LMFDB - Embedded newform 504.2.cc.b.293.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (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:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.5
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38810 - 0.270536i) q^{2} +(-1.21338 + 1.23600i) q^{3} +(1.85362 + 0.751060i) q^{4} +(2.17541 + 1.25598i) q^{5} +(2.01867 - 1.38743i) q^{6} +(-2.64254 - 0.130417i) q^{7} +(-2.36981 - 1.54401i) q^{8} +(-0.0554045 - 2.99949i) q^{9} +O(q^{10})$	\(q+(-1.38810 - 0.270536i) q^{2} +(-1.21338 + 1.23600i) q^{3} +(1.85362 + 0.751060i) q^{4} +(2.17541 + 1.25598i) q^{5} +(2.01867 - 1.38743i) q^{6} +(-2.64254 - 0.130417i) q^{7} +(-2.36981 - 1.54401i) q^{8} +(-0.0554045 - 2.99949i) q^{9} +(-2.67990 - 2.33194i) q^{10} +(-2.04252 - 3.53776i) q^{11} +(-3.17746 + 1.37976i) q^{12} +(3.56373 - 6.17257i) q^{13} +(3.63281 + 0.895932i) q^{14} +(-4.19200 + 1.16484i) q^{15} +(2.87182 + 2.78436i) q^{16} -3.33266 q^{17} +(-0.734563 + 4.17857i) q^{18} +2.59916 q^{19} +(3.08908 + 3.96197i) q^{20} +(3.36760 - 3.10793i) q^{21} +(1.87813 + 5.46332i) q^{22} +(-2.33076 - 1.34566i) q^{23} +(4.78390 - 1.05562i) q^{24} +(0.654951 + 1.13441i) q^{25} +(-6.61671 + 7.60400i) q^{26} +(3.77460 + 3.57105i) q^{27} +(-4.80031 - 2.22645i) q^{28} +(2.87189 + 4.97425i) q^{29} +(6.13403 - 0.482820i) q^{30} +(1.03437 + 0.597193i) q^{31} +(-3.23309 - 4.64189i) q^{32} +(6.85104 + 1.76809i) q^{33} +(4.62606 + 0.901606i) q^{34} +(-5.58481 - 3.60267i) q^{35} +(2.15010 - 5.60153i) q^{36} -7.31462i q^{37} +(-3.60788 - 0.703166i) q^{38} +(3.30514 + 11.8945i) q^{39} +(-3.21608 - 6.33530i) q^{40} +(1.92428 - 3.33296i) q^{41} +(-5.51536 + 3.40305i) q^{42} +(9.12590 - 5.26884i) q^{43} +(-1.12900 - 8.09172i) q^{44} +(3.64676 - 6.59472i) q^{45} +(2.87126 + 2.49846i) q^{46} +(-2.42213 - 4.19526i) q^{47} +(-6.92609 + 0.171081i) q^{48} +(6.96598 + 0.689264i) q^{49} +(-0.602237 - 1.75186i) q^{50} +(4.04380 - 4.11918i) q^{51} +(11.2418 - 8.76502i) q^{52} -10.7480 q^{53} +(-4.27341 - 5.97812i) q^{54} -10.2614i q^{55} +(6.06095 + 4.38918i) q^{56} +(-3.15378 + 3.21257i) q^{57} +(-2.64074 - 7.68169i) q^{58} +(3.31183 + 1.91208i) q^{59} +(-8.64524 - 0.989275i) q^{60} +(2.66315 + 4.61270i) q^{61} +(-1.27424 - 1.10880i) q^{62} +(-0.244776 + 7.93348i) q^{63} +(3.23204 + 7.31805i) q^{64} +(15.5052 - 8.95193i) q^{65} +(-9.03157 - 4.30773i) q^{66} +(-0.295540 - 0.170630i) q^{67} +(-6.17750 - 2.50303i) q^{68} +(4.49134 - 1.24802i) q^{69} +(6.77760 + 6.51175i) q^{70} -8.32016i q^{71} +(-4.49995 + 7.19378i) q^{72} +4.69448i q^{73} +(-1.97887 + 10.1534i) q^{74} +(-2.19684 - 0.566951i) q^{75} +(4.81786 + 1.95212i) q^{76} +(4.93606 + 9.61503i) q^{77} +(-1.36996 - 17.4048i) q^{78} +(-3.05771 - 5.29612i) q^{79} +(2.75031 + 9.66407i) q^{80} +(-8.99386 + 0.332370i) q^{81} +(-3.57278 + 4.10588i) q^{82} +(-6.95648 + 4.01632i) q^{83} +(8.57650 - 3.23166i) q^{84} +(-7.24993 - 4.18575i) q^{85} +(-14.0930 + 4.84477i) q^{86} +(-9.63289 - 2.48601i) q^{87} +(-0.621941 + 11.5375i) q^{88} +2.02849 q^{89} +(-6.84616 + 8.16752i) q^{90} +(-10.2223 + 15.8465i) q^{91} +(-3.30966 - 4.24488i) q^{92} +(-1.99322 + 0.553859i) q^{93} +(2.22719 + 6.47870i) q^{94} +(5.65425 + 3.26448i) q^{95} +(9.66036 + 1.63628i) q^{96} +(-5.39410 + 3.11428i) q^{97} +(-9.48298 - 2.84131i) q^{98} +(-10.4983 + 6.32254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38810	−	0.270536i	−0.981532	−	0.191298i
$2$	−1.38810	−	0.270536i	−0.981532	−	0.191298i
$3$	−1.21338	+	1.23600i	−0.700547	+	0.713606i
$3$	−1.21338	+	1.23600i	−0.700547	+	0.713606i
$4$	1.85362	+	0.751060i	0.926810	+	0.375530i
$5$	2.17541	+	1.25598i	0.972875	+	0.561690i	0.900111	−	0.435660i	$-0.143485\pi$
$5$	2.17541	+	1.25598i	0.972875	+	0.561690i	0.0727633	+	0.997349i	$0.476818\pi$
$6$	2.01867	−	1.38743i	0.824121	−	0.566414i
$7$	−2.64254	−	0.130417i	−0.998784	−	0.0492930i
$7$	−2.64254	−	0.130417i	−0.998784	−	0.0492930i
$8$	−2.36981	−	1.54401i	−0.837856	−	0.545891i
$9$	−0.0554045	−	2.99949i	−0.0184682	−	0.999829i
$10$	−2.67990	−	2.33194i	−0.847458	−	0.737425i
$11$	−2.04252	−	3.53776i	−0.615844	−	1.06667i	−0.990236	−	0.139403i	$-0.955482\pi$
$11$	−2.04252	−	3.53776i	−0.615844	−	1.06667i	0.374391	−	0.927271i	$-0.377852\pi$
$12$	−3.17746	+	1.37976i	−0.917255	+	0.398301i
$13$	3.56373	−	6.17257i	0.988402	−	1.71196i	0.362686	−	0.931912i	$-0.381860\pi$
$13$	3.56373	−	6.17257i	0.988402	−	1.71196i	0.625716	−	0.780051i	$-0.284807\pi$
$14$	3.63281	+	0.895932i	0.970909	+	0.239448i
$15$	−4.19200	+	1.16484i	−1.08237	+	0.300760i
$16$	2.87182	+	2.78436i	0.717955	+	0.696090i
$17$	−3.33266			−0.808290			−0.404145	−	0.914695i	$-0.632431\pi$
$17$	−3.33266			−0.808290			−0.404145	+	0.914695i	$0.632431\pi$
$18$	−0.734563	+	4.17857i	−0.173138	+	0.984898i
$19$	2.59916			0.596288			0.298144	−	0.954521i	$-0.403632\pi$
$19$	2.59916			0.596288			0.298144	+	0.954521i	$0.403632\pi$
$20$	3.08908	+	3.96197i	0.690739	+	0.885923i
$21$	3.36760	−	3.10793i	0.734871	−	0.678207i
$22$	1.87813	+	5.46332i	0.400419	+	1.16478i
$23$	−2.33076	−	1.34566i	−0.485996	−	0.280590i	0.236916	−	0.971530i	$-0.423863\pi$
$23$	−2.33076	−	1.34566i	−0.485996	−	0.280590i	−0.722912	+	0.690940i	$0.757197\pi$
$24$	4.78390	−	1.05562i	0.976509	−	0.215477i
$25$	0.654951	+	1.13441i	0.130990	+	0.226882i
$26$	−6.61671	+	7.60400i	−1.29764	+	1.49127i
$27$	3.77460	+	3.57105i	0.726422	+	0.687248i
$28$	−4.80031	−	2.22645i	−0.907173	−	0.420759i
$29$	2.87189	+	4.97425i	0.533296	+	0.923696i	0.999244	+	0.0388834i	$0.0123801\pi$
$29$	2.87189	+	4.97425i	0.533296	+	0.923696i	−0.465948	+	0.884812i	$0.654287\pi$
$30$	6.13403	−	0.482820i	1.11992	−	0.0881505i
$31$	1.03437	+	0.597193i	0.185778	+	0.107259i	0.590005	−	0.807400i	$-0.299126\pi$
$31$	1.03437	+	0.597193i	0.185778	+	0.107259i	−0.404226	+	0.914659i	$0.632459\pi$
$32$	−3.23309	−	4.64189i	−0.571535	−	0.820578i
$33$	6.85104	+	1.76809i	1.19261	+	0.307784i
$34$	4.62606	+	0.901606i	0.793363	+	0.154624i
$35$	−5.58481	−	3.60267i	−0.944005	−	0.608963i
$36$	2.15010	−	5.60153i	0.358349	−	0.933588i
$37$		−	7.31462i		−	1.20252i	−0.799055	−	0.601258i	$-0.794666\pi$
$37$		−	7.31462i		−	1.20252i	0.799055	−	0.601258i	$-0.205334\pi$
$38$	−3.60788	−	0.703166i	−0.585276	−	0.114069i
$39$	3.30514	+	11.8945i	0.529245	+	1.90464i
$40$	−3.21608	−	6.33530i	−0.508507	−	1.00170i
$41$	1.92428	−	3.33296i	0.300523	−	0.520521i	−0.675732	−	0.737148i	$-0.736172\pi$
$41$	1.92428	−	3.33296i	0.300523	−	0.520521i	0.976254	+	0.216627i	$0.0695056\pi$
$42$	−5.51536	+	3.40305i	−0.851039	+	0.525102i
$43$	9.12590	−	5.26884i	1.39169	−	0.803490i	0.398184	−	0.917306i	$-0.369641\pi$
$43$	9.12590	−	5.26884i	1.39169	−	0.803490i	0.993502	+	0.113815i	$0.0363072\pi$
$44$	−1.12900	−	8.09172i	−0.170203	−	1.21987i
$45$	3.64676	−	6.59472i	0.543627	−	0.983082i
$46$	2.87126	+	2.49846i	0.423344	+	0.368378i
$47$	−2.42213	−	4.19526i	−0.353305	−	0.611942i	0.633522	−	0.773725i	$-0.281609\pi$
$47$	−2.42213	−	4.19526i	−0.353305	−	0.611942i	−0.986826	+	0.161783i	$0.948275\pi$
$48$	−6.92609	+	0.171081i	−0.999695	+	0.0246934i
$49$	6.96598	+	0.689264i	0.995140	+	0.0984662i
$50$	−0.602237	−	1.75186i	−0.0851691	−	0.247750i
$51$	4.04380	−	4.11918i	0.566245	−	0.576801i
$52$	11.2418	−	8.76502i	1.55895	−	1.21549i
$53$	−10.7480			−1.47635			−0.738173	−	0.674611i	$-0.764311\pi$
$53$	−10.7480			−1.47635			−0.738173	+	0.674611i	$0.764311\pi$
$54$	−4.27341	−	5.97812i	−0.581538	−	0.813519i
$55$		−	10.2614i		−	1.38365i
$56$	6.06095	+	4.38918i	0.809929	+	0.586528i
$57$	−3.15378	+	3.21257i	−0.417728	+	0.425515i
$58$	−2.64074	−	7.68169i	−0.346746	−	1.00866i
$59$	3.31183	+	1.91208i	0.431163	+	0.248932i	0.699842	−	0.714298i	$-0.253254\pi$
$59$	3.31183	+	1.91208i	0.431163	+	0.248932i	−0.268679	+	0.963230i	$0.586587\pi$
$60$	−8.64524	−	0.989275i	−1.11610	−	0.127715i
$61$	2.66315	+	4.61270i	0.340981	+	0.590596i	0.984615	−	0.174737i	$-0.0559076\pi$
$61$	2.66315	+	4.61270i	0.340981	+	0.590596i	−0.643634	+	0.765333i	$0.722574\pi$
$62$	−1.27424	−	1.10880i	−0.161829	−	0.140817i
$63$	−0.244776	+	7.93348i	−0.0308389	+	0.999524i
$64$	3.23204	+	7.31805i	0.404005	+	0.914757i
$65$	15.5052	−	8.95193i	1.92318	−	1.11035i
$66$	−9.03157	−	4.30773i	−1.11171	−	0.530245i
$67$	−0.295540	−	0.170630i	−0.0361060	−	0.0208458i	0.481838	−	0.876260i	$-0.339969\pi$
$67$	−0.295540	−	0.170630i	−0.0361060	−	0.0208458i	−0.517944	+	0.855414i	$0.673303\pi$
$68$	−6.17750	−	2.50303i	−0.749131	−	0.303537i
$69$	4.49134	−	1.24802i	0.540694	−	0.150243i
$70$	6.77760	+	6.51175i	0.810078	+	0.778302i
$71$		−	8.32016i		−	0.987421i	−0.869626	−	0.493711i	$-0.835640\pi$
$71$		−	8.32016i		−	0.987421i	0.869626	−	0.493711i	$-0.164360\pi$
$72$	−4.49995	+	7.19378i	−0.530325	+	0.847795i
$73$			4.69448i			0.549448i	0.961523	+	0.274724i	$0.0885864\pi$
$73$			4.69448i			0.549448i	−0.961523	+	0.274724i	$0.911414\pi$
$74$	−1.97887	+	10.1534i	−0.230039	+	1.18031i
$75$	−2.19684	−	0.566951i	−0.253669	−	0.0654658i
$76$	4.81786	+	1.95212i	0.552646	+	0.223924i
$77$	4.93606	+	9.61503i	0.562516	+	1.09573i
$78$	−1.36996	−	17.4048i	−0.155118	−	1.97071i
