LMFDB - Embedded newform 945.2.cs.b.104.6

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			104.6
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50242 - 0.910806i) q^{2} +(0.792257 - 1.54024i) q^{3} +(3.90044 + 3.27286i) q^{4} +(0.778079 + 2.09633i) q^{5} +(-3.38541 + 3.13272i) q^{6} +(-2.51990 + 0.806302i) q^{7} +(-4.11657 - 7.13012i) q^{8} +(-1.74466 - 2.44053i) q^{9} +O(q^{10})$	\(q+(-2.50242 - 0.910806i) q^{2} +(0.792257 - 1.54024i) q^{3} +(3.90044 + 3.27286i) q^{4} +(0.778079 + 2.09633i) q^{5} +(-3.38541 + 3.13272i) q^{6} +(-2.51990 + 0.806302i) q^{7} +(-4.11657 - 7.13012i) q^{8} +(-1.74466 - 2.44053i) q^{9} +(-0.0377315 - 5.95457i) q^{10} +(-2.09866 + 0.370051i) q^{11} +(8.13113 - 3.41465i) q^{12} +(3.23828 - 1.17864i) q^{13} +(7.04022 + 0.277431i) q^{14} +(3.84528 + 0.462406i) q^{15} +(2.03892 + 11.5633i) q^{16} +(-1.36316 - 0.787020i) q^{17} +(2.14301 + 7.69626i) q^{18} +(3.42380 - 1.97673i) q^{19} +(-3.82613 + 10.7231i) q^{20} +(-0.754510 + 4.52003i) q^{21} +(5.58877 + 0.985451i) q^{22} +(-3.88783 - 3.26228i) q^{23} +(-14.2435 + 0.691612i) q^{24} +(-3.78919 + 3.26222i) q^{25} -9.17704 q^{26} +(-5.14121 + 0.753659i) q^{27} +(-12.4676 - 5.10233i) q^{28} +(1.17858 - 3.23813i) q^{29} +(-9.20134 - 4.65943i) q^{30} +(-0.359345 + 0.428250i) q^{31} +(2.57035 - 14.5772i) q^{32} +(-1.09271 + 3.52561i) q^{33} +(2.69437 + 3.21103i) q^{34} +(-3.65095 - 4.65516i) q^{35} +(1.18257 - 15.2291i) q^{36} +(5.35936 + 3.09423i) q^{37} +(-10.3682 + 1.82819i) q^{38} +(0.750171 - 5.92150i) q^{39} +(11.7440 - 14.1775i) q^{40} +(3.95181 - 1.43834i) q^{41} +(6.00497 - 10.6238i) q^{42} +(8.05221 - 1.41982i) q^{43} +(-9.39683 - 5.42526i) q^{44} +(3.75867 - 5.55630i) q^{45} +(6.75768 + 11.7046i) q^{46} +(-7.04960 - 8.40139i) q^{47} +(19.4256 + 6.02069i) q^{48} +(5.69975 - 4.06360i) q^{49} +(12.4534 - 4.71222i) q^{50} +(-2.29217 + 1.47607i) q^{51} +(16.4882 + 6.00123i) q^{52} -7.12367 q^{53} +(13.5519 + 2.79667i) q^{54} +(-2.40867 - 4.11156i) q^{55} +(16.1224 + 14.6480i) q^{56} +(-0.332104 - 6.83953i) q^{57} +(-5.89862 + 7.02970i) q^{58} +(1.15706 - 6.56201i) q^{59} +(13.4849 + 14.3886i) q^{60} +(-9.01686 - 10.7459i) q^{61} +(1.28928 - 0.744368i) q^{62} +(6.36416 + 4.74315i) q^{63} +(-7.96735 + 13.7999i) q^{64} +(4.99045 + 5.87143i) q^{65} +(5.94557 - 7.82730i) q^{66} +(-3.98422 - 10.9466i) q^{67} +(-2.74111 - 7.53115i) q^{68} +(-8.10484 + 3.40362i) q^{69} +(4.89626 + 14.9745i) q^{70} +(9.77658 + 5.64451i) q^{71} +(-10.2192 + 22.4862i) q^{72} +(-5.07402 - 8.78846i) q^{73} +(-10.5931 - 12.6244i) q^{74} +(2.02258 + 8.42076i) q^{75} +(19.8239 + 3.49548i) q^{76} +(4.99004 - 2.62464i) q^{77} +(-7.27058 + 14.1348i) q^{78} +(-13.9153 - 5.06477i) q^{79} +(-22.6541 + 13.2714i) q^{80} +(-2.91235 + 8.51576i) q^{81} -11.1991 q^{82} +(2.57446 - 7.07327i) q^{83} +(-17.7363 + 15.1607i) q^{84} +(0.589207 - 3.46999i) q^{85} +(-21.4432 - 3.78101i) q^{86} +(-4.05375 - 4.38073i) q^{87} +(11.2778 + 13.4404i) q^{88} +(-2.42818 - 4.20573i) q^{89} +(-14.4665 + 10.4808i) q^{90} +(-7.20980 + 5.58108i) q^{91} +(-4.48728 - 25.4486i) q^{92} +(0.374913 + 0.892760i) q^{93} +(9.98902 + 27.4446i) q^{94} +(6.80786 + 5.63935i) q^{95} +(-20.4159 - 15.5078i) q^{96} +(-0.468170 - 2.65512i) q^{97} +(-17.9643 + 4.97744i) q^{98} +(4.56456 + 4.47623i) 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 $

$2$	−2.50242	−	0.910806i	−1.76948	−	0.644037i	−0.999986	−	0.00537923i	$-0.998288\pi$
$2$	−2.50242	−	0.910806i	−1.76948	−	0.644037i	−0.769491	−	0.638658i	$-0.779490\pi$
$3$	0.792257	−	1.54024i	0.457410	−	0.889256i
$3$	0.792257	−	1.54024i	0.457410	−	0.889256i
$4$	3.90044	+	3.27286i	1.95022	+	1.63643i
$5$	0.778079	+	2.09633i	0.347968	+	0.937507i
$5$	0.778079	+	2.09633i	0.347968	+	0.937507i
$6$	−3.38541	+	3.13272i	−1.38209	+	1.27893i
$7$	−2.51990	+	0.806302i	−0.952431	+	0.304754i
$7$	−2.51990	+	0.806302i	−0.952431	+	0.304754i
$8$	−4.11657	−	7.13012i	−1.45543	−	2.52088i
$9$	−1.74466	−	2.44053i	−0.581552	−	0.813509i
$10$	−0.0377315	−	5.95457i	−0.0119317	−	1.88300i
$11$	−2.09866	+	0.370051i	−0.632770	+	0.111574i	−0.480828	−	0.876815i	$-0.659664\pi$
$11$	−2.09866	+	0.370051i	−0.632770	+	0.111574i	−0.151942	+	0.988389i	$0.548553\pi$
$12$	8.13113	−	3.41465i	2.34725	−	0.985726i
$13$	3.23828	−	1.17864i	0.898138	−	0.326895i	0.148632	−	0.988893i	$-0.452513\pi$
$13$	3.23828	−	1.17864i	0.898138	−	0.326895i	0.749506	+	0.661997i	$0.230291\pi$
$14$	7.04022	+	0.277431i	1.88158	+	0.0741465i
$15$	3.84528	+	0.462406i	0.992847	+	0.119393i
$16$	2.03892	+	11.5633i	0.509731	+	2.89083i
$17$	−1.36316	−	0.787020i	−0.330615	−	0.190881i	0.325499	−	0.945542i	$-0.394468\pi$
$17$	−1.36316	−	0.787020i	−0.330615	−	0.190881i	−0.656114	+	0.754662i	$0.727801\pi$
$18$	2.14301	+	7.69626i	0.505113	+	1.81403i
$19$	3.42380	−	1.97673i	0.785473	−	0.453493i	−0.0528937	−	0.998600i	$-0.516844\pi$
$19$	3.42380	−	1.97673i	0.785473	−	0.453493i	0.838366	+	0.545107i	$0.183511\pi$
$20$	−3.82613	+	10.7231i	−0.855549	+	2.39777i
$21$	−0.754510	+	4.52003i	−0.164648	+	0.986352i
$22$	5.58877	+	0.985451i	1.19153	+	0.210099i
$23$	−3.88783	−	3.26228i	−0.810669	−	0.680232i	0.140098	−	0.990138i	$-0.455258\pi$
$23$	−3.88783	−	3.26228i	−0.810669	−	0.680232i	−0.950767	+	0.309906i	$0.899703\pi$
$24$	−14.2435	+	0.691612i	−2.90743	+	0.141175i
$25$	−3.78919	+	3.26222i	−0.757837	+	0.652444i
$26$	−9.17704			−1.79977
$27$	−5.14121	+	0.753659i	−0.989426	+	0.145042i
$28$	−12.4676	−	5.10233i	−2.35616	−	0.964249i
$29$	1.17858	−	3.23813i	0.218858	−	0.601306i	−0.780869	−	0.624695i	$-0.785223\pi$
$29$	1.17858	−	3.23813i	0.218858	−	0.601306i	0.999726	+	0.0233886i	$0.00744552\pi$
$30$	−9.20134	−	4.65943i	−1.67993	−	0.850692i
$31$	−0.359345	+	0.428250i	−0.0645402	+	0.0769160i	−0.797349	−	0.603519i	$-0.793765\pi$
$31$	−0.359345	+	0.428250i	−0.0645402	+	0.0769160i	0.732808	+	0.680435i	$0.238209\pi$
$32$	2.57035	−	14.5772i	0.454378	−	2.57690i
$33$	−1.09271	+	3.52561i	−0.190217	+	0.613730i
$34$	2.69437	+	3.21103i	0.462081	+	0.550687i
$35$	−3.65095	−	4.65516i	−0.617124	−	0.786866i
$36$	1.18257	−	15.2291i	0.197095	−	2.53819i
$37$	5.35936	+	3.09423i	0.881073	+	0.508688i	0.871012	−	0.491262i	$-0.163464\pi$
$37$	5.35936	+	3.09423i	0.881073	+	0.508688i	0.0100610	+	0.999949i	$0.496797\pi$
$38$	−10.3682	+	1.82819i	−1.68194	+	0.296572i
$39$	0.750171	−	5.92150i	0.120123	−	0.948200i
$40$	11.7440	−	14.1775i	1.85690	−	2.24166i
$41$	3.95181	−	1.43834i	0.617170	−	0.224631i	−0.0144677	−	0.999895i	$-0.504605\pi$
$41$	3.95181	−	1.43834i	0.617170	−	0.224631i	0.631637	+	0.775264i	$0.282383\pi$
$42$	6.00497	−	10.6238i	0.926587	−	1.63929i
$43$	8.05221	−	1.41982i	1.22795	−	0.216521i	0.478205	−	0.878248i	$-0.341287\pi$
$43$	8.05221	−	1.41982i	1.22795	−	0.216521i	0.749745	+	0.661727i	$0.230176\pi$
$44$	−9.39683	−	5.42526i	−1.41662	−	0.817889i
$45$	3.75867	−	5.55630i	0.560309	−	0.828284i
$46$	6.75768	+	11.7046i	0.996365	+	1.72576i
$47$	−7.04960	−	8.40139i	−1.02829	−	1.22547i	−0.973907	−	0.226948i	$-0.927125\pi$
$47$	−7.04960	−	8.40139i	−1.02829	−	1.22547i	−0.0543835	−	0.998520i	$-0.517319\pi$
$48$	19.4256	+	6.02069i	2.80384	+	0.869012i
$49$	5.69975	−	4.06360i	0.814251	−	0.580514i
$50$	12.4534	−	4.71222i	1.76117	−	0.666409i
$51$	−2.29217	+	1.47607i	−0.320968	+	0.206690i
$52$	16.4882	+	6.00123i	2.28651	+	0.832220i
$53$	−7.12367			−0.978511			−0.489255	−	0.872141i	$-0.662731\pi$
$53$	−7.12367			−0.978511			−0.489255	+	0.872141i	$0.662731\pi$
$54$	13.5519	+	2.79667i	1.84418	+	0.380579i
$55$	−2.40867	−	4.11156i	−0.324785	−	0.554402i
$56$	16.1224	+	14.6480i	2.15444	+	1.95741i
$57$	−0.332104	−	6.83953i	−0.0439882	−	0.905918i
$58$	−5.89862	+	7.02970i	−0.774527	+	0.923045i
$59$	1.15706	−	6.56201i	0.150636	−	0.854301i	−0.812031	−	0.583614i	$-0.801638\pi$
$59$	1.15706	−	6.56201i	0.150636	−	0.854301i	0.962667	−	0.270687i	$-0.0872509\pi$
$60$	13.4849	+	14.3886i	1.74089	+	1.85757i
$61$	−9.01686	−	10.7459i	−1.15449	−	1.37587i	−0.914248	−	0.405155i	$-0.867218\pi$
$61$	−9.01686	−	10.7459i	−1.15449	−	1.37587i	−0.240242	−	0.970713i	$-0.577227\pi$
$62$	1.28928	−	0.744368i	0.163739	−	0.0945348i
$63$	6.36416	+	4.74315i	0.801808	+	0.597581i
$64$	−7.96735	+	13.7999i	−0.995919	+	1.72498i
$65$	4.99045	+	5.87143i	0.618989	+	0.728261i
$66$	5.94557	−	7.82730i	0.731850	−	0.963474i
$67$	−3.98422	−	10.9466i	−0.486750	−	1.33733i	−0.903607	−	0.428363i	$-0.859091\pi$
$67$	−3.98422	−	10.9466i	−0.486750	−	1.33733i	0.416857	−	0.908972i	$-0.363132\pi$
$68$	−2.74111	−	7.53115i	−0.332409	−	0.913286i
$69$	−8.10484	+	3.40362i	−0.975708	+	0.409747i
$70$	4.89626	+	14.9745i	0.585215	+	1.78979i
$71$	9.77658	+	5.64451i	1.16027	+	0.669880i	0.951368	−	0.308057i	$-0.0996787\pi$
$71$	9.77658	+	5.64451i	1.16027	+	0.669880i	0.208899	+	0.977937i	$0.433012\pi$
$72$	−10.2192	+	22.4862i	−1.20435	+	2.65003i
$73$	−5.07402	−	8.78846i	−0.593869	−	1.02861i	−0.993705	−	0.112025i	$-0.964266\pi$
$73$	−5.07402	−	8.78846i	−0.593869	−	1.02861i	0.399836	−	0.916587i	$-0.369067\pi$
$74$	−10.5931	−	12.6244i	−1.23142	−	1.46755i
$75$	2.02258	+	8.42076i	0.233547	+	0.972345i
$76$	19.8239	+	3.49548i	2.27395	+	0.400959i
$77$	4.99004	−	2.62464i	0.568667	−	0.299106i
$78$	−7.27058	+	14.1348i	−0.823231	+	1.60045i
