LMFDB - Embedded newform 504.2.bf.b.115.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.7
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37865 - 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 + 0.869029i) q^{4} +(-1.58477 + 2.74491i) q^{5} +(0.905257 - 2.27607i) q^{6} +(2.63076 + 0.281244i) q^{7} +(-2.20950 - 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +O(q^{10})$	\(q+(-1.37865 - 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 + 0.869029i) q^{4} +(-1.58477 + 2.74491i) q^{5} +(0.905257 - 2.27607i) q^{6} +(2.63076 + 0.281244i) q^{7} +(-2.20950 - 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +(3.04997 - 3.28478i) q^{10} +(2.67808 + 4.63857i) q^{11} +(-1.96539 + 2.85259i) q^{12} +(0.893100 + 1.54689i) q^{13} +(-3.53825 - 1.21689i) q^{14} +(-4.27771 - 3.44083i) q^{15} +(2.48958 + 3.13081i) q^{16} +(4.04061 + 2.33285i) q^{17} +(3.65555 + 2.15336i) q^{18} +(2.36047 - 1.36282i) q^{19} +(-5.24010 + 3.56727i) q^{20} +(-1.17941 + 4.42820i) q^{21} +(-2.23017 - 7.23901i) q^{22} +(-4.01783 - 2.31970i) q^{23} +(3.60864 - 3.31327i) q^{24} +(-2.52301 - 4.36999i) q^{25} +(-0.743727 - 2.41410i) q^{26} +(2.31328 - 4.65282i) q^{27} +(4.49446 + 2.79282i) q^{28} +(-2.85231 - 1.64678i) q^{29} +(4.81299 + 6.09191i) q^{30} -9.98908 q^{31} +(-2.44549 - 5.10094i) q^{32} +(-8.65000 + 3.35305i) q^{33} +(-4.83532 - 4.48967i) q^{34} +(-4.94115 + 6.77549i) q^{35} +(-4.36102 - 4.12086i) q^{36} +(-2.33249 + 1.34666i) q^{37} +(-3.68378 + 1.13488i) q^{38} +(-2.88464 + 1.11819i) q^{39} +(8.34856 - 3.26646i) q^{40} +(4.34585 - 2.50908i) q^{41} +(3.02165 - 5.73321i) q^{42} +(-0.212741 + 0.368479i) q^{43} +(0.793055 + 10.6829i) q^{44} +(7.02436 - 6.40879i) q^{45} +(4.80806 + 4.46436i) q^{46} +2.98331 q^{47} +(-6.01929 + 3.43047i) q^{48} +(6.84180 + 1.47977i) q^{49} +(2.10103 + 6.81986i) q^{50} +(-5.06503 + 6.29696i) q^{51} +(0.264472 + 3.56260i) q^{52} +(-5.19961 - 3.00200i) q^{53} +(-4.65565 + 5.68550i) q^{54} -16.9766 q^{55} +(-5.31604 - 5.26685i) q^{56} +(1.70630 + 4.40180i) q^{57} +(3.41331 + 3.16931i) q^{58} +4.47279i q^{59} +(-4.71539 - 9.91551i) q^{60} +11.6099 q^{61} +(13.7714 + 3.14830i) q^{62} +(-7.26641 - 3.19364i) q^{63} +(1.76378 + 7.80314i) q^{64} -5.66144 q^{65} +(12.9821 - 1.89641i) q^{66} -12.7934 q^{67} +(5.25116 + 7.71364i) q^{68} +(5.03648 - 6.26146i) q^{69} +(8.94756 - 7.78367i) q^{70} -2.92741i q^{71} +(4.71351 + 7.05569i) q^{72} +(-0.864336 - 0.499025i) q^{73} +(3.64011 - 1.12143i) q^{74} +(8.14914 - 3.15890i) q^{75} +(5.43632 - 0.403569i) q^{76} +(5.74082 + 12.9562i) q^{77} +(4.32933 - 0.632424i) q^{78} +7.46476i q^{79} +(-12.5392 + 1.87203i) q^{80} +(7.35000 + 5.19398i) q^{81} +(-6.78218 + 2.08943i) q^{82} +(-7.03493 - 4.06162i) q^{83} +(-5.97274 + 6.95172i) q^{84} +(-12.8069 + 7.39407i) q^{85} +(0.409430 - 0.440951i) q^{86} +(3.57546 - 4.44509i) q^{87} +(2.27365 - 14.9779i) q^{88} +(6.04395 - 3.48948i) q^{89} +(-11.7040 + 6.62155i) q^{90} +(1.91448 + 4.32069i) q^{91} +(-5.22156 - 7.67015i) q^{92} +(2.65044 - 17.0974i) q^{93} +(-4.11293 - 0.940264i) q^{94} +8.63904i q^{95} +(9.37967 - 2.83227i) q^{96} +(11.7930 + 6.80869i) q^{97} +(-8.96604 - 4.19644i) q^{98} +(-3.44397 - 15.6951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.37865	−	0.315175i	−0.974850	−	0.222862i
$2$	−1.37865	−	0.315175i	−0.974850	−	0.222862i
$3$	−0.265334	+	1.71161i	−0.153191	+	0.988197i
$3$	−0.265334	+	1.71161i	−0.153191	+	0.988197i
$4$	1.80133	+	0.869029i	0.900665	+	0.434514i
$5$	−1.58477	+	2.74491i	−0.708732	+	1.22756i	0.256595	+	0.966519i	$0.417399\pi$
$5$	−1.58477	+	2.74491i	−0.708732	+	1.22756i	−0.965328	+	0.261041i	$0.915934\pi$
$6$	0.905257	−	2.27607i	0.369569	−	0.929203i
$7$	2.63076	+	0.281244i	0.994334	+	0.106300i
$7$	2.63076	+	0.281244i	0.994334	+	0.106300i
$8$	−2.20950	−	1.76582i	−0.781176	−	0.624310i
$9$	−2.85920	−	0.908295i	−0.953065	−	0.302765i
$10$	3.04997	−	3.28478i	0.964484	−	1.03874i
$11$	2.67808	+	4.63857i	0.807472	+	1.39858i	0.914610	+	0.404338i	$0.132498\pi$
$11$	2.67808	+	4.63857i	0.807472	+	1.39858i	−0.107138	+	0.994244i	$0.534169\pi$
$12$	−1.96539	+	2.85259i	−0.567359	+	0.823471i
$13$	0.893100	+	1.54689i	0.247701	+	0.429031i	0.962888	−	0.269903i	$-0.0869915\pi$
$13$	0.893100	+	1.54689i	0.247701	+	0.429031i	−0.715186	+	0.698934i	$0.753658\pi$
$14$	−3.53825	−	1.21689i	−0.945636	−	0.325226i
$15$	−4.27771	−	3.44083i	−1.10450	−	0.888417i
$16$	2.48958	+	3.13081i	0.622395	+	0.782704i
$17$	4.04061	+	2.33285i	0.979993	+	0.565799i	0.902268	−	0.431176i	$-0.141901\pi$
$17$	4.04061	+	2.33285i	0.979993	+	0.565799i	0.0777247	+	0.996975i	$0.475234\pi$
$18$	3.65555	+	2.15336i	0.861621	+	0.507553i
$19$	2.36047	−	1.36282i	0.541530	−	0.312652i	−0.204169	−	0.978936i	$-0.565449\pi$
$19$	2.36047	−	1.36282i	0.541530	−	0.312652i	0.745699	+	0.666283i	$0.232116\pi$
$20$	−5.24010	+	3.56727i	−1.17172	+	0.797666i
$21$	−1.17941	+	4.42820i	−0.257368	+	0.966313i
$22$	−2.23017	−	7.23901i	−0.475473	−	1.54336i
$23$	−4.01783	−	2.31970i	−0.837776	−	0.483690i	0.0187314	−	0.999825i	$-0.494037\pi$
$23$	−4.01783	−	2.31970i	−0.837776	−	0.483690i	−0.856508	+	0.516134i	$0.827371\pi$
$24$	3.60864	−	3.31327i	0.736610	−	0.676317i
$25$	−2.52301	−	4.36999i	−0.504603	−	0.873997i
$26$	−0.743727	−	2.41410i	−0.145857	−	0.473444i
$27$	2.31328	−	4.65282i	0.445192	−	0.895435i
$28$	4.49446	+	2.79282i	0.849373	+	0.527793i
$29$	−2.85231	−	1.64678i	−0.529661	−	0.305800i	0.211217	−	0.977439i	$-0.432257\pi$
$29$	−2.85231	−	1.64678i	−0.529661	−	0.305800i	−0.740878	+	0.671639i	$0.765591\pi$
$30$	4.81299	+	6.09191i	0.878727	+	1.11222i
$31$	−9.98908			−1.79409			−0.897046	−	0.441938i	$-0.854291\pi$
$31$	−9.98908			−1.79409			−0.897046	+	0.441938i	$0.854291\pi$
$32$	−2.44549	−	5.10094i	−0.432306	−	0.901727i
$33$	−8.65000	+	3.35305i	−1.50577	+	0.583691i
$34$	−4.83532	−	4.48967i	−0.829251	−	0.769972i
$35$	−4.94115	+	6.77549i	−0.835207	+	1.14527i
$36$	−4.36102	−	4.12086i	−0.726837	−	0.686810i
$37$	−2.33249	+	1.34666i	−0.383458	+	0.221390i	−0.679322	−	0.733840i	$-0.737726\pi$
$37$	−2.33249	+	1.34666i	−0.383458	+	0.221390i	0.295864	+	0.955230i	$0.404393\pi$
$38$	−3.68378	+	1.13488i	−0.597589	+	0.184103i
$39$	−2.88464	+	1.11819i	−0.461913	+	0.179054i
$40$	8.34856	−	3.26646i	1.32002	−	0.516472i
$41$	4.34585	−	2.50908i	0.678707	−	0.391852i	−0.120660	−	0.992694i	$-0.538501\pi$
$41$	4.34585	−	2.50908i	0.678707	−	0.391852i	0.799368	+	0.600842i	$0.205168\pi$
$42$	3.02165	−	5.73321i	0.466250	−	0.884653i
$43$	−0.212741	+	0.368479i	−0.0324427	+	0.0561925i	−0.881791	−	0.471641i	$-0.843662\pi$
$43$	−0.212741	+	0.368479i	−0.0324427	+	0.0561925i	0.849348	+	0.527833i	$0.176995\pi$
$44$	0.793055	+	10.6829i	0.119558	+	1.61051i
$45$	7.02436	−	6.40879i	1.04713	−	0.955366i
$46$	4.80806	+	4.46436i	0.708910	+	0.658234i
$47$	2.98331			0.435161			0.217580	−	0.976042i	$-0.430184\pi$
$47$	2.98331			0.435161			0.217580	+	0.976042i	$0.430184\pi$
$48$	−6.01929	+	3.43047i	−0.868810	+	0.495145i
$49$	6.84180	+	1.47977i	0.977401	+	0.211396i
$50$	2.10103	+	6.81986i	0.297131	+	0.964473i
$51$	−5.06503	+	6.29696i	−0.709246	+	0.881750i
$52$	0.264472	+	3.56260i	0.0366757	+	0.494043i
$53$	−5.19961	−	3.00200i	−0.714221	−	0.412356i	0.0984008	−	0.995147i	$-0.468627\pi$
$53$	−5.19961	−	3.00200i	−0.714221	−	0.412356i	−0.812622	+	0.582791i	$0.801961\pi$
$54$	−4.65565	+	5.68550i	−0.633554	+	0.773699i
$55$	−16.9766			−2.28913
$56$	−5.31604	−	5.26685i	−0.710386	−	0.703812i
$57$	1.70630	+	4.40180i	0.226005	+	0.583033i
$58$	3.41331	+	3.16931i	0.448189	+	0.416151i
$59$			4.47279i			0.582308i	0.956676	+	0.291154i	$0.0940392\pi$
$59$			4.47279i			0.582308i	−0.956676	+	0.291154i	$0.905961\pi$
$60$	−4.71539	−	9.91551i	−0.608754	−	1.28009i
$61$	11.6099			1.48650			0.743248	−	0.669016i	$-0.233284\pi$
$61$	11.6099			1.48650			0.743248	+	0.669016i	$0.233284\pi$
$62$	13.7714	+	3.14830i	1.74897	+	0.399835i
$63$	−7.26641	−	3.19364i	−0.915481	−	0.402361i
$64$	1.76378	+	7.80314i	0.220473	+	0.975393i
$65$	−5.66144			−0.702216
$66$	12.9821	−	1.89641i	1.59798	−	0.233432i
$67$	−12.7934			−1.56296			−0.781480	−	0.623930i	$-0.785535\pi$
$67$	−12.7934			−1.56296			−0.781480	+	0.623930i	$0.785535\pi$
$68$	5.25116	+	7.71364i	0.636797	+	0.935416i
$69$	5.03648	−	6.26146i	0.606321	−	0.753791i
$70$	8.94756	−	7.78367i	1.06944	−	0.930327i
$71$		−	2.92741i		−	0.347420i	−0.984797	−	0.173710i	$-0.944424\pi$
$71$		−	2.92741i		−	0.347420i	0.984797	−	0.173710i	$-0.0555755\pi$
$72$	4.71351	+	7.05569i	0.555493	+	0.831521i
$73$	−0.864336	−	0.499025i	−0.101163	−	0.0584064i	0.448565	−	0.893750i	$-0.351935\pi$
$73$	−0.864336	−	0.499025i	−0.101163	−	0.0584064i	−0.549728	+	0.835344i	$0.685269\pi$
$74$	3.64011	−	1.12143i	0.423154	−	0.130363i
$75$	8.14914	−	3.15890i	0.940982	−	0.364758i
$76$	5.43632	−	0.403569i	0.623589	−	0.0462926i
$77$	5.74082	+	12.9562i	0.654227	+	1.47649i
$78$	4.32933	−	0.632424i	0.490200	−	0.0716080i
$79$			7.46476i			0.839851i	0.907559	+	0.419925i	$0.137944\pi$
$79$			7.46476i			0.839851i	−0.907559	+	0.419925i	$0.862056\pi$