$79$	−3.05771	−	5.29612i	−0.344020	−	0.595860i	0.641155	−	0.767411i	$-0.278455\pi$
$79$	−3.05771	−	5.29612i	−0.344020	−	0.595860i	−0.985175	+	0.171551i	$0.945122\pi$
$80$	2.75031	+	9.66407i	0.307494	+	1.08048i
$81$	−8.99386	+	0.332370i	−0.999318	+	0.0369300i
$82$	−3.57278	+	4.10588i	−0.394547	+	0.453418i
$83$	−6.95648	+	4.01632i	−0.763572	+	0.440849i	−0.830577	−	0.556904i	$-0.811989\pi$
$83$	−6.95648	+	4.01632i	−0.763572	+	0.440849i	0.0670045	+	0.997753i	$0.478656\pi$
$84$	8.57650	−	3.23166i	0.935773	−	0.352603i
$85$	−7.24993	−	4.18575i	−0.786365	−	0.454008i
$86$	−14.0930	+	4.84477i	−1.51969	+	0.522425i
$87$	−9.63289	−	2.48601i	−1.03275	−	0.266529i
$88$	−0.621941	+	11.5375i	−0.0662991	+	1.22990i
$89$	2.02849			0.215020			0.107510	−	0.994204i	$-0.465712\pi$
$89$	2.02849			0.215020			0.107510	+	0.994204i	$0.465712\pi$
$90$	−6.84616	+	8.16752i	−0.721648	+	0.860932i
$91$	−10.2223	+	15.8465i	−1.07159	+	1.66116i
$92$	−3.30966	−	4.24488i	−0.345056	−	0.442560i
$93$	−1.99322	+	0.553859i	−0.206687	+	0.0574325i
$94$	2.22719	+	6.47870i	0.229717	+	0.668227i
$95$	5.65425	+	3.26448i	0.580114	+	0.334929i
$96$	9.66036	+	1.63628i	0.985957	+	0.167002i
$97$	−5.39410	+	3.11428i	−0.547688	+	0.316208i	−0.748189	−	0.663486i	$-0.769076\pi$
$97$	−5.39410	+	3.11428i	−0.547688	+	0.316208i	0.200501	+	0.979693i	$0.435743\pi$
$98$	−9.48298	−	2.84131i	−0.957926	−	0.287016i
$99$	−10.4983	+	6.32254i	−1.05512	+	0.635439i
$100$	0.362022	+	2.59467i	0.0362022	+	0.259467i
$101$	−0.0324301	+	0.0187235i	−0.00322691	+	0.00186306i	−0.501613	−	0.865092i	$-0.667260\pi$
$101$	−0.0324301	+	0.0187235i	−0.00322691	+	0.00186306i	0.498386	+	0.866955i	$0.333926\pi$
$102$	−6.72757	+	4.62383i	−0.666128	+	0.457827i
$103$	−13.0957	−	7.56080i	−1.29036	−	0.744988i	−0.311639	−	0.950200i	$-0.600878\pi$
$103$	−13.0957	−	7.56080i	−1.29036	−	0.744988i	−0.978717	+	0.205213i	$0.934211\pi$
$104$	−17.9759	+	9.12539i	−1.76268	+	0.894818i
$105$	11.2294	−	2.53142i	1.09588	−	0.247041i
$106$	14.9192	+	2.90771i	1.44908	+	0.282422i
$107$	19.4573			1.88101			0.940503	−	0.339785i	$-0.110354\pi$
$107$	19.4573			1.88101			0.940503	+	0.339785i	$0.110354\pi$
$108$	4.31461	+	9.45432i	0.415174	+	0.909742i
$109$		−	7.56340i		−	0.724442i	−0.932092	−	0.362221i	$-0.882018\pi$
$109$		−	7.56340i		−	0.724442i	0.932092	−	0.362221i	$-0.117982\pi$
$110$	−2.77609	+	14.2439i	−0.264690	+	1.35810i
$111$	9.04089	+	8.87543i	0.858123	+	0.842419i
$112$	−7.22575	−	7.73230i	−0.682769	−	0.730634i
$113$	8.46746	+	4.88869i	0.796551	+	0.459889i	0.842264	−	0.539065i	$-0.181222\pi$
$113$	8.46746	+	4.88869i	0.796551	+	0.459889i	−0.0457124	+	0.998955i	$0.514556\pi$
$114$	5.24686	−	3.60614i	0.491413	−	0.337746i
$115$	−3.38024	−	5.85474i	−0.315209	−	0.545958i
$116$	1.58743	+	11.3773i	0.147389	+	1.05636i
$117$	−18.7120	−	10.3474i	−1.72992	−	0.956617i
$118$	−4.07985	−	3.55013i	−0.375580	−	0.326816i
$119$	8.80668	+	0.434637i	0.807307	+	0.0398431i
$120$	11.7328	+	3.71206i	1.07105	+	0.338863i
$121$	−2.84382	+	4.92563i	−0.258529	+	0.447785i
$122$	−2.44880	−	7.12335i	−0.221704	−	0.644918i
$123$	1.78465	+	6.42257i	0.160917	+	0.579104i
$124$	1.46880	+	1.88384i	0.131902	+	0.169174i
$125$		−	9.26935i		−	0.829076i
$126$	2.48606	−	10.9462i	0.221476	−	0.975166i
$127$	7.11318			0.631192			0.315596	−	0.948894i	$-0.397796\pi$
$127$	7.11318			0.631192			0.315596	+	0.948894i	$0.397796\pi$
$128$	−2.50659	−	11.0325i	−0.221553	−	0.975148i
$129$	−4.56091	+	17.6727i	−0.401565	+	1.55600i
$130$	−23.9445	+	8.23142i	−2.10007	+	0.721943i
$131$	4.43629	+	2.56129i	0.387600	+	0.223781i	0.681120	−	0.732172i	$-0.261493\pi$
$131$	4.43629	+	2.56129i	0.387600	+	0.223781i	−0.293520	+	0.955953i	$0.594827\pi$
$132$	11.3713	+	8.42290i	0.989744	+	0.733120i
$133$	−6.86837	−	0.338975i	−0.595563	−	0.0293929i
$134$	0.364076	+	0.316805i	0.0314514	+	0.0273678i
$135$	3.72617	+	12.5093i	0.320698	+	1.07663i
$136$	7.89780	+	5.14568i	0.677231	+	0.441239i
$137$	1.84435	−	1.06484i	0.157574	−	0.0909753i	−0.419140	−	0.907922i	$-0.637668\pi$
$137$	1.84435	−	1.06484i	0.157574	−	0.0909753i	0.576713	+	0.816946i	$0.304335\pi$
$138$	−6.57204	+	0.517297i	−0.559450	+	0.0440352i
$139$	0.458749	−	0.794577i	0.0389106	−	0.0673952i	−0.845914	−	0.533319i	$-0.820945\pi$
$139$	0.458749	−	0.794577i	0.0389106	−	0.0673952i	0.884825	+	0.465924i	$0.154278\pi$
$140$	−7.64629	−	10.8725i	−0.646230	−	0.918895i
$141$	8.12433	+	2.09669i	0.684192	+	0.176573i
$142$	−2.25090	+	11.5492i	−0.188892	+	0.969186i
$143$	−29.1161			−2.43481
$144$	8.19254	−	8.76825i	0.682712	−	0.730688i
$145$			14.4281i			1.19819i
$146$	1.27003	−	6.51639i	0.105108	−	0.539301i
$147$	−9.30434	+	7.77363i	−0.767409	+	0.641158i
$148$	5.49372	−	13.5585i	0.451581	−	1.11450i
$149$	11.4592	−	19.8479i	0.938775	−	1.62601i	0.171015	−	0.985268i	$-0.445295\pi$
$149$	11.4592	−	19.8479i	0.938775	−	1.62601i	0.767760	−	0.640738i	$-0.221371\pi$
$150$	2.89604	+	1.38131i	0.236461	+	0.112783i
$151$	−1.27819	−	2.21389i	−0.104018	−	0.180164i	0.809319	−	0.587370i	$-0.199837\pi$
$151$	−1.27819	−	2.21389i	−0.104018	−	0.180164i	−0.913336	+	0.407206i	$0.866503\pi$
$152$	−6.15953	−	4.01314i	−0.499604	−	0.325509i
$153$	0.184645	+	9.99629i	0.0149276	+	0.808152i
$154$	−4.25051	−	14.6820i	−0.342516	−	1.18311i
$155$	1.50012	+	2.59829i	0.120493	+	0.208699i
$156$	−2.80699	+	24.5302i	−0.224739	+	1.96399i
$157$	−6.26497	+	10.8513i	−0.499999	+	0.866024i	−1.00000		6.70514e-7i	$-1.00000\pi$
$157$	−6.26497	+	10.8513i	−0.499999	+	0.866024i	0.500001	+	0.866025i	$0.333333\pi$
$158$	2.81161	+	8.17874i	0.223680	+	0.650665i
$159$	13.0414	−	13.2845i	1.03425	−	1.05353i
$160$	−1.20321	−	14.1587i	−0.0951221	−	1.11934i
$161$	5.98360	+	3.85993i	0.471574	+	0.304205i
$162$	12.5743	+	1.97180i	0.987927	+	0.154919i
$163$			8.56795i			0.671094i	0.942023	+	0.335547i	$0.108921\pi$
$163$			8.56795i			0.671094i	−0.942023	+	0.335547i	$0.891079\pi$
$164$	6.07014	−	4.73279i	0.473998	−	0.369569i
$165$	12.6832	+	12.4511i	0.987384	+	0.969314i
$166$	10.7428	−	3.69306i	0.833804	−	0.286637i
$167$	3.59473	−	6.22625i	0.278168	−	0.481802i	−0.692761	−	0.721167i	$-0.743606\pi$
$167$	3.59473	−	6.22625i	0.278168	−	0.481802i	0.970930	+	0.239365i	$0.0769394\pi$
$168$	−12.7793	+	2.16560i	−0.985943	+	0.167080i
$169$	−18.9004	−	32.7364i	−1.45388	−	2.51819i
$170$	8.93120	+	7.77158i	0.684992	+	0.596053i
$171$	−0.144005	−	7.79615i	−0.0110123	−	0.596187i
$172$	20.8732	−	2.91233i	1.59156	−	0.222063i
$173$	−2.53004	+	1.46072i	−0.192355	+	0.111056i	−0.593085	−	0.805140i	$-0.702090\pi$
$173$	−2.53004	+	1.46072i	−0.192355	+	0.111056i	0.400729	+	0.916196i	$0.368757\pi$
$174$	12.6988	+	6.05687i	0.962695	+	0.459170i
$175$	−1.58279	−	3.08313i	−0.119647	−	0.233063i
$176$	3.98463	−	15.8469i	0.300352	−	1.19451i
$177$	−6.38186	+	1.77334i	−0.479690	+	0.133292i
$178$	−2.81574	−	0.548781i	−0.211049	−	0.0411329i
$179$	−3.19089			−0.238499			−0.119249	−	0.992864i	$-0.538049\pi$
$179$	−3.19089			−0.238499			−0.119249	+	0.992864i	$0.538049\pi$
$180$	11.7127	−	9.48517i	0.873015	−	0.706983i
$181$	−23.4653			−1.74417			−0.872083	−	0.489359i	$-0.837231\pi$
$181$	−23.4653			−1.74417			−0.872083	+	0.489359i	$0.837231\pi$
$182$	18.4766	−	19.2309i	1.36957	−	1.42549i
$183$	−8.93273	−	2.30532i	−0.660326	−	0.170414i
$184$	3.44574	+	6.78769i	0.254023	+	0.500395i
$185$	9.18699	−	15.9123i	0.675441	−	1.16990i
$186$	2.91662	−	0.229572i	0.213857	−	0.0168330i
$187$	6.80705	+	11.7902i	0.497781	+	0.862182i
$188$	−1.33883	−	9.59559i	−0.0976440	−	0.699830i
$189$	−9.50879	−	9.92889i	−0.691663	−	0.722221i
$190$	−6.96548	−	6.06109i	−0.505329	−	0.439718i
$191$	−17.7440	+	10.2445i	−1.28391	+	0.741268i	−0.977562	−	0.210650i	$-0.932442\pi$
$191$	−17.7440	+	10.2445i	−1.28391	+	0.741268i	−0.306353	+	0.951918i	$0.599109\pi$
$192$	−12.9668	−	4.88479i	−0.935801	−	0.352529i
$193$	−6.86905	+	11.8975i	−0.494445	+	0.856404i	−0.999980	−	0.00640258i	$-0.997962\pi$
$193$	−6.86905	+	11.8975i	−0.494445	+	0.856404i	0.505535	+	0.862806i	$0.331295\pi$
$194$	8.33005	−	2.86363i	0.598063	−	0.205596i
$195$	−7.74913	+	30.0266i	−0.554927	+	2.15025i
$196$	12.3946	+	6.50950i	0.885329	+	0.464964i
$197$	−8.82215			−0.628552			−0.314276	−	0.949332i	$-0.601762\pi$
$197$	−8.82215			−0.628552			−0.314276	+	0.949332i	$0.601762\pi$
$198$	16.2831	−	5.93612i	1.15719	−	0.421862i
$199$			12.0861i			0.856760i	0.903599	+	0.428380i	$0.140916\pi$
$199$			12.0861i			0.856760i	−0.903599	+	0.428380i	$0.859084\pi$
$200$	0.199430	−	3.69959i	0.0141018	−	0.261601i
$201$	0.569503	−	0.158249i	0.0401696	−	0.0111620i
$202$	0.0500815	−	0.0172165i	0.00352372	−	0.00121135i
$203$	−6.94033	−	13.5192i	−0.487116	−	0.948861i
$204$	10.5894	−	4.59827i	0.741408	−	0.321943i
$205$	8.37223	−	4.83371i	0.584742	−	0.337601i
$206$	16.1326	+	14.0380i	1.12401	+	0.978072i
$207$	−3.90716	+	7.06563i	−0.271567	+	0.491095i
$208$	27.4210	−	7.80378i	1.90131	−	0.541095i
$209$	−5.30885	−	9.19520i	−0.367221	−	0.636045i
$210$	−16.2724	+	0.475886i	−1.12290	+	0.0328393i
$211$	8.34941	+	4.82053i	0.574797	+	0.331859i	0.759063	−	0.651017i	$-0.225657\pi$