$79$	−13.9153	−	5.06477i	−1.56560	−	0.569831i	−0.593587	−	0.804770i	$-0.702289\pi$
$79$	−13.9153	−	5.06477i	−1.56560	−	0.569831i	−0.972010	+	0.234939i	$0.924511\pi$
$80$	−22.6541	+	13.2714i	−2.53280	+	1.48379i
$81$	−2.91235	+	8.51576i	−0.323594	+	0.946196i
$82$	−11.1991			−1.23674
$83$	2.57446	−	7.07327i	0.282584	−	0.776392i	−0.714469	−	0.699667i	$-0.753332\pi$
$83$	2.57446	−	7.07327i	0.282584	−	0.776392i	0.997052	−	0.0767245i	$-0.0244462\pi$
$84$	−17.7363	+	15.1607i	−1.93519	+	1.65417i
$85$	0.589207	−	3.46999i	0.0639085	−	0.376374i
$86$	−21.4432	−	3.78101i	−2.31228	−	0.407717i
$87$	−4.05375	−	4.38073i	−0.434608	−	0.469664i
$88$	11.2778	+	13.4404i	1.20222	+	1.43275i
$89$	−2.42818	−	4.20573i	−0.257386	−	0.445806i	0.708155	−	0.706057i	$-0.249528\pi$
$89$	−2.42818	−	4.20573i	−0.257386	−	0.445806i	−0.965541	+	0.260251i	$0.916195\pi$
$90$	−14.4665	+	10.4808i	−1.52490	+	1.10477i
$91$	−7.20980	+	5.58108i	−0.755792	+	0.585056i
$92$	−4.48728	−	25.4486i	−0.467831	−	2.65320i
$93$	0.374913	+	0.892760i	0.0388767	+	0.0925749i
$94$	9.98902	+	27.4446i	1.03029	+	2.83069i
$95$	6.80786	+	5.63935i	0.698471	+	0.578585i
$96$	−20.4159	−	15.5078i	−2.08369	−	1.58276i
$97$	−0.468170	−	2.65512i	−0.0475354	−	0.269587i	0.951772	−	0.306807i	$-0.0992607\pi$
$97$	−0.468170	−	2.65512i	−0.0475354	−	0.269587i	−0.999307	+	0.0372205i	$0.988150\pi$
$98$	−17.9643	+	4.97744i	−1.81467	+	0.502798i
$99$	4.56456	+	4.47623i	0.458756	+	0.449878i
$100$	−25.4563	+	0.322623i	−2.54563	+	0.0322623i
$101$	2.07897	−	1.74446i	0.206865	−	0.173580i	−0.533469	−	0.845820i	$-0.679112\pi$
$101$	2.07897	−	1.74446i	0.206865	−	0.173580i	0.740334	+	0.672239i	$0.234667\pi$
$102$	7.08038	−	1.60601i	0.701062	−	0.159019i
$103$	−2.13100	+	12.0855i	−0.209973	+	1.19082i	0.679446	+	0.733726i	$0.262220\pi$
$103$	−2.13100	+	12.0855i	−0.209973	+	1.19082i	−0.889419	+	0.457093i	$0.848891\pi$
$104$	−21.7345	−	18.2374i	−2.13124	−	1.78832i
$105$	−10.0625	+	1.93524i	−0.982004	+	0.188860i
$106$	17.8264	+	6.48827i	1.73145	+	0.630197i
$107$	2.19461			0.212161			0.106081	−	0.994358i	$-0.466170\pi$
$107$	2.19461			0.212161			0.106081	+	0.994358i	$0.466170\pi$
$108$	−22.5196	−	13.8868i	−2.16695	−	1.33626i
$109$	16.9721			1.62563			0.812816	−	0.582520i	$-0.197933\pi$
$109$	16.9721			1.62563			0.812816	+	0.582520i	$0.197933\pi$
$110$	2.28268	+	12.4827i	0.217645	+	1.19018i
$111$	9.01183	−	5.80325i	0.855365	−	0.550821i
$112$	−14.4614	−	27.4944i	−1.36647	−	2.59797i
$113$	−0.585245	+	3.31909i	−0.0550552	+	0.312234i	−0.999882	−	0.0153356i	$-0.995118\pi$
$113$	−0.585245	+	3.31909i	−0.0550552	+	0.312234i	0.944827	+	0.327569i	$0.106229\pi$
$114$	−5.39842	+	17.4179i	−0.505609	+	1.63133i
$115$	3.81377	−	10.6885i	0.355635	−	0.996706i
$116$	15.1949	−	8.77281i	1.41082	−	0.814535i
$117$	−8.52619	−	5.84680i	−0.788246	−	0.540536i
$118$	−8.87217	+	15.3670i	−0.816749	+	1.41465i
$119$	4.06960	+	0.884092i	0.373059	+	0.0810445i
$120$	−12.5324	−	29.3208i	−1.14404	−	2.67661i
$121$	−6.06918	+	2.20900i	−0.551743	+	0.200818i
$122$	12.7765	+	35.1033i	1.15673	+	3.17810i
$123$	0.915466	−	7.22627i	0.0825447	−	0.651570i
$124$	−2.80320	+	0.494280i	−0.251735	+	0.0443877i
$125$	−9.78697	−	5.40511i	−0.875373	−	0.483448i
$126$	−11.6057	−	17.6659i	−1.03392	−	1.57380i
$127$	−14.6488	+	8.45747i	−1.29987	+	0.750479i	−0.980381	−	0.197112i	$-0.936844\pi$
$127$	−14.6488	+	8.45747i	−1.29987	+	0.750479i	−0.319487	+	0.947591i	$0.603511\pi$
$128$	9.82859	−	8.24716i	0.868732	−	0.728953i
$129$	4.19256	−	13.5272i	0.369134	−	1.19100i
$130$	−7.14047	−	19.2381i	−0.626260	−	1.68729i
$131$	−6.23370	−	5.23069i	−0.544641	−	0.457008i	0.328481	−	0.944511i	$-0.393463\pi$
$131$	−6.23370	−	5.23069i	−0.544641	−	0.457008i	−0.873121	+	0.487503i	$0.837908\pi$
$132$	−15.8009	+	10.1751i	−1.37529	+	0.885632i
$133$	−7.03377	+	7.74177i	−0.609905	+	0.671296i
$134$			31.0217i			2.67987i
$135$	−5.58018	−	10.1912i	−0.480266	−	0.877123i
$136$			12.9593i			1.11125i
$137$	−0.377243	−	0.137305i	−0.0322300	−	0.0117308i	0.325855	−	0.945420i	$-0.394348\pi$
$137$	−0.377243	−	0.137305i	−0.0322300	−	0.0117308i	−0.358085	+	0.933689i	$0.616570\pi$
$138$	23.3817	−	1.13533i	1.99039	−	0.0966461i
$139$	10.5743	−	12.6019i	0.896899	−	1.06888i	−0.100365	−	0.994951i	$-0.532001\pi$
$139$	10.5743	−	12.6019i	0.896899	−	1.06888i	0.997263	−	0.0739314i	$-0.0235546\pi$
$140$	0.995365	−	30.1062i	0.0841237	−	2.54444i
$141$	−18.5252	+	4.20199i	−1.56011	+	0.353872i
$142$	−19.3240	−	23.0295i	−1.62164	−	1.93259i
$143$	−6.35990	+	3.67189i	−0.531842	+	0.307059i
$144$	24.6634	−	25.1501i	2.05528	−	2.09584i
$145$	7.70522	−	0.0488246i	0.639884	−	0.00405466i
$146$	4.69274	+	26.6138i	0.388374	+	2.20258i
$147$	−1.74323	−	11.9984i	−0.143779	−	0.989610i
$148$	10.7769	+	29.6093i	0.885855	+	2.43387i
$149$	8.00353	+	21.9895i	0.655674	+	1.80145i	0.595636	+	0.803255i	$0.296900\pi$
$149$	8.00353	+	21.9895i	0.655674	+	1.80145i	0.0600388	+	0.998196i	$0.480878\pi$
$150$	2.60834	−	22.9144i	0.212970	−	1.87096i
$151$	−2.69904	−	15.3070i	−0.219645	−	1.24567i	−0.872662	−	0.488325i	$-0.837608\pi$
$151$	−2.69904	−	15.3070i	−0.219645	−	1.24567i	0.653017	−	0.757344i	$-0.273503\pi$
$152$	−28.1886	−	16.2747i	−2.28640	−	1.32005i
$153$	0.457501	+	4.69991i	0.0369867	+	0.379965i
$154$	−14.8777	+	2.02300i	−1.19888	+	0.163018i
$155$	−1.17735	−	0.420092i	−0.0945672	−	0.0337426i
$156$	22.3062	−	20.6413i	1.78593	−	1.65262i
$157$	1.67561	−	9.50284i	0.133728	−	0.758410i	−0.842009	−	0.539464i	$-0.818627\pi$
$157$	1.67561	−	9.50284i	0.133728	−	0.758410i	0.975737	−	0.218946i	$-0.0702618\pi$
$158$	30.2090	+	25.3483i	2.40330	+	2.01660i
$159$	−5.64378	+	10.9721i	−0.447581	+	0.870146i
$160$	32.5585	−	5.95390i	2.57397	−	0.470697i
$161$	12.4273	+	5.08584i	0.979410	+	0.400820i
$162$	15.0441	−	18.6574i	1.18198	−	1.46587i
$163$			8.75844i			0.686014i	0.939333	+	0.343007i	$0.111445\pi$
$163$			8.75844i			0.686014i	−0.939333	+	0.343007i	$0.888555\pi$
$164$	20.1213	+	7.32355i	1.57121	+	0.571874i
$165$	−8.24106	+	0.452516i	−0.641565	+	0.0352283i
$166$	−12.8847	+	15.3554i	−1.00005	+	1.19181i
$167$	3.13632	+	0.553017i	0.242695	+	0.0427937i	0.293673	−	0.955906i	$-0.405122\pi$
$167$	3.13632	+	0.553017i	0.242695	+	0.0427937i	−0.0509772	+	0.998700i	$0.516234\pi$
$168$	35.3344	−	13.2273i	2.72611	−	1.02051i
$169$	−0.861296	+	0.722713i	−0.0662536	+	0.0555933i
$170$	−4.63493	+	8.14672i	−0.355483	+	0.624825i
$171$	−10.7976	−	4.90715i	−0.825714	−	0.375259i
$172$	36.0540	+	20.8158i	2.74909	+	1.58719i
$173$	17.4443	−	3.07590i	1.32626	−	0.233856i	0.534751	−	0.845009i	$-0.320405\pi$
$173$	17.4443	−	3.07590i	1.32626	−	0.233856i	0.791512	+	0.611153i	$0.209294\pi$
$174$	6.15418	+	14.6546i	0.466547	+	1.11096i
$175$	6.91802	−	11.2757i	0.522953	−	0.852361i
$176$	−8.55802	−	23.5130i	−0.645085	−	1.77236i
$177$	−9.19036	−	6.98095i	−0.690790	−	0.524720i
$178$	2.24571	+	12.7361i	0.168323	+	0.954609i
$179$	−11.7326	−	6.77380i	−0.876933	−	0.506298i	−0.00728712	−	0.999973i	$-0.502320\pi$
$179$	−11.7326	−	6.77380i	−0.876933	−	0.506298i	−0.869646	+	0.493676i	$0.835653\pi$
$180$	32.8454	−	9.37042i	2.44815	−	0.698430i
$181$	−4.04019	+	2.33261i	−0.300305	+	0.173381i	−0.642580	−	0.766219i	$-0.722136\pi$
$181$	−4.04019	+	2.33261i	−0.300305	+	0.173381i	0.342275	+	0.939600i	$0.388803\pi$
$182$	23.1252	−	7.39947i	1.71415	−	0.548485i
$183$	−23.6948	+	5.37460i	−1.75157	+	0.397302i
$184$	−7.25587	+	41.1501i	−0.534910	+	3.03363i
$185$	−2.31651	+	13.6425i	−0.170313	+	1.00302i
$186$	−0.125059	−	2.57553i	−0.00916975	−	0.188847i
$187$	3.15205	+	1.14725i	0.230501	+	0.0838953i
$188$		−	55.8415i		−	4.07266i
$189$	12.3476	−	6.04451i	0.898158	−	0.439673i
$190$	−11.8998	−	20.3126i	−0.863299	−	1.47363i
$191$	−0.796321	+	2.18787i	−0.0576198	+	0.158309i	−0.965163	−	0.261650i	$-0.915733\pi$
$191$	−0.796321	+	2.18787i	−0.0576198	+	0.158309i	0.907543	+	0.419959i	$0.137956\pi$
$192$	14.9429	+	23.2046i	1.07841	+	1.67465i
$193$	−6.33207	+	7.54626i	−0.455792	+	0.543192i	−0.944178	−	0.329436i	$-0.893141\pi$
$193$	−6.33207	+	7.54626i	−0.455792	+	0.543192i	0.488386	+	0.872628i	$0.337586\pi$
$194$	−1.24674	+	7.07064i	−0.0895110	+	0.507642i
$195$	12.9971	−	3.03479i	0.930742	−	0.217326i
$196$	35.5311	+	2.80467i	2.53794	+	0.200334i
$197$	11.2327	+	19.4555i	0.800293	+	1.38615i	0.919423	+	0.393270i	$0.128656\pi$
$197$	11.2327	+	19.4555i	0.800293	+	1.38615i	−0.119130	+	0.992879i	$0.538010\pi$
$198$	−7.34547	−	15.3588i	−0.522020	−	1.09150i
$199$	−1.59167	−	0.918954i	−0.112831	−	0.0651429i	0.442523	−	0.896757i	$-0.354084\pi$
$199$	−1.59167	−	0.918954i	−0.112831	−	0.0651429i	−0.555353	+	0.831614i	$0.687417\pi$
$200$	38.8585	+	13.5882i	2.74771	+	0.960828i
$201$	−20.0168	−	2.53585i	−1.41188	−	0.178865i
$202$	−6.79131	+	2.47184i	−0.477835	+	0.173918i
$203$	−0.358996	+	9.11006i	−0.0251966	+	0.639401i
$204$	−13.7714	−	1.74464i	−0.964192	−	0.122150i
$205$	6.09006	+	7.16516i	0.425348	+	0.500436i
$206$	16.3402	−	28.3020i	1.13847	−	1.97189i
$207$	−1.17875	+	15.1799i	−0.0819285	+	1.05508i
$208$	20.2316	+	35.0421i	1.40281	+	2.42973i
$209$	−6.45390	+	5.41546i	−0.446425	+	0.374595i
$210$	26.9433	+	4.32224i	1.85927	+	0.298263i
$211$	3.80013	−	21.5516i	0.261612	−	1.48368i	−0.516900	−	0.856046i	$-0.672914\pi$