$80$	−12.5392	+	1.87203i	−1.40193	+	0.209300i
$81$	7.35000	+	5.19398i	0.816667	+	0.577109i
$82$	−6.78218	+	2.08943i	−0.748967	+	0.230739i
$83$	−7.03493	−	4.06162i	−0.772184	−	0.445821i	0.0614690	−	0.998109i	$-0.480421\pi$
$83$	−7.03493	−	4.06162i	−0.772184	−	0.445821i	−0.833653	+	0.552288i	$0.813755\pi$
$84$	−5.97274	+	6.95172i	−0.651680	+	0.758494i
$85$	−12.8069	+	7.39407i	−1.38910	+	0.802000i
$86$	0.409430	−	0.440951i	0.0441500	−	0.0475490i
$87$	3.57546	−	4.44509i	0.383330	−	0.476564i
$88$	2.27365	−	14.9779i	0.242372	−	1.59665i
$89$	6.04395	−	3.48948i	0.640658	−	0.369884i	−0.144210	−	0.989547i	$-0.546064\pi$
$89$	6.04395	−	3.48948i	0.640658	−	0.369884i	0.784868	+	0.619663i	$0.212731\pi$
$90$	−11.7040	+	6.62155i	−1.23371	+	0.697973i
$91$	1.91448	+	4.32069i	0.200692	+	0.452931i
$92$	−5.22156	−	7.67015i	−0.544385	−	0.799669i
$93$	2.65044	−	17.0974i	0.274838	−	1.77292i
$94$	−4.11293	−	0.940264i	−0.424216	−	0.0969808i
$95$			8.63904i			0.886347i
$96$	9.37967	−	2.83227i	0.957309	−	0.289068i
$97$	11.7930	+	6.80869i	1.19740	+	0.691318i	0.959974	−	0.280089i	$-0.0903639\pi$
$97$	11.7930	+	6.80869i	1.19740	+	0.691318i	0.237423	+	0.971406i	$0.423697\pi$
$98$	−8.96604	−	4.19644i	−0.905707	−	0.423905i
$99$	−3.44397	−	15.6951i	−0.346132	−	1.57741i
$100$	−0.747135	−	10.0644i	−0.0747135	−	1.00644i
$101$	−0.434202	−	0.752060i	−0.0432047	−	0.0748327i	0.843614	−	0.536949i	$-0.180423\pi$
$101$	−0.434202	−	0.752060i	−0.0432047	−	0.0748327i	−0.886819	+	0.462117i	$0.847090\pi$
$102$	8.96753	−	7.08490i	0.887918	−	0.701510i
$103$	8.35409	−	14.4697i	0.823153	−	1.42574i	−0.0801693	−	0.996781i	$-0.525546\pi$
$103$	8.35409	−	14.4697i	0.823153	−	1.42574i	0.903323	−	0.428962i	$-0.141121\pi$
$104$	0.758227	−	4.99491i	0.0743503	−	0.489792i
$105$	−10.2859	−	10.2551i	−1.00380	−	1.00079i
$106$	6.22227	+	5.77748i	0.604360	+	0.561158i
$107$	−7.16839	−	12.4160i	−0.692994	−	1.20030i	−0.970852	−	0.239679i	$-0.922958\pi$
$107$	−7.16839	−	12.4160i	−0.692994	−	1.20030i	0.277858	−	0.960622i	$-0.410376\pi$
$108$	8.21042	−	6.37095i	0.790048	−	0.613045i
$109$	15.6663	+	9.04494i	1.50056	+	0.866348i	1.00000		0.000646449i	$0.000205771\pi$
$109$	15.6663	+	9.04494i	1.50056	+	0.866348i	0.500560	+	0.865702i	$0.333128\pi$
$110$	23.4047	+	5.35060i	2.23155	+	0.510159i
$111$	−1.68607	−	4.34961i	−0.160034	−	0.412847i
$112$	5.66896	+	8.93660i	0.535667	+	0.844430i
$113$	−2.83892	−	4.91715i	−0.267063	−	0.462567i	0.701039	−	0.713123i	$-0.252720\pi$
$113$	−2.83892	−	4.91715i	−0.267063	−	0.462567i	−0.968102	+	0.250556i	$0.919387\pi$
$114$	−0.965044	−	6.60631i	−0.0903847	−	0.618738i
$115$	12.7347	−	7.35239i	1.18752	−	0.685614i
$116$	−3.70685	−	5.44514i	−0.344173	−	0.505569i
$117$	−1.14851	−	5.23407i	−0.106180	−	0.483890i
$118$	1.40971	−	6.16639i	0.129774	−	0.567663i
$119$	9.97379	+	7.27357i	0.914295	+	0.666767i
$120$	3.37573	+	15.1562i	0.308161	+	1.38356i
$121$	−8.84424	+	15.3187i	−0.804022	+	1.39261i
$122$	−16.0060	−	3.65915i	−1.44911	−	0.331284i
$123$	3.14145	+	8.10413i	0.283255	+	0.730724i
$124$	−17.9936	−	8.68079i	−1.61588	−	0.779558i
$125$	0.145884			0.0130483
$126$	9.01125	+	6.69308i	0.802786	+	0.596267i
$127$		−	4.54442i		−	0.403252i	−0.979463	−	0.201626i	$-0.935377\pi$
$127$		−	4.54442i		−	0.403252i	0.979463	−	0.201626i	$-0.0646226\pi$
$128$	0.0277197	−	11.3137i	0.00245010	−	0.999997i
$129$	−0.574243	−	0.461899i	−0.0505593	−	0.0406680i
$130$	7.80513	+	1.78434i	0.684555	+	0.156497i
$131$	19.5820	+	11.3056i	1.71088	+	0.987779i	0.933373	+	0.358909i	$0.116851\pi$
$131$	19.5820	+	11.3056i	1.71088	+	0.987779i	0.777510	+	0.628870i	$0.216482\pi$
$132$	−18.4954	−	1.47715i	−1.60982	−	0.128569i
$133$	6.59313	−	2.92138i	0.571697	−	0.253316i
$134$	17.6375	+	4.03215i	1.52365	+	0.348325i
$135$	9.10552	+	13.7234i	0.783679	+	1.18112i
$136$	−4.80835	−	12.2894i	−0.412313	−	1.05381i
$137$	0.166825	+	0.288950i	0.0142528	+	0.0246867i	0.873064	−	0.487606i	$-0.162130\pi$
$137$	0.166825	+	0.288950i	0.0142528	+	0.0246867i	−0.858811	+	0.512293i	$0.828796\pi$
$138$	−8.91697	+	7.04496i	−0.759063	+	0.599707i
$139$	−1.30955	+	0.756069i	−0.111075	+	0.0641289i	−0.554508	−	0.832178i	$-0.687094\pi$
$139$	−1.30955	+	0.756069i	−0.111075	+	0.0641289i	0.443434	+	0.896307i	$0.353760\pi$
$140$	−14.7887	+	7.91089i	−1.24988	+	0.668592i
$141$	−0.791573	+	5.10626i	−0.0666625	+	0.430024i
$142$	−0.922647	+	4.03587i	−0.0774268	+	0.338682i
$143$	−4.78359	+	8.28542i	−0.400024	+	0.692861i
$144$	−4.27449	−	11.2129i	−0.356208	−	0.934407i
$145$	9.04054	−	5.21956i	0.750776	−	0.433461i
$146$	1.03433	+	0.960395i	0.0856021	+	0.0794829i
$147$	−4.34815	+	11.3178i	−0.358629	+	0.933480i
$148$	−5.37186	+	0.398784i	−0.441564	+	0.0327799i
$149$	15.4464	+	8.91798i	1.26542	+	0.730590i	0.974118	−	0.226042i	$-0.0725786\pi$
$149$	15.4464	+	8.91798i	1.26542	+	0.730590i	0.291301	+	0.956631i	$0.405912\pi$
$150$	−12.2304	+	1.78660i	−0.998607	+	0.145876i
$151$	−11.4870	+	6.63202i	−0.934799	+	0.539706i	−0.888326	−	0.459213i	$-0.848131\pi$
$151$	−11.4870	+	6.63202i	−0.934799	+	0.539706i	−0.0464728	+	0.998920i	$0.514798\pi$
$152$	−7.62196	−	1.15701i	−0.618222	−	0.0938460i
$153$	−9.43399	−	10.3401i	−0.762693	−	0.835951i
$154$	−3.83110	−	19.6713i	−0.308719	−	1.58516i
$155$	15.8304	−	27.4191i	1.27153	−	2.20236i
$156$	−6.16794	−	0.492606i	−0.493830	−	0.0394400i
$157$	5.84007			0.466088			0.233044	−	0.972466i	$-0.425131\pi$
$157$	5.84007			0.466088			0.233044	+	0.972466i	$0.425131\pi$
$158$	2.35270	−	10.2913i	0.187171	−	0.818729i
$159$	6.51787	−	8.10316i	0.516901	−	0.642622i
$160$	17.8772	+	1.37117i	1.41331	+	0.108401i
$161$	−9.91756	−	7.23256i	−0.781613	−	0.570006i
$162$	−8.49604	−	9.47720i	−0.667512	−	0.744599i
$163$	2.06173	+	3.57103i	0.161488	+	0.279705i	0.935402	−	0.353585i	$-0.115038\pi$
$163$	2.06173	+	3.57103i	0.161488	+	0.279705i	−0.773915	+	0.633290i	$0.781704\pi$
$164$	10.0088	−	0.743008i	0.781553	−	0.0580192i
$165$	4.50447	−	29.0573i	0.350673	−	2.26211i
$166$	8.41856	+	7.81677i	0.653407	+	0.606699i
$167$	5.25195	+	9.09665i	0.406408	+	0.703920i	0.994484	−	0.104886i	$-0.0334477\pi$
$167$	5.25195	+	9.09665i	0.406408	+	0.703920i	−0.588076	+	0.808806i	$0.700114\pi$
$168$	10.4253	−	7.70150i	0.804329	−	0.594184i
$169$	4.90475	−	8.49527i	0.377288	−	0.653482i
$170$	19.9866	−	6.15740i	1.53290	−	0.472251i
$171$	−7.98690	+	1.75256i	−0.610773	+	0.134022i
$172$	−0.703436	+	0.478874i	−0.0536365	+	0.0365138i
$173$	3.11457			0.236796			0.118398	−	0.992966i	$-0.462224\pi$
$173$	3.11457			0.236796			0.118398	+	0.992966i	$0.462224\pi$
$174$	−6.33028	+	5.00131i	−0.479897	+	0.379148i
$175$	−5.40841	−	12.2060i	−0.408837	−	0.922685i
$176$	−7.85522	+	19.9327i	−0.592109	+	1.50248i
$177$	−7.65566	−	1.18678i	−0.575435	−	0.0892041i
$178$	−9.43227	+	2.90585i	−0.706978	+	0.217803i
$179$	0.757866	−	1.31266i	0.0566456	−	0.0981130i	−0.836312	−	0.548254i	$-0.815293\pi$
$179$	0.757866	−	1.31266i	0.0566456	−	0.0981130i	0.892958	+	0.450141i	$0.148626\pi$
$180$	18.2226	−	5.43997i	1.35823	−	0.405471i
$181$	−2.75740			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$181$	−2.75740			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$182$	−1.27761	−	6.56009i	−0.0947031	−	0.486267i
$183$	−3.08050	+	19.8716i	−0.227717	+	1.46895i
$184$	4.78125	+	12.2201i	0.352478	+	0.900880i
$185$		−	8.53661i		−	0.627624i
$186$	−9.04268	+	22.7359i	−0.663041	+	1.66708i
$187$			24.9902i			1.82747i
$188$	5.37393	+	2.59258i	0.391934	+	0.189084i
$189$	7.39428	−	11.5899i	0.537854	−	0.843038i
$190$	2.72281	−	11.9102i	0.197533	−	0.864056i
$191$		−	7.75689i		−	0.561269i	−0.959815	−	0.280634i	$-0.909455\pi$
$191$		−	7.75689i		−	0.561269i	0.959815	−	0.280634i	$-0.0905448\pi$
$192$	−13.8239	+	0.948466i	−0.997655	+	0.0684496i
$193$	−4.94596			−0.356018			−0.178009	−	0.984029i	$-0.556966\pi$
$193$	−4.94596			−0.356018			−0.178009	+	0.984029i	$0.556966\pi$
$194$	−14.1124	−	13.1036i	−1.01321	−	0.940786i
$195$	1.50217	−	9.69017i	0.107573	−	0.693927i
$196$	11.0384	+	8.61128i	0.788456	+	0.615091i
$197$		−	7.54976i		−	0.537898i	−0.963154	−	0.268949i	$-0.913324\pi$
$197$		−	7.54976i		−	0.537898i	0.963154	−	0.268949i	$-0.0866763\pi$
$198$	−0.198677	+	22.7234i	−0.0141194	+	1.61488i
$199$	−7.62668	+	13.2098i	−0.540641	+	0.936418i	0.458226	+	0.888836i	$0.348485\pi$
$199$	−7.62668	+	13.2098i	−0.540641	+	0.936418i	−0.998867	+	0.0475821i	$0.984848\pi$
$200$	−2.14200	+	14.1107i	−0.151462	+	0.997775i
$201$	3.39452	−	21.8972i	0.239431	−	1.54451i
$202$	0.361580	+	1.17367i	0.0254407	+	0.0825794i
$203$	−7.04060	−	5.13449i	−0.494154	−	0.360371i
$204$	−14.5960	+	6.94124i	−1.02193	+	0.485984i
$205$			15.9053i			1.11087i
$206$	−16.0778	+	17.3156i	−1.12020	+	1.20644i
$207$	9.38081	+	10.2818i	0.652011	+	0.714638i
$208$	−2.61960	+	6.64724i	−0.181636	+	0.460903i
$209$	12.6431	+	7.29949i	0.874540	+	0.504916i
$210$	10.9485	+	17.3800i	0.755518	+	1.19933i
$211$	−0.449200	−	0.778038i	−0.0309242	−	0.0535623i	0.850149	−	0.526542i	$-0.176512\pi$
$211$	−0.449200	−	0.778038i	−0.0309242	−	0.0535623i	−0.881073	+	0.472980i	$0.843178\pi$
$212$	−6.75739	−	9.92619i	−0.464100	−	0.681734i