$211$	8.34941	+	4.82053i	0.574797	+	0.331859i	−0.184266	+	0.982876i	$0.558991\pi$
$212$	−19.9226	−	8.07236i	−1.36829	−	0.554412i
$213$	10.2837	+	10.0955i	0.704630	+	0.691735i
$214$	−27.0086	−	5.26389i	−1.84627	−	0.359832i
$215$	26.4701			1.80525
$216$	−3.43136	−	14.2908i	−0.233474	−	0.972363i
$217$	−2.65547	−	1.71300i	−0.180265	−	0.116286i
$218$	−2.04617	+	10.4987i	−0.138584	+	0.711063i
$219$	−5.80239	−	5.69621i	−0.392089	−	0.384914i
$220$	7.70696	−	19.0208i	0.519603	−	1.28238i
$221$	−11.8767	+	20.5711i	−0.798915	+	1.38376i
$222$	−10.1485	−	14.7658i	−0.681122	−	0.991018i
$223$	−11.3369	+	6.54535i	−0.759174	+	0.438309i	−0.828999	−	0.559250i	$-0.811089\pi$
$223$	−11.3369	+	6.54535i	−0.759174	+	0.438309i	0.0698251	+	0.997559i	$0.477756\pi$
$224$	7.93817	+	12.6880i	0.530391	+	0.847753i
$225$	3.36636	−	2.02737i	0.224424	−	0.135158i
$226$	−10.4311	−	9.07672i	−0.693865	−	0.603775i
$227$	−19.3302	+	11.1603i	−1.28299	+	0.740736i	−0.977394	−	0.211425i	$-0.932190\pi$
$227$	−19.3302	+	11.1603i	−1.28299	+	0.740736i	−0.305598	+	0.952161i	$0.598856\pi$
$228$	−8.25874	+	3.58621i	−0.546948	+	0.237503i
$229$	2.75707	−	4.77539i	0.182192	−	0.315566i	−0.760434	−	0.649415i	$-0.775014\pi$
$229$	2.75707	−	4.77539i	0.182192	−	0.315566i	0.942627	+	0.333848i	$0.108347\pi$
$230$	3.10818	+	9.04142i	0.204947	+	0.596174i
$231$	−17.8735	−	5.56573i	−1.17599	−	0.366198i
$232$	0.874478	−	16.2223i	0.0574123	−	1.06505i
$233$			8.22371i			0.538753i	0.963035	+	0.269377i	$0.0868176\pi$
$233$			8.22371i			0.538753i	−0.963035	+	0.269377i	$0.913182\pi$
$234$	23.1747	+	19.4254i	1.51498	+	1.26988i
$235$		−	12.1686i		−	0.793790i
$236$	4.70278	+	6.03166i	0.306125	+	0.392628i
$237$	10.2562	+	2.64687i	0.666211	+	0.171933i
$238$	−12.1069	−	2.98584i	−0.784776	−	0.193543i
$239$	−1.85396	−	1.07039i	−0.119923	−	0.0692375i	0.438839	−	0.898566i	$-0.355390\pi$
$239$	−1.85396	−	1.07039i	−0.119923	−	0.0692375i	−0.558762	+	0.829328i	$0.688723\pi$
$240$	−15.2820	−	8.32683i	−0.986448	−	0.537495i
$241$	16.1708	−	9.33620i	1.04165	−	0.601398i	0.121351	−	0.992610i	$-0.461277\pi$
$241$	16.1708	−	9.33620i	1.04165	−	0.601398i	0.920301	+	0.391212i	$0.127944\pi$
$242$	5.28005	−	6.06790i	0.339414	−	0.390059i
$243$	10.5022	−	11.5197i	0.673716	−	0.738991i
$244$	1.47205	+	10.5504i	0.0942381	+	0.675419i
$245$	14.2882	+	10.2485i	0.912840	+	0.654755i
$246$	−0.739730	−	9.39796i	−0.0471634	−	0.599192i
$247$	9.26272	−	16.0435i	0.589373	−	1.02082i
$248$	−1.52919	−	3.01232i	−0.0971036	−	0.191282i
$249$	3.47668	−	13.4716i	0.220326	−	0.853725i
$250$	−2.50769	+	12.8667i	−0.158600	+	0.813764i
$251$		−	18.2124i		−	1.14955i	−0.818310	−	0.574777i	$-0.805089\pi$
$251$		−	18.2124i		−	1.14955i	0.818310	−	0.574777i	$-0.194911\pi$
$252$	−6.41224	+	14.5218i	−0.403933	+	0.914789i
$253$			10.9942i			0.691199i
$254$	−9.87377	−	1.92437i	−0.619536	−	0.120746i
$255$	13.9705	−	3.88201i	0.874869	−	0.243101i
$256$	0.494684	+	15.9924i	0.0309178	+	0.999522i
$257$	−5.82025	+	10.0810i	−0.363057	+	0.628834i	−0.988462	−	0.151466i	$-0.951600\pi$
$257$	−5.82025	+	10.0810i	−0.363057	+	0.628834i	0.625405	+	0.780300i	$0.284934\pi$
$258$	11.1121	−	23.2976i	0.691808	−	1.45044i
$259$	−0.953952	+	19.3291i	−0.0592757	+	1.20105i
$260$	35.4642	−	4.94815i	2.19939	−	0.306871i
$261$	14.7611	−	8.88979i	0.913689	−	0.550264i
$262$	−5.46507	−	4.75550i	−0.337633	−	0.293796i
$263$	12.9717	−	7.48920i	0.799868	−	0.461804i	−0.0435572	−	0.999051i	$-0.513869\pi$
$263$	12.9717	−	7.48920i	0.799868	−	0.461804i	0.843425	+	0.537247i	$0.180536\pi$
$264$	−13.5057	−	14.7681i	−0.831221	−	0.908916i
$265$	−23.3813	−	13.4992i	−1.43630	−	0.829248i
$266$	9.44226	+	2.32867i	0.578942	+	0.142780i
$267$	−2.46134	+	2.50722i	−0.150632	+	0.153440i
$268$	−0.419666	−	0.538252i	−0.0256352	−	0.0328790i
$269$			9.77960i			0.596273i	0.954523	+	0.298136i	$0.0963650\pi$
$269$			9.77960i			0.596273i	−0.954523	+	0.298136i	$0.903635\pi$
$270$	−1.78807	−	18.3722i	−0.108818	−	1.11810i
$271$			10.1915i			0.619090i	0.950885	+	0.309545i	$0.100177\pi$
$271$			10.1915i			0.619090i	−0.950885	+	0.309545i	$0.899823\pi$
$272$	−9.57081	−	9.27934i	−0.580316	−	0.562642i
$273$	−7.18270	−	31.8626i	−0.434717	−	1.92841i
$274$	−2.84822	+	0.979133i	−0.172067	+	0.0591516i
$275$	2.67551	−	4.63412i	0.161339	−	0.279448i
$276$	9.26257	+	1.05992i	0.557541	+	0.0637995i
$277$	5.93338	−	3.42564i	0.356502	−	0.205827i	−0.311043	−	0.950396i	$-0.600678\pi$
$277$	5.93338	−	3.42564i	0.356502	−	0.205827i	0.667545	+	0.744569i	$0.267345\pi$
$278$	−0.851750	+	0.978841i	−0.0510846	+	0.0587070i
$279$	1.73397	−	3.13567i	0.103810	−	0.187727i
$280$	7.67238	+	17.1607i	0.458513	+	1.02555i
$281$	4.09471	−	2.36408i	0.244270	−	0.141029i	−0.372868	−	0.927885i	$-0.621625\pi$
$281$	4.09471	−	2.36408i	0.244270	−	0.141029i	0.617138	+	0.786855i	$0.288292\pi$
$282$	−10.7101	−	5.10833i	−0.637778	−	0.304197i
$283$	15.5265	−	26.8926i	0.922953	−	1.59860i	0.128131	−	0.991757i	$-0.459102\pi$
$283$	15.5265	−	26.8926i	0.922953	−	1.59860i	0.794821	−	0.606843i	$-0.207565\pi$
$284$	6.24894	−	15.4224i	0.370806	−	0.915152i
$285$	−10.8957	+	3.02760i	−0.645404	+	0.179340i
$286$	40.4159	+	7.87694i	2.38984	+	0.465773i
$287$	−5.51966	+	8.55650i	−0.325815	+	0.505074i
$288$	−13.7442	+	9.95480i	−0.809883	+	0.586592i
$289$	−5.89334			−0.346667
$290$	3.90331	−	20.0276i	0.229211	−	1.17606i
$291$	2.69584	−	10.4459i	0.158033	−	0.612352i
$292$	−3.52584	+	8.70179i	−0.206334	+	0.509234i
$293$	9.38258	+	5.41703i	0.548136	+	0.316467i	0.748370	−	0.663282i	$-0.230837\pi$
$293$	9.38258	+	5.41703i	0.548136	+	0.316467i	−0.200234	+	0.979748i	$0.564170\pi$
$294$	15.0184	−	8.27339i	0.875888	−	0.482514i
$295$	4.80306	+	8.31915i	0.279645	+	0.484360i
$296$	−11.2939	+	17.3343i	−0.656443	+	1.00754i
$297$	4.92378	−	20.6476i	0.285707	−	1.19809i
$298$	−21.2761	+	24.4507i	−1.23249	+	1.41639i
$299$	−16.6124	+	9.59116i	−0.960719	+	0.554671i
$300$	−3.64629	−	2.70087i	−0.210519	−	0.155935i
$301$	−24.8026	+	12.7329i	−1.42960	+	0.733913i
$302$	1.17531	+	3.41889i	0.0676317	+	0.196735i
$303$	0.0162078	−	0.0628025i	0.000931113	−	0.00360791i
$304$	7.46432	+	7.23700i	0.428108	+	0.415070i
$305$			13.3794i			0.766101i
$306$	2.44805	−	13.9258i	0.139946	−	0.796083i
$307$	14.6728			0.837422			0.418711	−	0.908120i	$-0.362482\pi$
$307$	14.6728			0.837422			0.418711	+	0.908120i	$0.362482\pi$
$308$	1.92812	+	21.5299i	0.109865	+	1.22678i
$309$	25.2353	−	7.01216i	1.43558	−	0.398908i
$310$	−1.37938	−	4.01251i	−0.0783437	−	0.227895i
$311$	3.16732	−	5.48596i	0.179602	−	0.311080i	−0.762142	−	0.647410i	$-0.775852\pi$
$311$	3.16732	−	5.48596i	0.179602	−	0.311080i	0.941744	+	0.336330i	$0.109186\pi$
$312$	10.5327	−	33.2909i	0.596295	−	1.88472i
$313$	12.3347	−	7.12143i	0.697198	−	0.402527i	−0.109105	−	0.994030i	$-0.534799\pi$
$313$	12.3347	−	7.12143i	0.697198	−	0.402527i	0.806303	+	0.591503i	$0.201465\pi$
$314$	11.6320	−	13.3677i	0.656434	−	0.754382i
$315$	−10.4967	+	16.9512i	−0.591425	+	0.955090i
$316$	−1.69014	−	12.1135i	−0.0950779	−	0.681438i
$317$	4.22200	+	7.31272i	0.237131	+	0.410723i	0.959890	−	0.280377i	$-0.0904595\pi$
$317$	4.22200	+	7.31272i	0.237131	+	0.410723i	−0.722759	+	0.691100i	$0.757126\pi$
$318$	−21.6966	+	14.9120i	−1.21669	+	0.836224i
$319$	11.7318	−	20.3201i	0.656855	−	1.13771i
$320$	−2.16027	+	19.9792i	−0.120763	+	1.11687i
$321$	−23.6091	+	24.0492i	−1.31773	+	1.34230i
$322$	−7.26157	−	6.97673i	−0.404671	−	0.388798i
$323$	−8.66213			−0.481974
$324$	−16.9208	−	6.13884i	−0.940046	−	0.341047i
$325$	9.33629			0.517884
$326$	2.31794	−	11.8931i	0.128379	−	0.658700i
$327$	9.34838	+	9.17730i	0.516967	+	0.507506i
$328$	−9.70633	+	4.92737i	−0.535942	+	0.272068i
$329$	5.85344	+	11.4020i	0.322711	+	0.628613i
$330$	−14.2370	−	20.7145i	−0.783721	−	1.14030i
$331$	3.80120	−	2.19462i	0.208933	−	0.120627i	−0.391882	−	0.920015i	$-0.628176\pi$
$331$	3.80120	−	2.19462i	0.208933	−	0.120627i	0.600815	+	0.799388i	$0.294843\pi$
$332$	−15.9112	+	2.22001i	−0.873239	+	0.121839i
$333$	−21.9401	+	0.405263i	−1.20231	+	0.0222083i
$334$	−6.67425	+	7.67013i	−0.365199	+	0.419691i
$335$	−0.428615	−	0.742382i	−0.0234177	−	0.0405607i
$336$	18.3247	+	0.451193i	0.999697	+	0.0246146i
$337$	−12.5711	+	21.7739i	−0.684794	+	1.18610i	0.288707	+	0.957417i	$0.406775\pi$
$337$	−12.5711	+	21.7739i	−0.684794	+	1.18610i	−0.973501	+	0.228681i	$0.926559\pi$
$338$	17.3792	+	50.5546i	0.945303	+	2.74981i
$339$	−16.3167	+	4.53395i	−0.886201	+	0.246250i
$340$	−10.2949	−	13.2039i	−0.558318	−	0.716083i
$341$		−	4.87913i		−	0.264220i
$342$	−1.90925	+	10.8608i	−0.103240	+	0.587283i
$343$	−18.3180	−	2.72989i	−0.989077	−	0.147400i
$344$	−29.7618	−	1.60434i	−1.60465	−	0.0865002i
$345$	11.3380	+	2.92606i	0.610418	+	0.157534i
$346$	3.90711	−	1.34315i	0.210048	−	0.0722082i
$347$	16.1985	−	28.0566i	0.869580	−	1.50616i	0.00715261	−	0.999974i	$-0.497723\pi$
$347$	16.1985	−	28.0566i	0.869580	−	1.50616i	0.862427	−	0.506182i	$-0.168943\pi$
$348$	−15.9886	−	11.8430i	−0.857077	−	0.634851i
$349$	−3.06629	−	5.31097i	−0.164135	−	0.284290i	0.772213	−	0.635364i	$-0.219150\pi$
