	+	18.6858i	0.604029	+	0.800414i
$546$	20.4558	+	23.5951i	0.875428	+	1.00978i
$547$	−19.1467	−	22.8181i	−0.818653	−	0.975633i	0.181316	−	0.983425i	$-0.441964\pi$
$547$	−19.1467	−	22.8181i	−0.818653	−	0.975633i	−0.999970	+	0.00779188i	$0.997520\pi$
$548$	−4.83635	−	8.37680i	−0.206599	−	0.357839i
$549$	0.221639	+	0.191891i	0.00945930	+	0.00818971i
$550$	−11.8425	+	24.3667i	−0.504966	+	1.03900i
$551$	−0.936238	−	5.30967i	−0.0398851	−	0.226200i
$552$	1.46833	−	15.4106i	0.0624962	−	0.655919i
$553$	11.1451	+	37.9499i	0.473937	+	1.61379i
$554$	12.4909	+	34.3185i	0.530688	+	1.45805i
$555$	7.85450	+	38.2738i	0.333405	+	1.62463i
$556$	34.1385	−	6.01954i	1.44780	−	0.255285i
$557$	−20.5290	+	35.5573i	−0.869843	+	1.50661i	−0.00768705	+	0.999970i	$0.502447\pi$
$557$	−20.5290	+	35.5573i	−0.869843	+	1.50661i	−0.862156	+	0.506642i	$0.830886\pi$
$558$	41.3070	−	33.5867i	1.74867	−	1.42184i
$559$	6.37475	−	3.68046i	0.269623	−	0.155667i
$560$	−18.2543	−	2.11007i	−0.771386	−	0.0891665i
$561$	27.0873	+	7.48284i	1.14363	+	0.315926i
$562$	−59.6153	−	10.5118i	−2.51472	−	0.443413i
$563$	11.2510	−	13.4084i	0.474172	−	0.565096i	−0.474947	−	0.880014i	$-0.657533\pi$
$563$	11.2510	−	13.4084i	0.474172	−	0.565096i	0.949119	+	0.314919i	$0.101977\pi$
$564$	1.50880	+	18.9291i	0.0635317	+	0.797061i
$565$	30.5188	−	15.5769i	1.28393	−	0.655323i
$566$	−40.9224			−1.72010
$567$	−19.4085	−	13.7952i	−0.815082	−	0.579345i
$568$			54.0845i			2.26933i
$569$	9.03351	−	24.8194i	0.378705	−	1.04048i	−0.593189	−	0.805063i	$-0.702131\pi$
$569$	9.03351	−	24.8194i	0.378705	−	1.04048i	0.971894	−	0.235419i	$-0.0756463\pi$
$570$	28.0138	+	22.2057i	1.17337	+	0.930095i
$571$	−8.64103	−	7.25069i	−0.361616	−	0.303432i	0.443819	−	0.896117i	$-0.353623\pi$
$571$	−8.64103	−	7.25069i	−0.361616	−	0.303432i	−0.805434	+	0.592685i	$0.798068\pi$
$572$	−23.9248	−	4.21859i	−1.00035	−	0.176388i
$573$	−11.8637	+	42.9459i	−0.495615	+	1.79409i
$574$	−17.5557	−	23.8413i	−0.732762	−	0.995115i
$575$	−8.28689	+	5.60638i	−0.345587	+	0.233802i
$576$	10.3219	−	27.0511i	0.430081	−	1.12713i
$577$	−14.8893	+	25.7890i	−0.619849	+	1.07361i	0.369664	+	0.929166i	$0.379473\pi$
$577$	−14.8893	+	25.7890i	−0.619849	+	1.07361i	−0.989513	+	0.144444i	$0.953860\pi$
$578$	−14.8752	−	84.3615i	−0.618727	−	3.50898i
$579$	16.8254	−	23.6382i	0.699239	−	0.982372i
$580$	−11.1883	−	4.73998i	−0.464570	−	0.196817i
$581$	−0.0953367	+	0.0279984i	−0.00395523	+	0.00116157i
$582$	3.41673	−	35.8598i	0.141628	−	1.48644i
$583$	−1.52813	+	0.269450i	−0.0632885	+	0.0111595i
$584$	−2.09479	+	3.62828i	−0.0866830	+	0.150139i
$585$	−17.2908	−	7.64259i	−0.714887	−	0.315982i
$586$	−41.6384	+	24.0399i	−1.72007	+	0.993081i
$587$	7.94765	+	9.47164i	0.328035	+	0.390936i	0.904704	−	0.426041i	$-0.140092\pi$
$587$	7.94765	+	9.47164i	0.328035	+	0.390936i	−0.576669	+	0.816978i	$0.695648\pi$
$588$	−37.1088	+	28.2592i	−1.53034	+	1.16539i
$589$	−4.86441	+	27.5874i	−0.200434	+	1.13672i
$590$	55.8562	−	6.89774i	2.29956	−	0.283976i
$591$	−17.2645	−	25.0663i	−0.710165	−	1.03109i
$592$	10.7172	−	29.4452i	0.440473	−	1.21019i
$593$		−	3.36070i		−	0.138008i	−0.997616	−	0.0690038i	$-0.978018\pi$
$593$		−	3.36070i		−	0.138008i	0.997616	−	0.0690038i	$-0.0219821\pi$
$594$	28.0971	−	1.80308i	1.15284	−	0.0739813i
$595$	31.1202	−	29.4354i	1.27580	−	1.20673i
$596$	22.0581	−	60.6041i	0.903534	−	2.48244i
$597$	−40.9782	−	19.4953i	−1.67713	−	0.797891i
$598$	−10.4458	−	8.76504i	−0.427159	−	0.358429i
$599$	−14.8989	−	2.62707i	−0.608752	−	0.107339i	−0.139230	−	0.990260i	$-0.544463\pi$
$599$	−14.8989	−	2.62707i	−0.608752	−	0.107339i	−0.469522	+	0.882921i	$0.655574\pi$
$600$	36.6526	−	12.3613i	1.49633	−	0.504649i
$601$	−0.690837	−	0.823307i	−0.0281798	−	0.0335834i	0.751770	−	0.659425i	$-0.229200\pi$
$601$	−0.690837	−	0.823307i	−0.0281798	−	0.0335834i	−0.779950	+	0.625841i	$0.784756\pi$
$602$	7.42136	+	14.9723i	0.302472	+	0.610224i
$603$	3.71347	+	6.66781i	0.151224	+	0.271534i
$604$	43.2181	−	74.8560i	1.75852	−	3.04585i
$605$	11.2173	+	7.27353i	0.456050	+	0.295711i
$606$	−24.7348	+	11.3022i	−1.00478	+	0.459119i
$607$	−20.2049	+	7.35397i	−0.820090	+	0.298489i	−0.717785	−	0.696265i	$-0.754844\pi$