$213$	5.01058	+	0.776742i	0.343319	+	0.0532215i
$214$	5.96946	+	19.3766i	0.408064	+	1.32456i
$215$	−0.674294	−	1.16791i	−0.0459864	−	0.0796509i
$216$	−13.3272	+	6.19557i	−0.906803	+	0.421555i
$217$	−26.2789	−	2.80937i	−1.78393	−	0.190712i
$218$	−18.7475	−	17.4074i	−1.26974	−	1.17898i
$219$	1.08347	−	1.34700i	0.0732142	−	0.0910215i
$220$	−30.5805	−	14.7532i	−2.06174	−	0.994658i
$221$			8.33387i			0.560597i
$222$	0.953602	+	6.52798i	0.0640016	+	0.438130i
$223$	−6.78219	+	11.7471i	−0.454169	+	0.786644i	−0.998640	−	0.0521356i	$-0.983397\pi$
$223$	−6.78219	+	11.7471i	−0.454169	+	0.786644i	0.544471	+	0.838780i	$0.316731\pi$
$224$	−4.99890	−	14.1071i	−0.334003	−	0.942572i
$225$	3.24455	+	14.7863i	0.216304	+	0.985753i
$226$	2.36410	+	7.67377i	0.157258	+	0.510452i
$227$	−3.04590	+	1.75855i	−0.202164	+	0.116719i	−0.597664	−	0.801746i	$-0.703904\pi$
$227$	−3.04590	+	1.75855i	−0.202164	+	0.116719i	0.395501	+	0.918466i	$0.370571\pi$
$228$	−0.751688	+	9.41192i	−0.0497818	+	0.623320i
$229$	−11.6852	+	20.2394i	−0.772181	+	1.33746i	0.164184	+	0.986430i	$0.447501\pi$
$229$	−11.6852	+	20.2394i	−0.772181	+	1.33746i	−0.936365	+	0.351027i	$0.885833\pi$
$230$	−19.8739	+	6.12268i	−1.31045	+	0.403718i
$231$	−23.6991	+	6.38832i	−1.55929	+	0.420320i
$232$	3.39427	+	8.67523i	0.222845	+	0.569557i
$233$	6.13808	+	10.6315i	0.402119	+	0.696491i	0.993981	−	0.109548i	$-0.0349404\pi$
$233$	6.13808	+	10.6315i	0.402119	+	0.696491i	−0.591862	+	0.806039i	$0.701607\pi$
$234$	−0.0662559	+	7.57791i	−0.00433128	+	0.495384i
$235$	−4.72787	+	8.18891i	−0.308412	+	0.534186i
$236$	−3.88698	+	8.05697i	−0.253021	+	0.524464i
$237$	−12.7767	−	1.98065i	−0.829938	−	0.128657i
$238$	−11.4579	−	13.1712i	−0.742704	−	0.853759i
$239$	25.0467	−	14.4607i	1.62014	−	0.935387i	0.633257	−	0.773942i	$-0.281718\pi$
$239$	25.0467	−	14.4607i	1.62014	−	0.935387i	0.986882	−	0.161446i	$-0.0516156\pi$
$240$	0.122896	−	21.9589i	0.00793291	−	1.41744i
$241$	3.52556	−	2.03548i	0.227101	−	0.131117i	−0.382133	−	0.924107i	$-0.624810\pi$
$241$	3.52556	−	2.03548i	0.227101	−	0.131117i	0.609234	+	0.792990i	$0.291477\pi$
$242$	17.0211	−	18.3315i	1.09416	−	1.17840i
$243$	−10.8403	+	11.2022i	−0.695403	+	0.718620i
$244$	20.9133	+	10.0893i	1.33884	+	0.645904i
$245$	−14.9045	+	16.4350i	−0.952216	+	1.04999i
$246$	−1.77673	−	12.1628i	−0.113280	−	0.775474i
$247$	4.21628	+	2.43427i	0.268275	+	0.154889i
$248$	22.0709	+	17.6389i	1.40150	+	1.12007i
$249$	8.81850	−	10.9634i	0.558850	−	0.694774i
$250$	−0.201123	−	0.0459790i	−0.0127201	−	0.00290797i
$251$			16.9156i			1.06770i	0.845578	+	0.533852i	$0.179256\pi$
$251$			16.9156i			1.06770i	−0.845578	+	0.533852i	$0.820744\pi$
$252$	−10.3138	−	12.0675i	−0.649710	−	0.760182i
$253$		−	24.8494i		−	1.56227i
$254$	−1.43229	+	6.26515i	−0.0898696	+	0.393110i
$255$	−9.25764	−	23.8823i	−0.579736	−	1.49557i
$256$	−3.60400	+	15.5888i	−0.225250	+	0.974301i
$257$	2.21508	+	1.27887i	0.138173	+	0.0797740i	0.567493	−	0.823378i	$-0.307913\pi$
$257$	2.21508	+	1.27887i	0.138173	+	0.0797740i	−0.429320	+	0.903152i	$0.641247\pi$
$258$	0.646099	+	0.817783i	0.0402244	+	0.0509129i
$259$	−6.51495	+	2.88675i	−0.404819	+	0.179374i
$260$	−10.1981	−	4.91996i	−0.632461	−	0.305123i
$261$	6.65956	+	7.29922i	0.412216	+	0.451810i
$262$	−23.4333	−	21.7582i	−1.44772	−	1.34423i
$263$	18.9865	−	10.9619i	1.17076	−	0.675938i	0.216900	−	0.976194i	$-0.430406\pi$
$263$	18.9865	−	10.9619i	1.17076	−	0.675938i	0.953859	+	0.300256i	$0.0970722\pi$
$264$	25.0331	+	7.86574i	1.54068	+	0.484103i
$265$	16.4804	−	9.51497i	1.01238	−	0.584500i
$266$	−10.0103	+	1.94957i	−0.613773	+	0.119536i
$267$	4.36895	+	11.2707i	0.267375	+	0.689759i
$268$	−23.0451	−	11.1178i	−1.40770	−	0.679128i
$269$	−6.10379	+	10.5721i	−0.372155	+	0.644591i	−0.989897	−	0.141790i	$-0.954714\pi$
$269$	−6.10379	+	10.5721i	−0.372155	+	0.644591i	0.617742	+	0.786381i	$0.288048\pi$
$270$	−8.22802	−	21.7896i	−0.500741	−	1.32607i
$271$	−12.1660	−	21.0722i	−0.739034	−	1.28004i	−0.952931	−	0.303188i	$-0.901949\pi$
$271$	−12.1660	−	21.0722i	−0.739034	−	1.28004i	0.213897	−	0.976856i	$-0.431384\pi$
$272$	2.75570	+	18.4582i	0.167089	+	1.11919i
$273$	−7.90329	+	2.13041i	−0.478329	+	0.128938i
$274$	−0.138923	−	0.450939i	−0.00839267	−	0.0272422i
$275$	13.5137	−	23.4064i	0.814905	−	1.41146i
$276$	14.5137	−	6.90211i	0.873625	−	0.415458i
$277$	−8.84759	+	5.10816i	−0.531600	+	0.306919i	−0.741668	−	0.670767i	$-0.765965\pi$
$277$	−8.84759	+	5.10816i	−0.531600	+	0.306919i	0.210068	+	0.977687i	$0.432632\pi$
$278$	2.04370	−	0.629615i	0.122573	−	0.0377618i
$279$	28.5607	+	9.07303i	1.70989	+	0.543188i
$280$	22.8817	−	6.24528i	1.36745	−	0.373227i
$281$	−14.3951	+	24.9330i	−0.858738	+	1.48738i	0.0143945	+	0.999896i	$0.495418\pi$
$281$	−14.3951	+	24.9330i	−0.858738	+	1.48738i	−0.873133	+	0.487482i	$0.837915\pi$
$282$	2.70066	−	6.79023i	0.160822	−	0.404353i
$283$			8.63820i			0.513488i	0.966479	+	0.256744i	$0.0826497\pi$
$283$			8.63820i			0.513488i	−0.966479	+	0.256744i	$0.917350\pi$
$284$	2.54401	−	5.27324i	0.150959	−	0.312909i
$285$	−14.7866	−	2.29223i	−0.875885	−	0.135780i
$286$	9.20623	−	9.91499i	0.544376	−	0.586286i
$287$	12.1385	−	5.37854i	0.716516	−	0.317485i
$288$	2.35899	+	16.8058i	0.139005	+	0.990292i
$289$	2.38437	+	4.12985i	0.140257	+	0.242932i
$290$	−14.1088	+	4.34657i	−0.828496	+	0.255240i
$291$	−14.7829	+	18.3784i	−0.866588	+	1.07736i
$292$	−1.12329	−	1.65004i	−0.0657355	−	0.0965614i
$293$	−5.36418	−	9.29102i	−0.313378	−	0.542787i	0.665713	−	0.746208i	$-0.268128\pi$
$293$	−5.36418	−	9.29102i	−0.313378	−	0.542787i	−0.979091	+	0.203420i	$0.934794\pi$
$294$	9.56166	−	14.2329i	0.557647	−	0.830078i
$295$	−12.2774	−	7.08836i	−0.714818	−	0.412700i
$296$	7.53159	+	1.14329i	0.437765	+	0.0664526i
$297$	27.7776	−	1.73028i	1.61182	−	0.100401i
$298$	−18.4844	−	17.1631i	−1.07077	−	0.994229i
$299$		−	8.28689i		−	0.479243i
$300$	17.4245	+	1.39161i	1.00600	+	0.0803449i
$301$	−0.663304	+	0.909547i	−0.0382322	+	0.0524254i
$302$	17.9268	−	5.52280i	1.03157	−	0.317801i
$303$	1.40244	−	0.543636i	0.0805680	−	0.0312311i
$304$	10.1433	+	3.99736i	0.581759	+	0.229264i
$305$	−18.3991	+	31.8681i	−1.05353	+	1.82476i
$306$	9.74718	+	17.2287i	0.557209	+	0.984902i
$307$		−	28.5013i		−	1.62666i	−0.581805	−	0.813328i	$-0.697653\pi$
$307$		−	28.5013i		−	1.62666i	0.581805	−	0.813328i	$-0.302347\pi$
$308$	−0.918173	+	28.3273i	−0.0523178	+	1.61410i
$309$	22.5498	+	18.1382i	1.28282	+	1.03185i
$310$	−30.4664	+	32.8119i	−1.73037	+	1.86359i
$311$	31.6953			1.79728			0.898639	−	0.438689i	$-0.144557\pi$
$311$	31.6953			1.79728			0.898639	+	0.438689i	$0.144557\pi$
$312$	8.34815	+	2.62311i	0.472621	+	0.148504i
$313$		−	10.9088i		−	0.616603i	−0.951289	−	0.308302i	$-0.900239\pi$
$313$		−	10.9088i		−	0.616603i	0.951289	−	0.308302i	$-0.0997606\pi$
$314$	−8.05139	−	1.84064i	−0.454366	−	0.103873i
$315$	20.2819	−	14.8844i	1.14275	−	0.838643i
$316$	−6.48709	+	13.4465i	−0.364927	+	0.756424i
$317$			11.5402i			0.648162i	0.946029	+	0.324081i	$0.105055\pi$
$317$			11.5402i			0.648162i	−0.946029	+	0.324081i	$0.894945\pi$
$318$	−11.5397	+	9.11712i	−0.647117	+	0.511263i
$319$		−	17.6409i		−	0.987700i
$320$	−24.2141	−	7.52479i	−1.35361	−	0.420649i
$321$	23.1534	−	8.97508i	1.29229	−	0.500940i
$322$	11.3933	+	13.0969i	0.634923	+	0.729862i
$323$	12.7170			0.707594
$324$	8.72606	+	15.7434i	0.484781	+	0.874636i
$325$	4.50661	−	7.80567i	0.249982	−	0.432981i
$326$	−1.71690	−	5.57299i	−0.0950905	−	0.308659i
$327$	−19.6382	+	24.4146i	−1.08599	+	1.35013i
$328$	−14.0327	−	2.13016i	−0.774827	−	0.117619i
$329$	7.84838	+	0.839039i	0.432695	+	0.0462577i
$330$	−15.3682	+	38.6400i	−0.845991	+	2.12706i
$331$	−0.928777			−0.0510502			−0.0255251	−	0.999674i	$-0.508126\pi$
$331$	−0.928777			−0.0510502			−0.0255251	+	0.999674i	$0.508126\pi$
$332$	−9.14257	−	13.4299i	−0.501764	−	0.737060i
$333$	7.89220	−	1.73178i	0.432490	−	0.0949012i
$334$	−4.37355	−	14.1963i	−0.239310	−	0.776789i
$335$	20.2746	−	35.1166i	1.10772	−	1.91863i
$336$	−16.8001	+	7.33185i	−0.916522	+	0.399985i
$337$	0.718049	+	1.24370i	0.0391146	+	0.0677485i	0.884920	−	0.465743i	$-0.154213\pi$
$337$	0.718049	+	1.24370i	0.0391146	+	0.0677485i	−0.845805	+	0.533492i	$0.820880\pi$
$338$	−9.43940	+	10.1661i	−0.513436	+	0.552964i
$339$	9.16950	−	3.55443i	0.498019	−	0.193050i
$340$	−29.4951	+	2.18959i	−1.59960	+	0.118747i
$341$	−26.7516	−	46.3351i	−1.44868	−	2.50918i
$342$	11.5635	+	0.101103i	0.625281	+	0.00546701i
$343$	17.5830	+	5.81714i	0.949391	+	0.314096i
$344$	1.12072	−	0.438492i	0.0604251	−	0.0236419i
$345$	9.20545	+	23.7477i	0.495605	+	1.27853i
$346$	−4.29388	−	0.981632i	−0.230841	−	0.0527729i
$347$	−14.7107			−0.789714			−0.394857	−	0.918743i	$-0.629206\pi$
$347$	−14.7107			−0.789714			−0.394857	+	0.918743i	$0.629206\pi$
$348$	10.3035	−	4.89990i	0.552325	−	0.262662i
$349$	11.1777	−	19.3603i	0.598328	−	1.03633i	−0.394740	−	0.918793i	$-0.629165\pi$
$349$	11.1777	−	19.3603i	0.598328	−	1.03633i	0.993068	−	0.117541i	$-0.0375012\pi$
$350$	3.60927	+	18.5323i	0.192924	+	0.990594i