$211$	3.80013	−	21.5516i	0.261612	−	1.48368i	0.778512	−	0.627629i	$-0.215975\pi$
$212$	−27.7854	−	23.3147i	−1.90831	−	1.60126i
$213$	16.4395	−	10.5863i	1.12641	−	0.725364i
$214$	−5.49183	−	1.99886i	−0.375414	−	0.136640i
$215$	9.24167	+	15.7753i	0.630276	+	1.07587i
$216$	26.5378	+	33.5549i	1.80567	+	2.28312i
$217$	0.560212	−	1.36889i	0.0380297	−	0.0929261i
$218$	−42.4713	−	15.4583i	−2.87652	−	1.04697i
$219$	−17.5562	+	0.852469i	−1.18634	+	0.0576045i
$220$	4.06165	−	23.9201i	0.273837	−	1.61269i
$221$	−5.34191	−	0.941922i	−0.359336	−	0.0633606i
$222$	−27.8370	+	6.31414i	−1.86830	+	0.423777i
$223$	3.67289	−	3.08192i	0.245955	−	0.206380i	−0.511473	−	0.859299i	$-0.670900\pi$
$223$	3.67289	−	3.08192i	0.245955	−	0.206380i	0.757428	+	0.652919i	$0.226456\pi$
$224$	5.27659	+	38.8054i	0.352557	+	2.59280i
$225$	14.5724	+	3.55616i	0.971491	+	0.237077i
$226$	4.48757	−	7.77270i	0.298509	−	0.517032i
$227$	14.3008	−	2.52161i	0.949175	−	0.167365i	0.322433	−	0.946592i	$-0.395499\pi$
$227$	14.3008	−	2.52161i	0.949175	−	0.167365i	0.626742	+	0.779227i	$0.284388\pi$
$228$	21.0895	−	27.7641i	1.39668	−	1.83872i
$229$	−0.246982	−	0.678577i	−0.0163210	−	0.0448417i	0.931265	−	0.364344i	$-0.118707\pi$
$229$	−0.246982	−	0.678577i	−0.0163210	−	0.0448417i	−0.947586	+	0.319502i	$0.896484\pi$
$230$	−19.2788	+	23.2735i	−1.27120	+	1.53461i
$231$	−0.0891802	−	9.76523i	−0.00586763	−	0.642505i
$232$	−27.9400	+	4.92658i	−1.83435	+	0.323446i
$233$	8.69085	−	15.0530i	0.569357	−	0.986155i	−0.427273	−	0.904123i	$-0.640526\pi$
$233$	8.69085	−	15.0530i	0.569357	−	0.986155i	0.996630	−	0.0820321i	$-0.0261410\pi$
$234$	16.0108	+	22.3968i	1.04666	+	1.46413i
$235$	12.1269	−	21.3152i	0.791073	−	1.39045i
$236$	25.9896	−	21.8078i	1.69178	−	1.41957i
$237$	−18.8255	+	17.4203i	−1.22285	+	1.13157i
$238$	−9.37860	−	5.91898i	−0.607924	−	0.383670i
$239$	−1.63975	+	1.95417i	−0.106066	+	0.126405i	−0.816466	−	0.577394i	$-0.804070\pi$
$239$	−1.63975	+	1.95417i	−0.106066	+	0.126405i	0.710400	+	0.703799i	$0.248514\pi$
$240$	2.49329	+	45.4070i	0.160941	+	2.93101i
$241$	−8.12041	+	22.3106i	−0.523081	+	1.43715i	0.343992	+	0.938973i	$0.388221\pi$
$241$	−8.12041	+	22.3106i	−0.523081	+	1.43715i	−0.867073	+	0.498181i	$0.834001\pi$
$242$	17.1996			1.10563
$243$	10.8090	+	11.2324i	0.693395	+	0.720557i
$244$		−	71.4245i		−	4.57248i
$245$	12.9535	+	8.78676i	0.827568	+	0.561365i
$246$	−8.87260	+	17.2493i	−0.565696	+	1.09978i
$247$	8.75737	−	10.4366i	0.557218	−	0.664066i
$248$	4.53274	+	0.799245i	0.287829	+	0.0507521i
$249$	−8.85487	−	9.56912i	−0.561155	−	0.606418i
$250$	19.5681	+	22.4399i	1.23759	+	1.41922i
$251$	−9.62123	−	16.6645i	−0.607287	−	1.05185i	−0.991686	−	0.128684i	$-0.958925\pi$
$251$	−9.62123	−	16.6645i	−0.607287	−	1.05185i	0.384399	−	0.923167i	$-0.374409\pi$
$252$	9.29934	+	39.3294i	0.585803	+	2.47752i
$253$	9.36645	+	5.40772i	0.588864	+	0.339981i
$254$	44.3604	−	7.82194i	2.78342	−	0.490792i
$255$	−4.87781	−	3.65665i	−0.305460	−	0.228988i
$256$	−2.15935	+	0.785938i	−0.134959	+	0.0491211i
$257$	8.57444	+	23.5581i	0.534859	+	1.46951i	0.853224	+	0.521544i	$0.174644\pi$
$257$	8.57444	+	23.5581i	0.534859	+	1.46951i	−0.318366	+	0.947968i	$0.603134\pi$
$258$	−22.8122	+	30.0320i	−1.42022	+	1.86971i
$259$	−15.9999	−	3.47587i	−0.994186	−	0.215980i
$260$	0.248610	+	39.2342i	0.0154181	+	2.43320i
$261$	−9.95898	+	2.77307i	−0.616445	+	0.171648i
$262$	10.8352	+	18.7671i	0.669399	+	1.15943i
$263$	−19.5520	+	16.4061i	−1.20563	+	1.01164i	−0.206178	+	0.978514i	$0.566103\pi$
$263$	−19.5520	+	16.4061i	−1.20563	+	1.01164i	−0.999451	+	0.0331286i	$0.989453\pi$
$264$	29.6363	−	6.72226i	1.82399	−	0.413726i
$265$	−5.54278	−	14.9335i	−0.340490	−	0.917360i
$266$	24.6527	−	12.9667i	1.51155	−	0.795042i
$267$	−8.40155	+	0.407950i	−0.514167	+	0.0249661i
$268$	20.2863	−	55.7362i	1.23918	−	3.40463i
$269$	−4.36266			−0.265996			−0.132998	−	0.991116i	$-0.542460\pi$
$269$	−4.36266			−0.265996			−0.132998	+	0.991116i	$0.542460\pi$
$270$	4.68170	+	30.5852i	0.284919	+	1.86136i
$271$			3.47386i			0.211022i	0.994418	+	0.105511i	$0.0336478\pi$
$271$			3.47386i			0.211022i	−0.994418	+	0.105511i	$0.966352\pi$
$272$	6.32119	−	17.3673i	0.383278	−	1.05305i
$273$	2.88417	+	15.5264i	0.174558	+	0.939703i
$274$	0.818961	+	0.687190i	0.0494753	+	0.0415147i
$275$	6.74503	−	8.24848i	0.406741	−	0.497402i
$276$	−42.7520	−	13.2504i	−2.57337	−	0.797580i
$277$	15.7325	+	18.7493i	0.945274	+	1.12653i	0.991823	+	0.127618i	$0.0407330\pi$
$277$	15.7325	+	18.7493i	0.945274	+	1.12653i	−0.0465496	+	0.998916i	$0.514823\pi$
$278$	−37.9392	+	21.9042i	−2.27544	+	1.31373i
$279$	1.67209	+	0.129841i	0.100105	+	0.00777335i
$280$	−18.1624	+	45.1950i	−1.08541	+	2.70092i
$281$	16.1218	−	2.84271i	0.961748	−	0.169582i	0.329334	−	0.944213i	$-0.393176\pi$
$281$	16.1218	−	2.84271i	0.961748	−	0.169582i	0.632413	+	0.774631i	$0.282065\pi$
$282$	50.1851	+	6.35774i	2.98848	+	0.378598i
$283$	−5.12427	+	1.86508i	−0.304606	+	0.110868i	−0.489801	−	0.871834i	$-0.662931\pi$
$283$	−5.12427	+	1.86508i	−0.304606	+	0.110868i	0.185195	+	0.982702i	$0.440708\pi$
$284$	19.6593	+	54.0134i	1.16656	+	3.20511i
$285$	14.0795	−	6.01790i	0.833998	−	0.356469i
$286$	19.2595	−	3.39597i	1.13884	−	0.200808i
$287$	−8.79842	+	6.81083i	−0.519354	+	0.402031i
$288$	−40.0603	+	19.1591i	−2.36058	+	1.12896i
$289$	−7.26120	−	12.5768i	−0.427129	−	0.739810i
$290$	−19.3262	−	6.89578i	−1.13487	−	0.404934i
$291$	−4.46043	−	1.38245i	−0.261475	−	0.0810405i
$292$	8.97247	−	50.8854i	0.525074	−	2.97784i
$293$	1.17227	−	1.39706i	0.0684850	−	0.0816172i	−0.730714	−	0.682683i	$-0.760813\pi$
$293$	1.17227	−	1.39706i	0.0684850	−	0.0816172i	0.799199	+	0.601066i	$0.205257\pi$
$294$	−6.56591	+	31.6127i	−0.382932	+	1.84369i
$295$	14.6564	−	2.68019i	0.853330	−	0.156047i
$296$		−	50.9505i		−	2.96144i
$297$	10.5108	−	3.48418i	0.609896	−	0.202173i
$298$		−	62.3166i		−	3.60990i
$299$	−16.4349	−	5.98183i	−0.950457	−	0.345938i
$300$	−19.6710	+	39.4643i	−1.13571	+	2.27847i
$301$	−19.1459	+	10.0703i	−1.10355	+	0.580443i
$302$	−7.18760	+	40.7629i	−0.413600	+	2.34564i
$303$	−1.03981	−	4.58417i	−0.0597353	−	0.263353i
$304$	29.8384	+	35.5600i	1.71135	+	2.03951i
$305$	15.5110	−	27.2634i	0.888160	−	1.56110i
$306$	3.13584	−	12.1778i	0.179264	−	0.696160i
$307$	13.9996	−	24.2480i	0.798997	−	1.38390i	−0.121272	−	0.992619i	$-0.538697\pi$
$307$	13.9996	−	24.2480i	0.798997	−	1.38390i	0.920270	−	0.391285i	$-0.127969\pi$
$308$	28.0534	+	6.09441i	1.59849	+	0.347261i
$309$	16.9262	+	12.8571i	0.962898	+	0.731412i
$310$	2.56360	+	2.12358i	0.145603	+	0.120611i
$311$	−2.41454	+	0.878820i	−0.136916	+	0.0498333i	−0.409569	−	0.912279i	$-0.634321\pi$
$311$	−2.41454	+	0.878820i	−0.136916	+	0.0498333i	0.272653	+	0.962112i	$0.412099\pi$
$312$	−45.3091	+	19.0275i	−2.56513	+	1.07722i
$313$	1.25274	+	7.10464i	0.0708090	+	0.401578i	0.999526	+	0.0307884i	$0.00980179\pi$
$313$	1.25274	+	7.10464i	0.0708090	+	0.401578i	−0.928717	+	0.370790i	$0.879087\pi$
$314$	−12.8483	+	22.2539i	−0.725072	+	1.25586i
$315$	−4.99139	+	17.0319i	−0.281233	+	0.959639i
$316$	−37.6996	−	65.2977i	−2.12077	−	3.67328i
$317$	17.8989	−	15.0190i	1.00531	−	0.843551i	0.0175945	−	0.999845i	$-0.494399\pi$
$317$	17.8989	−	15.0190i	1.00531	−	0.843551i	0.987711	+	0.156294i	$0.0499548\pi$
$318$	24.1166	−	22.3165i	1.35239	−	1.25145i
$319$	−1.27518	+	7.23188i	−0.0713962	+	0.404908i
$320$	−35.1283	−	5.96480i	−1.96373	−	0.333443i
$321$	1.73870	−	3.38022i	0.0970446	−	0.188666i
$322$	−26.4661	−	24.0458i	−1.47490	−	1.34002i
$323$	−6.22291			−0.346252
$324$	−39.2303	+	23.6835i	−2.17946	+	1.31575i
$325$	−8.42548	+	15.0301i	−0.467361	+	0.833718i
$326$	7.97723	−	21.9173i	0.441818	−	1.21389i
$327$	13.4463	−	26.1410i	0.743580	−	1.44560i
$328$	−26.5235	−	22.2558i	−1.46451	−	1.22887i
$329$	24.5383	+	15.4865i	1.35284	+	0.853799i
$330$	21.0347	+	6.37362i	1.15792	+	0.350856i
$331$	−12.7419	+	10.6917i	−0.700357	+	0.587669i	−0.921875	−	0.387487i	$-0.873343\pi$
$331$	−12.7419	+	10.6917i	−0.700357	+	0.587669i	0.221518	+	0.975156i	$0.428899\pi$
$332$	33.1913	−	19.1630i	1.82161	−	1.05171i
$333$	−1.79870	−	18.4780i	−0.0985679	−	1.01259i
$334$	−7.34468	−	4.24045i	−0.401883	−	0.232027i
$335$	19.8475	−	16.8695i	1.08439	−	0.921681i
$336$	−53.8050	+	0.491369i	−2.93530	+	0.0268064i
$337$	−1.80292	−	4.95349i	−0.0982114	−	0.269834i	0.880851	−	0.473393i	$-0.156971\pi$
$337$	−1.80292	−	4.95349i	−0.0982114	−	0.269834i	−0.979063	+	0.203560i	$0.934749\pi$
$338$	2.81357	−	1.02406i	0.153038	−	0.0557014i
$339$	4.64852	+	3.53099i	0.252473	+	0.191777i
$340$	13.6550	−	11.6061i	0.740544	−	0.629430i
$341$	0.595669	−	1.03173i	0.0322573	−	0.0558712i
$342$	22.5507	+	22.1143i	1.21940	+	1.19580i
$343$	−11.0863	+	14.8356i	−0.598604	+	0.801045i
$344$	−43.2710	−	51.5684i	−2.33302	−	2.78038i
$345$	−13.4413	−	14.3421i	−0.723656	−	0.772154i
$346$	−46.4544	−	8.19117i	−2.49740	−	0.440360i
$347$	−3.98716	−	3.34562i	−0.214042	−	0.179602i	0.529463	−	0.848333i	$-0.322393\pi$
$347$	−3.98716	−	3.34562i	−0.214042	−	0.179602i	−0.743505	+	0.668731i	$0.766838\pi$
$348$	−1.47389	−	30.3541i	−0.0790088	−	1.62715i
$349$	6.21325	−	17.0708i	0.332588	−	0.913777i	−0.654849	−	0.755760i	$-0.727268\pi$