$607$	−20.2049	+	7.35397i	−0.820090	+	0.298489i	−0.102305	+	0.994753i	$0.532622\pi$
$608$	1.85667	+	5.10117i	0.0752981	+	0.206880i
$609$	−6.04607	+	2.31163i	−0.244999	+	0.0936722i
$610$	−0.287468	+	0.443338i	−0.0116393	+	0.0179502i
$611$	6.95505	+	4.01550i	0.281371	+	0.162450i
$612$	−40.6597	−	73.0074i	−1.64357	−	2.95115i
$613$	−16.4661	+	9.50672i	−0.665061	+	0.383973i	−0.794203	−	0.607653i	$-0.792111\pi$
$613$	−16.4661	+	9.50672i	−0.665061	+	0.383973i	0.129142	+	0.991626i	$0.458778\pi$
$614$	−57.3756	+	48.1438i	−2.31549	+	1.94293i
$615$	15.7662	+	8.52575i	0.635754	+	0.343792i
$616$	6.24163	−	25.7338i	0.251482	−	1.03684i
$617$	−11.2361	−	9.42825i	−0.452350	−	0.379567i	0.387957	−	0.921678i	$-0.373181\pi$
$617$	−11.2361	−	9.42825i	−0.452350	−	0.379567i	−0.840307	+	0.542111i	$0.817625\pi$
$618$	0.115309	−	0.242373i	0.00463841	−	0.00974969i
$619$	4.10716	−	11.2843i	0.165081	−	0.453556i	−0.829377	−	0.558689i	$-0.811305\pi$
$619$	4.10716	−	11.2843i	0.165081	−	0.453556i	0.994458	+	0.105133i	$0.0335268\pi$
$620$	46.2023	+	43.0243i	1.85553	+	1.72790i
$621$	9.31914	+	4.61151i	0.373964	+	0.185054i
$622$	−54.3390			−2.17880
$623$	−0.292905	+	0.669363i	−0.0117350	+	0.0268174i
$624$	8.59990	+	12.4862i	0.344271	+	0.499847i
$625$	−21.2380	−	13.1889i	−0.849520	−	0.527556i
$626$	−6.25167	+	35.4550i	−0.249867	+	1.41707i
$627$	−10.5561	+	10.3942i	−0.421570	+	0.415105i
$628$	−25.1754	+	21.1246i	−1.00461	+	0.842965i
$629$	36.5222	+	63.2584i	1.45624	+	2.52228i
$630$	19.8029	−	38.0748i	0.788966	−	1.51694i
$631$	−6.00126	+	10.3945i	−0.238907	+	0.413798i	−0.960401	−	0.278622i	$-0.910122\pi$
$631$	−6.00126	+	10.3945i	−0.238907	+	0.413798i	0.721494	+	0.692420i	$0.243456\pi$
$632$	11.5948	+	65.7572i	0.461215	+	2.61568i
$633$	0.621225	−	6.51997i	0.0246915	−	0.259145i
$634$	−37.4052	+	13.6144i	−1.48555	+	0.540695i
$635$	−3.41933	−	1.44861i	−0.135692	−	0.0574863i
$636$	3.75922	+	2.67576i	0.149063	+	0.106101i
$637$	0.940556	+	19.7044i	0.0372662	+	0.780717i
$638$	3.82678	−	6.62817i	0.151503	−	0.262412i
$639$	−33.9400	−	12.9506i	−1.34265	−	0.512316i
$640$	44.6562	+	10.2770i	1.76519	+	0.406233i
$641$	21.6357	+	25.7844i	0.854558	+	1.01842i	0.999580	+	0.0289939i	$0.00923034\pi$
$641$	21.6357	+	25.7844i	0.854558	+	1.01842i	−0.145022	+	0.989428i	$0.546325\pi$
$642$	49.5448	+	13.6867i	1.95538	+	0.540170i
$643$	4.14026	−	23.4806i	0.163276	−	0.925983i	−0.787549	−	0.616252i	$-0.788650\pi$
$643$	4.14026	−	23.4806i	0.163276	−	0.925983i	0.950824	−	0.309730i	$-0.100239\pi$
$644$	14.0546	−	14.7414i	0.553827	−	0.580894i
$645$	−7.92770	−	6.28406i	−0.312153	−	0.247435i
$646$	62.7995	+	22.8571i	2.47081	+	0.899302i
$647$		−	37.9377i		−	1.49148i	−0.666235	−	0.745742i	$-0.732095\pi$
$647$		−	37.9377i		−	1.49148i	0.666235	−	0.745742i	$-0.267905\pi$
$648$	−29.9805	−	26.7783i	−1.17775	−	1.05195i
$649$			23.3240i			0.915549i
$650$	9.34598	−	32.7654i	0.366580	−	1.28516i
$651$	33.6269	−	0.542161i	1.31794	−	0.0212490i
$652$	22.8434	−	27.2237i	0.894617	−	1.06616i
$653$	1.60832	−	9.12124i	0.0629385	−	0.356942i	−0.937032	−	0.349244i	$-0.886439\pi$
$653$	1.60832	−	9.12124i	0.0629385	−	0.356942i	0.999970	−	0.00769797i	$-0.00245036\pi$
$654$	42.2639	+	11.6753i	1.65265	+	0.456541i
$655$	2.32124	−	44.8897i	0.0906985	−	1.75399i
$656$	−7.18733	−	12.4488i	−0.280618	−	0.486045i
$657$	−1.77528	−	2.18335i	−0.0692604	−	0.0851807i
$658$	−10.0982	+	15.1798i	−0.393670	+	0.591768i
$659$	19.5497	−	3.44714i	0.761549	−	0.134282i	0.220631	−	0.975357i	$-0.429188\pi$
$659$	19.5497	−	3.44714i	0.761549	−	0.134282i	0.540918	+	0.841076i	$0.318077\pi$
$660$	6.71185	+	32.7058i	0.261258	+	1.27307i
$661$	−11.1795	−	30.7153i	−0.434831	−	1.19469i	−0.942814	−	0.333320i	$-0.891831\pi$
$661$	−11.1795	−	30.7153i	−0.434831	−	1.19469i	0.507983	−	0.861367i	$-0.330391\pi$
$662$	−6.73616	+	2.45176i	−0.261808	+	0.0952904i
$663$	−35.1829	−	3.35223i	−1.36639	−	0.130190i
$664$	−0.165194	+	0.0291281i	−0.00641075	+	0.00113039i
$665$	5.23572	+	21.9665i	0.203032	+	0.851825i
$666$	55.3273	+	47.9014i	2.14389	+	1.85614i
$667$	2.44780	−	1.41324i	0.0947794	−	0.0547209i
$668$	46.0968	+	54.9361i	1.78354	+	2.12554i
$669$	14.2302	−	14.0120i	0.550171	−	0.541734i