$351$	9.26341	−	0.577024i	0.494444	−	0.0307992i
$352$	17.1118	−	25.0043i	0.912064	−	1.33274i
$353$	3.96945	−	2.29176i	0.211272	−	0.121978i	−0.390630	−	0.920548i	$-0.627743\pi$
$353$	3.96945	−	2.29176i	0.211272	−	0.121978i	0.601903	+	0.798570i	$0.294410\pi$
$354$	10.1804	+	4.04902i	0.541082	+	0.215203i
$355$	8.03548	+	4.63929i	0.426479	+	0.246228i
$356$	13.9196	−	1.03333i	0.737738	−	0.0547665i
$357$	−15.0959	+	15.1413i	−0.798958	+	0.801361i
$358$	−1.45855	+	1.57084i	−0.0770866	+	0.0830213i
$359$	−14.2343	+	8.21816i	−0.751256	+	0.433738i	−0.826148	−	0.563454i	$-0.809472\pi$
$359$	−14.2343	+	8.21816i	−0.751256	+	0.433738i	0.0748915	+	0.997192i	$0.476139\pi$
$360$	−26.8371	+	1.75649i	−1.41444	+	0.0925749i
$361$	−5.78544	+	10.0207i	−0.304497	+	0.527404i
$362$	3.80148	+	0.869063i	0.199801	+	0.0456769i
$363$	−23.8729	−	19.2024i	−1.25300	−	1.00787i
$364$	−0.306197	+	9.44672i	−0.0160491	+	0.495143i
$365$	2.73955	−	1.58168i	0.143395	−	0.0827890i
$366$	10.5099	−	26.4250i	0.549364	−	1.38126i
$367$	−6.68954	−	11.5866i	−0.349191	−	0.604817i	0.636915	−	0.770934i	$-0.280210\pi$
$367$	−6.68954	−	11.5866i	−0.349191	−	0.604817i	−0.986106	+	0.166118i	$0.946877\pi$
$368$	−2.74017	−	18.3542i	−0.142841	−	0.956777i
$369$	−14.7046	+	3.22663i	−0.765492	+	0.167972i
$370$	−2.69052	+	11.7690i	−0.139874	+	0.611839i
$371$	−12.8346	−	9.35989i	−0.666341	−	0.485941i
$372$	19.6324	−	28.4947i	1.01789	−	1.47738i
$373$	−15.5628	−	8.98519i	−0.805811	−	0.465235i	0.0396879	−	0.999212i	$-0.487364\pi$
$373$	−15.5628	−	8.98519i	−0.805811	−	0.465235i	−0.845499	+	0.533977i	$0.820697\pi$
$374$	7.87629	−	34.4527i	0.407273	−	1.78151i
$375$	−0.0387080	+	0.249697i	−0.00199887	+	0.0128943i
$376$	−6.59163	−	5.26798i	−0.339937	−	0.271675i
$377$		−	5.88297i		−	0.302988i
$378$	−13.8469	+	13.6478i	−0.712209	+	0.701968i
$379$	−16.4196			−0.843420			−0.421710	−	0.906731i	$-0.638570\pi$
$379$	−16.4196			−0.843420			−0.421710	+	0.906731i	$0.638570\pi$
$380$	−7.50758	+	15.5618i	−0.385131	+	0.798302i
$381$	7.77826	+	1.20579i	0.398492	+	0.0617744i
$382$	−2.44478	+	10.6940i	−0.125086	+	0.547153i
$383$	−11.0723	+	19.1778i	−0.565770	+	0.979942i	0.431208	+	0.902253i	$0.358088\pi$
$383$	−11.0723	+	19.1778i	−0.565770	+	0.979942i	−0.996978	+	0.0776894i	$0.975246\pi$
$384$	19.3572	+	3.04935i	0.987818	+	0.155611i
$385$	−44.6614	−	4.77457i	−2.27616	−	0.243335i
$386$	6.81873	+	1.55884i	0.347064	+	0.0793430i
$387$	0.942956	−	0.860321i	0.0479332	−	0.0437326i
$388$	15.3261	+	22.5131i	0.778066	+	1.14293i
$389$	−0.0236594	+	0.0136597i	−0.00119958	+	0.000692576i	−0.500600	−	0.865679i	$-0.666887\pi$
$389$	−0.0236594	+	0.0136597i	−0.00119958	+	0.000692576i	0.499400	+	0.866371i	$0.333554\pi$
$390$	−5.12506	+	12.8859i	−0.259517	+	0.652501i
$391$	−10.8230	−	18.7460i	−0.547343	−	0.948026i
$392$	−12.5040	−	15.3509i	−0.631545	−	0.775339i
$393$	−24.5466	+	30.5168i	−1.23821	+	1.53937i
$394$	−2.37949	+	10.4084i	−0.119877	+	0.524370i
$395$	−20.4901	−	11.8299i	−1.03097	−	0.595229i
$396$	7.43575	−	31.2649i	0.373660	−	1.57112i
$397$	12.3558	+	21.4009i	0.620121	+	1.07408i	0.989463	+	0.144787i	$0.0462498\pi$
$397$	12.3558	+	21.4009i	0.620121	+	1.07408i	−0.369342	+	0.929294i	$0.620417\pi$
$398$	14.6779	−	15.8079i	0.735736	−	0.792378i
$399$	3.25088	+	12.0600i	0.162748	+	0.603754i
$400$	7.40038	−	18.7785i	0.370019	−	0.938926i
$401$	14.5787	−	25.2511i	0.728027	−	1.26098i	−0.229688	−	0.973264i	$-0.573771\pi$
$401$	14.5787	−	25.2511i	0.728027	−	1.26098i	0.957716	−	0.287716i	$-0.0928960\pi$
$402$	−11.5813	+	29.1187i	−0.577622	+	1.45231i
$403$	−8.92124	−	15.4520i	−0.444399	−	0.769721i
$404$	−0.128579	−	1.73204i	−0.00639706	−	0.0861723i
$405$	−25.9051	+	11.9438i	−1.28723	+	0.593492i
$406$	8.08824	+	9.29766i	0.401413	+	0.461435i
$407$	−12.4932	−	7.21294i	−0.619264	−	0.357532i
$408$	22.3105	−	4.96921i	1.10453	−	0.246013i
$409$			0.135526i			0.00670134i	0.999994	+	0.00335067i	$0.00106655\pi$
$409$			0.135526i			0.00670134i	−0.999994	+	0.00335067i	$0.998933\pi$
$410$	5.01294	−	21.9277i	0.247571	−	1.08293i
$411$	−0.538833	+	0.208871i	−0.0265787	+	0.0103029i
$412$	27.6231	−	18.8048i	1.36089	−	0.926445i
$413$	−1.25795	+	11.7668i	−0.0618995	+	0.579008i
$414$	−9.69223	−	17.1316i	−0.476347	−	0.841973i
$415$	22.2975	−	12.8735i	1.09454	−	0.631935i
$416$	5.70654	−	8.33857i	0.279786	−	0.408832i
$417$	−0.946625	−	2.44205i	−0.0463564	−	0.119587i
$418$	−15.1297	−	14.0482i	−0.740019	−	0.687119i
$419$	−10.2755	+	5.93257i	−0.501991	+	0.289825i	−0.729536	−	0.683943i	$-0.760264\pi$
$419$	−10.2755	+	5.93257i	−0.501991	+	0.289825i	0.227544	+	0.973768i	$0.426930\pi$
$420$	−9.61638	−	27.4115i	−0.469231	−	1.33755i
$421$	22.5571	+	13.0233i	1.09936	+	0.634719i	0.936054	−	0.351856i	$-0.114449\pi$
$421$	22.5571	+	13.0233i	1.09936	+	0.634719i	0.163311	+	0.986575i	$0.447783\pi$
$422$	0.374070	+	1.21422i	0.0182095	+	0.0591071i
$423$	−8.52987	−	2.70973i	−0.414736	−	0.131751i
$424$	6.18757	+	15.8145i	0.300495	+	0.768018i
$425$		−	23.5432i		−	1.14201i
$426$	−6.66301	−	2.65006i	−0.322824	−	0.128396i
$427$	30.5429	+	3.26522i	1.47807	+	0.158015i
$428$	−2.12276	−	28.5949i	−0.102608	−	1.38219i
$429$	−12.9121	−	10.3860i	−0.623404	−	0.501442i
$430$	0.561516	+	1.82266i	0.0270787	+	0.0878963i
$431$	31.6669	+	18.2829i	1.52534	+	0.880655i	0.999549	+	0.0300416i	$0.00956397\pi$
$431$	31.6669	+	18.2829i	1.52534	+	0.880655i	0.525791	+	0.850614i	$0.323769\pi$
$432$	20.3262	−	4.34109i	0.977945	−	0.208861i
$433$		−	12.0347i		−	0.578349i	−0.957276	−	0.289174i	$-0.906619\pi$
$433$		−	12.0347i		−	0.578349i	0.957276	−	0.289174i	$-0.0933808\pi$
$434$	35.3438	+	12.1556i	1.69656	+	0.583486i
$435$	6.53507	+	16.8588i	0.313333	+	0.808316i
$436$	20.3599	+	29.9074i	0.975061	+	1.43230i
$437$	−12.6453			−0.604908
$438$	−1.91826	+	1.51555i	−0.0916582	+	0.0724157i
$439$	6.93057			0.330778			0.165389	−	0.986228i	$-0.447112\pi$
$439$	6.93057			0.330778			0.165389	+	0.986228i	$0.447112\pi$
$440$	37.5098	+	29.9776i	1.78821	+	1.42912i
$441$	−18.2180	−	10.4453i	−0.867523	−	0.497397i
$442$	2.62662	−	11.4895i	0.124936	−	0.546498i
$443$	−30.3331			−1.44117			−0.720584	−	0.693367i	$-0.756126\pi$
$443$	−30.3331			−1.44117			−0.720584	+	0.693367i	$0.756126\pi$
$444$	0.742776	−	9.30033i	0.0352506	−	0.441374i
$445$			22.1201i			1.04859i
$446$	13.0526	−	14.0575i	0.618060	−	0.665643i
$447$	−19.3625	+	24.0719i	−0.915817	+	1.13856i
$448$	2.44551	+	21.0243i	0.115539	+	0.993303i
$449$	22.7034			1.07144			0.535721	−	0.844395i	$-0.320040\pi$
$449$	22.7034			1.07144			0.535721	+	0.844395i	$0.320040\pi$
$450$	0.187173	−	21.4077i	0.00882344	−	1.00917i
$451$	23.2771	+	13.4390i	1.09607	+	0.632819i
$452$	−0.840684	−	11.3245i	−0.0395424	−	0.532661i
$453$	−8.30353	−	21.4209i	−0.390134	−	1.00644i
$454$	4.75347	−	1.46443i	0.223092	−	0.0687291i
$455$	−14.8939	−	1.59225i	−0.698237	−	0.0746457i
$456$	4.00271	−	12.7388i	0.187444	−	0.596549i
$457$	27.1520			1.27012			0.635059	−	0.772464i	$-0.280976\pi$
$457$	27.1520			1.27012			0.635059	+	0.772464i	$0.280976\pi$
$458$	22.4887	−	24.2201i	1.05083	−	1.13173i
$459$	20.2014	−	13.4037i	0.942921	−	0.625631i
$460$	29.3289	−	2.17725i	1.36747	−	0.101515i
$461$	0.861717	−	1.49254i	0.0401342	−	0.0695144i	−0.845261	−	0.534354i	$-0.820555\pi$
$461$	0.861717	−	1.49254i	0.0401342	−	0.0695144i	0.885395	+	0.464840i	$0.153888\pi$
$462$	34.6861	−	1.33787i	1.61374	−	0.0622433i
$463$	−9.97910	+	5.76144i	−0.463768	+	0.267757i	−0.713627	−	0.700525i	$-0.752949\pi$
$463$	−9.97910	+	5.76144i	−0.463768	+	0.267757i	0.249859	+	0.968282i	$0.419616\pi$
$464$	−1.94528	−	13.0299i	−0.0903075	−	0.604896i
$465$	42.7304	+	34.3707i	1.98157	+	1.59390i
$466$	−5.11147	−	16.5916i	−0.236784	−	0.768591i
$467$	16.4233	−	9.48200i	0.759980	−	0.438775i	−0.0693086	−	0.997595i	$-0.522079\pi$
$467$	16.4233	−	9.48200i	0.759980	−	0.438775i	0.829289	+	0.558821i	$0.188746\pi$
$468$	2.47971	−	10.4264i	0.114625	−	0.481960i
$469$	−33.6563	−	3.59806i	−1.55410	−	0.166143i
$470$	9.09900	−	9.79951i	0.419706	−	0.452018i
$471$	−1.54957	+	9.99590i	−0.0714003	+	0.460587i
$472$	7.89813	−	9.88263i	0.363541	−	0.454885i
$473$	−2.27895			−0.104786
$474$	16.9903	+	6.75752i	0.780392	+	0.310383i
$475$	−11.9110	−	6.87683i	−0.546515	−	0.315530i
$476$	11.6451	+	21.7696i	0.533754	+	0.997808i
$477$	12.1400	+	13.3061i	0.555853	+	0.609243i
$478$	−39.0882	+	12.0421i	−1.78785	+	0.550795i
$479$	0.225098	+	0.389881i	0.0102850	+	0.0178141i	0.871122	−	0.491067i	$-0.163393\pi$
$479$	0.225098	+	0.389881i	0.0102850	+	0.0178141i	−0.860837	+	0.508881i	$0.830059\pi$
$480$	−7.09033	+	30.2348i	−0.323628	+	1.38003i
$481$	−4.16629	−	2.40541i	−0.189966	−	0.109677i
$482$	−5.50203	+	1.69504i	−0.250611	+	0.0772071i
$483$	15.0108	−	15.0559i	0.683014	−	0.685068i
$484$	−29.2438	+	19.9081i	−1.32926	+	0.904913i
$485$	−37.3785	+	21.5805i	−1.69727	+	0.979918i
$486$	18.4755	−	12.0273i	0.838067	−	0.545567i
$487$	20.8671	+	12.0476i	0.945577	+	0.545929i	0.891704	−	0.452618i	$-0.149510\pi$
$487$	20.8671	+	12.0476i	0.945577	+	0.545929i	0.0538731	+	0.998548i	$0.482843\pi$