$349$	−3.06629	−	5.31097i	−0.164135	−	0.284290i	−0.936348	+	0.351074i	$0.885817\pi$
$350$	1.36296	+	4.70788i	0.0728533	+	0.251647i
$351$	35.4942	−	10.5727i	1.89454	−	0.564330i
$352$	−9.81820	+	20.9191i	−0.523312	+	1.11499i
$353$	−9.67212	−	16.7526i	−0.514795	−	0.891651i	−0.999853	−	0.0171689i	$-0.994535\pi$
$353$	−9.67212	−	16.7526i	−0.514795	−	0.891651i	0.485058	−	0.874482i	$-0.338799\pi$
$354$	9.33838	−	0.735040i	0.496329	−	0.0390669i
$355$	10.4499	−	18.0998i	0.554624	−	0.960637i
$356$	3.76006	+	1.52352i	0.199283	+	0.0807464i
$357$	−11.2231	+	10.3577i	−0.593989	+	0.548188i
$358$	4.42927	+	0.863251i	0.234094	+	0.0456243i
$359$		−	12.4559i		−	0.657396i	−0.944435	−	0.328698i	$-0.893390\pi$
$359$		−	12.4559i		−	0.657396i	0.944435	−	0.328698i	$-0.106610\pi$
$360$	−18.8245	+	9.99761i	−0.992137	+	0.526920i
$361$	−12.2444			−0.644440
$362$	32.5721	+	6.34822i	1.71195	+	0.333655i
$363$	−2.63746	−	9.49164i	−0.138431	−	0.498182i
$364$	−30.8499	+	21.6958i	−1.61697	+	1.13717i
$365$	−5.89616	+	10.2124i	−0.308619	+	0.534544i
$366$	11.7758	+	5.61663i	0.615531	+	0.293586i
$367$	23.7839	−	13.7316i	1.24151	−	0.716786i	0.272108	−	0.962267i	$-0.412279\pi$
$367$	23.7839	−	13.7316i	1.24151	−	0.716786i	0.969401	+	0.245481i	$0.0789458\pi$
$368$	−2.94670	−	10.3542i	−0.153607	−	0.539748i
$369$	−10.1038	−	5.58721i	−0.525982	−	0.290858i
$370$	−17.0573	+	19.6024i	−0.886766	+	1.01908i
$371$	28.4019	+	1.40172i	1.47455	+	0.0727736i
$372$	−4.11065	−	0.470382i	−0.213127	−	0.0243882i
$373$	4.35839	+	2.51632i	0.225669	+	0.130290i	0.608572	−	0.793498i	$-0.291743\pi$
$373$	4.35839	+	2.51632i	0.225669	+	0.130290i	−0.382904	+	0.923788i	$0.625076\pi$
$374$	−6.25918	−	18.2074i	−0.323654	−	0.941483i
$375$	11.4569	+	11.2473i	0.591634	+	0.580806i
$376$	−0.737530	+	13.6818i	−0.0380352	+	0.705585i
$377$	40.9386			2.10844
$378$	10.5130	+	16.3547i	0.540730	+	0.841196i
$379$			22.1229i			1.13638i	0.822898	+	0.568190i	$0.192356\pi$
$379$			22.1229i			1.13638i	−0.822898	+	0.568190i	$0.807644\pi$
$380$	8.02901	+	10.2978i	0.411880	+	0.528266i
$381$	−8.63101	+	8.79190i	−0.442180	+	0.450423i
$382$	27.4020	−	9.41999i	1.40201	−	0.481969i
$383$	−7.11772	+	12.3283i	−0.363699	+	0.629944i	−0.988566	−	0.150786i	$-0.951820\pi$
$383$	−7.11772	+	12.3283i	−0.363699	+	0.629944i	0.624868	+	0.780731i	$0.285153\pi$
$384$	16.6777	+	10.2885i	0.851080	+	0.525035i
$385$	−1.33827	+	27.1162i	−0.0682045	+	1.38197i
$386$	12.7536	−	14.6566i	0.649142	−	0.746002i
$387$	−16.3094	−	27.0811i	−0.829055	−	1.37661i
$388$	−12.3376	+	1.72141i	−0.626348	+	0.0873914i
$389$	12.3467	+	21.3852i	0.626004	+	1.08427i	0.988346	+	0.152226i	$0.0486440\pi$
$389$	12.3467	+	21.3852i	0.626004	+	1.08427i	−0.362342	+	0.932045i	$0.618023\pi$
$390$	18.8798	−	39.5833i	0.956016	−	2.00438i
$391$	7.76763	+	4.48464i	0.392826	+	0.226798i
$392$	−15.4439	−	12.3890i	−0.780032	−	0.625739i
$393$	−8.54868	+	2.37544i	−0.431224	+	0.119825i
$394$	12.2460	+	2.38671i	0.616944	+	0.120241i
$395$		−	15.3617i		−	0.772929i
$396$	−24.2085	+	3.83474i	−1.21652	+	0.192703i
$397$	20.2460			1.01612			0.508058	−	0.861323i	$-0.330363\pi$
$397$	20.2460			1.01612			0.508058	+	0.861323i	$0.330363\pi$
$398$	3.26972	−	16.7767i	0.163896	−	0.840938i
$399$	8.75294	−	8.07802i	0.438195	−	0.404407i
$400$	−1.27770	+	5.08144i	−0.0638850	+	0.254072i
$401$	30.9477	+	17.8676i	1.54545	+	0.892268i	0.998480	+	0.0551171i	$0.0175532\pi$
$401$	30.9477	+	17.8676i	1.54545	+	0.892268i	0.546973	+	0.837150i	$0.315780\pi$
$402$	−0.833336	+	0.0655933i	−0.0415630	+	0.00327150i
$403$	7.37243	−	4.25648i	0.367247	−	0.212030i
$404$	−0.0741756	+	0.0103494i	−0.00369037	+	0.000514900i
$405$	−19.9828	−	10.5730i	−0.992954	−	0.525378i
$406$	5.97642	+	20.6435i	0.296605	+	1.02452i
$407$	−25.8773	+	14.9403i	−1.28269	+	0.740563i
$408$	−15.9431	+	3.51802i	−0.789302	+	0.174168i
$409$	25.3670	+	14.6456i	1.25432	+	0.724180i	0.971964	−	0.235131i	$-0.0755519\pi$
$409$	25.3670	+	14.6456i	1.25432	+	0.724180i	0.282352	+	0.959311i	$0.408885\pi$
$410$	−12.9291	+	4.44466i	−0.638525	+	0.219506i
$411$	−0.921764	+	3.57168i	−0.0454673	+	0.176178i
$412$	−18.5958	−	23.8505i	−0.916151	−	1.17503i
$413$	−8.50225	−	5.48467i	−0.418368	−	0.269883i
$414$	7.33502	−	8.75074i	0.360497	−	0.430076i
$415$	−20.1776			−0.990480
$416$	−40.1742	+	3.41402i	−1.96970	+	0.167386i
$417$	0.425461	+	1.53114i	0.0208349	+	0.0749804i
$418$	4.88156	+	14.2001i	0.238765	+	0.694547i
$419$	17.4221	+	10.0586i	0.851125	+	0.491397i	0.861030	−	0.508554i	$-0.169820\pi$
$419$	17.4221	+	10.0586i	0.851125	+	0.491397i	−0.00990557	+	0.999951i	$0.503153\pi$
$420$	22.7163	+	3.74168i	1.10844	+	0.182575i
$421$	−30.6373	+	17.6885i	−1.49317	+	0.862083i	−0.999969	−	0.00783123i	$-0.997507\pi$
$421$	−30.6373	+	17.6885i	−1.49317	+	0.862083i	−0.493203	+	0.869914i	$0.664174\pi$
$422$	−10.2856	−	8.95017i	−0.500698	−	0.435688i
$423$	−12.4494	+	7.49760i	−0.605312	+	0.364546i
$424$	25.4707	+	16.5950i	1.23697	+	0.805925i
$425$	−2.18273	−	3.78060i	−0.105878	−	0.183386i
$426$	−11.5436	−	16.7957i	−0.559290	−	0.813754i
$427$	−6.43588	−	12.5365i	−0.311454	−	0.606686i
$428$	36.0664	+	14.6136i	1.74334	+	0.706374i
$429$	35.3289	−	35.9875i	1.70570	−	1.73749i
$430$	−36.7431	−	7.16112i	−1.77191	−	0.345340i
$431$			0.805267i			0.0387883i	0.999812	+	0.0193942i	$0.00617374\pi$
$431$			0.805267i			0.0387883i	−0.999812	+	0.0193942i	$0.993826\pi$
$432$	0.896892	+	20.7652i	0.0431518	+	0.999069i
$433$			29.6460i			1.42470i	0.701825	+	0.712349i	$0.252369\pi$
$433$			29.6460i			1.42470i	−0.701825	+	0.712349i	$0.747631\pi$
$434$	3.22262	+	3.09622i	0.154691	+	0.148623i
$435$	−17.8331	−	17.5068i	−0.855034	−	0.839386i
$436$	5.68057	−	14.0197i	0.272050	−	0.671421i
$437$	−6.05801	−	3.49759i	−0.289794	−	0.167313i
$438$	6.51325	+	9.47664i	0.311215	+	0.452811i
$439$	−28.8335	+	16.6470i	−1.37615	+	0.794518i	−0.991693	−	0.128627i	$-0.958943\pi$
$439$	−28.8335	+	16.6470i	−1.37615	+	0.794518i	−0.384453	+	0.923145i	$0.625610\pi$
$440$	−15.8438	+	24.3177i	−0.755324	+	1.15930i
$441$	1.68149	−	20.9326i	0.0800710	−	0.996789i
$442$	22.0513	−	25.3416i	1.04887	−	1.20538i
$443$	−1.92340	−	3.33143i	−0.0913836	−	0.158281i	0.816710	−	0.577048i	$-0.195796\pi$
$443$	−1.92340	−	3.33143i	−0.0913836	−	0.158281i	−0.908094	+	0.418767i	$0.862462\pi$
$444$	10.0924	+	23.2419i	0.478964	+	1.10301i
$445$	4.41282	+	2.54774i	0.209188	+	0.120774i
$446$	17.5074	−	6.01854i	0.829001	−	0.284986i
$447$	10.6277	+	38.2468i	0.502672	+	1.80901i
$448$	−7.58638	−	19.7597i	−0.358423	−	0.933559i
$449$		−	20.6012i		−	0.972229i	−0.873895	−	0.486115i	$-0.838414\pi$
$449$		−	20.6012i		−	0.972229i	0.873895	−	0.486115i	$-0.161586\pi$
$450$	−5.22130	+	1.90346i	−0.246135	+	0.0897301i
$451$	−15.7216			−0.740301
$452$	12.0238	+	15.4213i	0.565550	+	0.725359i
$453$	4.28731	+	1.10645i	0.201435	+	0.0519856i
$454$	29.8515	−	10.2621i	1.40100	−	0.481622i
$455$	−42.1405	+	21.6336i	−1.97558	+	1.01420i
$456$	12.4341	−	2.74372i	0.582281	−	0.128486i
$457$	10.5366	+	18.2500i	0.492883	+	0.853698i	0.999966	−	0.00819909i	$-0.00260988\pi$
$457$	10.5366	+	18.2500i	0.492883	+	0.853698i	−0.507084	+	0.861897i	$0.669277\pi$
$458$	−5.11899	+	5.88281i	−0.239195	+	0.274886i
$459$	−12.5795	−	11.9011i	−0.587160	−	0.555496i
$460$	−1.86842	−	13.3912i	−0.0871154	−	0.624370i
$461$	−11.6027	+	6.69882i	−0.540392	+	0.311995i	−0.745238	−	0.666799i	$-0.767664\pi$
$461$	−11.6027	+	6.69882i	−0.540392	+	0.311995i	0.204846	+	0.978794i	$0.434331\pi$
$462$	23.3044	+	12.5612i	1.08422	+	0.584400i
$463$	−0.633607	+	1.09744i	−0.0294462	+	0.0510023i	−0.880373	−	0.474282i	$-0.842708\pi$
$463$	−0.633607	+	1.09744i	−0.0294462	+	0.0510023i	0.850927	+	0.525284i	$0.176041\pi$
$464$	−5.60257	+	22.2815i	−0.260093	+	1.03439i
$465$	−5.03171	−	1.29856i	−0.233340	−	0.0602194i
$466$	2.22481	−	11.4153i	0.103062	−	0.528803i
$467$			9.31161i			0.430890i	0.976516	+	0.215445i	$0.0691202\pi$
$467$			9.31161i			0.430890i	−0.976516	+	0.215445i	$0.930880\pi$
$468$	−26.9134	−	33.2340i	−1.24407	−	1.53624i
$469$	0.758722	+	0.489440i	0.0350345	+	0.0226002i
$470$	−3.29204	+	16.8911i	−0.151850	+	0.779130i
$471$	−5.81037	−	20.9103i	−0.267728	−	0.963493i
$472$	−4.89613	−	9.64479i	−0.225363	−	0.443938i
$473$	−37.2797	−	21.5235i	−1.71412	−	0.989650i
$474$	−13.5205	−	6.44878i	−0.621017	−	0.296202i
$475$	1.70232	+	2.94851i	0.0781080	+	0.135287i
$476$	15.9978	+	7.42000i	0.733259	+	0.340095i
$477$	0.595485	+	32.2384i	0.0272654	+	1.47609i
$478$	2.28390	+	1.98736i	0.104463	+	0.0908999i
$479$	8.99766	+	15.5844i	0.411114	+	0.712070i	0.995012	−	0.0997572i	$-0.0318066\pi$
$479$	8.99766	+	15.5844i	0.411114	+	0.712070i	−0.583898	+	0.811827i	$0.698473\pi$
$480$	18.9602	+	15.6928i	0.865409	+	0.716274i
$481$	−45.1500	−	26.0674i	−2.05866	−	1.18857i
$482$	−24.9724	+	8.58477i	−1.13746	+	0.391025i
$483$	−12.0313	+	2.71218i	−0.547442	+	0.123408i
$484$	−8.97080	+	6.99438i	−0.407764	+	0.317926i
$485$	−15.6459			−0.710442
$486$	−17.6945	+	13.1493i	−0.802641	+	0.596463i
$487$	33.8968			1.53601			0.768005	−	0.640444i	$-0.221249\pi$
$487$	33.8968			1.53601			0.768005	+	0.640444i	$0.221249\pi$