$349$	6.21325	−	17.0708i	0.332588	−	0.913777i	0.987436	−	0.158017i	$-0.0505101\pi$
$350$	−27.5817	+	21.9155i	−1.47431	+	1.17143i
$351$	−15.7604	+	8.50018i	−0.841227	+	0.453706i
$352$			31.5437i			1.68128i
$353$	2.38447	−	6.55127i	0.126912	−	0.348689i	−0.859921	−	0.510427i	$-0.829488\pi$
$353$	2.38447	−	6.55127i	0.126912	−	0.348689i	0.986834	+	0.161737i	$0.0517098\pi$
$354$	16.6398	+	25.8399i	0.884398	+	1.37337i
$355$	−4.22580	+	24.8868i	−0.224282	+	1.32085i
$356$	4.29378	−	24.3512i	0.227570	−	1.29061i
$357$	4.58588	−	5.56771i	0.242710	−	0.294675i
$358$	23.1902	+	27.6370i	1.22564	+	1.46066i
$359$	−8.38133	+	4.83896i	−0.442350	+	0.255391i	−0.704594	−	0.709611i	$-0.748871\pi$
$359$	−8.38133	+	4.83896i	−0.442350	+	0.255391i	0.262244	+	0.965002i	$0.415537\pi$
$360$	−55.0899	−	3.92681i	−2.90349	−	0.206961i
$361$	−1.68508	+	2.91865i	−0.0886886	+	0.153613i
$362$	12.2348	−	2.15732i	0.643047	−	0.113386i
$363$	−1.40597	+	11.0981i	−0.0737941	+	0.582497i
$364$	−46.3874	−	1.82797i	−2.43136	−	0.0958117i
$365$	14.4755	−	17.4749i	0.757683	−	0.914680i
$366$	64.1896	+	8.13192i	3.35525	+	0.425062i
$367$	3.44104	+	19.5151i	0.179621	+	1.01868i	0.932674	+	0.360720i	$0.117469\pi$
$367$	3.44104	+	19.5151i	0.179621	+	1.01868i	−0.753053	+	0.657959i	$0.771420\pi$
$368$	29.7957	−	51.6078i	1.55321	−	2.69024i
$369$	−10.4049	−	7.13509i	−0.541656	−	0.371438i
$370$	18.2226	−	32.0294i	0.947346	−	1.66513i
$371$	17.9509	−	5.74383i	0.931964	−	0.298205i
$372$	−1.45955	+	4.70919i	−0.0756741	+	0.244160i
$373$	11.5633	+	2.03891i	0.598722	+	0.105571i	0.464792	−	0.885420i	$-0.346129\pi$
$373$	11.5633	+	2.03891i	0.598722	+	0.105571i	0.133930	+	0.990991i	$0.457240\pi$
$374$	−6.84282	−	5.74181i	−0.353834	−	0.296902i
$375$	−16.0789	+	10.7920i	−0.830313	+	0.557297i
$376$	−30.8827	+	84.8494i	−1.59265	+	4.37578i
$377$		−	11.8751i		−	0.611600i
$378$	−36.4043	+	3.87959i	−1.87243	+	0.199545i
$379$	7.19255			0.369457			0.184728	−	0.982790i	$-0.440859\pi$
$379$	7.19255			0.369457			0.184728	+	0.982790i	$0.440859\pi$
$380$	8.09685	+	44.2771i	0.415360	+	2.27137i
$381$	1.42091	+	29.2631i	0.0727955	+	1.49919i
$382$	3.98546	−	4.74968i	0.203914	−	0.243015i
$383$	2.05962	+	0.363166i	0.105242	+	0.0185569i	0.226021	−	0.974122i	$-0.427428\pi$
$383$	2.05962	+	0.363166i	0.105242	+	0.0185569i	−0.120779	+	0.992679i	$0.538539\pi$
$384$	−4.91581	−	21.6722i	−0.250859	−	1.10596i
$385$	9.38476	+	8.41858i	0.478292	+	0.429050i
$386$	22.7187	−	13.1166i	1.15635	−	0.667619i
$387$	−17.5134	−	17.1745i	−0.890259	−	0.873030i
$388$	6.86377	−	11.8884i	0.348455	−	0.603542i
$389$	10.3400	−	1.82323i	0.524260	−	0.0924412i	0.0947462	−	0.995501i	$-0.469796\pi$
$389$	10.3400	−	1.82323i	0.524260	−	0.0924412i	0.429514	+	0.903060i	$0.358685\pi$
$390$	−35.2883	−	4.24352i	−1.78689	−	0.214879i
$391$	2.73225	+	7.50681i	0.138176	+	0.379636i
$392$	−52.4374	−	23.9118i	−2.64849	−	1.20773i
$393$	−12.9952	+	5.45731i	−0.655521	+	0.275285i
$394$	−10.3886	−	58.9166i	−0.523370	−	2.96818i
$395$	−0.209816	−	33.1119i	−0.0105570	−	1.66604i
$396$	3.15374	+	32.3984i	0.158482	+	1.62808i
$397$	−2.85140	−	4.93877i	−0.143108	−	0.247870i	0.785558	−	0.618788i	$-0.212376\pi$
$397$	−2.85140	−	4.93877i	−0.143108	−	0.247870i	−0.928665	+	0.370919i	$0.879043\pi$
$398$	3.14605	+	3.74931i	0.157697	+	0.187936i
$399$	6.35160	+	16.9671i	0.317978	+	0.849419i
$400$	−45.4479	−	37.1641i	−2.27240	−	1.85821i
$401$	−7.46458	+	8.89594i	−0.372763	+	0.444242i	−0.919516	−	0.393052i	$-0.871419\pi$
$401$	−7.46458	+	8.89594i	−0.372763	+	0.444242i	0.546753	+	0.837294i	$0.315864\pi$
$402$	47.7808	+	24.5772i	2.38309	+	1.22580i
$403$	−0.658907	+	1.81033i	−0.0328225	+	0.0901791i
$404$	13.8183			0.687484
$405$	−20.1179	+	0.520707i	−0.999665	+	0.0258742i
$406$	9.19585	−	22.4702i	0.456382	−	1.11518i
$407$	−12.3925	−	4.51050i	−0.614273	−	0.223577i
$408$	19.9604	+	10.2671i	0.988187	+	0.508298i
$409$	3.30853	−	3.94295i	0.163596	−	0.194966i	−0.678018	−	0.735045i	$-0.737161\pi$
$409$	3.30853	−	3.94295i	0.163596	−	0.194966i	0.841615	+	0.540079i	$0.181606\pi$
$410$	−8.71382	−	23.4771i	−0.430345	−	1.15945i
$411$	−0.510356	+	0.472262i	−0.0251740	+	0.0232950i
$412$	−47.8659	+	40.1643i	−2.35818	+	1.97875i
$413$	2.37529	+	17.4685i	0.116881	+	0.859570i
$414$	16.7757	−	36.9129i	0.824479	−	1.81417i
$415$	16.8310	−	0.106651i	0.826202	−	0.00523528i
$416$	−8.85769	−	50.2345i	−0.434284	−	2.46295i
$417$	−11.0324	−	26.2709i	−0.540259	−	1.28649i
$418$	21.0828	−	7.67351i	1.03119	−	0.375323i
$419$	−13.6129	+	4.95471i	−0.665036	+	0.242053i	−0.652409	−	0.757867i	$-0.726242\pi$
$419$	−13.6129	+	4.95471i	−0.665036	+	0.242053i	−0.0126267	+	0.999920i	$0.504019\pi$
$420$	−45.5821	−	25.3850i	−2.22418	−	1.23866i
$421$	1.45063	+	8.22694i	0.0706994	+	0.400956i	0.999536	+	0.0304662i	$0.00969918\pi$
$421$	1.45063	+	8.22694i	0.0706994	+	0.400956i	−0.928836	+	0.370490i	$0.879190\pi$
$422$	−29.1389	+	50.4700i	−1.41846	+	2.45684i
$423$	−8.20468	+	31.8623i	−0.398925	+	1.54920i
$424$	29.3251	+	50.7926i	1.42415	+	2.46670i
$425$	7.73270	−	1.46476i	0.375091	−	0.0710512i
$426$	−50.7805	+	11.5183i	−2.46032	+	0.558064i
$427$	31.3860	+	19.8082i	1.51887	+	0.958584i
$428$	8.55995	+	7.18265i	0.413761	+	0.347186i
$429$	0.616902	+	12.7048i	0.0297843	+	0.613395i
$430$	−8.75824	−	47.8938i	−0.422360	−	2.30965i
$431$		−	4.63211i		−	0.223121i	−0.993758	−	0.111561i	$-0.964415\pi$
$431$		−	4.63211i		−	0.223121i	0.993758	−	0.111561i	$-0.0355849\pi$
$432$	−19.1973	−	57.9127i	−0.923631	−	2.78633i
$433$	−24.8339			−1.19344			−0.596720	−	0.802449i	$-0.703530\pi$
$433$	−24.8339			−1.19344			−0.596720	+	0.802449i	$0.703530\pi$
$434$	−2.64867	+	2.91528i	−0.127140	+	0.139938i
$435$	6.02932	−	11.9065i	0.289084	−	0.570875i
$436$	66.1986	+	55.5473i	3.17034	+	2.66023i
$437$	−19.7598	−	3.48418i	−0.945239	−	0.166671i
$438$	44.7095	+	13.8571i	2.13630	+	0.662117i
$439$	−18.1683	−	21.6522i	−0.867127	−	1.03340i	−0.999111	−	0.0421501i	$-0.986579\pi$
$439$	−18.1683	−	21.6522i	−0.867127	−	1.03340i	0.131984	−	0.991252i	$-0.457865\pi$
$440$	−19.4004	+	34.0996i	−0.924877	+	1.62564i
$441$	−19.8614	−	6.82083i	−0.945782	−	0.324801i
$442$	12.5098	+	7.22252i	0.595029	+	0.343540i
$443$	−1.74229	−	9.88099i	−0.0827785	−	0.469460i	−0.997814	−	0.0660866i	$-0.978949\pi$
$443$	−1.74229	−	9.88099i	−0.0827785	−	0.469460i	0.915035	−	0.403374i	$-0.132162\pi$
$444$	54.1433	+	6.85919i	2.56953	+	0.325523i
$445$	6.92727	−	8.36264i	0.328384	−	0.396427i
$446$	−11.9981	+	4.36696i	−0.568127	+	0.206781i
$447$	40.2099	+	5.09402i	1.90186	+	0.240939i
$448$	8.95005	−	41.1983i	0.422850	−	1.94644i
$449$	9.10468	+	5.25659i	0.429676	+	0.248074i	0.699209	−	0.714918i	$-0.253536\pi$
$449$	9.10468	+	5.25659i	0.429676	+	0.248074i	−0.269532	+	0.962991i	$0.586869\pi$
$450$	−33.2272	−	22.1716i	−1.56634	−	1.04518i
$451$	−7.76126	+	4.48097i	−0.365464	+	0.211000i
$452$	−13.1456	+	11.0305i	−0.618318	+	0.518830i
$453$	−25.7148	−	7.96994i	−1.20819	−	0.374461i
$454$	−38.0832	−	6.71509i	−1.78733	−	0.315155i
$455$	−17.3096	−	10.7716i	−0.811485	−	0.504979i
$456$	−47.3995	+	30.5234i	−2.21969	+	1.42939i
$457$	0.310143	−	0.852111i	0.0145079	−	0.0398601i	−0.932227	−	0.361873i	$-0.882137\pi$
$457$	0.310143	−	0.852111i	0.0145079	−	0.0398601i	0.946735	+	0.322013i	$0.104360\pi$
$458$			1.92304i			0.0898576i
$459$	7.60143	+	3.01888i	0.354804	+	0.140909i
$460$	49.8572	−	29.2079i	2.32461	−	1.36182i
$461$	33.7101	+	12.2695i	1.57004	+	0.571447i	0.973008	−	0.230773i	$-0.0741255\pi$
$461$	33.7101	+	12.2695i	1.57004	+	0.571447i	0.597029	+	0.802220i	$0.296348\pi$
$462$	−8.67106	+	24.5179i	−0.403414	+	1.14068i
$463$	−0.0443946	+	0.0529075i	−0.00206319	+	0.00245882i	−0.767075	−	0.641557i	$-0.778289\pi$
$463$	−0.0443946	+	0.0529075i	−0.00206319	+	0.00245882i	0.765012	+	0.644016i	$0.222733\pi$
$464$	39.8466	+	7.02603i	1.84983	+	0.326175i
$465$	−1.57981	+	1.48058i	−0.0732618	+	0.0686602i
$466$	−35.4585	+	29.7532i	−1.64258	+	1.37829i
$467$	−27.1219	+	15.6588i	−1.25505	+	0.724603i	−0.972108	−	0.234534i	$-0.924644\pi$
$467$	−27.1219	+	15.6588i	−1.25505	+	0.724603i	−0.282942	+	0.959137i	$0.591310\pi$
$468$	−14.1202	−	50.7101i	−0.652704	−	2.34407i
$469$	18.8661	+	24.3717i	0.871154	+	1.12538i
$470$	−49.7607	+	42.2943i	−2.29529	+	1.95089i
$471$	−13.3091	−	10.1095i	−0.613252	−	0.465823i
$472$	−51.5510	+	18.7630i	−2.37283	+	0.863639i
$473$	−16.3735	+	5.95945i	−0.752852	+	0.274016i
$474$	62.9757	−	26.4465i	2.89257	−	1.21473i
$475$	−6.52487	+	18.6594i	−0.299382	+	0.856150i
$476$	12.9797	+	16.7676i	0.594924	+	0.768540i
$477$	12.4284	+	17.3855i	0.569055	+	0.796027i
$478$	5.88320	−	3.39667i	0.269091	−	0.155360i
$479$	9.74199	−	8.17450i	0.445123	−	0.373502i	−0.392500	−	0.919752i	$-0.628390\pi$
$479$	9.74199	−	8.17450i	0.445123	−	0.373502i	0.837622	+	0.546250i	$0.183945\pi$
$480$	16.6243	−	54.8647i	0.758791	−	2.50422i
$481$	21.0021	+	3.70323i	0.957613	+	0.168853i
$482$	40.6413	−	48.4344i	1.85116	−	2.20613i
$483$	17.6790	−	15.1117i	0.804423	−	0.687607i
$484$	−30.9022	−	11.2475i	−1.40464	−	0.511249i
$485$	5.20173	−	3.04733i	0.236199	−	0.138372i
$486$	−16.8180	−	37.9530i	−0.762882	−	1.72158i
$487$			8.17203i			0.370310i	0.982709	+	0.185155i	$0.0592788\pi$
$487$			8.17203i			0.370310i	−0.982709	+	0.185155i	$0.940721\pi$