$488$	−25.6521	−	20.5010i	−1.16122	−	0.928035i
$489$	−6.65925	+	2.58136i	−0.301141	+	0.116733i
$490$	25.7280	−	17.9605i	1.16227	−	0.811374i
$491$	−13.3040	−	23.0432i	−0.600402	−	1.03993i	−0.992760	−	0.120114i	$-0.961674\pi$
$491$	−13.3040	−	23.0432i	−0.600402	−	1.03993i	0.392358	−	0.919812i	$-0.371659\pi$
$492$	−1.38393	+	17.3282i	−0.0623923	+	0.781216i
$493$	−7.68339	−	13.3080i	−0.346043	−	0.599364i
$494$	−5.04553	−	4.68486i	−0.227009	−	0.210782i
$495$	48.5395	+	15.4198i	2.18169	+	0.693067i
$496$	−24.8686	−	31.2739i	−1.11663	−	1.40424i
$497$	0.823318	−	7.70132i	0.0369308	−	0.345452i
$498$	−15.6130	+	12.3352i	−0.699634	+	0.552754i
$499$	6.47254	−	11.2108i	0.289751	−	0.501863i	−0.684000	−	0.729482i	$-0.739761\pi$
$499$	6.47254	−	11.2108i	0.289751	−	0.501863i	0.973750	+	0.227620i	$0.0730943\pi$
$500$	0.262786	+	0.126778i	0.0117521	+	0.00566967i
$501$	−16.9634	+	6.57563i	−0.757869	+	0.293777i
$502$	5.33137	−	23.3206i	0.237951	−	1.04085i
$503$	−19.2426			−0.857984			−0.428992	−	0.903308i	$-0.641131\pi$
$503$	−19.2426			−0.857984			−0.428992	+	0.903308i	$0.641131\pi$
$504$	10.4158	+	19.8875i	0.463954	+	0.885859i
$505$	2.75245			0.122482
$506$	−7.83189	+	34.2585i	−0.348170	+	1.52297i
$507$	13.2392	+	10.6491i	0.587972	+	0.472942i
$508$	3.94923	−	8.18600i	0.175219	−	0.363195i
$509$	1.92253	−	3.32991i	0.0852145	−	0.147596i	−0.820268	−	0.571979i	$-0.806176\pi$
$509$	1.92253	−	3.32991i	0.0852145	−	0.147596i	0.905483	+	0.424383i	$0.139509\pi$
$510$	5.23591	+	35.8430i	0.231850	+	1.58716i
$511$	−2.13351	−	1.55590i	−0.0943811	−	0.0688292i
$512$	9.88184	−	20.3556i	0.436720	−	0.899598i
$513$	−0.880506	−	14.1354i	−0.0388753	−	0.624095i
$514$	−2.65074	−	2.46125i	−0.116919	−	0.108561i
$515$	26.4787	+	45.8624i	1.16679	+	2.02094i
$516$	−0.632998	−	1.33107i	−0.0278662	−	0.0585970i
$517$	7.98955	+	13.8383i	0.351380	+	0.608608i
$518$	9.89164	−	1.92645i	0.434614	−	0.0846435i
$519$	−0.826400	+	5.33091i	−0.0362749	+	0.234001i
$520$	12.5090	+	9.99707i	0.548554	+	0.438401i
$521$	−6.35138	−	3.66697i	−0.278259	−	0.160653i	0.354376	−	0.935103i	$-0.384693\pi$
$521$	−6.35138	−	3.66697i	−0.278259	−	0.160653i	−0.632635	+	0.774450i	$0.718027\pi$
$522$	−6.88064	−	12.1620i	−0.301158	−	0.532315i
$523$	−22.2694	+	12.8572i	−0.973772	+	0.562207i	−0.900384	−	0.435096i	$-0.856714\pi$
$523$	−22.2694	+	12.8572i	−0.973772	+	0.562207i	−0.0733878	+	0.997303i	$0.523381\pi$
$524$	25.4486	+	37.3825i	1.11173	+	1.63306i
$525$	22.3269	−	6.01842i	0.974424	−	0.262665i
$526$	−29.6306	+	9.12847i	−1.29195	+	0.398020i
$527$	−40.3620	−	23.3030i	−1.75820	−	1.01510i
$528$	−32.0326	−	18.7339i	−1.39404	−	0.815287i
$529$	−0.738006	−	1.27826i	−0.0320872	−	0.0555767i
$530$	−25.7195	+	7.92356i	−1.11718	+	0.344178i
$531$	4.06261	−	12.7886i	0.176302	−	0.554977i
$532$	14.4152	+	0.467239i	0.624976	+	0.0202574i
$533$	7.76255	+	4.48171i	0.336233	+	0.194124i
$534$	−2.47098	−	16.9154i	−0.106930	−	0.731999i
$535$	45.4411			1.96459
$536$	28.2670	+	22.5908i	1.22095	+	0.975772i
$537$	2.04567	+	1.64546i	0.0882774	+	0.0710070i
$538$	11.7470	−	12.6514i	0.506450	−	0.545440i
$539$	11.4589	+	35.6992i	0.493569	+	1.53767i
$540$	4.47601	+	32.6334i	0.192617	+	1.40432i
$541$	24.8063	−	14.3219i	1.06650	−	0.615747i	0.139280	−	0.990253i	$-0.455521\pi$
$541$	24.8063	−	14.3219i	1.06650	−	0.615747i	0.927224	+	0.374506i	$0.122188\pi$
$542$	10.1312	+	32.8855i	0.435174	+	1.41255i
$543$	0.731632	−	4.71959i	0.0313973	−	0.202537i
$544$	2.01842	−	26.3159i	0.0865391	−	1.12828i
$545$	−49.6551	+	28.6684i	−2.12699	+	1.22802i
$546$	11.5673	−	0.446159i	0.495035	−	0.0190938i
$547$	19.2927	−	33.4159i	0.824896	−	1.42876i	−0.0771029	−	0.997023i	$-0.524567\pi$
$547$	19.2927	−	33.4159i	0.824896	−	1.42876i	0.901999	−	0.431739i	$-0.142100\pi$
$548$	0.0494016	+	0.665470i	0.00211033	+	0.0284275i
$549$	−33.1950	−	10.5452i	−1.41673	−	0.450059i
$550$	−26.0077	+	28.0099i	−1.10897	+	1.19435i
$551$	−8.97708			−0.382436
$552$	−22.1847	+	4.94120i	−0.944243	+	0.210311i
$553$	−2.09942	+	19.6380i	−0.0892764	+	0.835092i
$554$	13.8077	−	4.25380i	0.586631	−	0.180727i
$555$	14.6113	+	2.26505i	0.620216	+	0.0961461i
$556$	−3.01598	+	0.223893i	−0.127906	+	0.00949519i
$557$	12.7001	+	7.33238i	0.538119	+	0.310683i	0.744316	−	0.667827i	$-0.232776\pi$
$557$	12.7001	+	7.33238i	0.538119	+	0.310683i	−0.206197	+	0.978510i	$0.566109\pi$
$558$	−36.5155	−	21.5101i	−1.54583	−	0.910596i
$559$	−0.759997			−0.0321444
$560$	−33.5142	+	1.39829i	−1.41623	+	0.0590884i
$561$	−42.7735	−	6.63076i	−1.80590	−	0.279951i
$562$	27.7040	−	29.8368i	1.16862	−	1.25859i
$563$			29.1210i			1.22730i	0.789577	+	0.613651i	$0.210300\pi$
$563$			29.1210i			1.22730i	−0.789577	+	0.613651i	$0.789700\pi$
$564$	−5.86337	+	8.51015i	−0.246892	+	0.358342i
$565$	17.9962			0.757105
$566$	2.72254	−	11.9090i	0.114437	−	0.500573i
$567$	17.8753	+	15.7313i	0.750693	+	0.660651i
$568$	−5.16927	+	6.46812i	−0.216898	+	0.271396i
$569$	−20.6987			−0.867734			−0.433867	−	0.900977i	$-0.642851\pi$
$569$	−20.6987			−0.867734			−0.433867	+	0.900977i	$0.642851\pi$
$570$	19.6631	+	7.82055i	0.823597	+	0.327567i
$571$	−8.00204			−0.334875			−0.167438	−	0.985883i	$-0.553549\pi$
$571$	−8.00204			−0.334875			−0.167438	+	0.985883i	$0.553549\pi$
$572$	−15.8171	+	10.7677i	−0.661346	+	0.450220i
$573$	13.2767	+	2.05817i	0.554644	+	0.0859811i
$574$	−18.4299	+	3.58933i	−0.769251	+	0.149816i
$575$			23.4105i			0.976286i
$576$	2.04455	−	23.9128i	0.0851896	−	0.996365i
$577$	25.7178	+	14.8482i	1.07065	+	0.618139i	0.928358	−	0.371686i	$-0.121220\pi$
$577$	25.7178	+	14.8482i	1.07065	+	0.618139i	0.142289	+	0.989825i	$0.454554\pi$
$578$	−1.98558	−	6.44509i	−0.0825891	−	0.268080i
$579$	1.31233	−	8.46554i	0.0545386	−	0.351816i
$580$	20.8209	−	1.54566i	0.864542	−	0.0641799i
$581$	−17.3649	−	12.6637i	−0.720418	−	0.525378i
$582$	26.1728	−	20.6781i	1.08490	−	0.857135i
$583$		−	32.1584i		−	1.33186i
$584$	1.02857	+	2.62885i	0.0425623	+	0.108783i
$585$	16.1872	+	5.14226i	0.669257	+	0.212606i
$586$	4.46700	+	14.4997i	0.184530	+	0.598977i
$587$	−9.59608	−	5.54030i	−0.396072	−	0.228673i	0.288715	−	0.957415i	$-0.406772\pi$
$587$	−9.59608	−	5.54030i	−0.396072	−	0.228673i	−0.684788	+	0.728742i	$0.740105\pi$
$588$	−17.6680	+	16.6085i	−0.728615	+	0.684923i
$589$	−23.5790	+	13.6133i	−0.971554	+	0.560927i
$590$	14.6921	+	13.6419i	0.604865	+	0.561627i
$591$	12.9222	+	2.00321i	0.531549	+	0.0824009i
$592$	−10.0231	−	3.94996i	−0.411945	−	0.162342i
$593$	30.1862	−	17.4280i	1.23960	−	0.715682i	0.270585	−	0.962696i	$-0.412783\pi$
$593$	30.1862	−	17.4280i	1.23960	−	0.715682i	0.969012	+	0.247014i	$0.0794494\pi$
$594$	−38.8408	−	6.36935i	−1.59366	−	0.261337i
$595$	−35.7715	+	15.8502i	−1.46649	+	0.649794i
$596$	20.0741	+	29.4876i	0.822266	+	1.20786i
$597$	−20.5864	−	16.5589i	−0.842544	−	0.677710i
$598$	−2.61182	+	11.4247i	−0.106805	+	0.467190i
$599$		−	33.2106i		−	1.35695i	−0.734624	−	0.678475i	$-0.762641\pi$
$599$		−	33.2106i		−	1.35695i	0.734624	−	0.678475i	$-0.237359\pi$
$600$	−23.5836	−	7.41029i	−0.962795	−	0.302524i
$601$	14.6277	+	8.44532i	0.596677	+	0.344492i	0.767733	−	0.640770i	$-0.221385\pi$
$601$	14.6277	+	8.44532i	0.596677	+	0.344492i	−0.171056	+	0.985261i	$0.554718\pi$
$602$	1.20113	−	1.04489i	0.0489543	−	0.0425864i
$603$	36.5788	+	11.6202i	1.48960	+	0.473209i
$604$	−26.4553	+	1.96393i	−1.07645	+	0.0799111i
$605$	−28.0322	−	48.5533i	−1.13967	−	1.97397i
$606$	−2.10481	+	0.307468i	−0.0855019	+	0.0124900i
$607$	0.322354	−	0.558333i	0.0130839	−	0.0226620i	−0.859409	−	0.511288i	$-0.829168\pi$
$607$	0.322354	−	0.558333i	0.0130839	−	0.0226620i	0.872493	+	0.488626i	$0.162502\pi$
$608$	−12.7242	−	8.70786i	−0.516034	−	0.353150i
$609$	10.6563	−	10.6884i	0.431817	−	0.433116i
$610$	35.4098	−	38.1359i	1.43370	−	1.54408i
$611$	2.66439	+	4.61487i	0.107790	+	0.186698i
$612$	−8.00785	−	26.8244i	−0.323698	−	1.08431i
$613$	−12.0000	−	6.92823i	−0.484677	−	0.279829i	0.237686	−	0.971342i	$-0.423611\pi$
$613$	−12.0000	−	6.92823i	−0.484677	−	0.279829i	−0.722364	+	0.691513i	$0.756944\pi$
$614$	−8.98289	+	39.2932i	−0.362520	+	1.58575i
$615$	−27.2236	−	4.22021i	−1.09776	−	0.170175i
$616$	10.1939	−	38.7639i	0.410723	−	1.56184i
$617$	21.7443	+	37.6623i	0.875394	+	1.51623i	0.856343	+	0.516408i	$0.172731\pi$
$617$	21.7443	+	37.6623i	0.875394	+	1.51623i	0.0190506	+	0.999819i	$0.493936\pi$
$618$	−25.3715	−	32.1133i	−1.02059	−	1.29179i
$619$	−7.18168	+	4.14635i	−0.288656	+	0.166656i	−0.637336	−	0.770586i	$-0.719964\pi$
$619$	−7.18168	+	4.14635i	−0.288656	+	0.166656i	0.348679	+	0.937242i	$0.386630\pi$
$620$	52.3438	−	35.6337i	2.10218	−	1.43109i
$621$	−20.0875	+	13.3281i	−0.806085	+	0.534839i
$622$	−43.6967	−	9.98957i	−1.75208	−	0.400545i
$623$	16.8816	−	7.48015i	0.676347	−	0.299686i
$624$	−10.6824	−	6.24746i	−0.427638	−	0.250099i
$625$	12.3839	−	21.4495i	0.495355	−	0.857980i
$626$	−3.43819	+	15.0394i	−0.137418	+	0.601096i
$627$	−15.8485	+	19.7032i	−0.632928	+	0.786869i
$628$	10.5199	+	5.07519i	0.419789	+	0.202522i
$629$	−12.5662			−0.501048
$630$	−32.6527	+	14.1280i	−1.30091	+	0.562874i