$670$	−10.9800	+	8.28600i	−0.424194	+	0.320116i
$671$	−0.167744	−	0.140754i	−0.00647568	−	0.00543374i
$672$	5.59088	−	3.34922i	0.215673	−	0.129199i
$673$	2.94873	−	8.10156i	0.113665	−	0.312292i	−0.869796	−	0.493411i	$-0.835750\pi$
$673$	2.94873	−	8.10156i	0.113665	−	0.312292i	0.983461	+	0.181119i	$0.0579720\pi$
$674$		−	9.88390i		−	0.380714i
$675$	−1.01929	+	25.9608i	−0.0392326	+	0.999230i
$676$	−19.4595			−0.748442
$677$	12.6740	−	34.8215i	0.487101	−	1.33830i	−0.416194	−	0.909276i	$-0.636636\pi$
$677$	12.6740	−	34.8215i	0.487101	−	1.33830i	0.903294	−	0.429022i	$-0.141142\pi$
$678$	27.5715	−	57.9538i	1.05888	−	2.22570i
$679$	15.7023	−	16.4697i	0.602601	−	0.632051i
$680$	57.7225	−	43.5600i	2.21356	−	1.67045i
$681$	−43.8685	+	11.3920i	−1.68104	+	0.436541i
$682$	−30.4621	+	25.5608i	−1.16646	+	0.978773i
$683$	11.8779	+	20.5730i	0.454493	+	0.787206i	0.998659	−	0.0517722i	$-0.0164870\pi$
$683$	11.8779	+	20.5730i	0.454493	+	0.787206i	−0.544165	+	0.838978i	$0.683154\pi$
$684$	44.0485	+	0.680788i	1.68424	+	0.0260306i
$685$	1.64748	+	5.37527i	0.0629469	+	0.205379i
$686$	−44.7780	−	0.704007i	−1.70963	−	0.0268791i
$687$	−1.32814	−	2.90664i	−0.0506717	−	0.110895i
$688$	2.77484	+	7.62382i	0.105790	+	0.290655i
$689$	1.83380	−	0.667448i	0.0698621	−	0.0254277i
$690$	−5.91619	+	17.7818i	−0.225225	+	0.676940i
$691$	−38.3598	+	6.76387i	−1.45928	+	0.257310i	−0.846264	−	0.532763i	$-0.821154\pi$
$691$	−38.3598	+	6.76387i	−1.45928	+	0.257310i	−0.613013	+	0.790073i	$0.710042\pi$
$692$	23.1425	+	13.3613i	0.879745	+	0.507921i
$693$	14.6544	+	10.0788i	0.556673	+	0.382863i
$694$	29.1575	+	50.5024i	1.10681	+	1.91704i
$695$	−20.1216	−	1.04049i	−0.763256	−	0.0394679i
$696$	−10.5766	+	2.74658i	−0.400905	+	0.104109i
$697$	32.9996	+	5.81871i	1.24995	+	0.220399i
$698$	31.4513	−	37.4823i	1.19045	−	1.41872i
$699$	3.02850	−	6.36575i	0.114548	−	0.240775i
$700$	47.9575	+	17.0334i	1.81262	+	0.643801i
$701$			7.18864i			0.271511i	0.990742	+	0.135756i	$0.0433462\pi$
$701$			7.18864i			0.271511i	−0.990742	+	0.135756i	$0.956654\pi$
$702$	−34.4056	+	8.36925i	−1.29856	+	0.315877i
$703$	−38.5070			−1.45232
$704$	−7.39661	+	20.3220i	−0.278770	+	0.765915i
$705$	1.61288	−	10.9186i	0.0607445	−	0.411219i
$706$	−26.4377	+	31.5072i	−0.994997	+	1.18579i
$707$	−16.6950	−	4.04932i	−0.627882	−	0.152290i
$708$	49.4212	−	48.6633i	1.85736	−	1.82888i
$709$	−2.61921	+	2.19778i	−0.0983664	+	0.0825392i	−0.690645	−	0.723194i	$-0.742673\pi$
$709$	−2.61921	+	2.19778i	−0.0983664	+	0.0825392i	0.592278	+	0.805734i	$0.298229\pi$
$710$	14.6838	−	63.8052i	0.551074	−	2.39457i
$711$	−44.0414	−	8.46945i	−1.65168	−	0.317629i
$712$	−0.616726	+	1.06820i	−0.0231128	+	0.0400325i
$713$	−14.4624	+	2.55012i	−0.541622	+	0.0955026i
$714$	12.6568	−	79.2286i	0.473668	−	2.96506i
$715$	13.0017	+	5.50822i	0.486237	+	0.205996i
$716$	15.4416	+	42.4253i	0.577078	+	1.58551i
$717$	−2.41574	+	3.39391i	−0.0902174	+	0.126748i
$718$	−60.5535	+	10.6772i	−2.25984	+	0.398470i
$719$	17.4574	−	30.2371i	0.651050	−	1.12765i	−0.331818	−	0.943343i	$-0.607662\pi$
$719$	17.4574	−	30.2371i	0.651050	−	1.12765i	0.982868	−	0.184309i	$-0.0590047\pi$
$720$	11.6049	−	17.3054i	0.432489	−	0.644934i
$721$	0.151915	−	0.0753005i	0.00565763	−	0.00280434i
$722$	8.20643	−	6.88601i	0.305412	−	0.256271i
$723$	2.72871	−	9.87773i	0.101482	−	0.367357i
$724$	53.3999	+	9.41585i	1.98459	+	0.349937i
$725$	5.71948	+	4.14329i	0.212416	+	0.153878i
$726$	24.9617	−	1.98963i	0.926415	−	0.0738422i
$727$	−41.7271	−	15.1874i	−1.54757	−	0.563271i	−0.579727	−	0.814811i	$-0.696841\pi$
$727$	−41.7271	−	15.1874i	−1.54757	−	0.563271i	−0.967847	+	0.251540i	$0.919063\pi$
$728$	−2.11055	+	33.2354i	−0.0782222	+	1.23179i
$729$	23.9832	−	12.4018i	0.888268	−	0.459326i
$730$	3.45636	−	3.71167i	0.127926	−	0.137375i
$731$	−17.7718	−	6.46841i	−0.657314	−	0.239243i
$732$	0.0517382	+	0.649101i	0.00191230	+	0.0239915i
$733$	13.6247	+	11.4324i	0.503238	+	0.422267i	0.858742	−	0.512408i	$-0.171246\pi$
$733$	13.6247	+	11.4324i	0.503238	+	0.422267i	−0.355504	+	0.934675i	$0.615691\pi$
$734$	−9.54149	+	54.1125i	−0.352183	+	1.99733i
$735$	24.7031	−	11.1694i	0.911188	−	0.411991i
$736$	−2.18006	+	1.82929i	−0.0803580	+	0.0674284i