$488$	−39.5007	+	108.527i	−1.78811	+	4.91280i
$489$	13.4901	+	6.93893i	0.610042	+	0.313789i
$490$	−24.4120	−	33.7862i	−1.10282	−	1.52631i
$491$	16.5923	+	2.92567i	0.748801	+	0.132034i	0.535010	−	0.844846i	$-0.320308\pi$
$491$	16.5923	+	2.92567i	0.748801	+	0.132034i	0.213791	+	0.976879i	$0.431419\pi$
$492$	27.2213	−	25.1894i	1.22723	−	1.13563i
$493$	−4.15508	+	3.48652i	−0.187135	+	0.157025i
$494$	−31.4203	+	18.1405i	−1.41367	+	0.816181i
$495$	−5.83206	+	13.0517i	−0.262131	+	0.586630i
$496$	−5.68467	−	3.28204i	−0.255249	−	0.147368i
$497$	−29.1872	−	6.34071i	−1.30922	−	0.284420i
$498$	13.4430	+	32.0110i	0.602394	+	1.43445i
$499$	−11.9501	+	4.34950i	−0.534962	+	0.194710i	−0.595353	−	0.803465i	$-0.702988\pi$
$499$	−11.9501	+	4.34950i	−0.534962	+	0.194710i	0.0603906	+	0.998175i	$0.480765\pi$
$500$	−20.4833	−	53.1137i	−0.916042	−	2.37532i
$501$	3.33655	−	4.39254i	0.149066	−	0.196244i
$502$	8.89826	+	50.4645i	0.397149	+	2.25234i
$503$	34.0180	+	19.6403i	1.51679	+	0.875717i	0.999806	+	0.0197191i	$0.00627718\pi$
$503$	34.0180	+	19.6403i	1.51679	+	0.875717i	0.516980	+	0.855997i	$0.327056\pi$
$504$	7.62072	−	64.9027i	0.339454	−	2.89100i
$505$	5.27457	+	3.00087i	0.234715	+	0.133537i
$506$	−18.5134	−	22.0634i	−0.823021	−	0.980838i
$507$	0.430781	+	1.89918i	0.0191317	+	0.0843453i
$508$	−84.8167	−	14.9555i	−3.76313	−	0.663542i
$509$	−13.5579	−	11.3764i	−0.600942	−	0.504250i	0.290806	−	0.956782i	$-0.406077\pi$
$509$	−13.5579	−	11.3764i	−0.600942	−	0.504250i	−0.891748	+	0.452532i	$0.850521\pi$
$510$	8.87582	+	13.5932i	0.393028	+	0.601917i
$511$	19.8722	+	18.0548i	0.879092	+	0.798698i
$512$	−19.5412			−0.863607
$513$	−16.1127	+	12.7431i	−0.711391	+	0.562624i
$514$		−	66.7618i		−	2.94474i
$515$	−26.9932	+	4.93620i	−1.18946	+	0.217515i
$516$	60.6253	−	39.0402i	2.66888	−	1.71865i
$517$	17.9037	+	15.0230i	0.787403	+	0.660709i
$518$	36.8726	+	23.2709i	1.62009	+	1.02246i
$519$	9.08275	−	29.3052i	0.398688	−	1.28636i
$520$	21.3204	−	59.7527i	0.934961	−	2.62033i
$521$	14.8406	+	25.7046i	0.650177	+	1.12614i	0.983080	+	0.183179i	$0.0586388\pi$
$521$	14.8406	+	25.7046i	0.650177	+	1.12614i	−0.332902	+	0.942961i	$0.608028\pi$
$522$	27.4472	+	2.13133i	1.20133	+	0.0932856i
$523$	11.1625	−	19.3340i	0.488101	−	0.845415i	−0.511805	−	0.859101i	$-0.671023\pi$
$523$	11.1625	−	19.3340i	0.488101	−	0.845415i	0.999906	+	0.0136859i	$0.00435648\pi$
$524$	−7.19485	−	40.8040i	−0.314308	−	1.78253i
$525$	−11.8864	−	19.5886i	−0.518763	−	0.854918i
$526$	63.8701	−	23.2468i	2.78487	−	1.01361i
$527$	0.826886	−	0.300962i	0.0360197	−	0.0131101i
$528$	−42.9957	−	5.44695i	−1.87115	−	0.237048i
$529$	0.478869	+	2.71580i	0.0208204	+	0.118078i
$530$	0.268786	+	42.4184i	0.0116753	+	1.84254i
$531$	−18.0334	+	8.62463i	−0.782585	+	0.374277i
$532$	−52.7725	+	7.17577i	−2.28798	+	0.311109i
$533$	11.1018	−	9.31552i	0.480872	−	0.403500i
$534$	21.3958	+	6.63132i	0.925885	+	0.286965i
$535$	1.70758	+	4.60063i	0.0738252	+	0.198902i
$536$	−61.6489	+	73.4703i	−2.66283	+	3.17343i
$537$	−19.7285	+	12.7043i	−0.851346	+	0.548232i
$538$	10.9172	+	3.97353i	0.470674	+	0.171311i
$539$	−10.4581	+	10.6373i	−0.450463	+	0.458181i
$540$	11.5893	−	58.0135i	0.498726	−	2.49650i
$541$	−15.9227			−0.684572			−0.342286	−	0.939596i	$-0.611201\pi$
$541$	−15.9227			−0.684572			−0.342286	+	0.939596i	$0.611201\pi$
$542$	3.16401	−	8.69304i	0.135906	−	0.373398i
$543$	0.391893	+	8.07087i	0.0168177	+	0.346354i
$544$	−14.9763	+	17.8481i	−0.642104	+	0.765230i
$545$	13.2056	+	35.5791i	0.565667	+	1.52404i
$546$	6.92417	−	41.4806i	0.296327	−	1.77520i
$547$	−4.32526	−	5.15464i	−0.184935	−	0.220397i	0.665609	−	0.746300i	$-0.268172\pi$
$547$	−4.32526	−	5.15464i	−0.184935	−	0.220397i	−0.850544	+	0.525904i	$0.823727\pi$
$548$	−1.02203	−	1.77021i	−0.0436591	−	0.0756198i
$549$	−10.4943	+	40.7537i	−0.447884	+	1.73933i
$550$	−24.3917	+	14.4977i	−1.04006	+	0.618186i
$551$	−2.36568	−	13.4165i	−0.100781	−	0.571560i
$552$	57.6324	+	43.7772i	2.45300	+	1.86328i
$553$	39.1489	+	1.54273i	1.66478	+	0.0656034i
$554$	−22.2923	−	61.2477i	−0.947111	−	2.60217i
$555$	19.1774	+	14.3764i	0.814037	+	0.610243i
$556$	82.4887	−	14.5450i	3.49830	−	0.616844i
$557$	19.9442	−	34.5443i	0.845062	−	1.46369i	−0.0405052	−	0.999179i	$-0.512897\pi$
$557$	19.9442	−	34.5443i	0.845062	−	1.46369i	0.885567	−	0.464511i	$-0.153770\pi$
$558$	−4.06601	−	1.84786i	−0.172128	−	0.0782263i
$559$	24.4019	−	14.0884i	1.03209	−	0.595877i
$560$	46.3851	−	51.7086i	1.96013	−	2.18509i
$561$	4.26427	−	3.94598i	0.180038	−	0.166599i
$562$	−42.9327	−	7.57020i	−1.81101	−	0.319329i
$563$	4.62819	−	5.51566i	0.195055	−	0.232457i	−0.659648	−	0.751575i	$-0.729295\pi$
$563$	4.62819	−	5.51566i	0.195055	−	0.232457i	0.854703	+	0.519117i	$0.173739\pi$
$564$	−86.0090	−	44.2408i	−3.62163	−	1.86287i
$565$	−7.41327	+	1.35565i	−0.311878	+	0.0570325i
$566$	14.5218			0.610397
$567$	0.472529	−	23.8071i	0.0198443	−	0.999803i
$568$		−	92.9442i		−	3.89985i
$569$	−1.23699	+	3.39860i	−0.0518573	+	0.142477i	−0.962917	−	0.269797i	$-0.913043\pi$
$569$	−1.23699	+	3.39860i	−0.0518573	+	0.142477i	0.911060	+	0.412274i	$0.135265\pi$
$570$	−40.7139	+	2.23560i	−1.70532	+	0.0936390i
$571$	4.22067	+	3.54156i	0.176629	+	0.148210i	0.726816	−	0.686832i	$-0.240999\pi$
$571$	4.22067	+	3.54156i	0.176629	+	0.148210i	−0.550187	+	0.835041i	$0.685444\pi$
$572$	−36.8240	−	6.49306i	−1.53969	−	0.271489i
$573$	2.73895	+	2.95988i	0.114421	+	0.123651i
$574$	28.2207	−	9.02989i	1.17791	−	0.376900i
$575$	25.3740	−	0.321580i	1.05817	−	0.0134108i
$576$	47.5792	−	4.63148i	1.98247	−	0.192978i
$577$	−9.80690	+	16.9860i	−0.408267	+	0.707138i	−0.994696	−	0.102862i	$-0.967200\pi$
$577$	−9.80690	+	16.9860i	−0.408267	+	0.707138i	0.586429	+	0.810001i	$0.300533\pi$
$578$	6.71556	+	38.0859i	0.279331	+	1.58416i
$579$	6.60641	+	15.7315i	0.274553	+	0.653777i
$580$	30.2136	+	25.0277i	1.25455	+	1.03922i
$581$	−0.784179	+	19.8997i	−0.0325332	+	0.825578i
$582$	9.90271	+	7.52204i	0.410480	+	0.311799i
$583$	14.9502	−	2.63612i	0.619173	−	0.109177i
$584$	−41.7752	+	72.3567i	−1.72867	+	2.99414i
$585$	5.62275	−	22.4230i	0.232472	−	0.927075i
$586$	−4.20597	+	2.42832i	−0.173747	+	0.100313i
$587$	−4.04599	−	4.82182i	−0.166996	−	0.199018i	0.676056	−	0.736850i	$-0.263688\pi$
$587$	−4.04599	−	4.82182i	−0.166996	−	0.199018i	−0.843052	+	0.537832i	$0.819243\pi$
$588$	32.4696	−	52.5043i	1.33903	−	2.16524i
$589$	−0.383788	+	2.17657i	−0.0158137	+	0.0896839i
$590$	−39.1176	−	6.64220i	−1.61045	−	0.273455i
$591$	38.8653	−	1.88716i	1.59870	−	0.0776274i
$592$	−24.8522	+	68.2808i	−1.02142	+	2.80632i
$593$			6.01601i			0.247048i	0.992342	+	0.123524i	$0.0394196\pi$
$593$			6.01601i			0.247048i	−0.992342	+	0.123524i	$0.960580\pi$
$594$	−29.4757	−	0.854381i	−1.20940	−	0.0350557i
$595$	1.31312	+	9.21910i	0.0538327	+	0.377946i
$596$	−40.7513	+	111.963i	−1.66924	+	4.58619i
$597$	−2.67642	+	1.72351i	−0.109539	+	0.0705384i
$598$	35.6788	+	29.9381i	1.45901	+	1.22426i
$599$	−6.99679	−	1.23372i	−0.285881	−	0.0504085i	0.0288688	−	0.999583i	$-0.490810\pi$
$599$	−6.99679	−	1.23372i	−0.285881	−	0.0504085i	−0.314750	+	0.949175i	$0.601921\pi$
$600$	51.7149	−	49.0859i	2.11125	−	2.00392i
$601$	−9.80767	−	11.6883i	−0.400063	−	0.476777i	0.527976	−	0.849259i	$-0.322951\pi$
$601$	−9.80767	−	11.6883i	−0.400063	−	0.476777i	−0.928039	+	0.372482i	$0.878507\pi$
$602$	57.0832	−	7.76192i	2.32654	−	0.316352i
$603$	−19.7643	+	28.8216i	−0.804863	+	1.17371i
$604$	39.5703	−	68.5377i	1.61009	−	2.78876i
$605$	−9.35309	−	11.0042i	−0.380257	−	0.447385i
$606$	−1.57326	+	12.4186i	−0.0639092	+	0.504470i
$607$	31.4475	−	11.4460i	1.27642	−	0.464577i	0.387171	−	0.922008i	$-0.373452\pi$
$607$	31.4475	−	11.4460i	1.27642	−	0.464577i	0.889245	+	0.457431i	$0.151230\pi$
$608$	−20.0148	−	54.9901i	−0.811706	−	2.23014i
$609$	13.7472	+	7.77045i	0.557066	+	0.314874i
$610$	−63.6468	+	54.0969i	−2.57698	+	2.19032i
$611$	−32.7308	−	18.8971i	−1.32415	−	0.764496i
$612$	−13.5977	+	19.8290i	−0.549653	+	0.801541i
$613$	−27.5033	+	15.8790i	−1.11085	+	0.641348i	−0.939049	−	0.343784i	$-0.888291\pi$
$613$	−27.5033	+	15.8790i	−1.11085	+	0.641348i	−0.171799	+	0.985132i	$0.554958\pi$
$614$	−57.1179	+	47.9276i	−2.30509	+	1.93420i
$615$	15.8609	−	3.70349i	0.639574	−	0.149339i
$616$	−39.2559	−	24.7750i	−1.58166	−	0.998213i
$617$	−18.8843	−	15.8458i	−0.760255	−	0.637929i	0.177938	−	0.984042i	$-0.443057\pi$
$617$	−18.8843	−	15.8458i	−0.760255	−	0.637929i	−0.938193	+	0.346112i	$0.887502\pi$
$618$	−30.6462	−	47.5902i	−1.23277	−	1.91436i
$619$	−2.29170	+	6.29640i	−0.0921112	+	0.253074i	−0.977190	−	0.212368i	$-0.931882\pi$
$619$	−2.29170	+	6.29640i	−0.0921112	+	0.253074i	0.885078	+	0.465442i	$0.154105\pi$
$620$	−3.21729	−	5.49185i	−0.129209	−	0.220558i
$621$	22.4468	+	13.8419i	0.900759	+	0.555458i
$622$	6.84262			0.274364
$623$	9.50984	+	8.64015i	0.381004	+	0.346160i
$624$	70.0017	−	3.39904i	2.80231	−	0.136070i
$625$	3.71586	−	24.7223i	0.148634	−	0.988892i
$626$	3.33607	−	18.9198i	0.133336	−	0.756186i
$627$	3.22795	+	14.2310i	0.128912	+	0.568330i
$628$	37.6371	−	31.5812i	1.50188	−	1.26023i
$629$	−4.87044	−	8.43585i	−0.194197	−	0.336359i
$630$	28.0033	−	38.0748i	1.11568	−	1.51694i
$631$	−2.10229	+	3.64127i	−0.0836908	+	0.144957i	−0.904833	−	0.425768i	$-0.860004\pi$