$631$			13.1848i			0.524877i	0.964949	+	0.262439i	$0.0845267\pi$
$631$			13.1848i			0.524877i	−0.964949	+	0.262439i	$0.915473\pi$
$632$	13.1814	−	16.4934i	0.524328	−	0.656072i
$633$	1.45088	−	0.562414i	0.0576674	−	0.0223540i
$634$	3.63718	−	15.9098i	0.144451	−	0.631860i
$635$	12.4740	+	7.20188i	0.495016	+	0.285798i
$636$	18.7827	−	8.93224i	0.744783	−	0.354186i
$637$	3.82136	+	11.9051i	0.151408	+	0.471698i
$638$	−5.55996	+	24.3205i	−0.220121	+	0.962859i
$639$	−2.65895	+	8.37005i	−0.105187	+	0.331114i
$640$	31.0111	+	18.0057i	1.22582	+	0.711738i
$641$	−22.6543	−	39.2383i	−0.894790	−	1.54982i	−0.834065	−	0.551666i	$-0.813992\pi$
$641$	−22.6543	−	39.2383i	−0.894790	−	1.54982i	−0.0607246	−	0.998155i	$-0.519341\pi$
$642$	−34.7490	+	5.07610i	−1.37143	+	0.200338i
$643$	−35.4400	+	20.4613i	−1.39762	+	0.806914i	−0.994142	−	0.108078i	$-0.965530\pi$
$643$	−35.4400	+	20.4613i	−1.39762	+	0.806914i	−0.403473	+	0.914991i	$0.632197\pi$
$644$	−11.5795	−	21.6469i	−0.456296	−	0.853006i
$645$	2.17792	−	0.844239i	0.0857554	−	0.0332419i
$646$	−17.5323	−	4.00808i	−0.689798	−	0.157696i
$647$	4.58077	−	7.93413i	0.180089	−	0.311923i	−0.761822	−	0.647787i	$-0.775695\pi$
$647$	4.58077	−	7.93413i	0.180089	−	0.311923i	0.941911	+	0.335864i	$0.109028\pi$
$648$	−7.06821	−	24.4549i	−0.277665	−	0.960678i
$649$	−20.7474	+	11.9785i	−0.814405	+	0.470197i
$650$	−8.67316	+	9.34089i	−0.340189	+	0.366380i
$651$	11.7812	−	44.2337i	0.461742	−	1.73365i
$652$	0.610537	+	8.22431i	0.0239105	+	0.322089i
$653$	−5.94553	−	3.43265i	−0.232666	−	0.134330i	0.379135	−	0.925341i	$-0.376222\pi$
$653$	−5.94553	−	3.43265i	−0.232666	−	0.134330i	−0.611802	+	0.791011i	$0.709555\pi$
$654$	34.7690	−	27.4697i	1.35957	−	1.07415i
$655$	−62.0659	+	35.8338i	−2.42512	+	1.40014i
$656$	18.6748	+	7.35950i	0.729128	+	0.287340i
$657$	2.01805	+	2.21188i	0.0787314	+	0.0862937i
$658$	−10.5557	−	3.63035i	−0.411504	−	0.141526i
$659$	−21.7591	+	37.6878i	−0.847613	+	1.46811i	0.0357196	+	0.999362i	$0.488628\pi$
$659$	−21.7591	+	37.6878i	−0.847613	+	1.46811i	−0.883333	+	0.468747i	$0.844706\pi$
$660$	33.3656	−	48.4272i	1.29876	−	1.88503i
$661$	8.49405			0.330380			0.165190	−	0.986262i	$-0.447176\pi$
$661$	8.49405			0.330380			0.165190	+	0.986262i	$0.447176\pi$
$662$	1.28045	+	0.292727i	0.0497663	+	0.0113772i
$663$	−14.2643	−	2.21126i	−0.553980	−	0.0858781i
$664$	8.37161	+	21.3966i	0.324882	+	0.830347i
$665$	−2.42968	+	22.7273i	−0.0942189	+	0.881325i
$666$	−11.4264	−	0.0999040i	−0.442763	−	0.00387120i
$667$	7.64008	+	13.2330i	0.295825	+	0.512384i
$668$	1.55525	+	20.9502i	0.0601745	+	0.810586i
$669$	−18.3069	−	14.7254i	−0.707785	−	0.569315i
$670$	−39.0194	+	42.0234i	−1.50745	+	1.62350i
$671$	31.0923	+	53.8534i	1.20030	+	2.07899i
$672$	25.4722	−	4.81305i	0.982613	−	0.185668i
$673$	−9.53159	+	16.5092i	−0.367416	+	0.636383i	−0.989161	−	0.146837i	$-0.953091\pi$
$673$	−9.53159	+	16.5092i	−0.367416	+	0.636383i	0.621745	+	0.783220i	$0.286424\pi$
$674$	−0.597953	−	1.94093i	−0.0230323	−	0.0747618i
$675$	−26.1692	+	1.63010i	−1.00725	+	0.0627424i
$676$	16.2177	−	11.0404i	0.623758	−	0.424631i
$677$	16.5958			0.637829			0.318915	−	0.947783i	$-0.396682\pi$
$677$	16.5958			0.637829			0.318915	+	0.947783i	$0.396682\pi$
$678$	−13.7618	+	2.01030i	−0.528517	+	0.0772053i
$679$	29.1096	+	21.2287i	1.11713	+	0.814684i
$680$	41.3535	+	6.27745i	1.58583	+	0.240729i
$681$	−2.20177	−	5.67999i	−0.0843720	−	0.217658i
$682$	22.2773	+	72.3111i	0.853042	+	2.76893i
$683$	2.60938	−	4.51957i	0.0998451	−	0.172937i	−0.811775	−	0.583970i	$-0.801499\pi$
$683$	2.60938	−	4.51957i	0.0998451	−	0.172937i	0.911620	+	0.411033i	$0.134832\pi$
$684$	−15.9101	−	3.78390i	−0.608337	−	0.144681i
$685$	−1.05752			−0.0404058
$686$	−22.4073	−	13.5615i	−0.855514	−	0.517780i
$687$	−31.5414	−	25.3707i	−1.20338	−	0.967952i
$688$	−1.68327	+	0.251303i	−0.0641743	+	0.00958084i
$689$		−	10.7243i		−	0.408564i
$690$	−5.20640	−	35.6409i	−0.198204	−	1.35683i
$691$			21.7803i			0.828562i	0.910149	+	0.414281i	$0.135967\pi$
$691$			21.7803i			0.828562i	−0.910149	+	0.414281i	$0.864033\pi$
$692$	5.61036	+	2.70665i	0.213274	+	0.102891i
$693$	−4.64611	−	42.2586i	−0.176491	−	1.60527i
$694$	20.2809	+	4.63645i	0.769852	+	0.175997i
$695$		−	4.79279i		−	0.181801i
$696$	−15.7492	+	3.50782i	−0.596972	+	0.132964i
$697$	23.4132			0.886838
$698$	−21.5120	+	23.1681i	−0.814239	+	0.876926i
$699$	−19.8255	+	7.68510i	−0.749871	+	0.290677i
$700$	0.865008	−	26.6870i	0.0326942	−	1.00868i
$701$		−	32.2438i		−	1.21783i	−0.793235	−	0.608915i	$-0.791605\pi$
$701$		−	32.2438i		−	1.21783i	0.793235	−	0.608915i	$-0.208395\pi$
$702$	−12.9528	−	2.12408i	−0.488873	−	0.0801683i
$703$	−3.67051	+	6.35752i	−0.138436	+	0.239778i
$704$	−31.4719	+	29.0789i	−1.18614	+	1.09595i
$705$	−12.7617	−	10.2651i	−0.480635	−	0.386604i
$706$	−6.19477	+	1.90846i	−0.233143	+	0.0718258i
$707$	−0.930769	−	2.10061i	−0.0350052	−	0.0790014i
$708$	−12.7590	−	8.79077i	−0.479513	−	0.330378i
$709$		−	24.2078i		−	0.909142i	−0.890710	−	0.454571i	$-0.849793\pi$
$709$		−	24.2078i		−	0.909142i	0.890710	−	0.454571i	$-0.150207\pi$
$710$	−9.61590	−	8.92851i	−0.360878	−	0.335081i
$711$	6.78020	−	21.3432i	0.254277	−	0.800433i
$712$	−19.5159	−	2.96251i	−0.731389	−	0.111025i
$713$	40.1345	+	23.1716i	1.50305	+	0.867785i
$714$	25.5840	−	16.1166i	0.957457	−	0.603150i
$715$	−15.1618	−	26.2610i	−0.567019	−	0.982106i
$716$	2.50591	−	1.70593i	0.0936502	−	0.0637536i
$717$	18.1053	+	46.7071i	0.676157	+	1.74431i
$718$	22.2142	−	6.84365i	0.829026	−	0.255403i
$719$	−7.32742	−	12.6915i	−0.273267	−	0.473312i	0.696430	−	0.717625i	$-0.254771\pi$
$719$	−7.32742	−	12.6915i	−0.273267	−	0.473312i	−0.969696	+	0.244313i	$0.921437\pi$
$720$	37.5524	+	6.03680i	1.39950	+	0.224978i
$721$	26.0471	−	35.7168i	0.970046	−	1.33016i
$722$	11.1343	−	11.9915i	0.414377	−	0.446279i
$723$	2.54849	+	6.57445i	0.0947795	+	0.244507i
$724$	−4.96699	−	2.39626i	−0.184597	−	0.0890563i
$725$			16.6194i			0.617230i
$726$	26.8601	+	33.9975i	0.996873	+	1.26176i
$727$	10.3117	−	17.8604i	0.382439	−	0.662404i	−0.608971	−	0.793192i	$-0.708417\pi$
$727$	10.3117	−	17.8604i	0.382439	−	0.662404i	0.991410	+	0.130788i	$0.0417508\pi$
$728$	3.39950	−	12.9272i	0.125994	−	0.479113i
$729$	−16.2974	−	21.5266i	−0.603608	−	0.797281i
$730$	−4.27538	+	1.31714i	−0.158239	+	0.0487496i
$731$	−1.71921	+	0.992587i	−0.0635873	+	0.0367121i
$732$	−22.8180	+	33.1183i	−0.843377	+	1.22409i
$733$	−2.17331	+	3.76428i	−0.0802730	+	0.139037i	−0.903367	−	0.428868i	$-0.858913\pi$
$733$	−2.17331	+	3.76428i	−0.0802730	+	0.139037i	0.823094	+	0.567905i	$0.192246\pi$
$734$	5.57069	+	18.0822i	0.205618	+	0.667427i
$735$	−24.1756	−	29.8715i	−0.891731	−	1.10183i
$736$	−2.00704	+	26.1675i	−0.0739806	+	0.964548i
$737$	−34.2617	−	59.3430i	−1.26205	−	2.18593i
$738$	21.2894	+	0.186139i	0.783674	+	0.00685189i
$739$	21.9380	−	37.9978i	0.807004	−	1.39777i	−0.107926	−	0.994159i	$-0.534421\pi$
$739$	21.9380	−	37.9978i	0.807004	−	1.39777i	0.914930	−	0.403612i	$-0.132246\pi$
$740$	7.41856	−	15.3773i	0.272712	−	0.565279i
$741$	−5.28523	+	6.57071i	−0.194158	+	0.241381i
$742$	14.7444	+	16.9491i	0.541285	+	0.622222i
$743$	−37.5962	+	21.7062i	−1.37927	+	0.796323i	−0.992072	−	0.125673i	$-0.959891\pi$
$743$	−37.5962	+	21.7062i	−1.37927	+	0.796323i	−0.387200	+	0.921996i	$0.626558\pi$
$744$	−36.0470	+	33.0965i	−1.32155	+	1.21338i
$745$	−48.9581	+	28.2660i	−1.79369	+	1.03558i
$746$	18.6237	+	17.2924i	0.681862	+	0.633119i
$747$	16.4251	+	18.0028i	0.600963	+	0.658687i
$748$	−21.7172	+	45.0157i	−0.794061	+	1.64594i
$749$	−15.3664	−	34.6796i	−0.561476	−	1.26717i
$750$	0.132063	−	0.332043i	0.00482225	−	0.0121245i
$751$	22.9059	+	13.2247i	0.835847	+	0.482577i	0.855851	−	0.517223i	$-0.173034\pi$
$751$	22.9059	+	13.2247i	0.835847	+	0.482577i	−0.0200031	+	0.999800i	$0.506368\pi$
$752$	7.42719	+	9.34019i	0.270842	+	0.340602i
$753$	−28.9529	−	4.48828i	−1.05510	−	0.163562i
$754$	−1.85416	+	8.11053i	−0.0675246	+	0.295368i
$755$		−	42.0410i		−	1.53003i
$756$	23.3914	−	14.4513i	0.850739	−	0.525589i
$757$		−	24.3621i		−	0.885454i	−0.896656	−	0.442727i	$-0.854011\pi$
$757$		−	24.3621i		−	0.885454i	0.896656	−	0.442727i	$-0.145989\pi$
$758$	22.6369	+	5.17505i	0.822208	+	0.187966i
$759$	42.5323	+	6.59338i	1.54383	+	0.239324i
$760$	15.2550	−	19.0880i	0.553356	−	0.692393i
$761$	3.57672	+	2.06502i	0.129656	+	0.0748569i	0.563425	−	0.826167i	$-0.309483\pi$
$761$	3.57672	+	2.06502i	0.129656	+	0.0748569i	−0.433769	+	0.901024i	$0.642817\pi$
$762$	−10.3434	−	4.11387i	−0.374703	−	0.149030i
$763$	38.6705	+	28.2011i	1.39996	+	1.02095i
$764$	6.74096	−	13.9727i	0.243879	−	0.505515i
$765$	43.3335	−	9.50866i	1.56672	−	0.343786i
$766$	21.3092	−	22.9497i	0.769933	−	0.829208i
$767$	−6.91893	+	3.99465i	−0.249828	+	0.144238i
$768$	−25.7257	−	10.3049i	−0.928295	−	0.371845i
$769$	0.551842	−	0.318606i	0.0198999	−	0.0114892i	−0.490017	−	0.871713i	$-0.663009\pi$
$769$	0.551842	−	0.318606i	0.0198999	−	0.0114892i	0.509917	+	0.860224i	$0.329676\pi$
$770$	60.0674	+	20.6586i	2.16468	+	0.744484i
$771$	−2.77666	+	3.45201i	−0.0999991	+	0.124321i