$488$	0.810917	−	15.0432i	0.0367085	−	0.680973i
$489$	−10.5900	−	10.3962i	−0.478897	−	0.470133i
$490$	−17.0608	−	18.0914i	−0.770728	−	0.817287i
$491$	0.472690	−	0.818724i	0.0213322	−	0.0369485i	−0.855162	−	0.518360i	$-0.826543\pi$
$491$	0.472690	−	0.818724i	0.0213322	−	0.0369485i	0.876494	+	0.481412i	$0.159876\pi$
$492$	−1.51567	+	13.2454i	−0.0683317	+	0.597148i
$493$	−9.57103	−	16.5775i	−0.431058	−	0.746614i
$494$	−17.1979	+	19.7640i	−0.773769	+	0.889225i
$495$	−30.7791	+	0.568530i	−1.38342	+	0.0255535i
$496$	1.30772	+	4.59509i	0.0587184	+	0.206326i
$497$	−1.08509	+	21.9863i	−0.0486730	+	0.986221i
$498$	−8.47051	+	17.7592i	−0.379573	+	0.795811i
$499$	22.7475	+	13.1333i	1.01832	+	0.587927i	0.913617	−	0.406577i	$-0.133278\pi$
$499$	22.7475	+	13.1333i	1.01832	+	0.587927i	0.104702	+	0.994504i	$0.466611\pi$
$500$	6.96183	−	17.1819i	0.311343	−	0.768396i
$501$	3.33388	+	11.9979i	0.148947	+	0.536027i
$502$	−4.92710	+	25.2805i	−0.219907	+	1.12832i
$503$	21.0698			0.939454			0.469727	−	0.882812i	$-0.344352\pi$
$503$	21.0698			0.939454			0.469727	+	0.882812i	$0.344352\pi$
$504$	12.8295	−	18.4229i	0.571470	−	0.820623i
$505$	−0.0940652			−0.00418584
$506$	2.97432	−	15.2610i	0.132225	−	0.678434i
$507$	63.3957	+	16.3609i	2.81550	+	0.726613i
$508$	13.1851	+	5.34242i	0.584996	+	0.237032i
$509$	11.1901	+	6.46063i	0.495994	+	0.286362i	0.727058	−	0.686576i	$-0.240887\pi$
$509$	11.1901	+	6.46063i	0.495994	+	0.286362i	−0.231064	+	0.972939i	$0.574221\pi$
$510$	−20.4427	+	1.60908i	−0.905216	+	0.0712511i
$511$	0.612241	−	12.4053i	0.0270840	−	0.548780i
$512$	3.63984	−	22.3327i	0.160860	−	0.986977i
$513$	9.81080	+	9.28173i	0.433157	+	0.409798i
$514$	10.8063	−	12.4188i	0.476647	−	0.547769i
$515$	−18.9924	−	32.8957i	−0.836904	−	1.44956i
$516$	−21.7275	+	29.3331i	−0.956499	+	1.29132i
$517$	−9.89454	+	17.1378i	−0.435161	+	0.753722i
$518$	6.55340	−	26.5726i	0.287940	−	1.16753i
$519$	1.26445	−	4.89955i	0.0555034	−	0.215066i
$520$	−50.5663	−	2.72583i	−2.21748	−	0.119535i
$521$	−27.6537			−1.21153			−0.605766	−	0.795643i	$-0.707133\pi$
$521$	−27.6537			−1.21153			−0.605766	+	0.795643i	$0.707133\pi$
$522$	−22.8948	+	8.34647i	−1.00208	+	0.365315i
$523$	−27.1522			−1.18728			−0.593641	−	0.804730i	$-0.702310\pi$
$523$	−27.1522			−1.18728			−0.593641	+	0.804730i	$0.702310\pi$
$524$	6.29951	+	8.07958i	0.275196	+	0.352958i
$525$	5.73128	+	1.78469i	0.250134	+	0.0778904i
$526$	−20.0320	+	6.88642i	−0.873438	+	0.300262i
$527$	−3.44721	−	1.99025i	−0.150163	−	0.0866965i
$528$	14.7520	+	24.1534i	0.641996	+	1.05114i
$529$	−7.87839	−	13.6458i	−0.342539	−	0.593294i
$530$	28.8034	+	25.0636i	1.25114	+	1.08869i
$531$	5.55179	−	10.0397i	0.240927	−	0.435687i
$532$	−12.4768	−	5.78689i	−0.540936	−	0.250893i
$533$	−13.7153	−	23.7555i	−0.594074	−	1.02897i
$534$	4.09487	−	2.81439i	0.177202	−	0.121790i
$535$	42.3276	+	24.4379i	1.82998	+	1.05654i
$536$	0.436920	+	0.860680i	0.0188721	+	0.0371757i
$537$	3.87178	−	3.94395i	0.167079	−	0.170194i
$538$	2.64573	−	13.5750i	0.114066	−	0.585261i
$539$	−11.7897	−	26.0518i	−0.507820	−	1.12213i
$540$	−2.48833	+	25.9861i	−0.107081	+	1.11826i
$541$		−	33.9153i		−	1.45813i	−0.684442	−	0.729067i	$-0.739954\pi$
$541$		−	33.9153i		−	1.45813i	0.684442	−	0.729067i	$-0.260046\pi$
$542$	2.75717	−	14.1468i	0.118431	−	0.607656i
$543$	28.4724	−	29.0032i	1.22187	−	1.24465i
$544$	10.7748	+	15.4699i	0.461966	+	0.663265i
$545$	9.49945	−	16.4535i	0.406912	−	0.704792i
$546$	1.35029	+	46.1715i	0.0577871	+	1.97596i
$547$	8.23852	−	4.75651i	0.352254	−	0.203374i	−0.313424	−	0.949613i	$-0.601476\pi$
$547$	8.23852	−	4.75651i	0.352254	−	0.203374i	0.665677	+	0.746240i	$0.268143\pi$
$548$	4.21849	−	0.588586i	0.180205	−	0.0251432i
$549$	13.6882	−	8.24364i	0.584198	−	0.351830i
$550$	−4.96756	+	5.70878i	−0.211817	+	0.243423i
$551$	7.46449	+	12.9289i	0.317998	+	0.550789i
$552$	−12.5706	−	3.97713i	−0.535040	−	0.169278i
$553$	7.38941	+	14.3939i	0.314230	+	0.612093i
$554$	−9.16287	+	3.14992i	−0.389293	+	0.133827i
$555$	8.52035	+	30.6629i	0.361669	+	1.30157i
$556$	1.44712	−	1.12830i	0.0613717	−	0.0478504i
$557$	30.5678			1.29520			0.647599	−	0.761981i	$-0.275773\pi$
$557$	30.5678			1.29520			0.647599	+	0.761981i	$0.275773\pi$
$558$	−3.25522	+	3.88351i	−0.137805	+	0.164402i
$559$		−	75.1069i		−	3.17669i
$560$	−6.00742	−	25.8963i	−0.253860	−	1.09432i
$561$	−22.8322	−	5.89244i	−0.963977	−	0.248779i
$562$	−6.32342	+	2.17381i	−0.266737	+	0.0916965i
$563$	−0.848496	−	0.489879i	−0.0357598	−	0.0206459i	0.482014	−	0.876164i	$-0.339906\pi$
$563$	−0.848496	−	0.489879i	−0.0357598	−	0.0206459i	−0.517773	+	0.855518i	$0.673239\pi$
$564$	13.4847	+	9.98833i	0.567808	+	0.420584i
$565$	12.2802	+	21.2698i	0.516630	+	0.894829i
$566$	−28.8276	+	33.1291i	−1.21172	+	1.39252i
$567$	23.8099	+	0.294654i	0.999923	+	0.0123743i
$568$	−12.8464	+	19.7172i	−0.539025	+	0.827317i
$569$	−25.9899	+	15.0053i	−1.08955	+	0.629054i	−0.933457	−	0.358688i	$-0.883224\pi$
$569$	−25.9899	+	15.0053i	−1.08955	+	0.629054i	−0.156095	+	0.987742i	$0.549891\pi$
$570$	15.9433	−	1.25493i	0.667792	−	0.0525631i
$571$	3.21671	+	1.85717i	0.134615	+	0.0777201i	0.565795	−	0.824546i	$-0.308569\pi$
$571$	3.21671	+	1.85717i	0.134615	+	0.0777201i	−0.431180	+	0.902266i	$0.641903\pi$
$572$	−53.9701	−	21.8679i	−2.25660	−	0.914343i
$573$	8.86806	−	34.3622i	0.370468	−	1.43550i
$574$	9.97666	−	10.3840i	0.416418	−	0.433419i
$575$		−	3.52537i		−	0.147018i
$576$	21.7713	−	10.0999i	0.907139	−	0.420830i
$577$			3.22851i			0.134405i	0.997739	+	0.0672023i	$0.0214073\pi$
$577$			3.22851i			0.134405i	−0.997739	+	0.0672023i	$0.978593\pi$
$578$	8.18053	+	1.59436i	0.340265	+	0.0663167i
$579$	−6.37061	−	22.9264i	−0.264753	−	0.952790i
$580$	−10.8364	+	26.7442i	−0.449955	+	1.11049i
$581$	18.9065	−	9.70603i	0.784375	−	0.402674i
$582$	−6.56809	+	13.7706i	−0.272256	+	0.570811i
$583$	21.9530	+	38.0237i	0.909200	+	1.57478i
$584$	7.24835	−	11.1251i	0.299939	−	0.460358i
$585$	−27.7103	−	46.0117i	−1.14568	−	1.90235i
$586$	−11.5584	−	10.0577i	−0.477474	−	0.415479i
$587$	19.4303	−	11.2181i	0.801972	−	0.463019i	−0.0421879	−	0.999110i	$-0.513433\pi$
$587$	19.4303	−	11.2181i	0.801972	−	0.463019i	0.844160	+	0.536091i	$0.180099\pi$
$588$	−23.0852	+	7.42125i	−0.952016	+	0.306047i
$589$	2.68849	+	1.55220i	0.110777	+	0.0639574i
$590$	−4.41648	−	12.8472i	−0.181824	−	0.528910i
$591$	10.7046	−	10.9042i	0.440330	−	0.448539i
$592$	20.3665	−	21.0063i	0.837059	−	0.863352i
$593$	−26.3284			−1.08118			−0.540588	−	0.841287i	$-0.681798\pi$
$593$	−26.3284			−1.08118			−0.540588	+	0.841287i	$0.681798\pi$
$594$	−12.4206	+	27.3288i	−0.509623	+	1.12131i
$595$	18.6123	+	12.0065i	0.763030	+	0.492218i
$596$	36.1480	−	28.1840i	1.48068	−	1.15446i
$597$	−14.9384	−	14.6651i	−0.611390	−	0.600201i
$598$	25.6543	−	8.81921i	1.04908	−	0.360644i
$599$	7.08382	+	4.08985i	0.289437	+	0.167107i	0.637688	−	0.770295i	$-0.279891\pi$
$599$	7.08382	+	4.08985i	0.289437	+	0.167107i	−0.348251	+	0.937401i	$0.613224\pi$
$600$	4.33072	+	4.73552i	0.176801	+	0.193327i
$601$	15.1744	−	8.76094i	0.618976	−	0.357366i	−0.157494	−	0.987520i	$-0.550341\pi$
$601$	15.1744	−	8.76094i	0.618976	−	0.357366i	0.776470	+	0.630154i	$0.217008\pi$
$602$	37.8732	−	10.9645i	1.54359	−	0.446880i
$603$	−0.495429	+	0.895923i	−0.0201754	+	0.0364848i
$604$	−0.706516	−	5.06371i	−0.0287477	−	0.206040i
$605$	−12.3730	+	7.14353i	−0.503032	+	0.290426i
$606$	−0.0394883	+	0.0827911i	−0.00160410	+	0.00336316i
$607$	7.58509	+	4.37925i	0.307869	+	0.177748i	0.645973	−	0.763361i	$-0.276452\pi$
$607$	7.58509	+	4.37925i	0.307869	+	0.177748i	−0.338103	+	0.941109i	$0.609785\pi$
$608$	−8.40332	−	12.0650i	−0.340800	−	0.489301i
$609$	25.1310	+	7.82567i	1.01836	+	0.317112i
$610$	3.61960	−	18.5719i	0.146554	−	0.751953i
$611$	−34.5274			−1.39683
$612$	−7.16555	+	18.6680i	−0.289650	+	0.754609i
$613$			1.91951i			0.0775281i	0.999248	+	0.0387641i	$0.0123421\pi$
$613$			1.91951i			0.0775281i	−0.999248	+	0.0387641i	$0.987658\pi$
$614$	−20.3673	−	3.96953i	−0.821957	−	0.160197i
$615$	−4.18424	+	16.2132i	−0.168725	+	0.653781i
$616$	3.14819	−	30.4072i	0.126844	−	1.22514i
$617$	22.0778	+	12.7466i	0.888819	+	0.513160i	0.873556	−	0.486723i	$-0.161808\pi$
$617$	22.0778	+	12.7466i	0.888819	+	0.513160i	0.0152632	+	0.999884i	$0.495141\pi$
$618$	−36.9260	+	2.90651i	−1.48538	+	0.116917i
$619$	14.9276	+	25.8554i	0.599992	+	1.03922i	0.992821	+	0.119606i	$0.0381630\pi$
$619$	14.9276	+	25.8554i	0.599992	+	1.03922i	−0.392829	+	0.919611i	$0.628504\pi$
$620$	0.829188	+	5.94292i	0.0333010	+	0.238673i
$621$	−3.99225	−	13.4026i	−0.160203	−	0.537827i
$622$	−5.88069	+	6.75816i	−0.235794	+	0.270978i
$623$	−5.36037	−	0.264550i	−0.214759	−	0.0105990i
$624$	−23.6267	+	43.3615i	−0.945826	+	1.73585i
$625$	14.9168	−	25.8367i	0.596673	−	1.03347i
$626$	−19.0483	+	6.54826i	−0.761324	+	0.261721i
$627$	17.8070	+	4.59554i	0.711141	+	0.183528i
$628$	−19.7628	+	15.4087i	−0.788623	+	0.614876i
$629$			24.3772i			0.971982i
$630$	19.1564	−	20.6901i	0.763209	−	0.824313i
$631$	22.5104			0.896124			0.448062	−	0.894002i	$-0.352114\pi$