$737$	−2.85034	−	4.93694i	−0.104994	−	0.181854i
$738$	33.1480	−	5.31807i	1.22019	−	0.195761i
$739$	−10.0882	+	17.4732i	−0.371099	+	0.642762i	−0.989735	−	0.142916i	$-0.954352\pi$
$739$	−10.0882	+	17.4732i	−0.371099	+	0.642762i	0.618636	+	0.785678i	$0.287686\pi$
$740$	−47.2147	+	72.8152i	−1.73565	+	2.67674i
$741$	10.8042	−	15.1789i	0.396901	−	0.557612i
$742$	1.24835	+	4.25071i	0.0458282	+	0.156049i
$743$	−26.0534	+	9.48266i	−0.955807	+	0.347885i	−0.772389	−	0.635150i	$-0.780938\pi$
$743$	−26.0534	+	9.48266i	−0.955807	+	0.347885i	−0.183418	+	0.983035i	$0.558716\pi$
$744$	56.5194	+	5.38519i	2.07210	+	0.197431i
$745$	−20.3943	+	31.4523i	−0.747188	+	1.15232i
$746$	−21.3604	−	12.3325i	−0.782061	−	0.451523i
$747$	0.0212768	−	0.110640i	0.000778476	−	0.00404810i
$748$	31.2091	+	54.0557i	1.14112	+	1.97647i
$749$	19.2531	+	26.1463i	0.703493	+	0.955367i
$750$	−46.5963	+	4.63195i	−1.70146	+	0.169135i
$751$	1.59015	−	9.01816i	0.0580252	−	0.329077i	−0.941953	−	0.335746i	$-0.891012\pi$
$751$	1.59015	−	9.01816i	0.0580252	−	0.329077i	0.999978	+	0.00666864i	$0.00212271\pi$
$752$	−5.68973	+	6.78075i	−0.207483	+	0.247269i
$753$	−9.43845	−	13.7037i	−0.343956	−	0.499389i
$754$	−3.29210	+	9.04496i	−0.119891	+	0.329398i
$755$	−34.2377	+	36.7667i	−1.24604	+	1.33808i
$756$	−9.21886	−	52.0795i	−0.335287	−	1.89411i
$757$			26.3766i			0.958675i	0.877631	+	0.479338i	$0.159123\pi$
$757$			26.3766i			0.958675i	−0.877631	+	0.479338i	$0.840877\pi$
$758$	−47.0867	−	17.1381i	−1.71026	−	0.622486i
$759$	−7.01315	−	3.33650i	−0.254561	−	0.121107i
$760$	4.67225	+	37.8347i	0.169480	+	1.37241i
$761$	−2.18242	+	12.3771i	−0.0791128	+	0.448671i	0.919360	+	0.393418i	$0.128708\pi$
$761$	−2.18242	+	12.3771i	−0.0791128	+	0.448671i	−0.998472	+	0.0552527i	$0.982404\pi$
$762$	−6.73228	+	1.74827i	−0.243885	+	0.0633330i
$763$	16.4237	+	22.3040i	0.594579	+	0.807458i
$764$	−85.7031	+	49.4807i	−3.10063	+	1.79015i
$765$	13.5138	+	46.6535i	0.488594	+	1.68676i
$766$	70.7297	+	40.8358i	2.55557	+	1.47546i
$767$	−5.09368	−	28.8877i	−0.183922	−	1.04307i
$768$	47.6572	−	21.7762i	1.71968	−	0.785780i
$769$	14.5182	+	39.8884i	0.523539	+	1.43841i	0.866555	+	0.499082i	$0.166329\pi$
$769$	14.5182	+	39.8884i	0.523539	+	1.43841i	−0.343016	+	0.939330i	$0.611448\pi$
$770$	−14.3501	+	28.6644i	−0.517143	+	1.03299i
$771$	11.9658	+	26.1872i	0.430939	+	0.943110i
$772$	63.4668	−	11.1909i	2.28422	−	0.402770i
$773$	9.29725	+	5.36777i	0.334399	+	0.193065i	0.657792	−	0.753199i	$-0.271490\pi$
$773$	9.29725	+	5.36777i	0.334399	+	0.193065i	−0.323393	+	0.946265i	$0.604824\pi$
$774$	−18.9458	−	0.292816i	−0.680993	−	0.0105250i
$775$	−20.5618	−	30.3927i	−0.738600	−	1.09174i
$776$	29.4279	−	24.6929i	1.05640	−	0.886424i
$777$	8.76065	+	45.3923i	0.314286	+	1.62844i
$778$	−57.8603	−	10.2023i	−2.07439	−	0.365771i
$779$	−11.3547	+	13.5320i	−0.406825	+	0.484835i
$780$	−15.4554	−	39.0416i	−0.553393	−	1.39791i
$781$	25.4973	+	9.28026i	0.912365	+	0.332074i
$782$			35.0348i			1.25284i
$783$	0.808995	−	7.29487i	0.0289111	−	0.260697i
$784$	−21.5680	−	2.75036i	−0.770285	−	0.0982271i
$785$	17.0137	−	8.68381i	0.607243	−	0.309939i
$786$	−47.7565	−	69.3375i	−1.70342	−	2.47319i
$787$	10.2350	+	8.58818i	0.364838	+	0.306135i	0.806716	−	0.590940i	$-0.201243\pi$
$787$	10.2350	+	8.58818i	0.364838	+	0.306135i	−0.441878	+	0.897075i	$0.645687\pi$
$788$	11.7392	−	66.5765i	0.418193	−	2.37169i
$789$	34.4886	−	33.9596i	1.22782	−	1.20899i
$790$	4.17422	−	80.7238i	0.148512	−	2.87202i
$791$	36.3244	−	18.0051i	1.29155	−	0.640187i
$792$	22.6998	+	19.6531i	0.806602	+	0.698343i
$793$	0.238496	+	0.137696i	0.00846924	+	0.00488972i
$794$	−9.77201	−	55.4199i	−0.346796	−	1.96678i
$795$	−1.78052	−	2.00565i	−0.0631486	−	0.0711331i
$796$	−34.4734	−	94.7150i	−1.22188	−	3.35708i
$797$	3.56408	+	9.79224i	0.126246	+	0.346859i	0.986673	−	0.162715i	$-0.0520252\pi$
$797$	3.56408	+	9.79224i	0.126246	+	0.346859i	−0.860427	+	0.509574i	$0.829803\pi$
$798$	32.8352	+	26.6619i	1.16235	+	0.943822i
$799$	−3.58306	−	20.3205i	−0.126759	−	0.718888i
$800$	−6.39562	−	3.10834i	−0.226119	−	0.109896i
$801$	−0.522660	−	0.642800i	−0.0184673	−	0.0227122i
$802$	67.3296	−	38.8728i	2.37749	−	1.37265i