$772$	−8.90931	−	4.29818i	−0.320653	−	0.154695i
$773$	−18.4194	+	31.9033i	−0.662500	+	1.14748i	0.317457	+	0.948273i	$0.397171\pi$
$773$	−18.4194	+	31.9033i	−0.662500	+	1.14748i	−0.979957	+	0.199211i	$0.936162\pi$
$774$	−1.57115	+	0.888882i	−0.0564740	+	0.0319502i
$775$	25.2026	+	43.6521i	0.905303	+	1.56803i
$776$	−14.0337	−	35.8681i	−0.503782	−	1.28759i
$777$	−3.21234	−	11.9170i	−0.115242	−	0.427520i
$778$	0.0369231	−	0.0113751i	0.00132376	−	0.000407817i
$779$	6.83884	−	11.8452i	0.245027	−	0.424399i
$780$	11.1269	−	16.1498i	0.398408	−	0.578254i
$781$	13.5790	−	7.83985i	0.485896	−	0.280532i
$782$	9.01283	+	29.2552i	0.322298	+	1.04617i
$783$	−14.2604	+	9.46181i	−0.509625	+	0.338138i
$784$	12.4003	+	25.1044i	0.442868	+	0.896587i
$785$	−9.25519	+	16.0305i	−0.330332	+	0.572151i
$786$	43.4592	−	34.3354i	1.55014	−	1.22470i
$787$		−	32.8255i		−	1.17010i	−0.810997	−	0.585051i	$-0.801075\pi$
$787$		−	32.8255i		−	1.17010i	0.810997	−	0.585051i	$-0.198925\pi$
$788$	6.56096	−	13.5996i	0.233724	−	0.484466i
$789$	13.7246	+	35.4060i	0.488610	+	1.26049i
$790$	24.5201	+	22.7673i	0.872384	+	0.810023i
$791$	−6.08560	−	13.7343i	−0.216379	−	0.488335i
$792$	−20.1052	+	40.7597i	−0.714406	+	1.44833i
$793$	10.3688	+	17.9593i	0.368207	+	0.637753i
$794$	−10.2893	−	33.3985i	−0.365153	−	1.18527i
$795$	11.9131	+	30.7326i	0.422513	+	1.08997i
$796$	−25.2179	+	17.1674i	−0.893823	+	0.608482i
$797$	15.9448	+	27.6173i	0.564795	+	0.978254i	0.997069	+	0.0765115i	$0.0243782\pi$
$797$	15.9448	+	27.6173i	0.564795	+	0.978254i	−0.432273	+	0.901743i	$0.642288\pi$
$798$	−0.680813	−	17.6510i	−0.0241005	−	0.624840i
$799$	12.0544	+	6.95961i	0.426454	+	0.246213i
$800$	−16.1210	+	23.5565i	−0.569964	+	0.832848i
$801$	−20.4503	+	4.48741i	−0.722576	+	0.158555i
$802$	−28.0574	+	30.2175i	−0.990742	+	1.06702i
$803$		−	5.34572i		−	0.188646i
$804$	25.1440	−	36.4942i	0.886759	−	1.28705i
$805$	35.5698	−	15.7608i	1.25367	−	0.555496i
$806$	7.42914	+	24.1147i	0.261680	+	0.849402i
$807$	−16.4757	−	13.2524i	−0.579972	−	0.466507i
$808$	−0.368630	+	2.42840i	−0.0129684	+	0.0854307i
$809$	−11.3674	+	19.6890i	−0.399658	+	0.692228i	−0.993684	−	0.112218i	$-0.964205\pi$
$809$	−11.3674	+	19.6890i	−0.399658	+	0.692228i	0.594025	+	0.804446i	$0.297538\pi$
$810$	39.4783	−	8.30163i	1.38713	−	0.291690i
$811$		−	48.6530i		−	1.70844i	−0.519914	−	0.854218i	$-0.674036\pi$
$811$		−	48.6530i		−	1.70844i	0.519914	−	0.854218i	$-0.325964\pi$
$812$	−8.22043	−	15.3674i	−0.288481	−	0.539290i
$813$	39.2954	−	15.2323i	1.37815	−	0.534220i
$814$	14.9503	+	13.8816i	0.524009	+	0.486551i
$815$	−13.0695			−0.457806
$816$	−32.3244	−	0.180908i	−1.13158	−	0.00633305i
$817$			1.15971i			0.0405732i
$818$	0.0427144	−	0.186843i	0.00149347	−	0.00653280i
$819$	−1.54941	−	14.0926i	−0.0541407	−	0.492435i
$820$	−13.8221	+	28.6506i	−0.482690	+	1.00052i
$821$		−	30.9122i		−	1.07884i	−0.842036	−	0.539421i	$-0.818643\pi$
$821$		−	30.9122i		−	1.07884i	0.842036	−	0.539421i	$-0.181357\pi$
$822$	0.808691	−	0.118133i	0.0282063	−	0.00412036i
$823$		−	46.9111i		−	1.63522i	−0.575774	−	0.817609i	$-0.695299\pi$
$823$		−	46.9111i		−	1.63522i	0.575774	−	0.817609i	$-0.304701\pi$
$824$	−44.0092	+	17.2190i	−1.53313	+	0.599854i
$825$	36.4769	+	29.3406i	1.26996	+	1.02151i
$826$	5.44287	−	15.8258i	0.189382	−	0.550651i
$827$	14.2867			0.496798			0.248399	−	0.968658i	$-0.420096\pi$
$827$	14.2867			0.496798			0.248399	+	0.968658i	$0.420096\pi$
$828$	7.96271	+	26.6732i	0.276723	+	0.926957i
$829$	12.1872	−	21.1088i	0.423279	−	0.733140i	−0.572979	−	0.819570i	$-0.694212\pi$
$829$	12.1872	−	21.1088i	0.423279	−	0.733140i	0.996258	+	0.0864296i	$0.0275458\pi$
$830$	−34.7978	+	10.7204i	−1.20785	+	0.372110i
$831$	−6.39559	−	16.4990i	−0.221861	−	0.572342i
$832$	−10.4954	+	9.69737i	−0.363863	+	0.336196i
$833$	24.1930	+	21.9401i	0.838238	+	0.760179i
$834$	0.535390	+	3.66507i	0.0185390	+	0.126911i
$835$	−33.2926			−1.15214
$836$	16.4309	+	24.1360i	0.568274	+	0.834760i
$837$	−23.1076	+	46.4774i	−0.798715	+	1.60649i
$838$	16.0361	−	4.94033i	0.553957	−	0.170661i
$839$	−5.21888	+	9.03937i	−0.180176	+	0.312074i	−0.941940	−	0.335780i	$-0.891000\pi$
$839$	−5.21888	+	9.03937i	−0.180176	+	0.312074i	0.761764	+	0.647854i	$0.224333\pi$
$840$	4.61817	+	40.8216i	0.159342	+	1.40848i
$841$	−9.07621	−	15.7205i	−0.312973	−	0.542085i
$842$	−26.9936	−	25.0640i	−0.930261	−	0.863762i
$843$	−38.8560	−	31.2543i	−1.33827	−	1.07645i
$844$	−0.133021	−	1.79187i	−0.00457876	−	0.0616787i
$845$	15.5458	+	26.9262i	0.534792	+	0.926288i
$846$	10.9056	+	6.42415i	0.374943	+	0.220867i
$847$	−27.5754	+	37.8124i	−0.947501	+	1.29925i
$848$	−3.54614	−	23.7527i	−0.121775	−	0.815672i
$849$	−14.7852	−	2.29201i	−0.507427	−	0.0786615i
$850$	−7.42023	+	32.4578i	−0.254512	+	1.11329i
$851$	12.4954			0.428336
$852$	8.35070	+	5.75351i	0.286090	+	0.197112i
$853$	5.10824	−	8.84772i	0.174903	−	0.302940i	−0.765225	−	0.643763i	$-0.777372\pi$
$853$	5.10824	−	8.84772i	0.174903	−	0.302940i	0.940128	+	0.340823i	$0.110706\pi$
$854$	−41.0787	−	14.1279i	−1.40568	−	0.483448i
$855$	7.84680	−	24.7007i	0.268355	−	0.844747i
$856$	−6.08584	+	40.0913i	−0.208010	+	1.37029i
$857$	30.8384	−	17.8046i	1.05342	−	0.608193i	0.129816	−	0.991538i	$-0.458561\pi$
$857$	30.8384	−	17.8046i	1.05342	−	0.608193i	0.923605	+	0.383345i	$0.125228\pi$
$858$	14.5278	+	18.3882i	0.495972	+	0.627764i
$859$	−19.2042	−	11.0876i	−0.655240	−	0.378303i	0.135221	−	0.990815i	$-0.456826\pi$
$859$	−19.2042	−	11.0876i	−0.655240	−	0.378303i	−0.790461	+	0.612513i	$0.790159\pi$
$860$	−0.199677	−	2.68977i	−0.00680894	−	0.0917205i
$861$	5.98517	+	22.2035i	0.203974	+	0.756694i
$862$	−37.8951	−	35.1862i	−1.29071	−	1.19845i
$863$	6.83577	−	3.94664i	0.232692	−	0.134345i	−0.379121	−	0.925347i	$-0.623774\pi$
$863$	6.83577	−	3.94664i	0.232692	−	0.134345i	0.611814	+	0.791002i	$0.290440\pi$
$864$	−29.3909	−	0.421483i	−0.999897	−	0.0143392i
$865$	−4.93588	+	8.54920i	−0.167825	+	0.290681i
$866$	−3.79302	+	16.5915i	−0.128892	+	0.563803i
$867$	−7.70133	+	2.98531i	−0.261551	+	0.101387i
$868$	−44.8955	−	27.8977i	−1.52385	−	0.946909i
$869$	−34.6258	+	19.9912i	−1.17460	+	0.678156i
$870$	−3.69609	−	25.3020i	−0.125309	−	0.857817i
$871$	−11.4258	−	19.7900i	−0.387147	−	0.670559i
$872$	−18.6430	−	47.6486i	−0.631331	−	1.61359i
$873$	−27.5342	−	30.1789i	−0.931891	−	1.02140i
$874$	17.4334	+	3.98549i	0.589694	+	0.134811i
$875$	0.383787	+	0.0410291i	0.0129744	+	0.00138704i
$876$	3.12227	−	1.48482i	0.105492	−	0.0501673i
$877$	27.3184	+	15.7723i	0.922477	+	0.532592i	0.884424	−	0.466684i	$-0.154551\pi$
$877$	27.3184	+	15.7723i	0.922477	+	0.532592i	0.0380523	+	0.999276i	$0.487885\pi$
$878$	−9.55481	−	2.18434i	−0.322459	−	0.0737180i
$879$	17.3259	−	6.71614i	0.584387	−	0.226530i
$880$	−42.2646	−	53.1506i	−1.42474	−	1.79171i
$881$			37.4546i			1.26188i	0.775832	+	0.630939i	$0.217330\pi$
$881$			37.4546i			1.26188i	−0.775832	+	0.630939i	$0.782670\pi$
$882$	21.8241	+	20.1423i	0.734854	+	0.678225i
$883$	50.0676			1.68491			0.842454	−	0.538769i	$-0.181110\pi$
$883$	50.0676			1.68491			0.842454	+	0.538769i	$0.181110\pi$
$884$	−7.24237	+	15.0120i	−0.243587	+	0.504910i
$885$	15.3901	−	19.1333i	0.517332	−	0.643159i
$886$	41.8186	+	9.56022i	1.40492	+	0.321182i
$887$	12.6301	−	21.8759i	0.424076	−	0.734522i	−0.572257	−	0.820074i	$-0.693932\pi$
$887$	12.6301	−	21.8759i	0.424076	−	0.734522i	0.996334	+	0.0855523i	$0.0272655\pi$
$888$	−3.95525	+	12.5878i	−0.132730	+	0.422418i
$889$	1.27809	−	11.9553i	0.0428658	−	0.400967i
$890$	6.97170	−	30.4958i	0.233692	−	1.02222i
$891$	−4.40877	+	48.0034i	−0.147699	+	1.60818i
$892$	−22.4255	+	15.2665i	−0.750863	+	0.511160i
$893$	7.04203	−	4.06572i	0.235652	−	0.136054i
$894$	34.2809	−	27.0841i	1.14653	−	0.905827i
$895$	2.40209	+	4.16055i	0.0802931	+	0.139072i
$896$	3.25483	−	29.7558i	0.108736	−	0.994071i
$897$	14.1839	+	2.19879i	0.473586	+	0.0734155i
$898$	−31.3000	−	7.15555i	−1.04449	−	0.238784i
$899$	28.4920	+	16.4498i	0.950261	+	0.548633i
$900$	−7.00520	+	29.4546i	−0.233507	+	0.981820i
$901$	−14.0064	−	24.2598i	−0.466621	−	0.808211i
$902$	−27.8552	−	25.8640i	−0.927477	−	0.861177i
$903$	−1.38079	−	1.37665i	−0.0459498	−	0.0458120i
$904$	−2.41020	+	15.8775i	−0.0801620	+	0.528077i
$905$	4.36985	−	7.56881i	0.145259	−	0.251596i
$906$	4.69629	+	32.1489i	0.156024	+	1.06808i
$907$	−22.3047	−	38.6328i	−0.740615	−	1.28278i	−0.952216	−	0.305426i	$-0.901201\pi$
$907$	−22.3047	−	38.6328i	−0.740615	−	1.28278i	0.211601	−	0.977356i	$-0.432132\pi$
$908$	−7.01491	+	0.520757i	−0.232798	+	0.0172819i
$909$	0.558376	+	2.54467i	0.0185202	+	0.0844013i
$910$	20.0316	+	6.88933i	0.664041	+	0.228379i
$911$	−12.9121	−	7.45481i	−0.427797	−	0.246989i	0.270611	−	0.962689i	$-0.412774\pi$
$911$	−12.9121	−	7.45481i	−0.427797	−	0.246989i	−0.698408	+	0.715700i	$0.746108\pi$
$912$	−9.53327	+	16.3007i	−0.315678	+	0.539772i
$913$		−	43.5094i		−	1.43995i
$914$	−37.4330	−	8.55763i	−1.23817	−	0.283061i
$915$	−49.6638	−	39.9477i	−1.64183	−	1.32063i
$916$	−38.6375	+	26.3030i	−1.27662	+	0.869077i
$917$	48.3358	+	35.2498i	1.59619	+	1.16405i