$631$	−2.10229	+	3.64127i	−0.0836908	+	0.144957i	0.821142	+	0.570724i	$0.193337\pi$
$632$	21.1711	+	120.067i	0.842142	+	4.77603i
$633$	−30.1839	−	22.9275i	−1.19970	−	0.911288i
$634$	−58.4700	+	21.2814i	−2.32214	+	0.845190i
$635$	−29.1275	−	24.1280i	−1.15589	−	0.957492i
$636$	−57.9234	+	24.3249i	−2.29681	+	0.964543i
$637$	13.6679	−	19.8770i	0.541542	−	0.787556i
$638$	9.77786	−	16.9358i	0.387109	−	0.670493i
$639$	−3.28120	−	33.7078i	−0.129802	−	1.33346i
$640$	24.9362	+	14.1870i	0.985689	+	0.560790i
$641$	−4.49471	−	5.35658i	−0.177530	−	0.211572i	0.669940	−	0.742415i	$-0.266320\pi$
$641$	−4.49471	−	5.35658i	−0.177530	−	0.211572i	−0.847470	+	0.530843i	$0.821875\pi$
$642$	−7.42967	+	6.87511i	−0.293226	+	0.271339i
$643$	2.63072	−	14.9196i	0.103745	−	0.588370i	−0.887969	−	0.459904i	$-0.847884\pi$
$643$	2.63072	−	14.9196i	0.103745	−	0.588370i	0.991714	−	0.128465i	$-0.0410052\pi$
$644$	31.8268	+	60.5098i	1.25415	+	2.38442i
$645$	31.6195	−	1.73623i	1.24502	−	0.0683638i
$646$	15.5723	+	5.66786i	0.612684	+	0.222999i
$647$			23.4607i			0.922336i	0.887313	+	0.461168i	$0.152569\pi$
$647$			23.4607i			0.922336i	−0.887313	+	0.461168i	$0.847431\pi$
$648$	72.7073	−	14.2904i	2.85621	−	0.561381i
$649$			14.1996i			0.557384i
$650$	34.7735	−	29.9375i	1.36393	−	1.17425i
$651$	−1.66458	−	1.94737i	−0.0652399	−	0.0763234i
$652$	−28.6651	+	34.1617i	−1.12261	+	1.33788i
$653$	1.17289	−	6.65179i	0.0458987	−	0.260305i	−0.953220	−	0.302277i	$-0.902253\pi$
$653$	1.17289	−	6.65179i	0.0458987	−	0.260305i	0.999119	+	0.0419727i	$0.0133642\pi$
$654$	−57.4576	+	53.1689i	−2.24677	+	2.07907i
$655$	6.11494	−	17.1378i	0.238931	−	0.669628i
$656$	24.6895	+	42.7634i	0.963961	+	1.66963i
$657$	−12.5961	+	27.7161i	−0.491419	+	1.08131i
$658$	−47.2999	−	61.1034i	−1.84394	−	2.38206i
$659$	−28.0506	+	4.94607i	−1.09270	+	0.192672i	−0.690823	−	0.723024i	$-0.742752\pi$
$659$	−28.0506	+	4.94607i	−1.09270	+	0.192672i	−0.401872	+	0.915696i	$0.631640\pi$
$660$	−33.6248	−	25.2068i	−1.30884	−	0.981173i
$661$	9.43179	+	25.9136i	0.366854	+	1.00792i	0.976551	+	0.215288i	$0.0690691\pi$
$661$	9.43179	+	25.9136i	0.366854	+	1.00792i	−0.609697	+	0.792635i	$0.708709\pi$
$662$	41.6236	−	15.1497i	1.61775	−	0.588811i
$663$	−5.68295	+	7.48156i	−0.220707	+	0.290560i
$664$	−61.0312	+	10.7614i	−2.36847	+	0.417625i
$665$	−21.7021	−	8.72138i	−0.841572	−	0.338201i
$666$	−12.3288	+	47.8780i	−0.477731	+	1.85523i
$667$	−15.1458	+	8.74445i	−0.586449	+	0.338586i
$668$	10.4231	+	12.4217i	0.403280	+	0.480611i
$669$	−1.83701	−	8.09878i	−0.0710229	−	0.313117i
$670$	−65.0317	+	24.1373i	−2.51239	+	0.932507i
$671$	22.8998	+	19.2153i	0.884039	+	0.741797i
$672$	63.9499	+	22.6167i	2.46692	+	0.872457i
$673$	−16.4514	+	45.1998i	−0.634154	+	1.74232i	0.0352018	+	0.999380i	$0.488793\pi$
$673$	−16.4514	+	45.1998i	−0.634154	+	1.74232i	−0.669355	+	0.742942i	$0.733430\pi$
$674$			14.0378i			0.540716i
$675$	17.0224	−	19.6275i	0.655192	−	0.755463i
$676$	−5.72477			−0.220184
$677$	16.4729	−	45.2590i	0.633106	−	1.73944i	−0.0392638	−	0.999229i	$-0.512501\pi$
$677$	16.4729	−	45.2590i	0.633106	−	1.73944i	0.672370	−	0.740215i	$-0.265277\pi$
$678$	−8.41649	−	13.0699i	−0.323233	−	0.501946i
$679$	3.32057	+	6.31315i	0.127432	+	0.242276i
$680$	−27.1670	+	10.0834i	−1.04181	+	0.386680i
$681$	7.44600	−	24.0243i	0.285332	−	0.920614i
$682$	−2.43032	+	2.03928i	−0.0930616	+	0.0780879i
$683$	10.5572	+	18.2856i	0.403961	+	0.699680i	0.994200	−	0.107548i	$-0.0343000\pi$
$683$	10.5572	+	18.2856i	0.403961	+	0.699680i	−0.590239	+	0.807228i	$0.700967\pi$
$684$	−26.0550	−	54.4791i	−0.996238	−	2.08306i
$685$	−0.00568807	−	0.897660i	−0.000217330	−	0.0342978i
$686$	41.2549	−	27.0273i	1.57512	−	1.03191i
$687$	−1.24084	−	0.157197i	−0.0473411	−	0.00599745i
$688$	32.8357	+	90.2153i	1.25185	+	3.43942i
$689$	−23.0684	+	8.39622i	−0.878837	+	0.319871i
$690$	20.5729	+	48.1324i	0.783196	+	1.83237i
$691$	44.6281	−	7.86914i	1.69773	−	0.299356i	0.760832	−	0.648949i	$-0.224791\pi$
$691$	44.6281	−	7.86914i	1.69773	−	0.299356i	0.936902	+	0.349593i	$0.113680\pi$
$692$	78.1073	+	45.0953i	2.96919	+	1.71427i
$693$	−15.1114	−	7.59922i	−0.574035	−	0.288670i
$694$	6.93032	+	12.0037i	0.263071	+	0.455653i
$695$	34.6454	+	12.3619i	1.31418	+	0.468912i
$696$	−14.5476	+	46.9373i	−0.551424	+	1.77915i
$697$	−6.51896	−	1.14947i	−0.246923	−	0.0435392i
$698$	−31.0963	+	37.0591i	−1.17701	+	1.40271i
$699$	−16.2998	−	25.3118i	−0.616515	−	0.957381i
$700$	63.8870	−	21.3384i	2.41470	−	0.806516i
$701$			33.6369i			1.27045i	0.772327	+	0.635225i	$0.219092\pi$
$701$			33.6369i			1.27045i	−0.772327	+	0.635225i	$0.780908\pi$
$702$	47.1811	−	6.91636i	1.78073	−	0.261041i
$703$	24.4658			0.922745
$704$	11.6141	−	31.9096i	0.437724	−	1.20264i
$705$	−23.2229	−	35.5655i	−0.874623	−	1.33947i
$706$	−11.9339	+	14.2222i	−0.449137	+	0.535261i
$707$	−3.83222	+	6.07214i	−0.144126	+	0.228366i
$708$	−12.9988	−	57.3075i	−0.488525	−	2.15375i
$709$	−7.57960	+	6.36004i	−0.284658	+	0.238856i	−0.773924	−	0.633278i	$-0.781709\pi$
$709$	−7.57960	+	6.36004i	−0.284658	+	0.238856i	0.489267	+	0.872134i	$0.337265\pi$
$710$	33.2418	−	58.4283i	1.24754	−	2.19278i
$711$	11.9168	+	42.7970i	0.446914	+	1.60501i
$712$	−19.9915	+	34.6264i	−0.749215	+	1.29768i
$713$	2.79414	−	0.492683i	0.104641	−	0.0184511i
$714$	−16.5469	+	9.75590i	−0.619252	+	0.365105i
$715$	−12.6460	−	10.4754i	−0.472933	−	0.391759i
$716$	−23.5925	−	64.8198i	−0.881692	−	2.42243i
$717$	1.71079	+	4.07380i	0.0638905	+	0.152139i
$718$	25.3809	−	4.47534i	0.947208	−	0.167018i
$719$	13.0163	−	22.5448i	0.485425	−	0.840780i	−0.514435	−	0.857529i	$-0.671998\pi$
$719$	13.0163	−	22.5448i	0.485425	−	0.840780i	0.999860	+	0.0167491i	$0.00533167\pi$
$720$	71.9128	+	32.1338i	2.68003	+	1.19755i
$721$	−4.37466	−	32.1724i	−0.162921	−	1.19816i
$722$	6.87510	−	5.76890i	0.255865	−	0.214696i
$723$	27.9302	+	30.1831i	1.03874	+	1.12252i
$724$	−23.3928	−	4.12478i	−0.869387	−	0.153296i
$725$	6.09763	+	16.1147i	0.226460	+	0.598485i
$726$	13.6265	−	26.4914i	0.505727	−	0.983189i
$727$	−47.9478	−	17.4516i	−1.77829	−	0.647243i	−0.999808	−	0.0195708i	$-0.993770\pi$
$727$	−47.9478	−	17.4516i	−1.77829	−	0.647243i	−0.778478	−	0.627672i	$-0.784008\pi$
$728$	69.4734	+	28.4318i	2.57486	+	1.05375i
$729$	25.8640	−	7.74943i	0.957926	−	0.287016i
$730$	−52.1400	+	30.5452i	−1.92979	+	1.13053i
$731$	−12.0939	−	4.40181i	−0.447308	−	0.162807i
$732$	−110.011	−	56.5866i	−4.06611	−	2.09150i
$733$	24.0020	+	20.1401i	0.886533	+	0.743890i	0.967512	−	0.252826i	$-0.0813600\pi$
$733$	24.0020	+	20.1401i	0.886533	+	0.743890i	−0.0809784	+	0.996716i	$0.525804\pi$
$734$	9.16354	−	51.9690i	0.338232	−	1.91821i
$735$	23.7962	−	12.9901i	0.877735	−	0.479146i
$736$	−57.5478	+	48.2884i	−2.12124	+	1.77993i
$737$	12.4123	+	21.4988i	0.457213	+	0.791917i
$738$	19.5387	+	27.3318i	0.719228	+	1.00610i
$739$	11.7766	−	20.3977i	0.433209	−	0.750340i	−0.563939	−	0.825817i	$-0.690715\pi$
$739$	11.7766	−	20.3977i	0.433209	−	0.750340i	0.997148	+	0.0754769i	$0.0240479\pi$
$740$	−53.6855	+	45.6302i	−1.97352	+	1.67740i
$741$	−9.13678	−	21.7569i	−0.335648	−	0.799260i
$742$	−50.1522	−	1.97633i	−1.84114	−	0.0725532i
$743$	37.8049	−	13.7599i	1.38693	−	0.504800i	0.462657	−	0.886537i	$-0.346896\pi$
$743$	37.8049	−	13.7599i	1.38693	−	0.504800i	0.924271	+	0.381737i	$0.124674\pi$
$744$	4.82212	−	6.34829i	0.176788	−	0.232740i
$745$	−39.8699	+	33.8876i	−1.46072	+	1.24155i
$746$	−27.0790	−	15.6341i	−0.991434	−	0.572405i
$747$	−21.7540	+	6.05739i	−0.795939	+	0.221628i
$748$	8.53958	+	14.7910i	0.312238	+	0.540812i
$749$	−5.53019	+	1.76952i	−0.202069	+	0.0646568i
$750$	50.0657	−	12.3613i	1.82814	−	0.451371i
$751$	−5.75712	+	32.6502i	−0.210080	+	1.19142i	0.679163	+	0.733988i	$0.262343\pi$
$751$	−5.75712	+	32.6502i	−0.210080	+	1.19142i	−0.889243	+	0.457436i	$0.848768\pi$
$752$	82.7743	−	98.6466i	3.01847	−	3.59727i
$753$	−33.2897	+	1.61643i	−1.21314	+	0.0589060i
$754$	−10.8159	+	29.7165i	−0.393893	+	1.08221i
$755$	29.9885	−	17.5682i	1.09139	−	0.639371i
$756$	67.9440	+	16.8358i	2.47110	+	0.612312i
$757$		−	18.1046i		−	0.658022i	−0.944326	−	0.329011i	$-0.893285\pi$
$757$		−	18.1046i		−	0.658022i	0.944326	−	0.329011i	$-0.106715\pi$
$758$	−17.9988	−	6.55102i	−0.653745	−	0.237944i
$759$	15.7498	−	10.1422i	0.571682	−	0.368140i
$760$	12.1842	−	71.7556i	0.441966	−	2.60285i
$761$	−3.10822	+	17.6276i	−0.112673	+	0.638999i	0.875203	+	0.483755i	$0.160727\pi$
$761$	−3.10822	+	17.6276i	−0.112673	+	0.638999i	−0.987876	+	0.155244i	$0.950384\pi$
$762$	23.0972	−	74.5226i	0.836725	−	2.69967i
$763$	−42.7679	+	13.6846i	−1.54830	+	0.495417i
$764$	−10.2666	+	5.92742i	−0.371433	+	0.214447i
$765$	−9.49658	+	4.61597i	−0.343350	+	0.166891i
$766$	−4.82325	−	2.78471i	−0.174271	−	0.100616i
$767$	−3.98735	−	22.6134i	−0.143975	−	0.816523i
$768$	−0.500228	+	3.94857i	−0.0180504	+	0.142482i
$769$	−0.828479	−	2.27623i	−0.0298757	−	0.0820828i	0.923858	−	0.382735i	$-0.125018\pi$
$769$	−0.828479	−	2.27623i	−0.0298757	−	0.0820828i	−0.953734	+	0.300652i	$0.902796\pi$
$770$	−15.8169	−	29.6145i	−0.570002	−	1.06723i
$771$	43.0782	+	5.45739i	1.55142	+	0.196543i
$772$	−49.3957	+	8.70979i	−1.77779	+	0.313472i