$631$	22.5104			0.896124			0.448062	+	0.894002i	$0.352114\pi$
$632$	−0.931062	+	17.2720i	−0.0370357	+	0.687042i
$633$	−16.0892	+	4.47074i	−0.639489	+	0.177696i
$634$	−3.88219	−	11.2930i	−0.154181	−	0.448501i
$635$	15.4741	+	8.93398i	0.614071	+	0.354534i
$636$	34.1513	−	14.8296i	1.35419	−	0.588031i
$637$	29.0794	−	40.5416i	1.15217	−	1.60632i
$638$	−21.7822	+	25.0323i	−0.862364	+	0.991040i
$639$	−24.9562	+	0.460974i	−0.987253	+	0.0182359i
$640$	8.40374	−	27.1486i	0.332187	−	1.07314i
$641$	−21.1575	+	12.2153i	−0.835671	+	0.482475i	−0.855790	−	0.517323i	$-0.826929\pi$
$641$	−21.1575	+	12.2153i	−0.835671	+	0.482475i	0.0201196	+	0.999798i	$0.493595\pi$
$642$	39.2779	−	26.9955i	1.55018	−	1.06543i
$643$	−1.25117	+	2.16709i	−0.0493414	+	0.0854618i	−0.889641	−	0.456660i	$-0.849046\pi$
$643$	−1.25117	+	2.16709i	−0.0493414	+	0.0854618i	0.840300	+	0.542122i	$0.182379\pi$
$644$	8.19230	+	11.6489i	0.322822	+	0.459031i
$645$	−32.1184	+	32.7172i	−1.26466	+	1.28824i
$646$	12.0239	+	2.34342i	0.473073	+	0.0922006i
$647$	4.41702			0.173651			0.0868254	−	0.996224i	$-0.472328\pi$
$647$	4.41702			0.173651			0.0868254	+	0.996224i	$0.472328\pi$
$648$	21.8270	+	13.0990i	0.857444	+	0.514577i
$649$		−	15.6219i		−	0.613214i
$650$	−12.9597	−	2.52580i	−0.508320	−	0.0990701i
$651$	5.33938	−	1.20364i	0.209267	−	0.0471744i
$652$	−6.43504	+	15.8817i	−0.252016	+	0.621977i
$653$	9.85771	−	17.0741i	0.385762	−	0.668160i	−0.606113	−	0.795379i	$-0.707272\pi$
$653$	9.85771	−	17.0741i	0.385762	−	0.668160i	0.991875	+	0.127219i	$0.0406052\pi$
$654$	−10.4937	−	15.2680i	−0.410335	−	0.597028i
$655$	6.43384	+	11.1437i	0.251391	+	0.435422i
$656$	14.8063	−	4.21375i	0.578091	−	0.164519i
$657$	14.0810	−	0.260095i	0.549354	−	0.0101473i
$658$	−5.04048	−	17.4106i	−0.196499	−	0.678738i
$659$	9.56805	+	16.5723i	0.372718	+	0.645567i	0.989983	−	0.141189i	$-0.0450925\pi$
$659$	9.56805	+	16.5723i	0.372718	+	0.645567i	−0.617265	+	0.786756i	$0.711759\pi$
$660$	14.1583	+	32.6054i	0.551111	+	1.26916i
$661$	9.43468	−	16.3414i	0.366967	−	0.635605i	−0.622123	−	0.782919i	$-0.713730\pi$
$661$	9.43468	−	16.3414i	0.366967	−	0.635605i	0.989090	+	0.147315i	$0.0470630\pi$
$662$	−5.87016	+	2.01799i	−0.228150	+	0.0784313i
$663$	−11.0149	−	39.6403i	−0.427784	−	1.53950i
$664$	22.6868	+	1.22295i	0.880419	+	0.0474598i
$665$	−14.5158	−	9.36392i	−0.562899	−	0.363117i
$666$	30.5646	+	5.37305i	1.18436	+	0.208201i
$667$		−	15.4584i		−	0.598550i
$668$	11.3395	−	8.84125i	0.438740	−	0.342078i
$669$	5.66591	−	21.9544i	0.219057	−	0.848808i
$670$	0.394117	+	1.14645i	0.0152261	+	0.0442914i
$671$	10.8791	−	18.8431i	0.419982	−	0.727431i
$672$	−25.3144	−	5.58380i	−0.976526	−	0.215400i
$673$	19.5846	+	33.9214i	0.754929	+	1.30758i	0.945410	+	0.325884i	$0.105662\pi$
$673$	19.5846	+	33.9214i	0.754929	+	1.30758i	−0.190481	+	0.981691i	$0.561005\pi$
$674$	23.3406	−	26.8233i	0.899045	−	1.03319i
$675$	−1.57885	+	6.62080i	−0.0607699	+	0.254835i
$676$	−10.4471	−	74.8763i	−0.401813	−	2.87986i
$677$	7.15258	−	4.12954i	0.274896	−	0.158711i	−0.356215	−	0.934404i	$-0.615933\pi$
$677$	7.15258	−	4.12954i	0.274896	−	0.158711i	0.631110	+	0.775693i	$0.282599\pi$
$678$	23.8757	−	1.87930i	0.916942	−	0.0721741i
$679$	14.6602	−	7.52612i	0.562609	−	0.288826i
$680$	10.7181	+	21.1134i	0.411021	+	0.809663i
$681$	9.66079	−	37.4339i	0.370202	−	1.43447i
$682$	−1.31998	+	6.77270i	−0.0505447	+	0.259340i
$683$	21.3284			0.816108			0.408054	−	0.912958i	$-0.366207\pi$
$683$	21.3284			0.816108			0.408054	+	0.912958i	$0.366207\pi$
$684$	5.58844	−	14.5593i	0.213680	−	0.556687i
$685$	5.34964			0.204399
$686$	24.6886	+	8.74501i	0.942613	+	0.333886i
$687$	2.55701	+	9.20212i	0.0975559	+	0.351083i
$688$	40.8783	+	10.2786i	1.55847	+	0.391869i
$689$	−38.3029	+	66.3425i	−1.45922	+	2.52745i
$690$	−14.9466	−	7.12899i	−0.569008	−	0.271396i
$691$	−18.4593	−	31.9724i	−0.702223	−	1.21629i	−0.967684	−	0.252165i	$-0.918858\pi$
$691$	−18.4593	−	31.9724i	−0.702223	−	1.21629i	0.265461	−	0.964122i	$-0.414476\pi$
$692$	−5.78682	+	0.807408i	−0.219982	+	0.0306930i
$693$	28.5667	−	15.3384i	1.08516	−	0.582656i
$694$	−30.0753	+	34.5630i	−1.14164	+	1.31199i
$695$	1.99594	−	1.15236i	0.0757103	−	0.0437114i
$696$	18.9897	+	20.7647i	0.719803	+	0.787084i
$697$	−6.41299	+	11.1076i	−0.242909	+	0.420732i
$698$	2.81950	+	8.20168i	0.106720	+	0.310438i
$699$	−10.1645	−	9.97851i	−0.384458	−	0.377422i
$700$	−0.618267	−	6.90372i	−0.0233683	−	0.260936i
$701$	12.8202			0.484214			0.242107	−	0.970250i	$-0.422162\pi$
$701$	12.8202			0.484214			0.242107	+	0.970250i	$0.422162\pi$
$702$	−52.1297	+	5.07350i	−1.96751	+	0.191487i
$703$		−	19.0119i		−	0.717046i
$704$	19.2880	−	26.3815i	0.726943	−	0.994290i
$705$	15.0404	+	14.7651i	0.566454	+	0.556087i
$706$	8.89365	+	25.8709i	0.334717	+	0.973663i
$707$	0.0881395	−	0.0452481i	0.00331483	−	0.00170173i
$708$	−13.1614	−	1.50606i	−0.494637	−	0.0566013i
$709$	−25.0800	+	14.4799i	−0.941899	+	0.543805i	−0.890555	−	0.454876i	$-0.849684\pi$
$709$	−25.0800	+	14.4799i	−0.941899	+	0.543805i	−0.0513436	+	0.998681i	$0.516350\pi$
$710$	−19.4021	+	22.2972i	−0.728149	+	0.836798i
$711$	−15.7162	+	9.46501i	−0.589405	+	0.354965i
$712$	−4.80716	−	3.13202i	−0.180156	−	0.117378i
$713$	−1.60724	−	2.78382i	−0.0601917	−	0.104255i
$714$	18.3809	−	11.3412i	0.687886	−	0.424435i
$715$	−63.3395	−	36.5691i	−2.36876	−	1.36761i
$716$	−5.91471	−	2.39655i	−0.221043	−	0.0895633i
$717$	3.57257	−	0.992715i	0.133420	−	0.0370736i
$718$	−3.36976	+	17.2899i	−0.125758	+	0.645255i
$719$	29.4582			1.09860			0.549302	−	0.835624i	$-0.314894\pi$
$719$	29.4582			1.09860			0.549302	+	0.835624i	$0.314894\pi$
$720$	28.8349	−	8.78494i	1.07461	−	0.327396i
$721$	33.6198	+	21.6876i	1.25207	+	0.807688i
$722$	16.9964	+	3.31254i	0.632539	+	0.123280i
$723$	−8.08177	+	31.3155i	−0.300564	+	1.16464i
$724$	−43.4958	−	17.6239i	−1.61651	−	0.654986i
$725$	−3.76189	+	6.51579i	−0.139713	+	0.241990i
$726$	1.09321	+	13.8888i	0.0405730	+	0.515463i
$727$	−27.0277	+	15.6045i	−1.00240	+	0.578737i	−0.908958	−	0.416887i	$-0.863121\pi$
$727$	−27.0277	+	15.6045i	−1.00240	+	0.578737i	−0.0934443	+	0.995625i	$0.529788\pi$
$728$	48.6921	−	21.7698i	1.80465	−	0.806842i
$729$	1.49524	+	26.9586i	0.0553793	+	0.998465i
$730$	10.9473	−	12.5807i	0.405177	−	0.465634i
$731$	−30.4136	+	17.5593i	−1.12489	+	0.649453i
$732$	−14.8265	−	10.9822i	−0.548001	−	0.405914i
$733$	−18.0362	+	31.2397i	−0.666183	+	1.15386i	0.312780	+	0.949826i	$0.398740\pi$
$733$	−18.0362	+	31.2397i	−0.666183	+	1.15386i	−0.978963	+	0.204037i	$0.934594\pi$
$734$	−36.7292	+	12.6264i	−1.35570	+	0.466050i
$735$	−30.0043	+	5.22485i	−1.10672	+	0.192721i
$736$	1.28913	+	15.1698i	0.0475179	+	0.559164i
$737$			1.39407i			0.0513511i
$738$	12.5135	+	10.4890i	0.460627	+	0.386106i
$739$			5.28763i			0.194509i	0.995260	+	0.0972543i	$0.0310060\pi$
$739$			5.28763i			0.194509i	−0.995260	+	0.0972543i	$0.968994\pi$
$740$	28.9803	−	22.5954i	1.06534	−	0.830625i
$741$	8.59058	+	30.9156i	0.315583	+	1.13571i
$742$	−39.0453	−	9.62945i	−1.43340	−	0.353508i
$743$	−16.9518	−	9.78712i	−0.621901	−	0.359055i	0.155708	−	0.987803i	$-0.450234\pi$
$743$	−16.9518	−	9.78712i	−0.621901	−	0.359055i	−0.777609	+	0.628749i	$0.783567\pi$
$744$	5.57872	+	1.76501i	0.204526	+	0.0647086i
$745$	49.8571	−	28.7850i	1.82662	−	1.05460i
$746$	−5.36910	−	4.67199i	−0.196577	−	0.171054i
$747$	12.4323	+	20.6433i	0.454875	+	0.755301i
$748$	3.76258	+	26.9670i	0.137573	+	0.986011i
$749$	−51.4165	−	2.53756i	−1.87872	−	0.0927205i
$750$	−12.8605	−	18.7118i	−0.469600	−	0.683258i
$751$	−12.0067	+	20.7963i	−0.438132	+	0.758867i	−0.997545	−	0.0700218i	$-0.977693\pi$
$751$	−12.0067	+	20.7963i	−0.438132	+	0.758867i	0.559413	+	0.828889i	$0.311026\pi$
$752$	4.72518	−	18.7921i	0.172310	−	0.685278i
$753$	22.5105	+	22.0986i	0.820329	+	0.805316i
$754$	−56.8266	−	11.0754i	−2.06950	−	0.403340i
$755$		−	6.42151i		−	0.233703i
$756$	−10.1685	−	25.5461i	−0.369825	−	0.929101i
$757$		−	23.5249i		−	0.855026i	−0.904009	−	0.427513i	$-0.859390\pi$
$757$		−	23.5249i		−	0.855026i	0.904009	−	0.427513i	$-0.140610\pi$
$758$	5.98505	−	30.7088i	0.217387	−	1.11539i
$759$	−13.5889	−	13.3402i	−0.493244	−	0.484217i
$760$	−8.35912	−	16.4665i	−0.303217	−	0.597301i
$761$	21.3066	−	36.9042i	0.772365	−	1.33778i	−0.163898	−	0.986477i	$-0.552407\pi$
$761$	21.3066	−	36.9042i	0.772365	−	1.33778i	0.936264	−	0.351298i	$-0.114260\pi$
$762$	14.3592	−	9.86901i	0.520179	−	0.357516i
$763$	−0.986397	+	19.9866i	−0.0357100	+	0.723562i
$764$	−40.5850	+	5.66263i	−1.46831	+	0.204867i
$765$	−12.1534	+	21.9780i	−0.439408	+	0.794616i
$766$	13.2153	−	15.1872i	0.477489	−	0.548736i
$767$	23.6049	−	13.6283i	0.852325	−	0.492090i
$768$	−20.3668	−	18.7934i	−0.734925	−	0.678149i
$769$	−16.0999	−	9.29529i	−0.580578	−	0.335197i	0.180785	−	0.983523i	$-0.442136\pi$
$769$	−16.0999	−	9.29529i	−0.580578	−	0.335197i	−0.761363	+	0.648326i	$0.775469\pi$
$770$	9.19356	−	37.2779i	0.331313	−	1.34340i
$771$	−5.39792	−	19.4259i	−0.194401	−	0.699608i
$772$	−21.6684	+	16.8945i	−0.779862	+	0.608045i