$918$	−32.0751	+	12.1120i	−1.05864	+	0.399755i
$919$	4.04861	−	2.33746i	0.133551	−	0.0771058i	−0.431736	−	0.902000i	$-0.642099\pi$
$919$	4.04861	−	2.33746i	0.133551	−	0.0771058i	0.565287	+	0.824894i	$0.308765\pi$
$920$	−41.1203	−	6.24206i	−1.35570	−	0.205795i
$921$	48.7831	+	7.56237i	1.60746	+	0.249188i
$922$	−1.65841	+	1.78609i	−0.0546169	+	0.0588217i
$923$	4.52840	−	2.61447i	0.149054	−	0.0860564i
$924$	−48.2415	−	9.08774i	−1.58703	−	0.298965i
$925$	11.7698	+	6.79529i	0.386988	+	0.223428i
$926$	15.5735	−	4.79782i	0.511777	−	0.157666i
$927$	−37.0287	+	33.7838i	−1.21618	+	1.10960i
$928$	−1.42483	+	18.5767i	−0.0467722	+	0.609809i
$929$			1.35417i			0.0444290i	0.999753	+	0.0222145i	$0.00707168\pi$
$929$			1.35417i			0.0444290i	−0.999753	+	0.0222145i	$0.992928\pi$
$930$	−48.0773	−	60.8525i	−1.57652	−	1.99543i
$931$	18.1666	−	5.83118i	0.595385	−	0.191109i
$932$	1.81766	+	24.4850i	0.0595394	+	0.802032i
$933$	−8.40985	+	54.2500i	−0.275326	+	1.77606i
$934$	−25.6304	+	7.89611i	−0.838653	+	0.258369i
$935$	−68.5959	−	39.6039i	−2.24333	−	1.29518i
$936$	−6.70477	+	13.5927i	−0.219152	+	0.444293i
$937$		−	26.0498i		−	0.851009i	−0.904956	−	0.425505i	$-0.860097\pi$
$937$		−	26.0498i		−	0.851009i	0.904956	−	0.425505i	$-0.139903\pi$
$938$	45.2661	+	15.5681i	1.47799	+	0.508316i
$939$	18.6716	+	2.89448i	0.609325	+	0.0944578i
$940$	−15.6329	+	10.6423i	−0.509888	+	0.347113i
$941$	27.8960			0.909383			0.454691	−	0.890649i	$-0.349750\pi$
$941$	27.8960			0.909383			0.454691	+	0.890649i	$0.349750\pi$
$942$	5.28676	−	13.2924i	0.172252	−	0.433091i
$943$	−23.2812			−0.758140
$944$	−14.0035	+	11.1354i	−0.455774	+	0.362425i
$945$	20.0948	+	38.6639i	0.653685	+	1.25774i
$946$	3.14187	+	0.718269i	0.102151	+	0.0233529i
$947$	12.2487			0.398029			0.199015	−	0.979997i	$-0.436226\pi$
$947$	12.2487			0.398029			0.199015	+	0.979997i	$0.436226\pi$
$948$	−21.2939	−	14.6712i	−0.691592	−	0.476497i
$949$		−	1.78272i		−	0.0578694i
$950$	14.2537	+	13.2348i	0.462450	+	0.429392i
$951$	−19.7523	−	3.06200i	−0.640511	−	0.0992923i
$952$	−9.19330	−	33.6828i	−0.297957	−	1.09167i
$953$	−16.7007			−0.540987			−0.270494	−	0.962722i	$-0.587187\pi$
$953$	−16.7007			−0.540987			−0.270494	+	0.962722i	$0.587187\pi$
$954$	−12.5430	−	22.1706i	−0.406096	−	0.717799i
$955$	21.2919	+	12.2929i	0.688991	+	0.397789i
$956$	57.6842	−	4.28223i	1.86564	−	0.138497i
$957$	30.1943	+	4.68072i	0.976042	+	0.151306i
$958$	−0.187450	−	0.608453i	−0.00605622	−	0.0196582i
$959$	0.357612	+	0.807077i	0.0115479	+	0.0260619i
$960$	19.3043	−	39.4485i	0.623044	−	1.27319i
$961$	68.7817			2.21876
$962$	4.98571	+	4.62931i	0.160746	+	0.149255i
$963$	9.21843	+	42.0108i	0.297060	+	1.35378i
$964$	8.11959	−	0.602763i	0.261514	−	0.0194137i
$965$	7.83823	−	13.5762i	0.252321	−	0.437034i
$966$	−25.4398	+	16.0258i	−0.818511	+	0.515621i
$967$	−0.261329	+	0.150878i	−0.00840376	+	0.00485191i	−0.504196	−	0.863589i	$-0.668211\pi$
$967$	−0.261329	+	0.150878i	−0.00840376	+	0.00485191i	0.495792	+	0.868441i	$0.334878\pi$
$968$	46.5913	−	18.2293i	1.49750	−	0.585912i
$969$	−3.37425	+	21.7665i	−0.108397	+	0.699242i
$970$	58.3333	−	17.9711i	1.87297	−	0.577016i
$971$	−30.4664	+	17.5898i	−0.977713	+	0.564483i	−0.901579	−	0.432615i	$-0.857591\pi$
$971$	−30.4664	+	17.5898i	−0.977713	+	0.564483i	−0.0761342	+	0.997098i	$0.524258\pi$
$972$	−29.2619	+	10.7583i	−0.938576	+	0.345073i
$973$	−3.65775	+	1.62073i	−0.117262	+	0.0519583i
$974$	−24.9712	−	23.1862i	−0.800129	−	0.742933i
$975$	12.1645	+	9.78465i	0.389575	+	0.313359i
$976$	28.9038	+	36.3485i	0.925187	+	1.16349i
$977$	−19.4750			−0.623060			−0.311530	−	0.950236i	$-0.600841\pi$
$977$	−19.4750			−0.623060			−0.311530	+	0.950236i	$0.600841\pi$
$978$	9.99432	−	1.45996i	0.319583	−	0.0466844i
$979$	32.3724	+	18.6902i	1.03463	+	0.597342i
$980$	−41.1305	+	16.6524i	−1.31387	+	0.531942i
$981$	−36.5776	−	40.0909i	−1.16783	−	1.28000i
$982$	11.0789	+	35.9615i	0.353541	+	1.14758i
$983$	13.6550	+	23.6512i	0.435528	+	0.754357i	0.997339	−	0.0729091i	$-0.0232283\pi$
$983$	13.6550	+	23.6512i	0.435528	+	0.754357i	−0.561810	+	0.827266i	$0.689895\pi$
$984$	7.36936	−	23.4533i	0.234927	−	0.747664i
$985$	20.7234	+	11.9647i	0.660302	+	0.381226i
$986$	6.39833	+	20.7687i	0.203764	+	0.661409i
$987$	−3.51854	+	13.2107i	−0.111997	+	0.420502i
$988$	5.47946	+	8.04899i	0.174325	+	0.256072i
$989$	1.70952	−	0.986991i	0.0543595	−	0.0313845i
$990$	−62.0588	−	36.5568i	−1.97236	−	1.16185i
$991$	15.3988	+	8.89049i	0.489158	+	0.282416i	0.724225	−	0.689563i	$-0.242198\pi$
$991$	15.3988	+	8.89049i	0.489158	+	0.282416i	−0.235067	+	0.971979i	$0.575531\pi$
$992$	24.4282	+	50.9537i	0.775597	+	1.61778i
$993$	0.246436	−	1.58970i	0.00782041	−	0.0504476i
$994$	−3.56233	+	10.3579i	−0.112990	+	0.328533i
$995$	−24.1731	−	41.8691i	−0.766339	−	1.32734i
$996$	25.4125	−	12.0851i	0.805226	−	0.382931i
$997$	21.3724	+	37.0182i	0.676872	+	1.17238i	0.975918	+	0.218138i	$0.0699983\pi$
$997$	21.3724	+	37.0182i	0.676872	+	1.17238i	−0.299046	+	0.954239i	$0.596668\pi$
$998$	−12.4567	+	13.4157i	−0.394309	+	0.424666i
$999$	0.870066	+	13.9678i	0.0275277	+	0.441923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.7	✓	180
7.5	odd	6		504.2.cz.b.187.53	yes	180
8.3	odd	2	inner	504.2.bf.b.115.8	yes	180
9.4	even	3		504.2.cz.b.283.65	yes	180
56.19	even	6		504.2.cz.b.187.65	yes	180
63.40	odd	6	inner	504.2.bf.b.355.7	yes	180
72.67	odd	6		504.2.cz.b.283.53	yes	180
504.355	even	6	inner	504.2.bf.b.355.8	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.7	✓	180	1.1	even	1	trivial
504.2.bf.b.115.8	yes	180	8.3	odd	2	inner
504.2.bf.b.355.7	yes	180	63.40	odd	6	inner
504.2.bf.b.355.8	yes	180	504.355	even	6	inner
504.2.cz.b.187.53	yes	180	7.5	odd	6
504.2.cz.b.187.65	yes	180	56.19	even	6
504.2.cz.b.283.53	yes	180	72.67	odd	6
504.2.cz.b.283.65	yes	180	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37865 - 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 + 0.869029i) q^{4} +(-1.58477 + 2.74491i) q^{5} +(0.905257 - 2.27607i) q^{6} +(2.63076 + 0.281244i) q^{7} +(-2.20950 - 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +O(q^{10})\)	\(q+(-1.37865 - 0.315175i) q^{2} +(-0.265334 + 1.71161i) q^{3} +(1.80133 + 0.869029i) q^{4} +(-1.58477 + 2.74491i) q^{5} +(0.905257 - 2.27607i) q^{6} +(2.63076 + 0.281244i) q^{7} +(-2.20950 - 1.76582i) q^{8} +(-2.85920 - 0.908295i) q^{9} +(3.04997 - 3.28478i) q^{10} +(2.67808 + 4.63857i) q^{11} +(-1.96539 + 2.85259i) q^{12} +(0.893100 + 1.54689i) q^{13} +(-3.53825 - 1.21689i) q^{14} +(-4.27771 - 3.44083i) q^{15} +(2.48958 + 3.13081i) q^{16} +(4.04061 + 2.33285i) q^{17} +(3.65555 + 2.15336i) q^{18} +(2.36047 - 1.36282i) q^{19} +(-5.24010 + 3.56727i) q^{20} +(-1.17941 + 4.42820i) q^{21} +(-2.23017 - 7.23901i) q^{22} +(-4.01783 - 2.31970i) q^{23} +(3.60864 - 3.31327i) q^{24} +(-2.52301 - 4.36999i) q^{25} +(-0.743727 - 2.41410i) q^{26} +(2.31328 - 4.65282i) q^{27} +(4.49446 + 2.79282i) q^{28} +(-2.85231 - 1.64678i) q^{29} +(4.81299 + 6.09191i) q^{30} -9.98908 q^{31} +(-2.44549 - 5.10094i) q^{32} +(-8.65000 + 3.35305i) q^{33} +(-4.83532 - 4.48967i) q^{34} +(-4.94115 + 6.77549i) q^{35} +(-4.36102 - 4.12086i) q^{36} +(-2.33249 + 1.34666i) q^{37} +(-3.68378 + 1.13488i) q^{38} +(-2.88464 + 1.11819i) q^{39} +(8.34856 - 3.26646i) q^{40} +(4.34585 - 2.50908i) q^{41} +(3.02165 - 5.73321i) q^{42} +(-0.212741 + 0.368479i) q^{43} +(0.793055 + 10.6829i) q^{44} +(7.02436 - 6.40879i) q^{45} +(4.80806 + 4.46436i) q^{46} +2.98331 q^{47} +(-6.01929 + 3.43047i) q^{48} +(6.84180 + 1.47977i) q^{49} +(2.10103 + 6.81986i) q^{50} +(-5.06503 + 6.29696i) q^{51} +(0.264472 + 3.56260i) q^{52} +(-5.19961 - 3.00200i) q^{53} +(-4.65565 + 5.68550i) q^{54} -16.9766 q^{55} +(-5.31604 - 5.26685i) q^{56} +(1.70630 + 4.40180i) q^{57} +(3.41331 + 3.16931i) q^{58} +4.47279i q^{59} +(-4.71539 - 9.91551i) q^{60} +11.6099 q^{61} +(13.7714 + 3.14830i) q^{62} +(-7.26641 - 3.19364i) q^{63} +(1.76378 + 7.80314i) q^{64} -5.66144 q^{65} +(12.9821 - 1.89641i) q^{66} -12.7934 q^{67} +(5.25116 + 7.71364i) q^{68} +(5.03648 - 6.26146i) q^{69} +(8.94756 - 7.78367i) q^{70} -2.92741i q^{71} +(4.71351 + 7.05569i) q^{72} +(-0.864336 - 0.499025i) q^{73} +(3.64011 - 1.12143i) q^{74} +(8.14914 - 3.15890i) q^{75} +(5.43632 - 0.403569i) q^{76} +(5.74082 + 12.9562i) q^{77} +(4.32933 - 0.632424i) q^{78} +7.46476i q^{79} +(-12.5392 + 1.87203i) q^{80} +(7.35000 + 5.19398i) q^{81} +(-6.78218 + 2.08943i) q^{82} +(-7.03493 - 4.06162i) q^{83} +(-5.97274 + 6.95172i) q^{84} +(-12.8069 + 7.39407i) q^{85} +(0.409430 - 0.440951i) q^{86} +(3.57546 - 4.44509i) q^{87} +(2.27365 - 14.9779i) q^{88} +(6.04395 - 3.48948i) q^{89} +(-11.7040 + 6.62155i) q^{90} +(1.91448 + 4.32069i) q^{91} +(-5.22156 - 7.67015i) q^{92} +(2.65044 - 17.0974i) q^{93} +(-4.11293 - 0.940264i) q^{94} +8.63904i q^{95} +(9.37967 - 2.83227i) q^{96} +(11.7930 + 6.80869i) q^{97} +(-8.96604 - 4.19644i) q^{98} +(-3.44397 - 15.6951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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