$803$	1.35106	+	1.61013i	0.0476778	+	0.0568202i
$804$	−4.51390	+	16.3400i	−0.159193	+	0.576268i
$805$	−9.88248	+	6.51785i	−0.348312	+	0.229724i
$806$	32.1464	−	38.3105i	1.13231	−	1.34943i
$807$	35.4541	−	2.82596i	1.24804	−	0.0994784i
$808$	−27.2523	−	9.91903i	−0.958733	−	0.348950i
$809$		−	11.8876i		−	0.417946i	−0.977921	−	0.208973i	$-0.932988\pi$
$809$		−	11.8876i		−	0.417946i	0.977921	−	0.208973i	$-0.0670121\pi$
$810$	28.0987	+	39.7309i	0.987289	+	1.39600i
$811$			0.481738i			0.0169161i	0.999964	+	0.00845806i	$0.00269232\pi$
$811$			0.481738i			0.0169161i	−0.999964	+	0.00845806i	$0.997308\pi$
$812$	−13.1714	−	5.76363i	−0.462225	−	0.202264i
$813$	0.839746	+	10.5353i	0.0294512	+	0.369490i
$814$	−41.8736	−	35.1362i	−1.46767	−	1.23152i
$815$	−16.4878	+	12.4425i	−0.577543	+	0.435840i
$816$	10.3724	−	37.5473i	0.363106	−	1.31442i
$817$	7.63752	−	6.40864i	0.267203	−	0.224210i
$818$	21.8162	−	12.5956i	0.762784	−	0.440393i
$819$	−20.3511	−	9.28268i	−0.711123	−	0.324363i
$820$	11.6661	+	38.0634i	0.407399	+	1.32923i
$821$	−23.0072	+	4.05678i	−0.802955	+	0.141583i	−0.560041	−	0.828465i	$-0.689215\pi$
$821$	−23.0072	+	4.05678i	−0.802955	+	0.141583i	−0.242914	+	0.970048i	$0.578103\pi$
$822$	8.57904	+	6.10644i	0.299228	+	0.212987i
$823$	−0.497129	−	1.36585i	−0.0173288	−	0.0476106i	0.930727	−	0.365716i	$-0.119176\pi$
$823$	−0.497129	−	1.36585i	−0.0173288	−	0.0476106i	−0.948055	+	0.318105i	$0.896954\pi$
$824$	0.268974	−	0.0978985i	0.00937015	−	0.00341046i
$825$	0.461592	−	19.4003i	0.0160706	−	0.675433i
$826$	66.1813	−	7.38415i	2.30274	−	0.256928i
$827$	20.9368	−	36.2636i	0.728043	−	1.26101i	−0.229666	−	0.973270i	$-0.573763\pi$
$827$	20.9368	−	36.2636i	0.728043	−	1.26101i	0.957709	−	0.287738i	$-0.0929034\pi$
$828$	7.56255	+	21.8214i	0.262817	+	0.758347i
$829$	−47.0345	+	27.1554i	−1.63358	+	0.943146i	−0.650599	+	0.759421i	$0.725482\pi$
$829$	−47.0345	+	27.1554i	−1.63358	+	0.943146i	−0.982978	+	0.183725i	$0.941184\pi$
$830$	0.202792	+	0.0104864i	0.00703903	+	0.000363988i
$831$	−18.3542	−	18.6401i	−0.636700	−	0.646617i
$832$	4.72290	−	26.7849i	0.163737	−	0.928600i
$833$	37.2287	−	34.3932i	1.28990	−	1.19165i
$834$	−31.0802	+	21.4066i	−1.07622	+	0.741250i
$835$	−18.9493	−	37.1261i	−0.655766	−	1.28480i
$836$	−32.9051			−1.13805
$837$	−16.9130	+	34.1785i	−0.584599	+	1.18138i
$838$	26.7713			0.924799
$839$	−22.9949	−	8.36944i	−0.793871	−	0.288945i	−0.0869266	−	0.996215i	$-0.527705\pi$
$839$	−22.9949	−	8.36944i	−0.793871	−	0.288945i	−0.706944	+	0.707269i	$0.749927\pi$
$840$	43.5368	−	14.1154i	1.50216	−	0.487026i
$841$	20.6869	+	17.3584i	0.713341	+	0.598564i
$842$	−12.5569	+	71.2138i	−0.432740	+	2.45419i
$843$	41.9686	−	10.8986i	1.44548	−	0.375367i
$844$	11.1439	−	9.35084i	0.383589	−	0.321869i
$845$	11.0224	+	2.53663i	0.379181	+	0.0872628i
$846$	−10.0586	−	18.0609i	−0.345821	−	0.620946i
$847$	13.1705	+	8.76157i	0.452542	+	0.301051i
$848$	0.373500	+	2.11822i	0.0128260	+	0.0727401i
$849$	26.6610	−	12.1823i	0.915002	−	0.418095i
$850$	−79.9236	+	35.7176i	−2.74136	+	1.22511i
$851$	−6.90433	−	18.9695i	−0.236677	−	0.650266i
$852$	−33.5337	−	73.3884i	−1.14884	−	2.51425i
$853$	−5.44319	−	30.8698i	−0.186371	−	1.05696i	−0.924181	−	0.381955i	$-0.875251\pi$
$853$	−5.44319	−	30.8698i	−0.186371	−	1.05696i	0.737810	−	0.675009i	$-0.235860\pi$
$854$	−0.346279	+	0.520530i	−0.0118494	+	0.0178122i
$855$	−24.8614	−	6.12754i	−0.850244	−	0.209557i
$856$	27.4077	+	47.4715i	0.936774	+	1.62254i
$857$	3.53365	+	4.21124i	0.120707	+	0.143853i	0.823014	−	0.568021i	$-0.192291\pi$
$857$	3.53365	+	4.21124i	0.120707	+	0.143853i	−0.702307	+	0.711875i	$0.747846\pi$
$858$	25.5989	−	6.64764i	0.873934	−	0.226947i
$859$	10.8622	+	1.91530i	0.370614	+	0.0653492i	0.355853	−	0.934542i	$-0.384190\pi$
$859$	10.8622	+	1.91530i	0.370614	+	0.0653492i	0.0147606	+	0.999891i	$0.495301\pi$
$860$	−2.75386	−	22.3001i	−0.0939060	−	0.760427i
$861$	18.5349	+	10.3064i	0.631669	+	0.351240i
$862$	14.1149	−	38.7804i	0.480756	−	1.32087i
$863$	−30.6107			−1.04200			−0.521001	−	0.853556i	$-0.674441\pi$
$863$	−30.6107			−1.04200			−0.521001	+	0.853556i	$0.674441\pi$
$864$	0.473261	+	7.37476i	0.0161007	+	0.250894i
$865$	−11.3668	−	10.5849i	−0.386482	−	0.359898i