$773$		−	3.85877i		−	0.138790i	−0.997589	−	0.0693952i	$-0.977893\pi$
$773$		−	3.85877i		−	0.138790i	0.997589	−	0.0693952i	$-0.0221069\pi$
$774$	15.3126	+	42.0035i	0.550402	+	1.50978i
$775$			1.56453i			0.0561996i
$776$	17.5915	+	0.948287i	0.631498	+	0.0340415i
$777$	−22.7334	−	24.6327i	−0.815555	−	0.883694i
$778$	−11.3530	−	33.0249i	−0.407024	−	1.18400i
$779$	5.00152	−	8.66289i	0.179198	−	0.310380i
$780$	−36.9157	+	49.8378i	−1.32179	+	1.78448i
$781$	−29.4347	+	16.9941i	−1.05326	+	0.608098i
$782$	−9.56895	−	8.32653i	−0.342185	−	0.297756i
$783$	−6.92307	+	29.0315i	−0.247410	+	1.03750i
$784$	18.0859	+	21.3752i	0.645924	+	0.763401i
$785$	−27.2578	+	15.7373i	−0.972874	+	0.561689i
$786$	12.5090	−	0.984608i	0.446182	−	0.0351198i
$787$	−0.480598	+	0.832421i	−0.0171315	+	0.0296726i	−0.874464	−	0.485090i	$-0.838787\pi$
$787$	−0.480598	+	0.832421i	−0.0171315	+	0.0296726i	0.857333	+	0.514763i	$0.172120\pi$
$788$	−16.3529	−	6.62596i	−0.582549	−	0.236040i
$789$	−6.48294	+	25.1203i	−0.230799	+	0.894306i
$790$	−4.15588	+	21.3235i	−0.147860	+	0.758655i
$791$	−21.7380	−	14.0228i	−0.772914	−	0.498595i
$792$	34.6411	+	1.22627i	1.23092	+	0.0435738i
$793$	37.9630			1.34810
$794$	−28.1034	−	5.47727i	−0.997351	−	0.194381i
$795$	45.0555	−	12.5196i	1.59795	−	0.444026i
$796$	−9.07738	+	22.4030i	−0.321739	+	0.794054i
$797$	41.0332	+	23.6906i	1.45347	+	0.839162i	0.998676	−	0.0514334i	$-0.0163790\pi$
$797$	41.0332	+	23.6906i	1.45347	+	0.839162i	0.454796	+	0.890596i	$0.349712\pi$
$798$	−14.3353	+	8.84508i	−0.507465	+	0.313112i
$799$	8.07216	+	13.9814i	0.285573	+	0.494626i
$800$	3.14828	−	6.70786i	0.111309	−	0.237159i
$801$	−0.112388	−	6.08445i	−0.00397102	−	0.214983i
$802$	−38.1245	−	33.1745i	−1.34622	−	1.17143i
$803$	16.6079	−	9.58860i	0.586082	−	0.338374i
$804$	1.17450	+	0.134398i	0.0414213	+	0.00473984i
$805$	8.16884	+	15.9122i	0.287914	+	0.560832i
$806$	−11.3852	+	3.91389i	−0.401026	+	0.137861i
$807$	−12.0876	−	11.8664i	−0.425504	−	0.417717i
$808$	0.105763	+	0.00570124i	0.00372072	+	0.000200569i
$809$		−	5.02516i		−	0.176675i	−0.996091	−	0.0883376i	$-0.971845\pi$
$809$		−	5.02516i		−	0.176675i	0.996091	−	0.0883376i	$-0.0281554\pi$
$810$	24.8777	+	20.0825i	0.874113	+	0.705625i
$811$	14.3208			0.502871			0.251435	−	0.967874i	$-0.419097\pi$
$811$	14.3208			0.502871			0.251435	+	0.967874i	$0.419097\pi$
$812$	−2.71103	−	30.2720i	−0.0951385	−	1.06234i
$813$	−12.5967	−	12.3662i	−0.441786	−	0.433701i
$814$	39.9621	−	13.7378i	1.40067	−	0.481510i
$815$	−10.7611	+	18.6388i	−0.376946	+	0.652890i
$816$	23.0823	−	0.570156i	0.808044	−	0.0199595i
$817$	23.7197	−	13.6946i	0.829846	−	0.479112i
$818$	−31.2496	−	27.1922i	−1.09262	−	0.950754i
$819$	48.0976	+	29.7837i	1.68067	+	1.04073i
$820$	19.1493	−	2.67182i	0.668724	−	0.0933039i
$821$	8.71307	+	15.0915i	0.304088	+	0.526697i	0.977058	−	0.212974i	$-0.0683149\pi$
$821$	8.71307	+	15.0915i	0.304088	+	0.526697i	−0.672970	+	0.739670i	$0.734982\pi$
$822$	2.24577	−	4.70847i	0.0783301	−	0.164227i
$823$	−20.5337	+	35.5654i	−0.715759	+	1.23973i	0.246908	+	0.969039i	$0.420586\pi$
$823$	−20.5337	+	35.5654i	−0.715759	+	1.23973i	−0.962666	+	0.270691i	$0.912748\pi$
$824$	19.3604	+	38.1376i	0.674451	+	1.32859i
$825$	2.48136	+	8.92989i	0.0863900	+	0.310899i
$826$	10.3181	+	9.91341i	0.359014	+	0.344932i
$827$	12.5790			0.437414			0.218707	−	0.975791i	$-0.429816\pi$
$827$	12.5790			0.437414			0.218707	+	0.975791i	$0.429816\pi$
$828$	−12.5491	+	10.1625i	−0.436112	+	0.353171i
$829$	22.4963			0.781328			0.390664	−	0.920533i	$-0.372245\pi$
$829$	22.4963			0.781328			0.390664	+	0.920533i	$0.372245\pi$
$830$	28.0085	+	5.45877i	0.972188	+	0.189477i
$831$	−2.96537	+	11.4903i	−0.102867	+	0.398594i
$832$	56.6893	+	6.12960i	1.96535	+	0.212506i
$833$	−23.2153	−	2.29708i	−0.804362	−	0.0795893i
$834$	−0.176352	−	2.24047i	−0.00610656	−	0.0775813i
$835$	15.6400	−	9.02978i	0.541246	−	0.312488i
$836$	−2.93445	−	21.0317i	−0.101490	−	0.727396i
$837$	1.77173	+	5.94795i	0.0612398	+	0.205591i
$838$	−21.4623	−	18.6757i	−0.741403	−	0.645140i
$839$	−15.9121	−	27.5606i	−0.549347	−	0.951497i	−0.998319	−	0.0579515i	$-0.981543\pi$
$839$	−15.9121	−	27.5606i	−0.549347	−	0.951497i	0.448972	−	0.893546i	$-0.351790\pi$
$840$	−30.5202	−	11.3394i	−1.05305	−	0.391246i
$841$	−1.99546	+	3.45624i	−0.0688091	+	0.119181i
$842$	47.3129	−	16.2648i	1.63051	−	0.560522i
$843$	−2.04644	+	7.92961i	−0.0704831	+	0.273110i
$844$	11.8561	+	15.2063i	0.408105	+	0.523424i
$845$		−	94.9538i		−	3.26651i
$846$	19.3094	−	7.03937i	0.663870	−	0.242018i
$847$	8.15727	−	12.6453i	0.280287	−	0.434497i
$848$	−30.8662	−	29.9262i	−1.05995	−	1.02767i
$849$	14.3998	+	51.8218i	0.494200	+	1.77852i
$850$	2.00705	+	5.83835i	0.0688414	+	0.200254i
$851$	−9.84301	+	17.0486i	−0.337414	+	0.584418i
$852$	11.4798	+	26.4370i	0.393291	+	0.905717i
$853$	−15.9619	−	27.6469i	−0.546526	−	0.946611i	−0.998509	−	0.0545847i	$-0.982617\pi$
$853$	−15.9619	−	27.6469i	−0.546526	−	0.946611i	0.451983	−	0.892027i	$-0.350717\pi$
$854$	5.54203	+	19.1431i	0.189644	+	0.655062i
$855$	9.47851	−	17.1407i	0.324158	−	0.586200i
$856$	−46.1101	−	30.0423i	−1.57601	−	1.02682i
$857$	−7.89332	−	13.6716i	−0.269631	−	0.467014i	0.699136	−	0.714989i	$-0.253568\pi$
$857$	−7.89332	−	13.6716i	−0.269631	−	0.467014i	−0.968766	+	0.247975i	$0.920235\pi$
$858$	−58.7759	+	40.3964i	−2.00657	+	1.37911i
$859$	−24.0785	+	41.7052i	−0.821549	+	1.42296i	0.0829803	+	0.996551i	$0.473556\pi$
$859$	−24.0785	+	41.7052i	−0.821549	+	1.42296i	−0.904529	+	0.426413i	$0.859777\pi$
$860$	49.0656	+	19.8807i	1.67312	+	0.677925i
$861$	−3.87839	−	17.2046i	−0.132175	−	0.586332i
$862$	0.217854	−	1.11779i	0.00742012	−	0.0380720i
$863$		−	21.8744i		−	0.744614i	−0.928110	−	0.372307i	$-0.878567\pi$
$863$		−	21.8744i		−	0.744614i	0.928110	−	0.372307i	$-0.121433\pi$
$864$	4.37277	−	29.0668i	0.148765	−	0.988873i
$865$	−7.33851			−0.249517
$866$	8.02032	−	41.1516i	0.272542	−	1.39839i
$867$	7.15088	−	7.28419i	0.242857	−	0.247384i
$868$	−3.63567	−	5.16968i	−0.123403	−	0.175470i
$869$	−12.4909	+	21.6349i	−0.423725	+	0.733914i
$870$	20.0179	+	29.1256i	0.678670	+	0.987450i
$871$	−2.10645	+	1.21616i	−0.0713744	+	0.0412080i
$872$	−11.6780	+	17.9239i	−0.395467	+	0.606978i
$873$	9.64011	+	16.0070i	0.326268	+	0.541754i
$874$	7.46287	+	6.49390i	0.252435	+	0.219660i
$875$	−1.20888	+	24.4946i	−0.0408677	+	0.828068i
$876$	−6.47725	−	14.9165i	−0.218846	−	0.503983i
$877$	3.45422	+	1.99430i	0.116641	+	0.0673426i	0.557185	−	0.830388i	$-0.311881\pi$
$877$	3.45422	+	1.99430i	0.116641	+	0.0673426i	−0.440545	+	0.897731i	$0.645215\pi$
$878$	44.5272	−	15.3071i	1.50272	−	0.516591i
$879$	−18.0801	+	5.02395i	−0.609828	+	0.169454i
$880$	28.5716	−	29.4690i	0.963147	−	0.993400i
$881$	31.2214			1.05188			0.525939	−	0.850523i	$-0.323714\pi$
$881$	31.2214			1.05188			0.525939	+	0.850523i	$0.323714\pi$
$882$	−7.99709	+	28.6015i	−0.269276	+	0.963063i
$883$			4.37577i			0.147256i	0.997286	+	0.0736282i	$0.0234578\pi$
$883$			4.37577i			0.147256i	−0.997286	+	0.0736282i	$0.976542\pi$
$884$	−37.4651	+	29.2109i	−1.26009	+	0.982468i
$885$	−16.1104	−	4.15772i	−0.541547	−	0.139760i
$886$	1.76860	+	5.14469i	0.0594171	+	0.172839i
$887$	−2.38625	+	4.13310i	−0.0801223	+	0.138776i	−0.903302	−	0.429005i	$-0.858864\pi$
$887$	−2.38625	+	4.13310i	−0.0801223	+	0.138776i	0.823180	+	0.567780i	$0.192198\pi$
$888$	−7.72144	−	34.9924i	−0.259114	−	1.17427i
$889$	−18.7968	−	0.927680i	−0.630425	−	0.0311134i
$890$	−5.43616	−	4.73033i	−0.182220	−	0.158561i
$891$	19.5460	+	31.1392i	0.654817	+	1.04320i
$892$	−25.9302	+	3.61793i	−0.868209	+	0.121137i
$893$	−6.29552	−	10.9042i	−0.210671	−	0.364894i
$894$	−4.40513	−	55.9653i	−0.147330	−	1.87176i
$895$	−6.94151	−	4.00769i	−0.232029	−	0.133962i
$896$	5.18491	+	29.4808i	0.173216	+	0.984884i
$897$	8.30248	−	32.1707i	0.277212	−	1.07415i
$898$	−5.57336	+	28.5964i	−0.185985	+	0.954274i
$899$			6.86029i			0.228803i
$900$	7.76263	−	1.22964i	0.258754	−	0.0409879i
$901$	35.8194			1.19332
$902$	21.8231	+	4.25326i	0.726629	+	0.141618i
$903$	14.3572	−	46.1060i	0.477777	−	1.53431i
$904$	−12.5181	−	24.6592i	−0.416346	−	0.820151i
$905$	−51.0468	−	29.4719i	−1.69685	−	0.979679i
$906$	−5.65186	−	2.69573i	−0.187771	−	0.0895597i
$907$	−21.1939	+	12.2363i	−0.703731	+	0.406299i	−0.808735	−	0.588173i	$-0.799848\pi$
$907$	−21.1939	+	12.2363i	−0.703731	+	0.406299i	0.105005	+	0.994472i	$0.466514\pi$
$908$	−44.2130	+	6.16883i	−1.46726	+	0.204720i
$909$	0.0579577	+	0.0962363i	0.00192234	+	0.00319196i
$910$	64.3477	−	18.6290i	2.13311	−	0.617547i
$911$	2.86688	−	1.65519i	0.0949840	−	0.0548391i	−0.451756	−	0.892142i	$-0.649202\pi$
$911$	2.86688	−	1.65519i	0.0949840	−	0.0548391i	0.546740	+	0.837303i	$0.315869\pi$
$912$	−18.0020	+	0.444667i	−0.596107	+	0.0147244i
$913$	28.4175	+	16.4069i	0.940484	+	0.542988i
$914$	−9.68857	−	28.1832i	−0.320470	−	0.932219i
$915$	−16.5370	−	16.2343i	−0.546695	−	0.536690i
$916$	8.69716	−	6.78103i	0.287362	−	0.224052i
$917$	−11.3890	−	7.34687i	−0.376098	−	0.242615i
$918$	14.2419	+	19.9231i	0.470051	+	0.657560i
$919$	−28.0405			−0.924971			−0.462485	−	0.886627i	$-0.653042\pi$