$773$	−41.4365	−	23.9234i	−1.49037	−	0.860464i	−0.490428	−	0.871482i	$-0.663159\pi$
$773$	−41.4365	−	23.9234i	−1.49037	−	0.860464i	−0.999939	+	0.0110180i	$0.996493\pi$
$774$	28.1833	+	58.9292i	1.01303	+	2.11817i
$775$	−0.0354225	−	2.79498i	−0.00127242	−	0.100399i
$776$	−17.0041	+	14.2681i	−0.610411	+	0.512195i
$777$	−18.0297	+	21.8899i	−0.646812	+	0.785294i
$778$	−27.5357	−	4.85528i	−0.987201	−	0.174070i
$779$	10.6870	−	12.7363i	0.382901	−	0.456324i
$780$	60.6269	+	30.7007i	2.17079	+	1.09926i
$781$	−22.6065	−	8.22809i	−0.808924	−	0.294424i
$782$		−	21.2737i		−	0.760747i
$783$	−3.61890	+	17.5362i	−0.129329	+	0.626691i
$784$	58.6100	+	57.6227i	2.09321	+	2.05795i
$785$	21.2248	−	3.88134i	0.757547	−	0.138531i
$786$	37.4900	−	1.82038i	1.33722	−	0.0649308i
$787$	16.0590	+	13.4751i	0.572440	+	0.480334i	0.882455	−	0.470398i	$-0.155890\pi$
$787$	16.0590	+	13.4751i	0.572440	+	0.480334i	−0.310015	+	0.950732i	$0.600334\pi$
$788$	−19.8629	+	112.648i	−0.707586	+	4.01292i
$789$	9.77903	+	43.1126i	0.348143	+	1.53485i
$790$	−29.6335	+	83.0509i	−1.05431	+	2.95482i
$791$	−1.20143	−	8.83564i	−0.0427180	−	0.314159i
$792$	13.1257	−	50.9726i	0.466400	−	1.81123i
$793$	−41.8646	−	24.1705i	−1.48666	−	0.858321i
$794$	2.63713	+	14.9559i	0.0935884	+	0.530766i
$795$	−27.3925	−	3.29402i	−0.971512	−	0.116827i
$796$	−3.20062	−	8.79364i	−0.113443	−	0.311682i
$797$	8.04285	+	22.0976i	0.284893	+	0.782736i	0.996761	+	0.0804228i	$0.0256270\pi$
$797$	8.04285	+	22.0976i	0.284893	+	0.782736i	−0.711868	+	0.702313i	$0.752151\pi$
$798$	−0.440584	−	48.2439i	−0.0155965	−	1.70782i
$799$	2.99767	+	17.0006i	0.106050	+	0.601439i
$800$	37.8144	+	63.6206i	1.33694	+	2.24933i
$801$	−6.02785	+	13.2636i	−0.212984	+	0.468645i
$802$	26.7820	−	15.4626i	0.945704	−	0.546002i
$803$	13.9008	+	16.5664i	0.490550	+	0.584614i
$804$	−69.7749	−	75.4031i	−2.46077	−	2.65926i
$805$	−0.992148	+	30.0089i	−0.0349686	+	1.05768i
$806$	3.29772	−	3.93007i	0.116157	−	0.138431i
$807$	−3.45635	+	6.71953i	−0.121669	+	0.236539i
$808$	−20.9964	−	7.64208i	−0.738652	−	0.268848i
$809$			29.5467i			1.03881i	0.854529	+	0.519403i	$0.173846\pi$
$809$			29.5467i			1.03881i	−0.854529	+	0.519403i	$0.826154\pi$
$810$	50.8176	+	17.0204i	1.78555	+	0.598037i
$811$			23.8049i			0.835905i	0.908469	+	0.417952i	$0.137252\pi$
$811$			23.8049i			0.835905i	−0.908469	+	0.417952i	$0.862748\pi$
$812$	−31.2162	+	34.3583i	−1.09547	+	1.20574i
$813$	5.35056	+	2.75219i	0.187652	+	0.0965235i
$814$	26.9030	+	22.5743i	0.942950	+	0.791229i
$815$	−18.3606	+	6.81476i	−0.643142	+	0.238710i
$816$	−21.7418	−	23.4955i	−0.761114	−	0.822507i
$817$	24.7625	−	20.7782i	0.866330	−	0.726938i
$818$	−11.8706	+	6.85348i	−0.415045	+	0.239626i
$819$	26.1994	+	7.85863i	0.915481	+	0.274603i
$820$	0.303389	+	47.8792i	0.0105948	+	1.67201i
$821$	4.63838	−	0.817872i	0.161881	−	0.0285439i	−0.0921204	−	0.995748i	$-0.529364\pi$
$821$	4.63838	−	0.817872i	0.161881	−	0.0285439i	0.254001	+	0.967204i	$0.418253\pi$
$822$	1.70726	−	0.716963i	0.0595477	−	0.0250069i
$823$	−11.5893	−	31.8413i	−0.403978	−	1.10992i	−0.960304	−	0.278955i	$-0.910012\pi$
$823$	−11.5893	−	31.8413i	−0.403978	−	1.10992i	0.556326	−	0.830964i	$-0.312210\pi$
$824$	94.9433	−	34.5565i	3.30751	−	1.20383i
$825$	−7.36082	−	16.9239i	−0.256271	−	0.589213i
$826$	9.96646	−	45.8770i	0.346778	−	1.59627i
$827$	−9.36177	+	16.2151i	−0.325541	+	0.563853i	−0.981622	−	0.190838i	$-0.938880\pi$
$827$	−9.36177	+	16.2151i	−0.325541	+	0.563853i	0.656081	+	0.754690i	$0.272213\pi$
$828$	−54.2793	+	55.3505i	−1.88634	+	1.92356i
$829$	18.8369	−	10.8755i	0.654232	−	0.377721i	−0.135843	−	0.990730i	$-0.543374\pi$
$829$	18.8369	−	10.8755i	0.654232	−	0.377721i	0.790076	+	0.613009i	$0.210041\pi$
$830$	−42.2154	−	15.0629i	−1.46532	−	0.522841i
$831$	41.3425	−	9.37753i	1.43415	−	0.325303i
$832$	−9.53549	+	54.0785i	−0.330584	+	1.87483i
$833$	−10.9678	+	1.05350i	−0.380012	+	0.0365018i
$834$	3.68005	+	75.7891i	0.127430	+	2.62436i
$835$	1.28100	+	7.00504i	0.0443307	+	0.242419i
$836$	−42.8971			−1.48363
$837$	1.52471	−	2.47255i	0.0527017	−	0.0854637i
$838$	38.5780			1.33266
$839$	−1.56022	−	0.567872i	−0.0538646	−	0.0196051i	0.314947	−	0.949109i	$-0.398013\pi$
$839$	−1.56022	−	0.567872i	−0.0538646	−	0.0196051i	−0.368812	+	0.929504i	$0.620235\pi$
$840$	55.2217	+	63.7805i	1.90533	+	2.20064i
$841$	13.1188	+	11.0080i	0.452374	+	0.379587i
$842$	3.86306	−	21.9085i	0.133130	−	0.755016i
$843$	8.39418	−	27.0836i	0.289111	−	0.932808i
$844$	85.3576	−	71.6235i	2.93813	−	2.46538i
$845$	−2.18520	−	1.24323i	−0.0751732	−	0.0427685i
$846$	49.5519	−	72.2599i	1.70363	−	2.48435i
$847$	13.5126	−	10.4600i	0.464297	−	0.359411i
$848$	−14.5246	−	82.3732i	−0.498777	−	2.82871i
$849$	−1.18707	+	9.37022i	−0.0407403	+	0.321585i
$850$	−20.6845	−	3.37755i	−0.709474	−	0.115849i
$851$	−10.7421	−	29.5135i	−0.368233	−	1.01171i
$852$	98.7687	+	12.5126i	3.38376	+	0.428674i
$853$	−9.43834	−	53.5275i	−0.323163	−	1.83275i	−0.522285	−	0.852771i	$-0.674920\pi$
$853$	−9.43834	−	53.5275i	−0.323163	−	1.83275i	0.199122	−	0.979975i	$-0.436191\pi$
$854$	−60.4994	−	78.1548i	−2.07025	−	2.67440i
$855$	1.88561	−	26.4535i	0.0644864	−	0.904690i
$856$	−9.03428	−	15.6478i	−0.308785	−	0.534832i
$857$	−6.22697	−	7.42102i	−0.212709	−	0.253497i	0.649131	−	0.760677i	$-0.275133\pi$
$857$	−6.22697	−	7.42102i	−0.212709	−	0.253497i	−0.861841	+	0.507179i	$0.830688\pi$
$858$	10.0279	−	32.3547i	0.342346	−	1.10457i
$859$	43.3863	+	7.65018i	1.48032	+	0.261021i	0.854707	−	0.519111i	$-0.173737\pi$
$859$	43.3863	+	7.65018i	1.48032	+	0.261021i	0.625616	+	0.780131i	$0.284848\pi$
$860$	−15.5839	+	91.7774i	−0.531405	+	3.12958i
$861$	3.51967	+	18.9476i	0.119950	+	0.645732i
$862$	−4.21895	+	11.5915i	−0.143698	+	0.394807i
$863$	−15.9614			−0.543331			−0.271665	−	0.962392i	$-0.587574\pi$
$863$	−15.9614			−0.543331			−0.271665	+	0.962392i	$0.587574\pi$
$864$	−2.22848	+	76.8814i	−0.0758143	+	2.61556i
$865$	20.0211	+	34.1756i	0.680738	+	1.16201i
$866$	62.1448	+	22.6188i	2.11177	+	0.768620i
$867$	−25.1239	+	1.21993i	−0.853253	+	0.0414310i
$868$	6.66524	−	3.50576i	0.226233	−	0.118993i
$869$	31.0778	+	5.47985i	1.05424	+	0.185891i
$870$	−25.9324	+	24.3036i	−0.879192	+	0.823970i
$871$	−25.8041	−	30.7521i	−0.874337	−	1.04199i
$872$	−69.8669	−	121.013i	−2.36599	−	4.09802i
$873$	−5.66310	+	5.77486i	−0.191667	+	0.195449i
$874$	46.2738	+	26.7162i	1.56524	+	0.903689i
$875$	29.0203	+	5.72907i	0.981065	+	0.193678i
$876$	−71.2670	−	54.1340i	−2.40789	−	1.82902i
$877$	16.0054	+	43.9746i	0.540465	+	1.48492i	0.846235	+	0.532810i	$0.178864\pi$
$877$	16.0054	+	43.9746i	0.540465	+	1.48492i	−0.305770	+	0.952105i	$0.598914\pi$
$878$	25.7438	+	70.7306i	0.868812	+	2.38704i
$879$	−1.22306	−	2.91241i	−0.0412529	−	0.0982332i
$880$	42.6321	−	36.2354i	1.43713	−	1.22149i
$881$	−21.1616	+	36.6530i	−0.712953	+	1.23487i	0.250791	+	0.968041i	$0.419309\pi$
$881$	−21.1616	+	36.6530i	−0.712953	+	1.23487i	−0.963744	+	0.266829i	$0.914024\pi$
$882$	43.4891	+	35.1585i	1.46436	+	1.18385i
$883$	38.8368	−	22.4224i	1.30696	−	0.754575i	0.325374	−	0.945586i	$-0.394510\pi$
$883$	38.8368	−	22.4224i	1.30696	−	0.754575i	0.981588	+	0.191011i	$0.0611766\pi$
$884$	−17.7530	−	21.1572i	−0.597098	−	0.711594i
$885$	7.48353	−	24.6978i	0.251556	−	0.830206i
$886$	−4.63974	+	26.3133i	−0.155875	+	0.884011i
$887$	−9.32337	+	11.1112i	−0.313048	+	0.373076i	−0.899510	−	0.436901i	$-0.856076\pi$
$887$	−9.32337	+	11.1112i	−0.313048	+	0.373076i	0.586462	+	0.809977i	$0.300520\pi$
$888$	−78.4758	−	40.3659i	−2.63347	−	1.35459i
$889$	30.0941	−	33.1233i	1.00932	−	1.11092i
$890$	−24.9517	+	14.6174i	−0.836382	+	0.489977i
$891$	2.96076	−	18.9494i	0.0991893	−	0.634830i
$892$	24.4125			0.817392
$893$	−40.7437	−	14.8295i	−1.36343	−	0.496250i
$894$	−95.9823	−	49.3708i	−3.21013	−	1.65121i
$895$	5.07124	−	29.8659i	0.169513	−	0.998306i
$896$	−18.1173	+	28.7068i	−0.605257	+	0.959027i
$897$	−22.2341	+	20.5745i	−0.742376	+	0.686964i
$898$	−17.9960	−	21.4468i	−0.600534	−	0.715688i
$899$	0.963214	+	1.66834i	0.0321250	+	0.0556421i
$900$	45.1998	+	61.5638i	1.50666	+	2.05213i
$901$	9.71069	+	5.60647i	0.323510	+	0.186779i
$902$	23.5032	−	4.14425i	0.782571	−	0.137988i
$903$	0.342169	+	37.4675i	0.0113867	+	1.24684i
$904$	26.0747	−	9.49041i	0.867231	−	0.315646i
$905$	−8.03350	−	6.65462i	−0.267042	−	0.221207i
$906$	57.0901	+	43.3653i	1.89669	+	1.44072i
$907$	48.9204	−	8.62599i	1.62437	−	0.286421i	0.713981	−	0.700165i	$-0.246890\pi$
$907$	48.9204	−	8.62599i	1.62437	−	0.286421i	0.910394	+	0.413743i	$0.135779\pi$
$908$	64.0321	+	36.9690i	2.12498	+	1.22686i
$909$	−7.88449	−	2.03029i	−0.261512	−	0.0673405i
$910$	33.5050	+	42.7206i	1.11068	+	1.41618i
$911$	−22.4560	−	26.7620i	−0.743999	−	0.886664i	0.252725	−	0.967538i	$-0.418673\pi$
$911$	−22.4560	−	26.7620i	−0.743999	−	0.886664i	−0.996724	+	0.0808743i	$0.974229\pi$
$912$	78.4105	−	17.7855i	2.59643	−	0.588937i
$913$	−2.78545	+	15.7971i	−0.0921849	+	0.522807i
$914$	−1.55221	+	1.84986i	−0.0513427	+	0.0611878i
$915$	−29.7034	−	45.4903i	−0.981964	−	1.50386i
$916$	1.25755	−	3.45509i	0.0415506	−	0.114159i
$917$	19.9258	+	8.15456i	0.658008	+	0.269287i
$918$	−16.2723	−	14.4779i	−0.537067	−	0.477842i
$919$	−33.7123			−1.11207			−0.556033	−	0.831160i	$-0.687677\pi$