$866$	−66.8062	−	24.3155i	−2.27017	−	0.826274i
$867$	34.8050	+	50.5333i	1.18204	+	1.71620i
$868$	54.0652	+	51.5460i	1.83509	+	1.74959i
$869$	32.9897	+	5.81698i	1.11910	+	0.197328i
$870$	13.2232	−	0.368699i	0.448310	−	0.0125001i
$871$	4.60842	+	5.49210i	0.156150	+	0.186093i
$872$	23.3799	+	40.4952i	0.791744	+	1.37134i
$873$	8.44919	+	24.3798i	0.285962	+	0.825131i
$874$	−15.9950	−	9.23470i	−0.541038	−	0.312368i
$875$	−24.9440	−	15.8996i	−0.843261	−	0.537505i
$876$	0.592846	−	6.22212i	0.0200304	−	0.210226i
$877$	16.7324	+	45.9718i	0.565012	+	1.55236i	0.812194	+	0.583388i	$0.198273\pi$
$877$	16.7324	+	45.9718i	0.565012	+	1.55236i	−0.247182	+	0.968969i	$0.579505\pi$
$878$	−22.3369	−	61.3701i	−0.753834	−	2.07114i
$879$	19.9709	−	28.0575i	0.673602	−	0.946355i
$880$	−8.46728	+	13.0584i	−0.285432	+	0.440197i
$881$	1.20513	−	2.08734i	0.0406018	−	0.0703244i	−0.845010	−	0.534750i	$-0.820406\pi$
$881$	1.20513	−	2.08734i	0.0406018	−	0.0703244i	0.885612	+	0.464425i	$0.153739\pi$
$882$	23.9590	−	44.7722i	0.806741	−	1.50756i
$883$	−9.55430	+	5.51618i	−0.321528	+	0.185634i	−0.652073	−	0.758156i	$-0.726101\pi$
$883$	−9.55430	+	5.51618i	−0.321528	+	0.185634i	0.330546	+	0.943790i	$0.392767\pi$
$884$	−50.4587	−	60.1343i	−1.69711	−	2.02254i
$885$	−34.3369	+	21.1219i	−1.15422	+	0.710003i
$886$	6.83610	−	38.7695i	0.229663	−	1.30249i
$887$	−18.4652	+	22.0060i	−0.620001	+	0.738888i	−0.981071	−	0.193651i	$-0.937967\pi$
$887$	−18.4652	+	22.0060i	−0.620001	+	0.738888i	0.361070	+	0.932539i	$0.382412\pi$
$888$	6.20104	+	77.7975i	0.208093	+	2.61071i
$889$	−4.02538	−	1.76145i	−0.135007	−	0.0590773i
$890$	1.01759	−	1.09275i	0.0341096	−	0.0366291i
$891$	−17.7685	+	9.53902i	−0.595268	+	0.319569i
$892$	44.3579			1.48521
$893$	10.2217	+	3.72038i	0.342055	+	0.124498i
$894$	5.57874	+	69.9901i	0.186581	+	2.34082i
$895$	−3.21616	−	26.0437i	−0.107504	−	0.870544i
$896$	52.6914	+	12.7801i	1.76030	+	0.426953i
$897$	9.41470	+	2.60080i	0.314348	+	0.0868381i
$898$	−16.8594	−	20.0923i	−0.562606	−	0.670487i
$899$	5.18315	+	8.97748i	0.172868	+	0.299416i
$900$	−42.0704	+	39.4988i	−1.40235	+	1.31663i
$901$	−4.34220	−	2.50697i	−0.144660	−	0.0835193i
$902$	−24.6949	+	4.35438i	−0.822251	+	0.144985i
$903$	−9.29214	−	7.54514i	−0.309223	−	0.251087i
$904$	64.3143	−	23.4085i	2.13906	−	0.778554i
$905$	−29.0197	−	12.2943i	−0.964647	−	0.408676i
$906$	−8.92550	+	93.6762i	−0.296530	+	3.11218i
$907$	4.90265	−	0.864469i	0.162790	−	0.0287042i	−0.0916592	−	0.995790i	$-0.529217\pi$
$907$	4.90265	−	0.864469i	0.162790	−	0.0287042i	0.254449	+	0.967086i	$0.418106\pi$
$908$	−87.1825	−	50.3348i	−2.89325	−	1.67042i
$909$	12.7501	−	14.7267i	0.422895	−	0.488454i
$910$	11.5132	−	38.6359i	0.381660	−	1.28077i
$911$	−29.2746	−	34.8881i	−0.969911	−	1.15589i	−0.987749	−	0.156053i	$-0.950123\pi$
$911$	−29.2746	−	34.8881i	−0.969911	−	1.15589i	0.0178381	−	0.999841i	$-0.494322\pi$
$912$	14.4080	+	14.6324i	0.477097	+	0.484527i
$913$	−0.0146133	+	0.0828760i	−0.000483629	+	0.00274280i
$914$	14.8451	−	17.6917i	0.491032	−	0.585190i
$915$	0.0553074	−	0.374412i	0.00182841	−	0.0123777i
$916$	2.42769	−	6.67001i	0.0802130	−	0.220383i
$917$	3.37063	−	53.0783i	0.111308	−	1.75280i
$918$	73.2935	+	53.8950i	2.41905	+	1.77880i
$919$	−44.5852			−1.47073			−0.735366	−	0.677671i	$-0.762990\pi$
$919$	−44.5852			−1.47073			−0.735366	+	0.677671i	$0.762990\pi$
$920$	−17.8006	+	9.08545i	−0.586867	+	0.299538i
$921$	23.0481	−	48.4460i	0.759462	−	1.59635i
$922$	17.3189	+	14.5323i	0.570367	+	0.478595i
$923$	−33.6061	−	5.92565i	−1.10616	−	0.195045i
$924$	7.48617	+	38.7887i	0.246277	+	1.27606i
$925$	36.2354	−	35.0898i	1.19141	−	1.15374i
$926$	−8.00990	+	4.62452i	−0.263222	+	0.151971i
$927$	−0.00297104	+	0.192233i	−9.75818e−5	+	0.00631376i
$928$	1.73972	+	1.00443i	0.0571091	+	0.0329719i
$929$	6.05671	+	34.3493i	0.198714	+	1.12696i	0.907029	+	0.421068i	$0.138345\pi$
$929$	6.05671	+	34.3493i	0.198714	+	1.12696i	−0.708315	+	0.705897i	$0.750544\pi$
$930$	−65.2158	−	21.6980i	−2.13851	−	0.711506i
$931$	5.88906	+	26.0622i	0.193006	+	0.854153i
$932$	14.7135	−	5.35527i	0.481956	−	0.175418i
$933$	35.4019	−	16.1763i	1.15901	−	0.529589i