$919$	−28.0405			−0.924971			−0.462485	+	0.886627i	$0.653042\pi$
$920$	−1.02927	+	19.0938i	−0.0339340	+	0.629504i
$921$	−17.8037	+	18.1356i	−0.586653	+	0.597590i
$922$	17.9179	−	6.15966i	0.590096	−	0.202858i
$923$	−51.3568	−	29.6508i	−1.69043	−	0.975969i
$924$	−28.9505	−	23.7408i	−0.952403	−	0.781016i
$925$	8.29777	−	4.79072i	0.272829	−	0.157518i
$926$	1.17640	−	1.35194i	0.0386590	−	0.0444274i
$927$	−21.9530	+	39.6993i	−0.721030	+	1.30390i
$928$	13.8049	−	29.4132i	0.453167	−	0.965535i
$929$	22.1554	+	38.3743i	0.726895	+	1.25902i	0.958189	+	0.286135i	$0.0923705\pi$
$929$	22.1554	+	38.3743i	0.726895	+	1.25902i	−0.231295	+	0.972884i	$0.574296\pi$
$930$	6.63319	+	3.16379i	0.217511	+	0.103745i
$931$	18.1057	+	1.79151i	0.593391	+	0.0587143i
$932$	−6.17650	+	15.2436i	−0.202318	+	0.499322i
$933$	2.93749	+	10.5714i	0.0961690	+	0.346091i
$934$	2.51913	−	12.9254i	0.0824283	−	0.422932i
$935$			34.1980i			1.11839i
$936$	28.3674	+	53.4130i	0.927219	+	1.74586i
$937$		−	27.9959i		−	0.914588i	−0.889316	−	0.457294i	$-0.848819\pi$
$937$		−	27.9959i		−	0.914588i	0.889316	−	0.457294i	$-0.151181\pi$
$938$	−0.920768	−	0.884651i	−0.0300641	−	0.0288849i
$939$	−6.16459	+	23.8867i	−0.201174	+	0.779514i
$940$	9.13932	−	22.5559i	0.298092	−	0.735693i
$941$	−27.1490	−	15.6745i	−0.885033	−	0.510974i	−0.0127184	−	0.999919i	$-0.504049\pi$
$941$	−27.1490	−	15.6745i	−0.885033	−	0.510974i	−0.872315	+	0.488945i	$0.837382\pi$
$942$	2.40837	+	30.5973i	0.0784689	+	0.996915i
$943$	−8.97007	+	5.17887i	−0.292106	+	0.168647i
$944$	4.18704	+	14.7125i	0.136276	+	0.478850i
$945$	−8.21511	−	33.5423i	−0.267238	−	1.09113i
$946$	45.9250	+	39.9621i	1.49315	+	1.29928i
$947$	21.5828	+	37.3824i	0.701345	+	1.21477i	0.967994	+	0.250972i	$0.0807502\pi$
$947$	21.5828	+	37.3824i	0.701345	+	1.21477i	−0.266649	+	0.963794i	$0.585916\pi$
$948$	17.0231	+	12.6093i	0.552885	+	0.409531i
$949$	28.9770	+	16.7299i	0.940634	+	0.543075i
$950$	−1.56531	−	4.55336i	−0.0507854	−	0.147730i
$951$	−14.1614	−	3.65473i	−0.459216	−	0.118513i
$952$	−20.1991	−	14.6277i	−0.654657	−	0.474085i
$953$		−	17.2030i		−	0.557261i	−0.960398	−	0.278630i	$-0.910120\pi$
$953$		−	17.2030i		−	0.557261i	0.960398	−	0.278630i	$-0.0898804\pi$
$954$	7.89505	−	44.9111i	0.255612	−	1.45405i
$955$	−51.4675			−1.66545
$956$	−2.63262	−	3.37653i	−0.0851451	−	0.109205i
$957$	10.8805	+	39.1566i	0.351717	+	1.26575i
$958$	−8.27347	−	24.0668i	−0.267304	−	0.777564i
$959$	−5.01264	+	2.57334i	−0.161867	+	0.0830974i
$960$	−22.0731	−	26.9125i	−0.712405	−	0.868596i
$961$	−14.7867	−	25.6114i	−0.476991	−	0.826173i
$962$	55.6204	+	48.3987i	1.79327	+	1.56044i
$963$	−1.07802	−	58.3619i	−0.0347387	−	1.88069i
$964$	36.9865	−	5.16056i	1.19126	−	0.166210i
$965$	−29.8861	+	17.2547i	−0.962066	+	0.555449i
$966$	17.4343	−	0.509868i	0.560940	−	0.0164047i
$967$	4.72693	−	8.18728i	0.152008	−	0.263285i	−0.779958	−	0.625832i	$-0.784759\pi$
$967$	4.72693	−	8.18728i	0.152008	−	0.263285i	0.931965	+	0.362547i	$0.118093\pi$
$968$	14.3446	−	7.28195i	0.461052	−	0.234051i
$969$	10.5105	−	10.7064i	0.337645	−	0.343940i
$970$	21.7180	+	4.23277i	0.697321	+	0.135906i
$971$			57.3794i			1.84139i	0.390280	+	0.920696i	$0.372378\pi$
$971$			57.3794i			1.84139i	−0.390280	+	0.920696i	$0.627622\pi$
$972$	28.1191	−	13.4654i	0.901920	−	0.431904i
$973$	−1.31589	+	2.03987i	−0.0421854	+	0.0653952i
$974$	−47.0520	−	9.17030i	−1.50764	−	0.293835i
$975$	−11.3285	+	11.5397i	−0.362802	+	0.369565i
$976$	−5.19535	+	20.6620i	−0.166299	+	0.661374i
$977$	−18.3819	−	10.6128i	−0.588088	−	0.339533i	0.176253	−	0.984345i	$-0.443602\pi$
$977$	−18.3819	−	10.6128i	−0.588088	−	0.339533i	−0.764341	+	0.644812i	$0.776936\pi$
$978$	11.8874	+	17.2959i	0.380117	+	0.553062i
$979$	−4.14325	−	7.17632i	−0.132419	−	0.229356i
$980$	18.7876	+	29.7282i	0.600149	+	0.949632i
$981$	−22.6863	+	0.419046i	−0.724319	+	0.0133791i
$982$	−0.877634	+	1.00859i	−0.0280064	+	0.0321853i
$983$	−24.6157	−	42.6356i	−0.785117	−	1.35986i	−0.928929	−	0.370258i	$-0.879269\pi$
$983$	−24.6157	−	42.6356i	−0.785117	−	1.35986i	0.143811	−	0.989605i	$-0.454064\pi$
$984$	5.68725	−	17.9758i	0.181303	−	0.573049i
$985$	−19.1918	−	11.0804i	−0.611503	−	0.353051i
$986$	8.80070	+	25.6005i	0.280271	+	0.815286i
$987$	−21.1954	−	6.60013i	−0.674656	−	0.210085i
$988$	29.2192	−	22.7817i	0.929586	−	0.724782i
$989$	−28.3603			−0.901805
$990$	42.8781	+	7.53768i	1.36276	+	0.239563i
$991$	−12.7468			−0.404914			−0.202457	−	0.979291i	$-0.564893\pi$
$991$	−12.7468			−0.404914			−0.202457	+	0.979291i	$0.564893\pi$
$992$	−0.572104	−	6.73221i	−0.0181643	−	0.213748i
$993$	−1.89975	+	7.36121i	−0.0602868	+	0.233601i
$994$	7.45430	−	30.2256i	0.236436	−	0.958697i
$995$	−15.1798	+	26.2923i	−0.481233	+	0.833521i
$996$	16.5624	−	22.3600i	0.524800	−	0.708503i
$997$	−5.83244	−	10.1021i	−0.184715	−	0.319936i	0.758765	−	0.651364i	$-0.225803\pi$
$997$	−5.83244	−	10.1021i	−0.184715	−	0.319936i	−0.943480	+	0.331428i	$0.892470\pi$
$998$	−28.0227	−	24.3843i	−0.887044	−	0.771871i
$999$	26.1209	−	27.6098i	0.826427	−	0.873535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.5	✓	168
7.6	odd	2	inner	504.2.cc.b.293.6	yes	168
8.5	even	2	inner	504.2.cc.b.293.34	yes	168
9.2	odd	6	inner	504.2.cc.b.461.33	yes	168
56.13	odd	2	inner	504.2.cc.b.293.33	yes	168
63.20	even	6	inner	504.2.cc.b.461.34	yes	168
72.29	odd	6	inner	504.2.cc.b.461.6	yes	168
504.461	even	6	inner	504.2.cc.b.461.5	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.5	✓	168	1.1	even	1	trivial
504.2.cc.b.293.6	yes	168	7.6	odd	2	inner
504.2.cc.b.293.33	yes	168	56.13	odd	2	inner
504.2.cc.b.293.34	yes	168	8.5	even	2	inner
504.2.cc.b.461.5	yes	168	504.461	even	6	inner
504.2.cc.b.461.6	yes	168	72.29	odd	6	inner
504.2.cc.b.461.33	yes	168	9.2	odd	6	inner
504.2.cc.b.461.34	yes	168	63.20	even	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38810 - 0.270536i) q^{2} +(-1.21338 + 1.23600i) q^{3} +(1.85362 + 0.751060i) q^{4} +(2.17541 + 1.25598i) q^{5} +(2.01867 - 1.38743i) q^{6} +(-2.64254 - 0.130417i) q^{7} +(-2.36981 - 1.54401i) q^{8} +(-0.0554045 - 2.99949i) q^{9} +O(q^{10})\)	\(q+(-1.38810 - 0.270536i) q^{2} +(-1.21338 + 1.23600i) q^{3} +(1.85362 + 0.751060i) q^{4} +(2.17541 + 1.25598i) q^{5} +(2.01867 - 1.38743i) q^{6} +(-2.64254 - 0.130417i) q^{7} +(-2.36981 - 1.54401i) q^{8} +(-0.0554045 - 2.99949i) q^{9} +(-2.67990 - 2.33194i) q^{10} +(-2.04252 - 3.53776i) q^{11} +(-3.17746 + 1.37976i) q^{12} +(3.56373 - 6.17257i) q^{13} +(3.63281 + 0.895932i) q^{14} +(-4.19200 + 1.16484i) q^{15} +(2.87182 + 2.78436i) q^{16} -3.33266 q^{17} +(-0.734563 + 4.17857i) q^{18} +2.59916 q^{19} +(3.08908 + 3.96197i) q^{20} +(3.36760 - 3.10793i) q^{21} +(1.87813 + 5.46332i) q^{22} +(-2.33076 - 1.34566i) q^{23} +(4.78390 - 1.05562i) q^{24} +(0.654951 + 1.13441i) q^{25} +(-6.61671 + 7.60400i) q^{26} +(3.77460 + 3.57105i) q^{27} +(-4.80031 - 2.22645i) q^{28} +(2.87189 + 4.97425i) q^{29} +(6.13403 - 0.482820i) q^{30} +(1.03437 + 0.597193i) q^{31} +(-3.23309 - 4.64189i) q^{32} +(6.85104 + 1.76809i) q^{33} +(4.62606 + 0.901606i) q^{34} +(-5.58481 - 3.60267i) q^{35} +(2.15010 - 5.60153i) q^{36} -7.31462i q^{37} +(-3.60788 - 0.703166i) q^{38} +(3.30514 + 11.8945i) q^{39} +(-3.21608 - 6.33530i) q^{40} +(1.92428 - 3.33296i) q^{41} +(-5.51536 + 3.40305i) q^{42} +(9.12590 - 5.26884i) q^{43} +(-1.12900 - 8.09172i) q^{44} +(3.64676 - 6.59472i) q^{45} +(2.87126 + 2.49846i) q^{46} +(-2.42213 - 4.19526i) q^{47} +(-6.92609 + 0.171081i) q^{48} +(6.96598 + 0.689264i) q^{49} +(-0.602237 - 1.75186i) q^{50} +(4.04380 - 4.11918i) q^{51} +(11.2418 - 8.76502i) q^{52} -10.7480 q^{53} +(-4.27341 - 5.97812i) q^{54} -10.2614i q^{55} +(6.06095 + 4.38918i) q^{56} +(-3.15378 + 3.21257i) q^{57} +(-2.64074 - 7.68169i) q^{58} +(3.31183 + 1.91208i) q^{59} +(-8.64524 - 0.989275i) q^{60} +(2.66315 + 4.61270i) q^{61} +(-1.27424 - 1.10880i) q^{62} +(-0.244776 + 7.93348i) q^{63} +(3.23204 + 7.31805i) q^{64} +(15.5052 - 8.95193i) q^{65} +(-9.03157 - 4.30773i) q^{66} +(-0.295540 - 0.170630i) q^{67} +(-6.17750 - 2.50303i) q^{68} +(4.49134 - 1.24802i) q^{69} +(6.77760 + 6.51175i) q^{70} -8.32016i q^{71} +(-4.49995 + 7.19378i) q^{72} +4.69448i q^{73} +(-1.97887 + 10.1534i) q^{74} +(-2.19684 - 0.566951i) q^{75} +(4.81786 + 1.95212i) q^{76} +(4.93606 + 9.61503i) q^{77} +(-1.36996 - 17.4048i) q^{78} +(-3.05771 - 5.29612i) q^{79} +(2.75031 + 9.66407i) q^{80} +(-8.99386 + 0.332370i) q^{81} +(-3.57278 + 4.10588i) q^{82} +(-6.95648 + 4.01632i) q^{83} +(8.57650 - 3.23166i) q^{84} +(-7.24993 - 4.18575i) q^{85} +(-14.0930 + 4.84477i) q^{86} +(-9.63289 - 2.48601i) q^{87} +(-0.621941 + 11.5375i) q^{88} +2.02849 q^{89} +(-6.84616 + 8.16752i) q^{90} +(-10.2223 + 15.8465i) q^{91} +(-3.30966 - 4.24488i) q^{92} +(-1.99322 + 0.553859i) q^{93} +(2.22719 + 6.47870i) q^{94} +(5.65425 + 3.26448i) q^{95} +(9.66036 + 1.63628i) q^{96} +(-5.39410 + 3.11428i) q^{97} +(-9.48298 - 2.84131i) q^{98} +(-10.4983 + 6.32254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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