$919$	−33.7123			−1.11207			−0.556033	+	0.831160i	$0.687677\pi$
$920$	−91.9098	+	16.8073i	−3.03018	+	0.554122i
$921$	−26.2563	−	40.7733i	−0.865176	−	1.34352i
$922$	−73.1817	−	61.4067i	−2.41011	−	2.02232i
$923$	38.3122	+	6.75547i	1.26106	+	0.222359i
$924$	31.6124	−	38.3806i	1.03997	−	1.26263i
$925$	−30.4016	+	5.75880i	−0.999600	+	0.189348i
$926$	0.159282	−	0.0919617i	0.00523434	−	0.00302205i
$927$	33.2128	−	15.8843i	1.09085	−	0.521708i
$928$	−44.1734	−	25.5035i	−1.45006	−	0.837195i
$929$	−4.85160	−	27.5148i	−0.159176	−	0.902732i	−0.954868	−	0.297030i	$-0.904004\pi$
$929$	−4.85160	−	27.5148i	−0.159176	−	0.902732i	0.795692	−	0.605701i	$-0.207107\pi$
$930$	5.30185	−	2.26613i	0.173855	−	0.0743094i
$931$	11.4822	−	25.1798i	0.376313	−	0.825234i
$932$	83.1645	−	30.2694i	2.72414	−	0.991507i
$933$	−0.559345	+	4.41521i	−0.0183121	+	0.144548i
$934$	82.1323	−	14.4821i	2.68745	−	0.473870i
$935$	0.0475266	+	7.50038i	0.00155429	+	0.245289i
$936$	−6.58964	+	84.8615i	−0.215389	+	2.77378i
$937$	−11.0010	−	19.0543i	−0.359387	−	0.622476i	0.628472	−	0.777832i	$-0.283681\pi$
$937$	−11.0010	−	19.0543i	−0.359387	−	0.622476i	−0.987858	+	0.155356i	$0.950347\pi$
$938$	−25.0129	−	78.1715i	−0.816699	−	2.55239i
$939$	11.9353	+	3.69919i	0.389494	+	0.120718i
$940$	117.062	−	43.4491i	3.81814	−	1.41715i
$941$	−1.43771	−	1.20638i	−0.0468679	−	0.0393268i	0.619053	−	0.785349i	$-0.287517\pi$
$941$	−1.43771	−	1.20638i	−0.0468679	−	0.0393268i	−0.665921	+	0.746023i	$0.731961\pi$
$942$	24.0972	+	37.4203i	0.785128	+	1.21922i
$943$	−20.0563	−	7.29988i	−0.653122	−	0.237717i
$944$	78.2378			2.54642
$945$	22.2787	+	21.1816i	0.724726	+	0.689037i
$946$	46.4011			1.50863
$947$	12.2708	+	4.46620i	0.398747	+	0.145132i	0.533607	−	0.845733i	$-0.320836\pi$
$947$	12.2708	+	4.46620i	0.398747	+	0.145132i	−0.134860	+	0.990865i	$0.543059\pi$
$948$	−130.442	+	6.33379i	−4.23655	+	0.205712i
$949$	−26.7895	−	22.4791i	−0.869625	−	0.729702i
$950$	33.3230	−	40.7506i	1.08114	−	1.32213i
$951$	−8.95224	−	39.4675i	−0.290296	−	1.27982i
$952$	−10.4491	−	32.6561i	−0.338658	−	1.05839i
$953$	−19.7462	−	34.2014i	−0.639642	−	1.10789i	−0.985511	−	0.169609i	$-0.945749\pi$
$953$	−19.7462	−	34.2014i	−0.639642	−	1.10789i	0.345870	−	0.938283i	$-0.387584\pi$
$954$	−15.2661	−	54.8256i	−0.494259	−	1.77504i
$955$	−5.20610	+	0.0329888i	−0.168466	+	0.00106749i
$956$	−12.7915	+	2.25548i	−0.413705	+	0.0729474i
$957$	10.1285	+	7.69359i	0.327409	+	0.248698i
$958$	−31.8239	+	11.5830i	−1.02818	+	0.374228i
$959$	1.06132	+	0.0418231i	0.0342719	+	0.00135054i
$960$	−37.0178	+	49.3802i	−1.19475	+	1.59374i
$961$	5.32882	+	30.2213i	0.171898	+	0.974879i
$962$	−49.1831	−	28.3959i	−1.58573	−	0.915519i
$963$	−3.82884	−	5.35601i	−0.123383	−	0.172595i
$964$	−104.693	+	60.4443i	−3.37192	+	1.94678i
$965$	−20.7463	−	7.40250i	−0.667847	−	0.238295i
$966$	−58.0041	+	21.7137i	−1.86625	+	0.698626i
$967$	−3.75528	−	0.662158i	−0.120762	−	0.0212936i	0.112941	−	0.993602i	$-0.463973\pi$
$967$	−3.75528	−	0.662158i	−0.120762	−	0.0212936i	−0.233702	+	0.972308i	$0.575084\pi$
$968$	40.7346	+	34.1804i	1.30926	+	1.09860i
$969$	−4.93014	+	9.58475i	−0.158379	+	0.307906i
$970$	−15.7924	+	2.88793i	−0.507065	+	0.0927258i
$971$	16.5157			0.530015			0.265008	−	0.964246i	$-0.414625\pi$
$971$	16.5157			0.530015			0.265008	+	0.964246i	$0.414625\pi$
$972$	5.39775	+	79.1874i	0.173133	+	2.53994i
$973$	−16.4851	+	40.2816i	−0.528489	+	1.29137i
$974$	7.44313	−	20.4498i	0.238493	−	0.655255i
$975$	16.4747	+	24.8849i	0.527613	+	0.796955i
$976$	105.873	−	126.175i	3.38892	−	4.03875i
$977$	2.70094	−	15.3178i	0.0864106	−	0.490059i	−0.910633	−	0.413217i	$-0.864405\pi$
$977$	2.70094	−	15.3178i	0.0864106	−	0.490059i	0.997043	−	0.0768420i	$-0.0244837\pi$
$978$	−27.4378	−	29.6509i	−0.877363	−	0.948132i
$979$	6.65225	+	7.92785i	0.212607	+	0.253375i
$980$	21.7665	+	76.6671i	0.695305	+	2.44904i
$981$	−29.6105	−	41.4209i	−0.945390	−	1.32247i
$982$	−38.8562	−	22.4336i	−1.23995	−	0.715886i
$983$	−16.5849	+	2.92436i	−0.528975	+	0.0932726i	−0.431756	−	0.901990i	$-0.642106\pi$
$983$	−16.5849	+	2.92436i	−0.528975	+	0.0932726i	−0.0972192	+	0.995263i	$0.530995\pi$
$984$	−55.2927	+	23.2201i	−1.76267	+	0.740229i
$985$	−32.0453	+	38.6853i	−1.02105	+	1.23262i
$986$	13.5733	−	4.94027i	0.432261	−	0.157330i
$987$	43.2936	−	25.5255i	1.37805	−	0.812486i
$988$	68.3151	−	12.0458i	2.17339	−	0.383228i
$989$	−35.9375	−	20.7485i	−1.14275	−	0.659764i
$990$	26.4818	−	27.3489i	0.841646	−	0.869205i
$991$	27.1514	+	47.0275i	0.862492	+	1.49388i	0.869517	+	0.493904i	$0.164431\pi$
$991$	27.1514	+	47.0275i	0.862492	+	1.49388i	−0.00702502	+	0.999975i	$0.502236\pi$
$992$	5.31903	+	6.33898i	0.168879	+	0.201263i
$993$	6.37291	+	28.0961i	0.202238	+	0.891602i
$994$	67.2633	+	42.4509i	2.13346	+	1.34646i
$995$	0.687980	−	4.05169i	0.0218104	−	0.128447i
$996$	−3.21951	−	66.3045i	−0.102014	−	2.10094i
$997$	6.55947	+	2.38745i	0.207740	+	0.0756113i	0.443795	−	0.896129i	$-0.353632\pi$
$997$	6.55947	+	2.38745i	0.207740	+	0.0756113i	−0.236054	+	0.971740i	$0.575854\pi$
$998$	33.8658			1.07200
$999$	−29.8856	−	11.8689i	−0.945537	−	0.375516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.6	yes	816
5.4	even	2	inner	945.2.cs.b.104.131	yes	816
7.6	odd	2	inner	945.2.cs.b.104.5	✓	816
27.20	odd	18	inner	945.2.cs.b.209.132	yes	816
35.34	odd	2	inner	945.2.cs.b.104.132	yes	816
135.74	odd	18	inner	945.2.cs.b.209.5	yes	816
189.20	even	18	inner	945.2.cs.b.209.131	yes	816
945.209	even	18	inner	945.2.cs.b.209.6	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.5	✓	816	7.6	odd	2	inner
945.2.cs.b.104.6	yes	816	1.1	even	1	trivial
945.2.cs.b.104.131	yes	816	5.4	even	2	inner
945.2.cs.b.104.132	yes	816	35.34	odd	2	inner
945.2.cs.b.209.5	yes	816	135.74	odd	18	inner
945.2.cs.b.209.6	yes	816	945.209	even	18	inner
945.2.cs.b.209.131	yes	816	189.20	even	18	inner
945.2.cs.b.209.132	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)

\(f(q)\)	\(=\)	\(q+(-2.50242 - 0.910806i) q^{2} +(0.792257 - 1.54024i) q^{3} +(3.90044 + 3.27286i) q^{4} +(0.778079 + 2.09633i) q^{5} +(-3.38541 + 3.13272i) q^{6} +(-2.51990 + 0.806302i) q^{7} +(-4.11657 - 7.13012i) q^{8} +(-1.74466 - 2.44053i) q^{9} +O(q^{10})\)	\(q+(-2.50242 - 0.910806i) q^{2} +(0.792257 - 1.54024i) q^{3} +(3.90044 + 3.27286i) q^{4} +(0.778079 + 2.09633i) q^{5} +(-3.38541 + 3.13272i) q^{6} +(-2.51990 + 0.806302i) q^{7} +(-4.11657 - 7.13012i) q^{8} +(-1.74466 - 2.44053i) q^{9} +(-0.0377315 - 5.95457i) q^{10} +(-2.09866 + 0.370051i) q^{11} +(8.13113 - 3.41465i) q^{12} +(3.23828 - 1.17864i) q^{13} +(7.04022 + 0.277431i) q^{14} +(3.84528 + 0.462406i) q^{15} +(2.03892 + 11.5633i) q^{16} +(-1.36316 - 0.787020i) q^{17} +(2.14301 + 7.69626i) q^{18} +(3.42380 - 1.97673i) q^{19} +(-3.82613 + 10.7231i) q^{20} +(-0.754510 + 4.52003i) q^{21} +(5.58877 + 0.985451i) q^{22} +(-3.88783 - 3.26228i) q^{23} +(-14.2435 + 0.691612i) q^{24} +(-3.78919 + 3.26222i) q^{25} -9.17704 q^{26} +(-5.14121 + 0.753659i) q^{27} +(-12.4676 - 5.10233i) q^{28} +(1.17858 - 3.23813i) q^{29} +(-9.20134 - 4.65943i) q^{30} +(-0.359345 + 0.428250i) q^{31} +(2.57035 - 14.5772i) q^{32} +(-1.09271 + 3.52561i) q^{33} +(2.69437 + 3.21103i) q^{34} +(-3.65095 - 4.65516i) q^{35} +(1.18257 - 15.2291i) q^{36} +(5.35936 + 3.09423i) q^{37} +(-10.3682 + 1.82819i) q^{38} +(0.750171 - 5.92150i) q^{39} +(11.7440 - 14.1775i) q^{40} +(3.95181 - 1.43834i) q^{41} +(6.00497 - 10.6238i) q^{42} +(8.05221 - 1.41982i) q^{43} +(-9.39683 - 5.42526i) q^{44} +(3.75867 - 5.55630i) q^{45} +(6.75768 + 11.7046i) q^{46} +(-7.04960 - 8.40139i) q^{47} +(19.4256 + 6.02069i) q^{48} +(5.69975 - 4.06360i) q^{49} +(12.4534 - 4.71222i) q^{50} +(-2.29217 + 1.47607i) q^{51} +(16.4882 + 6.00123i) q^{52} -7.12367 q^{53} +(13.5519 + 2.79667i) q^{54} +(-2.40867 - 4.11156i) q^{55} +(16.1224 + 14.6480i) q^{56} +(-0.332104 - 6.83953i) q^{57} +(-5.89862 + 7.02970i) q^{58} +(1.15706 - 6.56201i) q^{59} +(13.4849 + 14.3886i) q^{60} +(-9.01686 - 10.7459i) q^{61} +(1.28928 - 0.744368i) q^{62} +(6.36416 + 4.74315i) q^{63} +(-7.96735 + 13.7999i) q^{64} +(4.99045 + 5.87143i) q^{65} +(5.94557 - 7.82730i) q^{66} +(-3.98422 - 10.9466i) q^{67} +(-2.74111 - 7.53115i) q^{68} +(-8.10484 + 3.40362i) q^{69} +(4.89626 + 14.9745i) q^{70} +(9.77658 + 5.64451i) q^{71} +(-10.2192 + 22.4862i) q^{72} +(-5.07402 - 8.78846i) q^{73} +(-10.5931 - 12.6244i) q^{74} +(2.02258 + 8.42076i) q^{75} +(19.8239 + 3.49548i) q^{76} +(4.99004 - 2.62464i) q^{77} +(-7.27058 + 14.1348i) q^{78} +(-13.9153 - 5.06477i) q^{79} +(-22.6541 + 13.2714i) q^{80} +(-2.91235 + 8.51576i) q^{81} -11.1991 q^{82} +(2.57446 - 7.07327i) q^{83} +(-17.7363 + 15.1607i) q^{84} +(0.589207 - 3.46999i) q^{85} +(-21.4432 - 3.78101i) q^{86} +(-4.05375 - 4.38073i) q^{87} +(11.2778 + 13.4404i) q^{88} +(-2.42818 - 4.20573i) q^{89} +(-14.4665 + 10.4808i) q^{90} +(-7.20980 + 5.58108i) q^{91} +(-4.48728 - 25.4486i) q^{92} +(0.374913 + 0.892760i) q^{93} +(9.98902 + 27.4446i) q^{94} +(6.80786 + 5.63935i) q^{95} +(-20.4159 - 15.5078i) q^{96} +(-0.468170 - 2.65512i) q^{97} +(-17.9643 + 4.97744i) q^{98} +(4.56456 + 4.47623i) 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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