$934$	23.1396	−	4.08014i	0.757152	−	0.133506i
$935$	−10.6312	−	34.6868i	−0.347678	−	1.13438i
$936$	−32.4066	−	19.3838i	−1.05924	−	0.633578i
$937$	11.1273	+	19.2731i	0.363513	+	0.629623i	0.988536	−	0.150983i	$-0.0482439\pi$
$937$	11.1273	+	19.2731i	0.363513	+	0.629623i	−0.625023	+	0.780606i	$0.714911\pi$
$938$	−13.1060	+	9.65075i	−0.427927	+	0.315108i
$939$	−6.48172	−	24.9600i	−0.211523	−	0.814539i
$940$	19.5682	−	14.7671i	0.638245	−	0.481649i
$941$	3.11118	+	2.61059i	0.101422	+	0.0851028i	0.692088	−	0.721813i	$-0.256691\pi$
$941$	3.11118	+	2.61059i	0.101422	+	0.0851028i	−0.590667	+	0.806915i	$0.701135\pi$
$942$	15.3706	−	32.3082i	0.500801	−	1.05266i
$943$	−8.70212	−	3.16731i	−0.283380	−	0.103142i
$944$	32.3308			1.05228
$945$	−1.56700	+	30.7009i	−0.0509746	+	0.998700i
$946$	14.1529			0.460151
$947$	12.3683	+	4.50169i	0.401915	+	0.146285i	0.535065	−	0.844811i	$-0.320287\pi$
$947$	12.3683	+	4.50169i	0.401915	+	0.146285i	−0.133150	+	0.991096i	$0.542509\pi$
$948$	−56.5042	−	82.0384i	−1.83517	−	2.66448i
$949$	−2.02497	−	1.69915i	−0.0657332	−	0.0551567i
$950$	4.76005	−	45.9033i	0.154436	−	1.48930i
$951$	20.3166	−	20.0050i	0.658810	−	0.648706i
$952$	68.8993	−	50.7346i	2.23304	−	1.64432i
$953$	−23.2846	−	40.3302i	−0.754264	−	1.30642i	−0.945740	−	0.324926i	$-0.894661\pi$
$953$	−23.2846	−	40.3302i	−0.754264	−	1.30642i	0.191476	−	0.981497i	$-0.438673\pi$
$954$	−4.93302	−	0.948652i	−0.159712	−	0.0307137i
$955$	54.9945	−	16.8554i	1.77958	−	0.545427i
$956$	−9.11238	+	1.60676i	−0.294715	+	0.0519663i
$957$	−0.519988	+	5.45746i	−0.0168088	+	0.176414i
$958$	−65.6366	+	23.8898i	−2.12062	+	0.771844i
$959$	1.87443	+	6.38258i	0.0605286	+	0.206104i
$960$	−36.6157	+	7.51422i	−1.18177	+	0.242520i
$961$	−3.96962	−	22.5128i	−0.128052	−	0.726220i
$962$	59.5354	+	34.3728i	1.91950	+	1.10822i
$963$	−36.3529	+	5.83225i	−1.17145	+	0.187942i
$964$	19.7121	−	11.3808i	0.634883	−	0.366550i
$965$	−37.4080	−	1.93437i	−1.20421	−	0.0622694i
$966$	−7.24694	+	20.9559i	−0.233166	+	0.674246i
$967$	−1.86066	−	0.328084i	−0.0598347	−	0.0105505i	0.143651	−	0.989628i	$-0.454116\pi$
$967$	−1.86066	−	0.328084i	−0.0598347	−	0.0105505i	−0.203485	+	0.979078i	$0.565227\pi$
$968$	20.4568	+	17.1653i	0.657506	+	0.551713i
$969$	−47.7183	+	3.80350i	−1.53293	+	0.122186i
$970$	−41.4211	+	21.1414i	−1.32995	+	0.678810i
$971$	−15.4395			−0.495476			−0.247738	−	0.968827i	$-0.579687\pi$
$971$	−15.4395			−0.495476			−0.247738	+	0.968827i	$0.579687\pi$
$972$	57.2844	+	17.7475i	1.83740	+	0.569250i
$973$	−23.7921	−	1.51087i	−0.762739	−	0.0484363i
$974$	−17.0085	+	46.7304i	−0.544987	+	1.49734i
$975$	3.66510	+	24.1289i	0.117377	+	0.772742i
$976$	−0.195107	+	0.232519i	−0.00624522	+	0.00744276i
$977$	−10.5099	+	59.6045i	−0.336241	+	1.90692i	0.0783786	+	0.996924i	$0.475026\pi$
$977$	−10.5099	+	59.6045i	−0.336241	+	1.90692i	−0.414620	+	0.909995i	$0.636085\pi$
$978$	−10.3020	+	37.2924i	−0.329420	+	1.19248i
$979$	0.397764	+	0.474037i	0.0127126	+	0.0151503i
$980$	56.5033	+	20.8197i	1.80493	+	0.665061i
$981$	−31.0106	+	4.97516i	−0.990091	+	0.158845i
$982$	10.9656	+	6.33102i	0.349928	+	0.202031i
$983$	18.7429	−	3.30488i	0.597806	−	0.105409i	0.133446	−	0.991056i	$-0.457396\pi$
$983$	18.7429	−	3.30488i	0.597806	−	0.105409i	0.464360	+	0.885647i	$0.346285\pi$
$984$	29.1679	+	20.7613i	0.929839	+	0.661846i
$985$	−15.3279	+	36.1804i	−0.488389	+	1.15280i
$986$	23.2392	−	8.45836i	0.740085	−	0.269369i
$987$	2.06010	−	12.8958i	0.0655737	−	0.410477i
$988$	40.7542	−	7.18607i	1.29656	−	0.228619i
$989$	4.52647	+	2.61336i	0.143933	+	0.0830999i
$990$	−21.4439	−	29.3484i	−0.681532	−	0.932752i
$991$	0.604174	+	1.04646i	0.0191922	+	0.0332419i	0.875462	−	0.483287i	$-0.160557\pi$
$991$	0.604174	+	1.04646i	0.0191922	+	0.0332419i	−0.856270	+	0.516529i	$0.827224\pi$
$992$	−6.70903	−	7.99551i	−0.213012	−	0.253858i
$993$	3.65874	−	3.60263i	0.116106	−	0.114326i
$994$	18.2603	−	75.2859i	0.579181	−	2.38792i
$995$	7.18011	+	58.1428i	0.227625	+	1.84325i
$996$	0.206095	−	0.141949i	0.00653036	−	0.00449781i
$997$	8.41912	+	3.06431i	0.266636	+	0.0970477i	0.471879	−	0.881664i	$-0.343576\pi$
$997$	8.41912	+	3.06431i	0.266636	+	0.0970477i	−0.205242	+	0.978711i	$0.565798\pi$
$998$	53.8301			1.70396
$999$	−50.3056	−	14.7373i	−1.59160	−	0.466266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.14	yes	816
5.4	even	2	inner	945.2.cs.b.104.123	yes	816
7.6	odd	2	inner	945.2.cs.b.104.13	✓	816
27.20	odd	18	inner	945.2.cs.b.209.124	yes	816
35.34	odd	2	inner	945.2.cs.b.104.124	yes	816
135.74	odd	18	inner	945.2.cs.b.209.13	yes	816
189.20	even	18	inner	945.2.cs.b.209.123	yes	816
945.209	even	18	inner	945.2.cs.b.209.14	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.13	✓	816	7.6	odd	2	inner
945.2.cs.b.104.14	yes	816	1.1	even	1	trivial
945.2.cs.b.104.123	yes	816	5.4	even	2	inner
945.2.cs.b.104.124	yes	816	35.34	odd	2	inner
945.2.cs.b.209.13	yes	816	135.74	odd	18	inner
945.2.cs.b.209.14	yes	816	945.209	even	18	inner
945.2.cs.b.209.123	yes	816	189.20	even	18	inner
945.2.cs.b.209.124	yes	816	27.20	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27225 - 0.827033i) q^{2} +(1.72657 - 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(-1.34694 - 1.78487i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(-1.56879 - 2.13047i) q^{7} +(-2.23324 - 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +O(q^{10})\)	\(q+(-2.27225 - 0.827033i) q^{2} +(1.72657 - 0.137621i) q^{3} +(2.94706 + 2.47288i) q^{4} +(-1.34694 - 1.78487i) q^{5} +(-4.03703 - 1.11522i) q^{6} +(-1.56879 - 2.13047i) q^{7} +(-2.23324 - 3.86809i) q^{8} +(2.96212 - 0.475226i) q^{9} +(1.58445 + 5.16963i) q^{10} +(-2.20675 + 0.389110i) q^{11} +(5.42865 + 3.86404i) q^{12} +(2.64817 - 0.963854i) q^{13} +(1.80272 + 6.13841i) q^{14} +(-2.57123 - 2.89634i) q^{15} +(0.539367 + 3.05890i) q^{16} +(-6.27053 - 3.62029i) q^{17} +(-7.12372 - 1.36994i) q^{18} +(3.30565 - 1.90852i) q^{19} +(0.444237 - 8.59094i) q^{20} +(-3.00183 - 3.46251i) q^{21} +(5.33610 + 0.940899i) q^{22} +(1.53289 + 1.28624i) q^{23} +(-4.38819 - 6.37121i) q^{24} +(-1.37150 + 4.80822i) q^{25} -6.81445 q^{26} +(5.04892 - 1.22816i) q^{27} +(0.645068 - 10.1581i) q^{28} +(0.483105 - 1.32732i) q^{29} +(3.44712 + 8.70771i) q^{30} +(-4.71738 + 5.62196i) q^{31} +(-0.246961 + 1.40059i) q^{32} +(-3.75657 + 0.975522i) q^{33} +(11.2541 + 13.4121i) q^{34} +(-1.68953 + 5.66970i) q^{35} +(9.90474 + 5.92445i) q^{36} +(-8.73664 - 5.04410i) q^{37} +(-9.08968 + 1.60276i) q^{38} +(4.43961 - 2.02861i) q^{39} +(-3.89598 + 9.19613i) q^{40} +(-4.34880 + 1.58283i) q^{41} +(3.95731 + 10.3503i) q^{42} +(2.57232 - 0.453569i) q^{43} +(-7.46566 - 4.31030i) q^{44} +(-4.83802 - 4.64689i) q^{45} +(-2.41934 - 4.19042i) q^{46} +(1.83180 + 2.18305i) q^{47} +(1.35223 + 5.20719i) q^{48} +(-2.07779 + 6.68452i) q^{49} +(7.09294 - 9.79123i) q^{50} +(-11.3248 - 5.38774i) q^{51} +(10.1878 + 3.70806i) q^{52} +0.692478 q^{53} +(-12.4882 - 1.38493i) q^{54} +(3.66687 + 3.41465i) q^{55} +(-4.73736 + 10.8261i) q^{56} +(5.44480 - 3.75012i) q^{57} +(-2.19548 + 2.61647i) q^{58} +(1.80747 - 10.2507i) q^{59} +(-0.415286 - 14.8940i) q^{60} +(0.0628143 + 0.0748592i) q^{61} +(15.3686 - 8.87309i) q^{62} +(-5.65940 - 5.56518i) q^{63} +(4.82558 - 8.35815i) q^{64} +(-5.28728 - 3.42837i) q^{65} +(9.34267 + 0.890173i) q^{66} +(0.870116 + 2.39062i) q^{67} +(-9.52710 - 26.1755i) q^{68} +(2.82366 + 2.00984i) q^{69} +(8.52807 - 11.4857i) q^{70} +(-10.4867 - 6.05448i) q^{71} +(-8.45335 - 10.3965i) q^{72} +(-0.469002 - 0.812335i) q^{73} +(15.6802 + 18.6870i) q^{74} +(-1.70628 + 8.49050i) q^{75} +(14.4615 + 2.54995i) q^{76} +(4.29092 + 4.09098i) q^{77} +(-11.7656 + 0.937811i) q^{78} +(-14.0479 - 5.11302i) q^{79} +(4.73324 - 5.08286i) q^{80} +(8.54832 - 2.81535i) q^{81} +11.1906 q^{82} +(0.0128448 - 0.0352908i) q^{83} +(-0.284204 - 17.6274i) q^{84} +(1.98430 + 16.0684i) q^{85} +(-6.22007 - 1.09677i) q^{86} +(0.651450 - 2.35820i) q^{87} +(6.43332 + 7.66694i) q^{88} +(-0.138079 - 0.239159i) q^{89} +(7.15008 + 14.5601i) q^{90} +(-6.20788 - 4.12975i) q^{91} +(1.33679 + 7.58129i) q^{92} +(-7.37122 + 10.3559i) q^{93} +(-2.35685 - 6.47540i) q^{94} +(-7.85896 - 3.32948i) q^{95} +(-0.233647 + 2.45220i) q^{96} +(1.49351 + 8.47013i) q^{97} +(10.2496 - 13.4705i) q^{98} +(-6.35175 + 2.20129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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